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Electrons and Photons

1. Tetep 2 te qd Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Light Emitting Diodes 132 Photonic Devices In the low injection limit the rise time Tstep is equal to the recom bination time 7 1 BIN P AN Bnp Tstep Tn r Tn r mee E Basically the level of injection remains low enough that the recom bination processes in the diode are still governed by the doping levels which of course are not dependent on time or current The output power of the light emitting diode during the step input can be calculated using Eq 6 15 Poult Nex VBINP n o N ANNP AN n o Net VBINGAN N P n lhw 6 32 where smaller terms have been neglected This result can be separat ed into two terms one representing the diode behavior before the cur rent pulse and the other being the transient response Polt Next VBIN P1 n7ho Ne VBN AN ho J 1 T NextV haw That od NextVhw JAN 6 33 r r nhol nestha Jia I 1 e step Tp rey n oll 1 1 e step I 6 34 Note that 1 1 1 1 BIN P AN Bnp Tstep Tr Thr Ty is identical to the total recombination rate determined earlier in Eq 6 21 for an LED operating in s
2. focal length Figure 10 1 A convex lens will focus a parallel beam of light to a point at a distance from the lens that is equal to the focal length of the lens To use a convex lens in the context of optical characterization there are only two simple rules to remember 1 A parallel beam of light is focused to a point by a convex lens at a distance equal to the focal length Fig 10 1 2 A point source of light at distance 2 times the focal length from a convex lens is focused to a point at 2 times the focal length on the other side of the lens Fig 10 2 These features are conveniently summarized in the lens equation 1 1 1 Xobj ect Ximage focal length 10 1 lt 4 2x Focal Length A 2x Focal Length _ _ Figure 10 2 A convex lens will focus a point source to a point of the same size when the lens is placed at a distance equal to twice the focal length as shown The image is formed on the other side of the lens at twice the focal length Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Measurements in Photonics 230 Characterizing Photonic Devices in the Laboratory Figure 10 3 A lens with a lower f number that is a larger aperture will focus parallel light to a point of smaller dimensions than a lens with a
3. 2 4 Properties of Electrons Electrons are the ONICS of photONICS Electrons can interact with photons one at a time mostly through the medium of a semiconduc tor crystal When a semiconductor absorbs a photon the energy of the photon can be transferred to an electron as potential energy When the electron loses potential energy the semiconductor can account for the energy difference by emitting a photon Exercise 2 4 A photon with energy 1 5 eV strikes GaAs The energy is absorbed by breaking one bond promoting one electron from a bonding state va lence band to an antibonding state conduction band and leaving a vacant state hole in the valence band Some time later the electron recombines with the hole completing the bond and releasing a photon of 1 42 eV the bonding energy of GaAs at room temperature Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Electrons and Photons Electrons and Photons 15 An electron can be characterized by its mass charge and magnetic moment all of which are fixed in magnitude It is also characterized by its energy and momentum which are variable Although the elec tron does not have a well defined size it behaves in many respects as a particle For example we could write down expressions for the mo mentum and ene
4. 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Optical Fibers and Optical Fiber Amplifiers 196 Advanced Topics 100 50 20 O H absorption peaks 10 E x Ss 2 gs Tail from the 5 2 fundamental O H absorption peak D i 2 i 0 5 0 2 Rayleigh Scattering 0 1 0 05 0 6 0 8 1 0 1 2 1 4 1 6 1 8 2 0 Wavelength um Figure 9 3 Attenuation of optical fiber as a function of wavelength Absorption peaks from residual O H groups can be seen at 1230 nm and 1370 nm The letters OVD IVD and VAD refer to different styles of vapor deposition used to make the glass preform from which the fiber is drawn Adapted from Wilson and Hawkes Optoelectronics Prentice Hall 1998 reproduced with permission Figure 9 4 A schematic diagram of the SiO network The silicon atoms dark circles are not located in a regular pattern The atomic potential associated with the silicon atoms is also irregular The fluctuations from regularity act to scatter light causing at tenuation in optical fibers Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Optical Fibers and Optical Fiber Amplifiers Optical Fibers and Optical Flber Amplifiers 197 versely on the fourth power of the wavelength This
5. Eg PHOTON ENERGY Figure 6 7 The emission spectrum of a real LED peaks below the band gap energy whereas the peak in the response of a photodetector using the same material occurs at an energy above the band gap There is some overlap in energy between the two de vices Thus a LED is a poor detector of the radiation emitted by another LED made from the same material 6 4 Quantum Efficiency The quantum efficiency ng of an LED is number of photons emitted Ne number of electrons injected Ne Poho Ng Iq 6 10 Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Light Emitting Diodes Light Emitting Diodes 115 To estimate the efficiency of an LED we can start out with the as sumption that the internal quantum efficiency is unity That is that for every electron injected there is a photon created However the ef ficiency measured in the laboratory is the external efficiency and this depends on the number of photons that manage to exit from the LED into free space This external efficiency is much less than unity In an LED structure having the same composition throughout called a homostructure a good assumption is that about half the pho tons are emitted with energy above the band gap and are absorbed be fore exiting the LED The unabsorbed
6. NON RADIATIVE RECOMBINATION Figure 8 2 There are interactions between the drive current and the carrier concentra tion and between the photon density and the carrier concentration These interactions act to increase or decrease the population of carriers and the population of photons The photon and carrier concentrations interact to produce stimulated emission An increase in the carrier concentration leads to an increased rate of photon emission An increase in the photon emission increases the rate of stimulated emission which decreases the carrier concentra tion The equations for dN dt and dN dt are coupled aN J N np BWP n ll a oa NP n 7 8 1 For this discussion let us rewrite this simply as ay 4 binati t recombination r a ad ecombination rate ae N Recombination rate By N4fKy 8 2 T r Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Direct Modulation of Laser Diodes 182 Advanced Topics where Bo stimulated recombination rate N photon density f photon frequency K optical gain coefficient aAN T effective recombination time In this equation we have isolated the stimulated recombination rate which depends on the photon density from the spontaneous and non radiative parts which d
7. Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Light Emitting Diodes Light Emitting Diodes 103 The range of colors and the level of efficiency are similar but the pro cessing of polymers is much less complicated and much less expen sive Direct screen printing is a leading technology for making poly mer circuits The substrate can be a flexible sheet of plastic instead of a more expensive single crystal substrate There is still a large but slowly disappearing body of thought that claims that polymers will never be used for commercial electronic applications because they are unstable or unreliable or perhaps another other excuse Be careful of such pessimism The history of progress in optoelectronics is clear on a couple of points this is a field that is marked with dramatic advances by engi neers and scientists who do not accept preconceptions of what is not possible a field with exciting possibilities for both commercial and fundamental scientific developments that will define the kind of world we live in LEDs built from semiconductor diodes operate on the principle of minority carrier injection that occurs in forward bias Operating con ditions for a polymer based LED are somewhat different hot carriers are injected over a barrier where they can recombine with carriers of the opposite type in order to produce luminescence All LEDs have the featu
8. Pumping excitation of the state is achieved by coupling the light from a GaAs based laser into the optical fiber as shown in Fig 9 15 The pump light A 980 nm and the signal light A 1550 nm prop agate in the same fiber core The pump power is typically hundreds of milliwatts whereas the entering signal is typically in the microwatt regime The two light beams do not interfere with each other in the amplifier section to any significant degree The erbium doped fiber is spooled into a coil and pumped from both ends The passage of the signal through the pumped erbium doped fiber provokes stimulated emission that amplifies the signal This occurs at the speed of light that is to say nearly instantaneously The amplifi cation is thus independent of the modulation rate A signal consisting of different wavelengths can be amplified using one erbium doped fiber amplifier because the amplifier does not mix or change the wave length These are the two key features of optical amplification In the case of electronic amplification the situation is different Electronic amplification starts by optical detection This conversion erases all Signal in Signal out 10 pWatts Er doped fiber 10 mWatts gt 980 pump in y Figure 9 15 Schematic diagram of an erbium doped fiber amplifier The pump light is coupled into the erbium doped section where it is strongly absorbed preparing the er bium ions in the 13 2 state The signal travels
9. Zero dispersion wavelength 1300 1320 nm Zero dispersion slope 0 092 psec nm km Effective group index of refraction 1 4690 at 1310 nm typical 1 4695 at 1550 nm Refractive index difference typical 0 34 Mode field diameter 9 3 microns at 1310 nm 10 5 microns at 1550 nm Cladding diameter 1251 Cladding noncircularity 1 5 Core diameter not given Core cladding concentricity error 0 6 a Using available data estimate the numerical aperture as sume that the index of the core is equal to the effective group index b Samsung has carefully avoided giving the core diameter in its specifications Show that 8 5 microns is a reasonable val ue What V number do you determine What mode field di ameters do you determine at 1310 and 1550 nm Would 9 mi crons be a better guess What would be the longest wavelength for which the fiber still behaves as single mode c Write and demonstrate a simple computer routine for calcu lating the core diameter of the fiber using only the data giv en d Calculate the time needed for the pulse broadening due to dispersion to cause overlap of adjacent bits at 2 5 Gbit sec 10 Gbit sec and 40 Gbit sec This occurs when the combined width at half maximum of the two broadened pulses is equal Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given
10. ple coating interference reflector introduces improved wavelength se lectivity so that only the wavelength range of interest is subject to feedback These features have all been applied to semiconductor structures in order to make laser diodes The majority of semiconduc tor lasers are fabricated using two plane parallel mirrors formed by cleaving the laser chip along parallel crystal planes The mirror re flectivity is determined by the index difference between the semicon ductor material n 3 4 and air n 1 0 The good news about semiconductor lasers is the gain coefficient is very large compared to that of gas lasers like He Ne or solid state laser materials like Nd YAG As a result the mirrors at each end of the cavity do not need to be as efficient as those required for other kinds of laser materials There are two big performance benefits one is that more power can be extracted from a semiconductor laser at modest input power levels and the other is that there is a much larg er tolerance in the design of the resonator needed to make a working device There is also a big space savings too This is why you can hold a semiconductor laser in the palm of your hand but you need a table top to hold a gas laser or a YAG laser These two features are impor tant reasons why semiconductor laser technology dominates the mar ket a trend that is likely to accelerate The role of the resonator is easy to understand A forward bias vol
11. 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Optical Fibers and Optical Fiber Amplifiers Optical Fibers and Optical Flber Amplifiers 209 modulation rate of 2 5 GHz the pulse width is four times longer and at the same time the modulation broadening is four times smaller so the dispersion problem becomes practically negligible Material dispersion also called chromatic dispersion is not the only source of dispersion There is also structural dispersion that de pends on the geometry of the fiber The geometry of the fiber and the index contrast are linked through the fiber V number as we have seen earlier The very interesting feature of the structural dispersion is that it depends on the wavelength in the opposite way from materi al dispersion That is Total dispersion Material dispersion Structural dispersion 9 20 This has the important implication that structural dispersion can be used to compensate for material dispersion In real optical fiber sys tems lengths of special fiber with a structure designed for just this purpose are spliced in periodically to correct for material dispersion Material dispersion and structural dispersion combine to form the static dispersion of the fiber This dispersion is built in when the fiber is drawn and does not change with time The structural dispersion can be represented as dAn ch sre a 8 vaa 22 a g
12. 80 Photonic Devices Conduction Band i Ohmic Contact Energy Valence Band III Distance Figure 5 2 Energy level diagram for a simple GaAs photoconductor based on interband absorption of light shown in Figure 5 1 Photoconductivity occurs when incident light with an energy greater than the band gap is absorbed The electron hole pairs that are thus created increase the conductivity by increas ing the number of charge carriers A schematic energy level diagram of this structure is shown in Fig 5 2 The absorption of a photon having at least the band gap energy creates an electron hole pair as shown in Fig 5 3 In the example that follows we will use GaAs for the semiconductor material In Photon Conduction Band Ohmic Contact Energy Valence Band Distance Figure 5 3 A photon is absorbed by GaAs creating an electron hole pair The conduc tivity of the GaAs is increased because there are more charge carriers Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Photoconductivity Photoconductivity 81 Conduction Band Ohmic Contact Energy Distance Figure 5 4 The applied electric field separates the electron hole pair The electron is moving 12 times faster than the hole this case the electron velocity is
13. A sin kx A semiconductor crystal is a periodic arrangement of atoms The peri odicity applies to all the physical properties of the crystal This means that the allowed values for energy and momentum have to be period ic too A sin kx A sin k x a where a the period of the crystal lattice A sin kx cos ka A cos kx sin ka This is true if ka 27 or _ 2m a At these special k values everything looks the same Since every thing looks the same we just keep the central zone that has the unique information between k m a and k ma This is called the Brillouin zone Brillouin was a classmate of de Broglie The diagram in Fig 2 7 has its characteristic shape because of the periodicity or to use a more general term the symmetry of the crys tal There are two essential components of the energy momentum re lationship in crystals of real materials symmetry and chemistry The component added by chemistry is the potential added by the atoms that make up the crystal Si atoms have a different potential from Ge atoms and the energy momentum relationship for Si is slightly dif ferent from that for Ge Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Electrons and Photons 24 Introductory Concepts 2n a hk Electron Momentum Figure
14. As sume Rz 100 Q d What would be the photocurrent 10 meters away 20 Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Source Photonics Essentials Chapter Electrical Response Time of Diodes 4 1 Introduction An optoelectronic device is characterized by its I V characteristics spectral response quantum efficiency speed of response and power consumption In Chapter 3 we considered the first two features There are two important aspects to the speed of response of a diode There is an intrinsic response speed associated with optical absorp tion or emission There is also an extrinsic response that character izes the electrical coupling of the diode to an external circuit such as a driver or amplifier In this chapter we will consider the response time of diode based devices like photodiodes and light emitting diodes LEDs The intrinsic response time is related to the minority carrier mobility in the case of a photodiode and the minority carrier recombi nation time in the case of an LED whereas the extrinsic response time is related to the device capacitance The case of the photodiode is a bit more complicated than that of the LED because the carriers are initially distributed throughout the diode by the absorption of pho to
15. Capture cross section Sn1 10715 cm Sn2 10 72 cm s 10715 cm s 10 15 cm p2 First we calculate the carrier lifetime in the absence of the type 2 recombination level We assume that n p 1015 cm and that s sp1 10 cm Then it follows that Tni Tp1 PnWSn1 Pn2VSnz 1077 sec 5 18 Now we add 2 x 1018 cm impurity states having a small cross section for electrons of 10 cm and a normal cross section for holes of 10715 cm Under illumination f n 7 p z is satisfied by each recombina tion level That is class 1 NP 1VSp1 P N 1VS 1 5 19 and class 2 N Pr2VSn2 P N 2USp2 5 20 Next P _ PrVSn1 Pr2VSn2 n NypWVSp1 N 2QUSp2 and Nyy Sn2 Sri Nyy Sn2 sd AeA n2 5 21 Pri pa ng Sp2 Sp1 p d n 2 Sp2 Under high enough illumination electron recombination will fill near ly all of the type 1 centers so that n N The holes will occupy the type 2 sites so that p N Since N lt N the vast majority of the type 2 sites will be occupied by electrons giving n N Using these approximations Eq 5 21 can be rewritten rri Sn Na Sn Pp e Sad St S22 IN 1071 10 10 N 5 22 Nye Sn2 N 2 Sn2 Before sensitization we assumed equal occupancy of the type 1 cen ters by electrons and holes Equation 5 22 shows how sensitization Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 Th
16. Conduction Band _ Trapping Level Recombination Level Valence Band Figure 5 9 Engineering of photoconductivity by introduction of shallow trapping cen ters The number of centers is designed to be much larger than the number of free car riers in the conduction band ulate photo excited carriers during photoconductivity We will consid er this important engineering tool in more detail in Section 5 6 when we discuss the principle of sensitization 5 5 Photographic Film and Photoconductivity Photoconductivity is the principle that underlies the operation of pho tographic film This is by far the most extensive use of the photocon ductive effect Unlike the examples we have discussed so far there are no contacts and no external bias voltage needed to exploit photo conductivity in film Photographic film consists of a gelatin coating on some kind of plas tic or polymer support For larger view cameras the gelatin is de posited on glass plates Inside the gelatin are dispersed grains of a photosensitive material Fig 5 10 Film is a digital medium The photosensitive grain can respond in only two ways either it absorbs a photon or it does not If it absorbs a photon the exposure and development process will render the entire grain black Otherwise the grain is dissolved and washed out of the gelatin leaving a transparent region behind For a fixed level of illu mination the chance that a grain absorbs a photon depen
17. Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Lasers Lasers 167 1 0 0 8 0 6 0 4 0 2 RELATIVE INTENSITY 0 1 30 1 32 134 1 36 1 38 140 142 144 1 46 ENERGY E eV a 1 0 0 8 0 6 0 4 0 2 RELATIVE INTENSITY 0 1 30 1 32 1 34 1386 138 140 142 1 44 1 46 ENERGY E eV b RELATIVE INTENSITY 1 389 1 391 1 393 1 395 1 397 ENERGY E eV c Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Lasers 168 Photonic Devices A prominent feature of this model is the wavelength dependence of the threshold current GaAs based lasers emit around 920 nm A laser emitting at half this wavelength would be deep blue in color and have a threshold current four times higher The wisdom based on our model might argue that such a laser could not be made to op erate continuously at room temperature I learned this argument in class It was used in the 1960s and 1970s by the managers at the best research laboratories in the world to justify stopping laser de vice research on larger band gap materials such as GaN E 3 48 eV 7 7 A True Story In the 1980 s Professor Isamu Akasaki at Nagoya University set his sights on the growth of GaN materials
18. E i E 10t tid m Fi ox gt Le Q Oo ec bs lt z3 a w o 1075 4 en i J 197 SE z 1077 L L LL i 0 2 04 0 6 0 8 FORWARD VOLTAGE Vep Figure 3 5 Current voltage characteristic of a light emitting diode The inset shows both forward and reverse bias behavior The graph is a semilog plot of forward current versus voltage The slope gives the ideality factor n In this case n 1 38 Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Photodiodes Photodiodes 47 a photodiode In fact light emitting diodes behave like photodiodes un der illumination In the inset we show the diode I V as captured on a curve tracer The graph shows the measurement of the forward char acteristic on a semilog scale There is a region near zero bias where the log of the current is proportional to the bias voltage The slope of the curve in this region is used to calculate n In this case n 1 38 The photocurrent is given accurately by Eq 3 14 and you should be able to verify the linear dependence of the photocurrent on the inci dent light intensity over several orders of magnitude of incident light intensity 3 3 Photodiode Operation The Photocurrent Mode and the Photovoltage Mode Photodiodes can be operated in two modes as a source of photocur rent or as a
19. For the high brightness red LED shown in Fig 6 4 this capacitance is 250 pF under operating condi tions The RC time constant is 1 25 10 sec giving a modulation bandwidth of about 120 MHz In the following sections we will formulate a model of the LED based on rate equations that describe the transient behavior of the ex cess carrier concentration This approach is an important stepping stone toward the description of the response time and modulation rate of semiconductor lasers To make a long story short the intrinsic modulation bandwidth of LEDs depends on the carrier concentration of electrons and holes in the region where recombination takes place 6 7 Steady State Input Electrical Current and Output LED Optical Power Light output cannot respond simultaneously to the electrical input signal There are delays associated with the buildup of the nonequi librium carrier concentration that is in competition with recombina tion Both nonradiative and radiative recombination are important Our treatment is based on the rate equation that shows how the num ber of charge carriers changes with time The modulation rate for the LED reflects the rate at which the car rier concentration can be changed The carrier concentration consists of an equilibrium component created by doping and a nonequilibri Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Compani
20. So the density of states in k space is dN 87k dk Starting with Eq 6 4 we can derive the energy densi ty of states 2 k Tp Ek Epl 2m k z E3 dk Eo EJE 6 5 OF 8 So the density of states can be written as 2 dN 87k dk s r Je E Z e E 2dE dN 82m 2 2 dE T E E 6 6 Thus the density of states is proportional to E E 0 9 0 8 0 7 0 6 0 5 0 4 0 3 Emitted Intensity 0 2 0 1 0 9 0 95 1 1 05 1 1 1 15 Photon Energy E E Figure 6 3 Equation 6 6 is a simple physical model of the LED electroluminescence spectrum This model predicts that the peak intensity occurs at an energy slightly above the band gap energy and that the shape of the luminescence spectrum is not symmetric about the peak energy Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Light Emitting Diodes Light Emitting Diodes 109 The probability that a state is occupied is given by Boltzmann sta tistics that is Pr const e E EgVkT The probability that an optical transition takes place is the square of the optical matrix element M It is a constant with a weak depend ence on energy and its value is written as M We can assemble all these elements to derive an expression for the energy spectrum of the emitted
21. The resolution depends on the length of the spectrome ter and the size of the grating If you are using a 0 25 m spectrometer the wavelength resolution in the visible region is about 0 05 nm The mode spacing of a semiconductor laser is about 10 times larger The measurement of mode spacing under these conditions is challenging but possible There is not much that you can do to change the length of the spec trometer in the lab but you will be surprised to learn that you can change the size of the grating By making the grating larger you can increase the resolution of your measurement If you are making a measurement of a He Ne laser or a laser point er consisting of a semiconductor laser and a collimating lens you will notice the well controlled beam of light that is easy to steer into the entrance slits of the spectrometer However let us look at what hap pens once this beam of light enters the spectrometer The well colli mated beam of light may have a diameter of about 1 mm and show lit tle divergence As it enters the spectrometer this beam is reduced to the size of the entrance slits set to 1 mm leaving the divergence un changed It reflects off the input mirror strikes the parabolic mirror at one spot and is sent to the grating This trajectory is shown schematically in Fig 11 9 The near absence of divergence in the beam means that it arrives at the grating with approximately the same diameter as the entrance slit
22. acteristic of an off the shelf silicon photodiode subjected to illumi nation The photocurrent is a linear function of light intensity over many orders of magnitude In the laboratory you can make measurements of the current ver sus voltage When you compare your experimental results to the theo retical model you will find that you can deduce the correct value for the built in voltage but you will also find that the reverse current is larger than your predictions and that the forward current is smaller The reverse or dark current is increased by leakage paths that are introduced by defects and impurities as well as by device processing The forward current is limited by series resistance introduced by the resistivity of the neutral p and n regions Recombination of minority carriers will also lead to a reduction in current below its expected val Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Photodiodes Photodiodes 45 a T I T T T T T T T 7 r Vert Div f 7 L 500 pA f Cursor i h Horiz Div i 1V 1 4 be f fas ba f 4 f H 4 4 _ i 4 L don 4 b T T T T T T F T F Vert Div f 7 L 50 pA 4 Cursor i b Horiz Div t 4 100 mV i i I L in the dark ___ under 4 4 illu
23. c The photovoltage response cannot be larger than Vg the built in voltage which is always less than the band gap energy q This means that the photovoltaic mode can be used to advantage in situations where circuit simplicity or battery free operation is an ad vantage and where accurate conversion of photon flux to an electrical signal is not an important requirement Examples of such an applica tion are optical burglar alarms or solar cells An application example where use of the photovoltaic mode will lead to erroneous results is its use in the measurement of the spectral line shape of a light emitting diode or a laser The lineshape is charac terized by its full width at half maximum FWHM The nonlinear re sponse of the photovoltaic mode will cause the line shape to appear broader than it actually is The amount of the error will depend on the details of the photodiode I V characteristic 3 4 Photodiode Properties There are four important components of the performance of a photodi ode detector 1 Spectral response What is the range of optical wavelengths that the photodiode can convert to electrical current 2 Quantum efficiency What is the ratio of the number of electrons created to the number of incident photons 3 Response time What is the shortest optical pulse that the photodi ode can detect 4 Noise What are the sources of noise generated by the photodiode that limit the minimum detectable signal We w
24. glass is a miracle Glass engineering has a lot to do with introducing desired impuri ties into SiO and suppressing unwanted elements An important un wanted impurity is water There is already oxygen in glass Hydrogen can easily diffuse into glass and form water like complexes of O H molecules Understanding how to keep water out of glass has been an important part of optical fiber research since 1970 Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Optical Fibers and Optical Fiber Amplifiers Optical Fibers and Optical Flber Amplifiers 195 To appreciate the role of water we can start by examining a spec trum of the air we breathe Fig 9 2 The transmittance spectrum of glass is similar to that of air The fundamental absorption occurs at 2730 nm This wavelength has a frequency that corresponds exactly to the molecular vibration frequency of H O The first overtone one octave higher occurs at 1370 nm Both of these absorption bands can be seen in Fig 9 2 It is easy to detect the band at 1370 nm by taking a spectrum of a tungsten lightbulb on a moderately humid day If you need to make measurements in this region on a humid day you can get rid of the absorption by purging the spectrometer with dry nitro gen gas The high transparency region around 1550 nm is
25. into a photoconductor The requirements for sensitization are e The density of the type 2 centers is greater than that of the type 1 centers e The recombination properties of the type 2 centers are different from those of the type 1 centers The level of illumination is high enough to saturate the type 1 cen ters with one type of carrier 5 7 Summary Photoconductivity occurs when the absorption of light creates electron hole pairs that are mobile in an electric field Photoconductive detec tors differ from photodiodes in several important ways Photoconduc tive detectors can be made from a wide variety of materials including those in which it is not possible to form a p n junction This range in Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Photoconductivity 98 Photonic Devices cludes all the materials from which photodiodes can be made plus in sulators and organic materials As a result there is a much wider va riety of applications for photoconductors than for photodiodes These applications include light and motion sensors photographic film pho tocopiers and television camera sensors Photoconductivity occurs in most materials because the number of mobile charge carriers is increased upon illumination The increase in conductivity is linearly
26. or in tensity I x I x Ax that is absorbed in the region Ax as dia grammed in Fig 3 8 is proportional to the incident intensity Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Photodiodes 50 Photonic Devices Spectral Response 2124 m w Eg Increasing Wavelength gt or Decreasing Energy gt Figure 3 6 Idealized spectral response for a photodiode S 1 if the photon energy is greater than the band gap Otherwise S is 0 I x I x Ax a I x Ax d ni a I x In T x zx x Xo in oe a x I xo set xo 0 and I x Io I x Ipe 3 22 The constant of proportionality a is called the absorption coeffi cient The absorption coefficient is proportional to the spectral re sponse function In Si and other indirect band gap materials a is about 10 cm7 at the band gap energy whereas in GaAs and direct band gap materials a is about 104 cm two orders of magnitude larger The inverse of the absorption coefficient gives an estimate of the average distance for absorption of a photon to occur For exam ple a photon with the band gap energy will penetrate nearly 100 um into a silicon photodiode on the average before it gets absorbed Wherever a photon is absorbed an electro
27. sary majority carriers is calculated from the capacitance of the photo diode and the series resistance of the circuit The resistance capaci tance RC charging time can be controlled to some degree because the capacitance of the diode depends on its bias voltage The diffusion and drift times are fixed by the conditions of diode fabrication In the following treatment will evaluate each of these terms with the objective of understanding their relative contributions Some of the results may appear to be counterintuitive For example the bias voltage has very little effect on the intrinsic speed of response of a photodiode However increasing the bias voltage will decrease the ca pacitance and this has a significant effect on the extrinsic response time Efficient photodiodes can be made from direct band gap materi als as well as from indirect band gap materials However the intrin sic speed of response of indirect band gap photodiodes is lower be cause the photo generated carriers are spread throughout a much larger spatial extent of the device and it takes more time to collect them In Fig 4 1 we show a schematic diagram of a photodiode at 0 bias In order to introduce the discussion we will assume that the diode is uniformly illuminated on the p and n sides The built in electric field at the junction creates a depletion region of width W The size of W is dependent on the carrier concentration In the case of a silicon photo dio
28. yrighted Material oR iy ay a CE Cof Copyrighted Matenal The McGraw Hill companies Cataloging in Publication Data is on file with the Library of Congress Copyright 2003 by The McGraw Hill Companies Inc All rights reserved Printed in the United States of America Except as permitted under the United States Copyright Act of 1976 no part of this publication may be reproduced or distributed in any form or by any means or stored in a data base or retrieval system without the prior written permission of the publisher 123457890 DOC DOC 098765432 ISBN 0 07 140875 4 The sponsoring editor for this book was Stephen S Chapman and the production supervisor was Pamela A Pelton It was set in Century Schoolbook by Ampersand Graphics Ltd Printed and bound by RR Donnelley containing a minimum of 50 recycled de inked fiber amp This book was printed on recycled acid free paper McGraw Hill books are available at special quantity discounts to use as premiums and sales promotions or for use in corporate training programs For more information please write to the Director of Special Sales Professional Publishing McGraw Hill Two Penn Plaza New York NY 10121 2298 Or contact your local bookstore Information contained in this work has been obtained by The McGraw Hill Compa nies Inc McGraw Hill from sources believed to be reliable However neither McGraw Hill nor its authors guarantee the accuracy
29. 2 7 Diagram of electron energy as a function of electron momentum for an elec tron in a periodic environment Each period of the structure reflects the same electron be havior just like a mirror The diagram of energy and momentum is a picture that shows which states are allowed to be occupied by electrons You need extra information to know which states actually are occupied In Fig 2 8 we show an analogous diagram for cars a road map On this road map we see some lines indicating roads These lines tell you what places or states can be occupied by automobiles under normal or equilibrium conditions However you need more information in order to know which states are actually occupied by automobiles The road map does not tell you much about the velocity of the cars either In Fig 2 8a we see that the shape of the road map with nice straight lines gives us some information about the terrain of the region it is probably rather flat In Fig 2 8b we show another road map Here the lines are not so simple indicating that there are rises and falls in the terrain of this region These changes in terrain are changes in po tential They play the same role in a road map as chemistry plays in the energy momentum relationship for electrons This energy momentum map is called the band structure It tells you what are the allowed or stable states of energy and momentum for electrons in the outermost band or valence band of the semicon ducto
30. 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Characterizing Photonic Devices in the Laboratory Downloaded from inglibrary com ght Hill p 3 Any use ien to the Terms of Use a n at the website Source Photonics Essentials Chapter 10 Measurements in Photonics 10 1 Introduction Characterization of photonic devices and materials most often in volves optical spectroscopy A typical example is the measurement of the emission spectrum of a light emitting diode One of the most im portant measurements one can make is the dependence of the intensi ty of light that is emitted as a function of photon energy while the diode is forward biased electrically Since the emission spectrum may depend on the level of operating current you can see that measure ments in photonics involve simultaneous electrical and optical charac terization In this chapter we present a brief introduction to the instruments that you are most likely to use in characterization of photonic devices Some of these you have seen already like lenses or curve tracers Others you have probably not seen such as a lock in amplifier Mea surement techniques specific to certain devices will be introduced in subsequent chapters In the spirit of experimentation we will try to present enough information for you to get started and leave you to de velop the know how to use these instruments
31. 70 Copyrighted Material vi Contents Chapter 5 Chapter 6 Chapter 7 Copyrighted Matenal 4 7 Measurement of Diode Capacitance and Carrier Concentration 4 8 Application of Light Emitting Diodes 4 9 Summary Bibliography Problems Photoconductivity 5 1 Introduction 5 2 Conductivity and Mobility 5 3 Gain and Bandwidth 5 4 Engineering Photoconductivity 5 5 Photographic Film and Photoconductivity 5 6 Sensitization 5 7 Summary Bibliography Problems Light Emitting Diodes 6 1 Introduction 6 2 Recombination of Excess Carriers Direct Generation of Light 6 3 The Energy Spectrum of Light 6 4 Quantum Efficiency 6 5 Beating the Experts New Thinking Creates a Pathway to Increased Efficiency 6 6 Response Time 6 7 Steady State Input Electrical Current and Output LED Optical Power 6 8 Rise Time of the Light Emitting Diode 6 9 Summary 6 10 Review of Important Concepts References Problems Lasers 7 1 Amplifiers and Feedback 7 2 Spontaneous and Stimulated Emission 7 3 Optical Gain 7 4 Obtaining Population Inversion Copyrighted Material 71 72 73 74 75 77 77 77 79 84 87 91 97 99 100 101 101 104 107 114 116 123 123 129 138 138 138 139 143 144 146 150 153 Chapter 8 Chapter 9 T5 7 6 7 7 7 8 Copyrighted Maternal Optical Feedback Making a Laser Threshold Going Over the Edge A True Story Summary Bibliography Problems and Exercises Part I
32. Bnp 4B Soo Tr V hr ad 2B AN Substitute values and solve for AN AN 1 67 x 101 cm 3 AN gt np N AN np 1 67 x 1019 5 x 101 1 7 x 1019 em Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Light Emitting Diodes Light Emitting Diodes 129 BN 1 41 x 10 sect Try B 1 41 x 10 0 74 hat 7 41x 10 05x10 1 24 Power 0 1 0 74 Tes 50 mA 3 4 mW In the example above we found the steady state output after an in crease in the current from 0 to 50 mA In the next section we will con sider the dynamic response of the LED to this step The step response time or the rise time Tstep can be used to determine the modulation bandwidth directly 1 Bandwidth 6 27 T Tstep Summarizing some of the important results so far e AN AP Excess electron concentration excess hole concen tration BNP n BN N np BN 1 z Radiative recombination rate Por nd qgho Optical power is proportional to electric current 6 8 Rise Time of the Light Emitting Diode The basic signal in a digital optical communications link is a pulse of photons The pulse is created by increasing the bias current from some initial value J to J and then from J to J Although the current through the L
33. Characterization in the Laboratory 255 T T T T T T T T Br 7 Ss 6 amp J o 4 5 4 O o 2 4 E a a Second order 4 transmission 4 i bs 4 i nei aean 4 Lon L 600 800 1000 1200 1400 1600 1800 2000 2200 Wavelength nm Figure 11 4 Spectrum of the response of a Ge photodiode to light from a tungsten light bulb This spectrum was obtained using a monochromator having a grating with a 300 nm blaze and 600 grooves mm similar to the type used to obtain the spectrum shown in Fig 11 3 You can see that the grating anomaly can be seen in the spectrum giving a false impression of the actual photodiode response which shows no peak in this region The abbreviation a u on the y axis stands for arbitrary units It is used to signify that the measurement shows only relative changes in photocurrent of a grating that you might choose in order to work from the near UV through the visible part of the optical spectrum The blaze wavelength is the wavelength at which the grating effi ciency is maximum A larger number of grooves gives a higher resolu tion but narrows the range of the wavelength where the grating effi ciency is close to the maximum Figures 10 3 and 10 4 show that the response of the gratings is not uniform Some gratings notably the UV grating in Fig 11 3 show sharp peaks in the response These anomalies appear in all ruled grat ings and are the result of multiple diffraction paths for
34. Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Electrons and Photons 10 Introductory Concepts 2 3 Properties of Photons a According to Maxwell light is an electromagnetic wave b According to Michelson and Morley light always travels at a con stant speed c speed of light c wavelength x frequency Af 3 x 10 cm sec d visible light 400 nm lt A lt 700 nm 400 nm blue 700 nm red near infrared 700 nm lt A lt 2000 nm 9 There are many important applications in the visible and near infrared regions of the spectrum including the wavelengths that opti mize optical fiber communications The most important properties of optical fibers for communications are attenuation of the signal by ab sorption and distortion of the signal noise High performance optical fibers are made from glass Attenuation is caused by fluctuations in the density of the glass on the atomic scale and from residual concentrations of water molecules The water molecules absorb light near specific wavelengths In between these wavelengths windows of lower attenuation are formed at A 1300 nm and 1500 nm A good picture of this situation is shown in Fig 2 2 for state of the art optical fibers The properties of several types of fibers all of which are made by chemical vapor deposition are shown The properties of optical fibers are covered in more
35. Determine the laser threshold current by graphic analysis of the light current curve Compare your value to that measured by your colleagues on other diodes of the same type Determine the relationship between current and spectral output peak wavelength What steps could you take to stabilize the output wavelength Analyze the mode spacing How long is the laser cavity Measure the half width of a mode in energy Is this greater or less than kT If you find a value less than kT explain how this might occur Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website
36. Ed London INSPEC 2000 J Hecht The Evolution of Optical Amplifiers Optics and Photonics News 13 8 36 2002 Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Optical Fibers and Optical Fiber Amplifiers 222 Advanced Topics Problems 9 1 The data sheet for Corning single mode fiber SMF 28 shows the following characteristics Attenuation 1310 nm lt 0 34 dB km 1550 nm lt 0 20 dB km Mode field diameter 1310 nm 9 2 microns 1550 nm 10 4 microns Effective group index 1310 nm 1 4677 1550 nm 1 4682 Cladding diameter 125 microns Core diameter 8 2 microns Core cladding concentricity lt 0 5 microns Numerical aperture 1310 nm 0 14 From these data determine the following a The fiber V number b The index contrast between the core and the cladding c The shortest wavelength at which the fiber is still single mode 9 2 Determine the limits on transmission distance imposed by mate rial dispersion assuming a laser source with a zero modulation linewidth of 0 3 nm and a transmission wavelength of 1550 nm Remember to use the appropriate group velocity a Determine the time duration of a single bit at 2 5 Gbit sec 10 Gbit sec and 40 Gbit sec b Using the data in Fig 9 10 determine the material disper sion coefficient and perform a li
37. Emitting Diodes Downloaded fror ringlibrary com d Source Photonics Essentials Chapter Lasers The word laser is an acronym for Light Amplification by Stimulated Emission of Radiation Laser action is most commonly used to gener ate light However a laser can also be used to amplify light generated by an external source An excellent example of this application is the erbium doped fiber amplifier that is used in optical fiber communica tions to amplify light signals at 1550 nm There is no battery hooked up to an erbium doped fiber amplifier It gets its power from an exci tation light beam at one wavelength and it uses this power to amplify light at another wavelength Laser action is a general principal of the behavior of light absorption and emission by matter As a result las ing has been observed in a wide range of conditions and materials where luminescence is generated including chemical reactions an tifreeze gases solids liquids and semiconductor p n junctions Even water can be made to support lasing in the far infrared It is probably true that any material that can be made to emit light can also be made to lase under some conditions It is thus not a surprise that these conditions are more easily achieved for some materials than for others Semiconductor p n junctions are among the materials in which we can achieve laser action most easily Semiconductor lasers cover a very wide range of optical wave lengt
38. Given this informa tion a Calculate the de Broglie wavelength of a conduction band electron in GaAs assuming a kinetic energy equal to the ther mal energy at room temperature b The wavelength corresponds to how many unit cells of the crystal c In three dimensions estimate how many atoms could be found in a sphere the diameter of which is equal to a de Broglie wavelength in GaAs 2 4 Show from first principles that the energy of a photon can be cal culated from its wavelength by the following relationship Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Electrons and Photons Electrons and Photons 33 124 A nm E eV where the energy is given in electron volts and the wavelength in nanometers 2 5 Make a graph to scale of wavelength on the lower horizontal axis and energy on the upper horizontal axis The wavelength range should vary from 200 nm to 2000 nm a What is the corresponding energy range b Mark the following regions blue light green light red light 1550 nm low loss region for optical fiber telecommunications c Which photons have more energy red or blue d Paste a copy of this graph in your lab notebook 2 6 The energy of an electron is equal to the square of its momentum divided by 2 times its mass From de Broglie we al
39. LEDS can fail but the lamp will still be usable You would like for the savings to pay for the cost of the Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Light Emitting Diodes Light Emitting Diodes 123 changeover If you aim to recover your costs in 8 years you can pay 480 per LED light and still face your voters This repre sents the net present value of the cash flows of 73 each year for the next 8 years discounted at 5 6 6 Response Time The light emitting diode is based on two considerations the intrinsic recombination lifetime of injected excess carriers and the extrinsic RC time calculated from the diode capacitance in forward bias and its series resistance This RC time representing the time necessary to charge the diode capacitance is usually the dominant factor determin ing the modulation speed of LEDs The series resistance of an LED is determined by the majority carri er doping and the conductivity of the substrate on one hand and pro cessing related features such as ohmic contact resistance on the oth er The typical series resistance found in commercial LEDs is a few ohms The capacitance is the diffusion capacitance Simple models for this capacitance are too inaccurate to be used even for estimates Both parameters should be measured
40. Photons 9 Figure 2 1 A schematic picture of a collection of atoms in a gas The arrows give the magnitude and direction of the velocity of each atom If the gas is contained in a bottle on your lab bench then the average velocity of the atoms relative to you is 0 However the average of the square of the velocity is a positive number So what is this constant Boltzmann s constant of course Pr E E A eE ks kpT 0 026 eV 295 K room temp 2 3 If the total number of gas molecules in the bottle is Ny the number of molecules having energy E4 is given by the total number of mole cules times the probability that a molecule has energy E n E NrPr E E Nr e EvkBT 2 4 The number of molecules at energy E relative to those at energy E is readily expressed n Ea e E2 E1 kBT 2 ney ai The Boltzmann relation given in Eq 2 5 is a fundamental tool that you use to determine how photonic devices operate The Boltzmann relation can be applied to electrons as well as to molecules provided that these electrons is are equilibrium With suitable and simple mod ifications it is possible to use this relationship under nonequilibrium conditions The current voltage expression for a p n diode is exactly that adjustment We will use this tool over and over throughout this book Its importance cannot be overestimated Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com
41. There was another big jolt in 1990 when optical amplifiers were rediscovered and adapted to op tical fiber telecommunications This implemented multiple wavelength transmission wave length division multiplexing and made it possible for the Internet to grow Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Introduction 6 Introductory Concepts changed dramatically as can be seen in Fig 1 1 This is the definition of a disruptive technology An important side effect of this growth is that the composition of the telecommunications industry is changing rapidly Old line compa nies like Alcatel Lucent and Philips that were masters at handling slow growth and predictable schedules for deployment of new technol ogy are being pushed to the sidelines For example Alcatel has re cently announced that it intends to own no factories by 2010 These are being replaced in the photonic devices industry sector by a very large number of smaller companies many of which have been in busi ness for only a few years Not all of these companies will succeed Making a career in the photonics industry is both exciting and punc tuated occasionally by moments of instability provoked by the reorga nization of this industry resulting from the implementation of new technologies take ove
42. a specification called the ITU grid Thirty years ago lasers were like the original Model T Ford They came in only one color 820 nm Measuring the emission wavelength was not so excit ing Development of new laser materials has made it possible to de sign lasers across much of the optical spectrum from 400 nm to 10 000 nm Measuring the emission spectrum is obviously essential In this laboratory exercise you will discover that the peak emission wave length can be tuned by varying the temperature and also by varying the drive current In order to be useful for telecommunications appli cations the emission wavelength needs to be stabilized usually by a temperature insensitive passive external filter This filter is typically formed by a periodic stack of two materials having different indices of refraction The longitudinal mode spacing of the laser is determined by the cavity length the longer the cavity the closer the modes are spaced A typical semiconductor laser has four or five modes with a mode spac ing equal to about 0 3 nm see Eq 7 14 and the related discussion Getting a good measurement will depend on your care in mechanical ly stabilizing of the laser optimizing the scan rate of the spectrome ter and choosing the right settings for the lock in amplifier Lasers can be forced to emit in a single mode and this is a require ment for fiber optic telecommunications lasers This is often accom plished by using the same e
43. achieved by ap plying positive feedback from the output to the input The result is a circuit that amplifies only one frequency This is a way to define an oscillator A simple positive feedback circuit element is a RC combina tion that produces a 180 phase shift in the output signal for the par ticular frequency Such a circuit is shown in Fig 7 2 The feedback circuit transmits a wide band of frequencies to the in put but the 180 phase shift leading to positive feedback is obtained for only a narrow band of frequencies Only these frequencies are am plified strongly and soon these frequencies dominate the transistor output spectrum leading to oscillation This band of frequencies is called the gain spectrum of the circuit Note that no independent sig nal on the base is necessary to start oscillation The oscillation builds up from the noise components having the same frequency as the high ly peaked gain spectrum Note that the single frequency characteristic of the oscillator is de termined largely by the elements of the feedback circuit Indeed you Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Lasers 146 Photonic Devices Gain Feedback 0 047 0 047 0 047 2N2926 COMMON Figure 7 2 A circuit diagram of a class A amplifier with feedb
44. aes AN 6 35 Note from the rate equation that the presence of a quadratic term means that the transient behavior of the diode during turn on will not be the same as its behavior during turn off That is the rise time will no longer equal the fall time In the heavy injection limit the excess carrier density AN N Np N We assume that the LED has been turned on at current density J2 After the LED has reached steady state we apply a small ac modulation around the steady state current The LED bandwidth can be determined for this small modulation in the approximation that d dtAN 0 The rate equation under these conditions is ex pressed as d J AN BN P ANJAN aul dt qd Tar N P AN 6 36 0 6 36 We will further assume that the LED is a good device so that nonra diative recombination is negligible This means that T gt T p q 3BN Li 0 qd Thap J 3 3 1 2 2 fy ee yeaa T 3BN 2 B BN B 6 37 Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Light Emitting Diodes 134 Photonic Devices where we have defined a response time for ac modulation around a steady state operating current as 7 1 BN Solving Eq 6 37 for the modulation rate 1 BJ r sa Sod 6 38 Tac Under these conditions t
45. are shown vapor axial deposition outside vapor deposition and inside vapor deposition The large loss peak at 1400 nm is the result of absorption by the first harmonic of residual OH molecules in the glass Please see Chapter 9 for more details Adapted from D Keck et al Proc SPIE by permission Let us look at Planck s study of incandescent radiation Observation when things get hot they begin to glow As they get hotter 1 they glow more brightly and 2 the color of the glow changes We can measure the color of the glow by the frequency of the light So there seems to be a relationship between temperature and frequency color Exercise 2 1 If you have an electric heating appliance you can try the following ex periment After turning off the room lights turn on the appliance and watch it as it heats up Record your observations Note Some people have sensitivity to infrared wavelengths beyond the range of normal vision According to Edwin Land inventor of the Polaroid camera who studied this effect the color associated with Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Electrons and Photons 12 Introductory Concepts this sensitivity is yellow It appears just before the dark red glow of the heating element appears in the visible range
46. as it warms up In my classes this effect is seen by about one out of thirty students Sen sitivity does not appear to depend on age or sex Planck s proposition was that temperature is proportional to fre quency But Boltzmann already knew that temperature is proportion al to energy Therefore we conclude that color is proportional to ener gy As the energy goes up how does the frequency change Remembering that Af c as the energy gets larger does the wave length increase or decrease As the energy gets larger does the fre quency increase or decrease So of the two things that characterize light A and f which one is proportional to the energy As the energy goes up the wavelength gets shorter or smaller However the frequency has to increase be cause Af c Thus energy is proportional to frequency E hf 2 6 h of course is Planck s constant Energy in a monochromatic beam of red light equal to n h fred light where n is the amplitude or the number of vibrations each one of which carries hf of energy energy y hf n over all frequencies 7 f where nsis the number of photons distributed according to Bose Ein stein statistics 1 Np const rr 2 7 When Af gt kgT such as in the case of an incandescent body like a stove element np is distributed to a good approximation by Boltz mann s law Some important results obtained so far are 1 Boltzmann s law For a group of electrons a
47. at the output will be close to common or 0 V The output voltage is thus essentially the opposite of the input voltage In fact if we vary the input voltage sinusoidally between 0 and 5 V the output voltage will also vary sinusoidally between 0 and 5 V but 180 out of phase with the input The input current that ac companies the input voltage is smaller than the output current so there is amplification given by the ratio of the output current to the input current In the next step we would like to introduce some feedback from the output to the input in order to see what happens The simplest feedback element is a direct connection between the output and the input Since the output is essentially 180 out of phase with the input the effect of the feedback on the small signal gain will be to oppose any changes in the input at the base This is a negative feedback circuit The result will be that the transistor will operate in a stable state that is midway between being totally on and totally off with the output pegged at V 2 More moderate degrees of negative feedback can be achieved by putting resistance in the feedback circuit This approach is commonly used to stabilize the amplifier and to im prove its frequency bandwidth at the expense of peak gain Now suppose that the goal is not to obtain a wide amplifier band width but rather the opposite extreme that is an amplifier with all the gain peaked around one frequency This could be
48. at the website Optical Fibers and Optical Fiber Amplifiers 224 Advanced Topics to 1 bit period or when the width of 1 pulse at half maximum is broadened by 50 e Determine the dispersion limited transmission distance at these three bit rates 9 4 Calculate the total information carrying bandwidth of an optical fiber in a telecommunications network Assume that communi cations are being sent at the low loss window between 1530 and 1560 nm where Er doped fiber amplifiers can be used a Estimate the channel bandwidth in wavelength or frequen cy required for modulation at 10 Gbit sec b If each channel is separated by 1 5 times the modulation bandwidth how many channels can be accommodated in the 30 nm transmission window c What is the total amount of information bandwidth that can be supported by the fiber d Repeat calculations a b and c for 40 Gbits sec e Compare your results with the standard established by the International Telecommunications Union called the ITU Grid Comment on the differences Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Source Photonics Essentials Part Characterizing Photonic Devices in the Laboratory Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright
49. bonded crys tal similar to table salt The bonding energy of silver and bromine is about 1 eV so that a photon of visible light can break the silver bromine bond The bromine ions are much larger than the sil ver ions and they tend to stay fixed in place during the photoconduc tive process The smaller silver atoms however can move around This is a crucial feature During manufacture silver sulfide impuri ties are intentionally introduced in the silver bromide crystal grains The silver sulfide sites have a lower energy level for electrons than the level for electrons in silver bromide Thus the electron level for sil ver sulfide resides inside the band gap of the silver bromide This makes the silver sulfide sites attractive for electrons The energy level situation is similar to that diagrammed in Fig 5 8 The behavior of these molecules is worthy material for a play Shelly Errington now a distinguised professor of anthropology drew the cartoons in Figures 5 11 to 5 13 to accompany the explanation of photographic photoconductivity The cast of characters is introduced in Figures 5 11 and 5 12 The silver bromide molecule is seen to be Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Photoconductivity Photoconductivity 89 Step pa d i Figure 5 11 P
50. close to 100 The amount of light emitted is proportional to the number of elec trons or the current In theory the LED is a linear transducer of cur rent to light An important measurement to make is the determina tion of the range over which the emitted light intensity is actually linearly proportional to the current The LED current is also related to the applied voltage The maxi mum energy that an electron can gain from the applied bias is there fore limited by the voltage If the bias is 2 V each electron cannot gain more than 2 eV in traversing the diode The emission spectrum of the LED is determined primarily by the bandgap energy the energy difference between an antibonding state an a bonding state The width of the emission spectrum at half of its maximum output often referred to as FWHM or full width at half maximum is a characteristic of LED quality LEDs with a FWHM close to the thermal limit of 3 kT eV are considered superior to those having a broader emission spectrum However we recall from Chap ter 6 that the emission linewidth can be distorted by absorption The LED is a diode and like all p n diodes the LED will function as a photodetector The absorption spectrum can be compared to the emission spectrum Procedure a Measure the Current Voltage Characteristic Using a curve tracer measure the current voltage characteristic over several orders of magnitude of current Carefully determine the value of curre
51. conclusions to those given in Example 6 3 6 5 Referring to Eq 6 40 a Show that the bandwidth is given by f V 3 27r b Derive corresponding expressions for the dependence of the bandwidth on the recombination coefficient for the high injec tion and the low injection cases Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Light Emitting Diodes Light Emitting Diodes 141 6 6 It is now common to find traffic lights with the red light com posed of LEDs and a red filter instead of an incandescent light bulb However it is less common to find a traffic light with a green LED signal and even less common to find a traffic light with an amber LED signal a Explain the rarity of green LED signals Is this a technologi cal or an economic problem Is the economic issue related more to the cost of the LED light or the difficulty of saving money during operation b Explain the even greater rarity of amber LED traffic lights by answering the same questions as in Problem 6 6a Are there other applications in which amber LEDs could be used Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Light
52. corresponding to the energy difference between the initial and final states There is a third process called spontaneous emission In this case an electron can make a transition to a lower energy state by emitting a photon in order to conserve energy This process can occur in the ab sence of other photons Notice that there is no reverse process for ab sorption that is an electron cannot make a transition from the va lence band to the conduction band without absorbing a photon To understand better how a laser works we need to develop some ideas concerning the absorption and emission of light In Figure 7 3 we diagram in a very schematic way the three possi ble transitions that can take place in the absorption or emission of light We choose a simple two level system having N states in the up per energy level occupied by electrons and N states in the lower ener gy level occupied by electrons In equilibrium N lt N and the ratio between the two occupation numbers is given by Boltzmann statistics L2 9 AE kpT The probability that an electron can make a transition from the lower energy state to the upper energy state by stimulated absorption Fig 7 3b is equal to B Because stimulated absorption is the reverse of stimulated emission the probability for stimulated emission to occur Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All
53. detail in Chapter 9 Another important application for infrared wavelengths is night vi sion binoculars These instruments are composed of detectors that im age the infrared heat radiation from objects and convert this signal to a visible image so that the wearer can see in the dark Light beams behave like waves and the wave properties of light are easy to observe e diffraction effects e dispersion effects for example a rainbow e interference effects e wavelength e frequency Light beams also display effects associated with particles These ef fects are not as apparent in everyday experience In the laboratory you will observe this behavior often Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Electrons and Photons Electrons and Photons 11 10 0 1 0 VAD f A P a 27 f IVD INTRINSIC SCATTERING ATTENUATION RATE dB km O I i 1000 1200 1400 1600 WAVELENGTH nm Figure 2 2 Optical fibers are made of glass and can be very transparent if the glass is pure At 1500 nm the loss is about 0 2 dB per kilometer This means that a kilometer of optical fiber is about as transparent as an ordinary windowpane Fibers are drawn like taffy from a preform The properties of preforms made in three different ways
54. digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Experimental Photonics Device Characterization in the Laboratory Experimental Photonics Device Characterization in the Laboratory 249 1 The presence of light creates a current in the diode and therefore creates a bias voltage Does the presence of light drive the diode to ward forward bias or reverse bias 2 What is the maximum value of the photovoltage that you were able to measure 3 The photodiode is an energy conversion device The electrical pow er generated by the photodiode is equal to the area that the I V characteristic creates in the 4th quadrant of the I V curve This can be approximated by the product of the voltage at zero current and the current at zero voltage What level of electrical power does the photodiode generate in your measurements 4 Compare the diode I V characteristic to that calculated by the model equation Eq 3 14 The theory we developed says that the current is proportional to the exponent of the voltage What about the experimental result Is it true If so over what range of volt age and current does this relationship apply Where do the largest differences between theory and experiment occur in forward bias or reverse bias Why does theory fail to give a good account Is the theory wrong or are there external influences to the p n juncti
55. directly and inde pendently of the capacitance The capacitance meter manual probably has excellent suggestions for external biasing circuits In the experiments that follow it pays to take data intelligently You will want to take data on a number of diodes over a range of bias voltages The objective is to take as much useful data as possible without getting so bored you quit before you get all the data you need to do reasonable analysis In this measurement you have three choic es 1 Measure capacitance at evenly spaced values of bias voltages 2 Measure capacitance with small intervals of bias voltage around 0 V and increasingly larger intervals as you proceed toward large values of reverse bias 3 Measure capacitance with large intervals of bias voltage around 0 V and increasingly smaller intervals as you proceed toward larger values of reverse bias Which choice is the best The approach I use is to try to choose voltage increments so that the values of measured capacitance are more or less equally spaced Let us examine Eq 4 7 Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Experimental Photonics Device Characterization in the Laboratory Experimental Photonics Device Characterization in the Laboratory 261 A e oQNp A 4 Cae Vzr V
56. ed in Fig 6 9 This technique is widely used in LED fabrication This modification does not help to increase the amount of light emitted However it gives an important clue about how to proceed The application of Fresnel s equation Eq 6 11 shows that 68 of the light that is incident perpendicular to the surface of an LED made from materials with a strong index contrast relative to air i e 3 3 to 1 can escape One way to improve the percentage of light that can es cape from an LED is to make the angle of incidence look more like 90 for all the light One could machine the surface of the LED so it looks like a hemisphere This is a complicated and expensive procedure There is a simpler version of this idea that is just as effective and much less expensive to implement A highly textured emitting surface of an LED one characterized by peaks and valleys is rather the opposite of the smooth planar inter face between the semiconductor and air The optical reflection of this surface is much more difficult to model using Eq 6 11 than the smooth interface However as can be seen in Fig 6 10 this interface offers some significant advantages for improving light emission To understand how such a surface can be used to advantage imagine for a moment the possibilities for a photon that reaches the surface The first encounter with the interface probably results in reflection be cause of the oblique angle of incidence However the photon
57. for optoelectronics Although this material was known to have a direct band gap and to emit light in the blue region of the spectrum researchers had only been able to make n type material Without p type material there could be no p n diode and no LEDs or lasers Twenty years earlier a thorough research of possible techniques had failed to produce p type GaN and some scientists published pa pers to explain why it would not be possible ever However during the intervening time many technology changes occurred including semiconductor synthesis under ultrahigh purity conditions These conditions were developed to solve problems with another material AlAs GaAs alloys in which residual concentrations of oxygen in the reactor would combine with Al rendering it inert As it turns out oxy gen was part of the problem with GaN too Akasaki was able to show in 1989 that magnesium which also readily oxidizes could be used to make GaN p type material under conditions of high purity synthesis It was a difficult battle but this breakthrough set the stage for GaN optoelectronic devices Akasaki and his team knew about Eq 7 25 and realized that a dif ferent kind of laser structure would be necessary to achieve laser op eration with practical values of threshold current The quantum well laser principle developed only a few years earlier was the second im portant key that was needed to unlock the door to blue light The Akasaki design uses an a
58. from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Experimental Photonics Device Characterization in the Laboratory 252 Characterizing Photonic Devices in the Laboratory Analysis Compare lock in detection to narrow band detection Could you pro pose and carry out an experiment that would measure the difference in sensitivity You have made measurements with the lamp on one side of the chopping wheel and the photodiode on the other Which gives a bigger signal a using lenses to focus the light from the lamp on the photodi ode or b putting the photodiode as close as possible to the lamp with the chopping wheel in between Analyze and explain your result Which gives a stronger signal a using lenses to focus the light from the LED on to the detector or b placing the LED and detector diode as close together as possible Some chopping wheel frequencies do not work as well as others leading to high levels of noise Which frequencies are these What is their origin Explain how to pick the right time constant What happens if the constant is too short What happens if it is too long 11 3 Optical Measurements Using the Monochromator and Spectrometer Objectives In the following experiments we will learn how to 1 Set the slits and control the scan rate and scan wavelen
59. greater than Vg The for ward bias voltage of the diode introduces excess charge densities on either side of the p n junction The ratio of this charge to the applied bias determines the capacitance in forward bias An no e 7 1 Q qAn qno ew F 1 4 9 It is just this excess charge that leads to the diffusion current of the forward biased diode The accompanying capacitance is called aptly the diffusion capacitance 220 eqV kT _ 1 4 10 d Q a or dV Caite Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website This measurement of this capacitance in forward bias is not so easy as the measurement of capacitance in reverse bias A typical electronic capacitance meter can make an accurate measurement of capacitance under the condition that the conductance parallel to the capacitance of the diode is small R giogeCaicde gt 1 measurement frequency This is true for diodes in reverse bias but it is no longer true in forward bias when the diode begins to conduct strongly The capacitance can still be measured but a technique different from lock in detection is re quired An example of such a technique would be the use of a resist ance capacitance bridge to determine the diode capacitance in for ward bias For devices that operate in f
60. injection Current mA Figure 6 12 The reason why texturing the surface is an interesting idea can be appre ciated from the results that compare the external efficiency before and after the opera tion Texturing more than triples the external efficiency Taken from I Schnitzer et al Applied Physics Letters 63 2174 1993 Reproduced by permission from the American Institute of Physics Emission band assume to be uniform from 400 nm to 1900 nm Bulb replacement once per year half hour labor for two men 40 hour loaded salary Red light diameter 200 mm Passband for filter used to generate red light 100 nm The red filter allows 1 part in 15 of the emitted optical radiation through The bulb is 15 efficient to begin with Total emitted optical power 15 W Total emitted red light 15 x 1 15 1 W Light emitting diodes Assume each LED emits 1 mW of optical power in the red Quantum efficiency 4 Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Light Emitting Diodes Photonic Devices Responsivity of a red LED is 2 W per ampere times the quan tum efficiency or 0 08 Current needed optical output power responsivity 12 5 mA electrical power needed 2 volts x 12 5 mA 25 mW Each LED has a diameter of 5 mm so 20 LEDs radius of the red stopligh
61. intensity Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Lasers 152 Photonic Devices To continue our discussion of absorption consider what happens to the number of photons N per unit volume or the photon density as a function of time The photon density will decrease as the number of electron transitions from level 1 to level 2 increases The density will increase when the number of transitions from state 2 to state 1 in creases d ae Ni plhf By2 Nop hf Bar No N plhf Boi 7 7 The photon density is closely related to the energy density p hf N hf Similarly the intensity is related to the energy density hfe I ohf N c n In Eq 7 6 we derived a relationship between the intensity and the distance Because of the relationship between the intensity and the photon density we can write another expression for the gradient hfe d hfe d dt d ae n a n dt dx 7 8 For the case of light dx dt c n Since this is a simple constant the inverse expression that we would like to substitute in Eq 7 8 is the arithmetic inverse that is dt dx n c Using these results we can determine the condition for generating optical gain d 1 d 1 a c aaa a a a Using Eq 7 7 d c GEN Wa NDPhPBa 5 phy h E
62. is not re pS Figure 6 10 This is a schematic diagram of a highly textured emitting surface Light intercepting the surface from below is initially reflected but will pass through the in terface on the second or third bounce because it lies inside the escape cone For the semiconductor air interface with an index contrast of 3 4 to 1 this cone has an angle of about 16 Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Light Emitting Diodes Light Emitting Diodes 119 flected back into the interior of the LED because of the textured na ture of the interface On the second or third encounter the photon will find itself in the escape cone and be emitted By texturing the surface we can increase its emissivity which is a measure of how easy it is for light to cross an interface This idea of using a textured surface to lo calize the emitted photons near the interface until they can cross the interface within the escape cone dictated by the index contrast has been applied to LED design Using this method LEDs with external emitting efficiencies greater than 30 have been measured A bright shiny smooth surface such as polished metal has lower emissivity than a rough surface of the same material The typical semiconductor wafer used as a substrate for a LED is h
63. less than 1 dB With further engi neering the coupling loss in SOAs may be further reduced The second important factor is the result of the excited state life time in a semiconductor amplifier The lifetime of an electron in an excited state in the conduction band is several nanoseconds This is three orders of magnitude less than the excited state lifetime for Er in glass The shorter lifetime makes it much harder to reach 100 popu lation inversion The rate of spontaneous recombination will be much higher in an SOA compared to an Er glass amplifier The higher rate of spontaneous recombination leads to an increase in the ASE noise The ASE noise is not increased by 1000 times fortunately but there is a difference of about 1 to 2 dB more ASE noise for the SOA com pared to the Er doped amplifier The third important factor is the output power The gain of Er doped fiber amplifiers is comparable to the gain of a SOA i e about 30 dB In an SOA this level of gain is achievable only for relatively low input power on the order of 20 to 30 dBm that is 10 to 1 mi crowatts When the input power is larger the gain falls off Typical output power from a SOA is limited to 15 mW at the present time With further engineering this figure may improve However an Er doped fiber amplifier can deliver much higher absolute levels of pow er This enables cascading of Er doped fiber amplifiers for boosting power in transmission applications Th
64. make a laser source at 1540 nm by putting the gain region in between two mirrors The primary interest for optical communication is not to make a laser source but rather a laser amplifier Amplification by 0 8 0 7 0 6 y 0 5 0 4 0 3 0 2 0 1 0 1400 1450 1500 1550 1600 1650 1700 Amplitude au Wavelength nm Figure 9 13 Luminescence spectrum of erbium doped glass The erbium doped glass is incorporated in a single mode optical fiber having the same dimensions as a transmis sion fiber The luminescence leads to laser amplification the magnitude of which de pends on the length of the gain section An erbium doped section several meters long can produce a gain of 30 dB Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Optical Fibers and Optical Fiber Amplifiers 214 Advanced Topics 4 Ns oul 2 Fast 10713 sec nonradiative transition 4 8 980 nm 2 N pump Long lifetime 10 sec laser transition at A 1535 nm N Ground state Figure 9 14 The energy level scheme for Er ions dissolved in glass The crystal elec tric field of the glass splits the energy levels of the electrons in the erbium ion into var ious values A semiconductor laser operating at 9800 nm is used to excite electrons to the upper state N where they relax t
65. means that light having a wavelength of 750 nm will suffer 16 times more attenuation than light having a wavelength of 1500 nm You can verify from Fig 9 3 that the Rayleigh law is at work As we have already seen attenu ation at longer wavelengths is limited by residual water molecules in the glass The best compromise in today s technology occurs at 1550 nm Glass engineers continue to experiment with ways to lower the attenuation further One approach is to introduce impurities that re duce the equilibrium water vapor content Another is to fabricate glass compositions that can be drawn at lower temperatures reducing the amplitude of structural fluctuations in the glass However atten uation is only part of the story that explains why glass optical fibers are a commercial success 9 3 Optical Fiber Engineering In the previous section we discussed the importance of low optical at tenuation This is certainly the feature that made optical fibers look attractive to telecommunications engineers But it is a long way from a piece of glass with low absorption to an optical fiber product that can be made to the same specifications day after day and sold as a product A commonly used process to make optical fiber starts with a hollow tube of high purity fused silica A soot of silica doped with germani um is deposited by chemical vapor deposition on the inside of the tube This is called inside vapor deposition or IVD The tube and soot a
66. messages These engi neers were not wrong The mobile telephone network that everyone uses is proof that radio has a place in modern communications These engineers did lack vision however In the 1960s engineers had developed optical fibers with relatively low losses but there were no convenient sources of light The semi conductor laser was a curiosity existing in a few laboratories and it operated at 77 K Lasers made from Nd doped glass could be bought commercially These emit light at 1060 nm and are a good match to a local minimum of the fiber attenuation On the other hand these lasers had to be pumped with flash lamps and they emitted about 10 Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Optical Fibers and Optical Fiber Amplifiers Optical Fibers and Optical Flber Amplifiers 193 pulses sec hardly the stuff of high bandwidth telecommunications The telephone companies were still focused on communications via copper cables In 1970 almost all telephone conversations were carried by elec trons moving in wires For high speed transmission coaxial cable was used There were some point to point radio links to relay signals over long distances but only wire cable was capable of going around cor ners passing through ducts and connecting people living or
67. naturally attract dust particles from the air Attempting to clean this dust from the mirror by blowing or scrubbing the mirror will result most often in damage to the mirror by grating scratches or leaving behind debris on the metal surface In most cases you will not improve the quality of the measurement Thus it is recommended that you keep the monochromator closed and that you do not attempt to improve your measurements by clean ing the components 10 6 The Spectrometer Monochromator System In Figs 10 7 and 10 8 you can see the interior of two typical designs for these instruments Figure 10 7 is called a Czerny Turner grating monochromator It corresponds closely to the diagram shown in Fig Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Measurements in Photonics 236 Characterizing Photonic Devices in the Laboratory Grating Entrance slit Mirrors Figure 10 7 Photograph of the interior of a grating monochromator spectrometer showing the various elements slits mirrors and grating Courtesy of the Acton Corp reproduced by permission 10 5 The wavelength of light that passes through the exit slit is de termined by the angle of the grating relative to that of the light beam This angle can be changed by rotation of the grating about an axis pe
68. nm Fig 3 Temperatura dependence of slope efficiency Fig 6 Temperature dependence of peak wavelength T E c E 03 gt a S ao o 2 3 D Q O 0 2 e N 0 20 0 60 Case temperature te C Case temperature 1 C b Figure 11 8 continued Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Experimental Photonics Device Characterization in the Laboratory 270 Characterizing Photonic Devices in the Laboratory Fig 7 Far field patterns in piane parelle to heterojunctions Fig 10 Lidi output vs monitoring output turrent 3 g A 3 o 0 1 02 03 04 05 Ofl axis angle deg Monitoring output Im mA Fig 8 Far tield patterns in plane perpendicuiar to heterojunctions Fig 11 Polarization ratio vs light output Relative light output Po Polarization ratio P PL Off axis angle deg Light output Po mW Fig 12 impedance characteristics Fig 9 Pulse response waveform CX Leu LINYA LTU AOR TORE xs Sy U7 Wh QO 9 Light output i QRH Hep L ia tr 400psec 1 M RC WID gt oa nloe Time nsec i Response E neteet Figure 11 8 continued Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com C
69. one round trip circuit must be greater than the losses incurred during the same circuit plus the fraction of the intensity that is emitted through the reflecting mirrors The lasing threshold is de fined as the point when the gain is equal to the loss We can treat any loss along the optical path by an effective absorp tion coefficient that we will denote by y The gain coefficient k be haves just like a loss with the opposite sign The net laser gain can be expressed as R Roe 7 12 R and R are the reflectivities of the mirrors at either end of the gain region and L is the cavity length In the case of a semiconductor laser R and R are usually the same During laser operation the only variable in this expression is the gain coefficient which depends ultimately on the forward current in the diode Everything else re mains constant The laser threshold is reached when the net gain is unity This also defines the threshold gain Threshold gain 1 R Ree th V2L and 1 1 kin y OL in In the case where R and R are the same 1 1 kin y L In R 7 13 Example 7 2 You can determine the necessary gain coefficient in order for laser ac tion to occur A typical length for a semiconductor laser cavity is 400 um Suppose that cavity losses are 30 cm and the reflectivity of the cleaved laser facet is 30 The estimated gain coefficient needed to reach threshold will be kin 30 1 n gt 60 cm 0 04
70. order to minimize series resistance Doping on the n side is typically mid 101 em and mid 101 cm on the p side Because of the relative p type to n type doping ratio most of the radiative recombination oc curs on the p side where the injection efficiency is higher The high concentration of impurities results in a density of states that extends into the forbidden gap This density of states enables optical recombi nation at energies below the band gap and determines the shape of the luminescence spectrum The LED material is relatively transparent below the band gap en ergy and relatively absorbing above In the case of a homostructure LED where the same material is used throughout the LED emission is filtered by the material itself For this reason the spectrum of the light that exits the homostructure LED lies principally below the band gap energy The absorption spectrum lies principally above the band gap energy Thus the region of the spectrum that is common to both light absorption and emission is rather narrow and is located near the band gap energy Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Light Emitting Diodes 114 Photonic Devices PHOTODIODE PHOTOCURRENT M absorption edge LIGHT EMITTING DIODE 1 EMITTED INTENSITY
71. output power visibility and oth er characteristics Class I lasers present minimum hazards and Class IV lasers present the most serious dangers In the table below we give a summary of theses classifications The lasers that are in tended for the lab experiments that follow fall into Class II a They are continuously emitting visible lasers with an output power of 5 milliwatts or less Such lasers will not cause skin burns Reflected beams are too weak to cause eye damage The principal hazard re sults from looking straight into the laser beam If your laser diode is properly mounted you can eliminate the possibility of looking di rectly into the beam It is possible to go on for many pages about the importance of work ing safely Laser accidents do happen They are usually the result of an improbable sequence of events and a failure of the experimenter to think through all the consequences beforehand These accidents can result in permanent damage Instead of a long discussion I would like to share with you a short description of a real accident that caused real damage Three researchers were working on a laser experiment involving a pulsed Nd YAG laser with an average output power of 10 W This is a Class IV laser which means that it can cause instant eye damage Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subje
72. photodiode model of Eq 3 14 Note the presence of a dark current equal to 1 x 10 amps The photocurrent in creases the negative current in proportion to the photon flux The photocurrent does not depend on the reverse bias voltage Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Photodiodes 44 Photonic Devices VOLTAGE volts 0 5 0 4 0 3 0 2 0 1 0 0 1 1E 11 5E 12 5E 12 CURRENT amps 1E 11 1 5E 11 Figure 3 3 The current voltage characteristic of the photodiode model around V 0 Note that the current is 0 when the voltage is 0 only for the case when the photon flux is also 0 This situation is indicated by the arrow that passes through the origin of 0 current 0 voltage is the result for 0 photon flux This point is indicated by the arrow in Fig 3 3 The presence of the I V characteristic in the fourth quadrant of the graph has important physical significance It means the photodiode is gener ating useful power The amount of power is given by the area of the curve in this quadrant This feature of all photodiodes is the basis for the photovoltaic solar cell which is a photodiode optimized for con verting photons from the sun for example into electrical power Real photodiodes behave like this In Fig 3 4 we show the I V char
73. photographic film and sensitization The photo excited electron in Fig 5 8 has a lifetime in the conduc tion band of 7 seconds Under steady state illumination the number of additional electrons in the conduction band is given by AN Note 5 8 where N is the number of photons absorbed per second The pho tocurrent is I AN 5 9 a T Photon Conduction Band _Impurity Level Valence Band Figure 5 8 Schematic representation of photoconductivity resulting from photo ioniza tion of an electron trapped on an impurity site Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Photoconductivity 86 Photonic Devices where T is the transit time between the contacts If the contacts are ohmic then this photocurrent will continue until the photo excited electrons are trapped on the impurity sites If this trapping time is longer than the transit time then more than one electron will flow in the external circuit per absorbed photon This ratio between the trap ping time and the transit time defines the photoconductive gain G I qNy7 4N G 5 10 The transit time across the device is L pales v pe and the photocurrent is Tee TeuV The photoconductive gain is seen to be Teu V G T2 5 12 where V is the voltage between the
74. polarization mode will travel faster than the remainder of the light pulse in the other mode At the end of the fiber the pulse will ap pear smeared out in time Just like chromatic dispersion this effect becomes more important as the modulation frequency increases The circular symmetry of an optical fiber can be changed by many things To be sure there are imperfections in manufacture However strains induced by cabling the fiber a truck passing over a buried ca ble local heating during the day in fact almost any kind of perturba tion will distinguish the two modes and thus also change the orienta tion of their principal axes in the fiber Polarization mode dispersion is not static but rather unpredictable and in fact is quite insidious To be able to send signals at bit rates above 20 GHz polarization mode dispersion must be compensated for This means that you have to monitor the channel performance continuously and compensate for the measured pulse broadening by inducing a polarization mode dis persion of the opposite sign Achieving this compensation in a com pact and efficient way poses a significant challenge to today s optical fiber engineers In summary the demand for more capacity in the optical fiber telecommunications system can be answered in two ways sending the information at higher and higher bit rates or sending multiple wave lengths over the same fiber When the bit rate is increased dispersion effects i
75. potentiometer in series with one of the feedback resistors The oscillation frequency using the components shown should lie close to the audio range Attach an oscilloscope lead to the output to measure the oscillation amplitude a Measure the range of frequencies over which oscillation oc curs Plot the amplitude of the oscillation as a function of fre quency b How does the oscillation frequency depend on the bias volt age c Use a soldering iron to locally heat a feedback resistor Do not touch the iron to the resistor just hold it nearby What hap pens to the frequency of the oscillation Record the circuit diagram components used and account of the measurement in your lab book 7 2 Laser action can occur when the stimulated emission rate ex ceeds the spontaneous emission rate see Eq 7 5 What would happen if you reduced the spontaneous emission rate to zero Would you have a threshold less laser Explain your answer 7 3 Estimate the threshold current density in A cm of a GaAs based laser with the following properties Emission wavelength 850 nm Line width of the gain spectrum 1 5 x 101 Hz Internal losses 30 cm Index of refraction 3 5 Cavity length 400 pm Thickness of the recombination region 200 nm Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use a
76. proportional to the photon flux In some mate rials the absorption of photons increases the number of carriers and their mobility at the same time Noncrystalline semiconductors such as amorphous silicon are examples of this kind of behavior Equation 5 7 shows that the photocurrent will be nonlinearly proportional to the photon flux because of its dependence on both the carrier concen tration and the mobility This nonlinear behavior is well suited for threshold detection Since amorphous silicon is inexpensive to deposit and to process compared to crystalline silicon it is widely used to make the photoconductive detector elements in motion sensors The photoconductive response depends on the ratio of the carrier lifetime to the transit time between the electrodes The sensitivity of the photoconductor is proportional to the carrier lifetime The quan tum efficiency is defined by the number of electrons collected per inci dent photon and it is straightforward to design a photoconductor with a quantum efficiency much greater than unity The gain is given by the ratio of the lifetime to the transit time Over a considerable range of applied bias the transit time will decrease in proportion to the applied voltage Thus the quantum efficiency of a photoconductor can be tuned by the bias voltage In comparison a quantum efficiency of unity is the best that can be achieved using a photodiode In addi tion the response of the photodiode does not d
77. proportional to the total recombination rate If radiative re combination dominates then it follows that the light intensity is lin early proportional to the current In experiments the light intensity is seen to be linearly proportional to the current over some range In Fig 6 2 we show some results measured in the laboratory for an inex pensive visible red LED The light current characteristic is linear up to about 80 mA after which the intensity appears to saturate As the current increases the radiative recombination rate stays relatively ad N a ba d oO a 0 0 0 01 0 02 0 03 0 04 0 05 0 06 0 07 0 08 0 09 0 10 Current through diode A Light intensity given by photodetector signal voltage measured on lockin amp V x 1074 oi Figure 6 2 A basic characterization measurement for a LED is the light current char acteristic This measurement shows the region where the light intensity is proportional to the forward current The saturation observed here is a general feature of all LEDs and has its origin in the relative resistance of the active region of the LED and the sur rounding contact regions At even higher levels of current ohmic heating becomes im portant and this causes the light intensity to decrease Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms
78. recombination rate must equal the pumping rate This is the optoelectronic equiva lent of the principle that absorption must be equal to emission The recombination rate is the population inversion necessary to achieve threshold divided by the recombination rate N Recombination rate electrons sec t cm 7 16 Tr We have already developed an expression for the population inver sion in Eq 7 10 nhfg f kin No Ni Bar F Therefore kin Cc Ny No N yy 7 17 th 2 Deh Bz nhfg f where B is the stimulated emission coefficient In Eq 7 4 we related Bo to the spontaneous recombination rate This is a useful relation ship to know because you can measure this rate directly 8an hf Agi 3 Boy c c3 B Aas nf 7 18 Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Lasers Lasers 165 Substituting 7 19 into 7 18 E kn 8m P AS Agi egf The spontaneous emission rate A is determined by the inverse of the spontaneous emission lifetime r21 This lifetime can be measured by exciting the laser material with a light pulse from an external laser emitting photons with energy above the band gap of the semi conductor The semiconductor will emit photoluminescence that dies out with the spontaneous emission lifetime Ty
79. region and therefore invisible to the eye Two of the people were working to align the laser beam and they were wearing special glasses to protect their eyes from the laser beam The third person was monitoring the measurement using some electronic equipment in another part of the room The laser beam was oriented so that its path was shielded from the third per son One of the two people working on the laser was wearing a ring By accident he slipped his hand into the beam He burned his hand When he pulled his hand out of the beam the beam struck his ring The beam was deflected out its path and straight into the eyes of the third person who turned his head toward his injured lab partner but who was not wearing protective glasses because he was working on the electronics far out of the beam path Result one hand with a skin burn that is not permanent and one eye with permanent reti nal damage The great difficulty of working with infrared lasers is that they are invisible and often very powerful Because you cannot see the light your body provides you with no defenses Eye damage occurs silently and painlessly Laser burns on your retina do not usually cause in stant blindness but if you accumulate a number of such injuries your vision will get increasingly fuzzy Several weeks after writing this text I was reading Optics and Pho tonics News the official monthly magazine of the American Optical Society On page 19 of the October 200
80. response of an electronic or an optoelectronic device can be given by the following relationship RO R 0 VI V1 4 407f 72 where R f is the output response of the LED Using this model the bandwidth is determined at the frequency where R f 6 40 Rf 1 R0 2 This model gives a slightly different value for the bandwidth than the standard expression that we have used in this text 1 Bandwidth TT To summarize these important results e Heavy injection modulation rate 1 BJ J 8qd Tac e Light injection modulation rate 1 1 Bnp Tac nr Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Light Emitting Diodes 136 Photonic Devices RY R 0 R 0 2 LED Response Frequency f Bandwidth Figure 6 15 A simple model for the frequency dependence of an electronic device is based on the idea that its response is frequency independent up to a certain limit that defines the bandwidth Here we plot Eq 6 40 as a function of frequency The bandwidth is defined as the frequency at which the response is one half its original value 6 9 Summary The transient response of light emitting diodes depends on the rela tionship of the injected excess carrier density to carrier concentration introduced by do
81. results are shown in the figure below How would you design the detec tion circuit to meet the bandwidth requirement Assume that 7 1 bandwidth 77 CAPACITANCE VOLTAGE PLOT Capacitance 10 Farads Bias Voltage V 4 2 Using Eq 4 7 calculate the capacitance per square centimeter for a silicon p n junction diode as a function of carrier concentra tion and bias voltage Assume that the carrier concentration of the heavily doped side of the diode is at least 101 cm Let the carrier concentration on the less doped side vary by powers of 10 between 104 cm 3 and 1018 cm Choose voltages of 0 1 5 and 10 V Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Electrical Response Time of Diodes 76 Photonic Devices Make a plot of capacitance versus carrier concentration using a log log scale There will be four curves corresponding to the four voltages Put a copy of this graph in your lab book 4 3 Using the data in Table 4 1 make a plot of C A versus bias voltage Determine the built in voltage using this plot 4 4 The series resistance of a p n diode and its capacitance are both determined primarily by the characteristics of the lightly doped side of the junction a Show that the RC time constant of a p n junction photodiode in
82. reverse bias is independent of the diode area b Why is it generally true that a diode with a smaller surface area will have a faster time response Hint There are two resistances the diode resistance and the circuit resistance What determines the overall resistance Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Source Photonics Essentials Chapter Photoconductivity 5 1 Introduction Photons that are incident on a semiconductor material can be ab sorbed if their energy lies above the band gap energy Energy is con served by the breaking of a bond that is the promotion of an electron from the valence band to the conduction band The presence of these additional charge carriers one electron and one hole increases the conductivity of the semiconductor This is photoconductivity If the semiconductor has been processed with ohmic contacts and is placed in a circuit it will behave like a light controlled resistor Ingenious implementations of photoconductivity have been devised by both mankind and by nature Detection of light by photoconductivity dif fers from the detection of light by a photodiode in one significant way The photoconductive detector can be designed to have built in gain That is the absorption of a photon can lead to the generation of m
83. source of photovoltage In the photocurrent mode the photodiode is given a reverse bias that is large enough to put the diode in the voltage independent dark current regime In Fig 3 4 you can see that 0 5 volts would be sufficient The dependence of photocur rent on photon flux has already been given in Eq 3 15 In the photovoltaic mode the output of the diode is measured with a high impedance voltmeter so that the photocurrent is near 0 This mode of operation has the advantage that it is about the simplest way to derive a signal from a photodiode It requires in principle no other circuit elements In some real applications this may be all that is needed Setting the current 0 in Eq 3 14 Don qOr PE eant n A NGL ea VA kT Dnm 3 17 where V is the photovoltage generated by the photodiode Solve for V by taking the natural log of both sides kT NGL Va q 1 Dn 1 3 18 This equation shows that the photovoltage is not a linear function of photon flux There are some important practical implications of this result When used in the photovoltage mode a The photovoltage response is nonlinear b The response is not easy to model for correction Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Photodiodes 48 Photonic Devices
84. specific condi tions of wavelength and angle of the grating relative to the incoming beam of light Although you cannot do anything about these peaks you can appreciate that it is a good idea to know where they are A few ini tial measurements to characterize the grating will save you the em barrassment of confusing a grating anomaly for a lasing mode The tungsten lightbulb is a nearly ideal light source for this meas urement It has a peak intensity near 1000 nm and usable spectral output between 400 and 2000 nm The spectrum is very smooth with no noticeable peaks characteristic of a thermal radiation source Start with the grating having the shortest blaze wavelength Start Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Experimental Photonics Device Characterization in the Laboratory 256 Characterizing Photonic Devices in the Laboratory Monochromator Tungsten bulb Chopper Detector Convex lens with f number that matches that of the monochromator Lock in Figure 11 5 Schematic diagram for measurement of grating properties A tungsten light source is used because of its broad and featureless spectrum The lamp is placed at two times the focal length from the lens as is the monochromator The f number of the lens matches that of the spectromet
85. than the band gap electrons are promoted to the con duction band These recombine preferentially on the type 1 sites which have the higher capture cross section The type 1 centers are less numerous than the type 2 centers and are saturated by electrons On the type 2 sites the shorter lifetime for holes relative to lifetime for holes on the type 1 centers means that most of the holes will be drawn to the type 2 sites As a result electrons will fill the type 1 sites and holes will mostly be attracted to type 2 sites This situation is dia grammed in Fig 5 17 We can calculate how the addition of type 2 centers affects the life time of electrons and holes and the sensitivity using the parameters given in Table 5 2 Conduction Band gt OO O ss i e gt Valence Band Type 1 Recombination Type 2 Recombination Figure 5 17 Energy level diagram of the sensitized photoconductor under illumination In effect the electrons are preferentially attracted to type 1 sites and the holes to type 2 sites Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Photoconductivity 96 Photonic Devices Table 5 2 Parameter Type 1 Value Type 2 Value Density of recombination N 2 x 1015 cm N 2 2 x 1016 cm centers Drift velocity v 107 cm sec t v 107 cm sec t
86. the Author Copyrighted Matenal 240 241 241 242 245 245 249 252 257 259 263 279 285 Source Photonics Essentials Part Introductory Concepts Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Introductory Concepts inglibrary com its res Copyright 2004 TI U n at the website Any use is subject to the T Ac Source Photonics Essentials Chapter Introduction Photons have been around ever since the Big Bang which is a long time Photons by definition are always on the move 3 x 101 cm sec in air Some of the important milestones in the history of the human civilization are those at which we have improved our ability to control the movement of photons A few notable examples are the control of fire the design of lenses the conception of Maxwell s equations the invention of photography broadcast radio and the laser Photonics is the study of how photons and electronics interact how electrical current can be used to create photons as in a semiconductor laser diode and how photons can create an electrical current as in a solar cell The field of photonics is in its infancy Great discoveries re main to be made in using photonics to improve our lives The list of applications in photonics is lon
87. the Experts New Thinking Creates a Pathway to Increased Efficiency The relatively low level of emission efficiency of LEDs that is summa rized in Eq 6 13 is based on two important assumptions a the sur Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Light Emitting Diodes Light Emitting Diodes 117 face of an LED structure is planar and b the light from recombina tion is emitted uniformly over 47 steradians It is clear that we could improve the external efficiency of LEDs if we could find a way to re place these assumptions In this section we explore ways to a defeat the restrictions seemingly imposed by Fresnel s equations and b change the angular distribution of light Fresnel s equation is straightforward to apply to a simple flat in terface between two materials Under these circumstances it is quite accurate Analysis of reflection and transmission for rough interfaces is a more difficult case particularly when the roughness has dimen sions similar to the wavelength of light Then Fresnel s equations can no longer be used because it becomes impossible to define the angle between the light ray and the interface So examination of this case has been largely ignored As we will see shortly this was a mistake New thinking has shown that explo
88. the signal amplitude with only a mi nor degradation in the bandwidth of the signal Note that in both cases the full photoconductive gain given by the ra tio of the carrier mobilities is obtained Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Photoconductivity 84 Photonic Devices The signal bandwidth will also depend on the RC product of the de tector The RC product is the time required to charge or discharge the photoconductor electrodes In many cases it is the RC product that determines the bandwidth not carrier transport properties Once the RC product has been determined by measurement or by calculation it can be compared to the photoconductor bandwidth For example if the RC charging time is much longer than the transit time of the slower charge carrier then photoconductive gain can be exploited with minor bandwidth degradation 5 4 Engineering Photoconductivity In the previous section we considered the photoconductive effect that occurs when an electron is excited by the absorption of a photon and moves from the valence band to the conduction band This is the mechanism exploited in many photoconductive detectors but it is not the only one Photoconductivity will result whenever light acts to move acharge carrier from a relatively immobile state
89. this case you can only place an upper limit on the reverse current dictated by the sensitivity of your instrument Remove the cover from the photodiode and record the change in the reverse current This is photocurrent resulting from the absorption of the photons that make up the room light If you have a desk lamp or flashlight nearby use this to change the light intensity on the diode Note the results Reduce the bias voltage to 0 volts and place the cover over the diode Adjust the curve tracer so the current voltage spot is centered in the viewing screen Change the voltage sensitivity to 100 millivolts per division Remove the cover from the photodiode and notice how the spot moves along both the current and voltage axes The effect of the light is to put a bias voltage on the diode Use another light source to vary this bias voltage Using the voltage control on the curve tracer slowly increase the bias voltage in both the positive and negative directions until the cur rent in the positive direction crosses the zero current axis Note the voltage intercept This voltage is the open circuit photovoltage Analysis Plot the forward I V characteristic as log current versus voltage De termine the ideality factor of the diode using Eq 3 16 Then deter mine the converted electrical power and the maximum value of the photovoltage Answer these questions in your write up Downloaded from Digital Engineering Library McGraw Hill www
90. to one in which the carrier can be transported by the drift of an applied electric field The current density in the sample can be written as JI GE amp Nobe Nan 5 6 For the case of photon absorption across the band gap the number of excess electrons created is equal to the number of photons created and the mobilities remain constant Tpnot ELW An Nz An uy 5 7 A photoconductive detector made from silicon and based on this mechanism would have a useful sensitivity to photon wavelengths up to 1100 nm corresponding to the silicon band gap energy How ever we can dope silicon with an impurity element The presence of this impurity creates an impurity level that lies inside the band gap The impurity level acts like a trap and attracts electronic charges in the same way that potholes in the road collect water after a rain storm The basic function of the semiconductor in this case is two fold It acts as a host for the impurity and it assures the transport of ionized charge carriers into to the conduction band or valence band The pho ton energy required to create a charge carrier is now a fraction of the band gap energy For example the energy required to ionize an elec tron of gold doped silicon is about 0 15 eV Each impurity element has its own particular energy level so that doping introduces the possibil ity of tuning the spectral response The maximum doping level that can be introduced depends on the eleme
91. to their full capacity There is an excellent shortcut that you can use to develop highly ef fective laboratory measurements Surprising as it may seem this shortcut is not used very often It is called the operator s manual It is full of valuable information such as suggested set ups and programs for computer automation Take the time to read the operator s manu al for each piece of equipment and keep it handy while experiments are going on 227 Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Measurements in Photonics 228 Characterizing Photonic Devices in the Laboratory There are many kinds of photonic devices and only a few of these are specifically covered in this book The elements of characterization are basically the same for all of these components 1 Spectral response that is the response of the device to different wavelengths of light or the analysis of the wavelengths of light that a device can generate 2 Current voltage relationship that is the amount of power and possibly noise that a device will consume when it is operating 3 Capacitance voltage characteristic that is the response time of the device to the generation or detection of light 4 Light current characteristic that is the conversion of electrons into photons
92. tum efficiency ignoring reflections To measure the responsiv ity you illuminate the photodiode with 1 pwatt of light at 1000 nm Your measurement of the photocurrent gives 0 65 wamps ap ow Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Photodiodes Photodiodes 59 a What is the responsivity of the diode when A 1000 nm b What is the quantum efficiency at A 1000 nm c You would like to use the diode for a free space optical link operating at A 600 nm You decide on an incident power of 1 watt What do you expect the photocurrent to be d To clarify the issue you decide to measure the responsivity as a function of wavelength Before measurement you make a trial calculation of responsivity based on the above informa tion Please make a graph of your estimate in the range 400 nm lt A lt 1400 nm 3 3 In the lab you measure the I V characteristic of a Ge photodiode using a curve tracer The result is shown in the figure below Ge area 8 x 10 cm Current 5 x 107 A div Voltage 1 V div a Identify and measure the photodiode dark current b Is this dark current larger or smaller than that for other diodes you have measured c What features of this photodiode contribute to the magnitude of the measured dark current 3 4 In the
93. y 2 Vgr V Lene 2ees qNp You can see from Eq 4 7 that the capacitance will change rapidly for small changes in the bias voltage if the forward bias close to Vgz At the other extreme as the reverse bias gets larger the capacitance gets closer to zero but only as the square root of the bias voltage So increasing the bias by a factor of four will only change the capacitance by a factor of two So Eq 4 7 tells you to take more data for small values of bias than for large values of reverse bias In most cases there is not much to learn beyond a reverse bias of 10 V In order to explore the capaci tance in the forward bias regime where the capacitance increases dra matically you may have an interest in take capacitance readings at increasingly smaller intervals of bias probably less than 0 05 V Read the instruction manual for the capacitance meter Check that you are measuring capacitance and parallel conductance G or capacitance and parallel dissipation factor D Then go through the procedure for correcting for short circuit and open circuit conditions This will require you to disconnect your diode from the meter for a moment When you have finished and you have reconnected your diode into the meter note the difference in the capacitance reading if any As you know from your work with the curve tracer the diode can be biased either in forward or reverse bias Therefore it is not necessary to determine the polarity of
94. your electron has an energy of 1 eV This is the energy of an electron that falls through a potential of 1V 1 eV 1 6 x 107 joules h 6 6 x 10 4 joule sec 12 V2mE V2 9 x 107 kg 1 6 x 10 19 joules In 1929 de Broglie received the Nobel prize for this revolutionary idea His reasoning was different from the simple analysis above and involved little math not to mention Maxwell s equations His insight was based on an analogy with his everyday experience and is present ed later on in Section 2 6 Nearly ten years later in 1937 the Nobel prize was awarded to Clint Davisson for his observation of electron diffraction a property of electrons that can be described only by its fundamental wave like nature His lab partner Lester Germer got left out of the prize list a mystery to this day The work of Davisson and Germer led directly to the invention of the electron microscope a widely used instrument in all branches of materials physics and engineering For a 1 eV photon A 12 400 A For a 1 eV electron A 12 A At 1 eV energy only Aphoton _ 1000 electron This ratio depends on the electron energy But 1 eV is characteristic of electrons in solids What does this mean Relative to the electron the photon has mostly energy but not very much momentum We can see this on the diagram of energy and mo mentum Fig 2 4 Except for the uninteresting case in which E 0 the energy mo mentum curves for fre
95. 0 3 Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Lasers Lasers 161 The two parallel mirrors of a semiconductor laser are formed by cleaving facets along a set of well defined crystal planes The fact that the mirror surfaces are directly related to atomic planes guarantees that the cleaved surfaces at either end of the laser device are parallel The reflectivity of the mirrors is given by the Frensel equation Eq 6 11 and is equal to about 30 So 70 of the photons are transmit ted to the outside world The rest are reflected and continue to pro voke stimulated emission inside the structure The two mirrors form a resonant cavity around the gain region The length of the gain region is many times longer than the wavelength of light Only selected wavelengths of light can exist in such a cavity ex actly the same condition that de Broglie cited for his proposal that electrons have a wavelength That is the lightwave must retrace the same path in amplitude and phase for each round trip circuit in the cavity The round trip distance 2L must therefore be an integral number of wavelengths pA where p is an integer This is the condi tion for constructive interference to occur All other wavelengths are excluded because they lead to destructive interference The e
96. 0 issue you can find a full color Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Experimental Photonics Device Characterization in the Laboratory Experimental Photonics Device Characterization in the Laboratory 267 photograph of a trained optical scientist from NIST making measure ments with an 8 W green laser He is wearing no safety glasses and he is wearing a ring The hand with the ring is only a few centimeters above the beam Never put yourself in this situation I have worked with lasers for 30 years with no accidents and so can you Safety in optical experiments means continual awareness of the situation and strict attention to the rules These skills take time to develop so these experiments are designed using lasers that are un likely to cause permanent damage even if an accident occurs Handling the Laser Getting good laser measurements depends on fix ing the laser in a stable mechanical mount with easy to use electrical connections This is also an essential part of safe operating practice You must spend the time first to make certain that this detail is taken care of before beginning measurements Semiconductor lasers are easy to burn out This is the number one difficulty you will face in these laboratory experiments In this regard lasers are
97. 7 Also see the User s Manual of each instrument Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Measurements in Photonics 242 Characterizing Photonic Devices in the Laboratory Problems 10 1 Measure the basic behavior of a lock in amplifier Equipment needed Si photodiode chopping wheel lock in amplifier visible light source such as a flashlight Optional equipment an oscillo scope Prepare a socket for the photodiode by soldering to the socket two leads that are compatible with the signal entry port of the lock in amplifier Construct a stable mount for the photodiode socket Connect the two leads of the photodiode into the socket Plug the socket leads into the signal entry of the lock in amplifier Place the chopping wheel between the light source and the pho todiode socket Synchronize the lock in amplifier to the chop ping wheel Observe Phase at which the maximum signal is detected Dependence of the phase on the movement of the light source Effect of the chopping frequency on the measurement Effect of other external light sources Repeat these observations using the oscilloscope instead of the lock in amplifier Compare the effects of external electrical and optical signals and noise in the two cases 10 2 The f number of a lens is a
98. 906 To learn more read this book David Lindley Boltzmann s Atom The Great Debate that Launched a Revolu tion in Physics New York Free Press 2001 C R Wie The Semiconductor Applet Service hitp jas eng buffalo edu applets A truly outstanding set of applets on semiconductor physics and devices has been written by Prof Chu R Wie of the University of Buffalo Bookmark this Web site The Britney s Guide to Semiconductor Physics http www britneyspears ac lasers htm Whether or not you are a fan of Ms Spears this site is an excellent introduction to semiconductor optoelectronic devices like lasers and new directions in photonics such as photonic crystals D Halliday R Resnick and K Krane Physics 4th Edition Wiley New York 1992 See page 883 for a discussion of the relationship E pc E Hecht Optics 2nd Edition Addison Wesley Reading 1987 J Wilson and J Hawkes Optoelectronics 3rd Edition Prentice Hall Europe London 1998 Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Electrons and Photons 32 Introductory Concepts Problems 2 1 A p n junction is a metallurgical junction between two materials having different numbers of free electrons in their respective conduction bands At equilibrium Boltzmann statistic
99. Advanced Topics 9 7 Summary The optical fiber is a key element in the telecommunications revolu tion that has changed the lives of people around the world during the last 15 years The possibility of using optical fibers to transmit signal over long distances had to wait until low loss fibers were demonstrated in the early 1970s Realistic widespread deployment of optical fibers had to wait until a compact optical source was avail able Coincidentally room temperature continuous operation of GaAs laser diodes was demonstrated at the same time Shortly af terward a whole new class of laser diode materials GaInAsP was developed to permit transmission at the low loss window for optical fibers at 1550 nm After this innovation further development of GaAs lasers for communications applications was largely abandoned By 1990 optical fiber telecommunications links were installed under the ocean using GaInAsP lasers and electronic repeater amplifiers Signal modulation was accomplished by direct current modulation of the gain The Er doped optical amplifier was rediscovered This am plifier is pumped by GaAs based lasers which reentered the optical communications industry after a 10 year absence The explosive growth of the Internet put huge pressure on network operators to in crease capacity This could be accomplished by raising the modula tion rate of the laser and by multiplexing many wavelengths into one fiber These two improvements wer
100. Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Direct Modulation of Laser Diodes 186 Advanced Topics threshold is to set in motion this cycle which leads quite naturally to oscillations in both the carrier density and the photon density In this section we will make an estimate of the two important parameters that define this dynamic process the frequency of the self pulsations or relaxation oscillations and the decay time of these oscillations The approach we will use will be to decouple the equations to the extent that we obtain a single equation that shows how the nonequi librium carrier concentration changes with time To do this we will have to make some approximations in order to discard some terms that are smaller than others Since the objective is not to solve for the time dependence of the carrier concentrations the errors introduced by these approximations do not play an important role in the result we are seeking Start with the photon equation dN N 4B Ng f Kn 7s 2 Boone N An 8 11 We presume that the fraction of spontaneous emission in the laser mode is so small it can be neglected Next we separate the photon density into a constant term plus a small change Ng ne AN Finally we parametrize the gain coefficient K aAN 8 12 With these con
101. ED can be increased as fast as the RC time constant of the diode will permit there is an additional delay associated with the appearance of additional light emission The pulse of photons appears only after the excess carrier density starts to recombine We will de scribe this transition using the rate equation The current pulse cre ates excess carriers just as we saw in the steady state analysis in the previous section There are only two possibilities either this excess carrier density is greater than the majority carrier density created by doping or it is not In the first case called the high injection or low doping limit it is not possible to solve the rate equation explicitly Nu merical modeling can be used to map out the LED time response De spite this difficulty we can still determine a functional form for the Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Light Emitting Diodes 130 Photonic Devices rise time In the second case known as the low injection limit or the high doping limit the rate equation can be solved explicitly to give the time response of the LED to a current pulse as well as the rise time We will treat this second case first We will analyze the response of the LED to a step increase in the drive current At time 0 the LED
102. Fibers Many of the important photonic properties of optical fibers can be un derstood knowing only the core diameter and the index difference be tween the core and the cladding In Fig 9 5 we show a cross section of an optical fiber taken along its length The condition that must be sat isfied in order for waveguiding to occur is given by Snell s law Core n Cladding n2 Figure 9 5 A simple schematic diagram of an optical fiber For waveguiding to occur n must be greater than n Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Optical Fibers and Optical Fiber Amplifiers Optical Fibers and Optical Flber Amplifiers 199 core n cladding n2 Figure 9 6 Schematic diagram of an optical fiber in cross section along its length The core diameter d and the indexes of the core and cladding are shown The index of the core is greater than the index of the cladding Different light paths are shown On the far left the angle of incidence is nearly perpendicular to the core cladding interface This path is not guided by the fiber When the angle of incidence is much less abrupt total internal reflection can assure low loss guiding in the fiber This is shown for the two cases on the right The light path in the middle illustra
103. GROOVES mm S 600 g 50 DIFFRACTION GRATING EFFICIENCY FOR RELATIVE COMPARISON ONLY 10 0 0 1 0 2 03 04 05 06 Efficiency 1 2 18 20 22 24 26 07 08 09 1 0 14 16 Wavelength um BLAZE ANGLE 8 6 BLAZE WAVELENGTH 500 nm GROOVES mm 08 09 10 12 14 16 18 20 22 24 26 Wavelength jm b Figure 10 6 Grating efficiency curves for three different grating structures a Blaze wavelength 300 nm 600 grooves mm b Blaze wavelength 500 nm 600 grooves mm Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Measurements in Photonics Measurements in Photonics 235 Polarized at 45 10r ae ae p EEEE el Zsllectance o Pe eae aa ae a j Hau A 80 PERS DIFFRACTION GRATING ie oh EFFICIENCY FOR RELATIVE pa COMPARISON ONLY Efficiency SS ee eee 0 01 02 03 04 05 06 07 08 09 10 12 14 16 18 20 22 24 26 Wavelength um 1st Order Cat No 35 53 15 280 Date 8 22 87 Serial No 2855 42 1 Blaze Angle 17 27 Grooves mm 1200 Blaze Wavelength 5000 Remarks c Figure 10 6 c Blaze wavelength 500 nm 1200grooves mm on the mirror surface always wear gloves while handling mirrors During use the mirror surface will
104. Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Optical Fibers and Optical Fiber Amplifiers 204 Advanced Topics If the numerical aperture of the fiber happens to be 0 1 then we know immediately that the core diameter of the fiber is 9 87 x 103 nm or 9 87 microns As it turns out this is not too different from the pa rameters for commercial optical fibers An important consideration comes from fiber manufacturing There are fluctuations that must oc cur in the position of the fiber core and its diameter during the draw ing process For example Corning Samsung and Alcatel control the position of the core inside the cladding to 0 5 microns These fluctua tions do not depend strongly on the fiber core diameter So increasing the core diameter makes these fluctuations less important overall At the same time increasing the core diameter means that the fiber nu merical aperture must be reduced and this means that the index of refraction difference needs to be reduced also The index of the core is differentiated from that of the cladding by Ge doping There are also fluctuations in the doping level that naturally occur during manufac ture As the intentional Ge doping is decreased in order to reduce the NA these fluctuations tend to become more important Hence you would prefer to make the index difference larger Thus
105. In a three or four level system the equilibrium between ab sorption and emission is maintained but the absorption takes place between one set of levels and the emission takes place between a dif ferent set Semiconductor lasers represent the largest class of lasers on the market because of their low cost small size high efficiency and pow er ease of use and wide range of output wavelengths A semiconduc tor laser is an example of a four level system Putting a forward cur rent through the diode causes recombination to occur generating photons Some of these photons will be emitted into the resonant modes of the cavity created by the mirrors Only these photons will be amplified by stimulated emission As the current is increased these amplified modes will account for a greater percentage of the total re combination Threshold is reached when the amplification per round trip in the cavity exceeds the absorption and scattering losses for the same round trip Bibliography G P Agrawal and N K Dutta Long Wavelength Semiconductor Lasers Van Nostrand Reinhold New York 1986 Figure 7 12 This figure show a sequence of optical spectra taken at increasing levels of current in a blue laser based on GaN The threshold current density is 3 kA cm only slightly larger than that measured in a typical GaAs based laser at 920 nm In the bot tom frame of the figure the spontaneous emission is seen to be filtered by the many longitudina
106. LEDs com pare to the photodiodes Analysis Determine the ideality factor of your LED from the I V characteristic Determine the region of linearity between current and light intensi ty Compare the minimum voltage at which light emission is observed with the peak photon energy Reconcile your result by invoking con servation of energy What is the half width of emission How do the peak energy of emission and the half width vary with drive current Compare the width of the absorption edge to the half width of the emission spectrum Explain the differences in these two spectra 11 5 Device Capacitance Objective This section covers measurement of diode capacitance in both reverse bias and forward bias and the use of capacitance to determine the built in voltage and majority carrier concentration Background The diode capacitance is a major factor in determining the response time of both photodiodes and LEDs Knowing both the capacitance and its dependence on bias voltage is a key element in circuit design involving optoelectronic devices The capacitance of a photodiode can be tuned by changing the bias voltage without any adverse effect on its sensitivity Capacitance determines the ac noise power generated by a photodi ode Higher capacitance means more noise Analysis of the capacitance versus voltage curve can be used to de termine the doping concentration of diodes The depletion model cov ered in Chapter 4 gives an exce
107. Maxwell s equations For example to solve for the electrical field wn VE r t g Els t 0 9 4 An optical fiber has cylindrical symmetry so an intelligent choice of coordinates is cylindrical coordinates using r the radius the angle Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Optical Fibers and Optical Fiber Amplifiers 202 Advanced Topics around the central axis and z the length of the fiber The Laplacian operator has the following form in cylindrical coordinates 2 _ 1a 1 P rer op r r 9 5 We can deal with the z dependence of the problem by substituting a trial solution for the z component that looks like a simple sinusoidal wave That is E z t AeVo 6 9 6 This leaves us with an equation in r and that describes the behavior of the electric field in the circular cross section of the fiber Fy LEAT e 2 ZJE 0 9 7 ar rotz r P 72 r 9 7 A similar equation can be written down for the magnetic field Because the fiber has a circular cross section the variable is quantized following the same reasoning as that of de Broglie in Chap ter 2 The number can only be an integer indicating how many peri ods of the wave are found when you complete a full circle around the fiber cross section
108. McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Measurements in Photonics Measurements in Photonics 239 Figure 10 10 An example of a chopping wheel design having two slots and two closed sections The modulation frequency of this wheel will be twice the actual rotation rate sent the lock in measures the noise at the input and subtracts this from the signal when the signal comes around again Most lock in amplifiers can function from 10 Hz to 100 kHz The usual range especially with a mechanical chopping wheel as a modu lator is 100 Hz to 1000 Hz Lock in amplifiers are used to measure weak signals in the range of 100 nanovolts to 100 millivolts Their ref erence signal range is anywhere between 0 5 V and 5 V Example 10 1 In the laboratory you can use the lock in amplifier to measure the spectrum of a light emitting diode as a function of wavelength In this case the diode could be modulated by an ac drive current or it could be modulated using a chopping wheel The output from the spectrom eter will be quite small at any given wavelength but the lock in am plifier will be able to pick it up the modulated signal easily Figure 10 11 A photo of the front panel of an analog lock in amplifier The most impor tant keys define the amplifier gain and the low pass filter time constant Photo cour tesy of Stanford Research Systems reproduced by permission Downl
109. NdBa t 7 9 So a is positive and absorption occurs when N gt No On the other hand a is negative and amplification occurs when N gt Nj This sim ple condition is called population inversion You may notice that al though simple it appears to violate the requirements of Boltzmann statistics The art of making a laser is understanding how this condi tion can be achieved in real materials Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Lasers Lasers 153 When ais negative you get gain rather than loss and instead of us ing a to describe this condition we should define a gain coefficient k where Gain coefficient k a h k We NDP t 7 10 7 4 Obtaining Population Inversion So far we have considered light emission from a system of electrons having two energy levels E and E Looking at Fig 7 3 again you can see that there is one way for electrons to get pumped into the up per level by stimulated absorption We know that this rate is equal to the stimulated emission rate However there is a second way for elec trons to be de excited from the upper level by spontaneous emission In addition we know that this rate is much bigger than the stimulat ed absorption rate The result is that there is no way you can obtain a population inver
110. On the other hand in reverse bias of a few volts the result is Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Photodiodes Photodiodes 43 Dan J aaa gC7 3 15 Dark Photocurrent current The dark current is just the reverse bias leakage current that re mains when the level of light is reduced to 0 The photocurrent can easily exceed the dark current for modest photon fluxes In this situa tion it is much easier to measure the photocurrent In Figs 3 2 and 3 3 we show the result of evaluating Eq 3 14 for sev eral values of photon flux Gz The photocurrent is easily resolved for all reverse bias greater than 1 volt Near 0 volts the photocurrent is still resolvable but the distinction between the various curves disappears rapidly as the diode becomes forward biased because of the dominance of the diffusion current imposed by the forward bias voltage In Fig 3 3 we expand these data around the origin The values of photon flux are the same as those in Fig 3 2 Note that the only curve 2E 11 1 5E 11 1E 11 GL 1x100 Q g et GL 2x1010 5 g Zimm GL 4x10 10 cc SE 12 GL 8x10 10 gt 1E 11 1 5E 11 2E 11 5 4 3 2 1 0 1 VOLTAGE volts Figure 3 2 The current voltage characteristic according to the
111. This equation has been solved by many people and the solutions are Bessel functions Bessel functions are specially designed to de scribe waves constrained by circular geometries like the vibrations of a drum for instance Although they do not appear on your calculator keyboard like the sine and cosine functions they make life much easi er for describing these kinds of situations In the radial direction they oscillate with declining amplitude We will not solve the equation be cause what you would really like to know is not what the electric field looks like but rather the relationship between k 6 and J This rela tionship is determined by the boundary conditions The boundary conditions are determined by conditions of continu ity of the electric and magnetic fields at the interface between the core and the cladding where there is a discontinuity in the index of refraction This leads to a somewhat tedious exercise in algebra the chief benefit of which is to bring the core diameter of the fiber into the problem for the discontinuity in the index of refraction occurs when r d 2 An important parameter involves the ratio of the fiber core diameter to the wavelength of light This is called the V param eter d aj d Voor 1 z i NA 9 8 Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of
112. Use as given at the website Optical Fibers and Optical Fiber Amplifiers Optical Fibers and Optical Flber Amplifiers 203 In Fig 9 9 we show a plot of the V parameter on the horizontal axis and the propagation constant of the propagating wave on the verti cal axis The V parameter is determined by structural parameters of the fiber and the wavelength you would like to work at These are all under the engineer s control If you have a V parameter of 2 you can see that there is only one mode that can propagate If you have a V parameter of 3 there are two modes that can propagate If you had such a fiber but you wanted single mode operation you could make a new fiber with a smaller core diameter or you could work at a longer wavelength Single mode fibers are the only practical fibers for mod ern high bandwidth communications The condition on V that assures single mode operation is V lt 24 9 9 The V parameter ties together much of what you would like to know about making an optical fiber To assure single mode operation we might fix V to be 2 0 at the wavelength we would like to operate near e g 1550 nm We conclude that d NA 9 87 x 10 10 nm 9 10 2 3 Fiber V parameter ad A NA Figure 9 9 Normalized propagation constant b k plotted as a function of fiber V pa rameter It is easy to see that single mode operation is obtained when V is less than 2 4 Downloaded from Digital Engineering Library McGraw
113. a few tens of picoseconds for either electrons or holes in all photodiode materials Unlike the diffusion time the drift time is linearly dependent on the drift distance This feature can be used to improve the response time of indirect band gap photodiodes i e Si or Ge by replacing dif fusion current with drift current This will be discussed in more detail shortly If we refer to the example above the effect of replacing all the diffusion by drift current would shorten the intrinsic response time from 2 x 10 6 sec to 5 x 10 sec If the diode were built on a p type substrate then electrons would be the minority carriers A drift dom inated response time would be closer to 10 sec To summarize so far the response time for diffusion depends on the carrier mobility and the diffusion length It does not depend on the size of the diode or on the bias voltage The diffusion time can be quite short in photodiodes made from materials in which electrons or holes have very high mobility For example in Fig 42 we show the time re sponse of an InGaAs photodiode in which electrons have a mobility of about 10 000 cm V sec a factor of 10 greater than that for elec trons in silicon The response time due to drift current depends on the thickness of the depletion region and on the saturated drift velocity The saturated drift velocity is approximately one order of magnitude higher for elec trons than for holes The velocity is independent
114. a kind of is land in between regions where the water absorption is high In glass this high transparency region occurs at the same wavelength 1550 nm The wavelength where minimum attenuation occurs is also influ enced by scattering due to random fluctuations in the glass itself Glass is amorphous This means that the atoms of silicon and oxygen are not arranged in a regular periodic pattern On the local molecular level each silicon atom is attached to two oxygen atoms but the over all network of SiO molecules is irregular as shown in Fig 9 4 The fluctuations are frozen into the glass fiber during the fiber drawing process at high temperature The SiO molecules are about a thou sand times smaller than the wavelength of visible light Scattering or diffusion of light by objects much smaller than the wavelength is called Rayleigh scattering This same phenomenon is responsible for the blue color of the sky Rayleigh scattering strength depends in Transmittance Cor CY 2 ae COV 0 0 5 1 1 5 2 0 2 5 3 0 3 5 Optical Wavelength um Low loss region 1 530 um lt lt 1 700 pm Figure 9 2 Transmittance of air as a function of wavelength Note that most of the ab sorption bands can be related to the presence of water and carbon dioxide Note that the transmission is close to 100 at wavelengths around 1550 nm Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright
115. about 12 times greater than the hole velocity In Fig 5 4 the electric field created by the applied voltage sepa rates the electron hole pair spatially The electron which has a high er mobility moves toward the positive contact faster than the hole moves toward the negative contact The electron will reach the positive contact first and exit the semi conductor as shown in Fig 5 5 This creates a net positive charge in the semiconductor which is compensated by the introduction of an electron by the negatively biased ohmic contact Conduction Band Ohmic Contact Energy Valence Band Distance Figure 5 5 The electron reaches the positive contact and is detected in the external cir cuit In order to maintain charge neutrality in GaAs the negative ohmic contact intro duces an additional electron Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Photoconductivity 82 Photonic Devices The action of the electric field continues The electron with a veloci ty more than 10 times greater than the hole traverses the semicon ductor and is collected on the positive contact causing yet another elec tron to be introduced at the negative contact The hole meanwhile is still trying to reach the negative contact This is shown in Fig 5 6 Finally t
116. ack The RC circuit cre ates a time delay in the signal output When the delay time is sufficient to induce a 180 shift in the phase relative to the output the circuit will begin to oscillate Since the feedback is positive the frequency with the highest gain dominates This frequency is determined by the characteristics of the transistor and of the feedback circuit can select the frequency of the oscillator by changing the resistance or the capacitance This circuit is called appropriately a phase shift oscillator You can easily build and test this circuit in a few minutes If one of the feedback resistors has a variable component for example a poten tiometer in series with a resistor you will be able to tune the output frequency by scanning the resonant frequency of the feedback circuit across the gain spectrum of the transistor amplifier The operating principles of this circuit are closely analogous to those of a laser as we shall see in the following sections 7 2 Spontaneous and Stimulated Emission A laser consists of two components a photon amplifier and a positive feedback circuit In Chapter 6 we discussed the idea of optical gain or amplification The gain spectrum is the range of optical wavelengths frequencies over which light emission exceeds absorption Positive feedback is achieved by two mechanisms One of these is external and Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibra
117. ai where A is a constant of proportionality The effect of the structural dispersion in a conventional fiber is to shift the zero dispersion point from 1280 nm toward longer wave lengths Popular high performance single mode fiber made by Alcatel Teralight and Corning LEAF use this trick to shift the zero dis persion all the way to 1550 nm thereby achieving zero dispersion and minimum loss at the same wavelength More complicated designs involving an intermediate cladding layer are used to flatten the dispersion over a range of wavelengths This design is shown schematically in Fig 9 11 Design rules for achieving a specific wavelength spectrum of dispersion are given by Jeunhomme see Bibliography The engineering control over the optical propagation properties of optical fibers is a key technology in the optical fiber telecommunica tion business The dispersion characteristics that we have discussed are summarized in Fig 9 12 In addition to the dispersion that is built into the fiber there is a second kind of dispersion called polarization mode dispersion The calculation of the transmission modes of a fiber assumes that the core and the cladding have perfect circular symmetry The lowest order Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Optical Fi
118. al Fiber Amplifiers Optical Fibers and Optical Flber Amplifiers 213 communications at 1550 nm They were benefiting from semiconduc tor laser diodes that emitted hundreds of milliwatts of optical power instead of those used by Julian Stone that emitted only hundreds of microwatts of optical power They saw that the amplification of light by the fiber introduced very little additional noise compared to con ventional electronic amplification but the big benefits are that the op tical amplifier does not care what the electronic modulation rate is and it does not care what the wavelength is at least over the range of wavelengths where erbium shows gain So you can send simultane ously different wavelengths and different bit rates through the same fiber The combined signals emerge from the erbium doped fiber am plifier with a gain that is significant typically 30 dB and independ ent of the modulation rate The erbium doped glass amplifier functions like every other laser The luminescence spectrum of erbium in glass is shown in Fig 9 13 The gain spectrum is very similar to the luminescence spectrum It is easy to see that the gain spectrum is not very flat This creates the need for gain equalization which is performed after the light passes through the amplifier section The useful part of the gain is centered in a 30 nm window around the peak as indicated in Fig 9 13 The op tical gain associated with erbium luminescence can be used to
119. al communications using optical fibers might be possible when he demonstrated an optical fiber with losses on the or 191 Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Optical Fibers and Optical Fiber Amplifiers 192 Advanced Topics water flowing in glass tube glass tube stream of water 7 gt 30 a light is trapped in the stream light in Figure 9 1 A schematic diagram of the experimental demonstration by Newton that light can be guided in a stream of water der of 20 dB per km In the early 1970s the team of Maurer Keck and Schultz at Corning used the wizardry of glass chemistry to show that the losses could be as low as 2 dB km This discovery heralded the beginning of serious work on optical fiber telecommunications Corning fiber still dominates the world market but we shall see that this involves a lot more than lowering the loss which today is typical ly about 0 2 dB km making glass fiber more transparent than air in most places In the 1950s the telecommunications world was dominated by engi neers who had worked on radio and radar during the Second World War The vision was that telecommunications would continue to im prove by building higher and higher bandwidth transmitters eventu ally using radio and even microwaves to send
120. alibrated in terms of wavelength There is an unfortunate tendency to report opto electronic properties as a function of wavelength simply because the spectrometer is calibrated in these units On the other hand the opti cal properties of optoelectronic devices are interpreted in terms of pho ton energy and not wavelength For example the half width of LED emission at room temperature is typically 100 meV independent of the peak emission wavelength For an LED emitting in the infrared spec trum at 1300 nm with an energy half width of 100 meV the half width expressed in wavelength would be 170 nm An LED emitting in the visible spectrum at 650 nm having the same energy half width as that above will have a halfwidth expressed in wavelength of only 85 nm However these two LEDs are displaying the same physical perform ance The monochromator spectrometer does not have a flat passband That is some wavelengths are transmitted with greater efficiency than others Sometimes the effect can be dramatic These differences are the result of the optical properties of gratings and also the result of the absorption by our atmosphere especially evident around 1400 nm on a muggy day Photodetectors do not have an ideal flat spectral response either As a result your measured spectrum in an optical measurement will depend on several factors e The spectral content of the light source for example tungsten light bulb versus LED The characterist
121. ally it reaches the silver sulfide site that has been activated by the presence of an extra electron The d nouement is shown in Figure 5 13 The silver atom the silver sulfide and the electron form a new group on the left hand side of the cartoon The bromine atom becomes a stand alone figure as shown on the right Photons having an energy in the visible wavelength range 2 eV to 4 eV can be absorbed by the silver bromide breaking the sil Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Photoconductivity 90 Photonic Devices eis saat f A 5L tif Vie AF e ee Se Sep 2 y aosire to Liga Figure 5 12 Upon exposure to light a photon is absorbed by the silver bromide break ing the atomic bond and liberating an electron to the conduction band The electron is attracted to the silver sulfide because of the latter s positive charge The silver atom is also mobile but moves more slowly than the electron Professor Shelly Errington of the University of California at Santa Cruz drew this original illustration dep 3 posed flm Figure 5 13 The camera shutter closes ending exposure to light This stops the gener ation of electrons and movement of silver atoms ending the photoconductive process The internal physical structure of the silver bromide
122. amental physical arguments about the difficulty of obtaining useful levels of p type doping in wide band gap semicon ductors Fortunately many of these scientists retired after becoming managers and deciding to stop research on blue LEDs An unintended benefit of stopping research on blue LEDs was that people also stopped remarking that such a device was impossible The quiescence in this discussion has permitted a few innovative device engineers to look at the challenge with fresh ideas and energy The first commer cial blue LEDs made from SiC were demonstrated by Cree Research in the latter part of the 1980s At the beginning of the 1990s new ex periments from the group of Isamu Akasaki then at Nagoya Univer sity showed that efficient blue LEDs and eventually lasers could be made from GaN This work is recognized as the critical step that al lowed Shuji Nakamura of the Nichia Corporation to move GaN opto electronic devices from the list of unobtainable effects to commercial reality Now there are blue and ultraviolet semiconductor lasers and LEDs made from GaN and related compounds The new age of LEDs is made possible by more than p n junctions of semiconductors like GaAs and InP Efficient bright emission is also achieved using organic crystals and polymers It is now evident that polymer LEDs will be formidable competitors of semiconductor LEDs Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com
123. and the photon density Models of the modulation rate lead directly to coupled differential equations Sim plifying assumptions can be use to decouple these equations but the result leads to an underestimation of the laser modulation rate This approach allows qualitative appreciation of the important physical parameters that affect the transient response Numerical simulation is probably a better approach if quantitative prediction is sought When the laser is pulsed from off to on there is a time delay that occurs before any laser light appears This delay is proportional to the difference between the off state current and the threshold current As the laser turns on there is oscillation of the light output that occurs in time The frequency of this oscillation increases as the difference between the threshold current and the final steady state current increases These oscillations eventually die out with a time proportional to the excess carrier lifetime These parameters limit the bandwidth that is achievable using cur rent modulation of laser output power Note that the small signal ac bandwidth of the laser may by much greater than the bit rate for digi tal communications In a similar vein the laser transient properties cannot be correctly deduced from a simple experiment in which a small ac modulation is applied to the laser and the modulated output power is measured as a function of signal frequency Bibliogra
124. any electrons in the resulting photocurrent whereas a photodiode has a gain that is less than or equal to unity under normal operating condi tions 5 2 Conductivity and Mobility The electrical conductivity of a semiconductor material is the product of the density of free charge carriers N the charge on the electron and the mobility of the charge carrier u o Nqp O em 5 1 The mobility u is a measure of how easily an electronic charge can propagate through the semiconductor structure The mobility of an 77 Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Photoconductivity 78 Photonic Devices electron is different from the mobility of holes and for the vast major ity of semiconductors it turns out that u gt up The mobilities for elec trons and holes are different for each semiconductor material For ex ample in silicon He 1500 cm V 1 sec t and HUn 600 cm V sec whereas for GaAs He 8000 cm V sec t and Hn 600 cm V 1 sec The mobilities in any given material will depend also on the tempera ture and on the level of impurities and this feature can be exploited to optimize the performance of a photoconductive device For simplici ty however we will concentrate first on the behavior of undoped semiconductor materia
125. arge in the hundreds of gigabits per second However this is still less than the capacity of a single optical fiber which is in the terabit per second regime You can imagine that it would be very expensive to launch and maintain all these satellites The entire communications network would have the same capacity as one optical fiber but real telephone companies work with millions of fiber optic links Teledesic was not a financial success 9 2 Glass Optical fibers are made from glass Glass is made from silicon and oxygen in the form of silicon dioxide SiO Silicon dioxide is sand It is far the most plentiful compound in the earth s crust Glass is an as tonishing material a true gift from nature to the human race Some properties of glass are It is chemically inert It is transparent to light over a broad wavelength range It can be blown into arbitrary shapes It can be colored to make beautiful artwork It can be molded It holds liquids without leaking It can hold nuclear waste without leaking It is stronger than steel It is an excellent electrical insulator It is a heat insulator It is the key element in the SiO Si MOSFET which makes the in tegrated circuit possible It is the basis of optical fibers making the telecommunications rev olution possible Clearly so to speak glass should be worth much more than gold But on top of everything else glass is one of the cheapest primary materials there is Basically
126. aser Diodes 188 Advanced Topics 3 The principal assumption that we used to obtain results in closed form was to presume that the radiative recombination time re mains constant as a function of carrier density The results in Eq 8 8 and 8 19 should not be used to make quantitative calculations They can be used to understand the systematic behavior of the turn on delay and the relaxation oscillations Prebiasing the laser close to threshold and driving it on well beyond threshold will min imize the turn on delay This action will also increase the average photon density with the result that the relaxation oscillation fre quency will go up and the decay rate of the oscillations will become shorter Current semiconductor laser engineering is following this path An alternative approach to controlling relaxation oscillations is to illuminate the active region with an independent constant light source The intensity of this light source is not coupled to the electron density and its presence interferes with the resonant oscillation be tween the electron density and the photon density diminishing the amplitude of the relaxation oscillations but probably not having a strong an effect on the decay time These considerations show that the current model for laser modula tion is incomplete Development of a more realistic model could be made possible by allowing the important parameters to vary with the electrical pumping rate and the photon densi
127. ate HE because the energy difference is smaller and therefore easier to make up by phonon emission After step 2 there are electrons in state E but not in state E Thus a population inver sion between these two levels now exists The recombination that fol lows is an example of optical gain since emission between these levels far exceeds absorption which is practically zero step 3 This transi tion can be a lasing transition if suitable feedback is provided Final ly electrons that reach level E are recycled to level E leaving state E empty again step 4 In this example the number of photons ab sorbed is still equal to the number of photons emitted However there is now one set of levels that does most of the absorption and another set that generates most of the emission Optical amplification occurs if the emission rate exceeds the absorption rate and this is the case for emission between states 4 and 3 A semiconductor laser is a good example of a four level system and this can be understood quickly from a simple band structure diagram such as that in Fig 7 6 Optical stimulation of lasing is relatively easy to demonstrate in a direct gap material and it proceeds following the cycle outlined above However the cycle for obtaining gain by electri cal excitation is quite different In this case the behavior of the p n junction is used to create a population inversion The pumping cycle in Fig 7 6 is different from the cy
128. ates in the lower level N and the number of photons present having the right en ergy p w N B p Under steady state conditions the number of Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Lasers Lasers 149 absorbing transitions equals the number of emitting transitions We can summarize the discussion so far in a set of simple equations Emission rate Wai By pho Ag Absorption rate Wy Byop Tiw NB yop hw NoBoiplha NA 7 1 This allows us to solve for the photon density at the energy of the transition z N B iye Ast Z 21 7 2 N Bi2 No Bo1 Ni Big i N Boi Now we will compare this expression for p fiw to another one based on the Planck radiation law We discussed Planck s experiments in Chapter 1 The result of his work was to derive an expression for the energy density of photons We recall that Planck discovered that the energy density depends on the temperature and on the color or ener gy of an individual photon Planck s radiation law states sae 16xth 7 3 3 eho kpT _1 In comparing Eqs 7 2 and 7 3 we can see some similarities For example we know from Boltzmann statistics that N N e4 B7 Therefore it follows that N N e4 BT o kBT We can see that the two equations are ident
129. ating of the light out put cannot be exceeded Because of the size of each device each of the labels shown right are attached to the individual laser container They are illustrated to comply with the requirements of DHHS standards under the Radiation Control for Health and Satety Act of 1968 The taser beam trom the laser diode mainly consists of near infrared rays and ts very harmful to the human eyes though it is invisible Take great care not to took directly into the luminous point when the laser ts in op eration The laser beam can be observed by with an IR viewer ITV camera or a simpler IR phosphor device made by KODAK corp which can all detect infrared rays Gancen INVISIBLE LASER RADIATION AVOID DIRECT EXPOSURE TO BEAM SEMICONDUCTOR LASER padl AVOID EXPOSURE Invisibie Aaser Radiation is emitted front Wie aperture a PEAK POWER 30 mw 1 7 l WAVELENGTH 209m CLASS Il b LASER PRODUCT Warning Labe Aperture Lable d Figure 11 8 continued 271 Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Experimental Photonics Device Characterization in the Laboratory 272 Characterizing Photonic Devices in the Laboratory Measurements to Make 1 The light current characteristic 2 The peak wavelength of the laser
130. ator Detector arrays that operate in the visible region of the optical spectrum are much more sensitive and inexpensive than detector arrays that can operate in the infrared A gt 1 pm 10 7 Lock in Amplifier A lock in amplifier is a kind of electronic strobe for measuring period ic signals that might be too weak to be seen under ordinary amplifica tion The signal to be measured is compared to a reference signal for both its frequency and relative phase difference In the optical charac terization measurements discussed here the reference signal is pro vided by an optical chopping wheel which interrupts the optical beam periodically The reference signal and the signal to be measured are combined to generate a difference and a sum frequency Fig 10 9 In the example shown in Fig 10 9 the light from the LED is period ically interrupted by a chopping wheel The frequency of the modula tion provides the reference frequency and we are interested in meas uring signals from the detector that have the same frequency so w w The signals entering the mixer are A cos w p and B cos a 1 The signal exiting the mixer is AB AB AB cos a t cos w t ey Ollos w t dl z Oslos a t o Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Measureme
131. ber Amplifiers 9 1 Introduction It has been known and understood from at least the time of Isaac Newton that light beams could be trapped and guided in a medium of higher index of refraction material surrounded by lower index of re fraction material Newton s demonstration consisted of trapping a light beam inside a stream of water Fig 9 1 Three hundred years later we figured out how to use this observation and revolutionized the telecommunications industry How did it happen It was also known in Newton s time that glass was transparent to visible light and that it could be fashioned into prisms and lenses that could be used to bend light beams through fixed angles Glass technol ogy was already thousands of years old at that time However the telephone was still 200 years in the future About 50 years ago well after the telephone was in widespread use interest developed in us ing optical fiber bundles as a way to transmit images from one place to another The principal applications were in the medical field for im aging inside the body particularly during surgery This work let the cat out of the bag One of the pioneers of fiber bundle imaging was a young British medical student named Narinder Kapany He soon left medicine to promote the use of optical fibers for telecommunications and is still working in the field In 1966 Charles Kao at Standard Telephone and Cable in England obtained the first results that showed that practic
132. bers and Optical Fiber Amplifiers 210 Advanced Topics CORE CLADDING OUTER LAYER BUFFER AND PROTECTIVE COATING ny n refractive index no 1 454 n3 n3 1 458 2 d d digmeter d dj 3 um 2 d2 40 m d3 d3 1004m Figure 9 11 By varying the structure of the fiber cladding as illustrated here a disper sion flattened fiber is obtained 20 Dispersion unshifted Dispersion flattened 10 Dispersion shifted 1 4 1 5 Wavelength um D A ps km nm o 20 Figure 9 12 Typical fiber dispersion properties Intelligent structural design is used to shift dispersion to the desired wavelength region or to modify the spectral appearance of dispersion Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Optical Fibers and Optical Fiber Amplifiers Optical Fibers and Optical Flber Amplifiers 211 HE mode see Fig 9 9 has two propagation vectors that are ab solutely identical for a symmetric fiber If the fiber loses its circular symmetry these two modes separate which means that they will have different characteristic group velocities A light pulse coupled into a fiber will split its power between these two modes The effect of the difference in group velocities is that the part of the light pulse in one
133. between energy on the vertical axis and mo mentum on the horizontal axis It is identical to the first frame shown in Fig 2 10 because we start from the same situation the free electron In succeeding frames we add the peri odic potential due to the actual Ge atoms This causes the crossings to separate By the time we arrive at Ge there is a band gap between the valence band and the conduction band However the minimum of the conduction band and the maximum of the valence band do not occur at the same value of momentum This is an indirect energy gap Si and Ge are examples of indirect gap semiconductors the gap in a direct fashion This is called a direct transition and GaAs is called a direct gap semiconductor The band structure is a visual display of the states of energy and momentum that can be occupied by an electron Since the semicon ductor crystal is a solid we know that the states in the valence band are nearly completely occupied by electrons Undoped semiconductors have just enough electrons to complete the bonding Therefore even Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Electrons and Photons 30 Introductory Concepts at room temperature there are not very many occupied states in the conduction band compared to the occupied states in the valenc
134. bjectives The experiments in this section will explore the following areas 1 Current voltage measurements determination of the minimum voltage at which light emission can be observed 2 Light current measurements region of linearity region of satu ration 3 Emission spectrum peak emission wavelength photon energy emission half width 4 The LED as a detector absorption edge comparison of the absorp tion spectrum with the emission spectrum Background The LED is a quantum electron to photon transducer Electrons en tering the depletion region are converted into photons This conver Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Experimental Photonics Device Characterization in the Laboratory 258 Characterizing Photonic Devices in the Laboratory sion is the physical manifestation of the laws of conservation of ener gy and conservation of momentum By recombination with a hole the electron completes a chemical bond and gives up the bonding energy This energy appears as a photon The law of momentum conservation ensures that the energy appears entirely as one photon and not as heat which would be the creation of a large number of phonons con verving energy but not momentum In the typical commercial LED the efficiency of this conversion is
135. bright and they tend to degrade during operation An obstacle to obtaining bright and long lived polymer based optoelectronic devices is the poor purity of the starting materi als Do you suppose you could solve this problem Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Lasers 170 Photonic Devices Intensity a u 395 400 405 4 Wavelength nm Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Lasers Lasers 171 7 8 Summary A laser is an amplifier with positive feedback Amplification is gener ated by simulated emission of photons and positive feedback is achieved using mirrors In a laser that is optically excited the absorp tion rate of photons is equal to the emission rate The emission rate is composed of both spontaneous and stimulated emission The absorp tion rate is due only to stimulated absorption Optical gain will occur if the stimulated emission rate exceeds the stimulated absorption rate Such a situation cannot occur in a two level system because the same two levels are responsible both for absorption and emission of photons
136. bulb The commer cial stakes in this industry are very high in my opinion even higher than those in the communications industry This application of LEDs may solve an important problem faced by engineers in optoelectron ics a marketing problem how to achieve product sales volumes that grow faster than product prices decline This is a requirement for the existence of a business The circumstances imposed by the communications industry have led to the simultaneous development of high reliability lasers with continuously improving bandwidth and at the same time optical fibers with reduced loss and dispersion Initially a result of this progress was to reduce the need for large numbers of optoelectronic devices in optical fiber telecommunications systems As a result mak ing a growing business out of the design and manufacture of optoelec tronic components like detectors LEDs and lasers for telecommuni cations has not been a simple task During the past few years the explosive growth of the Internet has prompted network equipment in stallers to develop wavelength division multiplexing Basically this 101 Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Light Emitting Diodes 102 Photonic Devices means that where there was once one laser now there are about
137. by a light emitting diode or laser Your technique in the laboratory will improve from week to week as you learn how to obtain repeatable spectra from optoelectronic de vices The ultimate characterization you will make in the laboratory is the measurement of the output spectrum for a semiconductor laser diode These measurements are a real test of your skills in the labo ratory 10 2 Lenses A lens is a piece of glass that has been shaped to focus light in a par ticular way Lenses are either converging convex or diverging con cave You will work mostly with converging or convex lenses The performance of a lens is determined by 1 Focal length 2 Diameter 3 Absorption of the glass 4 Aberrations spherical and chromatic For the work presented in this book you need to be concerned only with the first two items The ratio of the focal length to the diameter of the lens is the fnumber A lens with a smaller f number is said to have a larger aperture or opening For example if you have an f 1 4 lens and an f 2 lens and the focal lengths are the same the area of the f 1 4 lens will be twice that of the f 2 lens i e 1 1 ee m 1 4 m 22 Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Measurements in Photonics Measurements in Photonics 229
138. ces does not depend on its reverse bias voltage but the time of response does In fact the response time can be adjusted by tuning the reverse bias voltage Bibliography R F Pierret Semiconductor Device Fundamentals Addison Wesley Read ing 1996 Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Electrical Response Time of Diodes Electrical Response Time of Diodes 75 Problems Refer to Chapter 11 laboratory exercise 11 2 In the laboratory you will use lenses consult Chapter 10 Sections 10 1 and 10 2 to control the incident light beam and a lock in amplifier to detect a modulated light beam that is incident on the photodiode The lock in amplifier al lows you to make reliable measurments even when the room lights are on Consult Chapter 10 Sections 10 6 10 7 and 10 8 for more in formation 4 1 You are responsible for the design of a photodetector for an opti cal fiber telecommunications link at the A 1300 nm low loss re gion for optical fiber transmission a You have the choice between silicon or germanium photodi odes Which is the better choice Explain your answer b Your circuit must be fast enough to detect signals up to 4 MHz You are required to use a 50 Q load resistor You have measured the capacitance of the diode and the
139. chro mator with several gratings already installed There is usually a wide selection of gratings with different blaze angles and grooves per mm In most cases you can change gratings at the push of a button In the following Figs 11 3 to 11 5 we show the representative characteristics Replicas made from classically ruled masters measured under near Littrow conditions with 8 between incident and diffracted beams relative to reflectance of aluminum Polarized _L to grooves S Plane ies Polarized to grooves P Plane BLAZE ANGLE 70 a BLAZE WAVELENGTH 3 300 nm 7 60 GROOVES mm S 2 50 wi 40 DIFFRACTION GRATING EFFICIENCY FOR RELATIVE COMPARISON ONLY 10 J Lo 0 1 0 2 03 04 05 06 07 08 09 10 12 14 16 18 20 22 24 26 Wavelength um Figure 11 3 The spectral response of this grating shows a spectacular anomaly near 1200 nm The grating is blazed at 300 nm and is intended for use in the ultraviolet re gion 200 to 400 nm The anomaly at 1200 nm is the result of the grating design That is it is not due to damage or some other mistake Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Experimental Photonics Device Characterization in the Laboratory Experimental Photonics Device
140. citance Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Experimental Photonics Device Characterization in the Laboratory Experimental Photonics Device Characterization in the Laboratory 263 3 5E 23 7 3E 23 am m 25E 23 gee 0 H i H H 0 5 10 15 20 25 30 35 Bias voltage Figure 11 7 1 C versus reverse bias voltage plot for a silicon p n diode The result does not give a straight line as predicted by theory However the curve is well behaved and gives important information about the doping concentration in the diode interior Caite q qLp n e a VBI VA kT a LT 9 e 11 1 It is not easy to measure all the parameters in this equation The good news is that you do not have to know all the parameters The only variable in the equation is the bias voltage This equation says that the capacitance in forward bias depends exponentially on the bias voltage in the same way that the current depends on the voltage That is the capacitance divided by the current should be some constant number You can therefore easily test this model in the laboratory Do your results appear to be consistent with this model 11 6 Characterization of Lasers Objectives In this section we will learn how to 1 Correctly bias and turn on the laser 2 Determine t
141. cle in Fig 7 5 Initially level is fully occupied by electrons Optical excitation pro ceeds by the absorption of a photon step 1 In order to conserve ener gy and momentum the electron that is excited to the conduction band must originate deep in the valence band as shown Then nearly simul taneously the excited electron in the conduction band relaxes to state E and the electron in state E relaxes to state E leaving a hole be hind step 2 Relaxation takes place by emission of phonons and is completed in 10 sec Now there is an electron in state E and a hole in state E creating a population inversion This situation can persist for about 10 sec That is three orders of magnitude longer than the relaxation process Finally recombination occurs across the gap step 3 This transition can be used to make a laser if suitable feedback is provided In a semiconductor material both spontaneous and stimulated emission proceed by this four step process No matter what the en ergy of the optical excitation above the band gap the energy of the Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Lasers Lasers 155 Conduction Band Emission 1 ENERGY Excitation E Valence Band D D MOMENTUM Figure 7 6 A direct band gap semicon
142. contacts The gain bandwidth product is still given by Eq 5 5 The first step in engineering photoconductivity is to separate the trapping sites from the recombination sites by adding a set of shallow trapping levels as shown in Fig 5 9 The transit time for carriers re mains unchanged by this addition The ratio of carriers in the traps to the carriers in the conduction band is maintained by the Boltzmann relation When light is incident on the structure additional mobile carriers in the conduction band are balanced by a proportional in crease in carriers in the traps The traps act as an overflow reservoir allowing the gain to be increased without proportionately diminishing the bandwidth The gain bandwidth product of this configuration can be written as Niraps Pompy 4 5 13 G B new M G B oia where M Napa The gain bandwidth product is increased by the sum of the number of trapped electrons plus the number of empty recombination sites di vided by the number of trapped electrons In general this increase is not very large so the ratio M is close to unity This illustrates that the addition of energy levels in the gap opens the way to store and manip Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Photoconductivity Photoconductivity 87
143. crosecond determine the steady state photo excited carrier concentration 5 4 Illustrate the photoconductive process in photography by using energy level diagrams to describe the three steps shown in Figs 5 10 through 5 12 5 5 Following the example in Eqs 5 18 through 5 23 calculate the hole lifetime as modified by sensitization 5 6 Consider the sensitization of the photoconductor discussed in the text with a level having the property that s 2 10 cm and s 2 10 cm Consider that all other parameters remain the same Calculate the electron lifetime and the hole lifetimes of the sensitized photoconductor Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Source Photonics Essentials Chapter Light Emitting Diodes 6 1 Introduction Light emitting diodes LEDs can be used for displays for signals such as traffic lights or for sending information at very high frequen cies Of course all of these applications could be grouped under the heading of communications LEDs have been made and sold for decades Recent innovative research has led to dramatic improve ments in LED output power and efficiency The situation has evolved to the point that it is now clear that LEDs will be used in some light ing applications by displacing the tungsten light
144. crystal has changed Professor Shelly Errington of the University of California at Santa Cruz drew this original illus tration Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Photoconductivity Photoconductivity 91 ver bromine bond The bonding electron contributed by the silver atom is promoted to the conduction band of the silver bromide crys tal This electron is highly mobile and is attracted to the silver sul fide site which has a lower energy level for electrons see Fig 5 8 The lower energy level acts like the positive terminal of a battery This movement of charge constitutes photoconductivity In less than a microsecond the electron will be trapped on a silver sulfide site which now has a net negative charge The ionized silver atom has a net positive charge and is also mobile but much less so than the electron It will diffuse through the crystal looking for a region with a net negative charge It is attracted to the silver sulfide site The bromine atom stays put because of its larger size and its neutral charge Fig 5 12 In the context of photography the flux of photons from an object that you are trying to image is quite high A silver bromide crystal that is exposed will receive 10 to 108 photons The photoconductivity process does not have
145. cs Device Characterization in the Laboratory 246 Characterizing Photonic Devices in the Laboratory sponding course work There are six activities covering I V character istics lock in detection the monochromator spectrometer light emit ting diodes capacitance and lock in detection The information in this chapter is intended as a guideline because the actual details of the experimental program will depend on the resources that are avail able as well as on the objectives of your instructor 11 1 Current Voltage Characteristics of Photodiodes and LEDs Objectives 1 Using a curve tracer to study the electrical properties of diodes 2 Understanding the effect of light on current voltage characteris tics 3 Measuring the relationship between the light emitted from an LED and the bias voltage and current Background The mathematical model of the current voltage relationship for the photodiode from Chapter 3 gives a good overall account of the behav ior you will encounter in the laboratory There are some exceptions however and you should aim to identify the experiments in which the correspondence between the model and the experiment are satisfacto ry You should also identify the cases in which the correspondence is not so good and suggest how the model could be improved In the fol lowing measurements you will learn to determine the polarity of the diode and to measure the photoresponse in both photocurrent modes Recomm
146. ct to the Terms of Use as given at the website Experimental Photonics Device Characterization in the Laboratory 266 Characterizing Photonic Devices in the Laboratory Table 11 1 R sum of classes for continuously emitting lasers Output Spectral Danger to Skin Fire Class power regime eyes burns hazard I lt 0 005 W IR Visible Minimal No No lt 0 000001W II lt 0 001 W Visible No if less No No than 0 25 sec II a lt 0 5 W UV Visible IR Yes Yes No III b lt 0 5 W UV Visible IR Yes Yes No IV gt 0 5 W UV Visible IR Yes Yes Yes This table gives an approximate idea of the different laser safety classes Class I lasers present limited hazard even if the beam enters the eye However there are not very many of these lasers around Class IV represents lasers that cause immediate injury even from reflections CO lasers used to cut steel are a good example of Class IV devices Most lasers fall into Class III Damage to the eye will happen if the beam of a Class III laser is viewed directly Many types of IR lasers which are invisible fall into this class They are particularly dangerous because there is no natural defensive reflex to help protect you Most semiconductor lasers are Class III a Class II a lasers represent a danger only if viewed directly Class III b lasers can be harmful if a diffuse reflection enters the eye skin burns and can start a fire This laser emits light at 1060 nm which is in the infrared
147. ctates that the laser will want to emit light whose frequency lies as close as possible Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Lasers 166 Photonic Devices to the peak of the gain distribution We can use this approximation to make a practical estimate of the threshold current density tN kinn f ZaxA Jy GONE a a th f f oe A Tp c or tN kipn A Jre a 2 n l Mens 7 23 Ty Ty max All the variables in this expression are easily accessible The width of the recombination region t is controlled during fabrication In a het erostructure laser this is typically about 10 cm and in a quantum well laser about one order of magnitude less or 10 6 cm We esti mated k in Exercise 7 2 The width of the gain spectrum in energy is about 0 02 eV and can be estimated from the emission spectrum in the middle frame of Fig 7 11 The peak of the gain curve occurs at an energy close to the band gap energy The ratio of the luminescence time to the recombination time is always greater than 1 because the recombination time includes both radiative and nonradiative recombi nation modes as you will recall from the discussion of light emitting diode rise time in Chapter 6 However in a reasonably good laser this ratio is close to 1 The equation we de
148. cteristic in a p n junction The results show that the photocurrent varies linearly with the flux of photons and is independent of the photon energy as long as the pho ton energy exceeds the band gap The photovoltage generated in open circuit operation does not vary linearly with the flux of photons Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Photodiodes Photodiodes 57 The performance of photodiodes is determined by four properties quantum efficiency range of spectral sensitivity response time and noise We have considered the first two properties in this chapter The response time of a photodiode will be determined in most applications by the product of the photodiode capacitance and the series resistance of the measuring circuit and is discussed next in Chapter 4 The effect of detector properties on system noise can be related to the dark cur rent and the capacitance See the Bibliography of this chapter for a treatment of the noise generated in photodetection The quantum efficiency of a photodiode with a properly designed structure is close to 100 Reflections due to the difference in index of refraction between the semiconductor and air lead to a reduction of 25 in the quantum efficiency The use of an antireflection coating can entirely eliminate this
149. ctive region only 2 to 3 nm thick a 100 fold reduction over that for the laser shown in Fig 7 11 Akasaki took a third crucial step he encouraged others to work on these developments in GaN This was not an easy idea to sell because Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Lasers Lasers 169 many people believed that GaN was a hopeless material and many more were interested in another semiconductor ZnSe in which p n junctions could be made easily and which emits blue green light Akasaki s message reached the ears of Shuji Nakamura a student at Tokushima University on Shikoku Island Mr Nakamura was a stu dent of Prof Sakai one of Akasaki s students Professor Sakai put Nakamura in touch with Prof Akasaki and thus he began to work on GaN too Nakamura successfully made GaN blue LEDs for his mas ter s thesis Nakamura got a job at Nichia Chemical Company Nichia is a big manufacturer of phosphors for color TV and so they have a lot of ex perience in luminescent materials There he successfully convinced his management to invest significant resources in GaN materials preparation and device fabrication to make optoelectronic diodes In 1994 Nichia introduced a commercial blue LED based on GaN Three years later Nakamura demonstrated a blue lase
150. d ing more information means going to higher frequencies Using electrons to accomplish this is a losing battle Transmission of optical ly modulated signals does not have this problem The introduction of optical fiber communications changed the rules see Fig 1 1 This is what we call a killer technology Since 1980 telephone companies around the world have been mining copper as they pull thousands of kilometers of copper cable out of the ground in order to replace it with optical fiber Two components of optical fibers that distinguish this technology from the other options are the ability to carry very high bandwidth communications and the ability to confine the communication in a fiber cable so that lines can be installed in buildings or passed under the ocean This latter feature is what distinguishes optical fiber communi cations from radio communications A good comparison can be made by Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Optical Fibers and Optical Fiber Amplifiers 194 Advanced Topics considering the Teledesic satellite communications system This com pany proposed to launch satellites several hundred in all in low earth orbit Telephone conversations could then be relayed to any point on the globe The capacity of satellite network was l
151. d Photons Electrons and Photons 21 S ars A N 988 vs THESES PR SENT ES A LA FACULT DES SCIENCES DE L UNIVERSIT DE PARIS POUR OBTENIR LE GRADE DE DOCTEUR S SCIENCES PHYSIQUES PAR Louis de BROGLIE 4e THESE RECHERCHES SUR LA TH ORIE DES QUANTA 20 THESE Pxorosrrions DONN ES PAR LA Facute Soutenues PA ovembre 1924 devant la Commission d examen MM J PERRIN Pr sideni CARTAN 0 ESOR MAUGUIN Esaminaleurs aeS fix Oy poy PEL a Paul LANGEVIN N N PARIS MASSON ET C DITEURS LIBRAIRES DE L ACADEMIB DE M DECINE 420 BOULEVARD SAINT GERMAIN DSSS Figure 2 5 Cover page for the doctoral thesis of Louis de Broglie Each doctoral candi date had to write on two subjects one chosen by the candidate and one assigned The ti tle of his chosen subject is Research on the Theory of Quanta Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Electrons and Photons 22 Introductory Concepts un des rayons de son onde de phase celle ci doit courir le long de la trajectoire avec une fr quence constante puisque P nergie totale est constante et une vitesse variable dont nous avons appris a calculer Ja valeur La propagation est donc analogue c
152. d majority carriers in the same spatial region The balance means that the generation rate and recombination rates must be equal The current in the diode is Ang x 0 Npole9aT 1 Aprl 0 Pno e4 1 Figure 6 1 Energy distance diagram of a p n junction in forward bias The applied voltage V4 induces excess concentrations of holes and electrons and also reduces the spatial separation between holes and electrons The steady state is maintained by re combination of electrons and holes in proportion to the excess carrier densities Direct electron hole recombination causes light emission Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Light Emitting Diodes Light Emitting Diodes 105 proportional to A n p as shown in Chapter 3 In order to main tain a steady state value of the minority carrier concentration the re combination rate is also proportional to A n p and thus propor tional to the current The excess carrier density is localized near the p n junction and falls off exponentially away from the junction An x An 0 e e where L VD 7 and r the recombination time Since light emission is caused by recombination the light intensity is proportional to the radiative recombination rate The current in the diode is
153. damental materials characteristics Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Light Emitting Diodes Light Emitting Diodes 113 The external efficiency of the LED which is based on the actual light that gets emitted can be optimized by placing the light emission region close to the physical surface The minority carrier injection effi ciency for electrons which we will call y in order to distinguish it from the quantum efficiency is given in Eq 6 9 Dn Es X Danp DiPn Ey Da Using the Einstein relation D u kT q and n p n UhNnLe y e 1 6 9 x MeP pLp In II V direct gap semiconductors L and L are similar and it is always the case that ue gt up The only design parameter available to the device engineer is the majority carrier doping ratio It can be seen in Eq 6 9 that the injection efficiency is improved by heavy p type doping i e Pp gt n The majority of the direct recombination leading to light emission will take place in the heavily doped p lay er If we design the LED so that this layer is also the emitting sur face with the n layer confined to the diode interior we will have op timized the external emission efficiency by minimizing absorption LEDs are typically produced on a heavily doped n type substrate in
154. de eee Uncoated photodiode Responsivity amps watt Increasing wavelength gt Figure 3 10 Quantum efficiency can be improved by reducing or eliminating reflec tions at the wavelength of interest This will also result in increasing the reflection losses at other wavelengths emissivity surface This means that the reflection coefficient is rela tively elevated The emissivity of the surface can be raised by roughen ing the surface so that it looks more matte eventually appearing like black velvet Such a surface has very low reflectance If the roughening is done carefully the minority carriers that are generated when the light is absorbed will be collected at the junction creating a photocur rent Achieving such surface roughening for a photodetector is not a simple task The inverse property the case of a light emitting diode is easier to implement and is discussed in Chapter 6 3 5 Summary A photon can be absorbed by a semiconductor if the energy of the pho ton exceeds the band gap energy The absorption of a photon creates an electron and a hole and increases the nonequilibrium concentra tion of minority carriers If this absorption takes place in a p n junc tion structure the minority carriers will diffuse to the junction creat ing a photocurrent and a photovoltage at the contacts The photocurrent can be calculated using the same approch as that used to calculate the current voltage chara
155. de having 101 cm carriers on the lightly doped side W is about 0 5 pm at 0 applied bias Photocurrent in a photodiode is maintained by the motion of minor ity carriers First the minority carriers must diffuse 1 and 3 in Fig 4 1 from the point of absorption to the depletion region and then they are transported by drift across the depletion region where they become majority carriers 2 and 4 The external circuit reacts to Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Electrical Response Time of Diodes Electrical Response Time of Diodes 63 Figure 4 1 A schematic diagram showing the motion of minority carriers created by photoabsorption in a diode Minority carriers will diffuse to the junction where they are collected and transformed into majority carriers L is the diffusion length for electrons and L is the diffusion length for holes In the low injection limit the concentration of majority carriers is constant over distance Hence motion of majority carriers by diffu sion is negligible these new carriers by supplying the appropriate carriers at the con tacts in order to maintain charge neutrality 4 3 Diffusion Time The time required for minority carriers to diffuse to the junction de pends on the minority carrier diffusion length and th
156. de required for electrical contact This region can easily be reduced in thickness to 0 5 um of p type material In this case the diffusion response time is shorter still 10 picoseconds Note that the diffusion time depends on the square of the diffusion length The diffusion length is the average distance a minority carrier can move before it recombines with a majority carrier In a direct band gap material like InGaAs this distance is a few microns For an indi rect band gap material this distance is longer typically by a factor of 100 The diffusion length is longer because recombination also involves the participation of phonons Note that increasing L by 100 means that Tis now 10 000 times longer and the response time required to collect all the diffusing photo generated carriers is closer to the microsecond regime than the picosecond regime Example 4 1 A silicon photodiode produced on an n type substrate is uniformly il luminated The diffusion length for minority electrons is 10 2 cm The diffusion length for holes is 5 x 10 cm The mobility of electrons is 1000 cm V sec whereas the mobility of holes is 500 cm V sec Estimate the diffusion limited response time The pn junction would be formed by diffusion of p dopants into the n type substrate This depth is typically 1 um or less Since the thick ness of the p region is much less than a diffusion length we can neg lect the contribution of diffusing minority carri
157. ditions we can write ANo Bafra AN ngt TE 8 13 where the remaining terms are small by comparison and will be neg lected This equation is solved for AN AN l 2 AN 8 14 Baang dt ot Toh i The equation for the carrier density is dN J N a a TET 8 15 By substituting N n AN and N n AN this equation becomes d gos B21 fKr AN 4 T 8 16 Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Direct Modulation of Laser Diodes Direct Modulation of Laser Diodes 187 Now insert the expression for AN in this equation dn 1 dn 1 1 1 dn 1 dt EA oo aa a et Baf Kn AN4 d 1d eae 1 geet nde ea aK ngAN T T4 0 8 17 This is a second order differential equation that describes a damped oscillation with an angular frequency R V Boif aK mng 8 18 and a decay time of 27 The solution will be of the form AN t e r sin wgt 8 19 We have obtained some results that we would like to use to direct modulation of semiconductor lasers in communications applications 1 The relaxation oscillation dies out in a time 27 This would put a limit on the bit rate which must be low enough to allow the optical output power to come to steady state A typical value for the free carrier recombination time in GaAs
158. ds quite ob viously on its size Thus to make the film more sensitive to light you need only make the grain size larger The resolution of the image also depends on the grain size As the grain size increases the resolution of the image decreases Thus there is a direct trade off between film sensitivity or speed and the resolu tion or graininess of the image An important part of the film manu Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Photoconductivity 88 Photonic Devices _ Support 0000000000000000 SA Y Photosensitive SeN EF AA Grains ee Figure 5 10 A schematic diagram of the structure of photographic film Grains of silver bromide with a well controlled size are dispersed in a gelatin solution and coated on a transparent backing During exposure and development each grain location becomes either all black or all transparent The resolution of the film is determined by the grain size during manufacture facturing process is maintaining control over the grain size in the gel atin coating The photoconductive effect takes place entirely within a single grain During exposure and development there is no communication between the grains in the film of either photons or electrons The grain is typically a crystal of silver bromide an ionically
159. ductor is a good example of a four level medium for laser action There is a significant difference in the pumping scheme because level E is initially fully occupied by electrons However as soon as a photon is absorbed electrons leave this level to fill the hole in the valence band that is created by the exci tation photons emitted during recombination is always close to the band gap energy Optical gain only occurs in this range of energies which we can denote by a distribution function g f called the optical gain spectrum This is always the situation because the lifetime for optical recombination is orders of magnitude longer than the time for phonon emission Typical values for the energy width of the gain spectrum lie in the range of 0 01 to 0 02 eV In order to take account of this feature we will modify the equation for the gain coefficient Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Lasers 156 Photonic Devices h k Np NP BP 7 11 An optically excited semiconductor can be used to make a laser but the really interesting application of semiconductors is the use electrical current to turn the laser on You know that current injection into a p n junction diode creates light In order to turn this light into laser light we need gain and to
160. e McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Photoconductivity Photoconductivity 97 has changed this situation Recombination takes place when a hole meets an electron on a recombination site Sensitization has reduced the hole occupancy of the type 1 sites by six orders of magnitude in this example The main result is that all recombination through the type 1 centers has been cut off Recombination now takes place almost entirely on the type 2 sites where there are both electron and hole sites available Our objective is to calculate the electron lifetime for the sensitized material Since generation equals recombination in the steady state we can write n f as N Pr1VSn1 Pr2VSn2 1 1 ia PriVSni ProUSno 10 N 107 10715 Nna 107 10720 1 1 1018 102 5 23 Na 10 10 8 W TO see ae In analyzing Eq 5 3 it can be seen that the longer lifetime for elec trons reflects the recombination properties of the type 2 centers The electron lifetime has been increased by five orders of magnitude from 10 77 seconds to 107 seconds and the sensitivity of the photoconductor is increased by this amount The calculation of the hole lifetime for the sensitized material is left as an exercise at the end of the chapter This example shows that it is possible to increase the lifetime of one of the carriers by addition of an appropriate impurity or vacancy
161. e T Ac Source Photonics Essentials Chapter 11 Experimental Photonics Device Characterization in the Laboratory Introduction Experimental measurement is an important key to understanding photonic devices Although there are many kinds of devices there are relatively few measurements and the laboratory exercises proposed in this chapter will help you to understand the mathematical presen tations in the previous chapters their accuracy and their limitations The aim of this work is to help you acquire the basic experimental skills you will need for further investigations There are four important objectives of the laboratory exercises 1 Safety Always maintain safe working conditions in the laboratory 2 Technique Develop techniques for obtaining reproducible data in an efficient manner 3 Record keeping Learn to use a lab notebook as a tool to help you and your supervisor understand what works and what does not work in the laboratory 4 Relationship to theory Learn to apply judgment to evaluate the expectations of theory The exercises can be started after the first week and are most effec tive if the laboratory work is assigned in the week following the corre 245 Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Experimental Photoni
162. e amplifier r RC 4 4 The n and p regions of a p n junction diode form a capacitor Capac itance is defined as A C 0m 4 5 Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Electrical Response Time of Diodes Electrical Response Time of Diodes 67 where W the width of the region separating the charge is easily cal culated by using Poisson s equation zem Nat Nn i W gt N N Vz V 4 6 The relative dielectric constant of common semiconductors is in the range of 10 138 and A is the area of the diode The capacitance is ob tained by substitution of Eq 4 5 into Eq 4 4 In nearly all diodes the concentration of donors Np is orders of magnitude different from the concentration of acceptors N4 For example if N is 1019 cm Np might typically be 1016 cm 3 Assuming that N gt Np we can simplify the expression for the capacitance further Pas eeoQNp Vz V pumas Ue sah 2 C amp bee Bi A XVa V 4 7 qNp In Eqs 4 6 and 4 7 Vp is the built in voltage of the diode and Np is the impurity concentration on the less heavily doped side of the junc tion This relationship shows that the capacitance will be larger if the im purity concentration on the less heavily doped side of the junction Np is increas
163. e band Under most conditions Boltzmann statistics can be used as we have done in Eqs 2 1 2 5 to calculate the number of states in the conduc tion band that are occupied by electrons or the number of empty sites in the valence band These are called holes 2 7 Summary The behavior of electrons in semiconductors at equilibrium is ruled by the Boltzmann distribution under almost all circumstances The Boltz mann distribution says that the probability of finding an electron with energy E decreases exponentially as E increases The three funda mental energy excitations in semiconductors are electrons photons and phonons We treat the indivisible units of these excitations as par ticles Each particle has a wavelength that is proportional to the recip rocal of its momentum Each particle obeys the two basic laws of con servation of energy and momentum These two laws are the foundation that determines all the possibilities that photonics has to offer The map of allowed electron states is called a band structure For semiconductors like GaAs and Si the electron states are generally filled up to and including the valence band states or the bonding states This is followed by an energy gap that results because there is an energy difference between the bonding and the antibonding or conduction band states If the highest energy valence band state oc curs at the same momentum as the lowest energy conduction band state the material is ca
164. e circuit that is proportional to the number of photons detected So the larger the resistance the larger the volt age generated across the resistor In most cases 10 kQ to 100 KQ is a good choice for Rz 10 10 Curve Tracer The curve tracer allows you to get a current voltage trace of your de vices This will enable you to determine the cathode and anode of a photodiode light emitting diode or laser This is important because you can burn out your laser instantly by putting it into substantial re verse bias Photodiode shown here in reverse bias Load Resistor Figure 10 12 Photodiode detector circuit Photocurrent mode Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Measurements in Photonics Measurements in Photonics 241 Take some time to experiment with the curve tracer using a resis tor instead of your device When you turn on the tracer note that the current scale is 2 A and the voltage scale is 2 V per division These values are very large You should adjust the curve tracer to the appro priate scales for both current and voltage before applying any voltage to the device to be tested Typical values of voltage are 5 V to 2 V Typical values of current are 10 pA to 100 mA in forward bias and only 10 pA in reverse bias Be aware at all ti
165. e diffusion coeffi cient L Te D and Li Th D 4 1 for electrons and holes respectively The diffusion coefficient can be calculated from the carrier mobility using the Einstein relation g RT From these equations it is easy to see that the time to diffuse a giv en distance will be shorter for the minority carrier with the higher mo D 4 2 Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Electrical Response Time of Diodes 64 Photonic Devices bility For example in a photodiode made from InGaAs E 0 75 eV Az 1 6 um the electron mobility is about 10 000 cm V sec whereas the hole mobility is only 500 cm V sec Therefore D 250 and D 12 at room temperature The minority carrier diffusion length for elec trons and holes is similar L L 4 wm If the photodiode is designed so that most of the light is incident on and absorbed on the n side then the characteristic diffusion time would be about 20 nanoseconds If we design the diode so that most of the light is absorbed on the p side then the diffusion time is much shorter 600 picoseconds In a well designed photodiode made of direct band gap material most of the light can be absorbed in the depletion region so that diffusion operates only on the uppermost part of the dio
166. e electrons and photons do not intersect That is there is no point on the curves where the energy and momentum of an electron are equal to the energy and momentum of a photon This Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Electrons and Photons Electrons and Photons 17 photon N electron MOMENTUM Figure 2 4 The energy of a photon is linearly proportional to its momentum When plotted on the same graph as that for an electron the energy momentum relationship for a photon looks like a vertical line means that a free electron and a photon cannot interact with each other However in a solid material the situation is different Elec trons and photons can interact because the host material can supply the momentum that is missing in the case of a free electron and a pho ton This is discussed in more detail in Section 2 7 Imagine a vapor of single atoms of the same element Before atomic bonding occurs the constituent atoms are free to wander around They are in an antibonding state We could take silicon as an exam ple When two such free silicon atoms meet they may bond together They will do so because the bonding state is at a lower energy than what existed previously The valence electrons have thus fallen into some kind of potent
167. e falls off exponentially with increasing energy Fresnel s law of reflection and refraction at the interface between two materials in this case between a semiconductor and air shows that only 2 of the total emitted light can escape through one surface of a diode structure that has smooth faces However semiconductor wafers with smooth faces are also low emissivity structures Two structures were discussed that have been shown to improve the exter nal quantum efficiency One structure is a lens The other structure increases the emissivity of the surface Modulation bandwidth is determined by limitations of the external circuit and the internal response of the LED recombination process In most cases the bandwidth of an LED will be determined by ex ternal factors namely the series resistance of the LED and its ca pacitance in forward bias The bandwidth due to the diode materials properties depends principally on the carrier concentration There are two ways to increase this concentration high injection or high doping The easiest way to determine which situation holds is to measure the rise time or fall time of the LED as a function of the drive current If the rise time is independent of the drive current then the diode is in the high doping regime If the rise time gets shorter as the drive current increases then the diode is in the high injection regime Downloaded from Digital Engineering Library McGraw Hill www digitalengin
168. e figure Sup pose that the density of the recombination sites is N We can now define some parameters that we will need for the discussion of sensiti zation 1 n the density of centers occupied by electrons 2 p the density of centers unoccupied by electrons When an electron recombines on an unoccupied site p the site changes to an occupied site and counts as part of n At all times n Pr N The chance that an electron recombines on an unoccupied site is measured by the cross section of the site s which has units of cm The capture cross section for holes by a site occupied by an electron is Sp In the steady state n ft lt n P f Pr 5 15 A charge carrier moving with a velocity v will travel a distance ut on the average before it recombines The product of the capture cross section with this distance gives the effective volume of the recombina tion center as shown in Fig 5 15 The density of unoccupied centers for electrons p is just the in verse of this volume Thus 1 volume of a center 7 vs 5 16 and n ft f 5 17 D VS To appreciate what these equations mean we give some typical val ues for these parameters in Table 5 1 for electrons in silicon Since recombination centers promote recombination their presence in general shortens the carrier lifetime It is always true that increas Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrar
169. e in particular neodymium Nd was developed into a high powered laser source at 1060 nm and is still a workhorse of the laser industry Laser engi neers for the next twenty years focussed on making sources of light with higher output power When the room temperature semiconduc tor laser was developed in 1970 people began to think about smaller devices that could be pumped electrically instead of by a flashlamp With this background Julian Stone working in my department Bell Labs demonstrated an optical fiber laser based on Nd doping of a glass fiber in 1973 Shortly afterward he was able to show that a GaAs laser diode could be used to pump the fiber laser His discovery was treated as a big nonevent because optically pumped lasers were old technology everyone else was concentrating on new compact semiconductor laser diode sources As we shall see shortly his inven tion was key to the commercial success of optical communications About 15 years later in 1987 research temas in the U K and at Bell Labs in the U S rediscovered the fiber based optical amplifier They were using erbium doped glass because Snitzer had shown that erbium was the rare earth element to use if you were interested in Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Optical Fibers and Optic
170. e is subject to the Terms of Use as given at the website Light Emitting Diodes Light Emitting Diodes 137 are currently being made from both semiconductor p n diodes and polymer structures The light emission principle for LEDs is the re combination of excess concentrations of electrons and holes Semicon ductor LEDs and polymer LEDs differ primarily in the physics of how the excess carrier concentrations are created Measurement and device characterization methods of LEDs are largely independent of the materials used to fabricate the devices The principal performance specifications are spectral response effi ciency and modulation bandwidth Brightness which we have not discussed in this chapter is a measure of the light intensity gener ated per unit area High brightness is not particularly useful for dis play applications A very high brightness LED may begin to resem ble a point source The light from such an LED could be coupled more efficiently into an optical fiber with core dimensions compara ble to the wavelength of light such as a single mode fiber The light intensity emitted from an LED is peaked at an energy that is closely related to the band gap of the material The spectral shape of the emission is affected at higher energies through self absorption by the emitting material and secondarily through Boltz mann statistics that remind us that the number of higher energy elec trons and holes that are available to recombin
171. e only possible because of the Er doped fiber amplifier Increasing the modulation rate of lasers has proved to be difficult because of chirp which we discussed in Chapter 8 The optical wavelength of the emission changes in time when the laser is switched on Since this feature is fundamental to laser operation modulation is now being achieved by an external waveguide modulator that is independent from the laser a kind of very fast chopper The emphasis in transmission laser development is no longer modulation speed but on spectral purity and output power This brief history illustrates that the technology in this field has not developed in a straight line path over the years Optical ampli fiers were developed before people had any ideas about optical fiber communications GaAs lasers have gone in and out of style Electronic signal regeneration has fallen out of favor because of optical amplifi cation However we should all keep our eyes on the silicon VLSI in dustry which is starting to take optical fiber communications serious ly The power of VLSI is legendary and it is not hard to imagine new VLSI chips with some optical functionality hybridized with advanced fast signal processing circuits Such developments may reintroduce electronic signal processing as the technology of choice for optical Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All r
172. e short lifetime of the excited state of electrons in a SOA increas es the level of ASE noise as presented above On the other hand there is an advantage associated with this situation and that is that the gain in an SOA can be switched on and off rapidly This can be done electrically by modulating the electrical pumping current However it can also be accomplished optically by coupling an additional optical beam into the SOA at a different wavelength from the signal and thereby reducing the gain by depleting the excited state carrier densi ty This kind of high speed modulation of the gain is a way to modu late one light beam by another The SOA has a significant advantage over the Er doped fiber amplifier because of this functionality It is an important element in the implementation of all optical signal process ing such as switching wavelength conversion and all optical signal regeneration Because of its small size SOA chips are starting to be incorporated into other optical devices such as filters and modulators so that there is no net loss in signal power Of course there will al ways be a degradation in the SNR that accompanies the use of a SOA as an amplifier Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Optical Fibers and Optical Fiber Amplifiers 220
173. e term C A 1 versus bias voltage is shown A straight line dependence is predicted by theo ry The intercept V Vg C A 0 gives the built in voltage of the diode Here the measurement determines Vg 0 76 V The slope of the line gives the net majority car rier concentration on the more lightly doped side of the diode Np 5 x 1016 cm Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Electrical Response Time of Diodes 70 Photonic Devices 3 0 ji 6 g i F j T T F T T T T F T o ay In As InP HETEROPHOTODIODE J T 295K Ng 1 3 x10 cm5 y 20H E Qa E x O l a o L A i L 4 D T 10 Q Vp Bias voltage Figure 4 5 Analysis of the capacitance voltage measurement C A versus bias volt age is shown for a GalnAs photodiode The intercept V Vg C A 0 gives a built in voltage of 0 80 V The free carrier concentration is Np 1 3 x 10 em 4 6 Capacitance of Diodes in Forward Bias The expression for the capacitance given in Eq 4 6 is valid in general for applied voltages less than 0 volts In forward bias the capacitance does not become infinite at V Vz as Eq 4 6 suggests The measured capacitance does however continue to increase in forward bias in a reasonable fashion even for forward biases
174. ecade ago it was felt that modulation rates above 2 GHz would be quite difficult to achieve based on the theoretical understanding of laser dynamics At the time of this writing the state of the art modu lation bandwidth exceeds 10 GHz Existing understanding is based entirely on the properties of the materials used to make these lasers Yet knowledge about the electronic properties of these materials has not changed during this time Clearly there is room for improvement in the theory and perhaps one of you will bring this contribution to the field soon Like the case of the LED laser modulation properties are based on the change in the carrier concentration that is caused by a change in the drive current An increase in the carrier concentration will cause an increase in the photon density However in the case of the laser this increase in the photon density will cause a decrease in the free carrier density by stimulating recombination of excess carriers The most significant difference between the transient properties of a laser and the properties of the LED is directly related to this coupling be tween the carrier density and the photon density that is fundamental to laser action Our approach in this chapter will be to examine this coupled inter action The coupled equations that describe the electron density and the photon density can be solved only numerically However we will be able to extract the delay time for light emission and
175. ed Since Np is fixed at the moment of fabrication there is nothing you can do about this parameter except to measure it and look for a photodiode from another source with a lower value for Np The ca pacitance also depends directly on the area That is size matters The capacitance varies inversely with the square root of the bias voltage and you can lower the capacitance significantly by increasing the bias voltage The reduction of capacitance leads to a corresponding reduc tion in the extrinsic response time Furthermore this is the only post fabrication means of changing the response time of a photodiode Example 4 2 Find the capacitance of a silicon photodiode at 0 bias The diode is a square chip 1 mm x 1 mm and has a doping concentration of 1 x 1016 cm _ Esq Np C A AVV VaV farads C 0 1 x 0em 9 5 8 85 x 10 4 F em 1 6 x 107 1 C 10 cm 3 2 0 8 0 volts C 289 picofarads Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Electrical Response Time of Diodes 68 Photonic Devices In the laboratory you can easily measure the capacitance versus bias voltage The capacitance will decrease with increasing reverse bias The capacitance decreases because the width of the depletion re gion increases with increasing re
176. ed in terms of the photon wavelength This is because almost all spectrome ters continue to be calibrated in terms of optical wavelength rather than photon energy The origin of this difference is both historical and functional being related to the wavelength interference that is the basis for the operation of the diffraction grating inside the spectrome ter Optical absorption however is not a phenomenon related to wave length It has its physical basis in the quantum nature of light and conservation of energy A single photon must have enough energy to break a single bond Two photons each having three quarters the needed energy will not suffice even though the combined energy of these two photons would exceed the bond energy Fortunately there is a simple relationship between the energy of a photon and its wave length in air _h 2m _ he S S 3 20 E photon 7 ho And as we showed in Chapter 1 the relationship between the photon energy in eV and the wavelength of the photon in air is expressed as 1 24 eV 1 24 um or A gt 3 21 Erao SF phot A microns E photon e V In the ideal model we can plot the spectral response as a function of energy or wavelength as shown in Fig 3 6 The spectral response function for real photodiodes is not too different from this model as shown in Fig 3 7 Photons that are incident on the photodiode continue to propagate into the diode until they are absorbed The number of photons
177. ed operation Part 2 After the laser has reached threshold Tg lt t lt To where To is the bit period Now the laser is on The drive current density is constant and the equations for the photon and carrier densities are Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Direct Modulation of Laser Diodes Direct Modulation of Laser Diodes 185 dN N a BoiN 4 f Kin BasontN As 8 9 To dN J N de 7 gd PNoy 8 10 As we have already noted these equations are coupled by the stimu lated optical emission term that appears in both equations However this term appears with the opposite sign and so an increase in the photon density causes a decrease in the carrier density which leads to a decrease in the photon density which leads to an increase in the carrier density The response of the system is not immediate There is a delay that is governed by the recombination time 7 between the stimulus and the response We can imagine the process in the dia gram shown in Fig 3 The resulting effect of bringing the laser above Increasing photon density decreasing increasing carrier carrier density density decreasing photon density Figure 8 3 Schematic diagram of the relaxation oscillation cycle in a semiconductor laser Downloaded from
178. een made possible only because of the vast improvements in speed and capacity of fiber optic telecommunications At the heart of this revolution are the semiconductor laser fast light modulators photodiodes and communications grade optical fiber From this text you can learn what makes these key devices work and how they perform Laboratory measurements are emphasized for an important reason there are many different kinds of photonic de vices but only a few basic characterization measurements When you learn these laboratory techniques you can measure and understand almost any kind of device The experiments are based on components that you can find easily in any electronics store This means that the laboratory fees should be reasonable and that you can quickly find a replacement device when you need one This course is an excellent preparation for subsequent work in the Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Introduction Introduction 5 physics of semiconductor devices the design of biomedical instru mentation optical fiber telecommunications sensors and micro opto electro mechanical systems MOEMS You may also want to consider a summer internship as a test and measurement engineer with one of the growing number of start up companies in the opto
179. eeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Light Emitting Diodes 138 Photonic Devices References A A Bergh and P J Dean Light Emitting Diodes Clarendon Press Oxford 1976 This book gives a good picture of light emitting diodes according to old wisdom and old technology The book is strong on the physics of op tical properties and electronic transport but short on concepts of device engineering that have led to dramatic advances in LED performance The next three texts each give a good short tutorial on LED operation but the old preconceptions about limits to LED efficiency are still present R F Pierret Semiconductor Device Fundamentals Addison Wesley Read ing 1996 J Wilson and J Hawkes Optoelectronics 3rd Edition Prentice Hall Europe London 1998 P K Bhattacharya Semiconductor Optoelectronic Devices Prentice Hall En glewood Cliffs 1994 Exciting research articles I Schnitzer E Yablonovitch C Caneau T J Gmitter and A Scherer 30 External Quantum Efficiency from Surface Textured Thin Film Light Emitting Diodes Applied Physics Letters 63 2174 2176 1993 P K H Ho D S Thomas R H Friend and N Tessler All polymer Opto electronic Devices Science 285 5425 233 236 1999 Polymer semicon ductors will replace inorganic crystalline semiconductors in
180. effect but only in a narrow wavelength range The spectral sensitivity covers the entire spectral range having a wavelength shorter than the optical wavelength corresponding to the band gap energy Bibliography C R Wie The Semiconductor Applet Service hitp jas eng buffalo edu ap plets A truly outstanding set of applets on semiconductor physics and de vices has been written by Prof Chu R Wie of the University of Buffalo In addition at this URL you will find links to many other related Web sites for semiconductor device applets Bookmark this now P K Bhattacharya Semiconductor Optoelectronic Devices Prentice Hall En glewood Cliffs 1994 G W Neudeck The PN Junction Diode 2nd ed Addison Wesley Reading 1989 A Rose Concepts in Photoconductivity and Allied Problems Wiley Inter science New York 1963 This short book of 168 pages may be the best you will ever find on photodetection I emphasize find because it has been out of print for years The cover is an unimposing mousey beige Keep your eyes peeled for this at garage sales or in the discard pile of retiring profes sors If you find it buy it Price should be no object W T Tsang Ed Lightwave Communications Technology Photodetectors Semiconductors and Semimetals Vol 22D Academic Press Orlando 1985 A Yariv Optical Electronics in Modern Communications Oxford University Press New York 1997 Downloaded from Digital Engineering Lib
181. electronics industry The largest market for photonic devices today is the telecommuni cations industry Historically this industry has been growing at about 5 per year The development of the optical fiber and the inter net have changed all that see Fig 1 1 An optical fiber is generally a thin strand of glass that is used to carry a beam of light Once the light is introduced in the fiber by us ing a lens for example it can only escape by propagating to the other end of the fiber The light beam is prevented from leaking out of the sidewalls by an effect called total internal reflection Thus the fiber acts as a guide for photons When engineers showed that sending high speed communications by light waves was far superior to send ing communications by electricity growth rates in the industry 1014 Multi channel 5E WDM OPTICAL 1010 FIBER SYSTEMS Single channel i ETDM m Communication Satellites nir e Advanced 104 coaxial and microwave systems Early coaxial cable links Carrier Telephony first used 12 voice 10 e channels on one wire pair T Telephone lines first constructed 2 l l 1880 1900 1920 1940 1960 1980 2000 2020 2040 Year 102 Relative Information Capacity bit s Figure 1 1 The growth of telecommunications systems got a big jolt with the deployment of optical fibers in 1980 creating the first optical fiber telecommunications networks
182. elle dune onde liquide dans un canal ferm sur lui m me et de profondeur variable Il est physi quement vident que pour avoir un r gime stable la lon gueur du canal doit tre en r sonance avec l onde autre ment dit les portions d onde qui se suivent une distance gale un multiple entier de la longueur du canal et qui se trouvent par suite au m me point de celui ci doivent tre en phase La condition de r sonance est nisi la lon gueur d onde est constante et gt dl n entier dans le cas g n ral Figure 2 6 The proposition by de Broglie in his thesis that the stable orbits of electrons in atoms are like waves of water in a closed circular tank Translation of the boxed portion The propagation of the electron is therefore analogous to that of a wave of liquid in a tank that forms a closed path In order to have a stable condition for the wave it is physi cally evident that the length of the tank must be in resonance with the wave In other words the portions of the wave that are located a full length of the tank behind preceding portion of the wave must be in phase with the preceding portion The condition for reso nance is n tion for the existence of a standing wave is that the length of the cir cuit be an integral number of wavelengths of the standing wave There are only certain fixed lengths of the tank that can support standing waves The possible tank lengths are g
183. ended Equipment 1 Silicon photodiode 2 Germanium photodiode or GaInAs photodiode 3 A device socket 4 Curve tracer Procedure a Build a Mount for the Photodiode A photodiode is typically packaged with two pliable metal leads These are often long enough so that alli gator clips can be attached directly to the diode This procedure al though tempting usually results in the leads being broken off where they enter the photodiode package Thus the first step consists of Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Experimental Photonics Device Characterization in the Laboratory Experimental Photonics Device Characterization in the Laboratory 247 building a mount for the diode A transistor socket can be soldered onto one end of a BNC cable in a few minutes The cable consists of two conductors one for each terminal of the diode The diode can then be held in place for measurements by applying a clamp to the cable not the device b I V Measurements Using the Curve Tracer The curve tracer is the most reliable instrument you can use to determine which lead con nects to the p side of the diode This instrument comes in many differ ent varieties A quick reading of the instruction manual will save both time and burned out diodes The initial conditions
184. epend on the bias volt age Photoconductive gain is achieved at the expense of bandwidth Photoconductors and photodiodes of the same material can be com pared under unity gain conditions and their performance is quite similar The response of a photoconductor can be engineered Using a single material for example silicon it is possible to engineer the spectral re sponse from the visible to the far infrared The spectral response is tuned by the introduction of specific impurities having a well defined level with an energy in the band gap that corresponds to the spectral region of interest The sensitivity and the bandwidth can be engineered through both the geometry of the electrodes and the introduction of specific levels The lifetime can be engineered to match the bandwidth of the events one is detecting and the resulting gain acts like a built in amplifier This feature has made photoconductive detectors the element of Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Photoconductivity Photoconductivity 99 choice in television recording The vidicon tube is a photoconductive detector that has been designed using a variety of photoconducting materials including silicon lead oxide and antimony In conclusion photoconductors are not better than photodiode
185. epend only on N They have been grouped to gether with an effective recombination time We assume that NP gt n and N gt np dN J N a S 8 3 gain due to loss due to loss due to all other electrical pumping stimulated emission recombination On the other hand the equation for the photon density can be writ ten as daN N a B N g f Kn Boron N An 8 4 Th gain due to loss due to gain due to fraction stimulated emission emission from cavity of spontaneous and absorption emission that falls in the laser mode These equations are complicated to solve and we will not attempt a comprehensive solution Instead we will look at some of the features that appear in transient behavior Part 1 Before the laser reaches threshold 0 lt t lt Tg First let us suppose that the laser is off This means that there may be some spontaneous emission coming out of the laser but that the stimulated term is turned off In this state the current density is J and the carrier density is N Then we will turn the laser on by step ping the current to J which is well above the threshold current At some time T4 after the current is stepped the laser will turn on However before this time the stimulated emission is zero even though the current is already at Jz Setting the stimulated emission term 0 in Eq 8 3 gives Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyrigh
186. er The chopper is placed at the exit slit so that only light passing through the monochromator is modulated Both the detector and the tungsten light source are placed in mounts that allow you to adjust their position in a controlled way the scan at 400 nm the wavelength output limit of the tungsten lamp Use the silicon photodiode first If you take the scan from 400 to 800 nm the resulting spectrum will be a first order transmission spectrum In the next range from 800 nm to 1600 nm both first order and second order diffraction compo nents will be in the spectrum However since silicon is no longer sen sitive beyond 1100 nm any detected signal that appears beyond a wavelength of 1100 nm is definitely from second order transmission of shorter wavelengths through the monochromator Repeat these measurements using the other available gratings For example you can try two gratings blazed at the same wavelength but with different numbers of grooves per millimeter Try to gain a practi cal sense of what happens to your measured spectrum when you change either the blaze wavelength or the number of grooves per mil limeter Try to test the gratings over the widest range of wavelengths possible Repeat the same measurements using a Ge or a GaInAs photodiode These diodes generally have little or no response in the visible region Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 T
187. er electrons compared to that of the holes kT 2 Diffusion constant of holes D 1 0 025 x 500 12 5 gt Diffusion time Diffusion time of holes 5x10 25x10 6 T 125 125 2 x 10 sec Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Electrical Response Time of Diodes Electrical Response Time of Diodes 65 4 4 Drift When the minority carrier reaches the depletion region 2 and 4 in Fig 4 1 Then it moves across the depletion region under the action of the electric field The carrier velocity is proportional to the electric field until a velocity saturation is reached The saturation electric field is about 3 x 103 V cm for common semiconductor materials such as GaAs Ge InGaAs and Si The electric field in the depletion region at 0 bias is much larger than the saturation field This fact means that the carriers drift across the depletion region at constant velocity regardless of the reverse bias voltage For electrons in Si this is about 10 cm sec whereas for GaAs and InGaAs it is about a factor of two larger The saturation velocity for holes in all semiconductors is about 10 cm sec The typical value for the depletion width is 1 um 10 cm Therefore the drift time for carriers to cross the depletion region of this size is
188. er emission wavelength by a nanometer then significant crosstalk interference between adja cent channels will occur in today s wavelength division multiplexing communications systems A meaningful physical model of chirp will require detailed knowl edge of the semiconductor band structure and the procedure needed to calculate the chirp effect is too complicated for presentation here There are possible remedies In order to minimize turn on delay and as we will see shortly in or der minimize the effects of relaxation oscillations you would like to drive the laser well above threshold This is not good news as far as chirp is concerned One approach that has been used with some suc cess is wavelength stabilization In the lasers we have discussed so far the output wavelength is determined by the process of stimulated emission which chooses the wavelength where the gain is maximum To force the laser operation to occur at one specific wavelength an ad ditional optical resonator having only one mode in the entire laser gain spectrum can be imposed on the laser structure This is achieved by cutting a periodic grating into the laser close to the gain region The grating acts like a narrow band optical interference filter The de vice is called a distributed Bragg reflector laser The presence of this grating significantly extends the region of laser drive current over which single wavelength chirp free emission can be obtained under puls
189. er photons to create the same optical power The photocurrent is proportional to the num ber of photons and is not related to the energy of the photons provid ed the energy is at least greater than the band gap energy If you make a plot of the photocurrent versus optical wavelength you will find that the photocurrent drops as the wavelength gets shorter even though the optical power and the quantum efficiency remain con stant see Fig 3 90 The responsivity is a parameter of photodiode per formance that is commonly found on a photodiode data sheet It must be cited for a particular wavelength or the number is meaningless Some handy reference points to remember are the following For 100 quan tum efficiency at A 1 24 um R 1 amp watt At A 0 62 um R 0 5 amp watt The quantum efficiency of a well designed photodiode is near 100 There are two things that can degrade the quantum efficiency 1 Optical reflection some photons just do not get in the diode 2 Recombination some photocarriers just do not make it to the junction Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Photodiodes 54 Photonic Devices Quantum efficiency is constant Optical power is constant Photocurrent Energy Gap Increasing wavelength gt Fig
190. eringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Light Emitting Diodes Light Emitting Diodes 111 er the energy of the emitted photon is determined primarily by the energy band gap of the semiconductor Electrons that are injected into the conduction band by a bias voltage that exceeds the band gap will have energy in two forms kinetic and potential energy The potential energy is represented by the band gap The kinetic energy is the dif ference between the energy imparted by the bias voltage gVz and the band gap energy This kinetic energy is rapidly dissipated in the form of heat until the electron is sitting at the bottom of the conduction band where it waits for a hole to appear in the vicinity so that radia tive recombination can take place In most cases the luminescence at room temperature from a real LED peaks at an energy slightly less than the band gap energy in dicating that the luminescence has its origin in recombination from electrons and holes lying in impurity levels formed by the p type and n type doping Further evidence of impurity based recombination comes from the extended tail of luminescence at energies well into the forbidden gap In addition to the effect of Boltzmann statistics the intensity emitted by the LED falls off above the band gap ener gy because the emitting material is also a strong absorber of these hi
191. ermine the scan range of interest of the spectrometer For a semiconductor laser this will be a range of 2 to 3 nm around the wavelength of peak emission intensity Next the scan rate needs to be adjusted so that this range is scanned in 1 minute Then successive scans should be taken while re ducing the exit slit width Some improvement in resolution can be ob tained by also reducing the exit slit width as well You will notice that the signal strength on the lock in amplifier will decrease during this iteration However since the scan time is slow you can compensate to some degree by increasing the averag ing time of the lock in in order to maintain an acceptable signal to noise ratio You will want to be sure that the alignment of the opti cal elements is maintained so that you optimize the signal as you decrease the slit openings Using a 0 25 m spectrometer you should begin to resolve the longitudinal modes of a semiconductor laser with a slit opening of about 100 microns A successful measurement will combine your knowledge and experience with both the spec trometer and the lock in amplifier Getting the results will be an ex citing and rewarding experience Questions to Think About Why does the laser output spectrum depend on current What role does the slit width play in resolving laser modes Based on your lab experience which slit is more important the entrance or the exit slit Suppose that you had a photodiode detector li
192. erms of Use as given at the website Optical Fibers and Optical Fiber Amplifiers Optical Fibers and Optical Flber Amplifiers 217 average of the square of the photocurrent power rms and so it is pro portional only to GSinput Similarly the ASE power can be expressed as Bq S inputG G DAF L SE hf m 9 24 where B is a constant and m is the fraction of the population inversion between states N and Nj N N m N Note that m 1 Under conditions of high gain that is G gt 100 40 Sin u G Af ise aa 9 25 The SNR at the output is approximated by Sinpat m S output AhfAf 9 26 whereas the SNR at the input is the signal power divided by the shot noise q S input j hf S input 2qS eg 2hf Af hf Now we can compare the SNR at the output to the SNR at the in put SNRinput 9 27 SN R output m SNRinput 2 ae Under the very best conditions 100 of the population is inverted and the SNR at the output is reduced by 3 dB compared to the SNR at the input after passage through each amplifier This situation howev er has been obtained so far only in the laboratory In typical commer cial amplifiers the signal to noise ratio is degraded by a factor of about 3 5 dB The actual noise penalty is comprised of additional but less important contributions It is furnished by the vendor with the specifications of the optical amplifier package If one starts from a transmitter w
193. es All rights reserved Any use is subject to the Terms of Use as given at the website Light Emitting Diodes 124 Photonic Devices Drive Radiative Modulated R binati Light Current ecombination Output Nonradiative Modulation Current Recombination Figure 6 13 A schematic diagram of LED modulation The drive current determines the operating point of the diode The modulation current is smaller These currents generate excess electron hole pairs Some pairs recombine radiatively while the rest do not um component created by the LED drive current We can assume that the optical recombination is occurring in a n type region with doping np Then we can write the basic expressions for the total carrier con centration N and P as N np AN P po AP 6 14 where nppo n and AN AP always First we will develop the expressions for the LED output optical power in terms of the drive current There are some important basic ideas to keep in mind e The input current of the LED creates a nonequilibrium excess den sity of electrons and holes AN AP e Some of these electrons and holes recombine by emitting photons Mint e Some of these photons actually escape the LED structure and are emitted into free space constituting the measurable output of the LED next e The output power of the LED in watts is proportional to the num ber of photons emitted The number of photons emitted is propor tional to the
194. es of lasers with a collimated output The angular spread or divergence in the beam is low and so very little of the grating is illuminated by the laser beam The result is the same as if the grating were quite small on the order of a few millimeters Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Experimental Photonics Device Characterization in the Laboratory Experimental Photonics Device Characterization in the Laboratory 275 sense also find a way to increase the effective size of the grating Beam divergence is the key to this To get a better measurement we need to find a way to increase the beam divergence so that we can fill the grating A simple and effective solution is to direct the laser beam toward a rough reflecting surface White filter paper works well The light beam scattered from this surface has a large divergence This light should then be focussed on the entrance slit using a lens with an f number equal to that of the spectrometer Measuring the Mode Spectrum You should now be confident that you are getting the best performance possible from your spectrometer Having set the entrance and exit slits to 1 mm you should be able to measure the laser output spectrum The procedure that follows de scribes iterative measurements in which you first det
195. f 1 um has an energy of 1 24 eV what is the ener gy of a photon having a wavelength of 0 5 um 500 nm Answer E 2 48 eV What is the energy of red photons A 612 nm Answer E 2 0 eV Exercise 2 3 Prove that the energy of any photon is given by 1 24 pm E eV 2 9 Prove that the wavelength of any photon is given by 1 24 eV Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Electrons and Photons 14 Introductory Concepts Since photons always travel at the speed of light it is natural to think about the flow of energy or power in a light beam Power is measured in watts Watts power that comes out of the light bulb energy sec Watts number of photons of frequency f sec x energy summed over all f Power Ss ne Er f So the total power is made up of the sum of all these little packets of E hf It is sometimes more convenient in many applications to use angu lar frequency w instead of regular frequency w 2nf To make everything work out right you have to divide Planck s con stant by 27 h 2a h E hw In photonics you will use and E almost always Rarely will you calculate f The most important reason for this is experimental in ori gin There are no instruments that measure frequency of photons di rectly
196. f length L the transmission time of the peak of a light pulse is 2 4 ro 9 16 ia Us ary l If the laser source has a linewidth of AA then we can estimate the range of the pulse spreading in time as ee dt 3s gt 9 17 T RA ae eO da AN Ao The material dispersion is defined as 1 d n SA 2 1 a a ae ps nm km 9 18 35 Material dispersion ps nm km 154 1200 1300 1400 1500 1600 1700 Wavelength nm Figure 9 10 The material dispersion of light by SiO The material dispersion becomes negligible near 1280 nm Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Optical Fibers and Optical Fiber Amplifiers 208 Advanced Topics The material dispersion of SiO has been measured and is shown in Fig 9 10 Estimation of the pulse spreading due to material dispersion can be written simply Aty L AA M 9 19 where Ad is the linewidth of the laser source under modulation Example 9 2 To illustrate the importance of the role of modulation bandwidth in dispersion consider the pulse broadening of a narrow line width sin gle mode laser operating near 1300 nm at which the material disper sion is small The line width of a single mode distributed feedback laser diode is typically less than 0 1 nm Under low frequency mod
197. ffusion justifying the all important boundary conditions we used to develop the I V model for the p n junction diode even in strong forward bias To summarize a laser is an amplifier with positive feedback We have determined that the condition necessary for amplification to oc cur is a population inversion and we have described how this can be Electrons ENERGY Holes Region of Population Inversion ee gt DISTANCE Figure 7 9 Energy level diagram in a degenerately doped p n junction diode in strong forward bias V gt Vpr The depletion region is increasingly more narrow but does not decrease to zero Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Lasers Lasers 159 achieved in a p n junction The other half of the requirement is to cre ate optical feedback This is easy it s all done with mirrors 7 5 Optical Feedback Making a Laser The simplest kind of optical resonator that you could think of is formed by two parallel mirrors In fact the first lasers were made in this way with metallized front surface flat mirrors Improvements on this simple beginning were to give the mirrors a concave surface so that the light intensity would be focused to a maximum in the center of the gain region Replacing one of the metallized mirrors by a multi
198. fiers Optical Fibers and Optical Flber Amplifiers 205 was 1550 nm at which losses are at a minimum The maximum mod ulation rate of these lasers was initially 565 megabits sec In long haul networks signals could be carried for 70 to 100 km before they needed to be regenerated This means cutting the fiber and coupling it to a photodiode followed by an amplifier and a lot of electronics to re condition the signal and using it to drive another laser that launches the signal back into the fiber This kind of repeater was the exact ana log of electrical repeaters that the telecommunications companies used in the days of transmission by copper cables In only a few years after the first installations progress in laser de velopment led to the direct modulation laser at 2 5 Gbit sec more than four times faster than 565 megabits That means that four times as much information could be carried over the same fiber However the change meant replacing all the repeater amplifiers This could be done in principle for a long haul terrestrial link but is totally imprac tical for submarine optical cable Soon thereafter fiber optical engi neers began to propose transmission systems that could carry several wavelengths of light simultaneously This was a way to boost the ca pacity of the optical fiber but it meant redesigning the repeater so that there is a complete detection and using reconditioning electronics for each wavelength of light This wave
199. fifty This has produced a windfall for component manufacturers But once these systems are installed what next A business needs to grow every year in the world of semiconductor devices because prices of in dividual devices are continually declining When we were working in the laboratory developing new LED structures we would often ask each other what we would have to do so that everyone in the world would own at least one LED hopefully under circumstances that would require periodic replacement At the beginning of the 1990s the best that had been achieved along these lines was that almost everyone owned an LED in the form of a red lamp that shows that the television is on The more fortunate had LED displays in microwave ovens or CD players However the pres ence of LEDs in lighting means that everyone will own thousands of these devices in perhaps the not too distant future In the beginning a light emitting diode was a p n junction made from a semiconductor with a direct band gap Most of these devices emitted light at wavelengths invisible to the human eye These LEDs have found a home in the remote control of televisions and other elec tronic devices Red green and blue RGB emitters are needed in or der to produce a light source capable of displaying all the visible col ors and of course white light In the 1970s it was widely accepted by intelligent scientists that a blue LED was probably not possible to make because of fund
200. for measurement require modest values of voltage that is 1 volt to 1 volt and low values of current 10 microamps full scale Insert the photodiode into the socket that you have prepared The center conductor of the BNC should be connected to the positive voltage terminal of the curve trac er You will get one of two possible results as shown in Fig 11 1 In the curve on the left a the n side of the diode is connected to the center conductor of the BNC cable In the curve on the right b it is the p side that is connected to the center conductor Although ei ther orientation will work for all experiments the usual configuration is the case on the right with the p side connected to the center con ductor Forward bias means placing a positive bias on the p side of the diode relative to the n side and negative bias means placing a positive bias on the n side of the diode relative to the p side If your a b Current 0 0 Voltage Voltage Figure 11 1 The current voltage characteristic that you see on the screen of the curve tracer depends on how you hook up the diode In a the positive connection to the curve tracer is connected to the n side of the diode In b the positive connection is con nected to the p side of the diode Although both measurements are correct b shows the way that the I V characteristic is conventionally displayed Roman numerals I to IV mark the diffe
201. fraction efficiency This can be determined from the an gle of the grooves relative to the grating surface A specification of a grating typically used in the characterization of GaAs lasers has a blaze wavelength of 600 nm and 1200 grooves mm The output spectrum of the grating depends on the wavelength The output spectrum of a light bulb depends on wavelength When you use a light bulb and a monochromator to create a tunable source of light the wavelength dependence of the output will be a combination of the output of the light bulb and the grating in the monochromator Most measurements in optoelectronics are concerned with relative response of a component as a function of wavelength If the absolute optical pow er is required a careful calibration of the light source and monochro mator must be made over the entire optical range of interest Typical transmission spectra of some gratings are shown in Fig 10 6 These graphs are not a substitute for your own calibration if needed They are useful to help in understanding that there are peaks and valleys in the optical spectrum that are due to features of every grating The grating shown in Figure 10 6a has a blaze wavelength of 300 nm so it is designed to be used in the blue to ultraviolet part of the spectrum Note that if you were to use this grating to make a meas urement near 1200 nm you would have to deal with a huge peak in the transmission of the grating You might mistake this trans
202. g Some of the rapidly growing areas are Ecology Solar cell energy generation Air quality and pollution monitoring Imaging Camcorders Satellite weather pictures Digital cameras Night vision Military surveillance 3 Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Introduction 4 Introductory Concepts Information displays Computer terminals Traffic signals Operating displays in automobiles and appliances Information storage CD ROM DVD Life Sciences Identification of molecules and proteins Lighting Medicine Minimally invasive diagnostics Photodynamic chemotherapy Telecommunications Lasers Photodetectors Light modulators Telecommunications is an application of considerable activity and economic importance because of the transformation of the world wide communications network from one that used to support only voice traffic to one that now supports media transmitted through the Inter net including voice data music and video Of course in the digital world these different media are all transmitted by ones and zeros However if a picture can be said to be worth more than a thousand words a transmitted picture counts for about a million words The growth of the internet and its capacity to transmit both images and sound has b
203. ge This shows a typi cal experimental result The capacitance decreases as the reverse bias is increased Analysis For reverse bias data the capacitance is defined as C s amp A W W equals the depletion width of the junction We would like to know A the diode area This parameter may be included in the specification sheet For LEDs you can usually make a measurement because the chip can be seen Determine the built in voltage of each of your diodes by plotting C A versus the reverse bias voltage The plot should be a straight line if the majority carrier concentration is constant see Fig 4 5 The intercept with the voltage axis gives the built in voltage The slope of this line gives the majority carrier concentration Do a least squares fit to the data to determine the majority carrier concentration If you are unable to determine the area obtain the built in voltage but not the carrier concentration Suppose the plot is not a straight line In Fig 11 7 we show such a result The corresponding capacitance voltage data shows a relatively high capacitance near zero bias that rapidly decreases as the diode is put into reverse bias What would this result tell you about the struc ture of the diode The capacitance in forward bias is determined by different physics so the analysis is different too It is called diffusion capacitance to distinguish it from the capacitance in reverse bias which is called de pletion capa
204. get gain we need a population inversion In order to see how this can be achieved we show in Fig 7 7 the energy level di agram for a p n junction This p n junction is different from others we have looked at It is heavily doped on both the p side and the n side so that the Fermi level actually lies in the conduction band on the n side and in the valence band on the p side This is called degenerate doping It is not a requirement but it does make lasing easier to obtain From the work you have done to characterize diodes you know that there are two important things that happen when a diode is subjected to forward bias One is that the energy difference between the conduc tion band on the p side and the conduction band on the n side be comes smaller The other thing that occurs is that the width of the de Electrons Fermi Level ENERGY p DISTANCE Figure 7 7 Energy level diagram for a p n junction with degenerate doping on both the p and the n sides Vz refers to the valence band and Cz refers to the conduction band The Fermi level is constant throughout so no bias is applied to the diode and there is no current Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Lasers Lasers 157 pletion region decreases There are other important changes
205. gher energy photons The width of the luminescence curve at half maximum value or FWHM Full Width at Half Maximum is slightly less than 3 2 kT at room temperature from the model This is about 40 meV The experi mental values for this parameter are invariably larger on the order of 150 to 300 meV This result further supports the picture of recombi nation from impurity levels that are distributed in energy near the edges of the conduction and valence bands The model behavior predicted in Eq 6 7 treats only the spectrum of the light at emission without considering either the presence of impurities or the effects of absorption of this light by the surround ing material It is possible to minimize these two effects For exam ple self absorption which is responsible for cutting off the high energy end of the external emission spectrum can be nearly elimi nated by using a thin active region that is less than a wavelength in thickness and by surrounding the active region with window lay ers having a higher band gap This is called a heterostructure LED and its emission spectrum conforms much more closely to the expec tations of the model as can be seen in Fig 6 6 Note in particular that there is now an extended spectral region above the band gap on the high energy side in harmony with the simple model introduced in Eq 6 7 The radiative efficiency of a light emitting diode can be expressed as a ratio of the radiative and nonradiat
206. gineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Experimental Photonics Device Characterization in the Laboratory Experimental Photonics Device Characterization in the Laboratory 277 ots Slas ih kre E Joh to Ny peak imh Clos day fly shir huh we Caw judt see Arm pak S z OAT mm S a Off Maw T 30mS8 pre Pt 00 uo S pest Shin fined ve 09 j OS OF EL RECSA DINC GHAATSI GRAPHIC CONTROLS CORPORATION RUEFALO li oO Figure 11 11 Continuation of the experiment in Fig 11 10 Successful resolution of the laser mode spectrum is obtained by reducing the spectrometer scan rate and narrowing the slits The student has obtained the ultimate resolution of the spectrometer A good measurement like this one takes patience and time Courtesy of J O Cross reprduced by permission Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Experimental Photonics Device Characterization in the Laboratory 278 Characterizing Photonic Devices in the Laboratory Analysis
207. gital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Photodiodes Photodiodes 53 Example 3 1 Suppose we measure I photocurrent in amperes fiw in joules q in coulombs and Poptical in watts In our measurement fiw 1 eV 1 6 x 10 19 joules and we determine that the quantum efficiency is unity I photocurrent i 1 6 x 10 9 I photocurrent ih P optica 1 6 x 10 19 P optica 1 3 26 This means that 1 watt of optical power will produce 1 ampere of photocurrent when the quantum efficiency is 100 and the photon energy is 1 eV optical wavelength 1 24 um in air Note that if you measure I photocurrent 1n amperes fiw in eV q 1 elec tron and Po tical in watts the result is the same The ratio of the photocurrent to the optical power can be thought of as the transfer function for the photodiode The ratio is called the re sponsivity The responsivity is not the same thing as the quantum ef ficiency What is more important the two are not proportional photocurrent Nea I Responsivity R E optical amps watt 3 27 at A 1 24 um where Ey hw 1 eV R 1 amp watt implies that ng 1 0 However please note that at A 0 62 um where Ey hw 2 eV R 0 5 amp watt implies that ng 1 0 3 28 When the photon energy is higher it takes few
208. gt p Use n p n to confirm this Therefore D In etVa 1 Grr 3 13 Jror J 47 Finally we can simplify this expression by noting the following re lationships 2 n n and ODz 7 L P N Jror E leVA kT 1 qLeGr i Regular I V Current from photons 3 14 Illuminating the photodiode with a flux of photons with energy greater than the band gap will create an excess minority carrier flux of G L Equation 3 14 shows that the photodiode current will be lin early proportional to this flux Since no approximations were neces sary to derive this result we can expect the linear relationship to hold over many orders of magnitude of photon flux This result is key to the performance of photodiode detectors The linear photodetection response can be compared to the dependence of the photodiode cur rent on an applied voltage The current voltage relationship is quite nonlinear A second equally important result is that the photodiode response to a photon flux is independent of the bias voltage on the pho todiode Equation 3 14 shows that the photodiode response to a photon flux is superimposed on the current voltage equation When the diode is forward biased the forward current will soon exceed the photocur rent While the photocurrent is independent of the bias voltage it may be swamped by the conventional forward diffusion current of the diode resulting from the applied bias
209. gth range of a spectrometer 2 Measure the output spectrum of a tungsten lamp in the spectrome ter mode using a Ge photodiode as a detector 3 Compare the diffraction spectrum of different gratings 4 Measure the absorption edge of several different kinds of detectors in the monochromator mode 5 Observe second order transmission in the monochromator mode Background The monochromator spectrometer is the key instrument for many opto electronic measurements Typically measurements are made by cou pling a light beam into and out of the instrument while scanning be tween two limits of wavelength The slits at the entrance and the exit of the instrument both play a role in determining the resolution and the throughput as the slit width is decreased the resolution improves and the throughput drops Exactly the same thing happens when you squint your eyes to see more clearly Despite their similar functions Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Experimental Photonics Device Characterization in the Laboratory Experimental Photonics Device Characterization in the Laboratory 253 the entrance slit plays a greater role in determining throughput whereas the output slit has a greater effect on the resolution The monochromator spectrometer is traditionally c
210. he McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Experimental Photonics Device Characterization in the Laboratory Experimental Photonics Device Characterization in the Laboratory 257 of the spectrum Therefore they can be used to probe the infrared grating response in the first order Compare your measurements Here are some questions to think about 1 Which condition gives the most throughput first order or second order transmission 2 Which gratings show anomalies Where are these located 3 Where is the wavelength region relative to the blaze wavelength in which the grating response seems to be most uniform Analysis Write an evaluation of the characteristics of each grating you have tested in your lab book You should try to identify the spectral region in which each grating works best and spectral regions where the grating should not be used at all Be sure to identify the criteria you have selected for this evaluation Try measuring the optical response of a silicon or germanium pho todetector using different gratings You can use either the photocon ductive mode or the photocurrent mode Demonstrate and explain second order transmission Using a tung sten source for illumination and the monochromator set at 1100 nm what are the characteristics of the light you can see exiting the mono chromator 11 4 Optical Properties of Light Emitting Diodes O
211. he hole reaches the negative contact and is collected in the external circuit The photoconductivity stops because there are no extra charge carriers The length of the photoconductivity event is deter mined by the transit time of the slower carrier the hole From this time we can determine the bandwidth of the detector During this time 12 electrons have traversed the sample and the external circuit in order to maintain charge neutrality The current due to these 12 electrons was initiated by the absorption of one photon The ratio of the number of electrons collected per incident photon is the photoconductive gain The sequence of events illustrated in Figs 5 2 through 5 7 illus trates the origin of photoconductive gain and bandwidth The band width is determined by the transit time of the slower charge carrier In the discussion that follows we will assume that this is the hole L L V mg t where L is the electrode separation and V L is the electric field The bandwidth of the photoconductive detector is 1 V ee 5 3 at mL Conduction Band Ohmic Contact Energy Valence Band l Figure 5 6 The electron traverses the space between the contacts and is about to be collected by the positive contact Meanwhile the hole is still moving more slowly to ward the negative contact Distance Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Cop
212. he laser threshold current 3 Resolve laser emission modes Background The basic properties of laser diodes to be measured are simple threshold current emission wavelength and mode structure You will Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Experimental Photonics Device Characterization in the Laboratory 264 Characterizing Photonic Devices in the Laboratory be able to measure the first two performance parameters easily Re solving the mode structure will be a good test of your skills in device characterization The threshold current tells a lot about the quality of the device It is a basic indication of efficiency since the current required to reach threshold is largely converted to heat Above threshold one is often interested in the differential quantum efficiency that is what per centage of injected electrons are converted to laser photons In high quality commercial devices this efficiency approaches 80 The emission wavelength is key for many important applications Fiber optic telecommunications takes place in a band of wavelengths 30 nm wide Inside this band one would like to have 100 different wavelengths That means one communications band every 0 3 nm These wavelengths have been fixed by the International Telecommu nications Union in
213. he low injection limit which is always true for photodiodes n o An no because n o is many orders of magnitude larger than An We can use this approximation to derive the excess minority carrier densi ty that is induced by the bias voltage at the edge of the depletion region An n eta Bi VaveTH Npo Npo e aVBi kT e la VBi VAVkTI _ No An njo etV4 1 3 4 In Eq 3 4 note the appearance of the term n o This term is re quired to make the current 0 when the applied voltage is 0 and it is also the origin of the dark current of the photodiode Current is car ried in the diode by both drift and diffusion However at the edge of the depletion region for example at x 0 the current is carried only by diffusion If we calculate the I V characteristic at this point we can work with only one equation the diffusion equation An x Te d2 d This equation says that the time rate of change of the excess carrier concentration is given by the generation rate inside the diode less any recombination and plus any additional carriers generated by light We need to write a similar equation for the excess hole minority carrier density on the n side of the diode That equation is completely analogous to Eq 3 4 so we can solve 3 4 and deduce the answer for the n side of the diode Equation 3 4 is a second order differential equation for An which is a function of distance in the diode The gen eration rate of m
214. he modulation bandwidth will be proportion al to the square root of the dc drive current around which the ac mod ulation is taking place Example 6 5 Calculate the ac Modulation Bandwidth of an LED in the High Injection Limit Using the same parameters as before the ac modulation bandwidth can be calculated E 50 x 10 100 x 10 4 B 8 x 1071 cm sect d 105 cm 1 x 10 5 x 108 A cm 1 2 9 x 108 sec Tac ac bandwidth 90 MHz Example 6 6 Calculate the ac Modulation Bandwidth of an LED in the Low Injection Limit In this case the excess carrier density introduced by the current re mains much less than the doping density therefore N np As before we assume that the LED is being modulated around a steady state operating point d J AN AN B N P AN AN 0 dt qd Trop J AN BNAN qd Tar Bno Jan Jan 6 39 Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Light Emitting Diodes Light Emitting Diodes 135 Using the following parameters B 8 x 101 cm sect Np 5 x 1018 cm3 T 2 x 10 sec 9 x 108 sec Tac ac bandwidth 286 MHz The ac modulation rate 1 1 Bnp Tac Tn r is independent of the current A practical model for the frequency
215. hs Lasers can be built that span a range from less than 400 nm to more than 10 000 nm No other materials system has this flexibili ty Semiconductor lasers are relatively inexpensive The cheapest ex amples sell for less than a dollar and the most expensive for less than 10 000 This is a lot less than you would pay for a TiAlO Ti sap phire laser that sells for 60 000 or a tunable dye laser that sells for 150 000 As a result of these and other considerations the semicon 143 Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Lasers 144 Photonic Devices ductor laser is by far the industry leader in terms both of the number of units sold and the volume of revenues Semiconductor laser diodes are the key component in a number of common devices such as a CD players scanners printers and DVD readers They are also the key components in optical fiber telecommunications for generating the light waves that travel down the fiber In this chapter we will discuss the principles of laser action start ing first with a short example of an electronic amplifier that you can build in a few minutes in the lab The physical principles that cause laser action to occur are analogous to those that cause oscillation to occur in electronic circuits We will build on this analog
216. iagrammed schematically in Fig 7 10 These are the wave lengths at which amplification by stimulated emission will occur That is laser action can occur at the wavelength of those cavity modes that lie within the gain spectrum of the laser medium Pho tons that have the wavelength of one of the cavity modes will be reflected back into the cavity provoking more emission at that wave length creating more photons that will be reflected back into the cavity stimulating more emission and so forth Almost all the photons in a cavity mode are the result of stimulated emission because the spontaneous emission occurs in all directions but the photons are stimulated only along the directions defined by the cavity modes Therefore there is strong optical gain for the modes of the resonant cavity and very little gain for other directions or wavelengths of light composing the spontaneous emission Although spontaneous emission diverts light from lasing modes reducing the laser efficiency its presence is absolutely required to make the laser work in the first place The spontaneous emission primes the pump in the beginning by filling all possible radiation modes with photons Gain and laser action then builds up out of the noise in the much smaller number of modes that overlap in energy with the gain spectrum and which are resonant modes of the reflecting cavity In general there are a number of modes that lie in the gain spec trum The exact
217. ial well and to do so they gave up some of their energy This energy that separates the bonding state from the higher energy antibonding state is called the bonding energy In silicon this energy difference is about 1 eV If a photon comes along or if the thermal energy is large enough one of those bonds might happen to break and now there would be an electron that is promoted from the bonding state to the antibonding state Of course if all the bonds were broken the silicon would melt But what does the situation look like for us At room temperature in perfect silicon are there any broken bonds How could you estimate this Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Electrons and Photons 18 Introductory Concepts Exercise 2 5 For each broken bond in a perfect crystal of silicon an electron is pro moted from the valence band to the conduction band Using Boltz mann statistics you can write N antibonding 2 e AE kT Nponding At room temperature we will approximate kT by 0 025 eV N antibonding e 1 0 025 _ e 40 1074 atoms cm p40 24 _ N antibonding e 10 4 2 2 24 This is an interesting number Take the log of both sides 1ogio antibonding 24 40logio e 24 40 0 4 24 16 8 Nantibonding 108 bonds cm Thi
218. iated with the radiative recombination rate we can define 1 BN 6 20 Tr where 7 _ is the radiative recombination time So J 1 1 N np qd Tr r Tn r The total recombination time can be calculated by combining the rates from the two recombination channels radiative and nonradia tive 1 1 1 1 BN 6 21 Tp Tyr Tn r Tar and J N 6 22 qd Tp The ratio of the radiative recombination rate to the total recombi nation rate l Tr r Tr r Tr Tint 6 23 1 2 1 Taz Tr T r r r gives the fraction of photons created with respect to the total number of electron hole recombination events This ratio is the internal quan tum efficiency or Nint From Eq 6 22 we have N np 7 J qd Rearranging Eq 6 15 gives N np 1 J J 2 T e hss B NP n 7 Tp qd Nint qd 6 24 Tr r Ter Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Light Emitting Diodes Light Emitting Diodes 127 Using this equation we can now simplify the expression for the LED output power in Eq 6 15 so that the optical output power is ex pressed in terms of the drive current Pout Next V BNP n fiw J Next V Taig A I I Next Nint q fiw nN q ha 6 25 The overa
219. ical and optical properties current voltage relationship quan tum efficiency and spectral response 3 2 The Current Voltage Equation for Photodiodes A silicon photodiode can absorb photons that have an energy greater than the band gap E Si 1 1 eV at room temperature Absorption creates an electron in the conduction band and a hole in the valence band Most of this absorption takes place in neutral material creating one majority carrier and one minority carrier The minority carrier will diffuse to the p n junction and be carried to the other side where it be comes a majority carrier and contributes to the photocurrent We can determine the current voltage relationship for a photodiode if we know the functional dependence of the excess minority carrier concentration as a function of position in the p n junction This depends on the ap plied voltage The current can be obtained directly from the diffusion equation d J 4D nx In order to examine the details let us consider the energy level dia Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website POTENTIAL ENERGY Photodiodes Photodiodes 39 DISTANCE Figure 3 1 The energy level diagram for a p n junction at equilibrium This is a plot of potential energy versus distance Note that the Fermi ene
220. ical when By Boy and Ao _ 16r _ 8an hf By X 7 4 The two expressions in Eq 7 4 are called the Einstein relations in which c is the speed of light and n is the index of refraction of the medium involved For semiconductors like GaAs or InP n is about 3 4 The ratio of the spontaneous emission rate to the stimulated emis sion rate is Agi 2 gho kpT _1 i R Ko Bz e 7 5 Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Lasers 150 Photonic Devices This ratio is normally much greater than unity that is the sponta neous emission rate far exceeds the stimulated emission rate If we consider photons with an energy of 1 eV A 1240 nm then fia k pT 40 at room temperature R as a result is a very big number However in order to have laser action the reverse must be true that is the stimu lated emission rate must be greater than the spontaneous emission rate To see how this can happen read on through the next section 7 3 Optical Gain Optical gain and optical absorption are closely related We will start by recalling some ideas about optical absorption that we already have discussed in Chapter 3 When light is incident on a semiconductor surface only two things can happen reflection or transmission Nor mally both can occur at
221. icient light emission from p n junctions occurs only in forward bias Note that the answer is not current This is a result of light emission 6 3 Right on time you receive an expected shipment of 500 000 red LEDs for your company s bar code reader production You have specified a quantum efficiency greater than 0 001 0 1 The cost of the shipment is 75 000 It is your job to inspect and ap prove the shipment You assign the task to a new recruit who Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Light Emitting Diodes 140 Photonic Devices runs a spectrum on a sample diode which is shown in the figure below 0 10 0 08 4 Drive current 20 mA 0 06 Optical power mW 0 02 4 400 450 500 550 600 650 Wavelength A nm a What is the energy width at half maximum b What is the quantum efficiency at the wavelength of maxi mum output c Do you accept the shipment 6 4 Perform an engineering estimate for the profitability of LED based traffic lights in your city Try to improve on the estimate procedure given in the text For example you may be able to learn the maintenance cost per light from your city engineer s of fice The savings will depend on the price the city pays for elec tricity etc Compare your
222. ics of the grating used in the monochromator spec trometer Spectral absorption by the medium along the optical path for ex ample air is a strong absorber around 1400 nm on humid days The spectral characteristics of the device under test for example a filter e The spectral characteristics of the detector Each of these responses can be probed individually by keeping every thing else constant In this laboratory exercise a principal objective is to probe the spectral properties of diffraction gratings Recommended Equipment 1 Light source tungsten light bulb with power supply 2 Detectors a germanium or GalnAs photodiode and a silicon photo diode Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Experimental Photonics Device Characterization in the Laboratory 254 Characterizing Photonic Devices in the Laboratory 3 Lenses optional as needed 4 Monochromator with more than one grating installed or two monochromators having different gratings 5 Lock in amplifier and chopping wheel Data acquisition device either a strip chart recorder or a computer 7 Cables connectors and optical mounts aD Procedure Most monochromators and spectrometers are built so that different gratings can be installed easily In fact you can purchase a mono
223. ide open for development of a new mod el that is both more accurate and more useful 8 2 Time Dependent Behavior of Laser Diodes during Current Modulation When you turn on a laser by a pulse of current there are three things that happen First there is a time delay while the population inver sion builds up to the threshold level Next the laser begins stimulated emission of light at energy E As time goes on this energy decreases and the wavelength of emission increases The emission of light de pletes the level of carrier inversion and causes the light intensity to decrease When the recombination decreases the level of inversion in creases completing the cycle These events are diagrammed schemat ically in Fig 8 1 To put these events in perspective consider the current systems specification for optical fiber telecommunications In order to carry the maximum amount of information in an optical fiber communica tion channels are assigned on the basis of wavelength This is called wavelength division multiplexing or WDM The useful amplification band of Er amplifiers is 30 nm The current specification calls for 100 channels in this band This means that the spacing in wave length between each channel is 0 3 nm This is called dense wave length division multiplexing or DWDM If the wavelength of a laser changes by more that 0 2 nm during modulation clearly there will be a problem In Fig 8 2 we show a flow diagram for lase
224. ificantly from taking the shortest dis tance between two points 2002 California State Automobile Association Used by per mission Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Electrons and Photons 26 Introductory Concepts ENERGY hk MOMENTUM MOMENTUM Band Gap Figure 2 9 The relationship between energy and momentum displays bands of energy that an electron can have When the electron is in a crystal the periodic atomic potential causes gaps to open up in this structure The gap means that an electron is not allowed to have these energies cation of these different roads you know that the velocity of an auto mobile is limited to a speed of 50 km h on a residential street but 100 km h on the superhighway The size of an electron is not well defined and so it is not very meaningful to try to specify its position A totally free electron be haves like a wave That means it can exist over all space Since the lo cation of such a wave is difficult to specify it is equally difficult to specify its velocity On the other hand energy and momentum for an electron can be specified Furthermore the conditions that define the interaction of electrons in solids with photons phonons or other electrons are con servation of energy and conservatio
225. ighly planar and polished and consequently has a low emissivity surface Emissiv ity is proportional to absorbance Light incident on a semiconductor with a highly textured surface is more likely to be absorbed than if the surface is a smooth low emissivity structure High emissivity sur face treatment is also used to prepare solar cells with absorption bet ter than that presented by a smooth planar surface Schnitzer and coworkers at UCLA have shown how this concept can be turned into reality They covered the surface of an LED with glass spheres and then they sandblasted the surface using the spheres as a mask The result was to transfer the pattern of the spheres into the surface of the LED The result of this is shown in Fig 6 11 The effect of texturing the surface triples the external efficiency The inven tion of this technique is a key event that has changed thinking about the application of LEDs to lighting applications Light is an electromagnetic wave just like a radio wave Radio en gineers have long understood that the most efficient way to emit radio waves is to use an antenna Radio antennas do not have flat polished surfaces like the top surface of most semiconductor wafers from which LEDs are made The external emission efficiency of LEDs could be further improved by implementing a photon antenna on the surface of the LED using principles learned from radio antenna design The interest in improving the external emissio
226. ightly lower in energy than the type 1 level and we will call it type 2 The capture cross section for electrons by the type 2 center is much smaller than the capture cross section for electrons by the type 1 cen ter As a result the electron recombination time is longer 7 2 10 seconds and the hole lifetime is shorter 7 2 lt 10 78 seconds Following the addition of these vacancies the new energy level diagram is Table 5 1 Parameter Symbol Value Density of recombination centers N 1016 cm Drift velocity v 107 cm sec Capture cross section Sns Sp 10 to 10 15 cm Photon absorption rate f 101 cm sec t Lifetime Tn Tp 10 sec Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Photoconductivity Photoconductivity 95 Conduction Band Coro oO P j Fermi Level Valence Band Type 1 Recombination Type 2 Recombination Figure 5 16 To sensitize the photoconductor a second recombination level is intro duced To be effective its concentration of centers must be larger than the density of centers of the type 1 level shown in Fig 5 16 In the absence of illumination the Fermi level lies at the class 1 level All the class 2 centers are filled and some of the class 1 centers are empty Under illumination by photons having an energy greater
227. ights reserved Any use is subject to the Terms of Use as given at the website Optical Fibers and Optical Fiber Amplifiers Optical Fibers and Optical Flber Amplifiers 221 fiber communications Such a development might well constitute the next technology breakthrough What everyone knows is that the demand for increased communica tion capacity will continue for many years to come There is much in vention and ingenuity that will be needed to implement this growth Bibliography J Wilson and J Hawkes Optoelectronics an Introduction 3rd Edition Lon don Prentice Hall 1998 L B Jeunhomme Single Mode Fiber Optics Principles and Applications New York Marcel Dekker 1983 This is a truly excellent book both for learning the fundamentals of optical fibers and as a reference for engineer ing optical fibers and optical fiber communications systems Its treatment is both rigorous and clear Especially valuable are the engineering models and approximations that allow you to design and use optical fibers for real systems with quantitative accuracy J M Senior Optical Fiber Communications Principles and Practice Engle wood Cliffs Prentice Hall 1985 A Yariv Optical Electronics in Modern Communications 5th Edition New York Oxford University Press 1997 G van den Hoven and L Spiekmann InP based Alloys in Optical Amplifiers and Lasers In Properties Processing and Applications of Indium Phos phide T P Pearsall
228. igital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Measurements in Photonics 232 Characterizing Photonic Devices in the Laboratory a Exit Slit Focussing mirrors j Pan Slit Grating a b Figure 10 5 a A schematic diagram of the light path through a grating monochroma tor Light focused on the input slit is analyzed for wavelength by the grating and refo cused on the exit slit b A demonstration of how light that enters a spectrometer is dis persed in wavelength by the grating so that the exit slit selects only a narrow range of wavelengths that can exit the spectrometer Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Measurements in Photonics Measurements in Photonics 233 grooves per millimeter and the second is the blaze wavelength The number of grooves per millimeter gives an indication of the possible wavelength resolution of the grating All other things being constant a grating having 1200 grooves per millimeter will have a higher reso lution than a grating having 600 grooves per millimeter The blaze wavelength is the wavelength for which the grating has the highest dif
229. ill consider the first two properties in this chapter The speed of response is covered in Chapter 4 The noise generated by the photodi ode needs to be considered relative to the amplification system that follows the photodetector 3 4 1 Spectral Response The spectral response of the photodiode is directly related to the op tical absorption of the semiconductor materials used to make the photodiode Optical absorption occurs in an ideal semiconductor when an incident photon has enough energy to break a bond in the valence band thereby promoting an electron into the conduction band Only those photons that have an energy greater than the band Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Photodiodes Photodiodes 49 gap energy are absorbed Furthermore all of these energetic photons have an equal chance of being absorbed The photodiode acts there fore as a threshold discriminator all photons having an energy greater than or equal to the band gap are absorbed and all the rest are not absorbed We can define a spectral response function S For this simple model S E S hw 1 if E hw Eg S E S hw 0 if E hw lt Eg 3 19 When you measure the response in the laboratory you will find it more convenient to modify this relationship so that it is express
230. ination Radiative recombination requires the following condi tions 1 Tradiative lt Tnonradiative 2 Electrons and holes in the same place i e within a de Broglie wavelength 100 A at the same time i e Tradiative 3 Energy is conserved 4 Momentum is conserved When a GaAs p n diode is forward biased the excess minority carri ers recombine and emit light The energy of the emitted light fiw sat isfies Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Light Emitting Diodes Light Emitting Diodes 107 hw E E where E is the energy of the electron in the conduction band and E is the energy of the hole in the valence band At room temperature the momentum change of the electron in radiative transition is negligible The three most important performance characteristics of a light emitting diode are 1 Spectral lineshape What is the wavelength energy of the emission peak What is the width of the emission spectrum in energy at one half the maximum emission 2 Quantum efficiency What is the internal quantum efficiency What is the external quantum efficiency 3 Modulation bandwidth What is the frequency at which the direct current modulation of the output is half its low frequency lt 1 kHz value 6 3 The Energy Spectrum
231. ing considered for application in display screens or as light bulbs for illumination In these applications the response time of an LED is so short compared to other characteristic times such as the response time of the brain that it is not a limitation on system performance On the other hand the bandwidth of an optical communication channel is several gigahertz This is well beyond the capability of currently known LEDs The response time of almost all photodiodes is determined by the resistance capacitance product The dominant resistance is that of the resistance of the following amplifier which is usually tens to hun dreds of ohms depending on the bandwidth of the detection electron ics Thus the relevant resistance is external to the photodiode The capacitance of a photodiode that is in reverse bias is much smaller than the capacitance of the same diode in forward bias In this sense photodiodes are intrinsically faster than light emitting diodes There is much that can be learned about a diode from its capaci tance voltage characteristic built in voltage doping concentration and of course its capacitance The detection efficiency of a photodiode Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Electrical Response Time of Diodes 74 Photonic Devi
232. ing wheel and start it up Check that the wheel is in the light path between the lamp and the detector You should observe a modu lation of the signal on the oscilloscope screen that corresponds to the frequency of the chopping wheel If you switch the amplifier of the os cilloscope to the ac coupling mode you can eliminate some of the background noise and better resolve the modulation This is some what similar to narrow band detection Note the amplitude of the modulated signal at the chopping frequency b Lenses Lenses may be used to improve the signal to noise ratio by controlling the flow of light Treat the light bulb as a point source and Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Experimental Photonics Device Characterization in the Laboratory Experimental Photonics Device Characterization in the Laboratory 251 place the lens at 2f distance from the light bulb Place the chopping wheel at 2f on the other side of the lens so that the light is focused en tirely in the wheel opening if possible Use another lens to focus this light on the detector c Lock in Amplifier The lock in amplifier is your friend learn to use it well Instruments vary from one manufacturer to another However no matter who makes the unit that you are using there are three
233. inority carriers from photon absorption is given by Gz and the minority carrier recombination time is given by 7 The minority carrier diffusion coefficient for electrons in p type material is D We will first look at steady state conditions and this means that gA De d An x i A 0 D Age An x GL d An x Dega Aux P Gr d An x Gz de An x De D 3 6 Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Photodiodes Photodiodes 41 This is a differential equation of the type d fix dx where M is a constant driving term The solution is f x Ae Y Be V C which we will verify presently The constant k 1 D 7 This is just mathematics The most important part of the solution however is the physics of the problem This is summarized in the boundary conditions that allow us to solve for A B and C hkf x M a When no light is present An at x 0 b When light is present An at x GLTe 0 To see that this must be so set the second derivative 0 in Eq 3 6 c At x 0 An x 0 ngo etVA 7 1 3 7 First note that Vk must have units of 1 L where L is length Then An x Ae e Beto C 3 8 where L V Det diffusion length for electrons Then apply the bou
234. input current Therefore the output power of the LED is proportional to the input current This is a direct result of the quantum nature of electrons and photons The rate equation for the change in the carrier concentration is written as rate of change in carrier concentration electrical pump Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Light Emitting Diodes Light Emitting Diodes 125 ing rate radiative recombination rate nonradiative recombination rate or AORE a a 6 15 dt qd E i where dN dt the rate of change in the electron density at the p n junction B NP n the net change in electron hole concentration due to radiative recombination N np t _ the change in the carrier concentration due to nonra diative recombination In these expressions the majority carrier doping density np and the intrinsic carrier concentration n are written in lower case to remind us that these quantities remain constant during the LED operation The optical output comes from the net electron hole recombination rate The output power can be written as Pout N photons sec x A photon Next Volume B NP n hw 6 16 In this expression next is the external quantum efficiency and is the fraction of photons created that actuall
235. iode Vr 0V f 1 MHz 7 pF Note 2 R is load resistance of the photodiode PIN OUT 3 PD LD 2 1 Electrical arrangement 1 Laser diode cathode 2 Photo diode anode 3 Laser diode anode and Photo diode cathode 2 a Bottom view of Laser diode a Figure 11 8 A data sheet for a AlGaAs GaAs laser emitting in the infra red at 820 nm This data sheet gives the electrical connections the operating conditions and a typical output spectrum The vendor identifies the laser as a class III b device because of its output power and the fact that the emission from this laser is invisible Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Experimental Photonics Device Characterization in the Laboratory Experimental Photonics Device Characterization in the Laboratory 269 Fig 1 Light output vs forward current Fig 4 Forward current vs voltage characteristics 40 Light output Po mW Forward current lp mA 1 0 Forward current I mA Forward voltage Vp V Fig 2 Temperature dependence of threshold current Fig 5 Emission spectra under CW operation 40 T ES F amp 2 3 E D 2 E 3 E E 5 E w a 10 0 20 40 60 ase temperature t C c P Te CC Wavelength
236. ion of a photon Since the photon provides very little momentum both energy and momentum can be conserved for this transition which is called a direct transition By comparison an electron occupying a state at the bottom of the conduction band in an indirect gap material is in a different situation The difference in momentum between these two states is no longer negligible The electron can make a transition to a state at the top of the valence band by the emission of a photon to conserve energy and the simultaneous emission of a phonon to conserve momentum This is called an indirect transition because two steps are involved In the case of Fig 2 10 there is no difference in momentum be tween a state at the top of the valence band and a state at the bottom of the conduction band In Fig 2 11 the situation is different In this case the lowest energy state in the conduction band does not have the same momentum as the highest energy state in the valence band At equilibrium and at T 0 K all the valence band states are occupied and none of the conduction band states are occupied Now let us break a bond in Ge That means that one electron has enough extra energy to go from a bonding state to an antibonding state The least amount of extra energy is the band gap energy In germanium this is 0 7 eV We use eV to measure energy so you do not have to carry around mind boggling powers of 10 in your calculations For silicon the indirect ene
237. ion or its velocity is a hopeless task Furthermore the semiconductor is full of many absolutely identical electrons They are all moving around at a frenetic pace Clearly a different approach is needed An important new idea in this chapter is to introduce a road map for electrons in a semiconductor It tells you what states the electrons are allowed to occupy just as a road map tells you where the roads are located that cars may travel on The road map for electrons does not tell you where the electrons are or how fast they are moving just as a roadmap for cars does not tell you where the cars are or how fast they are moving This road map is called a band structure Position and velocity are not very useful ideas for describing either 7 Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Electrons and Photons 8 Introductory Concepts electrons or photons However two fundamental physical laws always apply conservation of energy and conservation of momentum The be havior of electrons and photons can be tracked by their respective en ergies and momenta The band structure is a particularly useful tool for this task 2 2 The Fundamental Relationships There are two simple principles that support almost all the science of photonic devices One is the Boltz
238. is about 2 nanoseconds If the relaxation oscillation dies out in 5 nanoseconds the corresponding modulation bandwidth would be estimated at Af 1 5 x 10 r 60 MHz However modulation rates of 10 GHz in semiconductor lasers can be obtained experimentally This would imply a much shorter carrier lifetime on the order of 30 picoseconds Such a com parison suggests that the recombination time is not constant but in fact depends strongly on the injection rate This is an under standable result Photon emission must be balanced with the pumping rate So the recombination rate must increase in order to maintain equilibrium at high carrier injection rates 2 In order to reach higher modulation rates you would want to push the relaxation oscillation frequency well above the modulation rate The relaxation oscillation frequency will depend on the stimu lated emission rate By and the band gap of the material E Af Whereas the band gap will not change there is no physical reason why the stimulated emission rate could not increase as the photon density increases The frequency also depends through n and Ky on the amount by which the laser is driven beyond threshold in or der to send a 1 Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Direct Modulation of L
239. is effect is based on the coupling between the probability of recombination and the availability of optical modes that can carry away the emission Theoretical descriptions of this effect use the framework of advanced quantum mechanics to estimate the improve ment in the matrix element The effort to understand and optimize this effect is a current research topic in the many advanced opto elec tronics laboratories around the world Example 6 3 Traffic Lights An Engineering Estimate Suppose you are working as a traffic engineer for a metropolitan area Manhattan and you are considering using LEDs instead of incan descent light bulbs for traffic lights Could you make an initial esti mate to help you judge the conditions that would make this change beneficial to taxpayers There are three parts to this problem 1 Properties of the lightbulbs and LEDs Incandescent light bulbs Power consumed 100 W Power efficiency 15 Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Light Emitting Diodes Light Emitting Diodes 121 10 oz a aoe B G q a 7 eg 1 TEXTURED a E 30 ext eff g E O 2 2 E jas E PLANAR 04 9 ext eff wad s a 2 kd 5i 0 01 T j k T err i a i T n aaau aiite ie bi di g 5 rera 0 4 1 10 100
240. is operating at steady state at current density J gt First let us look at the steady state current before and after the current step Tn r N n I t 0 d qa BP n Sire At t gt 0 the current density is raised to Jo where it remains N n I t Jz qd BNP n Sante The key to the transient analysis is the excess current density which is now a function of time AN t N N P P The rate equation for t gt 0 can be written as J N 2 _ B NP n D 6 28 qd Tew 2 NO fy AN t d ANO dt nt dt 5 Next we substitute for N and P d J N AN AN t BI N AN P AP n L bi dt qd Thr In this last equation we can identify the current density before the current pulse was applied d Ja Ny np AN BIN P n B ANP APN APAN dt qd Tn r Tn r Jom AN 1 _ BANIP N AP qd Tret J 1 z aa D AN BP N AN 6 29 Tn r As we have done before we recognize in the second term a relaxation time This is the transient response term that we are looking for 1 6 30 z n r Be N AN Tstep Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Light Emitting Diodes Light Emitting Diodes 131 Equation 6 30 sh
241. itation of this situation is the back door that allows you to beat the limits of Fresnel s equations The escape angle of the LED can be enlarged by capping the diode with a transparent material such as an acrylic plastic the refractive index of which will be greater than 1 typically 1 5 This improves the fraction of light that can escape by nearly a factor of two The inter face between the plastic and the air can be shaped into a hemisphere This geometry allows almost all the light to exit normal to the surface with only 5 losses The hemispherical cap acts like a lens and more of the light is focussed in the forward direction as shown in Fig 6 9 The example of Fig 6 9 shows that it is possible to recover and use some of the emitted light that is not propagating in the forward direc Figure 6 9 The amount of light emitted in the forward direction can be increased dur ing the packaging operation by deposition of a hemispherical lens on the LED surface This tends to project more of the emitted light in the forward direction Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Light Emitting Diodes 118 Photonic Devices tion Precise analysis is complicated since the actual path of the light depends on where it is emitted within the LED structure as illustrat
242. ith an excellent signal to noise ratio typically on the or Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Optical Fibers and Optical Fiber Amplifiers 218 Advanced Topics der of 50 dB passage though several amplifier stages is possible be fore signal regeneration is required An optical amplifier can also be made out of a semiconductor laser simply by removing the mirrors on each end This is achieved by put ting on antireflection coatings and tilting the propagation path rela tive to the coated laser facets A semiconductor optical amplifier 100 microns in length can achieve the same gain as an erbium doped opti cal fiber that is several meters long Furthermore the SOA is electri cally pumped by current so no additional pump lasers are needed The usable gain spectrum at 1550 nm is typically larger about 50 nm instead of 30 nm The gain spectrum can be tuned at will by changing the material composition of the SOA With all these addi tional advantages semiconductor lasers have not replaced erbium doped fiber amplifiers This is not due to oversight There are three important differences between these two kinds of optical amplifiers Fig 9 16 Both of the differences lead to a higher contribution to the noise of the SOA compared to the Er doped fiber a
243. ive recombination lifetimes Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Light Emitting Diodes 112 Photonic Devices R302 MQW LED T 295K Ip 500MA RELATIVE OUTPUT POWER 1 4 4 5 4 6 4 7 EMISSION WAVELENGTH pm Figure 6 6 The emission spectrum of a heterostructure LED with a peak emission wavelength near 1600 nm This diode is a laboratory specimen and is not commercially available The active region is approximately one half wavelength in thickness and is surrounded by wider band gap window materials This allows the light to escape with out being absorbed Note that the emission spectrum corresponds more closely to that predicted by our simple model Careful control over impurities has limited the longer wavelength tail The half width of the emission is 60 eV which is significantly narrow er than that measured for the diodes in Figs 6 4 and 6 5 probability of radiative recombination 1 probability for all kinds of recombination Tar n 6 8 Trr There is no straightforward way to estimate the radiative recombi nation time and the nonradiative recombination times from funda mental parameters In particular the nonradiative recombination time usually depends on the density of defects in the material which is not related to fun
244. iven by the relation L nd The argument of de Broglie contains no equations If we substitute the resonance condition of de Broglie into Eq 2 29 remember that R 1 27 we get h meon 2T On mou na nh h mov 2 30 Equation 2 30 says that the electron has a wavelength that is in versely proportional to its momentum This simple equation does not appear in de Broglie s thesis nor does the extension of this result to free electrons or other particles like photons However de Broglie let Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Electrons and Photons Electrons and Photons 23 the cat out the bag so to speak for which he was awarded the Nobel Prize in 1929 He claimed credit in his thesis for the first plausible physical explanation for the condition of stable orbits as proposed by Bohr and Sommerfeld I find that the most interesting part of de Broglie s reasoning to be the notion that because quantization exists there must be an associ ated wave behavior 2 6 Changing Places How Electrons Behave in Solids The energy momentum relationship for an electron is the same as the energy momentum relationship for a baseball But because the elec tron has a wavelength we can represent its behavior by a wavefunc tion W k x
245. jority carrier If this hap pens there will be no contribution to the external current from the absorption of the photon 3 4 2 Quantum Efficiency The ratio of the number of photocarriers to the number of incident photons is called the quantum efficiency If the absorption of every photon resulted in a minority carrier reaching the p n junction the quantum efficiency would be unity If the p n junction is too far away from the point of absorption then the quantum efficiency could be considerably less than unity In a well designed photodiode the rela tionship between the absorption coefficient and the diffusion length is taken into account so that nearly all photocarriers are collected by the p n junction The resulting quantum efficiency is close to unity The photocurrent is just the product of the number of electrons per second n and the charge on each electron q T sheteounwent q Ne so I otocurrent Ne electrons sec 3 23 The optical power is the number of photons per second ny times the energy per photon fiw P aie HNg ho so optical P ng or photons sec 3 24 The quantum efficiency for a photodiode is defined as ng n n In an experiment you will measure J photocurrent ANd Poptica and not n or Ng Using Eas 3 23 and 3 24 Ne Iq I hotocurrent fiw tum effici 1Ng sa 3 25 Quantum efficiency ng a Bie hoe and P optica I photocurrent 4 ue 3 25a Downloaded from Di
246. l modes of the reflecting cavity As the current is raised the gain begins to increase and this results in a concentration of the emitted intensity in the modes where the gain is largest as well as a global increase of the light emitted This process continues until threshold is reached as shown in the top frame At threshold all the gain is concentrated in a few modes only Reproduced with permission from S Naka mura MRS Internet J Nitride Semicond Res 4S1 G1 1 1999 Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Lasers 172 Photonic Devices P K Bhattacharya Semiconductor Optoelectronic Devices Prentice Hall En glewood Cliffs 1994 H C Casey Jr and M B Panish Heterostructure Lasers Academic Press New York 1978 A Yariv Optical Electronics in Modern Communications 5th Edition Oxford University Press New York 1997 Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Lasers Lasers 173 Problems and Exercises 7 1 Build and test the circuit shown in Fig 7 2 Any general purpose transistor with a current 6 gain greater than 50 will be satisfac tory Include a
247. l rights reserved Any use is subject to the Terms of Use as given at the website Photodiodes Photodiodes 55 tor and the air Fresnel s equations show that the reflected light can be reduced to zero however this will occur only at one wavelength of interest To accomplish this the intermediate antireflection layer must have an index of refraction that is equal to the geometric mean of the air and the semiconductor That is Nap V1 3 5 19 3 31 And the thickness must be equal to one quarter the optical wave length in the antireflection layer M Thickness t 3 32 Silicon nitride n 2 is often used for antireflection coatings If we wished to make such a coating on a silicon photodiode to minimize re flection at A 1 um the optimum thickness of the coating would be about 1200 A In practice the coating may be deposited while the diode is operating under illumination at the wavelength of interest so that the optimum thickness can be determined directly Bear in mind that the antireflection coating will reduce reflections only at the de sign wavelength they increase reflection loss at other wavelengths see Fig 3 10 In order to eliminate recombination as an issue the photons must all be absorbed within a minority carrier diffusion length of the junc tion In addition it is equally important to eliminate defects that may act as recombination centers There is higher density of recombina tion centers at the semic
248. laboratory you measure the following current voltage characteristic of a p n diode in the forward direction see figure at the top of the next page a What does the dashed line imply about the relationship be tween current and voltage b Determine the ideality factor of the diode 3 5 As an engineer you are designing a free space optical communi cations link using a red LED the peak wavelength of which is A Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Photodiodes 60 Photonic Devices Piot of Log Current vs Voltage for Clear Diode 1 10 F T 3 T T si _ st Q QO an o z4 OQ wv 104 ef 4 Forward Current in Amps S oo 108 a 40 8 g 4 F i ree l e n i a ji 0 01 0 02 0 03 0 04 0 05 0 06 0 07 0 10 Forward Voltage Volts 0 62 um or 620 nm The LED is capped with a lens so that the light is emitted in a circular cone of 20 as shown in the figure below The LED is emitting 10 watts Your detector is a silicon photodiode with quantum efficiency at A 620 nm 0 75 and di mensions 0 3 cm x 0 3 cm a At 1 meter from the LED what is the optical power intercept ed by the photodiode b What is the responsivity of the photodiode in amps watt c What is the photocurrent generated by the photodiode
249. larger f number In addition the diameter of the point of focused light depends on the f number The smaller the f number the smaller the diameter On the other hand if you want to make a parallel beam of light out of a source that is much bigger than a point you will have better luck with a larger f number lens Figs 10 3 and 10 4 You will run into situations where you will be focusing light on the entrance slit of a spectrometer focusing down to a point or taking the light from the monochromator exit slit and steering it somewhere taking light from a point source and turning it into a parallel beam Most optical measurements involve this kind of manipulation of light beams 10 3 Monochromators and Spectrometers A monochromator and a spectrometer are the same instrument The name depends on whether you are using the instrument to select a certain wavelength of light from a beam containing many wave lengths such as white light in which case it is called a monochroma tor or whether you are trying to tell what wavelengths are present in a beam of light in which case it is called a spectrometer i ee Filament Figure 10 4 A lens with a larger f number that is a smaller aperture will do a better job than a smaller f number lens of producing a parallel beam of light from a point source with a finite size such as a light bulb filament Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlib
250. length division multiplexing sounded like a great idea but no practical solutions were in sight In 1987 laser light amplifiers were rediscovered Using this technique the light wave signals could be amplified optically without having to use detectors or electronic amplifiers Just like optical fibers this am plification is completely independent of the modulation frequency It can also be used over a significant range of wavelengths This just in time solution meant that the operator could install such an amplifi er even under the ocean and it would continue to perform in just the same way even if more wavelengths were added or if the bit rate were upgraded A short history of this discovery has been written by Jeff Hecht see Bibliography This development occurred during the same time as the birth of the internet Telecommunications network companies asked for more and more capacity to meet the demand There are basically two ways to increase capacity 1 Increase the modulation rate of the channel 2 Increase the number of channels Raising the modulation rate means creating optical pulses that are shorter so that more of them can be sent per second However it was immediately discovered that short pulses launched into an optical fiber do not stay short They spread out in time This is called disper Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hi
251. lete periods to traverse the cavity For visible red semiconductor lasers with an output wave length of 600 nm there are about 1000 periods If we suppose that a mode exists at 600 nm that is that an integral number of wave lengths n at 600 nm is equal to the cavity length then the nearest mode will occur when n 1 wavelengths equal the same cavity length To fit n 1 wavelengths in the same physical space you must de crease the wavelength Using the information given in Example 7 3 show that the mode spacing is given by AA 2L p p 1 which is ap proximately 2L p for a semiconductor laser in which the typical mode spacing is about 0 3 nm A He Ne laser which emits visible red light at 632 8 nm has a cav ity that is about one order of magnitude longer than that of a semi Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Experimental Photonics Device Characterization in the Laboratory Experimental Photonics Device Characterization in the Laboratory 273 conductor laser Will the longitudinal modes be spaced closer together or farther apart Spectrometer Resolution Measuring the mode spacing with a spec trometer is a good demonstration of your skill as an experimental sci entist A key parameter in this measurement is the resolution of the spectrometer
252. light will be reflected at the in terface between the LED and the air according to Fresnel s equations Example 6 2 Calculate the reflection coefficient for light exiting a light emitting diode perpendicular to the surface Fresnel s equations give the reflec tion of light from a surface for a given angle of incidence and polariza tion For the case of light incident perpendicular to the surface these equations take on the same simple form independent of the polariza tion n No 0 32 1 n 3 6 6 11 1 no n s N2 From the example above about 70 of the light can exit perpendi cular to the surface However not all the light that reaches the sur face can exit because its angle of incidence is different from 90 For light hitting the surface at an angle Snell s law comes into play refer to Figure 6 8 n sin 6 n sin 6 Snell s Law ni 1 sin sin 6 sin 6 Ng 3 6 The maximum value for 6 is 90 At this condition 1 3 6 0a 16 6 12 sin 6 0 28 Only light that intercepts the planar interface between a semiconduc tor and air with an angle less than 16 can be transmitted from the semiconductor LED into free space The percentage transmitted is given by Fresnel s equation We refer to this light as lying within the escape cone of the structure Any light intercepting the surface at a Downloaded from Digital Engineering Library McGraw Hill ww
253. ligible wavelengths inside the cavity are separated from each other by a constant increment of frequency of the lightwave 2L fr and A n p pe c po 7 14 f Ln Therefore Af Ln where n is the index of refraction For example nmp 3 4 Example 7 3 Find the mode index of laser emission in a cavity of GaInAsP at 1500 nm This is equivalent to finding the number of wavelengths that can fit in a cavity The mode index is equal to 1 when one round trip in the cavity equals one wavelength Assume that the cavity length is 400 um The refractive index of GaInAsP at A 1500 nm is about 3 5 Note that the wavelength inside the cavity is only 1500 3 5 429 nm The cavity length in number of wavelengths A 466 Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Lasers 162 Photonic Devices The mode spacing of the laser cavity is determined by the cavity length As the cavity length is reduced the modes are spaced further and further apart in frequency and also in wavelength The cavity modes tell you which wavelengths energies will be reflected effi ciently in the cavity The gain spectrum of the laser is independent of the cavity modes If you superpose the gain spectrum on the spectrum of cavity modes there should be a region of overlap This is d
254. ll Advanced Topics Direct Modulation of Laser Diodes 8 1 8 2 8 3 Introduction Time Dependent Behavior of Laser Diodes during Current Modulation Summary Bibliography Problems and Exercises Optical Fibers and Optical Fiber Amplifiers 9 1 9 2 9 3 9 4 9 5 9 6 9 7 Introduction Glass Optical Fiber Engineering Waveguiding in Optical Fibers More Capacity Optical Amplifiers Summary Bibliography Problems Contents PartiV Characterizing Photonic Devices in the Laboratory Chapter 10 Measurements in Photonics 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 Introduction Lenses Monochromators and Spectrometers Gratings Mirrors The Spectrometer Monochromator System Lock in Amplifier Chopping Wheel or Chopper Photon Detectors Copyrighted Matenal vii 159 164 168 171 171 173 177 177 179 188 189 190 191 191 194 197 198 204 212 220 221 222 227 227 228 230 231 233 235 237 238 240 Copyrighted Matenal viii Contents 10 10 Curve Tracer 10 11 Summary Bibliography Problems Chapter 11 Experimental Photonics Device Characterization in the Laboratory 11 1 Current Voltage Characteristic of Photodiodes and LEDs 11 2 Detection Using the Lock in Amplifier 11 3 Optical Measurements Using the Monochromator and Spectrometer 11 4 Optical Properties of Light Emitting Diodes 11 5 Device Capacitance 11 6 Characterization of Lasers Index About
255. ll Companies All rights reserved Any use is subject to the Terms of Use as given at the website Optical Fibers and Optical Fiber Amplifiers 206 Advanced Topics sion Dispersion can come from several sources but the result is the same If the pulse spreads out into the bit period then it acts as if noise has been added to the signal The signal needs to be recondi tioned As the modulation rate is increased the distance that a signal can propagate before it must be reconditioned gets shorter Today it is often the case that dispersion and not loss limits the propagation distance in an optical fiber Pulse dispersion in single mode optical fibers can be divided into two categories structural dispersion and polarization mode disper sion Both kinds are important Structural dispersion refers to effects that are frozen into the fiber It can be measured in the factory This makes the effect straightforward to characterize and correct Polar ization mode dispersion changes over time with temperature fluctua tions and changes in stress on the fiber To correct for polarization dispersion continuous monitoring of the fiber performance is required while it is being used The group velocity of an optical pulse is defined as the change in its frequency with respect to its wavevector k dw a 9 13 U where w 2af and k 27 d For light propagating in air v is a con stant c For light traveling in glass v is no longer a cons
256. ll quantum efficiency of the LED is defined as number of photons out _ number of electrons in P oct Popt q 6 26 1E hola hw I 620 Example 6 4 Steady State Analysis of an LED A light emitting diode with a length of 100 um having an emitting stripe width of 1 um is driven by a current step of 50 mA The thick ness of the emission region is 0 1 um Some of the other properties of the diode are listed below see Fig 6 14 I 50 mA 1 35 pm Next 0 1 T 2 x 10 sec B 8 x 10 cm sec np 5 x 10 cm Find the excess carrier density the radiative recombination rate the internal quantum efficiency and the steady state output power of the LED First write down the expression for the steady state electrical pumping rate J 1 BN N np N np qd Tr Next rewrite this equation in terms of the excess carrier density AN N np Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Light Emitting Diodes 128 Photonic Devices emitted light Figure 6 14 A schematic diagram of an edge emitting LED showing some typical phys ical dimensions Tn r J qd B AN np AN BAN BANnp n r This is a quadratic equation for AN 1 J BAN AN Bnp 3 0 Tr qd 1 1 2 J Bnp
257. lled a direct band gap semiconductor GaAs and InP are examples of direct band gap semiconductors If the mini mum energy of the conduction band occurs at a different momentum than the maximum energy on the valence band then the material is known as an indirect band gap semiconductor Si and Ge are exam ples of indirect band gap materials The thermal energy available from the environment can act to break bonding states This action creates vacancies in the occupation of the valence band called holes because the electrons that main tained those bonds are absent The liberated electrons are now in an tibonding states in the conduction band The Boltzmann distribution is used to keep track of the number of electron states that are occu pied in the conduction band as a function of temperature Bibliography C Cercignani Ludwig Boltzmann The Man Who Trusted Atoms New York Oxford Univeristy Press 1998 Boltzmann s ideas about the direction of Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Electrons and Photons Electrons and Photons 31 time and statistical mechanics form the core science of the physics and the technology semiconductor devices These ideas were not accepted by his peers and this rejection may have been a factor in his suicide by hanging in 1
258. llent quantitative account of the diode capacitance throughout the low injection regime in both forward and Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Experimental Photonics Device Characterization in the Laboratory 260 Characterizing Photonic Devices in the Laboratory reverse bias Capacitance measurements are nondestructive They can even be made is a straightforward way on unprocessed semicon ductor wafers yielding the majority carrier type the built in voltage of diodes that could be made in this material the carrier concentra tion and the variation of carrier concentration as a function of depth in the wafer This is a wide range of information for a measurement that takes only a few minutes to make Recommended Equipment 1 Selection of diodes made from different materials both photodi odes and LEDs 2 Device socket 3 Capacitance meter Procedure The operating principles of a capacitance meter were introduced in Section 4 6 The meter gives a direct reading of the device capacitance and contains an internal de power supply that permits direct biasing of the diode In place of the internal supply an external de supply can also be used provided that it is connected in series with the diode and that the voltage drop across the diode is measured
259. ls at room temperature The mobility is a key parameter for charge transport It relates the velocity of charge propagation to the electric field v u cm sect 5 2 Equation 5 2 implies some important assumptions A free electron in a vacuum is accelerated by an electric field which provides a con stant force In Eq 5 2 the application of a constant force produces a constant velocity This kind of relationship is typically used to de scribe resistive or viscous fluid flow Skydivers speak of terminal ve locity in free fall conditions This is the velocity produced by gravita tional acceleration opposed by air resistance In analogy a constant terminal drift velocity of an electric charge is the result of the op posing forces of acceleration by an electric field and the resistive force of the semiconductor material The mobility is the constant of proportionality reducing to a single number the complex movement of electronic charge through the semiconductor material The unusu al units attributed to the mobility are needed to relate electric field to velocity Example 5 1 Determine the transit time of an electron and a hole across a photo conductive detector made of GaAs with an electrode separation of 10 microns and a bias voltage of 1 V The photoconductive device structure is often an interdigitated ar ray as shown in Fig 5 1 First determine the drift velocity v u v 8000 Tror 8 x 108 cm sec fo
260. mann relationship and the other is Planck s equation relating the energy of a photon to the frequency of the light wave associated with the photon Ludwig Boltzmann Boltzmann studied gases and the motion of molecules in gases In a dense gas Boltzmann said the velocities of the molecules are statisti cally distributed about the average velocity vo 0 Since the Law of Large Numbers in statistics says that all distributions tend toward a Gaussian or normal distribution Boltzmann started from this point too The probability of finding a particular velocity v is given by a Gaussian distribution v4 vo Priv v A e 2 2 1 where Uy means the average velocity 0 and v means the average of the square of the velocity Even though Uo 0 v is definitely not equal to zero This is the spread of the distribution Remember that Exinetic mv Ftv Priv v1 A e mv 4m v spread in the energy E Priv v A e 2 2 From Brownian motion studies more than a century earlier as well as mechanical equivalent of heat studies energy is proportional to temperature That is E constant T and Pr v v Pr E E A i e E constant sP Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Electrons and Photons Electrons and
261. many impor tant applications It is a certainty This article will bring you up to date on a new important field Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Light Emitting Diodes Light Emitting Diodes 139 Problems 6 1 In Fig 6 4 we showed the emission spectrum of a red LED We also measured the intensity of visible light emission as a func tion of the applied voltage across the LED This result is shown in the figure below 108 10 10 High Brightness LED red light w clear housing on 1 40 V dark current 0 016 pA light sensitive VISIBLE LIGHT OUTPUT au 10 107 EE ae aeRO CMe E E 0 0 0 5 1 0 1 5 2 0 2 5 V volts a Calculate the photon energy corresponding to the emission peak b Note from the experimental result obtained in the figure that the first visible emission is seen when the forward voltage across the diode is 1 4 V Given that the light is produced by the recombination of a single electron that can gain at most 1 4 eV from the applied voltage explain how it is possible to obtain emission of photons with the energy measured in a c What would you expect to see if you repeated the voltage light curve measurement at a lower temperature say 77 K 6 2 What are the two most important reasons why eff
262. mes which lead is the an ode and which lead is the cathode of your diodes In forward bias the anode is biased positive with respect to the cathode 10 11 Summary Basic optoelectronic device characterization is easy to learn but it takes skill and patience to make high precision measurements You will be able to note your own progress in setting up experiments and obtaining measurements as you use this book Although experience is a great teacher you can often learn even more by reading the owner s manual of your instruments carefully There you will often find en lightening details of the principles of operation and suggested experi mental set up schematic diagrams A critical detail in most experiments is mounting the sample so that it can be characterized The most important concern is stabilizing the device so that it does not move during the measurement The time you spend initially to mount a device socket so that it can be attached to a x y z manipulator will pay back big dividends in the validity of your measurements and also in reduced mechanical strain on the device electrical leads Bibliography R F Pierret Semiconductor Device Fundamentals Reading Addison Wes ley 1996 This book is rich in techniques and set ups for experimental characterization of electronic devices J Wilson and J Hawkes Optoelectronics 3rd Edition London Prentice Hall Europe 1998 E Hecht Optics 2nd edition Reading Addison Wesley 198
263. mination i kd L E Eo L L _j Figure 3 4 Measured current voltage charateristic of a real photodiode a Forward bias b Reverse bias in the dark and under illumination ue In practice the measured forward current is many orders of mag nitude less than Eq 3 13 predicts This difference is usually modeled by assuming an ideality factor n or fudge factor in the relationship between current and voltage I A et T 1 gt A e9V kT _ 1 where n is greater than 1 3 16 The ideality factor for a perfect diode is 1 This means that there is perfect transport of electrons and holes across the junction When n gt Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Photodiodes 46 Photonic Devices 1 it means that carriers are getting lost due to recombination at traps or that there are substantial ohmic losses in the contacts This is bad news of course but more so for light emitting diodes and lasers where large current densities are present than for photodiodes In Fig 3 5 we show the current voltage characteristic of a p n light emitting diode The I V characteristic obeys the same laws as that for 1078 T T i aN i A g i R302 4073 MQW LED 7 z i qV f E O Ip aexpl A i P nkT n 1 38 i
264. mission artifact for something real 10 5 Mirrors The mirrors that we use for everyday applications are sheets of glass coated with metal The reflecting surface is protected by the glass from possible damage during use such as scratching etc There are two reflections from such a mirror One comes from the metal surface and the other which is somewhat weaker comes from the front sur face of the glass The mirrors used in optics experiments including the mirrors inside a monochromator are front surface mirrors That is the metal usually aluminum is coated on the front surface of the glass This procedure eliminates the second reflection Front coating comes at the price of having an exposed metal surface that is soft eas ily scratched and difficult to clean To avoid leaving your fingerprints Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website 234 Measurements in Photonics Characterizing Photonic Devices in the Laboratory Replicas made from classically ruled masters measured under near Littrow conditions with 8 between incident and diffracted beams telative to reflectance of aluminum Polarized _l to grooves S Plane 100 i I to grooves P Plane Polarized BLAZE ANGLE 70 J BLAZE WAVELENGTH zL 300 nm 60
265. modes Only the few that happen to occur in the gain spectrum of the semiconductor material will participate in the necessary positive pho ton feedback Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Lasers 164 Photonic Devices 7 6 Threshold Going Over the Edge You are sitting at the lab bench The laser is mounted in a test socket and you are ready to increase the forward current The question you would really like to answer before beginning the test is How much current will I have to supply in order for the laser to reach threshold The answer is that the threshold current is attained when the num ber of electrons per second being injected into the diode is equal to the threshold population density taking into account that some of the electrons will be lost to recombination before a suitable population in version is built up The number of electrons injected per second per square cm into the diode is just the current density divided by the electronic charge J q If we consider the rate of electrons per second in the recombination re gion we need to divide this expression by the thickness Aw in Figs 7 8 and 7 9 of the recombination region J Pumping rate a electrons sec t cm 7 15 What goes in must come out so to speak and so the
266. mplifier The first important factor has to do with coupling loss between the semiconductor optical amplifier and an optical fiber The mode diame ter of the optical fiber is about 9 microns The mode diameter of a semiconductor laser is much smaller about 1 micron The mode mis match can be appreciated by comparing the ratio of the area of each mode 80 to 1 This mismatch in size leads to coupling losses going from the fiber to the SOA and from the SOA to the fiber Special mode adapters are used to reduce the mode size mismatch and antireflec tion coatings are used to eliminate Fresnel reflection losses between Figure 9 16 An erbium doped fiber amplifier on the left and a semiconductor optical amplifier on the right Both components shown here are made by the same company The semiconductor optical amplifier is much more compact JDS Uniphase repro duced by permission Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Optical Fibers and Optical Fiber Amplifiers Optical Fibers and Optical Flber Amplifiers 219 the semiconductor with an index of refraction of about 3 5 and the op tical fiber having an index of refraction of 1 45 In a typical SOA the coupling losses are about 2 dB In the case of an Er doped fiber the losses due to coupling are much
267. n 6 I s to 6 s or 9 2 lt C lt 15 2 in steps of 1 that is 9 2 11 2 13 2 and 15 2 These are the four states as indicated by the letter A Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Optical Fibers and Optical Fiber Amplifiers Optical Fibers and Optical Flber Amplifiers 215 Many rare earth elements can be dissolved in glass to make optical amplifiers Some common examples are neodymium praseodymium holmium and erbium However the laser transition in erbium doped glass occurs at a wavelength that is very close to the wavelength of minimum attenuation of glass fibers and this gives erbium special importance The relatively long spontaneous lifetime of the 13 2 state compared to other transitions in this schematic means that it is possible to build up a substantial electron population in this state and this feature fa cilitates the population inversion that is required for laser action As indicated in Fig 9 14 this state is not characterized by a single well defined energy level but rather a distribution of energy levels result ing from variations in the local environment of glass molecules that surround the erbium ions This distribution is advantageous because it makes amplification possible over a relatively large band of wave lengths
268. n band Because the minimum of the conduction band and the maximum of the valence band oc cur at the same value of momentum this is a direct energy gap GaAs InP GalnAsP and GaN are examples of direct gap semiconductors This splitting is shown symbolically in Fig 2 9 In Eqs 2 10 and 2 11 we show how the splitting occurs in the real band structures of GaAs and Ge The crystalline potential is the direct expression of the atoms that make up the material So the difference between direct band gap and indirect band gap materials is a matter of chemistry The band gap expresses the difference in energy between an electron in a bonding state and an electron in an antibonding state In the anti Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Electrons and Photons 28 Introductory Concepts bonding state the electron is free to carry electrical current So this up per band the antibonding state is also called the conduction band The bonding state or lower band is also called the valence band An electron that occupies a state at the minimum energy of the con duction band can make a transition to the top of the valence band presuming this state is not already occupied These two states have a negligible difference in momentum Energy is conserved by the emis s
269. n be manipulated and in particular how the carrier lifetime can be increased thereby increasing the sensitivity of the photodetec tor The density of excited carriers is determined by the absorption rate of photons and the carrier lifetime n from And the photocurrent is given by I n fr q q Tiransit Transit We take the absorption rate of photons to be equal to the generation Conduction lt _ O DN se oo Fermi Level Valence Band Recombination Centers Figure 5 14 Schematic energy level diagram for a photoconductor with one type of re combination level Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Photoconductivity Photoconductivity 93 rate of electrons f where f has units of cm sect In the steady state the generation rate and the recombination rate must be the same The treatment that follows is based on the description of sensitiza tion given by Rose in Concepts in Photoconductivity see Bibliogra phy In Fig 5 14 we show an energy level diagram for a typical pho toconductor material such as CdS A recombination level is formed by addition of a single type of impu rity that forms a level near the center of the band gap The Fermi lev el will fall in the center of these levels as shown in th
270. n efficiency of LEDs is motivated in large part by the challenge of demonstrating a light source more efficient than a tungsten light bulb the overall power ef ficiency of which is about 10 There is an active area of research to improve the performance of LEDs by modifying the matrix element defined as the probability that a radiative transition will occur in Eq 6 3 in a way that increases the radiative recombination rate The improvement in the quantum efficiency by such a change can be esti mated from Eq 6 8 The improvement is achieved by building a mi croresonant cavity around the emitting region The dimensions of the cavity are chosen to be a fixed multiple of the light for which one Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Light Emitting Diodes 120 Photonic Devices Figure 6 11 Roughening the surface of an LED in order to improve external emission efficiency Glass spheres are sprinkled on the surface The spheres are used as a mask for sandblasting the surface Taken from I Schnitzer et al Applied Physics Letters 63 2174 1993 Reproduced by permission from the American Institute of Physics would like to enhance the emission probability The microcavity effect was first discussed by Purcell in the context of decay of radioactive atoms Th
271. n hole pair is created The Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Photodiodes Photodiodes 51 80 T T T T T 60t 5 40F A 5 Oo D ko 3 t 20 4 fe O 5 Gap 47INo sgAs InP S T 295K gt 10 4 c 2 F a 5 absorption edge o r of Si filter 4 E B 4b fom T E Oo LW ak 1 4 i L L i f 1 0 1 2 1 4 1 6 1 8 Optical Wavelength microns Figure 3 7 Measured absorption spectrum of a GalInAs photodiode at room tempera ture IX xt AX AX Figure 3 8 Light of intensity I x is incident on an absorbing medium such as a photodi ode At position x Ax the intensity is less because some photons have been absorbed The number of photons absorbed is proportional to the number of photons present Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Photodiodes 52 Photonic Devices minority carrier of this pair will diffuse toward the p n junction If the p n junction is located more than a minority carrier diffusion length from the point of absorption there is a good chance that the minority carrier will recombine with a ma
272. n of momentum So a road map that summarizes the possible states of electron energy and momen tum is particularly useful All band structures can be divided into two groups There are two bands that form the band gap If the minimum energy of the upper band occurs at the same value of momentum as the maximum energy of the lower band the corresponding material has a direct band gap Such a band structure is shown in Fig 2 9 For all other situations the corresponding material has an indirect band gap Whether a material has a direct band gap or an indirect band gap de pends entirely on the crystalline potential that splits apart the bands Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Electrons and Photons Electrons and Photons 27 Figure 2 10 In this sequence of calculations we show how the periodic potential modifies the energy momentum relationship for a real three dimensional semiconductor GaAs In the first frame you can clearly see the parabolic relationship between energy on the verti cal axis and momentum on the horizontal axis In succeeding frames we add the periodic potential due to the actual atoms This causes the crossings to separate By the time we arrive at GaAs there is a band gap between the valence band and the conductio
273. n which the pulse width broadens as it propagates down the fiber also become more important At 20 GHz and above it is disper sion and not loss that will determine the maximum transmission dis tance before the signal needs to be reconditioned One solution to the dispersion problem is to send more information using multiple wave lengths of light for each channel rather than raising the bit rate A number of problems associated with this approach appear the need for separate receivers to detect and to recondition each signal chan nel the need to replace each such repeater unit every time the bit rate is changed and intractably large and complicated switching and sig nal processing circuits In 1986 an idea that was 25 years old was re discovered the all optical amplifier In an instant all of these prob lems vanished as it was demonstrated that the laser remember that laser stands for Light Amplification by Stimulated Emission of Radia tion was capable of amplifying simultaneously a signal consisting of many wavelengths without having to do any detection or demodula Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Optical Fibers and Optical Fiber Amplifiers 212 Advanced Topics tion that is one simple device could replace literally thousands of dif ferent c
274. ndary condition at x An x GLTe Ae Be C GLT If this equation is true A must be zero As a result C GLT 3 9 However nothing is learned about B Next apply the boundary condi tion for An x 0 An x 0 0 Bee GLT n etVA F 1 B n e9VA kT 1 GLT 3 10 The solution for An x is written An x eton etVA 1 GLT GLTe 3 11 B C The diffusion current in the photodiode is calculated from the diffu sion equation D a nle VAT 1 Gy7 3 12 e d J gD Ano Lo Dq The extra factor of 1 comes from a change of variable from x to x The derivative is evaluated at x 0 because at that point all the cur rent is carried by diffusion Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Photodiodes 42 Photonic Devices The same procedure can be followed to calculate the current carried by holes The total current is obtained by adding together the two ex pressions In practice it is almost always the case that the diode is doped much more heavily on one side than the other Low doping on one side of a photodiode is necessary to keep the capacitance low and the breakdown voltage suitably large In this case we will assume that n gt pp Then it follows that n
275. ndex difference of 1 is about 0 2 This corresponds to an angle of about 2 x 11 or 22 A typ ical optical fiber for telecommunications has a numerical aperture of 0 1 This implies a much smaller index step than 1 Example 9 1 Calculate the index difference between the core and the cladding of a fiber with an NA of 0 1 We will solve this in two ways First we will make an estimate sin 6 Vn n2 NA 0 1 n n2 0 01 ny nan n 0 01 A n Ng 0 01 0 01 _ 0 01 A Ni Nng 2 90 0 003448 In this case we assume that n na 1 45 Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Optical Fibers and Optical Fiber Amplifiers Optical Fibers and Optical Flber Amplifiers 201 cladding Figure 9 8 The angle of aperture of the fiber depends on the ratio of ng to n In the second case we will evaluate the approximation made above taking the index of the cladding to be 1 45 A n Ng 0 01 A n 2na 2na no A2 2AN3 0 01 2n V 4n2 0 04 A 9 1 45 1 453445 0 003444 The index difference is less much less the 1 The accuracy of the ap proximation is better than three significant figures The propagation of light in an optical fiber is completely and accu rately described by
276. near array calibrated in wavelength instead of a single photodiode detector How could you use this to make the measurement of the mode spectrum Would this lead to simplifications in the measurement Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Experimental Photonics Device Characterization in the Laboratory 276 Characterizing Photonic Devices in the Laboratory 7 as GaAs lose Dyke intSs Satsa f EI rein l 2 Smm dnan PIN ee Chapa pe Oa Gieperte Tue Lech ej ant pnt dinke wt an fee red oh hat TA 18 63 mV fone mr hh oe 593A 13 05 mV Meath nit i Tie Fi 413 IE atig Thee 33 9 0 49 han ned a Land au Btu 9 93 sguv yat mhe S S alma yaa Go FAST Stan F0 Bia oe fA At hina Mi pert 13 ad how PO feros oe Figure 11 10 Page from a student s lab book showing measurement of the mode spec trum of an infrared GaAs AlGaAs laser using a 0 25 m spectrometer Note the setup and the measurement of laser threshold You can follow the procedure used by the stu dent Julie O Cross in successively narrowing the slit width and homing in on the peak Courtesy of J O Cross reprduced by permission Downloaded from Digital Engineering Library McGraw Hill www digitalen
277. near fit to determine an ex pression for the dispersion as a function of wavelength around 1550 nm c Calculate the total wavelength broadening due to laser line width plus modulation rate at modulation rates of at 2 5 Gbit sec 10 Gbit sec and 40 Gbit sec d Calculate the time needed for the pulse broadening due to dispersion to cause overlap of adjacent bits at 2 5 Gbit sec 10 Gbit sec and 40 Gbit sec This occurs when the combined width at half maximum of the two broadened pulses is equal to 1 bit period or when the width of 1 pulse at half maximum is broadened by 50 e Determine the dispersion limited transmission distance at these three bit rates Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Optical Fibers and Optical Fiber Amplifiers Optical Fibers and Optical Flber Amplifiers 223 9 3 Below are some of the specifications for Samsung single mode optical fiber Attenuation 1310 nm 0 35 dB km 1550 nm 0 21 dB km Attenuation versus Wavelength The attenuation for the wavelength region 1285 1330 nm does not exceed the attenuation at 1310 nm by more than 0 03 dB km The attenuation for the wavelength region 1525 1575 nm does not exceed the attenuation at 1550 nm by more than 0 03 dB km Dispersion 1285 1330 nm 3 5 ps nm km 1550 nm 18 ps nm km
278. nother way of expressing its focusing angle for parallel light This is also known as the aperture of the lens a Determine this angle for the following cases f 2 f 5 6 and f 8 b Make a graph showing the angle of aperture as a function of f number Paste a copy of this graph in your lab book 10 3 A beam of parallel light is incident from the left as shown in the figure below Your objective is to use a lens to completely illumi Screen Lens h 6 cm 2 cm Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Measurements in Photonics Measurements in Photonics 243 nate the screen behind the slit You are free to place the lens wherever you wish For simplicity consider this to be a one di mensional problem Show using diagrams how much of the screen is illuminated when the lens is a f 2 b 4 c 8 What is the f number that exactly fills the screen Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Measurements in Photonics inglibrary com its res Copyright 2004 TI U n at the website Any use is subject to th
279. ns In the LED the photons are all generated in a narrow region at the p n junction If we can understand the photodiode response then the LED behavior follows as a special case In almost every case the response time of a photodiode or an LED will be determined by the product of its capacitance and series resist ance Photodiodes are operated in reverse bias and the diode capaci tance in reverse bias is much less than the diode capacitance in for ward bias Therefore photodiodes tend to operate much faster than LEDs of the same size 61 Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Electrical Response Time of Diodes 62 Photonic Devices 4 2 Modeling the Response Time of Photodiodes The response time of a photodiode is determined by three different factors 1 The time required for minority carriers created by the absorption of a photon to diffuse to the p n junction 2 The time required for these carriers to drift across the depletion re gion 3 The time required for the external circuit to supply the necessary majority carriers to balance the movement of minority carriers so that charge neutrality is maintained In almost every case the response time will be determined by the third factor The rate at which the external circuit supplies the neces
280. ns having an energy greater than the band gap E 1 43 eV at room tempera ture For photons that are less energetic than the band gap energy a is three orders of magnitude smaller When the absorption coefficient is a positive number the intensity of the beam decreases as the light propagates through the material However suppose that a could be made to be negative what would be the result Excercise 7 1 A beam of light of monochromatic photons of energy 1 5 eV strikes the surface of GaAs at normal incidence What percentage of the original photon beam penetrates 1 um beneath the surface What percentage penetrates 10 um beneath the surface Solution There are only two things that can happen to photons incident on an interface Either they are reflected or transmitted Some of the trans mitted photons are subsequently absorbed To answer these questions you need to find first of all the percentage of light that is transmitted and then find out what fraction of those photons are absorbed The percentage of light reflected is calculated from Fresnel s equa tion at normal incidence 2 2 E n 1 2 2 4 0 25 n 1 4 4 T 1 R 0 75 So 75 of the light is transmitted and J 0 75 x in cident intensity To calculate the intensity I Ige I I e704 em 1 x I 1 e for 1 wm penetration so I 1 0 37 0 75 0 37 0 28 x incident intensity For 10 um penetration I 0 75 4 6 10 3 4 10 gt x incident
281. nt and voltage at which you can first see light emission b Measure the Light Current Characteristic Using the lock in measure the light current characteristic Increase the current until output sat uration is reached Continue to raise the current 10 beyond this lim it What do you observe Is this reversible c Measure the Output Spectrum Using the lock in amplifier and the spectrometer measure the output spectrum of your LED Determine the peak energy of emission and spectral half width Repeat this measurement at different values of drive current Demonstrate sec Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Experimental Photonics Device Characterization in the Laboratory Experimental Photonics Device Characterization in the Laboratory 259 ond order transmission by setting the spectrometer at a wavelength twice as long as that corresponding to the peak emission and repeat ing a measurement of the emission spectrum d Measure the Photoresponse of Your Light Emitting Diodes You will probably want to experiment with various gratings to see which one works best The sensitive area of these diodes is quite a bit smaller than that of the photodetectors about a factor of 100 so the signal is likely to be smaller Taking this into account how do the
282. nt involved but remains Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Photoconductivity Photoconductivity 85 much less than 1 Since photon absorption by an impurity occurs in the physical vicinity of the impurity the quantum efficiency of this kind of photoconductive detector is usually much less than unity This may be an acceptable trade off for the access to spectral response at a particular photon energy and the technological advantage of working with a well known host material like silicon On the other hand the photoconductivity continues until an electron is trapped on the ion ized center This can be a long time Consequently the gain which is given by the ratio of the time to trap an electron on the center divided by the electron transit time can be quite large There are even some kinds of devices that exhibit persistent photoconductivity This means that one exposure to light raises the conductivity of the materi al indefinitely for hours or even days The engineering of photoconductivity is based on the intentional in troduction of impurity atoms or molecules in order to modify the life time of the photoexcited charge carriers There are a number of varia tions on this theme and we will discuss here only two of the important applications
283. nts in Photonics 238 Characterizing Photonic Devices in the Laboratory LED C Detector wo r Phase Lock Differential Loop Amplifier Low Pass Filter Figure 10 9 The lock in amplifier circuit combines a signal A cos w t f with a refer ence B cos w t to generate outputs at the sum and difference of the frequencies The higher frequency output is eliminated by the low pass filter and the remainder is a de signal since w The phase difference between reference and signal can be adjusted to zero and the low pass filter eliminates the sum frequency term The resulting signal is dc since w 10 8 Chopping Wheel or Chopper This is essentially an electric fan It is smaller and turns faster with a rotation rate up to about 5 000 rpm The modulation frequency of he light depends on the rotation rate of the chopping blade and the num ber of slots in the blade The chopping wheel is a blade whose slots are arranged about the circumference so that the openings are exactly as wide as the closed parts Fig 10 10 The lock in amplifier Fig 10 11 looks for signals at the input that have the same frequency as the chopping wheel and the same phase This is what makes a lock in amplifier work like a strobe When the signal is present the lock in amplifies it but when the signal is ab Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The
284. number can always be calculated if you know the width of the gain spectrum the cavity length and the wavelength Because the gain of semiconductor materials is so large lasing action often occurs at several modes simultaneously If you were trying to design an audio oscillator you would call this effect harmonic distor tion In laser design one often tries to design for single mode oscilla tion also It is easy to see that this could be achieved by making the cavity much more wavelength selective so that only one mode is pres ent in the gain spectrum At this point we have assembled all the elements of a laser gain population inversion and a resonant cavity for feedback It remains only to determine the level of current injection into the diode that is required in order to achieve laser action Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Lasers Lasers 163 Gain spectrum Frequency Cavity reflectivity Frequency Reflectivity gain Frequency Figure 7 10 The resonant wavelengths of a laser cavity are those select wavelengths for which a standing wave can be established between the two mirrors at either end of the cavity The special wavelengths are called modes and are equally spaced in fre quency There are many such
285. o the upper laser level N The laser transition ex ists because the optical transition lifetime for spontaneous transitions to the ground state is relatively long compared with the thermalization time between adjacent levels stimulated emission introduces a minimum of additional noise just as the original inventors of the maser discovered when operated un der high gain conditions The erbium doped glass laser can be represented by a three level system that is diagrammed in Fig 9 14 Erbium doping of the glass is rather dilute much less than a percent In order for the ions to emit light efficiently the individual ions need to be completely surrounded by glass molecules so that they are well isolated each other Under these conditions the local electric field of the glass molecules will modify the levels of the erbium ions The notation for these levels was developed by specialists in atomic spectroscopy These states are identified as B In this scheme B refers to the total angular mo mentum or shell of the electrons In this case it is indicated by the letter J correspon ding to an angular momentum of 6 S 0 P 1 D 2 F 3 G 4 H 5 and I 6 Each electron has its own magnetic moment and the term A gives the number of possi ble combinations of the magnetic moments of the electrons in the sixth shell This is equal to 2s 1 4 so s is equal to 3 2 The term C identifies the actual state involved C can vary betwee
286. o threshold The space of time between the build up of the carrier concentration Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Direct Modulation of Laser Diodes 184 Advanced Topics caused by the current step and the emission of light is shown schemat ically in Fig 8 1 What happens to the carriers during this time They are filling hole and electron states near the band gap Carriers that continue to arrive must seek unoccupied states at higher energy We call this effect band filling Electrons and holes in these higher energy states will have a shorter lifetime and thus a higher recombination rate than electrons and holes near the band edge Spontaneous optical re combination will be dominated by these higher energy states seeding stimulated emission at photon energies above the band gap energy The onset of stimulated emission will deplete this excess carrier con centration proceeding from the higher energy states to the band edge states in an orderly progression The energy of the emitted photons re flects this process starting at higher energy and progressing toward the band gap energy This effect is called wavelength chirp The degree of chirp increases as the laser is driven over the threshold If the wave length shift is large enough to modulate the las
287. oaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Measurements in Photonics 240 Characterizing Photonic Devices in the Laboratory 10 9 Photon Detectors There is a choice of device for light detection photodiodes charge coupled devices CCDs photomultiplier tubes etc We will limit our discussion to photodiode detectors the most widely used devices for detecting light Photodiode detector circuits can be used in two ways 1 Photovoltaic mode This means that you plug the leads into a volt meter such as the lock in amplifier and measure the voltage de veloped by absorbing photons No power supply is needed 2 Photocurrent mode In this case you connect the photodiode so that it is reverse biased in a circuit with a load resistor The volt age drop across the load resistor is then measured by a voltmeter The photocurrent is the voltage divided by the load resistance Fig 10 12 You choose the load resistor It must be less than the input impedance of the lock in amplifier or 100 MQ On the oth er hand if you are working at f 1000 Hz the R C product must be smaller than 1 f If C 1000pF then Rz must be less than 100 kQ However the larger Rz the larger the signal at the lock in This is the case because the photodiode drives a certain current through th
288. of Light The intensity of the emitted light is proportional to the number of states in the conduction band that are occupied by an electron multi plied by the number of empty states in the valence band with the same momentum This can be expressed as an integral over all possi ble transition energies I fiw J energy density of states at E hia x probability that a conduction band state is occupied x probability that a valence band state is unoccupied x probability that a rediative transition will occur dE 6 3 The energy density of states is the total number of states between E and E AE The form of the density of states can be directly deter mined from the electronic bandstructure There are two electron states for each value of momentum fik The energy of an electron near the edge of the conduction band can be expressed as Hk E k Eg 6 4 2m In three dimensions the number of k states having energy less than E k is the volume of k space That is one electron spin up plus one electron spin down equals two electrons times the volume in k Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Light Emitting Diodes 108 Photonic Devices space 2 nk The number of k states between k and k dk is the surface area d dk E k 87k dk
289. of Use as given at the website Light Emitting Diodes 106 Photonic Devices constant while the nonradiative rate increases By forming a simple ratio between the linear extrapolation of the light intensity and the actual light intensity it is possible to deduce the ratio of the radiative and nonradiative recombination rates at a given injection current There are only two possibilities for recombination either it is radia tive that is a photon is emitted or it is not Thus there are two com ponents to the recombination time a radiative time and a nonradia tive time 1 1 1 Ttotal Tradiative Tnonradiative There is a contest between these two recombination channels If the radiative recombination time is much shorter than the nonradiative recombination time most of the recombination will involve the emis sion of photons This is the case for GaAs InP GaN and other direct band gap semiconductors On the other hand if the radiative recombi nation time is much longer than the nonradiative recombination time then carrier recombination will produce very little light This is the case for Si Ge and other indirect band gap semiconductors Example 6 1 In Si Tyadiative 10 sec gt Tponradiative 1077 sec and Ttotal 10 8 10 7 108 107 1 0001 x 10 Total 0 999 x 1077 sec So most recombination takes place nonradiatively Light emission from a light emitting diodes is the result of radiative recomb
290. of the electric field The response time due to drift current does not depend on the size of the diode but it can depend on the bias voltage because an increase in the bias voltage will make the depletion region wider The speed of transport by diffusion cannot be compared directly to the speed of transport by drift current since these two mechanisms do not have the same dependence on distance Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Electrical Response Time of Diodes 66 Photonic Devices Laser pulse duration 140 psec Photodiode diffusion time 180 psec Gao 47lNg 53As InP heterophotodiode Vg 14 V Figure 4 2 The measured time response for a GaInAs photodiode The intrinsic re sponse time for the photodiode is about 200 psec as measured by the fall time in this oscillograph The response time is determined mostly by the diffusion of minority carri ers and by the resistance capacitance product of the diode which is discussed in the next section 4 5 The Resistance Capacitance Response Time The extrinsic response is determined by the time is takes for the pho todiode to charge up the first stage of the amplifier that it is driving This time is simply the product of the capacitance of the photodiode times the input resistance of th
291. om the device is focused into the instrument and the grating is fully illuminated lead ing to maximum usage of available light This happens when the f number of the lens you choose to focus light into the monochromator matches the f number of the monochromator 10 4 Gratings Gratings are made by scribing a series of closely spaced lines on a sheet of glass To make it easy to do the scribing the glass is soft but as a result very easily scratched When the grating is doing its job in a spectrometer it is completely illuminated or filled That means that each part of the grating is contributing an equal part to the total sig nal So it is easy to understand that if there is a piece of dust a spot or even a small scratch in one part of the grating the basic perform ance will not be affected For example if you are looking at the grating and an eyelash falls out and lands on the grating leave it alone Above all do not ever try any of the following touch the grating wipe the grating with tissue rinse the grating with water or alcohol blow on the grating or rub the grating with your finger or any other instrument All of these actions affect the entire grating and thus may ruin it forever You can easily scratch a grating by rubbing it with your finger or a piece of lens tissue and you will scratch the grating over a sizable fraction of it surface A grating is characterized by two numbers one is the number of Downloaded from D
292. omponents detectors transistors power supplies lasers and modulators Needless to say the introduction of laser amplifier tech nology caused a quantum leap in the growth of telecommunications networks and was instrumental in enabling the worldwide installa tion of the Internet 9 6 Optical Amplifiers The laser was originally proposed as a maser with the M standing for microwave It was first used as a microwave amplifier for radio as tronomy and was based on atomic transitions in ammonia gas The big advantage of the maser amplifier was its lower noise compared to conventional electronic amplification via vacuum tubes Shortly af terward it was shown that the maser could be made to work at short er wavelengths in the optical regime The first solid state lasers were made by introducing isolated impurities in a transparent host for ex ample chromium in aluminum oxide known as ruby In order to function these lasers needed to be pumped by an external light source typically a flashlamp With the addition of mirrors to form an optical cavity the amplifier could be made into a source of light rather than just an amplifier About this time in 1961 Elias Snitzer now a professor emeritus at Rutgers introduced the idea of putting rare earth ions like erbium in a glass host and developed an optical ampli fier He showed that a large number of these rare earth ions could be used each having a characteristic wavelength On
293. on that need to be considered What are the physical sources of these influences Why might this be the case 11 2 Detection Using the Lock in Amplifier Objectives In these experiments we provide an introduction to lock in amplifier operation and observe the optical absorption properties of various semiconductors Background Your experiments in the laboratory will be made in the presence of many sources of noise You would probably like to take data with the room lights on so you can see what is going on However you have al ready observed in Section 11 1 that stray light from a lamp changes the photocurrent Stray light is a source of noise There is also electri cal noise to deal with The ac line frequency varies widely The lock in amplifier is designed to handle these problems When used correctly you can reduce the level of noise by many orders of magnitude The principles of lock in operation are explained in Section 10 7 You need to modulate your signal at a frequency that is different from that where noise occurs This is called narrow band amplification De pending on the filter characteristics and on the quality of the modula Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Experimental Photonics Device Characterization in the Laboratory 250 Cha
294. onductor air interface The effect of surface recombination can be mitigated by passivation of the surface This can be accomplished by the same coating used to reduce reflections The manufacture of silicon and GaAs has reached such a state of ex cellence that the presence of defects can be ignored for photodiode ap plications In addition it is straightforward to design the photodiode device so that all of the photons can be collected However because of the long absorption length for photons in sili con photocarriers will have to diffuse to the junction over substantial distances This feature means that high quantum efficiency can be achieved in silicon photodiodes at the cost of degradation in the speed of response This trade off is not present in direct band gap photodi odes like GaAs because the speed of response is usually not limited by photocarrier diffusion This discussion of antireflection coatings is pertinent because it ap plies to the way most commercial photodiodes are manufactured How ever this is not the only way to achieve lower reflection losses The flat shiny surface of a typical semiconductor like silicon or InP is a low Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Photodiodes 56 Photonic Devices Antireflection coated photodio
295. opening or about 1 mm The grating has 600 grooves per millime ter and so 600 periods of the grating participate in dispersing the light It is this dispersion that determines the resolution of the grat ing that is the spatial separation of different wavelengths Although this may sound like a large number of periods a grating having a size of 10 cm has 60 000 periods In this case you would be using only 1 of the resolving power of the grating In other words the diagram shown in Fig 11 9 illustrates that a nondivergent laser beam may sample only a small percentage of the grating area This is equivalent to using a very small grating with a corresponding degradation of resolution If you look at this situation from another point of view which we have already discussed in Chapter 10 the grating is not filled by the light If we can devise a way to fill the grating we will in a very real Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Experimental Photonics Device Characterization in the Laboratory 274 Characterizing Photonic Devices in the Laboratory gt am Exit Slit Mirrors Ta Entrance Slit Grating Laser Beam Figure 11 9 Path of a collimated laser beam through a spectrometer A laser pointer and He Ne lasers are exampl
296. opyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Experimental Photonics Device Characterization in the Laboratory SAFETY CONSIDERATIONS WSafety considerations for laser diodes Mistubisht laser diodes are all put given operating aging tests at high temperature and have high reliability in order to keep this reliability take care with the following points Maximum rating Laser is a semiconductor device which has high current density and high optical density of about 2 5umX0 7um near field ML4000 series Degradation of devices should be considered more carefully than silicon semi conductor devices Therefore the absolute maximum ratings should never be exceeded even for a short time Surge current and heat radiation in operating laser diodes sufficient surge protection measures are required Surge current is easily pro duced during power switching and output adjustment Referring to the example of connections for laser opera tion and make sure that sufficient care is taken The beam emitted from the laser diode ts invisibie and may be harmful to the human eye Avoid any possibility of look ing into the laser package or the collimated beam along its optical axis when the device ia in operation Operation over the maximum ratings may cause failure of the device or a safety hazard Power supplies for the de vice must be such that the maximum r
297. or completeness of any infor mation published herein and neither McGraw Hill nor its authors shall be responsi ble for any errors omissions or damages arising out of use of this information This work is published with the understanding that McGraw Hill and its authors are supplying information but are not attempting to render engineering or other pro fessional services If such services are required the assistance of an appropriate professional should be sought Copyrighted Material Copyrighted Material Preface Chapter 1 Chapter 2 Chapter 3 Chapter 4 Contents ix PartI Introductory Concepts Introduction 1 Electrons and Photons 7 2 1 Introduction 7 2 2 The Fundamental Relationships 8 2 3 Properties of Photons 10 2 4 Properties of Electrons 14 2 5 Some History 20 2 6 Changing Places How Electrons Behave in Solids 23 2 7 Summary 30 Bibliography 30 Problems 32 Part Il Photonic Devices Photodiodes 37 3 1 Introduction 37 3 2 The Current Voltage Equation for Photodiodes 38 3 3 Photodiode Operation The Photocurrent Mode 47 and the Photovoltage Mode 3 4 Photodiode Properties 48 3 4 1 Spectral Response 48 3 4 2 Quantum Efficiency 52 3 5 Summary 56 Bibliography 57 Problems 58 Electrical Response Time of Diodes 61 4 1 Introduction 61 4 2 Modeling the Response Time of Photodiodes 62 4 3 Diffusion Time 63 4 4 Drift 65 4 5 The Resistance Capacitance Response Time 66 4 6 Capacitance of Diodes in Forward Bias
298. orward bias the product of the diffu sion capacitance and series resistance of the device will limit the elec trical bandwidth of the junction Examples of such devices are LEDs bipolar transistors and lasers Since excess charge is neiharge09of sTjT 0 03 Electrical Response Time of Diodes 72 Photonic Devices BOONTON 7200 CAPACITANCE METER Figure 4 6 The front panel of a capacitance voltage meter showing a measured value of 199 2 pF at a diode bias of 100 V This instrument can measure both conductance charge flow in phase with the voltage and capacitance charge flow 90 behind the voltage pacitance of the diode leads This is on the order of a few picofarads If the diode capacitance is greater than 100 pF this stray capacitance will have a negligible effect on the results so further precautions are not necessary Results for an InP diode in reverse bias and forward bias are given in Table 4 1 Note the experimental error indicated by the two measurements of capacitance at 0 bias 4 8 Application to Light Emitting Diodes The speed of response of LEDs is limited by the RC time constant The series resistance is usually on the order of a few ohms being de termined by the surface area and quality of the contacts The capaci tance is dominated by the diffusion capacitance and varies with the current injected in the diode As the current is modulated so is the ca pacitance This feature makes the modeling of the time re
299. output spectrum 3 Dependence of the laser peak wavelength on drive current from Lp to 1 2 x Ly 4 Resolution of the mode spectrum of a semiconductor laser Light Current Characteristic In this measurement you increase the drive current while monitoring the light output using a photodiode A lock in amplifier is helpful in order to get good quantitative data The measurement is identical to the light current characteristic that you have already measured for the LED When you exceed the threshold current the light output will increase dramatically due to laser ac tion The resulting plot of light output versus current will resemble in its shape the forward I V characteristic for a p n junction diode The current value of the knee in the curve determines the threshold cur rent Laser Output Spectrum Measuring the output spectrum is a story of good news and bad news The good news is that all the output pow er is concentrated in a narrow wavelength range that is given in the specification sheet so finding the right spectral range is easy The difficulties arise in measurements of the longitudinal mode spec trum A Short Review of Laser Mode Spacing The longitudinal modes of laser emission wavelength are determined by the physical cavity length In the gain spectrum of the laser there are certain values of wavelength that fit exactly in the cavity Since a typical semiconductor cavity is about 400 microns long it takes many comp
300. ows the basic physics of the situation In a good LED we can neglect the nonradiative term compared to the radiative term Thus the transient response time Tstep is inversely proportion al to the carrier concentration This could be the carrier concentration due to doping or induced by the current pulse The rate equation can now be expressed as d J J AN dt aN qd Tstep 6 31 This is a simple in appearance differential equation in AN Howev er since 1 7 also depends on AN a closed form solution will be pos sible only under special circumstances If AN lt Nj we can treat Tetep as a constant This condition corresponds to the limit of high doping or low injection Then Eq 6 31 can be solved analytically Otherwise only a numerical solution is possible Case 1 Low Injection Limit In the low injection limit Tstep is treated as a constant Eq 6 31 is a first order differential equation with a driving term AN Tstep The so lution is written as AN t Ae tstep Bet step C where A B and C are constants to be determined by the boundary conditions Boundary conditions 1 At time 0 AN 0 2 At time t AN Ja a J qd Tstep Applying boundary condition 1 A B C 0 Applying boundary condition 2 it follows that B 0 and J J1 C qd j Tstep A So the particular solution is expressed Jo J1 J J1 AN t Tetep step Ha Tstep Jz J1
301. photon can contribute energy with very little mo mentum As the electron interacts with light the electric field etc both phonons and photons interact with the electron so that both en ergy and momentum are conserved Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Electrons and Photons 20 Introductory Concepts 2 5 Some History The proposition of de Broglie pronounced duh Broy yuh was ab solutely revolutionary but not at all obvious at the time The princi pal result of his idea was to open the way for the development of Schr dingers wave equation and the first quantitative description of the behavior of electrons and atoms de Broglie had the advantage that he was a student He knew a little bit but not too much This fea ture was key in my opinion because it allowed him to see the forest in spite of the trees Later in life when he knew more he was much less productive and because of his celebrity his views took on an im portance unsupported by their content alone de Broglie defended his thesis in late November of 1924 The cover page is shown in Fig 2 5 The thesis is short about 100 pages in all Almost all of the chapters are concerned with the effect of special rela tivity on the properties of various fundamental particles such as the energ
302. phy 1 M Ming Kang Liu Principles and Applications of Optical Communica tions Irwin New York 1996 2 A Yariv Optical Electronics in Modern Communications 5th Edition Ox ford University Press New York 1997 Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Direct Modulation of Laser Diodes 190 Advanced Topics Problems and Exercises 8 1 Using a sequence in time of energy band diagrams for a direct band gap semiconductor show how application to a laser diode of an electrical pulse that is shorter than the recombination time will lead to band filling and once recombination begins why the wavelength of emission modulates from shorter toward longer wavelengths 8 2 Develop a set of design curves for turn on delay using the follow ing parameters t 1071 sec J 0 9 Sy Ja 1 1 dy 5 Jins 10 Jin 20 Sip Repeat for J 0 1 and 0 5 J n Plot your results Comment on the optimum practical conditions for obtaining a negligible turn on time for the laser Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Source Photonics Essentials Chapter Optical Fibers and Optical Fi
303. pical values for t are several nanoseconds Although this may seem short it is easily meas ured with conventional equipment The threshold current density can be expressed by combining Eqs 7 15 7 16 and 7 19 7 19 gtN ip T21 p c g f You would prefer to have a lower threshold current There are some variables in this expression that are under the control of the laser de signer The thickness of the recombination region can be reduced physically This was first done by making a heterostructure and has been developed into the currently used quantum well design where the recombination is restricted to a potential well of thickness compa rable to the de Broglie wavelength that is about 10 nm The quan tum well laser design has a second equally important effect of lower ing the threshold current This structure narrows the gain spectrum increasing g f In a semiconductor laser having a band structure similar to that shown in Fig 7 6 the gain function can be adequately represented by a Gaussian distribution The value of the distribution at its maximum value can be expressed in terms of its full width at half maximum usually abbreviated FWHM Jn A cm 7 20 r r E fmax Gaussian gain distribution 7 21 2 TAf The exact form of the gain distribution function is almost never known It can be adequately approximated by 1 E f max z Af 7 22 The fundamental nature of stimulated emission di
304. ping If the excess carrier density is less than the doping level the LED response time is independent of drive current and the rate equation can be solved explicitly for the light output as a function of time In this limit the modulation of the carrier density by the drive current has a negligible effect on equilibrium conditions in the diode The near equilibrium carrier recombination time is the equivalent to the LED rise time When the drive current introduces an excess carrier density com parable to the doping concentration the transient response of the LED depends on the drive current with the response time becoming shorter as the drive current is increased Under these conditions the LED rate equation can be solved only by numerical methods to give the output power as a function of time for a step change in the drive current Under the assumption of a small ac modulation amplitude around a dc operat ing point we were able to derive a simple expression for the modulation bandwidth This expression shows that the ac modulation bandwidth increases as the square root of the dc operating point current 6 10 Review of Important Concepts Efficient LEDs are commercially available in red green and blue for full color RGB visual displays and for lighting applications LEDs Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any us
305. plifiers 198 Advanced Topics well defined mechanical structure for automated assembly and splic ing of optical fibers Splicing of fibers is needed to produce spools of fiber that are sold to fiber optic cable manufacturers To splice two fibers the ends to be joined are cleaved This is a special process of breaking a fiber so that its end face is flat This can be done in the laboratory by trial and error If you want to make money however this process must be automatic and this means that the mechanical properties of the fiber are consistent from one fiber to another The fiber ends are held together and fused by heating Note that it is the fiber cores that need to be aligned Again you could do this in the laboratory by sending light down one of the fibers and adjusting the position of the second fiber for maximum transmission However in a commercial manufacturing process one relies on the mechanical alignment of the exteriors of the fibers and depends on the control of the core position at the center of the fiber Control of the fiber core position to better than 0 5 micron for a 125 micron fiber is now rou tine These manufacturing processes have made it possible to produce high volumes of glass fiber with carefully controlled optical physical thermal and mechanical properties It is the mastery of these pro cesses that have made exploitation of optical fiber telecommunication a commercial reality 9 4 Waveguiding in Optical
306. r It is analogous to a road map that tells you the streets and highways allowed or stable states for an electron that your car can have when it is freed from the garage Just like the road map the band structure does not tell you where the electron is Rather the band structure tells you what the possible states are and about the properties that an electron would have if it occupied a particular state For example from a road map you can tell the difference be tween a residential street and a superhighway In addition to the lo Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Electrons and Photons Ayrshire L i mA i Rush Curlew o i Lake CO Electrons and Photons 25 Figure 2 8 A conventional road map identifies the stable states that automobiles can oc cupy The road map does not tell you where the automobiles are or how fast they are mov ing The location of the states depends in general on the shortest distance between two points in the context of the barriers imposed by the terrain In a we show a road map of a flat terrain There are few potential variations and the roads are straight BP Amoco used by permission In b we show a road map of a more rugged terrain This can result in roads with many curves or roads that deviate sign
307. r based on GaN oper ating continuously at room temperature with a threshold current den sity of 3 6 kA cm very close to that for the GaAs based laser men tioned above Akasaki now in retirement continues to develop and demon strate new laser devices including an ultraviolet laser that has a wavelength so short that it is invisible The emission color can also be bent in the other direction to make bright green emitters These achievements are regarded by many of my colleagues as among the most important developments in laser device technology Both Akasa ki and Nakamura have received numerous awards for their work the results of which can be seen on your local street corner in the form of the green LED lamp in the stoplight In Fig 7 12 we show the optical output spectrum of a GaN laser made by Nakamura and his team The evolution of the laser spectrum with increasing current is shown in four stages starting at 1 mA which is well below threshold to 53 mA which is just above thresh old What can we learn from this wonderful story Models are useful but they have limits Sometimes as in this case the limits are not al ways easy to see However predictions of failure or impossibility are often proved incorrect As a postscript I would like to mention that a somewhat similar situation exists today in the field of polymer based optoelectronics There is resistance to using optoelectronic polymers Devices to date are not very
308. r electrons Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Photoconductivity Photoconductivity 79 and 1 _ _ hr 5 1 1 v 600 fox io 6 x 10 cm sec for holes The linear relationship between drift velocity and electric field no longer holds for GaAs when the electric field is larger than 10 V cem The transit time is 10 x 10 at 10 t 3x 108 1 25 x 107 sec for electrons and 10 x 10 _ 1 ee for holes th 6x 105 1 67 x 10 sec for holes This example shows that the transit time of electrons and holes can be quite different This difference plays a very important role in deter mining the device properties of photoconductive detectors 5 3 Gain and Bandwidth A frequently used photoconductor design consists of a semiconductor material with ohmic contacts across which a voltage is maintained as 10 microns GaAs wafer Figure 5 1 Schematic diagram of a GaAs photoconductive detector created by deposit ing two ohmic contacts in an interdigitated array on a GaAs wafer Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Photoconductivity
309. r emission This figure is somewhat more complicated than the corresponding diagram for LEDs shown in Fig 6 13 The photon density is increased by both in creases in the carrier density and the optical gain We will use this schematic diagram to build a model of the time dependence of laser action The laser modulation properties are based on ae change in the electron hole concentration and dN ae change in the photon population Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Direct Modulation of Laser Diodes 180 Advanced Topics CURRENT x DRIVE CURRENT TIME LASER WAVELENGTH CURRENT SELF PULSATIONS TIME Figure 8 1 A schematic representation of the behavior of laser output wavelength and amplitude as a function of time when the laser is subjected to a current pulse Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Direct Modulation of Laser Diodes Direct Modulation of Laser Diodes 181 CAVITY LOSS PHOTON DENSITY LIGHT EMISSION STIMULATED EMISSION LASER ACTION DRIVE CURRENT CARRIER DENSITY SPONTANEOUS RECOMBINATION
310. racterizing Photonic Devices in the Laboratory tion significant noise reduction can be obtained However the lock in goes even further and allows you to choose only the signal that is in phase with the modulation This results in even more discrimination power and subsequent improvement in signal to noise ratio Recommended Equipment 1 Photodiode s Silicon wafer GaAs wafer Tungsten light bulb a low voltage flashlight bulb with incorporat ed lens and small filament size lt 2mm is a convenient choice AeA DN Lenses Mounts to hold the photodiodes lenses and light Chopping wheel Oscilloscope oonNnn a Lock in amplifier Procedure a Optical Setup Set up the light source on one side of the chopping wheel and the photodiode on the other Connect the photodiode cable to the oscilloscope amplifier Set the amplifier to the de coupling mode Turn on the oscilloscope and increase the sensitivity so that you can tell the difference in the position of the trace on the screen when you block the room light from the photodiode The room light is a major source of background noise Take a measurement of the back ground noise level Next increase the current to the light bulb until the signal from the light source on the oscilloscope screen is greater than the noise level You may need to remove the chopping wheel from the path to accom plish this Pick a convenient frequency try around 200 Hz for the chopp
311. radiation I E I E Ky E E e E EgVkT 6 7 g where Ko is a constant and E is the energy of the emitted photon The spectra of real light emitting diodes are not well described by this model In Figs 6 4 and Fig 6 5 we show the spectra for some commercial diodes that are used in display applications In common with the model the spectra of real light emitting diodes are not sym metric about the peak in the luminescence In both spectra it can be Red LED LED Intensity a u 600 650 700 750 800 850 900 Wavelength nm Figure 6 4 The emission spectrum of a red LED The peak intensity occurs at 700 nm already outside the range of normal human vision Thus only about half of the emitted light can be seen and this occurs in the red part of the visible spectrum The energy width at half maximum is 240 meV much larger than expected from the thermal broadening given by the Boltzmann distribution Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Light Emitting Diodes 110 Photonic Devices SiC Blue LED LED Intensity a u 0 420 440 460 480 500 520 540 560 Wavelength nm Figure 6 5 The emission spectrum of a SiC LED The peak intensity occurs at 490 nm and corresponds to the blue region of the visible spectrum The energy width a
312. rary McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Photoresponse Photodiodes 58 Photonic Devices Problems Refer to Chapter 11 laboratory exercise 11 1 In the laboratory you will measure experimental data that you will compare to the theoreti cal models developed in this chapter You will first design and make a sturdy and reusable mount for diode devices and next measure the current voltage I V characteristic in reverse and forward bias You will observe the effect of photons on the I V characteristic 3 1 In the figure below you will find the spectrum of a photodiode de tector The light source is an incandescent lamp with a silicon filter in front Temp 300 K Sensitivity 100 pV Time constant 300 ms Slits 1 mm Photo volt probe f 387 Hz Tungsten bulb Luise gullies acide al T T T T T T T 2000 1900 1800 1700 1600 1500 1400 1300 1200 1100 100 Photon wavelength nm What is the lowest photon energy where detection first occurs What is the upper photon energy where detection cuts off What causes the detection to cut off What effect does second order transmission of visible light by the monochromator have on this spectrum e What kind of photodiode is doing the detection Ge or Si 3 2 You are working with a silicon photodiode of near unity quan
313. rary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Measurements in Photonics Measurements in Photonics 231 The monochromator consists of focussing mirrors and a wave length dispersive element This is usually a grating scribed into a piece of soft glass The grating spatially separates light of different wavelengths similar to the way that Newton s prism works Fig 10 5 The mirrors are curved so that they act as convex lenses The en trance slit is treated as a point source and the light is focused into a parallel beam and directed to the grating In a good instrument the grating is uniformly illuminated by the light When the light leaves the grating it is still parallel and the process is reversed so that light is now focused on the exit slit You can see that the size of the grating and the length that the light travels to reach the grating define an angle of acceptance for light that enters the monochromator If the angle of the entering light beam lies within this angle it will strike the grating If it lies outside then it can still enter the monochromator but some of the light will not hit the grating and will be scattered around inside the monochro mator generating background noise The length of this path divided by the width of the grating defines the f number of the monochroma tor In a well designed optical system all the light fr
314. ration of holes in the valence band Note also that the distance Aw becomes smaller and smaller as the bias voltage increases This feature brings the con centrations of electrons and holes into spatial overlap Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Lasers 158 Photonic Devices Laser diodes operate normally at higher forward bias voltages than that shown in Fig 7 8 Of course the appropriate variable is not volt age but current This situation is shown schematically in Fig 7 9 There are some important features to note in this diagram The most important is that the physical overlap of occupied conduction and va lence band states is even more complete This improves optical gain There is now a perceptible electric field in the contact regions which we have up to now presumed to have negligible resistance The width of the space charge region does not go to zero when the bias voltage equals the built in voltage as implied by Eq 4 5 This indicates that the depletion model breaks down in forward bias On the other hand the only region where the electric field remains zero is at the edges of the depletion region where the slope of the energy level versus dis tance is zero That is at the edges of the depletion region the current is carried entirely by di
315. re heated so that the soot turns to glass The tube is pulled at high temperature like taffy along its long axis until the hollow region in the center disappears creating a preform The germanium dopant gives the core region an index of refraction n that is higher than that of the cladding n This assures that the fiber will act as a waveguide The index difference between n and nz is controlled carefully If there is too much germanium in the core the fiber will still act as a wave guide but the difference in thermal expansion between the core and the cladding will result in stress that will cause cracks that will lead to mechanical failure of the fiber The preform is heated again in a fiber drawing tower and the fiber is pulled from the preform The outer diameter of the fiber is about 125 microns and the core diameter is about 9 microns The core and the diameters are very carefully controlled As we will show present ly the core diameter is determined by the index difference Careful control of the core diameter and its position inside the fiber are cru cial for obtaining low loss splicing of one fiber to another Careful control of the cladding diameter is required to present a Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Optical Fibers and Optical Fiber Am
316. re that the emitted light comes from the recombination of elec trons and holes The excess carrier concentrations are created in dif ferent ways but the recombination of excess carriers leads directly to light emission Although some of the operating conditions vary from semiconductor to polymers the methods of experimental analysis re main the same In this chapter we will investigate the performance characteristics of LEDs from an analytical and experimental view point In order to maintain continuity with the presentation on detec tors in Chapter 3 we present LEDs in the framework of p n junctions The operating characteristics of primary concern are output optical power optical wavelength efficiency and modulation bandwidth The LED output intensity is proportional to the drive current It is a direct quantum conversion of electrons to photons The optical wavelength of emission is located near the band gap energy A primary concern in high bit rate communications applications is the modulation band width of the emitter and the detector The bandwidth of all electronic devices depends on both circuit factors i e the resistance capaci tance RC product and intrinsic factors such as carrier transit time and carrier lifetime The structure of detectors low doping low ca pacitance diodes has the result that detector diodes have a natural advantage over LEDs in terms of the RC time constant LEDs are by design highly doped diode
317. rent quadrants of the I V curve Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Experimental Photonics Device Characterization in the Laboratory 248 Characterizing Photonic Devices in the Laboratory orientation looks like the one on the right simply remove the diode from the socket and reinsert it with the lead positions exchanged In any case mark the p side lead with red nail polish for future refer ence Take some I V characteristics of the p n diode In reverse bias you can usually apply several volts before the current increases beyond 1 microamp It is good practice to keep the reverse current below this level In forward bias the diode can handle several milliamps usually at a forward bias of less than 2 volts Because of the very different conditions between forward bias and reverse bias you will want to measure them separately In order to keep light from affecting the measurements place a cover such as a cardboard box over the diode Measure the forward current voltage relationship starting from the minimum detectable current over as many decades of current as pos sible until 1 milliamp is reached In reverse bias you may have difficulty measuring any current in the range from 0 to 10 volts particularly for the case of the Si photo diode In
318. rgy gap is 1 1 eV You can see from the energy band structure diagram for germani um that the electron needs to get some momentum in addition to en ergy to make a transition at this least energy near the band gap So the transition to the antibonding state is not direct There are two steps required first obtain the energy and second obtain at the same time the required momentum from a physical vibration of the crystal lattice This is called an indirect transition and germanium is called an indirect band gap semiconductor By referring to the band structure of GaAs you can see that this transition can be made in one step with little or no change in momen tum required This happens because the maximum valence band en ergy occurs at the same momentum as the minimum conduction band energy Since the photon can convey energy with no momentum the electron can absorb a single photon and make the transition across Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Electrons and Photons Electrons and Photons 29 Ars ae petra pet An a a ae Figure 2 11 In this sequence of calculations we show how the periodic potential modifies the energy momentum relationship for a different semiconductor Ge In the first frame you can clearly see the parabolic relationship
319. rgy is constant indicating that the potential for electrons is constant throughout the structure This means that the electric current is 0 Note that the direction of distance for holes is opposite to that for electrons gram for a photodiode Fig 3 1 In this energy level diagram we can plot out the energy levels of electrons and holes in the photodiode as a function of distance It is different from the energy band diagram that we have used to find the allowed states of energy and momentum for electrons in semiconductors The Fermi level is constant so the photo diode is at equilibrium In the absence of illumination the concentration of electrons on the p side npo is related to the concentration of electrons on the n side by the Boltzmann relation n PO 9 qVBi kT 3 1 Nno where V3 is the built in voltage of the diode refer to the book by G W Neudeck in the bibliography for more details When a bias voltage V is applied the Boltzmann relation still rules and n No An Pe PE 9 al VBi VAkT 3 2 Nn Nn Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Photodiodes 40 Photonic Devices In this expression both n and n change to accommodate the bias voltage Vy n po gt Np Npo An and Nao gt Nn Nno An 3 3 In t
320. rgy of a baseball momentum mv p Buse m 1 mv pP inetic energy mv z 2 2m 2m 2 21 The same thing is true for electrons Photons of course don t have any mass So this equation does not work for photons A graph of the energy of a free electron as a function of its momen tum just like that of a baseball is a parabola see Fig 2 3 Remem ber that a 1 eV photon has A 1240 nm On the other hand we know from Maxwell s equations that photons do have a momentum that is equal to E h p Zi 2 22 c e But since c fA h 2 p 7 hk where k a 2 23 So photons don t have mass but they have momentum ENERGY 0 MOMENTUM E Figure 2 3 The kinetic energy of a particle with mass like that of an electron is propor tional to the square of its momentum Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Electrons and Photons 16 Introductory Concepts Electrons have momentum but can they have a wavelength Well if your name were Prince Louis Victor Duke de Broglie and the year was 1924 maybe such an idea would not seem so strange If this were the case then the energy of an electron would be 1 Rk T 2m A Using this equation you could actually calculate the wavelength if you knew the electron energy Suppose
321. rights reserved Any use is subject to the Terms of Use as given at the website Lasers 148 Photonic Devices N3 Stimulated Emission AANA A A ES E a N a N Stimulated ANANS Absorption N b N Spontaneous NNN Emission N c Figure 7 3 Diagram of the three possible electron photon interactions Stimulated emission and stimulated absorption refer to the fact that the probability for absorption or emission depends on how many other photons having the energy difference of the transition are already present In a spontaneous emission process shown in c the probability of emission does not depend on the presence of other photons Fig 7 3a is given by B21 The probability for spontaneous emission is different and we will call this A1 We would like to compare the num ber of absorption transitions to the number of emission transitions in order to calculate the gain The number of spontaneous transitions is given by the number of occupied states N multiplied by the probability of a transition N4931 The number of stimulated transitions also depends on the number of photons present with an energy equal to the transition energy We will call this number p w The number of transitions from stimulated emission is NjB 1p w The total number of transitions in which a pho ton is emitted is just the sum of these two terms The number of ab sorbing transitions depends on the number of occupied st
322. rior to exposure the photosensitive grain is composed of a silver bromide single crystal with silver sulfide impurities or sensitive spots introduced during manu facture The bromine atoms are so large that they stay fixed in place but the silver atoms are smaller and much more mobile Professor Shelly Errington of the University of California at Santa Cruz drew this original illustration the large figure on the left hand side of Figure 5 11 The bromine an ion is physically much larger than the silver cation This size differ ence plays an important role in the events to follow Over on the right we see the silver sulfide molecule This molecule gives the film its sensitivity to light This molecule is so sensitive it is speaking French Two new characters are introduced in Figure 5 12 and the action begins A photon is absorbed by the silver bromide molecule breaking a bond and freeing both a bonding electron and the silver atom The molecule is split apart into its atomic components The newly liberated electron moves very quickly through the crystal and is attracted to the silver sulfide site on the right hand side of the cartoon This action gives the silver sulfide site the charge it needs to attract the silver atom The silver atom is attracted to the silver sulfide site and diffuses through the silver bromide crystal The silver atom can move through the silver bromide crystal because of its smaller size relative to bromine Eventu
323. rpendicular to the surface of this page permitting a continuous range of wavelengths to be selected In Fig 10 8 we show a fixed grating spectrometer that uses a de tector array to detect and analyze the wavelengths present in an opti cal beam In this instrument the complete dispersion of the grating is imaged on the detector array so that the entire spectrum of the light is obtained at the same time instead of requiring the grating to scan through a range of wavelengths A spectrometer with this capability is called a spectrograph The fixed grating spectrograph actually is a variation on the very first spectrometer designs in which film was used at the exit plane in stead of a detector array The current design offers great advantages in speed of detection and alignment of the optical components in a measurement This convenience is achieved at the expense of some sensitivity in the detector that can be easily achieved using a grating Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Measurements in Photonics Measurements in Photonics 237 Figure 10 8 Interior of a fixed grating spectrograph with a detector array The detector array replaces the exit slit of Fig 10 7 and all components of the spectrum to be ana lyzed are detected simultaneously monochrom
324. rs and creation of new start up companies For tunately there is a strong and steady growth rate much greater than 5 that is underlying this effervescence To succeed you need to keep a close watch on both the technology and the opportunities Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Source Photonics Essentials Chapter Electrons and Photons 2 1 Introduction You will discover by measurement that all p n diodes are sensitive to light even if they are intended for some other application A photodi ode is a simple and inexpensive component that you will use to meas ure the particle behavior of light This is a fundamental quantum mechanical property of matter and is the effect for which Albert Ein stein was awarded the Nobel Prize in physics in 1921 Photonic devices are used to convert photons to electrons and vice versa Photons and electrons are two of the basic quantum mechani cal particles Like all quantum mechanical particles electrons and photons also behave like waves In this chapter you will learn about the wave like and particle like aspects of the behavior of electrons and photons Each electron that carries current in a semiconductor is spread out over many thousands of atoms that is it is delocalized Trying to specify its posit
325. ry com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Lasers Lasers 147 consists of a pair of mirrors so that light exiting the laser amplifier is returned back to the amplifier medium The other mechanism is the principle of stimulated emission which says that the probability for photon emission is proportional to the number of photons already present In this section we will develop a relationship between the amount of stimulated emission and the amount of spontaneous emis sion A popularly recognized feature of a laser is the emission of a well collimated beam of monochromatic light This characteristic is deter mined entirely by the properties of the feedback element just as in the case of the phase shift oscillator circuit The principle of stimulat ed emission says that an emission of a photon that accompanies the transition of an electron to a lower energy state depends on the num ber of similar photons already present within a space determined by the wavelength of the electron These photons encourage the electron to make the transition with the probability increasing linearly with the density of photons This process of stimulated emission is the re verse of the property of stimulated absorption in which the probabili ty that an electron makes a transition to a higher energy state de pends on the number of photons present that have the energy
326. s but they are far more versatile Bibliography Albert Rose Concepts in Photoconductivity and Allied Problems New York Wiley 1963 R E Simon Ed RCA Electro optics Handbook RCA Commercial Engineer ing 1974 RCA is now a trademark of Thomson Multimedia but in the past RCA made many fundamental contributions to the development of television including photoconducting television tubes This book is a gold mine of information R K Willardson and A C Beer Eds Semiconductors and Semimetals Vol ume 5 Infrared Detectors New York Academic Press 1970 Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Photoconductivity 100 Photonic Devices Problems 5 1 A light pulse from a laser A 600 nm with a duration of 1 nanosecond and an intensity of 10 7 W is absorbed by a Si photo conductor having an area of 1 cm How many electron hole pairs are created 5 2 Using energy level diagrams explain why the maximum photo conductive gain is unity in a photodiode 5 3 A Si photoconductor having an area of 1 cm and a thickness of 2 microns is uniformly illuminated by a steady state beam of pho tons with energy 2 eV The intensity of the light beam is 1 mi crowatt Consider that all the light is absorbed If the lifetime of electron hole pairs is 1 mi
327. s and they are operated in forward bias further increasing capacitance which will limit the modulation band width Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Light Emitting Diodes 104 Photonic Devices 6 2 Recombination of Excess Carriers Direct Generation of Light LEDs made from semiconductors generate light via the same mecha nism as do LEDs made from polymers by recombination of excess concentrations of electrons and holes The wavelength of the emitted light results from conservation of energy that is the energy differ ence between the hole state and the electron state before recombina tion is the energy of the photon emitted The usual conversion A 1240 nm Energy eV gives the corresponding wavelength In this chapter we will describe light emission principles for semiconductor LEDs since they are commercially available whereas polymer LEDs are still in the laboratory stage The forward bias voltage on a p n junction creates excess minority carrier concentrations near the edge of the depletion region The ener gy versus distance diagram is shown in Fig 6 1 The excess carrier density is maintained at a constant value by a balance between the carrier generation caused by the bias voltage and recombination of the excess minority carriers an
328. s back of the envelope estimate shows that on the average a semiconductor whose band gap antibonding bonding energies 1 eV will have about 108 broken bonds per cm A more detailed calcula tion for silicon based on the same principles gives 10 cm broken bonds at room temperature When the bond is broken the electron is promoted from the valence band or bonding orbitals to the conduction band or antibonding or bitals Another name of the conduction band is simply the set of unoc cupied levels that are closest in energy to the valence band levels When the bonds are not broken they act like springs that hold the atoms in the crystal at the right distance from each other These springs vibrate as a way of storing the thermal energy of the crystal The vibrational energy of each atom kT for each degree of freedom or 3 kT So the average vibrational energy at room temperature is about 40 meV These vibrations have a frequency and a wavelength that are related by the speed of sound v fA The speed of sound in solid materials is about 10 cm sec 10 m sec Exercise 2 6 What is the ratio of v to the speed of light Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Electrons and Photons Electrons and Photons 19 v e 105 101 10 5 So for
329. s can be applied Use this information to determine the energy difference in electron volts between the conduction bands on each side of the junction if the n side has 1018 cm free electrons and on the p side there are 104 cm electrons Assume that the junction is at room temperature 2 2 We know that a photon cannot interact with a free electron be cause simultaneous conservation of energy and momentum is not possible That is their energy band structures do not inter sect In a collision between an electron a photon and a phonon an interaction is possible This can happen in a solid like Si or GaAs a Calculate the wavelength the frequency and the energy of the phonon in silicon that will allow a 1 eV photon to transfer all its energy to an electron Assume that the electron is initially at rest E 0 that is T 0 The velocity of sound in silicon is about 8 5 x 10 meters per second at room temperature b What is the final energy of the electron c If the collision takes place in silicon at room temperature what is the likely initial energy of the electron 2 3 Electrons in a semiconductor have the full electronic charge q but often their mass appears to be different from the free elec tron mass In GaAs for example the effective mass of an elec tron is equal to 0 065 the value of the free electron mass The size of the effective mass depends on both the structure and the crystalline potential of the semiconductor
330. s given at the website Lasers inglibrary com its res Copyright 2004 TI U n at the website Any use is subject to the T Ac Source Photonics Essentials Part Advanced Topics Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Advanced Topics ringlibrary com Downloaded fror el fed Source Photonics Essentials Chapter Direct Modulation of Laser Diodes 8 1 Introduction Information can be carried by an optical beam only if the beam is modulated There are many ways to modulate the laser emission out put wavelength frequency intensity etc Intensity modulation is used most often because it is well adapted to digital communications and relatively simple to implement The two forms of intensity modu lation are external modulation and internal modulation External modulation can be achieved by a mechanical wheel such as a compact disc or by an electro optic modulator that changes the optical density or index of refraction of the propagation path to mention two possibil ities In some applications the laser beam is not optically modulated at all internally or externally An important example of this use is the laser pump at 980 nm for Er optical fiber amplifiers in optical communications Internal modula
331. set tings that must be made 1 the sensitivity 2 the time constant and 3 the frequency Fig 11 2 is a photograph of a common lock in am plifier made by Stanford Research Systems We have identified the lo cation on the front panel of the basic controls It is now usually the case that the correct frequency and phase are detected and set auto matically by the amplifier In your measurements you will want to explore the effects of changing the frequency and the time constant in order to optimize performance d Absorption by GaAs and Si GaAs and Si each have an optical absorp tion edge At wavelengths shorter than the edge all photons are ab sorbed For wavelengths longer than the edge each material is rela tively transparent The energy of the absorption edge gives the fundamental band gap Place a wafer of GaAs between an incandes cent light source and the detector What happens Repeat using a Si wafer Repeat the same experiment using a Ge or GaInAs photodiode detector Develop an explanation for what you measure Analog output Numeric output Frequency TET Amplifier sensitivity Time constant Figure 11 2 Diagram of the front panel of a typical lock in amplifier The amplifier was introduced in Chapter 10 The principal adjustments for sensitivity and time constant are made by the buttons on either side of the output displays Courtesy of Stanford Re search Systems reproduced by permission Downloaded
332. sheet On the other hand you will not have to know how to hook up the power supply or measure the threshold current with these lasers either Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Experimental Photonics Device Characterization in the Laboratory MITSUBISHI LASER DIODES ML3XX1 SERIES ABSOLUTE MAXIMUM RATINGS Symbol Parameter Conditions Ratings Unit CW 3 5 Po Light output Pulse Note 1 6 mW VRL Reverse voltage Laser diode 3 V VRo Reverse voltage Photodiode 15 V lpp Forward current Photodiode 10 mA Te Case temperature 40 60 C Ting Storage temperature 55 100 C Note 1 Duty less than 50 pulse width less than 1 us ELECTRICAL OPTICAL CHARACTERISTICS Tg 25 C Limits Symbol Parameter Test conditions Min Typ Max Unit lin Threshold current CW 20 40 mA lop Operating current CW Po 3 mW 30 50 mA Vop Operating voltage Laser diode CW Po 3 mW 1 6 2 5 V Po Light output CW le l 10mA 3 mW Ap Lasing wavelength CW Po 3 mW 795 815 905 nm he 8 11 18 deg Y Full angle at half maximum CW Po 3 mW 20 30 50 deg CW Po 3 mW lmn Monitoring output current Vro 1V 0 1 0 3 0 7 mA R 10 Q Note 2 lo Dark current Photodiode Vap 10 V 0 5 pa C Capacitance Photod
333. sion in a two level system Of course you might be able to get an inversion if electrons were somehow fed into the upper level by another source a third level This turns out to be the road to the solution In general lasing is easiest to obtain in a four level arrangement this is diagrammed schematically in Fig 7 5 At the beginning of the cycle all the electrons are in the ground Excited State E4 Lasing transition Ground State Figure 7 5 Population inversion can be obtained in a four level system in this case be tween level 4 and level 3 The excitation and recombination cycle is given in sequence by the numbers in the figure There are four steps to the complete cycle Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Lasers 154 Photonic Devices state If level E is a few kpT above level Fj it will be nearly empty by Boltzmann statistics The cycle starts when a high energy photon with energy hf E E excites an electron from the ground state to the excited state step 1 The photon is a particle so all its energy must be absorbed making a direct transition to E or E impossible After excitation the electron can be scattered into state E during a collision step 2 Electrons are more likely to end up in state E than state E or st
334. so de velop a relationship for the current voltage relationship in a p n junc tion The p n diode is a device that puts the Boltzmann relation to work So it is no surprise to find expressions like e 4 7 in the rela tionship between voltage and current Without any voltage applied across the terminals of a p n junction there is no current In the lan guage of Boltzmann the probability of finding a free electron on the p side of the junction is equal to the probability of finding a free electron on the n side Thus the energy difference must be zero When a volt age is applied between the p side and the n side the energy difference is no longer zero and so the probabilities are no longer the same This difference leads to a current in the diode The p n junction is the basic device structure for all semiconductor op toelectronic devices for example lasers LEDs modulators optical switches semiconductor optical amplifiers and so on By characterizing the electrical and optical properties of the p n junction much can be learned about the internal composition and structure of the device for example the band gap and the level of background impurities in the material being used This chapter includes results from suggested labo ratory experiments that are given in Chapter 11 The problems are large ly based on real data measured at the bench during these experiments The chapter reviews the fundamentals of photodiodes and their electr
335. so know that the electron behaves like a wave a By taking the second derivative with respect to x of the simple wave function W x A sin kx show that you get the follow ing relationship d 3 b Multiply both sides of this relationship by the appropriate constants to derive a formula for the energy of the electron This formula is the basis for the Schr dinger equation the mathematical foundation of quantum mechanics 2 7 Silicon has a band gap of 1 1 eV at room temperature Using a monochromator you send a beam of photons with a wavelength of 1240 nm on the surface of a silicon wafer 0 5 mm thick Only three things can happen absorption reflection and transmis sion of the beam of light Which things actually happen under these circumstances 2 8 When a photon passes from air into glass its trajectory is changed according to Snell s law n sin 6 na sin and the velocity of light is reduced by the ratio of the index of refraction of air n 1 to that of glass nz 1 5 When the photon travels in glass it still obeys the relationship V fA where V is the Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Electrons and Photons 34 Introductory Concepts speed of light in glass c n On the other side of the equation the product fA m
336. sponse diffi cult except under small signal conditions However LEDs are rarely used in the small signal regime This important point is examined in full detail in Chapter 6 The result is that typical commercial LED has a frequency cut off in forward bias on the order of a few mega hertz The same diode operating in reverse bias as a detector might have a bandwidth of 1 GHz Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Electrical Response Time of Diodes Electrical Response Time of Diodes 73 Table 4 1 Capacitance voltage data for an InP p n junction diode Reverse bias V Capacitance pF Forward bias V Capacitance pF 0 00 48 64 8 73 84 0 05 47 20 75 72 97 0 1 45 78 7 71 88 0 15 44 46 65 70 48 0 2 43 21 6 68 90 0 25 42 07 55 67 01 0 3 41 03 5 64 96 0 35 40 06 45 62 80 0 4 39 15 4 60 71 0 45 38 32 35 58 65 0 5 37 58 3 56 87 0 55 36 87 25 55 29 0 6 36 18 2 53 89 0 65 35 53 15 52 72 0 7 34 93 1 51 54 0 75 34 38 0 05 50 25 0 8 33 83 0 00 48 83 0 85 33 37 0 9 32 88 0 95 32 43 1 00 32 00 4 9 Summary The speed of response of semiconductor devices such as photodiodes or LEDs determines their usefulness in communications applications LEDs are now be
337. t 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Direct Modulation of Laser Diodes Direct Modulation of Laser Diodes 183 aN J N SG 8 5 dt qd During the time 0 lt lt 74 we will assume that 7 remains constant This is probably not an accurate assumption but it is necessary in or der to obtain an analytic solution This equation is now the same as Eq 6 18 and we can write down the solution right away J Tr qd At time r4 the laser turns on because threshold has been reached so by definition the carrier concentration at threshold is N t 1 e r Niet 8 6 JoT Nin Ta T L e a tr Nye7a r Combining terms J Tr J Tr Ni ear ad Nih Solving for rtg de Na qd f m FO N Mi Ta T ln Ts Ma 8 7 qd Tp Remember that we can write a and Na Tun Tr qd Ts qd so Ja J 7 In gt 8 8 Ta Tr nl J da where Ja gt Jin gt J4 This result is an estimate that shows that there is a time delay be tween the electrical pulse and the appearance of light This delay lim its the maximum bit rate for the laser when it is used in a communi cation system even though the ac modulation bandwidth of the laser may be higher The delay is caused by the time needed to build up the carrier concentration to threshold The delay time can be reduced by prebiasing the laser closer t
338. t Total number of LEDs to fill space 7 20 1250 Actually it is about 10 less because the LEDs are circular and do not entirely fill the space To be safe we will use only 1000 LEDs Total emitted red light 1000 x 1 mW 1 W This is the end of part one We conclude that there can be a reasonable balance between the light emitted from a light bulb and the light emitted from an array of LEDs However the light bulb consumes 100 Watts of electrical power and the LED light consumes only 25 Watts 2 Cost of electrical power Assume electricity costs 5 cents kW h Stoplights run 24 hours a day 365 days a year 24 365 9000 hours Number of kW hours for lightbulb 900 kW h 45 00 per year Number of kW hours for LED 225 kW h 12 00 per year Manhattan is an island approximately 10 avenues wide and 200 streets long There are 2000 intersections There are on the average 10 stoplights at each intersection so we estimate 20 000 stoplights The cost of running an incandescent stoplight per year is a com bination of electricity 45 00 plus maintenance 40 00 The cost of running an LED light is only electricity 12 00 Cost of operating 20 000 red lights per year incandescent 1 700 000 LED 240 000 Savings by using LEDs 1 460 000 per year Savings per light 73 00 3 How much should you pay for the changeover Assume that an LED light lasts 10 years It should last forever Furthermore 10 of the
339. t age applied to the diode creates excess concentrations of electron hole pairs Electron hole recombination generates photons that depart in all directions by spontaneous emission Some of these photons will travel along the line that is perpendicular to the reflecting surface of the two parallel mirrors These photons will be reflected and will trav el back into the diode along the same path Of course there will be some loss in this process Some photons will be absorbed by impuri ties along the way Others will be scattered out of alignment by de fects in the optical path These events constitute the losses Most im portant of all some will traverse the mirror and be emitted into free space This loss constitutes the useful output of the device At the same time the photons that traverse the gain region will stimulate Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Lasers 160 Photonic Devices the emission of other photons These stimulated photons contribute to the electromagnetic field creating gain That is they must have the same wavelength and the same phase as the stimulating photon If it were otherwise these photons would interfere destructively with the electromagnetic field In order for lasing to occur the gain initiated by a photon during
340. t equilbrium n Ey _ e E2 EykBT nF 2 Energy is proportional to frequency E hf where h is Planck s constant equal to 6 63 x 10 4 joule sec Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Electrons and Photons Electrons and Photons 13 Exercise 2 2 Take A 1000 nm 1 pm 10 cm For a tungsten light bulb this is the wavelength of peak intensity What is the energy associated with this wavelength Procedure Af c or f c f 3 101 cm sec 7 10 cm f 3 10 sec whew E 6 6 10 4 x 3 10 14 1 98 10 9 joules This sounds small which it is according our everyday scale Howev er it is very close to the energy that an electron would have if it were accelerated through a potential of one volt 1 eV 1 6 107 coul x 1 V 1 6 10 8 joule In photonics the typical energies that you work with involve electrons in a potential of 1 or 2 V So we use the energy of an electron acceler ated through a potential of 1 V as a handy unit the electron volt eV The energy of a photon with a wavelength of 1000 nm or 1 um is 1 98 10 9 E 7 1 24 2 1 6 10 a ae It is easy to show that reverse is true That is a photon with an en ergy of 1 eV has a wavelength of 1 24 wm 1240 nm If a photon with a wavelength o
341. t half maximum is 375 meV much larger than expected from the thermal broadening given by the Boltzmann distribution There is a considerable emitted intensity across the green 530 nm and yellow 550 nm spectral regions The LED appears to be emitting a combination of blue and white light seen that the spectrum dies out much faster for energies above the peak than for energies below the peak just the contrary of the pre diction of the model The model predicts that the spectra of all diodes falls off as e s above the energy for the peak in intensi ty this is independent of material properties and the model spec trum could be fit to determine the value of temperature It is quite clear that the high energy side of the room temperature spectra varies from one diode to another so that a fit to the experiment will not yield the temperature The simple model is not wrong but it does not include all the things that are going on An important additional feature that we did not take into account is the absorption of the light by the very semi conductor that is emitting the light You can easily verify in the laboratory that the emission spectrum of an LED does not depend on the bias voltage or the current over the whole range of useful operating conditions This may come as a sur prise since the electron gets its energy from the bias voltage Howev Downloaded from Digital Engineering Library McGraw Hill www digitalengine
342. t the transmis sion station These can be changed at will with no effect on the cable performance Optical gain will also introduce noise Spontaneous emission still occurs in the background Without a resonator it is no longer possi ble to single out a specific mode These spontaneous photons get am plified along with the signal This is called amplified spontaneous emission ASE When the gain is greater than 20 dB this form of noise dominates and since it is proportional to the signal further levels of gain do not really improve the signal to noise ratio SNR further An excellent analysis of this noise has been given by Yariv see Bibliography The basic elements of this analysis are given below The signal to noise ratio of the amplified signal is expressed as SNRoutput Amplified signal power 9 22 Shot noise power Amplified spontaneous emission power To detect the amplified signal power at the output you would use a photodiode the photocurrent has been given in Eq 3 25a The output power is proportional to the square of this photocurrent i2 GS input i output h f where G is the gain of the amplifier and Sinput is the signal entering the amplifier The shot noise power is proportional to the square root of the 9 23 Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the T
343. tant because the index n varies with wavelength df df Ug A AT 9 14 al where A is the wavelength of light inside the fiber The wavelength of light inside the fiber is related to the free space wavelength by the index of refraction A n It is more convenient to continue in terms of the free space wavelength because this is what you measure df df dry _ df 1 o dn y s ae 1 Xr dn y d d d ddr n_ n2 dr wz An n dry perm 9 15 dn x 7 wae The quantity in the denominator of Eq 9 15 acts like an effective index and it is called the material group index This equation shows that different wavelengths travel in general with different velocities Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Optical Fibers and Optical Fiber Amplifiers Optical Fibers and Optical Flber Amplifiers 207 This is not discouraging for sending signals on different wavelengths down the fiber These signals may travel at different speeds but they can be easily distinguished from each other A problem occurs because a laser emits light over a finite range of wavelengths typically about 0 1 nm Although this is small it is not zero This leads to a spread in the arrival time of a laser pulse that grows with the transmission dis tance For a fiber o
344. teady state This result is obtained be cause the current does not induce an excess carrier concentration as large as the carrier concentration from the doping Recombination dy namics are therefore determined by the doping and not by the smaller amount of nonequilibrium carriers induced by current injection Case 2 The High Injection Limit In this analysis we will consider the case where the excess carrier density injected during the current pulse is comparable to the equilibrium carrier density introduced by doping We start from the same expression for the response time B N P AN Tstep Tn r Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Light Emitting Diodes Light Emitting Diodes 133 which is no longer constant The rate equation is d Ja J gon S aa BAN N P AN a2 Since we cannot solve the rate equation explicitly we will develop an expression for the rise time of the LED in response to a current pulse To carry out this analysis we will focus on the variables that are changing with time To simplify the rate equation we will assume that the current at time 0 is also 0 J 0 Define a relaxation time 7 9 BIN P Tr 0 The simplified rate equation is expressed as d Jo AN AN B a pf ee
345. tectors The electrical current is proportional to the energy in the optical beam In the second group are quantum threshold detectors Photons can be absorbed in these devices if the energy of a photon exceeds a certain threshold value All absorbed photons generate the same cur rent regardless of their energy above the threshold value Photodi odes fall into this second category Photons can be absorbed in a photodiode if their energy exceeds the band gap energy of the photo diode material In principle each photon absorbed contributes one electron to the current This is a direct exchange of quanta one electron for one photon In most photodiodes this exchange is near ly 100 efficient Photodiode detectors were developed along with the transistor Sili con is the most common photodiode material for two reasons Silicon photodiodes are sensitive to a range of light wavelengths that include the region of visible light Silicon photodiode manufacture benefits from the same advanced processing technology used to make silicon integrated circuits 37 Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Photodiodes 38 Photonic Devices In this chapter we will develop a model for the conversion of light into electrical current by a photodiode Along the way we will al
346. tes the critical angle for to tal internal reflection This is analyzed in more detail Fig 9 7 Applying Snell s law to this light path n sin 6 na sin 6 05 90 0i 6 sin 9 2 9 1 ny It is also helpful to have the cosine of the critical angle cos 6 V1 sin 9 1 27 9 2 1 The complement of the critical angle 90 0 represents the largest angle with respect to the longitudinal axis that can propagate in a fiber In communications fibers it is usually less than 10 as we will show shortly because n is less than 1 larger than ns This means that light rays are nearly axial Fig 9 7 In the next step we will look at the angle that the light cone makes when it exits the fiber To apply Snell s law to this situation note that we need to take the sine of the complement of the critical angle Nz cos 0 1 sin 6 sin 0 Vn nz 9 3 Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Optical Fibers and Optical Fiber Amplifiers 200 Advanced Topics cladding Figure 9 7 Schematic diagram showing a light path incident on the core cladding in terface at the critical angle The quantity sin 0 is called the numerical aperture or NA of the fiber Fig 9 8 The NA of a fiber having an i
347. th industry and the research laboratory to characterize diodes for all kinds of applications Such measurements are shown in Figs 4 4 and 4 5 The time to charge the diode capacitance will depend on the resist ance in series with the diode The intrinsic resistance of the diode will depend inversely on its surface area For most commercial photodi odes this area tends to be large enough so that the series resistance of the diode is negligibly small compared to the load resistance of the measurement circuit For a high speed measurement the input re sistance of the measurement circuit might be chosen to match the line impedance of the coaxial cable or 50 Q In this case the RC time con stant of the diode in Example 4 2 would be 288 picofarads x 50 Q or 14 400 picoseconds This is quite a bit longer than either the drift or diffusion times discussed earlier In most cases you will find that the time response of a photodiode will be limited by the RC time constant You can control this time constant over a range that is about a factor of 2 by adjusting the reverse bias on the diode Indium Phosphide 506 cee neem ah y T J 1 C V Plot q BIAS 4 amp START 0 V STEP 05 u STOP 1 00 FREQ 1 MHz lt Nd E 4 95 x 10 ns Vibi 0 76V Ta J N a N foa ad 2 0 4 E EN L L 0 0 0 2 0 4 0 6 0 8 1 0 Reverse Bias Voltage Volts Figure 4 4 Analysis of the capacitance voltage measurement of Fig 4 3 Here th
348. the device before you begin You will ob serve that increasing the reverse bias decreases the capacitance and increasing the forward bias increases the capacitance If you observe the opposite behavior reverse the leads of your diode Now measure the capacitance versus voltage from 0 to 5 V Take at least 10 readings You should get a result that looks like the curve in Fig 11 6 In forward bias you can make the same measurement but you need to be careful not to burn out the diode Basically you want to stay below the forward knee of the diode This means only 1 V of bias or so For the light emitting diodes you can increase the bias until light starts being emitted Try to take 10 measurements For the silicon and germanium photodiodes no light will be emitted at any bias so you have to take a different approach For these mate rials do not exceed the band gap potential Si 1 1 V Ge 0 6 V Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Experimental Photonics Device Characterization in the Laboratory 262 Characterizing Photonic Devices in the Laboratory 50 45 40 35 30 25 20 Capacitance pF 15 10 0 0 5 1 1 5 2 2 5 3 3 5 4 4 5 5 Reverse bias voltage V Figure 11 6 A plot of the capacitance of a p n diode versus volta
349. the frequency of the self pulsations of the light emission The materials parameter that plays a determining role in the model of rise time is the carrier lifetime 7 This is the amount of time an excess electron can last in the conduction band before recombining In our treatment we assume that this is a constant in order to proceed toward a solution of the equations describing the time dependence of light emission This as sumption is convenient but not realistic It would be more realistic to recognize that the relaxation time will be a function of both the excess carrier density and the coupling between the photon density and the excess carrier density The current models for modulation rate of laser diodes have been developed during the last decade by looking for closed form solutions to the modulation rate equations so that the role of physical parame Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Direct Modulation of Laser Diodes Direct Modulation of Laser Diodes 179 ters on the modulation rate could be appreciated and used in design Finding closed form solutions was an important consideration be cause few people had access to supercomputers that might better model the situation But now that we all have supercomputers sitting on our desktops the door is w
350. the same frequency f same energy s _ g What is the frequency of a 40 meV vibration E 40 x 10 1 6 x 10 19 f h 66 x 1034 9 x 1012 1018 Hz 2 27 What is the wavelength A v f 10 1013 10 8 cm Well this is only a few times larger than the lattice parameter of Si Does this make sense The lower limit on the wavelength is the interatomic distance which is about 0 12 x 108 cm in silicon So lattice vibrations have a wavelength that is an integral multiple of the lattice parameter These vibrational quanta are called phonons They are important be cause they allow the semiconductor to reach equilibrium To summarize our story so far Wavelength of a 1 eV electron 12 A Wavelength of a 1 eV photon 1240 nm 1000 x Agiectron only true around 1 eV So what is the wavelength of a 1 eV phonon The answer is a 1 eV phonon does not exist It cannot exist because its wavelength would be much smaller than the separation between atoms and the phonon represents vibrations of atoms However the wavelength of a 40 m eV phonon is about the same as that for the 1 eV electron Since momentum h A at room temperature the momentum of a typical phonon is similar to the momentum of 1 eV electron As electrons move around in the semiconductor they need to con serve energy and momentum In this never ending struggle the phonon acts as a source of momentum that contributes very little en ergy whereas the
351. the same time Absorption can take place if the energy of the incident photons is greater than the band gap Ab sorption does not occur all in one spot at the surface but rather pro gressively as the photons propagate into the semiconductor At any point inside the semiconductor the amount of light that gets absorbed is proportional to the total intensity that is present The constant of proportionality is called the absorption coefficient The simple model shown in Fig 7 4 gives an excellent description of this reality We can write down an equation that describes this situation I x Ax I x Al x and Al x a I x je x gt AALSA A S I x I x Ax Figure 7 4 A simple schematic diagram of light passing through a section of material in which absorption is taking place Absorption causes the intensity of light to decrease as a function of distance traveled The change in the intensity between points x and x Ax is proportional to the intensity at point x Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Lasers Lasers 151 By letting Av become small we can write d nl al x z U x Io W cm 7 6 The value of a depends on the material and on the photon energy For example in the case of GaAs a is about 104 cm for photo
352. there are com peting tendencies in manufacturing both to raise the index difference and to increase the fiber core diameter A compromise solution is a core diameter of about 9 microns and a numerical aperture of about 0 1 The lowest order HE mode propagates alone under single mode conditions It has a simple spatial structure having circular symme try and maximum intensity in the center of the core The radial mode field amplitude is described by a Bessel function but it can be well ap proximated by a simple Gaussian function I r pe 9 11 The mode field diameter is defined as 279 The mode field diameter depends on the fiber V parameter and it can be either larger than or smaller than the fiber core physical diameter d A convenient and ac curate empirical expression developed by Jeunhomme see Bibliogra phy can be used to determine r 2 0 65 1 619V 1 2 879V 9 12 9 5 More Capacity Cables of optical fiber with low losses were installed in the ground and under the ocean during the 1980s Simultaneously engineers were developing the semiconductor lasers for the transmitters There was general agreement in the industry that the wavelength of choice Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Optical Fibers and Optical Fiber Ampli
353. through the same section and is ampli fied by laser action causing a transition by electrons from the 13 2 state to the ground state 980 pump in Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Optical Fibers and Optical Fiber Amplifiers 216 Advanced Topics wavelength related information So a different detector and electronic channel are required for each wavelength Electronic amplifiers must be specially designed for the modulation rate that they are intended to amplify The optical amplifier was exactly the right solution to launch the new age of high capacity optical communications using wavelength division multiplexing There is now much research activity directed at achieving all optical signal processing transmission amplification adding dropping channels dispersion compensation and even signal retiming and reshaping It is an ambitious but worthy goal The optical amplifier has revolutionized the architecture of optical communications systems Its impact was first seen in undersea fiber optic cables Instead of having to bury complex electronics under the ocean one now installs erbium doped optical amplifiers The ampli fiers automatically handle whatever combination of wavelengths and modulation rates that the operator wishes to feed in a
354. tion is accomplished by modulating the drive cur rent of the laser Current modulation has the advantage that it is both simple and economical to implement The disadvantages of cur rent modulation are related primarily to transient effects associated with turning on or turning off the laser Some of the main difficulties are chirping and self pulsations The laser chirp refers to the change of the laser output wavelength with time as the laser is being pulsed on or off The chirp may be large enough to increase the communica tions error rate beyond acceptable limits Self pulsations are the re sult of a resonant coupling between the population of photons and the 177 Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Direct Modulation of Laser Diodes 178 Advanced Topics population of excited carriers in the laser structure The presence of self pulsations or relaxation oscillations puts a limit on the modula tion bandwidth of the laser This chapter is somewhat different from the others in this book There are no suggested laboratory experiments because they are sometimes difficult to set up and involve specialized equipment In addition the ultimate bandwidth that can be obtained by direct mod ulation of laser emission is a subject of current research Less than a d
355. to be sure The nonequilibrium carrier density at the edge of the depletion region rises exponentially and there is current in the diode However for a moment concentrate on the first two changes In forward bias the Fermi level on the n side of the diode is at high er energy than the Fermi level on the p side Electrons will move from the n side to p side in an attempt to redress this difference and there will be current in the diode In Fig 7 8 we show the situation as the applied voltage is close to the magnitude of the built in potential The effect of forward bias in the diode is to create a population inver sion in a four level system It does this by bringing the populations of electrons and holes into physical spatial overlap Recombination of electrons and holes requires that the electrons and holes be in the same place at the same time that is within a de Broglie wavelength of each other at the same time This is a distance of about 10 nm Of course energy and momentum must be conserved This condition is as sured by choosing a diode made from direct band gap materials such as GaAs InP or direct bandgap alloys made from these materials Electrons s t X Aw gt e Oo Vg m Z NI T7 Holes p DISTANCE Figure 7 8 Energy level diagram of a degenerately doped p n junction diode in forward bias Note that the concentration of electrons in the conduction band lies higher in en ergy than the concent
356. to be 100 efficient in order to produce an im age In the final step Fig 5 13 the liberated silver atom diffuses through the lattice and finds the silver sulfide site neutralizing its negative charge This motion of silver atoms is also part of the photo conductive process This means that the site can capture another elec tron and subsequently another silver atom This regeneration of the silver sulfide center means that each such center may eventually at tract many silver atoms The agglomeration of silver atoms forms a latent image The image cannot yet be visualized but it is physically present in the film Development of the photographic film fixes the latent image and renders it visible The development consists of three steps amplifica tion desensitization to light and stabilization The initial step of am plification consists of a chemical reaction that causes all the silver atoms in an exposed silver bromide crystal to be separated from the bromine atoms and attached to the silver sulfide sites thus amplify ing the exposure to light In the next step the bromine atoms and the silver bromide molecules are dissolved leaving behind only the silver atoms in the exposed grains At this point there are no more silver bromide atoms The film is no longer light sensitive so it can be viewed and the image is now apparent Finally the film is stabilized or fixed 5 6 Sensitization In Section 5 4 we showed that the in
357. troduction of shallow trapping centers can change the response time of a photoconductive detector so that it is different from the carrier lifetime This change occurs be Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Photoconductivity 92 Photonic Devices cause the traps act like reservoirs for carriers that are excited and move into the conduction band or the valence band Electrons can re combine with holes at recombination centers and they need to be free to move in space to find the recombination center A carrier in a trap does not have this mobility and it can recombine only by being ther mally excited and moving into the conduction or valence band The re sponse time is associated with the time it takes for this movement into a band plus the subsequent relaxation time For electrons this can be expressed as Ny Tres 1 tr 5 14 where n is the density of shallow electron traps and n is the density of excited carriers moving into the conduction band There is an anal ogous expression for holes Equation 5 14 makes it explicit that the response time of a photoconductor will depend on the excitation level even though the carrier lifetime remains unchanged In this section we will take this idea one step further and show how the carrier life time ca
358. ty These changes will generate differential equations that cannot be solved in closed form This is an inconvenience the importance of which will continue to di minish as computer power continues to increase A decade ago the current model was used to predict that the limit to direct modulation of semiconductor lasers was about 5 GHz Many experiments showed this to be incorrect and 10 GHz lasers are now commercially available Today s systems engineers would like to have lasers that can be driven at 40 GHz There is debate about whether or not this is possible Having a better model for predicting the time re sponse would be a big help in designing these components An alter native solution is to run the laser at dc and use an external modula tor This is a more costly solution but one that can provide the required performance 8 3 Summary Semiconductor lasers are used in communication systems where the light output is modulated directly by changes in drive current The transient response of laser to a change in drive current is more com Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Direct Modulation of Laser Diodes Direct Modulation of Laser Diodes 189 plicated than the transient response of LEDs because of the interac tion between the carrier density
359. ulation condi tions e g a modulation frequency less than 1 MHz the broadening of a pulse due to material dispersion is Aty L AA M L 0 1 3 0 3 psec km However at a modulation frequency of 1 MHz the pulse width itself is already 10 psec in width After transmission through 100 km of fiber the intrinsic pulse duration is still four orders of magnitude larger than the broadening due to dispersion Now consider a laser modulated at 10 Gbits sec The time duration of this pulse is approximately 1 oe 10 x 109 100 psec The frequency bandwidth of the pulse is Af 2x 10 He At The central frequency of the light pulse at 1300 nm is 2 3 x 1014 Hz The modulation of the laser broadens the frequency by 2 x 101 2 3 x 1014 0 9 x 10 4 The wavelength spread of the emission is the same percentage so that AA 0 1 nm As a result the wavelength broaden ing under modulation is now significant 0 1 nm 0 1 nm 0 2 nm The pulse width broadening is now two times larger than the case at 1 MHz or 0 6 psec per km After 100 km this results in a broad ening of 60 psec Remember that the width of the pulse at 10 Gbits sec is 100 psec So dispersion has broadened the signal pulse to almost two thirds more than its allotted bit period Clearly this is a problem Some dispersion correction is needed At the next lower Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright
360. ure 3 9 Responsivity gives the photocurrent that results from a fixed incident opti cal power Since it takes more photons to produce 1 watt of optical power as the photon wavelength increases the responsivity will also increase as the wavelength increases provided of course that the quantum efficiency stays constant Optical reflection occurs at the photodiode surface because the index of refraction of the semiconductor n 3 4 is different from the re fractive index of air n 1 Fresnel s equation can be used to calculat ed the required reflection coefficient Frensel s equation can be ap plied if the interface between the semiconductor surface and air is flat and planar over many wavelengths distance For light impinging on the photodiode at normal incidence the reflection coefficient Fres nel s law is calculated as follows o 3 29 E ni N where Ep and E are the amplitudes of the reflected and the inci dent light beams respectively The reflection coefficient is given by the square of this ratio ni no _ 4 ni No E 16 25 3 30 In the case of a photodiode having a planar surface the maximum possible quantum efficiency for any kind of semiconductor detector is actually only 75 If you introduce a third layer situated in between the semiconduc Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies Al
361. ust also change to maintain equality How is this change accomplished Does the frequency change the wave length change or some combination of both Use conservation of energy to support your argument Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Source Photonics Essentials Part Photonic Devices Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Photonic Devices Downloaded from inglibrary com ght Hill p 3 Any use ien to the Terms of Use a n at the website Source Photonics Essentials Chapter Photodiodes 3 1 Introduction There are a number of solid state devices that can generate an elec tric signal when they are illuminated We can divide all these de vices into two categories In one category are the devices that con vert the energy in a beam of light into an electric signal An example of this is the bolometer This is really a collection of thermocouples inside an efficient photon absorber The energy of the photons is con verted to heat and the rise in temperature is converted by the ther mocouples into an electric signal These devices are energy de
362. veloped for the threshold current can be used as a model to show the dependence of the threshold current on ma terial parameters This model does a good job of estimating the threshold current in semiconductor laser materials based on GaAs and InP A typical value for the threshold current of GaAs based heterostructure lasers is about 3 kA cm A GaAs laser with a threshold twice this high will not work in continuous operation at room temperature Figure 7 11 Light emission from a GaAs AlGaAs laser structure at room temperature In a the laser device is operating in the LED mode The emission line width is deter mined by the density of states and the relative transparency of the diode for photon en ergies higher than the band gap In b the first effects of gain can be seen The emis sion linewidth narrows and centers on the energy region where the gain is highest which occurs at a slightly lower energy In c the current is above threshold and light emission occurs in only a few resonant cavity modes where the gain is highest A wave length marker shows the linewidth 1 5 A and the spacing 3 A of these modes This is close to the resolution 0 5 A of a 0 25 m spectrometer at this wavelength Re produced with permission from H C Casey Jr and M B Panish Heterostructure Lasers Part A p 179 Academic Press New York 1978 Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com
363. verse bias This effect can easily be seen in Fig 4 3 However there is a more interesting way to plot your results of capacitance versus reverse bias voltage To see what this is we will square both sides of Eq 4 6 C E oq Np A2 2 Vz V C2 1 eeqgNp Vapi v S i 4 8 In most cases the impurity concentration is constant so that a graph of C A versus the bias voltage will be a straight line From the slope of this line Np can be directly determined If the straight line is extrapolated to the point where C A would equal 0 then the val ue of the corresponding voltage is the built in voltage of the p n junc Indium Phosphide 50 C V Plot BIAS i 40 steps ov 4 STOP 10 00 poe FREQ 1 MHz co t a l 304 a L EENI a cS Q La i 0 oy oe OPE J i 0 2 4 6 8 10 Reverse Bias Voltage Volts Figure 4 3 The capacitance voltage characteristic for an InP diode Note that the ca pacitance decreases with increasing reverse bias voltage By tuning the capacitance electrically it is possible to change the response time of the photodiode Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Electrical Response Time of Diodes Electrical Response Time of Diodes 69 tion This technique is widely used in bo
364. very different from LEDs which are practically indestructi ble Most lasers cannot stand up to reverse bias beyond 1 V and few will survive forward bias current greater than 1 2 times the threshold current Thus you have a strong interest in knowing the current voltage relationship for your device In the data sheet shown in Fig 11 8 you can find the important in formation you will need to operate the laser safely and effectively Re ferring to part d of the figure we can see that the class of the laser is indicated in the fine print at the bottom of the sign marked DAN GER This device which is a GaAs AlGaAs laser emitting in the in frared at 820 nm is identified as a Class III b laser with an output of 30 mW under pulsed conditions In part a of the figure there is a diagram of the pin out showing the correct polarity and the output lead for the monitor photodiode The pin out is essential because it is not recommended to measure the current voltage characteristic on a curve tracer This measurement might burn out the laser Part b shows the threshold current The threshold current in the data sheet is a typical value and you can expect to measure a thresh old current that is within 10 of this value You can find the output wavelength This value should be accurate to within a few nanome ters If you are making measurements on a He Ne laser or a laser pointer you probably will not have the benefit of referring to a data
365. w digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Light Emitting Diodes 116 Photonic Devices interface Light Source Figure 6 8 An interface between two materials having different indices of refraction Light traveling from the GaAs toward the air will be partially transmitted and partial ly reflected at the interface greater angle has no chance of transmission and is reflected back into the semiconductor structure If we assume that the diode is emitting with equal intensity through 47 steradians the fraction of the emis sion that can escape the diode is 4 We can estimate the fraction of the intensity that reaches the outside world as follows outside linside 0 75 0 04 0 02 Tinside 6 18 This estimate shows that the external efficiency of a semiconductor LED is small about 2 Specific improvements to the geometry and the surface of the LED can improve this figure to about 30 under op timum conditions Some of these changes are discussed below Howev er before going into these modifications it is worthwhile to recall that the index of refraction of a typical polymer material is about 1 5 This means that the escape cone will be much larger for light in a polymer LED than for light in a semiconductor LED The comparative advan tage of polymer LEDs is the subject of Problem 6 6 6 5 Beating
366. working in buildings with their counterparts around the world The difficulty with this technology is fundamentally related to electrons Electrons have mass and they become harder to move as the frequency increas es Eventually only the outer skin of a wire can carry the current and the resistance of the wire is much higher than it was at lower fre quencies Resistance means loss and loss means that the signal can not travel as far Photons on the other hand have no mass There is no analogous loss mechanism for photons when the frequency is increased Optical fibers are ideally adapted to carry very high bandwidth communica tions right up to the frequency of the light beam itself Coaxial elec tric cable can be used to transmit electrical signals at high frequency However high means perhaps 1 GHz for distances of a few meters Optical fibers can carry signals with three more orders of bandwidth in the terahertz regime over distances of hundreds of kilometers An easy way to appreciate the limits of coaxial cable is to look around your neighborhood for the boxes where the cable TV vendor has to in stall amplifiers to boost the TV signals which are sent at approxi mately 10 MHz There are lots of these boxes because the signals have to be amplified every few hundred meters Basically transmis sion of a modulated electrical current becomes more and more diffi cult as the frequency of modulation goes up On the other hand sen
367. xternal filter described above Recommended Equipment 1 Regulated power supply 2 Current source 3 Voltage source 4 Spectrometer Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Experimental Photonics Device Characterization in the Laboratory Experimental Photonics Device Characterization in the Laboratory 265 Diode lasers Laser pointer He Ne laser Lock in Si photodiode 10 Chopping wheel 11 Lenses Oo ongoa Procedure Safety A laser light source presents a potential safety hazard when the power of the light beam is sufficiently strong that it can overheat and burn the surface it strikes If this surface is the eye laser damage can cause permanent damage or even blindness Lasers can be made with a wide range of output power from a milliwatt to many watts of output power Pulsed lasers present the additional danger that whereas the average power may seem moderate the output power in the pulse itself can be quite high Damage to the human organism is the most serious consideration but a high power laser beam can ig nite the surface it strikes causing an unintended fire Fortunately it is always possible to work safely with a laser To help the user appreciate the safety issues lasers are divided into four classes depending on the
368. y and phase of a propagating light beam In Chapter 3 of the thesis there is an abrupt change of subject and de Broglie addresses hypothesis proposed by Bohr to explain the exis tence of discrete atomic energy levels Seven years earlier Neils Bohr proposed that the electrons in atoms traveled in stable orbits thus al lowing atoms to have long lifetimes an experimental truth we all rec ognize The condition originally proposed by Bohr was h moR n 2 28 20 where m is the mass of the electron w the angular frequency of rota tion around the atom and R the radius of its orbit For a circular or bit v R and Bohr s condition becomes h myvR n 2 29 27 This has the simple interpretation that the angular momentum of the electron mvR is quantized in units of h 2m However in 1924 there was no idea about why this quantization oc curred or what properties of the electron assured this behavior On page 44 of his thesis Fig 2 6 de Broglie offered an interpreta tion that was consistent with his everyday experience the Bohr condi tion was similar to the behavior of waves of water in a closed circular tank Stable states occur when there are standing waves The condi Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Electrons an
369. y are emitted in free space Be cause of the large index of refraction of semiconductor materials we re call from Section 6 4 that most of the photons emitted are trapped by total internal reflection inside the LED A typical value for next is 0 02 In steady state dN dt 0 and N Np J B NP n qd om 6 17 We would like to rewrite this equation in terms of N np This will al low us to combine the two terms on the right hand side of the equa tion and to compare the recombination rates for radiant recombina tion to those for nonradiant recombination This comparison gives the internal quantum efficiency We can use the charge neutrality condition to write NP N po AP and AP AN N np n2 i N np N npN n 6 18 Note that B NP n BN N np Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Light Emitting Diodes 126 Photonic Devices Here we have assumed that N np 1 Note that N and npN are each much greater than n The next step is to substitute the result of Eq 6 18 in Eq 6 17 J N N np lt 7 BUN npN n n P _ BN N np 6 19 Tn r n r By comparing the two terms in Eq 6 19 you can see that BN looks like a reciprocal relaxation time Since this term is assoc
370. y com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Photoconductivity 94 Photonic Devices __ Recombination Center K7 Pi d Pi Area Capture Cross section k L vr gt Figure 5 15 The volume of a recombination center is given by the capture cross section s times the recombination length vr ing the density of recombination centers of the same type will always reduce the lifetime and reduce the sensitivity However if we add re combination centers of a different type it becomes possible to length en the lifetime of one carrier while decreasing the lifetime of the oth er Under the right conditions these new centers deactivate the first type of centers causing all the recombination to pass through the sec ond type of centers The result can be a dramatic increase in sensitiv ity of the photoconductive material This is the principle of sensitiza tion Cadmium sulfide is a semiconductor that is widely used as a photo conductive cell in light meters In its undoped state the residual im purity level is about 1015 cm and the recombination level lies in the middle of the band gap as diagrammed in Fig 5 15 We will call these recombination centers type 1 The electron and hole lifetimes are about 10 7 seconds To sensitize this material we will add cadmium vacancies to the level of 1016 cm 3 This new recombination level is sl
371. y to develop a model for the level of current required to induce lasing in a p n diode and how this current depends on the parameters of the laser struc ture The laser is a special kind of LED You already know about many of the measurements such as the I V characteristic and the light current characteristic of these devices 7 1 Amplifiers and Feedback If you were to imagine the simplest amplifier circuit you could think of it might resemble the circuit in Fig 7 1 This shows an NPN tran sistor with an input on the base a bias on the collector and the emit ter shorted to ground This amplifier works as follows When the po tential of the gate is close to common the transistor is turned off and y 470k 4 7k OUTPUT INPUT 2N2926 COMMON Figure 7 1 A circuit diagram of a simple class A transistor amplifier Downloaded from Digital Engineering Library McGraw Hill www digitalengineeringlibrary com Copyright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Lasers Lasers 145 its resistance to common between the output and common is very high compared to the 10 kW resistor in the collector circuit The voltage at the output relative to common is very close to the bias voltage of 5 V On the other hand if the bias on the gate is raised so it is close to 5 V the transistor will turn on and its resistance will now be low com pared to 10 kW So the voltage
372. yright 2004 The McGraw Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Photoconductivity Photoconductivity 83 Conduction Band Ohmic Contact Energy Valence Band 4 Figure 5 7 Finally the hole reaches the negative contact The sample is now back to its condition before the absorption of the photon At this point the photoconductivity stops Assuming that the sample was uniformly illuminated 12 electrons will flow in the external circuit for every incident photon absorbed Distance The gain of the photoconductor is the ratio of the transit time of the slower charge carrier to the faster charge carrier t G t 5 4 te Mp The gain and the bandwidth are interrelated and this relationship is expressed by the gain bandwidth product t 1 1 eV G B h h te Tmt Tte TL2 5 5 It will be helpful to think about the following two cases 1 The incoming signal has a duration in time much less that the transit time of the slower charge carrier In this case the action of photoconductive gain will be to increase the signal amplitude by elongating the signal in time to the transit time for the slower car rier In this case signal bandwidth is exchanged for signal ampli tude 2 The incoming signal has a time duration that is longer than the transit time of the slower charge carrier In this case the photo conductive gain will increase

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