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Williams Thesis - Center for Quantum Devices

1. 04 86 8 2 He Ion Etching of Suspended Graphene 204 87 8 3 Image of Etched Suspended Graphene 02 005 88 8 4 He Ion Etching of Graphene on SiO2 202 00 89 A 1 Graphite source material oaoa ee 93 A 2 Cleaving the graphite and preparing the tape 94 A 3 Transfer chip to glass 2 ee 95 A 4 Heat assisted deposition 2 0 a 96 A 5 Optical image of graphene 2 2 20 2000 ee ee 96 B 1 Schematic of a graphene p n junction 0 0200 4 129 B 2 Charge carrier arrangement in a graphene p n junction 130 B 3 Schematic of a multiple top gate graphene p n junction device 131 B 4 Charge carrier arrangements in multiple top gate graphene p n junction device132 B 5 Charge carrier arrangements in multiple top gate graphene p n junction de Vice continued Seine arai 4 e pooma Wot Sg eta tte note al ne Re 133 B 6 Reconfigurable graphene wires in p n junctions 134 B 7 Schematic of the molecular species in the functionalization layer on graphene and method of coating on a nanotube 0 005005 135 B 8 Effect of electron beam irradiation on the doping level in a nanotube 186 B 9 Differential conductance in a graphene p n junction 137 B 10 Quantum Hall differential conductance in a graphene p n junction 138 C 1 DXF to CEL conversion menu 2 a ee ee 141 C 2 Elionix sample holders
2. 0 0 02 02 eee ee ee 141 C 3 5mm by 5mm Elionix sample holder 2 142 C 4 Elionix load lock exchange position soo o 00004 142 C 5 Isolation valv s s srra dt fe eek laos Se Ae oe ae Wao a 143 C 6 Opening the airlock 0 0 0 0 00 00 02 ee eee ee 143 C 7 Loading the plate into the load lock 00 0000 4 144 C 8 Locking the transfer rod 2 0 ee 145 C 9 Unlocking the plate The White Stripes 0 145 C 10 Setting the beam current ooo ee 147 C 11 Measuring the beam current 2 2 a a 147 C 12 Focusing the beam lt 2 meni a Bebo ble ha ee Pas Se ee JP a 149 Cols The ELUCID aoet bs ee Se eae te Se ee oR Ga Be i 150 C 14 Setting up the write 1 Job 2 Menu 0 2 0 0 0 00004 150 C 15 Loading the CEL file 0 0 0 00 000000200004 151 C 16 Creating a chip matrix ooa ee 153 C 17 Setting up the write 2 Exposure Home 00 154 C 18 Setting the exposure conditions 0 00000 eee eee 154 C 19 Completed field correction sosoo o e ee 155 C 20 Setting up the exposure ooa ee 156 C 2L Alignment process erari esi oe y niens ae Bee hag Re ates 157 C 22 Area around the load lock 2 2 ee 159 C 23 Control panel deis ee 159 Acknowledgements Graduate school would have been unbearably long if it weren t for my family friends and colleagues First I would like to thank my advisor Charlie Marcus There is nothin
3. Figure 2 2 The Savannah 100 by Cambridge Nanotech temperature of about an atmosphere The dinitrogen tetroxide bottle was mounted on the side of the gas cabinet 1 4 16 Figure 2 3 1 liter lecture bottle of dinitrogen tetroxide obtained from Matheson TriGas stainless steel tubing was attached to the lecture bottle and runs up the Parker solenoid value The total volume of the tube is 3 5 in No regulator is required as the vapor pressure is low Initially the water precursor value was split into two lines and the water precursor was fed into one line and the NO into the other Over time I have found that water and or NOg collects in the piping and at some point forms nitric acid and bubbles into the reaction chamber Now only one line goes to the solenoid valve and when switching is needed between water and NOs one line is disconnected and the other is attached Ideally a fixed line going to the chamber that never sees atmosphere would go to the chamber but this is not possible as the Savvannah 100 has only two for the older models or 1 for the newer models port to the reaction chamber To accommodate the safety concerns of having NO in the lab the gas cabinet was completely closed and a pipe was mounted on the back panel on the cabinet see inset of Fig 2 3 and connected to house vacuum The present gas cabinet is shown in Fig 2 3 17 AA i 4 jean Controller Figure 2 4 The standard gas cabi
4. in Graphene Phys Rev Lett 98 116802 2007 168 90 91 92 93 94 97 98 99 D C Bell Contrast Mechanisms and Image Formation in Helium Ion Microscopy Microscopy and Microanalysis 15 2 p 147 2009 L Scipioni L A Stern J Notte S Sijranddij and B J Griffin Helium ion micro scope Adv Mater Proc 166 27 2008 L A Ponomarenko F Schedin M I Katsnelson R Yang E W Hil K S Novoselov and A K Geim Chaotic Dirac Billard in Graphene Quantum Dots Sci ence textbf320 356 2008 M D Fischbein and M Drndic Electron beam nanosculpting of suspended graphene sheets Appl Phys Lett 93 113107 2008 M C Lemme D C Bell J R Williams L A Stern B W H Baugher P Jarillo Herrero and C M Marcus Etching and Doping of Graphene Devices with a Helium Ion Beam submitted for publication R S Averbeck and M Ghaky A model for Surface Damage in Ion Irradiated Solids Journal of Applied Physics 76 6 3908 1994 J Zeigler J Biersack and U Littmark The Stopping Range of Ions in Matter New York Pergamon Press also at http srim org J C Meyer C O Girit M F Crommie and A Zettl Hydrocarbon lithography on graphene membranes Appl Phys Lett 92 123110 2008 R Vane Immobilization and Removal of Hydrocarbon Contamination Using the Evac tron De Contaminator Microscopy and Microanalysis 12 S02 p 1662 200
5. A w 5 5 6 we obtain the required mapping which straightens out the contact 3 5 6 4 The second approximation is necessary because the mapping 5 2 5 6 while straight ening the segments 3 5 6 4 distorts the rest of the boundary We notice however that sufficiently far from the contact 3 5 6 4 the mapping 5 2 is close to the identity z w gt 1 w 0 1 w z 5 gt 1 5 7 This property and the relatively small size of the segments 3 5 6 4 compared to the strip width guarantees that the distortion is small This is shown schematically in Fig 5 7 b where the curved grey polygon represents the actual image of the sample with the deviation of its boundary from the strip of the same asymptotic width shown in red and exagger ated for clarity The deviation is indeed small by investigating the mapping 5 2 5 6 numerically we found that the boundary is displaced the most at point 2 which is shifted 59 by approximately 0 3 away from its original position 2 along the real axis This is small compared to the sample width equal to 6 which allows us to neglect the displacement of the boundary Thus we assume that the mapping 5 2 5 6 transforms sample C into the semi infinite strip shown in Fig 5 7 c After this approximation is made it is straightforward to transform the semi infinite strip in Fig 5 7 c into the upper half plane which can be done by the mapping C cosh 5 8 In the plane the conta
6. The voltage at V and V Fig 6 3 b are vro X us VRi x Ha vri vRi eVi us eV 6 1 where vpi vpro is the filling factor of Region 1 Region 2 and us ua is the chemical potential of the source drain Using these values at Vig 20V vri 2 vr2 10 the Hall resistance at B 8T should be reduced from h 2e to V2 V1 I 2kQ which is approximately the resistance observed for Sz in the bipolar regime Fig 6 3 a In addition to the reduction of resistance a peak in resistance appears at Vig 5 5V at 8T Fig 6 3 a indicated by black arrow of magnitude 2kQ The peak in resistance corresponds to the transition of filling factor in Region 1 vp 2 6 suggesting that the peak is due to contributions the 69 2 3 4 5 63 4 5 6 Vr V Vr V Figure 6 3 a Szy Vig at B 8T shows well developed QH platueas of 2 6 and 10 e h in the unipolar regime The resistance is lower in the p n regime for values of Vig on the right of the dashed red line a result of edge state transport in Region 2 A peak in resistance indicated by the black arrow develops on the bipolar side Inset This peak yellow line indicated by the black arrow is reduced in magnitude as Vpg approaches the CNP Vig 40V of Region 1 b Schematic of the edge states present in the two regions of the device When the edge states propagate as shown the voltage difference between V1 and V2 is reduced c Szy Vig B for B between 0 and 8T
7. gt Graphene Ese gt gt Graphene Graphene a Si02 1 Vacuum _ Silicon yhd pe yd q 132re 1 a a sIxX 4 sa yydeq 1 yiq yoare aTxy A 8a y4doq 0009 0009 0009 Figure 7 3 TRIM simulations comparing a 30 kV Ga ions and b 30kV He ions for range and trajectory in graphene layers on SiO2 on silicon substrate c Range and trajectory of 30 kV He ions through a suspended graphene layer over vacuum SiO2 and silicon substrate Insets Schematic comparison between Ga ion and He ion interaction with graphene samples from molecular dynamics simulations 96 99 6 of the ions pass directly through the graphene with no ion interaction at all Instead the majority of the ion energy is deposited deep within the silicon substrate Fig 7 3b The helium ions lighter mass and higher speed results in smaller interaction volume with the surface layers and hence in better resolution and potential milling feature size From the perspective of sputtering and patterning the result is a reduced proximity effect in the surface layer The light ion mass results in low energy transfer and hence a relatively lower sputtering yield compared to gallium Figure 3c shows the situation for a suspended layer of graphene over SiO2 and silicon substrate The thickness of the vacuum gap and the SiO2 add up to 285 nm as would be the case in a device fabricated
8. 0 30 WV af 0 25 A i 20 0 Vbg V 20 Sample A2 0 T 1 1K T 0 3K 0 Figure 4 2 a Inset Conductivity o RW L calculated using R Vpg data in Fig 4 1 a and W L 5 7 Solid black circles correspond to o Vsq 0 at the Vig settings of noise measurements shown in b Main Excess noise Sf as function of Vzq near the charge neutrality point Vig 0 75 V The solid red curve is the single parameter best fit to Eq 4 1 giving Fano factor F 0 349 using Te 303 mK as calibrated by JNT b Best fit F at 25 Vig settings across the charge neutrality point for electron and hole densities reaching ns 1 4 x 101 cm c R left axis and right axis of sample A2 as a function of Vig W L 1 4 with Vga 0 at 0 3 K solid markers and at 1 1 K open markers d e Crossover width Tw normalized to JNT calibrated T and F obtained from best fits using Eq 4 1 to S7 Vsa data over Vsa lt 350 650 uV for Te 0 3 1 1 K 38 was independent of bias within 0 5 not shown in the V g lt 350 uV range used for the fit Note that the observed quadratic to linear crossover agrees well with that in the curve fit indicating weak inelastic scattering in Al 62 63 and negligible series resistance e g from contacts which would broaden the crossover by reducing the effective Vsq across the sample Figure 4 2 b shows similarly measured values for F as a function of Vig F i
9. 5 0 5 Backgate voltage V Backgate voltage V 136 10 neutrality point 10 2 2 i mo 14 gle s h oo ih aa a 20 B 4T a T 250mK gh a shay Jo E 20 s 7 L PE EET T EE oS a v N J 20 10 FEIN 138 Appendix C Elionix 7000 User Guide 139 The first step is to take the dxf file you created in DesignCAD or any other CAD software and covert it into the file type that Elionix uses called a CEL file To this open the dxfTOcel DOS window and perform the following Open new command shell DOS by typing cmd into Run window Type cd desktop Type dxfcel or gds2cel chose the one that is appropriate for your file type Enter filename that is on the desktop Enter name you want the CEL file to be Enter units of your drawing choose 0 for mm and 1 for microns Do you want to specific layers If yes make sure your layers are named with 1 2 in the CAD program Arc divison No Elliptic Arc No Arc in Polygon No Paint Yes Way of painting ellipse 1 Pitch 0 1 Depends on your preference Dose Conversion No Choose the layer number you want to convert by 1 2 4 Choose the appropriate sample holder see Fig 2 Load the sample on the sample plate Do not use metal tweezers or anything that will scratch the metal surface Make sure the sample is secure and that it is flat against the sample holder
10. Electronic properties of disordered two dimensional carbon Phys Rev B 73 125411 2006 D A Syphers and P J Stiles Contiguous two dimensional regions in the quantized Hall regime Phys Rev B 32 6620 1985 R J Haug A H MacDonald P Streda and K von Klitzing Quantized multichannel magnetotransport through a barrier in two dimensions Phys Rev Lett 61 2797 1988 S Washburn A B Fowler H Schmid and D Kern Quantized Hall effect in the presence of backscattering Phys Rev Lett 61 2801 1988 E H Hwang S Adam and S D Sarma Carrier transport in two dimensional graphene layers Phys Rev Lett 98 186806 2007 Y M Blanter and M B ttiker Shot noise in mesoscopic conductors Phys Rep 336 1 2000 165 58 61 62 65 66 68 P San Jose E Prada and D S Golubev Universal scaling of current fluctuations in disordered graphene Phys Rev B 76 195445 2007 C W J Beenakker and M B ttiker Suppression of shot noise in metallic diffusive conductors Phys Rev B 46 1889 R 1992 M J M de Jong and C W J Beenakker Mesoscopic fluctuations in the shot noise power of metals Phys Rev B 46 13400 1992 Y V Nazarov Limits of universality in disordered conductors Phys Rev Lett 73 134 1994 A H Steinbach J M Martinis and M H Devoret Observation of hot electron shot noise in a metallic resistor Phys Rev
11. Lett 76 3806 1996 M Henny S Oberholzer C Strunk and C Sch nenberger 1 3 shot noise suppres sion in diffusive nanowires Phys Rev B 59 2871 1999 R J Schoelkopf P J Burke A A Kozhevnikov D E Prober and M J Rooks Frequency dependence of shot noise in a diffusive mesoscopic conductor Phys Rev Lett 78 3370 1997 C H Lewenkopf E R Mucciolo and A H Castro Neto Conductivity and Fano factor in disordered graphene Phys Rev B 77 081410R 2008 L DiCarlo Y Zhang D T McClure C M Marcus L N Pfeiffer and K W West System for measuring auto and cross correlation of current noise at low temperatures Rev Sci Instrum 77 073906 2006 E McCann and V I Fal ko Landau level degeneracy and quantum Hall effect in a graphite bilayer Phys Rev Lett 96 086805 2006 A Rycerz J Tworzydlo and C W J Beenakker Anomalously large conductance fluctuations in weakly disordered graphene Europhys Lett 79 57003 2007 166 69 71 72 73 74 75 76 77 78 G B Lesovik Excess quantum noise in 2d ballisic point contacts Pis ma Zh Eksp Teor Fiz 49 513 1989 JETP Lett 49 592 1989 M B ttiker Scattering theory of current and intensity noise correlations in conduc tors and wave guides Phys Rev B 46 12485 1992 D Graf F Molitor T Ihn and K Ensslin Phase coherent transport measured in a si
12. Vectors ti t2 and f3 connect the A atoms to the 3 B atoms equation det H ES 0 1 3 The simplest solution is obtained by considering only nearest neighbor interaction thus only H44 Hgg and Hyp where A and B the two atoms of the graphene unit cell need to be evaluated Evaluation of energies H4 4 and Hpgp gives Haa Hen D FED a R H xaf R A R R where p is the orbital energy of the 2p level The off diagonal elements H4g Hpa are calculated for the 3 nearest neighbor B atoms see Fig 1 1 c using the three vectors ti t2 and t3 Hap yule cP eS tlk 1 5 Sap sle e8 ei yat k 1 6 where yn val R H xB R 0 and ys xar R xB 0 The determinants for H and S are then H p Yhtlk ynt k p ue 1 qst k yst k 1 Using these two matrices the solution to the secular equation 1 3 is na e EA 1 7 1 ysulk u k j 4 cos wis cos Faa 4 cos me 1 8 The resulting band structure is shown in Fig 1 2 using the parameters 2 0 y 3eV and ys 0 129 1 Note that the energy dispersion curves for E gt 0 meet the curves for E lt 0 at the K points in the Brillouin zone For small k values around these K points the energy E is linear in k It is this low energy linear relationship that gives graphene its unique electronic properties 1 3 Quantum Hall effect in graphene Discovered 29 years ago the quantum Hall effect il
13. a first device electrode connected to a 126 first region of the graphene layer a second device electrode connected to a second region of the graphene layer a dielectric layer blanket coating the second graphene surface and the device electrodes and a top gate electrode disposed on the dielectric layer over one of the device electrodes 19 The device of claim 18 further comprising a second top gate electrode disposed on the dielectric layer over a second one of the device electrodes 20 The device of claim 18 further comprising a functionalization layer under the dielectric layer that is non covalently bonded to the second graphene surface and that provides chemically functional groups bonded to the dielectric layer 21 The device of claim 20 wherein the functionalization layer comprises NO2 and a species selected from the group consisting of trimethylaluminum and tetrakis dimethylamido hafnium 22 The device of claim 18 wherein the dielectric layer comprises an oxide selected from the group consisting of A1203 HfO2 and ZrO2 23 The device of claim 18 wherein the graphene layer is disposed on a substrate on top of a layer of oxide coating one surface of the substrate 24 The device of claim 23 wherein the substrate comprises a silicon wafer 25 The device of claim 23 wherein the substrate forms the backgate electrode 26 The device of claim 18 wherein the first and second graphene regions form a circuit wiring connection betwee
14. charge carrier types electrons or holes The entire modern bipolar electronics industry is based on devices that employ holes and electrons in device materials In the semiconductor materials conventionally used for bipolar electronics mainly silicon and germanium the control of the particular charge carrier type in a device material is primarily achieved by a physical doping process such ion implantation resulting in the creation of hole and electron regions in the implanted material Such a doping method permanently fixes the location of the electron or hole regions in a semiconducting device In addition ion implantation fixes the charge carrier density i e the number of charge carriers either electron or holes per square meter of the semiconducting material and device 006 It has been established that in startling contrast to this conventional charge carrier control by doping control of electronic charge carrier type in graphene can be accomplished in a temporal fashion by the application of an electric field in the vicinity of a graphene region Such an electric field can be produced by e g a metal gate electrode provided near or at the surface of a graphene layer A positive voltage on the gate electrode shifts the Fermi level of the graphene region under the electrode to produce a predominance of electron charge carriers in that region A negative voltage on the gate electrode shifts the Fermi level of the graphene region under the el
15. following subtraction of the best fit quadratic polynomial to g Vbg at each B setting to maximize contrast Dashed lines correspond to filling factors nsh eB 6 10 14 and 18 with ns a Vbg 1 1 V and lever arm a 6 7 x 10 em 2 V Their alignment with local minima in dg Vpg identifies Al as single layer graphene 33 67 The Drude mean free path h 2e o kp 68 where kp 7 ngl is found to be 40 nm away from the charge neutrality point using the B 0 conductivity o RW L Fig 4 2 a inset Current noise spectral density Sr is measured using a cross correlation technique de scribed in Ref 66 see Fig 4 1 c Following calibration of amplifier gains and electron temperature T using Johnson noise thermometry JNT for each cooldown the excess noise Sy Sr 4kgTeg Vza is extracted S5 Vsa for sample Al is shown in Fig 4 2 a Linearity of S at high bias indicates negligible extrinsic 1 f or telegraph resistance fluc tuations within the measurement bandwidth For these data a single parameter fit to the scattering theory form for energy independent transmission 69 70 4 1 s 2kple Si 2elF ott Ved kp 2kBTe eVza gives a best fit Fano factor F 0 349 Simultaneously measured conductance g 22 2 e h 37 Sr 2 e nA Sample A1 Vbg 0 75 V Te 0 3K e data fit OF 300 Ved uV 300 0 45F j i 0 40 K u 0 35
16. inverse square root of the level number one may expect mixing between non nearest LLs to increase at high energies Such mixing can lead to the longitudinal conductivity values in excess of those of Ref 81 which only considers mixing between nearest LLs see the discussion in Ref 82 To take these effects into account we extend the model of Ref 75 by assuming that the contribution of the nt LL to the conductivity tensor in monolayer graphene is described 53 2xSV gt 8 9 SV Bilayer B 8T T 250mK s 0 2 mn 0 3 A 0 25 40 20 ON Vig VI Figure 5 4 Measured g Vpg for sample B2 black and the calculated g using 0 25 for Es 0 2 dashed blue trace and amp 0 3 solid red trace Two key features in the curve suggest this sample is a gapless bilayer namely a pronounced peak in g near the CNP and the larger spacing between the two minima straddling the CNP compared to the spacing Vig 9 5 V between other consecutive minima by a modified semicircle elliptic law OnO2g A2 bnOxy Tra One ny Thyn 0 5 1 where nOrr and nOgry are the effective longitudinal and Hall conductivities Plyn and a are the quantized Hall conductivities at the neighboring plateaus Here n and n are zy n neighboring LL indices related by n n 1 except the doubly degenerate v 0 LL for the bilayer in which case n 1 and n 1 The A account for departures f
17. the latter relies on transferring graphene flakes onto TEM grids which is not suit able for larger scale fabrication of devices This work focuses on process considerations of He ion etching of graphene while specifics of graphene field effect transistors are reported elsewhere 94 7 2 Helium ion beam process considerations The design principle of HeIM is based on the field ion microscope operating in a UHV environment with a cryogenically cooled sharp tungsten tip to which He ions are introduced 75 Final Lens MCP E T SE detector detector Sample Figure 7 1 Schematic of a graphene device Inset Photograph of the microscope chamber with installed chip Fig 7 1 The tip is manufactured in such a way that it is truncated by a trimer of atoms inset of Fig 7 1 the gun is centered in such a way that only a single atom emission is used for imaging The beam current can be modified by changing the imaging gas pressure with typical operation in the range of fA to pA The exact details of the microscope operation have been described elsewhere 91 The physical interactions of the ion beam with the sample are critical to determine the ultimate spot size for the highest possible resolution it also ultimately controls the quality of the generated ion etched pattern when combined with sample proximity effects Typical beam specimen interactions in HeIM and the variety of resulting signals and emitted particles are indica
18. which places limits on the speed at which the device can operate Also for a given electric field range extrinsic doping limits the carrier density and if the doping is strong enough the carrier type that can be utilized in a graphene device The level of doping in a graphene device can be ascertained by sweeping the voltage V on a gate electrode while measuring the resistance of the device If the peak in resistance or corresponding dip in conductance is at or very near the point of zero voltage bias the device is undoped If the peak in resistance occurs very far away from the zero voltage bias the device is doped 042 It is recognized in accordance with the invention that permanent prevention of ex ternal doping of graphene in a graphene device is particularly preferred to preserve graphene device performance characteristics To prohibit such external doping in accordance with the invention a graphene layer to be employed in a device or circuit is protected to prevent environmental changes to the device in which the graphene is employed The form of this graphene protection can be implemented as a function of a desired device configuration For example where one or more local top gates are employed to control regions of a graphene sheet the gates are separated from the graphene sheet by a gate oxide layer The gate oxide layer can operate to shield the graphene from the environment if in accordance with the invention the oxide layer is
19. 0 0 ee ee 3 7 Acknowledgements 20 00 e 4 Shot noise in graphene Al SIntroduction s 22466 224 444 be eA Gace ee ee ka ae ha AD Methods iei gr ecto hee a a a ee ee ee Hee Ae Dee A 4 3 Shot noise in single layer devices 2 20 20 0000 eee ee ee 4 4 Shot noise ina p n junction 2 0 e 4 5 Shot noise in a multi layer device 2 0 0 0 20000200002 2 4 6 Summary and acknowledgements 00 00000 eee 5 Quantum Hall conductance of two terminal graphene devices Dede TILLOGUCTION gs ae p Boe SoBe ee Pe Ae eh See ee Hes De a Pe A 22 23 24 25 26 28 30 32 5 2 Phenomenology of conductance in two terminal graphene devices 47 5 3 Sample fabrication and measurement 00 a eee eee 48 5 4 Monolayer samples 2 2 50 5 5 Bilayer samples v 42 4c iu ara eng oe oh ed ha pe ee ep es 55 5 6 Non rectangular samples o ooa ee 56 5 7 Summary and discussion a a p Ta p R pli O E K y E E E 60 5 8 Acknowledgements 0 0 e 62 6 Snake States in Graphene p n Junctions 63 6 1 Antrodictions 4 55th Atets 28 al Veet bhatt ake ee tats ae toe 64 6 2 Devices fabrication and measurement setup 0 002 085 66 6 3 Low magnetic field properties of transport along p n junctions 67 6 4 Sry in the quantum Hall regime fn e ety eae AE ge eS 69 6 5 Vig dependence of the snake state oo Lb th Se oe we he 71 6 6 lt Discussion lt o 84s ke De eo ee ea A ee ae Boe a gd 71
20. 088 There was found some departures between the experimental data and Expressions 1 and 2 as represented in the grid of Fig 10E For instance the plateau near 3 2 e h in Fig 10D is seen at a value of 1 4 e h and no clear plateau at 3 e h is observed for v Vv2 6 It was speculated that the conductance in these regions being lower than their expected values is an indication of incomplete mode mixing Also observed was an unexpected peak in conductance at a region in gate voltage between the two 1 e h plateaus at v v 2 This rise in conductance is clearly seen for VTG values between 1 and 2 V and VBG values between 5 and 2V This may result from the possible existence of puddles of electrons and holes near the charge neutrality points of regions 1 and 2 as previously suggested 089 These examples demonstrate that graphene p n junction devices of the invention enable both device operation and the study of physical phenomena in graphene layers 090 With this description it is demonstrated that the invention provides carbon based 123 structures such as graphene p n junction devices that can be arranged and controlled to include any number of p n junctions including a single p n junction with one or more device electrodes on the graphene layer being disposed underneath a top gate Each region of graphene to be controlled with a selected charge carrier type by a local top gate can be individually contacted if desire
21. 6 3 1 3 2 3 3 3 4 4 1 4 2 4 3 4 4 5 1 5 2 5 3 5 4 5 9 5 6 5 7 6 1 6 2 6 3 Real space and reciprocal lattice of graphene oaoa a 4 Band structure of graphene aoaaa ee 6 Landau levels in graphene 2 0 0 0 a 7 Klein Paradox in graphene aoaaa ee 8 Etched graphene nanoribbons 0 0 00 eee ee es 10 Schematic of the Atomic Layer Deposition process 14 Cambridge Nanotech Savannah 100 0 20008 16 Dinitrogen Tetroxide 2 2 ee 17 Modified gas cabinet 26 18 Pulse heights for deposition of the functionalization layer 20 Top gate and back gate sweeps after functionalization layer and oxide growth 21 Realization of a graphene p n junction 2 20 4 24 Transport through the p n junction at B O 27 Transport through the p n junction in the quantum Hall regime 29 Transport through the p n junction in the quantum Hall regime at other fields and temperatures sooo a 33 Characterization of graphene devices using dc transport at By 0 and in quantum Hall regime 2 20 20 ee ee 36 Shot noise in single layer devices 2 2 2 ee ee 38 Shot noise in a p n junction ooa ee 40 Shot noise in a multi layer device ooo aa ee 41 Effect of two terminal geometry on quantum Hall conductance 49 Quantum Hall conductance of two terminal large and small aspect ratio single layer graphene
22. 6 7 Acknowledgements 2 2 0 ee ee 73 7 Precision Etching of Graphene with a Helium Ion Beam 74 EA Wntroductions 55 422th Ann be oo eS cae es Be LG Se D 75 7 2 Helium ion beam process considerations 00000 eee 75 7 3 He ion beam microscope 2 00 ee ee 79 7 4 Results and discussions 0 2 0 0 eee ee ee 81 7 5 Conclusions pa mani aoe kG be eo ee ee a ae Dee we a 83 8 Etching of Graphene Devices with a Helium Ion Beam 84 Sil Introduction asne sigh tes Se ee ee ee a ea ee ed PS 85 8 2 Experimental setup i beech be one Rd ae ee aata ia 86 8 3 Results and discussion 2 2 2 e 87 8 4 Conclusions and acknowledgements 00000254 89 A Graphene Deposition by Mechanical Exfoliation 91 Graphene p n Junction Device Patent 97 B 1 Cross reference to related application 202 00 98 B 2 Background of the invention 0 0 0020 0000 2 eee ee 98 B 3 Summary of the invention 2 2 ee 100 B 4 Brief description of the drawings 00 000002 ee 100 B 5 Detailed description of the invention 20 002 00048 101 B 6 Example i sn gg ood oh eed dele Oe ee ee eA 118 Bf Example suns ti Sia th Bie ti hh Re ee dee Saida 119 BECUS betas th ees tes eel eh a hs Patt Ta eh aa ae Sa Meee aun eds 125 B 9 Fig res i Bd aod ao ba So ey tes a ak WG a ee S 128 C Elionix 7000 User Guide 139 vi List of Figures 1 1 1 2 1 3 1 4 1 5 2 1 2 2 2 3 2 4 2 5 2
23. B the bulk is not localized If we take the added conduction channel as adding in parallel with the bulk resistance 1kQ the resulting change in resistance would be 12 9 1 12 94 1 kQ 0 1kQ which is about the reisistance drop observed in Fig 6 2 b The observed reduction of this phenomena with increase Vpg Fig 6 4 may be due to the incomplete mixing of edge states observed for higher Landau levels resulting in a destruction of the quantized conductance plateaus as was observed in Ref 40 A more interesting interpretation would be the collapse of the Landau levels at higher perpendicular electric fields 89 If this phenomena is a result of Landau level like edge modes the low B fields in which it is observed should allow for experimentally realizable electric fields to collapse the Landau levels completely removing the additional conduction channel completely 72 If the p n interface is providing an additional channel for conduction this would be an important contribution to the measured Omin where many PNJs are present Charge transport in disordered graphene samples has been studied experimentally 9 34 and the oretical predictions have been made for amin 35 36 however consensus has yet to be reached Taking into account the resistance of the PNJs and appropriate values for the size of density fluctuations a value Omin 2 5e7 h was obtained 2 to 6 times lower than the ex perimentally reported values 9 34 The add
24. B field range Ray Vig traces Fig 6 2 c at Vig 20V for B 2 are similar to those for single gate 68 graphene 5 in the low B field regime As the CNP is crossed Rzy changes sign indicating a change in carrier type p gt n as a function of Vig These curves are antisymmetric with respect to the CNP and B see black curves and lower inset of 2 c By comparison this is not the case for Sz Fig 6 2 d The resistance curves there are not antisymmetric and have resistance values greater on the p n side Sry gt ReyP This increase in resistance is quantified in Fig 6 2 e where a plot of the difference Sz y Rzy is consistantly larger in the p n regime for the entire low B field range inset of Fig 6 2 e The increase in Szy occurs even at B OT at a value of 0 5kQ and persists in for a range of 1V in Vig while Rzy shows no systematic change in resistance At larger B this difference increases reaching a value of 1 5kQ at B 2T 6 4 Sry in the quantum Hall regime Measurements of Syy were carried out in the QH regime where current is carried entirely by one dimensional edge channels Szy Vig in the unipolar regime shows the typical QH effect for graphene producing quantized conductance values of 2 6 and 10 e h Fig 6 3 a left of the red dashed line Once in the p n regime Fig 6 3 a right of the red dashed line the quantization plateaus disappear and a series of peaks develop in the resistance
25. Door Control Button to Close Vent the chamber and take you sample and the sample plate out of the loadlock Close loadlock and EVAC Need to find something See Figures 22 and 23 158 Load Lock Transfer Rod ai Aanhin am i ree Gee s Er o gt Figure C 23 Things around the Control Panel 159 Bibliography 1 R Saito G Dresselhaus M S Dresselhaus Physical Properties of Carbon Nanotubes p 1 1998 2 M Eizenberg and J M Blakely Carbon Monolayer Phase Condensation on Ni 111 Surface Science 82 228 1978 3 H W Kroto J R Heath S C O O Brien R F Curl and R E Smalley Ceo Buckminsterfullerene Nature 318 162 1985 4 S Ijima Helical microtubules of graphitic carbon Nature 354 56 1991 5 K S Novoselov A K Geim S V Morozov D Jiang Y Zhang S V Dubonos I V Grigorieva and A A Firsov Electric field effect in atomically thin carbon films Science 306 666 2004 6 K von Klitzing The quantized Hall effect Rev Mod Phys 58 519 1986 7 A K Geim and K S Novoselov The rise of graphene Nat Mater 6 183 2007 8 M I Katsnelson and K S Novoselov Graphene New bridge between condensed matter physics and quantum electrodynamics Solid State Communications 143 3 2007 160 9 10 12 13 14 16 17 18 K S Novoselov A K Geim S V Morozov D Jiang M I Kats
26. In addition to this reduction in resistance a peak forms that moves linearly in the Vig B space d horizontal cuts corresponding to the colored lines in Fig 6 3 c show a gradual evolution black dashed line of the zero B field peak to the resistance peak in the QH regime resistance from pgz This case is unlikely as the contribution from pz in the p p regime is not as large as this peak observed in the p n regime The reduction of resistance and peak disappear as the CNP of Region 1 is approached inset of Fig 6 3 a Szy Vie B 70 reveals that this peak black arrow moves linearly away from the CNP of Region 1 as B is increased Fig 6 3 c One dimensional cuts of Sz Vieg B Fig 6 3 d in the p n region demonstrate that the zero field peak in the transverse resistance S B OT gradually evolves into the peak in the QH regime suggesting that these phenomena have similar origins 6 5 Vi dependence of the snake state The Vig dependence of the peak resistance in Szy Rzy is shown in Fig 6 4 plotted for five different B between 0 and 2T in 0 5T increments in the Vig range of 20V to 40V black lines are guides to the eye It is found that the position of the peak moves linearly in the Vig Vbg space data not shown but decreases as the magnitude of Vig Vig is increased i e as the electric field perpendicular to the junction increases The change in resistance gets stronger for increases in the B field chan
27. In some cases the two terminal geometry can strongly distort the conductance leading to a large difference between values of the two terminal conductance at the local extrema and the quantized conductance values observed in multiterminal samples In sample B2 Fig 5 4 g reaches a maximum of 13 5 e h at the CNP with adjacent minima of 5 e h Away from the CNP conductance plateaus appear at values of 16e h and 23e h neither of which are near expected values for monolayer or bilayer graphene Since there are no strong peaks or dips in g away from charge neutrality as is expected for a device with a Es lt 1 it is difficult to determine the number of layers from the location of the conductance extrema There are two conductance features however that suggest the sample is gapless bilayer graphene First the peak at v 0 is much more pronounced than any other peak 55 in the conductance Second the spacing in Vj between the two lowest LLs is twice as large as the spacing between any other two successive LLs in Fig 5 4 OVbg 9 5 V Both features arise in bilayers as a result of the zero energy LL being eightfold degenerate twice as much as all other bilayer LLs and the zero energy LL in single layer graphene 67 The theoretical result for 0 3 solid red line and 0 2 dashed blue line for sample B2 are shown in Fig 5 4 5 6 Non rectangular samples In this section we extend the comparison of theory and experim
28. Tony F Heinz Mark S Hybertsen and George W Flynn High resolution scanning tunneling microscopy imaging of mesoscopic graphene sheets on an insulating surface Proceedings of the National Academy of Sciences 104 9209 2007 162 28 29 31 33 34 36 37 Yuanbo Zhang Victor W Brar Caglar Girit Alex Zettl Michael F Crom mie Origin of Spatial Charge Inhomogeneity in Graphene available at http arxiv org abs 0902 4793 Jannik C Meyer A K Geim M I Katsnelson K S Novoselov T J Booth and S Roth The structure of suspended graphene sheets Nature 446 60 2007 Masa Ishigami J H Chen1 W G Cullen M S Fuhrer and E D Williams Atomic Structure of Graphene on SiO2 Nano Letters 7 1643 2007 T M MohiuddinL A Ponomarenko R Yang S M Morozov A A Zhukov F Schedin E W Hil K S Novoselov M I Katsnelson and A K Geim Effect of high k environment on charge carrier mobility in graphene available at http arxiv org abs 0809 1162 J H Chen C Jang S Adam M S Fuhrer E D Williams and M Ishigami Charged impurity scattering in graphene Nature Physics 4 377 2008 J Martin N Akerman G Ulbricht T Lohmann J H Smet K von Klitzing and A Yacoby Observation of electronhole puddles in graphene using a scanning single electron transistor Nature Physics 4 144 2008 Y W Tan Y Zhang K Bolotin Y Zhao S Adam E H H
29. a blanket layer not a regional or sectioned area and the blan ket layer covers the entire graphene surface not just the regions directly beneath the gate electrodes to protect the entire graphene surface from the environment and thereby pre vent unintended doping of the graphene surface Thus it is preferred to blanket passivate a graphene layer or device to limit the transient nature of the device properties that would be produced in a humid environment Local oxide formation rather than blanket formation would not fully passivate a graphene device leaving exposed graphene surface areas that can absorb molecules resulting in reduced device functionality In addition local oxide formation requires serial processing in turn requiring long processing times for wafer scale 109 device fabrication 043 Because graphene is very reactive with even its immediate environment the choice of a blanket gate oxide material is particularly important Many physical deposition meth ods result in amorphous oxides that can dope a graphene layer such that the layer exhibits the aforementioned degraded qualities It is further discovered in accordance with the in vention that the surface of graphene is chemically inert to many oxide deposition methods like Atomic Layer Deposition ALD preventing all oxide growth by that technique 044 In accordance with the invention to enable the formation of a selected oxide blanket layer on a graphene sheet a
30. a diode or other single junction device 035 Referring to Fig 4C in a further embodiment of the invention a two junction graphene device 74 is produced with a graphene layer 12 that is here configured with three device electrodes 18 20 23 adjacent to the graphene layer for applying device voltage biases 60 62 63 between the three device electrodes The third device electrode 23 is contacted at an edge of the device the representation of this contact arrangement is schematic only to provide clarity of the device regions In the configuration of Fig 4C a sole local top gate 39 is provided and is located over the third device electrode 23 This top gate 39 is biased with an appropriate positive voltage 69 that forms an n type graphene region 43 under the top gate 39 and two p type graphene regions 40 42 adjacent to each side of the n type region 43 Only one top gate is here employed to form the three distinct graphene regions and the three device electrodes provided for making electrical contact to 106 each of the three graphene regions enable complete device control with one of the three device electrodes provided under the top gate 036 Referring also to Fig 4D the polarity of this two junction graphene device 74 can be reversed by simply reversing the polarity of the top gate bias to an appropriate negative voltage 69 The two p type regions are then reversed to n type regions 40 42 and the n type region is reversed to a p ty
31. an experimental graphene device having a configuration like that of the example device in Fig 1A and 018 Figs 10 10F are plots of conductance and magnetic field as a function of applied voltage for an experimental graphene device having a configuration like that of the example device in Fig 1A B 5 Detailed description of the invention 019 Referring to Fig 1A there is shown a schematic cross sectional view of an example graphene p n junction device 10 provided by the invention For clarity the dimensions of the device are not shown to scale The device includes a layer of graphene 12 that in this example is configured with voltage biasing to produce one region of the layer biased as p type and one region of the layer biased as n type in the manner described below A global electrical connection is made to one side of the graphene layer e g the backside surface with a backgate electrode 14 that can be electrically insulated from the graphene 12 by e g an insulating layer 16 if desired Electrical device connection to the regions of the graphene to be biased n type and p type are made with device electrodes 18 20 that directly contact the graphene A local top gate 22 is provided directly above one of the device electrodes in this example over the left electrode 18 The top gate is electrically insulated from the graphene 12 and the device electrodes 18 20 by a gate oxide layer 24 As explained in detail 101 below the i
32. at high bias We may now compare these results to expectations based on theoretical and numerical results for ballistic and disordered graphene Theory for ballistic single layer graphene with W L 4 gives a universal F 1 3 at the charge neutrality point where transmission is evanescent and F 0 12 for ns gt 7 L where propagating modes dominate transmission 25 While the measured F at the charge 42 neutrality point in samples Al and B W L 5 7 and 6 7 respectively is consistent with 2 is well within this prediction the absence of density dependence is not 7 L 3x 109 cm7 the range of carrier densities covered in the measurements Theory for ballistic graphene p n junctions 16 predicts F 0 29 lower than the value 0 38 observed in sample C in both p n and n p regimes We speculate that these discrepancies likely arise from the presence of disorder Numerical results for strong smooth disorder 58 predict a constant F at and away from the charge neutrality point for W L 1 consistent with experiment However the predicted value F 0 30 is 20 lower than observed in all single layer devices Recent numerical simulations 65 of small samples L W 10 nm investigate the vanishing of carrier dependence in F with increasing disorder strength In the regime where disorder makes F density independent the value F 0 35 0 40 is found to depend weakly on disorder strength and sample size Since theory fo
33. carbon surface 2 The method of claim 1 wherein exposing the chemically functionalized carbon surface to a beam of electrons comprises rastering a beam of electrons across the carbon surface 3 The method of claim 1 further comprising before exposing the chemically functionalized carbon surface to a beam of electrons exposing the chemically functionalized carbon sur face to at least one material layer precursor species that deposits a material layer on the chemically functionalized carbon surface 4 The method of claim 1 wherein the carbon surface comprises a surface of a layer of graphene 5 The method of claim 1 wherein the carbon surface comprises a cylindrical wall of a carbon nanotube 6 The method of claim 1 wherein the functionalization species comprises NO2 7 The method of claim 1 wherein the functionalization species comprises a precursor se 125 lected from the group consisting of trimethylaluminum and tetrakis dimethylamido hafnium 8 The method of claim 1 wherein the functionalization species comprises NO2 and tetrakis dimethylamido hafnium 9 The method of claim 1 further comprising forming a layer of oxide on the chemically functionalized carbon surface before exposing the carbon surface to a beam of electrons 10 The method of claim 9 wherein forming a layer of oxide comprises forming a layer of HfO2 11 The method of claim 1 wherein exposing a carbon surface of the carbon structure to at least one functional
34. current of 1 pA to 1 6 pA While hydrocarbons have been used previously to write patterns onto graphene 97 here avoiding contamination in the instrument is critical to producing a clean working result As such the HeIM chamber is cleaned with air plasma overnight prior to sample patterning This is performed using an Evactron type plasma cleaner attached to the chamber with a cycle time of 15 minutes on and 45 minutes off for a minimum of 10 cycles at 12 Watts power 98 A commercial pattern generation system Nanometer Pattern Generation System NPGS was installed on the HeIM in order to perform controlled etching of the samples using a variety of conditions The NPGS system allowed for dose variations the use of random patterns and pattern alignment to existing structures i e devices 94 Test writing was performed on 285 nm thick SiO2 on a Si substrate Initial dose expo sures indicated a dose of 1 2 nC cm as an optimal initial setting for ion beam and dwell 79 Onm height 10nm Figure 7 4 a Test patterns written into a 285 nm SiO2 film on silicon substrate as measured with AFM and b showing etching of boxes and line box patterns Figure 7 5 HeIM image of a hole etched into a multi layer graphene film grey on a SiO2 substrate black times in the pattern generation system AFM and HeIM images Fig 4 a b shown sharp well defined patterned etched in SiO2 Graphene flakes were then deposited onto the SiO2 by mechan
35. edge states common to both regions propagate from source 28 A T 250 mK 0 1 2 20 10 Figure 3 3 a Differential conductance g as a function of Vig and Vpg at By 4 T and T 250 mK b Vertical slice at Vig 0 traversing p p and n n quadrants Plateaus are observed at 2 e h and 6 e h the quantum Hall signature of single layer graphene c Horizontal slice at v 6 showing conductance plateaus at 6 2 and 3 2 e h d Horizontal slice at v2 showing QH plateaus at 2 1 and 3 2 e h e Table of conductance plateau values as a function of filling factors calculated using Eqs 3 1 and 3 2 Black purple and red lines correspond to slices in b c and d respectively f Schematic of counter circulating edge states at filling factors v v2 2 to drain while the remaining v 12 edge states in the region of highest absolute filling factor circulate internally within that region and do not contribute to the conductance This picture is consistent with known results on conventional 2D electron gas systems with inhomogeneous electron density 53 54 55 Recent theory 50 addresses QH transport for filling factors with opposite sign in regions 29 1 and 2 n p and p n In this case counter circulating edge states in the two regions travel in the same direction along the p n interface Fig 3 3 f which presumably facilitates mode mixing between paralle
36. from a typical substrate as in Fig 7 3b In this case there is little to no observable backscattering to the graphene layer This suggests suspended graphene as an ideal substrate for resolution tests of helium ion etching In addition the lack of interaction of backscattered ions with the graphene film should make suspended devices particularly suitable for He ion etching Based on the TRIM calculations the milled line width for helium ions compared with 78 gallium ions is about a factor of 10 smaller Gallium ions also could leave ionic contamination in samples which would be problematic for graphene devices were as the helium ions do not appear to present issues as severe An important result from these simulations is the indication that the lack of helium ion beam divergence in the vicinity of the surface of the sample down to a depth of about 100 nm should enable nanometer scale fine etching and cutting Following from molecular dynamics 96 a schematic can be constructed to detail the collision cascade a form of proximity effect during ion bombardment that shows clearly the differences between using gallium ions and helium ion bombardment for milling and etching Insets in Fig 7 3 7 3 He ion beam microscope The helium ion microscope imaging and etching was done using the ORIONTM helium ion microscope Instrument Serial 4 manufactured by Carl Zeiss SMT The instrument was operated at 30kV acceleration voltage with a measured beam
37. graphene 063 In one example compensation process provided by the invention an energetic beam e g an electron beam is rastered across the surface of the oxide layer In one example a high energy electron beam of electrons at a voltage of e g about 30 keV is rastered very quickly over the oxide surface to expose the oxide to the electron beam for e g about 10 ms m2 This process can be carried out a number of cycles and the beam voltage and raster rate can be adjusted in a manner suitable for a given application such that electrons penetrate a selected depth through the oxide and functionalization layers 116 064 It is understood in accordance with the invention that the electron beam exposure of a functionalization layer and or oxide layer can passivate molecular dangling bonds that can exist in the oxide and underlying functionalization layer The resulting passivated oxide and functionalization layers then do not need to accept or donate electrons from the graphene rendering the graphene charge neutral and preserving the unique electronic properties of the graphene With this understanding it can be preferred in accordance with the invention to evaluate the charge state of a graphene layer after top gate oxide formation to determine if this charge compensation process of the invention is warranted 065 Now referring back to Fig 1A with an oxide layer 25 in place on a functionalization layer 25 over the graphene 12 one or
38. heard sto ries of professors traveling to obscure foreign places to try and find the highest quality graphene The time constraints of graduate school preclude such excursion but fortu nate I ve had luck with commercially available graphite Graphite crystals were obtained from SPI supplies www 2spi com A variety of sample sizes and quality is available and highly ordered pyrolytic graphite HOPG works the best Many grades are available see http www 2spi com catalog new hopgsub php and I started off using SPI 1 Grade 5mm x 5mm I have since found that although more expensive the ZYA grade Fig A 1 a produces the largest flake size The size and lot number of our graphite source used for the most recent experiments is HOPG ZYA 12x12x2mm Lot 1130605 shown in Fig A 1 b The zeroth step is to go in the cleanroom all this should be done in a clean environment The first step in mechanical exfoliation is to cleave the graphite crystal with tape I have used a variety of tape types mainly to attempt to remove the residual contamination left by the tape For example water soluable and blue cleanroom tape were each staples of this method for a long time I have found that if done correctly use of standard Scotch gives the largest flake size and does not contaminate the graphene Cleaving the graphite is performed by pressing the tape with a gloved finger over the graphite Rub plastic tipped tweezers over the graphite to ensure th
39. in graphene These two differences are summarized in Fig 1 3 1 4 Potential barriers in graphene In the last section the difference between graphene and other 2D materials was demon strated at large magnetic fields In addition the linear energy dispersion in graphene results Figure 1 4 In graphene pseudospin is linked with direction of propagation inset in upper left corner For pseudospin preserving barriers and for motion perpendicular to the barrier turning around is prohibited and the transmission through the barrier is unity The effect is known as the Klein paradox in differences at zero magnetic field There are a number of ways to create potential bar riers in 2D materials Traditionally it is done via the electric field effect 14 and focus is given to this method as it is the sole technique used in the experiments of this thesis For gapped materials an electric field can either switch off the current field effect transistor or can result in rectifying behavior p n diode Graphene is a gapless system so the off state is not achievable for creating a gap in graphene so that an off state is possible see the section below on nanoribbons Rectification in p n junctions is a result of a depletion region a by product of a gapped system hence graphene p n junctions cannot rectify It was recognized 80 years ago that the solution to a step potential H z a 2 H a a 2 where H is th
40. more top gates 22 are formed on the oxide layer surface It is to be recognized that any suitable gate dielectric material can be employed and the oxide layers described above are examples of such but are not limiting 066 The top gates can be formed in the manner of the device electrodes with metal evaporation and lift off patterning processes For example a resist such as PMMA can be spin coated over the oxide surface and patterned by e g electron beam lithography to define regions for location of top gates The top gate electrodes are then deposited by e g thermally evaporating a 5 nm thick layer of titanium and 40 nm thick layer of gold in the manner described above with a lift off process employed to remove the metals and the resist in formation of one or more top gates With the top gate formation complete a locally gated graphene p n junction device in accordance with the invention is produced 067 This graphene device production process can be extended to the production of electrically gated carbon nanotube devices or indeed production of any carbon based ma terial device whether or not including a gate electrode in accordance with the invention Referring to Fig 7 there is provided by the invention such an example here a gated carbon nanotube device 150 The carbon nanotube device includes a carbon nanotube 152 having a coaxial functionalization layer 154 on its cylindrical wall surface A coaxial gate oxide layer 156 is p
41. one Chip and two Regis tration Marks Save your Schedule by pressing S twice After the save the name of your Schedule File should appear in the Schedule File Name area of the Job 3 window Press E to start the Exposure Two new windows should open see Fig 19 one for starting the exposure left and the other to display your empty Chips and Registration Marks Left click on the left window and select exposure to start the exposure First the stage will drive to the Registration Mark A The initial magnification of the image is set by the chip size for example a 75 micron Chip Size corresponds to a 2000X initial magnification Using the Track Ball see Fig 20A to align the markers on the screen with the Cross Hairs Fig 20B misaligned to Fig 20C aligned If the marks are far away initally use the Stage Drive to center the marks followed by a fine alignment using the Track Ball You can zoom in and out using the Mag Wheel and adjust the scan speed by pressing the SCAN SPEED button and using the Mag Wheel to adjust the scanning speed Once you are happy with the align press the LOAD 156 Exe Track Ball Figure C 21 Beam controller and process for aligning chip with the Registration Marks created in Job 1 button The stage will move to Marker B Perform the same steps to align Mark B with the cross hairs Press LOAD when you are happy with the alignment make sure the magnification is the same as when y
42. oxides are produced by thermal growth of a dry oxide Dry oxide means that there is no water vapor present in the reactor when oxide is grown This is a much slower and more expensive process but the the quality of the films for graphene electronics is better They will try to sell you wet oxide but don t buy it Before graphene deposition alignment marks with a registry of 100um are fabricated on the sample using the Elionix e beam writer Also cleaning the chip thoroughly is in order The standard Marcus Lab recipe is to clean in acetone and isopropanol at room temperature for 5 minutes each Then bake the chip at 200 C for 5 mins on a hot plate to remove any alcohol residue Lastly put the chip in a Samco UV Ozone cleaner for 10 mins 93 Figure A 2 a Cleave the graphite crystal by pressing the tape on the graphite surface and rubbing tweezers over the tape b Peel the tape off the graphite producing a thinner graphite square c Take another piece of tape and press it on the tape covered with the graphite square producing a tape graphite tape sandwich d Peel apart the two pieces of tape Take a fresh piece of tape and repeat the peel process until the tape surface looks like the tape in e at room temperature The flow rate of the O2 gas should be 1 SLM Place the chip oxide side up on a glass bowl that is roughly 1 thick Fig A 3 a Take the tape with the light grey graphite on it making sure no exposed areas of th
43. plate and then fully retract the transfer rod 144 Rotate 1 2 turn couterclockwise NSc _ Figure C 8 Transfer Rod Lock Figure C 9 Make sure the two white stripes have the same width before retracting the transfer rod e Close the gate valve by switching the Door Control Button to Close e Lock the transfer rod into place Close the gate valve by toggling the Door Control Button to CLOSE You are now ready to get everything set up This includes setting and measuring beam 145 current and adjusting focus and stigmation First open the isolation valve by pressing and holding the Isolation Open Button for 2 seconds see Fig 5 The press the FC Faraday Cup on the stage controller to drive the sample to the Faraday Cup The FC button is located 2 buttons to the left of the EX button on the Stage Controller see Fig 4 To set the current perform the following e Using the Condition Memory inputs and the Memory Settings Display see Fig 10 set the current you desire There are 3 values for current preset into the memory They are Setting 1 20pA Setting 2 100pA and Setting 3 2nA Setting 4 9 are available to users to set their own values To set a current use the up down buttons to select the appropriate memory element Once the appropriate element is chosen press the Call button twice to change the current Once you press the call button twice the Setting Memory Window should now re
44. pulses This cyclic HfO2 deposition can be performed at a variety of temperatures e g between about 80C and about 300C The invention contemplates other functionalization layers and other oxide layers 061 It has been discovered in accordance with the invention that even with a function alization layer provided on a graphene surface some dielectric layers cause extrinsic doping of the graphene This is not in general true for example an A1203 gate oxide layer formed on a TMA based functionalization layer does not extrinsically dope or otherwise impact the electronic properties of an underlying graphene layer But other oxide layers for example HfO2 can extrinsically dope the underlying graphene layer even in the presence of the functionalization layer and further can reduce the electronic charge carrier mobility of the underlying graphene 062 In accordance with the invention after a functionalization layer is formed or after a top gate oxide layer is formed on a functionalized graphene device or circuit layer it is preferred to conduct a current voltage measurement of the device or circuit to determine if the functionalization layer or the oxide layer has impacted the electronic properties of the graphene If the graphene does not exhibit the undoped current voltage relation that is characteristic of pristine graphene then a compensation process is carried out in accordance with the invention to restore the undoped characteristic of the
45. reaction cannot start and the precursor is pumped out of the chamber Once all the cataytic sites are occupied further reactions are not permitted making this process self limited to adsorption of a single monolayer of the precursor Fig 2 1 b After enough precursor 1 is introduced into the chamber to fill all the sites a second precursor is pulsed into the chamber Here it is precursor 1 that provides the catalytic sites for precursor 2 to chemically adsorb on the surface Again this process is self limiting terminating when all the sites of the precursor 1 layer are occupied By repeating this process oxides can be built up a single atomic layer at a time with a high degree of uniformity and oxide quality 13 a Pulse Precursor 1 b Saturate Surface of Substrate Substrate Pulse Precursor 2 Saturate Surface Substrate Substrate Figure 2 1 Schematic of the Atomic Layer Deposition Process a Precursor 1 is introduced into the ALD chamber b Precursor 1 chemically reacts with the surface at specific sites indicated by triangles and adsorbs on the surface This process is self limiting and ceases after the all the sites on the substrate surface are occupied c A second precursor Precursor 2 is introduced into the chamber d Precursor 1 provides the catalytic sites for Precursor 2 to adsorb This process is also self limiting By repeating this cycle oxides can be built up layer by layer 2 2 Atomic Layer Depos
46. regions 1 and 2 as previously suggested 56 3 6 Supplementary Information Graphene Preparation Graphene is synthesized using a method similar to that pioneered in Ref 5 A thin piece of graphite is first extracted from a 5 mm square of highly oriented pyrolytic graphite 30 SPI 1 grade from SPI supplies www 2spi com using adhesive tape 3M Mask Plus II Water Soluble Wave Solder Tape http www 3m com The graphite is thinned further by repeated exfoliation with tape Prior to the final exfoliation a n Si substrate with 300 nm thermally grown SiO is cleaned in acetone and isopropyl alcohol IPA Tape from the final exfoliation is immediately pressed against the substrate and rubbed gently with the back of a tweezer for 10 s Following immersion in water at 60 C to dissolve the tape the substrate is again cleaned in acetone and IPA to remove any tape residue left on the substrate surface The sample is next viewed under an optical microscope to identify potential single layers Metallic contacts are then patterned as described in the main text Oxide Layer Synthesis The oxide separating the graphene sheet and metallic contact from the top gate consists of two layers a non covalent functionalization layer NCFL and 30 nm of Aluminum oxide AlgO3 Both layers are deposited using a Cambridge Nanotech Savannah Atomic Layer Deposition Tool http www cambridgenanotech com The growth recipe described below is ada
47. resistance being a main source of discrepancy with theory There are scenarios however in which contact effects can play a role in altering the aspect ratio One is that only part of the contact actually injects current reducing the width causing st to be greater than as observed in sample Al Another possibility is that the contacts locally dope the graphene causing the actual aspect ratio to be smaller However for doping to make ft lt s in sample B1 it would have to penetrate 500nm into the graphene at least two orders of magnitude more than expected 85 61 Another more interesting possibility could be that the picture of an effective medium characterized by local conduction on which the argument leading up to the semi circle relation 81 is based may not hold This might arise for instance from large density fluctuations giving rise to electron and hole puddles 33 forming a network of p n interfaces along which conduction occurs In this case the effect of the back gate is to alter the percolation properties of this p n network Magnetotransport across multiple p n interfaces cannot be accurately described in terms of a local conductivity model This situation arises when the distance between contacts is much greater than the scale of disorder which we take to be S 500 nm following Ref 33 This suggests that samples Al and B1 should show greater deviation from the present theory than samples A2 and B2 which
48. ribbons Nanometer size effect and edge shape dependence Phys Rev B 54 9858 1996 161 19 Xiaolin Li Xinran Wang Li Zhang Sangwon Lee and Hongjie Dai Chemically De rived Ultrasmooth Graphene Nanoribbon Semiconductors Science 319 1229 2008 20 Liying Jiao Li Zhang Xinran Wang Georgi Diankov and Hongjie Dai Narrow graphene nanoribbons from carbon nanotubes Nature 458 877 2009 21 Zhihonn Chen Yu Ming Lin and Michael J Rooks and Phaedon Avouris Graphene non ribbon electronics Physica E 40 228 2007 22 Melinda Y Han and Barbaros zyilmaz and Yuanbo Zhang and Philip Kim Energy Band Gap Engineering of Graphene Nanoribbons Phys Rev Lett 98 206805 2007 23 A W W Ludwig M P A Fisher R Shanker and G Grinstein Integer quantum Hall transition An alternative approach and exact results Phys Rev B 50 7526 1994 24 K Ziegler Delocalization of 2D Dirac Fermions The Role of a Broken Supersymme try Phys Rev Lett 80 3113 1998 25 J Tworzydlo B Trauzettel M Titov A Rycerz and C W J Beenakker Sub Poissonian shot noise in graphene Phys Rev Lett 96 246802 2006 26 A F Morpurgo and F Guinea Intervalley Scattering Long Rang Disorder and Ef fective Time Reversal Symmetry Breaking in Graphene Phys Rev Lett 97 196804 2006 27 Elena Stolyarova Kwang Taeg Rim Sunmin Ryu Janina Maultzsch Philip Kim Louis E Brus
49. source drain dc transport measurement was again made at room temperature as a function of gate voltage Fig 8B is a plot of differential conductance g as a function of voltage V for the structure As shown by the plot the neutrality point for the device was dramatically shifted away from the 0 volt point by the functionalization and oxide layers 073 The HfO2 coated nanotube was then exposed to rastering of an electron beam across the oxide surface to impose a dose of 100 uC cm2 on the structure 074 Fig 8C is a plot of differential conductance g as a function of voltage V for the structure after the electron beam processing The electron beam processing was found to clearly compensate for the extrinsic doping of the carbon nanotube to set the neutrality point back to around 0 V B 7 Example II 075 A graphene device having the configuration of Fig 1A was microfabricated in accordance with the invention A 300 nm thick layer of SiO2 was thermally grown on a degenerately doped Si wafer Graphene was exfoliated with a taping technique and applied to the oxide surface and was identified by thin film interference Two device electrodes 119 were formed by electron beam lithography and lift off with layers of titanium and gold of 5 nm and 40 nm in thickness respectively A functionalization layer was then formed by the ALD process described above employing 50 pulsed cycles of NO2 and TMA at room temperature in the manner give
50. the corresponding electron wavelength This gives the beam an ultimate resolution of 0 5nm or better 91 making it a highly attractive tool for precision modification of graphene devices While process details are published elsewhere 102 this letter focuses on the modification of device properties of graphene 85 SiO chip He jon column Silicon Gate chip socket to feedthrough Vg hi k g Figure 8 1 Schematic of a graphene device Inset Photograph of the microscope chamber with installed chip 8 2 Experimental setup Graphene was deposited onto 300 nm of silicon dioxide on degenerately doped sil icon by mechanical exfoliation 40 similar to the method described in Ref 5 Next mono and few layer graphene flakes were identified with an optical microscope Con tacts to the graphene were defined by electron beam lithography followed by evaporation of chromium gold 3 nm 150 nm and titanium gold 5 nm 40 nm Suspension of the graphene sheet was obtained by wet etching of the underlying SiO2 in diluted HF followed by critical point drying All devices were measured in a standard graphene transistor con figuration with the evaporated contacts acting as source and drain and the highly doped silicon substrate as a back gate electrode Fig 8 1a The drain current Id through the flake is then measured as a function of gate voltage Vg for a constant drain voltage Vd Electrical data of suspended devices w
51. the electron spin As such it has become conventional to associate o with the spin like properties of the amplitude on the two sublattices called pseudospin In a single valley when K K scattering is small i e for potential steps that vary slowly on the scale of the lattice constant a to change from a right mover to a left mover requires a flip of pseudospin which is prohibited if the barrier is pseudospin conserving This pseudospin spin conservation prevents the particle from turning around anywhere in the barrier Fig 1 4 and the transmission is unity 1 5 Graphene nanoribbons As mentioned in the previous section graphene cannot be put in an off state due to lack of a band gap making it useless for creating transistors with large on off ratios Like in carbon nanotubes reducing the dimensions of graphene one further to produce one dimensional graphene wires called nanoribbons can induce a gap Nanoribbons can be terminated in two separate ways called zig zag or arm chair and this termination along with the width of the ribbon dictate the size of the band gap 18 In a nanoribbon the states perpendicular to the ribbon direction are quantized resulting in a few allowed boundary condition defined k vectors Where these allowed k vectors cut through the Brilliuon zone Figure 1 5 By forming a one dimensional wire in graphene producing a graphene nanorib bon the gapless band structure can be altered and can beco
52. was introduced to one of the funnest people I ve ever met David Reilly His impressions and love for all things brown will live in my memory always He also helped me get through a lot of tough times always having something funny to say in the end Thank you for the Big Mac and The Button and for showing how good coffee could be More recently I had the pleasure of getting to know a few others around lab Ferdinand Keummeth Ferdy you have to be one of the most interesting and intelligent people I ve even met Chrisitian Barthel Bartel the most innocently inappropriate and funny person known to physics thanks for the laughs Maja Cassidy Mah Jah you re the toughest in the lab hands down And thanks to Danielle Reuter for sharing her love of photographs with me Most importantly to Leo If Charlie was my physics father you re my physics older brother You taught me how to do physics correctly on a day to day basis You taught me how to be thorough and to be passionate I mean come on Thanks for everything Leo That s just a small slice of the people I ve met through the Marcus and Friend Labs I ve learned things from all the lab members I worked with Thanks to Jason Petta Dominik Zumbhul Sang Chu Abram Falk Nathaniel Craig Susan Watson Andrew Bestwick Jen Harlow Hugh Churchill Yiming Zhang Doug McClure Yongie Hu James Medford Angela Kou Patrick Herring Sandro Erni Shu Nakaharai Max Lemme Tom
53. would like to zoom in or zoom out on e Next you need to Place Chips that is define the fields size determined in Chip Size in Job 2 that you will write your pattern If you need to write something that is equal to or less than the set Chip Size you can use the Place Chip command left click in the message window Chip Place Chip and you will be asked to save the CCC file we will call it chipTest ccc created when you place the chip The software 151 will then ask you to identify the center of where you would like to place the chip For exmaple If I would like to place a chip at 111 6mm and 116mm I would enter 111 6 116 for the coordinates for more on the Coordinate System see page 11 of the Elionix user manual More likely you CAD drawing will be bigger than your Chip size In this case you need to define a chip matrix by left clicking in the Message Window Chip Matrix Chip 2 You can then left click on the lower left corner of you loaded CEL file followed by the left clicking on the upper right corner of your drawing Then you are prompted ALL chipTest Y which you should should say N type N then press Return Next x direction Y Which asks if you want to write in the x direction first Then Auto Reverse Y Which asks if you want to write from left to right on the first line followed by right to left on the second line This will create a matrix of chips that should encompass your entire
54. 0 mK and 4 2 K Differential resistance R dV dI where I is the current and V the source drain voltage was measured by standard lock in techniques with a current bias of 1 10 nA ms at 95 Hz for T 250 mK 4 2 K The voltage across two contacts on the device one outside the top gate region and one underneath the top gate was measured in a four wire configuration eliminating series resistance of the cryostat lines A schematic of the device is shown in Fig 3 1 c 25 3 4 Transport at zero magnetic field The differential resistance R as a function of back gate voltage Vpg and top gate voltage Vig at By 0 Fig 3 2 a demonstrates independent control of carrier type and density in the two regions This two dimensional 2D plot reveals a skewed cross like pattern that separates the space of top gate and back gate voltages into four quadrants of well defined carrier type in the two regions of the sample The horizontal diagonal ridge corresponds to charge neutrality i e the Dirac point in region 1 2 The slope of the charge neutral line in region 2 along with the known distances to the top gate and back gate gives a dielectric constant amp 6 for the functionalized Al203 The center of the cross at Vig Vig 0 2 V 2 5 V corresponds to charge neutrality across the entire graphene sample Its proximity to the origin of gate voltages demonstrates that the functionalized oxide does not chemically dope the graphene si
55. 10 etc implies that the sample is a single layer whereas alignment with filling factors 4 8 12 etc implies that the sample is a bilayer This type of analysis can be extended to non rectangular samples the equivalent rectangle approach appears to work well We find for the five samples measured that conductance as a function of gate voltage shows relatively good agreement with theory for short samples L lt 1 um in longer samples the best fit aspect ratio differs considerably from the measured sample aspect ratio We note that using the fit value ft for the effective aspect ratio can be more reliable than using the value measured from the micrograph because invisible partial contact can alter the effective aspect ratio What could be the physical mechanism of such partial contact One effect to consider is contact resistance which would lead to an overall reduction in the experimentally observed values of conductance In devices fabricated using similar methods to the two terminal devices in this experiment but with four or more terminals it is found that contact resistance in the quantum Hall regime at the charge neutrality point is of the order 5002 dropping to 1002 away from charge neutrality for contacts with similar contact area as the ones used in this experiment This contact resistance is a small fraction of the resistances measured in the graphene sheet in the quantum Hall regime hence we rule out the possibility of contact
56. 2 ee 51 Quantum Hall conductance of two terminal large aspect ratio bilayer graphene 53 Quantum Hall conductance of two terminal small aspect ratio bilayer graphene 54 Quantum Hall conductance of two terminal single layer graphene with asym MET CAS incr os 5 Bede he ee Gh eos She kb ode a Rete fe ee He oh Y 57 Polygon device representation for conformal mapping of asymmetric contact GE VAGC Es ch om ot es tet va Soke gaits Usa Ents ath apenas ey sth pao eed de Gasp bes amp ob et Bld 58 Steps used in the conformal mapping of asymmetric contact device 58 Geometry of the snake state device 2 ee 65 Low magnetic field measurements of Rrr Sze Rey and Spy 68 High magnetic field measurement of Spy ooo es 70 vil 6 4 Back gate voltage dependence of p n junction enhanced transport 72 7 1 Device Schematic and He Ion Microscope 0 76 7 2 Interaction of He Ions with Graphene on a SiO2 Substrate 2 77 7 3 TRIM Simulations of Ga and He Ions Interacting with Suspended and On surface Graphene renia Coa Sac eet ae a ek a ee E Sa 78 7 4 AFM of Test Etch on SiOz soaa o a ee 80 7 5 He Ion Milling of Graphite 0 20 2 02020 00 80 7 6 Effect of Dose Variations on He Ion Milling 81 7 7 AFM Height Profile of He Ion Milling 82 7 8 Etch of Harvard Logo in Graphene 0 20200004 82 8 1 Device Schematic and He Ion Microscope
57. 3 Chapter 8 Etching of Graphene Devices with a Helium Ion Beam D C Bellt M C Lemme J R Williams L A Stern B W H Baugher P Jarillo Herrero C M Marcus 1 School of Engineering and Applied Sciences and the Center for Nanoscale Systems Harvard University Cambridge MA 02138 USA 2 Department of Physics Harvard University Cambridge Massachusetts 02138 USA 3 School of Engineering and Applied Sciences Harvard University Cambridge MA 02138 USA 4Carl Zeiss SMT Peabody MA USA 5 Department of Physics Massachusetts Institute of Technology Cambridge MA 02139 USA We report on the etching of graphene devices with a helium ion beam The etching process can be used to nanostructure and electrically isolate different regions in a graphene device as demonstrated by etching a channel in a suspended graphene device with etched gaps down to about 10nm Graphene devices on SiO2 substrates etched with lower He ion doses are found to have a residual conductivity after etching We attribute this effect to hydrocarbon contamination This chapter is being submitted to App Phys Lett 84 8 1 Introduction Graphene a thermally stable two dimensional carbon based crystal has attracted an immense research interest as both a model system for fundamental physics as well as for nanoelectronics applications 5 7 Many experiments in the field are targeted at graphene films or devices where artificial confineme
58. 56 Single Layer B 8T T 4K X 0 9 Xf n 0 9 0 7 20 10 10 20 Veg IVI Figure 5 5 Measured g Vpg for sample C black and calculated conductance solid red curve for Ess 0 9 A 0 7 The asymmetric contacts of this sample can be conformally mapped onto a rectangle producing a device aspect ratio of s 0 9 dashed blue curve The dashed blue curve was vertically displaced for clarity allowing the desired mapping to be constructed as a composition of a few simple mappings The steps involved in this construction are illustrated in Fig 5 7 First the rectangular shape in Fig 6 is replaced by a semi infinite strip shown in Fig 5 7 a This approximation should not significantly affect the conductance as the current flows mostly in the region between contacts 1 2 and 3 4 Without loss of generality we set the length scale a 1 The next step is to straighten out the contact 3 5 6 4 For that let us consider an auxiliary mapping that maps the upper w plane onto the upper plane with a removed 2_ 4 1 2 z iA d 5 2 We choose the parameter A to be equal 1 1 2 A 9 d 0 60 5 3 0 57 rectangle 84 4a 2a Figure 5 6 A polygon representing sample C see Fig 5 5 Black regions correspond to contacts length scale a 200 nm a 2 j 3 4 Figure 5 7 Three steps used to map the polygon in Fig 5 6 sample C onto the upper half plane schematic First t
59. 6 C Stampfer J Gttinger F Molitor D Graf T Ihn and K Ensslin Tunable Coulomb blockade in nanostructured graphene Appl Phys Lett 92 012102 2008 169 100 D V Kosynkin A L Higginbotham A Sinitskii J R Lomeda A Dimiev B K Price and J M Tour Longitudinal unzipping of carbon nanotubes to form graphene nanoribbons Nature 458 872 16 2009 101 J Morgan J Notte R Hill and B Ward An Introduction to the Helium Ion Micro scope Microscopy Today 14 4 p 24 2006 102 D C Bell M C Lemme J R Williams L Stern and C Marcus Helium Ion Etching of Graphene submitted 2009 103 K I Bolotin K J Sikes Z Jiang M Klima G Fudenberg J Hone P Kim H L Stormer Ultrahigh electron mobility in suspended graphene Solid State Communica tions 146 351 2008 170
60. Al Black dashed lines correspond to filling factors v 6 10 14 18 and align with the local mazima of conductance Main black Horizontal cut of inset giving g Vpg at B 8 T and calculated g for the best fit equivalent aspect ratio ft 1 7 solid red curve and for the measured sample aspect ratio 0 7 dashed blue curve using Landau level broadening parameter A 1 2 b Inset Conductance g in the quantum Hall regime as a function of B and Vig at T 250mK for sample A2 Black dashed lines correspond to v 6 10 14 18 and align with the local minima of conductance Main black Horizontal cut of inset giving g Vp at B 8T and calculated g for fs 0 2 solid red curve and s 0 2 dashed blue curve A 1 2 the same as sample Al The dashed blue curve was vertically displaced for clarity 5l sample the dashed lines representing the incompressible filling factors 6 10 14 18 now align with the minima in g Here we used a 6 7 x 10 cm V the same as for sample Al and Vogsep 1 1 V The observed features in g for samples Al and A2 can be compared to theory 75 for two terminal quantum Hall conductance which uses a model of a conducting rectangle L x W with a spatially uniform conductivity The filling factor dependence of the conduc tivity tensor is obtained using the semicircle relation for quantum Hall systems derived in Ref 81 which is applied independently for
61. B are partially under and partially outside the top gate Under certain values of Vig and Vig a p n junction forms black dashed line connecting contacts A and B c Close up of the PNJ Modulation of the density across the junction allows for an additional conduction channel to appear between contacts A and B in a magnetic field B The change of the Lorentz force a consequence of the changing sign of the carrier charge creates a snake shaped trajectory between the two contacts interface connects two electrical contacts to the sample Using a comparative longitudinal and transverse measurement scheme a study of transport parallel to the PNJ is performed as a function of top gate Vig back gate Vig and perpendicular magnetic field B It is observed that transport is enhanced in the bipolar regime by states that exist at the interface at all B including zero field Studying the evolution of this enhanced transport into the QH regime a transition between the low field states at the PNJ to the high field edge states is observed Further Vig is used to tune the electric field across the junction and an increase in the electric field results in a decrease in the effect of the interface state 65 in the low B regime At a PNJ the density n makes a transition from positively charged carriers holes to negatively charged carriers electrons over a length of order the distance between the graphene sheet and the top gate The change in t
62. Baker Andreas Klust Xiaoling Liu Ryan Quiller and Dilini Pinnaduwage Now to friends and family Kasey Russell thanks for teaching me about climbing for always wanting to talk about physics and for being my guitar buddy Oh ya and thanks for lending me Trip Thanks to all the people at Greyhound Welfare my sanctuary away form physics Prof Betty Young thank you for introducing me to physics and for helping me at the early stages of my physics career To Chulo Mo and Pelo your silliness kept me smiling when I was sad during graduate school Thanks to my mom for being a source of strength and inspiration She taught me about hard work and determination None of this would have been possible without you I love you ma Laura thanks giving up many days and nights with me so I could work Thanks for uprooting you life to move here with me and for being by my side for all this xi For Murphy and Zeppy xii Chapter 1 Introduction to the Electronic Properties of Graphene Carbon is only the fifteenth most common element accounting for a very modest 0 048 percent of the Earth s crust but we would be lost without it What sets the carbon atom apart is that it is shamelessly promiscuous It is the party animal of the atomic world latch ing on to many other atoms including itself and holding tight forming molecular conga lines of hearty robustness the very trick of nature necessary to build proteins and DNA Bil
63. C by clicking EXIT in the Job 2 menu e Two windows will open the left one called the Message Window allows you to open CEL file position your drawings etc The right window called the Graphics Window will display the files chip and Registration Marks that you have loaded The right window contains a display of the entire stage drive area see Fig 15A 150 Message Window Figure C 15 Loading the CEL file into the Graphics Window e Left click in the message window and choose File Load CEL Fig 15B e The software will then ask you where you would like to place the CAD drawing origin defined in you CAD program on the Graphics window For example the lower right corner of my chip is 116mm 116mm When I want to write my alignment pattern which covers the whole 5mm X 5mm chip I place the origin of my drawing at 111 3mm 116mm If you would like to specific the point in mm you need to include a in every number For example for the 116 in the y coordinate above I would enter it as 116 this distinguishes it from a dot coordinate which uses dot count to identify where to put the pattern For 111 3mm I can enter it just as 111 3 that is I don t need to write 111 3 Once you give the coordinates to place your origin your design will appear in the Graphics Window You can zoom in and zoom out in the Graphics window by pressing i zoom in or o zoom out on the keyboard and left clicking on the area you
64. CAD drawing see Fig 16A e Now you may want to align a pattern with a pattern that you ve already defined on a chip This works best with patterns that you created using the Elionix if you re using another machine please see the Manual page 76 S correction function To do this you ll need to input 2 Registration marks that prior to exposure you will either automatically or manually align This allows for any rotation of the pattern with respect to the global x y coordinate system to be corrected for this is similar to setting the u v coordinate system on the Raith To enter these two marks left click in the Message Window select Chip Reg 2 Mark Then enter the coordinates of the two marks when prompted The two markers should appear in the Graphics Window at the position you specified Fig 16B e Finally create the CON file by left clicking in the Message window and selecting File SAVE and entering the CON file name into the prompt Finally on to the exposure Select exposure by choosing Job 3 in the ELC menu Once 152 Registration Marks Figure C 16 A Chip matrix red defined for the Cel pattern blue B Once Registra tion marks are entered they should appear as white circles around the area you specified the program is open you will see a window consisting of Schedule File Name Schedule List Exposure Conditions and Command Explanation Fig 17 e First set the Exposure Conditio
65. Electronic Transport in Graphene p n Junctions Shot Noise and Nanoribbons A dissertation presented by James Ryan Williams to The School of Engineering and Applied Sciences in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the subject of Applied Physics Harvard University Cambridge Massachusetts May 2009 2009 by James Ryan Williams All rights reserved Dissertation Advisor Professor Charles M Marcus Author James Ryan Williams Electronic Transport in Graphene p n Junctions Shot Noise and Nanoribbons Abstract Novel two dimensional materials have allowed for the inception and elucidation of a plethora of physical phenomena On such material a hexagonal lattice of carbon atoms called graphene is a unique truly two dimensional molecular conductor This thesis de scribes six experiments that elucidate some interesting physical properties and technological applications of graphene with an emphasis on graphene based p n junctions A technique for the creation of high quality p n junctions of graphene is described Transport measurements at zero magnetic field demonstrate local control of the carrier type and density bipolar graphene based junctions In the quantum Hall regime new plateaus in the conductance are observed and explained in terms of mode mixing at the p n interface Shot noise in unipolar and bipolar graphene devices is measured A density independent Fano fact
66. L at zero energy for n 0 where in conventional 2D case the LL energy is always gt hw 2 This zero energy LL is comprised on equal parts of electron and holes see Fig Landau Levels in Gapped 2D Systems DOS DOS Landau Levels in Graphene E E Figure 1 3 Landau levels in graphene left and in conventional 2D materials right The two main differences are the presence of a zero energy Landau level and the yn spacing of the levels in graphene 1 3 a demand of particle hole symmetry in graphene As carriers in the zero energy LL approach the edge of the sample the energy of the electron like excitations is increased while the energy for the hole like excitations decreases This splitting of the zero energy LL results in the first edge state above E 0 to have half the degeneracy of the of the remaining LL giving rise to the half integer quantum Hall effect observed experimentally 9 10 and predicted theorectically 11 12 The quantized transverse conductivity values occur at Ory 4 n 1 2 e h 2 6 10 e7 h 1 12 different from conventional 2D materials 6 and from 2 layers of graphene 13 Consequen tially this unique conductance quantization provides a useful method for distinguishing one graphene layer from two The second important difference between conventional 2D materials is that in Eq 1 11 the energy levels are spaced as y n resulting in relatively more closely spaced LL at higher energies
67. M has been introduced as an ultra high resolution imaging technology for a variety of materials applications with unique contrast mechanisms and imaging abilities 90 The HeIM has been developed primarily as an imaging tool However being a charged ion beam instrument it is also possible to perform milling and sputtering tasks more commonly associated with a conventional gallium ion beam systems FIB One advantage is the ability to mill and sputter soft materials with extremely low rates The Helium ion microscope also has been shown to have an extremely small probe size in the order of 0 5 nm or better 91 The combination of these features has the capability to make this instrument one of the most precise direct fabrication tools currently available for materials especially for low z materials for example graphene layers Graphene is a two dimensional carbon based crystal that has only recently been dis covered experimentally 5 It is desirable for many experiments and potential applications involving graphene that it is patterned at the nanoscale Lithography based nanostructuring methods reported thus far include electron beam lithography in conjunction with reactive ion etching 21 22 92 and direct etching with a focused electron beam in a transmission electron microscope TEM 93 Both methods are suitable to produce patterns in the tens of nanometer range While the former is limited by random underetching effects in oxygen plasma
68. M image of a suspended graphene device after etching with minimum feature sizes of about 10 nm b Electrical measurement of the device before and after etching indicates the region of the graphene flake where etching occurred initially Each scan with the He ion beam resulted in an increase of etched area After thirteen scans the dwell time and hence the image quality was increased to 500 ps equivalent to a line dose of 8 nC cm still not sufficient to complete etch the device Fig 8 2 scans 1 14 These images indicate that removal of edge atoms is favorable over atoms within in the graphene crystal The remaining graphene film was etched using live scanning mode with a 100 nm to 10 nm field of view Here etching was confirmed via the live screen image A resultant cut with minimum feature sizes in the 10 nm range is shown in the HeIM image in Fig 8 3a The gap was measured with DesignCAD software after importing the original image After etching a trench across the entire graphene flake the device was removed from the He ion microscope and its drain current was measured as a function of back gate voltage Fig 8 3b Vd 0 5 mV note that the gate voltage range is limited in suspended graphene devices 103 and hence Id changes little with Vg The current dropped to about 15 pA compared to 1 uA prior to etching While the latter is typical for a functional graphene device of the given dimensions the post etching value corresponds to the nois
69. Make sure the Elionix is in the right position to load the sample To do this press the EX button on the Stage Controller Fig 4 If you can t find the Stage Controller 140 WINDOWS system32 cmd exe init de ion Cunit degree ellipses line i r u i sa Number of record lt DXF file gt 6 Completed Conversion gt Docunent and Settings Jimnmy Desktop Figure C 1 Command Prompt for the DXF to CEL conversion Figure C 2 Choices of sample holders Cassette for small piece used in this manual see the last section of this manual Where is everything Wait until the red light on the Stage Limit panel turns on before proceding e Close the isolation valve by pressing the green Open button and holding it for 2 seconds see Fig 5 You will hear a noise when the isolation valve closes 141 Figure C 3 Small piece sample holder shown with 5mm by 5mm sample Do not use metal tweezers or anything that will scratch the surface of the sample holder Light will turn on when system is in exchange position Figure C 4 To ready the Elionix for sample loading press the Sample Exchange button on the Stage Controller Wait until the red light comes on in the Stage Limit before proceding e Vent the load by toggling Vacuum Toggle Button to vent see Fig 6 Make sure the gate valve door is closed before venting the loadlock e When the vent the loadlock is a atmosphere it will au
70. N Brown C Naud D Mayou T Li J Hass A N Marchenkov E H Conrad P N First and W A de Heer Electronic confinement and coherence in patterned epitaxial graphene Science 312 1191 2006 A Rycerz J Tworzydlo and C W J Beenakker Valley filter and valley valve in graphene Nature Phys 3 172 2007 H B Heersche P Jarillo Herrero J B Oostinga and L M K Vnersypen Bipolar supercurrent in graphene Nature 446 56 2007 M C Lemme T J Echtermeyer M Baus and H Kurz A graphene field effect device IEEE Electron Device Lett 28 283 2007 164 47 48 49 50 51 52 53 54 57 B Huard J A Sulpizio N Stander K Todd B Yang and D Goldhaber Gordon Transport measurements across a tunable potential barrier in graphene Phys Rev Lett 98 236803 2007 V V Cheianov V Fal ko and B L Altshuler The focusing of electron flow and a Veselago lens in graphene p n junctions Science 315 1252 2007 D R Smith J B Pendry and M C K Wiltshire Metamaterials and negative refractive index Science 305 788 2004 D A Abanin and L S Levitov Quantized transport in graphene p n junctions in a magnetic field Science 317 641 2007 D A Abanin P A Lee and L S Levitov Spin filtered edge states and quantum Hall effect in graphene Phys Rev Lett 96 176803 2006 N M R Peres F Guinea and A H Castro Neto
71. acts A and B straddle the top gate Fig 6 1 b so that transport along the PNJ can be studied Fig 6 1 c Electrical measurements on two similar devices measurements from a single device are presented are performed at a temperature of 4K using a current bias lock in method in B up to 8T This device shows QH signatures of single layer graphene i e 66 conductance quantization at 2 6 10 e h and has a CNP at Vbg 40V All measurements presented are taken in the Vpg range of 20V to 40V p type in Region II where the carrier type is well defined i e at densities larger than the disorder induced density fluctuations Similar results were obtained data not shown for smaller range of Vig gt 40V A comparative measurement scheme is employed to understand how the presence of a PNJ parallel to transport affects conduction Four terminal longitudinal S Rcp aB where Rij k is a resistance measurement where current is injected at i and drained at j and the voltage is measured between k and l Fig 6 1 a and transverse 5 y Rap Bc resistance measurements along the PNJ are compared to those in which all the contacts are completely under the top gate Riz Rcp er and Ryy Rcrpe If an additional conduction channel is introduced between contacts A and B as shown schematically in Fig 6 1 c a decrease in Sz and an increase in Sz should result A measurement scheme similar to Sz was employed to study electron focusing in pairs of qua
72. alve is removed and the water line is attached A heater jacket is placed around the water canister and the temperature is set to 40 C Before raising the temperature 5 cycles of a standard ALD process at room temperature is performed to prevent desorption of the FL 5 cycles of the recipe in Table 2 3 Stabilizing the FL Finally the temperature of the reaction chamber can be raised to perform the oxide growth The temperature of the base of the reaction chamber is set to 160 C and the walls of the chamber to 150 C Wait until the chamber has reached its set temperature 5 mins and perform the Oxide Growth recipe in Table 2 4 Repeat the process to suit the 20 Table 2 3 Stabilizing the FL Line Pulse Time sec Pump Time sec H20 0 2 5 TMA 0 1 30 Table 2 4 Oxide Growth Line Pulse Time sec Pump Time sec H2O 0 2 5 TMA 0 1 30 8 6 6 Q 4 L o or 2 2 0 0 4 0 2 4 20 10 0 10 20 Vig V Vac V Figure 2 6 Two terminal resistance R as a function of Vig left and Vpg right after deposition of the functionalization layer and 30 nm of AlgO3 desired oxide thickness each cycle deposits about 0 09 nm If done properly the mobility of the graphene should be very close to the mobility before deposition and the charge neutrality point should be around zero Fig 2 5 shows the results for a device with 10 000 cm V s mobility 21 Chapter 3 Quantum Hall effect in a gate
73. an image similar to Fig 12A which has a black strip in the center of two gold pads e Zoom in to 200 400kX and use the focus and stigmation to sharpen the image of the gold islands When the focus and stigmation are correct the gold islands should appear clear and sharp see Fig 12B e Go back to the FC and measure current again to make sure the value is still what you want e Press the appropriate value of voltage under the Accelerating Voltage right above Condition Memory in Fig 10 100kV used here to reset the voltage Once voltage is reset the current should still be set to what you want e The stage height should now be 2 5mm now Using the Stage Driver drive to the center of your chip you can find the center by finding the lower left hand corner of your chip and extrapolating to the center For my chip the lower right hand corner is usually around 116mm 116mm and use the Z Control to raise lower the stage to bring your chip into focus The value of the laser monitor should be 0 see Fig 12B when your chip is in focus and won t come on until your chip is in reasonable focus 3 4mm for my chips that are 1mm in height 5mm X 5mm is on the lower end of when the laser can effectively measure the chip height and the chip needs to be flat against the sample plate for this method to work Your sample should now be in focus and you are ready to write Using the interface computer open the ELC Program A window sh
74. arrangements in which more than one in a plurality of graphene regions are separately controlled by a corresponding 103 local top gate As demonstrated below these arrangements are temporally reconfigurable with any selected number of p type and n type graphene regions each that can be individ ually addressed and with local top gate control can be individually reversed in electronic charge carrier type 027 Referring to Figs 3A 3B this configuration is schematically represented for a first example of a single p n junction graphene device 50 The graphene device here includes a graphene layer 12 having a first region 40 and a second region 42 that are defined with charge carrier types based on the applied top gate voltages as described below For clarity a global backgate electrode 14 is here shown biased at ground Device electrodes 18 20 are biased with a selected device voltage VD applied between the electrodes 028 Local top gate electrodes 35 37 are provided over the graphene separated from the graphene by a gate insulator 24 and a functionalization layer that is not here shown for clarity With the first top gate electrode 35 biased with an appropriate positive voltage 66 and the second top gate electrode 37 biased with an appropriate negative voltage 68 an n type graphene region 40 is formed under the first top gate electrode 35 and a p type graphene region 42 is formed under the second top gate electrode 37 The required top g
75. asured by atomic force microscopy prior to electron beam lithography 71 suggests this device is likely multi layer Further indications include the broad R Vbg peak 72 and the large minimum conductivity amin 8 e h at By 0 Fig 4 4 a as well as the absence of QH signature for B lt 8 T at 250 mK not shown Two parameter fits of S7 Vsq data to Eq 4 1 show three notable differences from results in the single layer samples Figs 4 4 b and 4 4 c First F shows a measurable dependence on back gate voltage decreasing from 0 33 at the charge neutrality point to 0 25 at ns 6 x 101 cm for Te 0 3 K Second F decreases with increasing temperature Finally Tw Te is 1 3 1 6 instead of very close to 1 We interpret the last two differences as well as the sublinear dependence of SF on Vea see Fig 4 4 inset as indicating sizable inelastic scattering 59 60 in sample D An alternative explanation in terms of series resistance would require it to be density bias and temperature dependent which is inconsistent with the independence of g on Vsa and Te 4 6 Summary and acknowledgements Summarizing the experimental results we find that in four single layer samples F is insensitive to carrier type and density temperature aspect ratio and the presence of a p n junction In one multi layer sample F does depend on density and temperature and S Vsa shows a broadened quadratic to linear crossover and is sublinear in Vzq
76. at B 0 and T 4 2 K demonstrating independent control of carrier type and density in regions 1 and 2 Labels in each of the four quadrants indicate the carrier type first letter indicates carrier type in region 1 b and c Horizontal Vertical slices at Vig Vig settings corresponding to the colored lines superimposed on Fig 3 2 a d I V curves at the gate voltage settings corresponding to the solid circles in Fig 3 2 a are representative of the linear characteristics observed everywhere in the plane of gate voltages asymmetry is studied in greater detail The changing background resistance results from the different density in region 1 at each Vig setting Current voltage T V characteristics measured throughout the Vig Vog plane show no sign of rectification in any of the four quadrants or at either of the charge neutral boundaries between quadrants Fig 3 2 d as expected for reflectionless Klein tunneling at the p n interface 16 17 27 3 5 Transport in the quantum Hall regime At large B the Dirac like energy spectrum of graphene gives rise to a characteristic series of QH plateaus in conductance reflecting the presence of a zero energy Landau level that includes only odd multiples of 2 e h that is 2 6 10 x e h for uniform carrier density in the sheet 11 51 52 These plateaus can be understood in terms of an odd number of QH edge states including a zero energy edge state at the edge of t
77. at the tape is pressed firmly against the surface Fig A 2 a Next peel the tape off the graphite Fig A 2 b A sqaure of roughly the same lateral dimensions of the graphite should be stuck to the tape Take another piece of tape and press it against the piece of tape used to cleave the graphite with the graphite side up Rub your tweezers over the tape graphite tape sandwich until the two pieces of tape 92 Figure A 1 a a picture of the ZYA grade graphite material currently used in the Marcus Lab to produce graphene b Size quality and Lot Number of the graphite are pressed firmly together Fig A 2 c Take the tape on the left hand side of Fig A 2 d and use a fresh piece of tape to make another tape graphite tape sandwich With these two pieces of tape repeat the press and peel process several 10 times until the piece of tape covered in smaller faint grey graphite islands as shown in Fig A 2 e It is important that the area of the tape that will be placed on your oxidized Silicon chip is completely covered with these faint grey islands This helps to prevent transfer of tape residue to the graphene or substrate surface Next get a chip comprised of 285nm of SiO on a degenerately doped Silicon wafer Wafers were obtained from Nova Electronic Materials http www novawafers com Not all oxides are created equal The samples deposited on the flattest oxides seem to have on average higher mobilities The flattest
78. atalytically suitable for the formation on the graphene of a gate oxide layer by a se lected process such as ALD Additional details and alternatives for functionalization layer formation are provided in U S Patent Application Publication US2008 0296537 entitled Gas phase functionalization of carbon nanotubes published December 4 2008 the entirety 114 of which is hereby incorporated by reference 058 The invention is not limited to a particular functionalization layer formation pro cess or functionalization layer material and can be conducted with any suitable set of pre cursors that non covalently bind with the graphene surface to form a catalytically active surface on which can be formed an oxide layer For many applications it can be preferred to employ as a functionalization layer precursor one of the precursors that is to be employed in formation of the subsequently formed oxide layer Where a high k dielectric is to be employed as the oxide layer e g Hafnium Oxide HfO2 or zinc oxide ZnO or it can be preferred to provide a functionalization layer that is based on the selected oxide layer 059 For example given a graphene device process in which HfO2 is to be employed as a top gate oxide material a functionalization layer in accordance with the invention can em ploy an HfO2 precursor in the formation of the PFL In one example process provided by the invention for producing such a graphene layer provided on a substrate a
79. ate bias voltages are to be understood to include a consideration of device capacitances as in Figs 2B 2C 029 As shown in Fig 3B the top gate voltages can be each controlled to reverse the polarity of the p n junction configuration of Fig 3A With the first top gate electrode 35 biased with an appropriate negative voltage 66 and the second top gate electrode 37 biased with an appropriate positive voltage 68 the graphene region 40 under the first top gate electrode 35 is reversed to p type and the graphene region 42 under the second top gate electrode 37 is reversed to n type the polarity of the p n junction is thusly reversed This localized control can be extended as shown in Fig 3C with both the first and second top gate electrodes 35 37 biased with appropriate positive voltages 66 68 whereby the graphene region 40 under the first top gate electrode 35 is reversed back to n type as in 104 Fig 3A and as in the adjacent n type graphene region 42 This configuration eliminates the p n junction from the device 030 This example demonstrates that the graphene layer can be electrically controlled locally with top gates to form two adjacent graphene regions of opposite conductivity type producing a p n junction at the interface of the regions then can be controlled to reverse the polarity of the p n junction and further can be controlled to set the regions to be of the same conductivity type thereby eliminating the p n junction en
80. brium originates from the partial transmission of quantized charge 57 Mechanisms that can lead to shot noise in mesoscopic conductors include tunneling quantum interference and scattering from impurities and lattice defects Shot noise yields information about transmission that is not available from the dc current alone In graphene 7 12 a zero gap two dimensional semi metal in which carrier type and density can be controlled by gate voltages 5 density dependent shot noise signatures un der various conditions have been investigated theoretically 16 25 For wide samples of ballistic graphene width to length ratio W L 4 the Fano factor F i e the current noise normalized to the noise of Poissonian transmission statistics is predicted to be 1 3 at the charge neutrality point and 0 12 in both electron n and hole p regimes 25 The value F 1 1 2 0 29 is predicted for shot noise across a ballistic p n junction 16 For strong smooth charge puddle disorder theory predicts F 0 30 both at and away from the charge neutrality point for all W L 1 58 Disorder may thus have a similar effect on noise in graphene as in diffusive metals where F is universally 1 3 59 60 61 62 63 64 regardless of shape and carrier density Recent theory investigates numerically the evolution from a density dependent to a density independent F with increasing disorder 65 To our knowledge experimental data for shot noise in gra
81. ce on a selected substrate or other structure It is recognized that many techniques exist and are being developed to 110 produce graphene sheets The invention is not limited to any particular graphene production process or resulting graphene configuration In one example process to produce a piece of graphene a thin piece of graphite is first extracted from e g a bulk piece of highly oriented pyrolytic graphite such as SPI 1 grade graphite from SPI Supplies Structure Probe Inc www 2spi com The extraction is carried out using e g an adhesive tape such as 3M Mask PlusII Water Soluble Wave Solder Tape from 3M www 3m com by applying the tape to the graphite The graphite region that is extracted onto the tape is thinned by repeated exfoliation of the region with additional tape 047 Prior to a final exfoliation step a selected substrate is provided onto which the graphene is to be arranged In one example where a graphene device with a backgate electrode is desired a heavily doped substrate such as an n Si substrate can be employed as the support substrate and as the backgate electrode Where the backgate electrode is to be electrically isolated from the graphene as in the configurations of Figs 1A 1B a layer of oxide is provided on the top surface of the Si substrate In one example a layer of SiO2 e g a 300 nm thick thermally grown layer of SiO2 is formed on the silicon substrate and then is cleaned in acetone an
82. cess nitrogen dioxide gas NO2 and trimethylaluminum TMA vapor are employed to form a functionalization layer In this example process the chamber is pumped down to a pressure of e g about 0 3 torr Next the functionalization layer is deposited at room temperature with a number of cycles e g about 50 cycles of the following sequence A 100 torr dose of NO2 is first introduced into the chamber for e g about 0 5 seconds and then pumped out Following a 7 second purge under continuous flow of 20 sccm of nitrogen gas N2 a 1 torr dose of trimethylaluminum TMA vapor is pulsed into the chamber The chamber is then purged for 2 minutes before beginning the next cycle 055 With this functionalization layer in place a thin layer is applied to prevent the functionalization layer from desorbing Then the gate oxide is formed on the stabilized functionalization layer For many applications it can be preferred to form the gate oxide 113 layer by the same process as the functionalization layer e g by ALD In one example process of such immediately after the functionalization layer cycles e g 50 ALD cycles of the process just above a thin layer of A1203 is formed by ALD on the functionalization layer to prevent desorption This thin layer is grown by e g 5 ALD cycles at room temperature of e g a 1 torr pulse of H2O vapor followed by a 1 torr pulse of TMA vapor under continuous flow of N2 with 5 second intervals provided between
83. conductance exhibits a series of maxima with values slightly above 6 10 14e h Maxima on the hole side consistently have slightly higher values a feature observed in all the samples measured The inset of Fig 5 2 a shows g in the QH regime as a function of Vpg and B Dashed black lines indicating the filling factors v nsh eB where ns is the carrier density of 6 10 14 and 18 align with the local maxima of g Vpg B Here Vig was converted to ns using a parallel plate capacitance model 5 giving ns a Vig Vofset with a 6 7 x 10 cm V and Vogset 2V Although the values of Vig at the CNP and Voffset are slightly different we note that the value of Vpg for the CNP is not well defined below 2V a result of the underlying disorder in the sample 33 and since these two values do not differ by more than this value we do not ascribe any significance to this discrepancy Measured g Vpg black curve in Fig 5 2 b for sample A2 s 0 2 made using the same graphene flake as Al shows distinctive differences from the measured g Vig of sample Al In particular at the CNP Vig 1 5 V g exhibits a sharp peak with a maximal value 8 8e h Away from the CNP the conductance has maxima which are much stronger than those of sample Al The inset of Fig 5 2 b shows g Vpg B For this 50 Figure 5 2 a Inset Conductance g in the quantum Hall regime as a function of B and Vpg at T 250mK for sample
84. controlled p n junction in graphene J R Williams School of Engineering and Applied Sciences Harvard University Cambridge Massachusetts 02138 L DiCarlo C M Marcus Department of Physics Harvard University Cambridge Massachusetts 02138 The unique band structure of graphene allows reconfigurable electric field control of carrier type and density making graphene an ideal candidate for bipolar nanoelectronics We report the realization of a single layer graphene p n junction in which carrier type and density in two adjacent regions are locally controlled by electrostatic gating Transport measurements in the quantum Hall regime reveal new plateaus of two terminal conduc tance across the junction at 1 and 3 2 times the quantum of conductance e h consistent with recent theory Beyond enabling investigations in condensed matter physics the local gating technique demonstrated here sets the foundation for a future graphene based bipolar technology This chapter is adapted with permission from Science 317 638 2007 2007 by the American Association for the Advancement of Science This chapter is adapted from Ref 40 22 3 1 Introduction Graphene a single layer hexagonal lattice of carbon atoms has recently emerged as a fascinating system for fundamental studies in condensed matter physics 7 as well as a candidate for novel sensors 41 42 and post silicon electronics 5 21 22 43 44 46 47 The unusua
85. cts are mapped on the real axis with the end points 1 2 3 and 4 mapped to q 1 1 G3 2 11 G 23 57 From these values following the procedure described in Ref 75 Appendix we compute the cross ratio Rrus G1 a l G2 0 64 5 9 C1 C2 C3 Ca and then obtain the aspect ratio from the relations fs sae A1234 1 k 2k 5 10 where K k is the complete elliptic integral of the first kind and k 1 k This procedure yields the value 0 9 identical to that found from the best fit to a conducting rectangle model see Fig 5 5 7 Summary and discussion In summary we have studied the effect of geometry on the conductance of two terminal graphene devices in the QH regime comparing experiment and theory The QH plateaus typically exhibit conductance extrema that are stronger for wide short samples For wide samples fj lt 1 minima of the two terminal conductance are expected at filling factors where plateaus would be found in multiterminal devices On the other hand for narrow samples fs gt 1 conductance maxima appear at those filling factor values Having in 60 hand a value for the aspect ratio of the sample one can then use the alignment of either the minima for q lt 1 or the maxima for g_ gt 1 with particular filling factors to infer the number of layers For instance alignment of the appropriate extrema with filling factors 2 6
86. d This enables distinct control of p type and n type regions that can be adjacent to each other and that can be provided even as a single p n junction device or multiple junction device or circuit arrangement Unlike state of the art silicon bipolar electronics in which ion implantation is used to create fixed p type and n type re gions having carrier densities that are also fixed p type and n type charge carrier regions regions of a graphene device of the invention can be temporally and separately controlled to be either n type or p type and can be reversed to the opposite charge carrier type with precise control over the carrier density tailored to suit the function of the device Com pletely reconfigurable bipolar graphene electronics are thereby provided by the invention The graphene devices are temperature insensitive because graphene is itself insensitive to temperature variation and therefore graphene device operation from 4K all the way up to room temperature can be achieved with a wide array of p n junction device and circuit configurations 091 Also as demonstrated above the invention provides a microfabrication process for producing carbon based structures such as graphene p n junction devices and circuits with a technique for functionalizing a carbon surface prior to gate oxide formation The functionalization layer blanket coats the carbon surface to prevent extrinsic doping of the surface by the ambient environment and enab
87. d at the junction between each p type and n type region With this condition set the arrangement of the circuit 80 in Fig 5A results in an enhancement of conductance between the first and third device electrodes 94 98 thereby forming a path of enhanced conduction or a one dimensional wire 102 between these electrodes 94 98 solely through control of the top gate voltages to set the p type and n type regions as shown 107 039 Referring also to Fig 5B the circuit therefore can be rewired to provide a different selected wiring connection 105 e g to connect the first and fourth device electrodes 94 100 by switching the polarity of the top gate over one region 92 reversing the charge carrier type of that region 92 from n type to p type Here the circuit connection of the first arrangement 80 is eliminated and a new path of enhanced conduction 104 is formed between the first and fourth device electrodes 94 100 Any number of p n junction circuit configurations like these can be controlled to thusly form temporal wiring connections between selected device electrodes 040 These examples demonstrate that in accordance with the invention each desig nated region of graphene to be controlled as a specific charge carrier type can be individually controlled with a corresponding top gate as desired but need not be in either case ad jacent n type and p type conducting regions of graphene can be controlled to coexist by individual biasing
88. d isopropyl alcohol IPA 048 Tape from the final graphene exfoliation is pressed against the oxide layer on the substrate and rubbed gently e g with the back of a tweezers for some reasonable time e g 10 seconds The structure is then immersed in water e g at 60C to dissolve the tape from the graphene and the substrate is preferably again cleaned in acetone and IPA to remove any tape residue left on the graphene and substrate surface The structure can then be viewed under an optical microscope to identify potential regions of graphene using the well established condition in which a single layer of graphene causes a characteristic color shift that arises from thin film interference and that is distinct from two three or more such layers 049 Other graphene formation and arrangement techniques can be employed and the invention contemplates the future development of graphene formation processes that are 111 more efficient and effective than those currently employed The invention is not limited to current graphene production processes and is applicable to a graphene layer produced by any method 050 With a graphene sheet layer or region in place on a selected platform such as a microelectronic substrate a graphene device circuit or other system in accordance with the invention can be produced with the functionalization and blanket oxide layers described above To demonstrate the graphene microfabrication processes of the in
89. d magnetic fields B A 2D image at T 4 2 K and B 4 T Fig 3 4A reveals quantum Hall QH signatures similar to those observed at T 250 mK Fig 3 3A The black curve in Fig 3 4B is a slice at constant filling factor v 2 The same slice at T 250 mK reproduced from Fig 3 3D is shown in red The similarity between the two curves suggests that mode mixing at the p n interface is only weakly dependent on temperature most likely as a result of the large Landau level separation in graphene 11 Data in Fig 3 4A shows oscillations at high conductance g gt 6 e h in the p p and n n quadrants We interpret these as Shubnikov de Haas oscillations contributing to the two terminal measurement 2D images in Figures 3 4C and 3 4D show g at B 8 T for T 4 2 K and T 250 mk respectively A clear doubling of the Landau level spacing in gate voltage is observed in comparison to images at B 4 T Figs 3A and S1A These data show cleaner conductance quantization in n n regions than in p p regions and also weak temperature dependence as observed in Fig 3 3A and 3 4A 3 7 Acknowledgements We thank L S Levitov D A Abanin C H Lewenkopf and P Jarillo Herrero for useful discussions We thank Z Chen at IBM T J Watson Research Center for suggesting the 32 T 42K B 4T 250 mK 1 0 0 5 00 0 5 0 0 1 2 Figure 3 4 A Differential conductance g as a function of top gate voltage Vig and back
90. de gated mesoscopic graphite wire Phys Rev B 75 245429 2007 Y Zhang J P Small M E S Amori and P Kim Electric field modulation of gal vanomagnetic properties of mesoscopic graphite Phys Rev Lett 94 176803 2005 I Snyman and C W J Beenakker Ballistic transmission through a graphene bilayer Phys Rev B 75 045322 2007 B zyilmaz P Jarillo Herrero D Efetov D A Abanin L S Levitov P Kim Electronic Transport and Quantum Hall Effect in Bipolar Graphene p n p Junctions Phys Rev Lett 99 166804 2007 D A Abanin and L S Levitov Conformal invariance and shape dependent conduc tance of graphene samples Phys Rev B 78 035416 2008 Eduardo V Castro K S Novoselov S V Morozov N M R Peres J M B Lopes dos Santos Johan Nilsson F Guinea A K Geim and A H Castro Neto Biased bilayer graphene semiconductor with a gap tunable by the electric field effect Phys Rev Lett 99 216802 2007 Jeroen B Oostinga Hubert B Heersche Xinglan Liu Alberto F Morpurgo Lieven M K Vandersypen Gate induced insulating state in bilayer graphene devices Nature Material 7 151 2007 R F Wick Solution of the Field Problem of the Germanium Gyrator J Appl Phys 25 741 1954 167 79 80 82 83 86 87 89 H H Jensen and H Smith Geometrical effects in measurements of magnetoresistance J Phys C 5 2867 1972 R W Rend
91. e h 25 In real graphene devices disorder plays an important role in charge transport 26 Three main types of disorder are possible dislocations ripples and charged impurity scattering Scanning tunneling microscopy studies have shown that the amount of dislocations in ex foliated graphene is small 27 Ripples are slow smooth variations of the graphene height and can arise from corrugations of the surface 28 or intrinsically from long wavelength fluctuations of the graphene membrane 29 The last main source of disorder is charge impurities either from the SiO2 substrate or from charges trapped beneath or lying on top of the graphene sheet 30 It is currently unclear whether ripples 31 or charge impuri ties 32 are the more important factor in determining the conductivity in graphene It is known that at the Dirac point disorder produces a series of interconnected puddles of electrons and holes 33 Therefore it is not possible to define a Ep where the the energy is positioned exactly at the Dirac point Instead a value of Ep can be assigned such that the entire sheet of graphene is charge neutral this point is called the charge neutrality point The minimum conductivity at the charge neutrality point has been studied exper imentally 13 34 and theoretically 35 36 though no consensus has been reached It is important to point out that since the charge neutrality point is made up entirely of p n puddles and p n junctions unde
92. e Heavyside function and a is the length of the potential step for the Dirac equation was very different from the solution for the same potential in the Schr dinger equation 15 Unlike the Schr dinger equation where transmission through the barrier is exponentially suppressed with increased height and width Klein demonstrated that for Dirac carriers with rest energy A 2mc approaching the barrier at normal incidence had unity transmission for barrier heights V gt A This effect which now bears the author s name is called the Klein Paradox In graphene the carriers lack mass and it is expected that unity transmission will occurs for all values of V One explanation for this effect can be understood by the lack of the band gap in the eigen energies of the Dirac equation This leads to a vanishing distance between classical turning points 16 outside and inside the barrier Another interpretation comes from the pseudospin concept of carriers in graphene The wavefunction of Eq 1 9 is a two component wavefunction each component coming from the amplitude of the wavefunction on sublattice A and B It can be shown 17 that the right movers those states with 6E dk gt 0 shown in red in the inset of Fig 1 4 come from the A atoms and the left movers 6E 6k lt 0 blue in the inset of Fig 1 4 come from the B atoms The Pauli matrices of Eq 1 9 affect the amplitude of the wavefunction on the A and B atoms and are not operating on
93. e level of the measurement setup Adjacent non imaged devices made from the same graphene flake showed conductivity similar to the investigated device prior to imaging These results confirm that the graphene was etched successfully using the He ion beam Next the drain current of a graphene device on SiO2 substrate was measured inside 88 graphene i H l 400 800 1200 b 500nm a Au contacts ED time s Figure 8 4 a HeIM image of a graphene device The boxes indicate the field of view used for etching The window was subsequently moved in the direction of the arrow b Drain current vs time of exposure of the graphene device The etching window was moved as the current saturated the He ion microscope while part of it was exposed to the ion beam A field of view of 1 um x 1 um was chosen indicated by the yellow box in Fig 8 4a After about 150 seconds the current saturated indicating complete etching of the graphene inside the field of view Fig 8 4b At this point the imaging window was moved to the next part of the device in the direction of the white arrow in Fig 4a The current was again monitored until it saturated A beam current of 1 pA dwell time of 3 us and pixel spacing of 1 nm allowed us to estimate a suitable He ion line dose for etching graphene on SiO2 1 5 nC cm A residual drain current of about 4 nA was measured after etching the entire device which could not be reduced further by subsequent He ion beam ex
94. e nanoribbons is discussed Contents IDS UAC tc ins e a BE ioe thle pets anette Yateley th Bee eae De ee te Table of Contents ncn sse Ske th Shed epi es a e de Rae ee a ein Listeof Figures oo anu geet ee geod ee EA ace a Se Ye ee ay eas Acknowledgements oaoa aa ee 1 Introduction to the Electronic Properties of Graphene 1 1 Allotropes of carbon araci y haog Poets te Ep ee Boke as Ge ee 1 2 Band structure of graphene 020000 eee eee 1 3 Quantum Hall effect in graphene 2 02 0004 1 4 Potential barriers in graphene 2 00000052 2b ee 1 5 Graphene nanoribbons 0 000 ee ee 1 6 Minimum conductivity in graphene 2 0 22004 2 Functionalization of and Atomic Layer Deposition on Graphene 2 1 Atomic Layer Deposition 0 0 0000 ee ee 2 2 Atomic Layer Deposition on graphene 02 004 2 3 NO and gas cabinet modification 0 0200000002 ee eee 2 4 Deposition of the functionalization layer ooo a 25 Deposition of Alo O9 guede aeeai ei Ge PRE Hts ee GO ee Sec 3 Quantum Hall effect in a gate controlled p n junction in graphene el troduction er tears the ee Sept ee re a ot herds AnA 3 2 Device fabrication aooaa 3 3 Measurement setup 2 00 0 2 ee ee 3 4 Transport at zero magnetic field 0 2 020002 00 4 3 5 Transport in the quantum Hall regime 000 4 3 6 Supplementary Information 2 0 0
95. e tape touch the chip and place it on the chip and rub the tweezers over it about 10 times Fig A 3 b The resulting chip tape bowl configuration should look something like Fig A 3 c Place the bowl on a hot plate at 180 C for a total of 3 mins Fig A 4 a At 1 5 mins take 94 Figure A 3 a Place the on a glass bowl on the hot plate for the bowl off the hot plate and tap it 5 times with a cleanroom swab Fig A 4 b and then place it back on the hot plate for the ramaining 1 5 mins A nice feature of this deposition method is that the tape is never rubber over the surface of chip resulting in less transfer of tape residue to the surface After the sample has cooled remove the tape slowly and image the sample in the microscope Initial characterization on the graphene deposition is done via optical microscopy Thin film interference is used to distinguish single layer graphene from bi and multi layer graphene sheets There is an effervescent light purple glow that single layer graphene sheets will give off so faint that it can be hard to see at first An optical image of an area on the SiO 95 Figure A 4 a Place the chip on top of a glass bowl on a hot plate at 1800C for 1 5 mins b Remove the plate and tap with a cleanroom swab 10 times Place back on the hot plate for another 1 5 mins Bilayer Single Layer ee 20 um Figure A 5 An image of single bi and multi layer graphene taken by an opt
96. each Landau level Landau level broadening 2 m Mv vn where Vp is due to disorder is included in the theory as a gaussian broadening e7 the center of the LL and 4 is a fitting parameter The total conductivity tensor is taken to be a sum of the contributions of individual Landau levels The current density distribution for a rectangular sample with an arbitrary aspect ratio is found analytically by conformal mapping 78 79 80 The current density is then integrated numerically along suitably chosen contours to evaluate total current and voltage drop from which g I V is obtained Along with the experimental traces Figs 2 a b also show the theoretical curves for Ent solid red trace and for dashed blue trace ratios For sample Al amp 1 7 differs considerably from 0 7 For sample Al the best fit gives A 1 2 This theoretical curve Eft 1 7 reproduces the essential features of the data local maxima align with the filling factors 2 6 10 and g exhibits a dip at the CNP The alignment of conductance minima with densities corresponding to the integer filling factors as well as a peak at the CNP observed for sample A2 are consistent with theoretical predictions for a short wide monolayer graphene sample As illustrated in Fig 5 2 b Ent 0 2 matches the measured for sample A2 We observe that the size of peaks and dips in Fig 5 2 a b increases for higher LL In contrast th
97. ectrode to produce a predominance of hole charge carriers in that region A reversal of the voltage produces a corresponding reversal in charge carrier type This phenomenon enables bipolar electronics in graphene to be completely reconfigurable that is a simple change in the gate electrode voltage allows for on demand control of the carrier type and density that can be tuned to suit a particular graphene device application and obviates the need for conventional physical and fixed doping for instance via ion implantation 99 B 3 Summary of the invention 007 The invention provides graphene configurations for producing robust and repro ducible gate controlled p n junction devices having an arbitrary number of p n junctions defined by regions having selected charge carrier types that are controlled temporally by one or more local gates The summary language will directly paraphrase the claims and therefore will be added once we finalize the claims B 4 Brief description of the drawings 008 Figs 1A 1B are schematic side views of two example graphene p n junction devices provided by the invention and having a single top gate 009 Figs 2A 2C are a schematic side representations of the device of Fig 1B and two different charge carrier arrangements of that device respectively in accordance with the invention 010 Figs 3A 3C are schematic side views of a further example graphene p n junction device provided by the invention havi
98. ell and S M Girvin Hall voltage dependence on inversion layer geometry in the quantum Hall effect regime Phys Rev B 23 6610 1981 A M Dykhne and I M Ruzin Theory of the fractional quantum Hall effect The two phase model Phys Rev B 50 2369 1994 C P Burgess and B P Dolan Quantum Hall effect in graphene Emergent modular symmetry and the semicircle law Phys Rev B 76 113406 2007 T A Driscoll and L N Trefethen Schwarz Christoffel Mapping Cambridge Uni versity Press Cambridge 2002 Online Conformal Mapping dictionary example 51 http math fullerton edu mathews c2003 ConformalMap Dictionary 5 html G Giovannetti P A Khomyakov G Brocks V M Karpan J van den Brink and P J Kelly Doping Graphene with Metal Contacts Phys Rev Lett 101 026803 2008 J E M ller textitEffect of a nonuniform magnetic field on a two dimensional electron gas in the ballistic regime Phys Rev Lett 68 385 1992 C W J Beenakker Colloquium Andreev reflection and Klein tunneling in graphene Rev Mod Phys 80 1337 2008 H van Houten C W J Beenakker J G Williamson M E I Broekaart P H M van Loosdrecht B J van Wees J E Mooji C T Foxon and J J Harris Coherent electron focusing with quantum point contacts in a two dimensional electron gas Phys Rev B 39 8556 1989 V Lukose R Shankar and G Baskaran Novel electric field effects on Landau levels
99. ent to a non rectangular device sample C shown schematically in the inset of Fig 5 5 The measured two terminal conductance of sample C black curve in Fig 5 5 has properties very similar to those expected for a square monolayer sample around the CNP the conductance is nearly flat with value 2e h monotonically increasing on the electron and hole sides at filling factors v gt 2 Theoretical curve shown in Fig 5 is obtained from the conducting rectangle model using Est 0 9 and A 0 7 This choice of parameters yields particularly good agreement for v lt 6 At higher fillings the plateaus are washed out suggesting that the LL broadening is stronger for LLs n gt 2 It is interesting to compare amp g to an effective aspect ratio obtained from conformal mapping of sample C to a rectangle As discussed below this conformal mapping can be constructed directly owing to the relatively simple geometry of sample C The effective aspect ratio obtained in this way is s 0 9 consistent with ft Before we proceed to construct the conformal mapping we note that the geometry of sample C pictured in Fig 5 6 is that of a polygon In principle any polygon can be mapped onto the upper half plane by inverting a Schwarz Christoffel mapping 83 However since this mapping is defined by a contour integral the inverse mapping can only be found numerically In order to circumvent this difficulty two approximations are employed below
100. eory 75 predicts that peaks and dips at v gt 0 LLs are all roughly the same This discrepancy may reflect the inapplicability of the two phase model approach of Ref 81 which underlies the semicircle law obtained in this work to higher LLs Indeed 52 16 5 40 0 v v 40 12 A A s bg N D 8 Bilayer 4f B 8T T 4K Es 25 0 n 0 8 X 0 7 40 20 20 40 Vig V Figure 5 3 a Inset Conductance g in the quantum Hall regime as a function of B and Vpg at T 250mK for sample Al Black dashed lines correspond to filling factors v 6 10 14 18 and align with the local mazima of conductance Main black Horizontal cut of inset giving g Vpg at B 8 T and calculated g for the best fit equivalent aspect ratio g 1 7 solid red curve and for the measured sample aspect ratio s 0 7 dashed blue curve using Landau level broadening parameter 1 2 b Inset Conductance g in the quantum Hall regime as a function of B and Vpg at T 250 mK for sample A2 Black dashed lines correspond to v 6 10 14 18 and align with the local minima of conductance Main black Horizontal cut of inset giving g Vbg at B 8T and calculated g for amp g 0 2 solid red curve and 0 2 dashed blue curve A 1 2 the same as sample Al The dashed blue curve was vertically displaced for clarity because for Dirac particles the spacing between LLs decreases at higher energies as an
101. ere taken before and after He ion etching with two Keithley 2400 source meters in a Lakeshore probe station at a pressure of 5x10 3 mbar The second set of graphene devices on SiO2 substrate were wirebonded to chip carriers and placed in a chip socket inside the Helium ion microscope to enable in situ electrical measurements inset in Fig 8 1 These were taken at a pressure of 1x10 6 mbar with an Agilent 4155B parameter analyzer connected to the device via a vacuum feedthrough All measurements were taken at room temperature 86 i graphene Eee Se Figure 8 2 a HeIM image of suspended graphene devices The yellow box indicates the area that was subsequently imaged and etched The red circle indicates the area where etching occurred initially color online b Sequence of images of progressive etching of a suspended graphene sheet 8 3 Results and discussion A suspended graphene device with a length of 150 nm and a width of 1 5 wm shown in the HeIM microscope image in Fig 8 2a was He ion etched by sequential imaging in high resolution The graphene was exposed to the He ion beam at a field of view of 2 um x 2 um and an image size of 2048 x 2048 pixels which resulted in a pixel spacing of 1 nm The dwell time was chosen to be 50 ps resulting in an effective line dose of 0 8 nC cm Fig 8 2b shows a sequence of images taken under these conditions 1 14 The red circle 87 before etching Vg 0 5 mV Figure 8 3 a HeI
102. ergy spectrum of graphene gives rise to a characteristic series of QH plateaus in conductance reflecting the presence of a zero energy Landau level that includes only odd multiples of 2 e h that is 2 6 10 times e h for uniform carrier density in the graphene layer These plateaus can be understood in terms of an odd number of QH edge states including a zero energy edge state at the edge of the graphene layer circulating in a direction determined by the direction of B and the carrier type The situation is somewhat more complicated when varying local density and carrier type across the graphene layer 083 QH features were investigated for differing filling factors v and vz in regions 1 and 2 of the graphene layer A horizontal slice through Fig 10A at filling factor v 6 is shown in Fig 10C Starting from the n n quadrant plateaus are observed at 6 e h and 2 e h at top gate voltages corresponding to filling factors v2 6 and 2 respectively Crossing over to the n p quadrant by further decreasing VTG a new plateau at 3 2 e h appears for y 2 In the v2 6 region no clear QH plateau is observed Fig 10D provides a plot of data from a horizontal slice at v 2 in Fig 10A showing 2 e h plateaus at both v2 6 and 2 Crossing into the n p quadrant the conductance exhibits QH plateaus at 1 e h for v 2 and near 3 2 e h for v2 6 084 For v and 12 of the same sign n n or p p the observed conductance plateaus follow an expressi
103. flect the values you just chose Also the beam current display to the left of the Condition Memory inputs should now reflect the value you entered You can enter the current settings into a memory element use only 4 9 don t touch 1 3 by pressing the enter button twice e To measure the current first un blank the beam using the Beam Blanking Manual On Button see Fig 11A When the current light under the button is off it means the beam is not blanked Next using the Magnification knob Fig 11B zoom out until you are at 200 or 400 X magnification the Current Status menu will display the current Magnification You should now see an image similar to the one shown in Fig 11D Center the FC in the image using the Stage Driver Fig 11C and zoom in to 100kX The Pico Ammeter should now read the current Fig 11E If not try adjusting the current range using the up down buttons at the bottom left of the Pico Ammeter To set focus and stigmation first drive to the Ref position using the bottom button of 146 Figure C 10 Elements used in setting up the beam current Figure C 11 Elements used in reading the beam current the Stage Limit controller see Fig 4 right The stage will drive to the Ref position and it will attempt to set the focal height using the laser position monitor Wait until you hear 147 two beeps which indicates that the process is complete If you unblank the beam now you will see
104. g as energizing as watching him doing physics He has an uncanny clairvoyance for research and for what the most interesting experiments are He has taken me from physics childhood to adulthood and I will always be grateful for the lessons advice and humor he shared with me along the way Next is Prof Cynthia Friend I had the pleasure of working in her research group for a year and picked up some very important tools along the way Most important was a solid understanding of surface science much of which played a very important role in the development of the functionalization layer for graphene Thanks to Prof Levitov and Dima Abanin Their insight into our experiments were essential and we would have been scooped on at least one occasion if it weren t for them It was a pleasure to work with you both Then there are my partners in crime My first year in graduate school was quite an adjustment but I got a lot of laughs from my workmates Michael Biercuk and Alex Johnson were nice enough to pummel me with pennies call me Jimmah and make sure everyone in the lab knew about Peeps Upon returning to the Marcuslab I got to know Jeff Miller better finding out we share a great passion for tea although he was a black tea guy Thanks for turning me on the Upton Tea and teaching me that the first pot of good tea should be thrown out Also I had a lot of fun running with Edward Laird Thanks for introducing me to the sport Soon after I
105. gate voltage Vig at T 4 2 K and B 4 T B Slice of Fig 3 4A at constant v 2 black The same slice at T 250 mK is reproduced from Fig 3 3D red C and D g as a function of Vig and Vig at B 8 T for temperatures of 4 2 K and 250 mK respectively NO functionalization process and D Monsma for assistance in implementing it Research supported in part by INDEX an NRI Center and by the Harvard NSEC 33 Chapter 4 Shot noise in graphene L DiCarlo J R Williamst Yiming Zhang D T McClure C M Marcus t Department of Physics Harvard University Cambridge Massachusetts 02138 USA t School of Engineering and Applied Sciences Harvard University Cambridge Massachusetts 02138 USA We report measurements of current noise in single and multi layer graphene devices In four single layer devices including a p n junction the Fano factor remains constant to within 10 upon varying carrier type and density and averages between 0 35 and 0 38 The Fano factor in a multi layer device is found to decrease from a maximal value of 0 33 at the charge neutrality point to 0 25 at high carrier density These results are compared to theories for shot noise in ballistic and disordered graphene This chapter is adapted with permission from Phys Rev Lett 100 156801 2008 2008 by the American Physical Society 34 4 1 Introduction Shot noise the temporal fluctuation of electric current out of equili
106. ging 0 2kQ at B 0T to 1kQ at B 2T over the Vg range shown here 6 6 Discussion What could be a possible origin for this increased conduction channel provided by the PNJ In the QH regime the conduction along the PNJ is provided for by the counter propagating edge states in the p and n sides of the junction The change in sign at the interface allows for snake state propagation along the junction 87 enhancing conductance The formation of the snake states takes place at a B gt B h mng eB 16 87 At the p n interface where the density ng goes from positive to negative values i e through ns 0 this condition can always be met suggesting that formation of Landau level like edge states can exist even at B 0T The behavior however of B as B OT and n gt 0 is not currently understood If a Landau like level did form an additional conductance channel with resistance of order h 2e 12 9kQ would appear In the QH regime this would 71 Figure 6 4 Back gate voltage dependence of the difference S R for B between 0 and 2T in 0 5T increments S y Rzy is reduced as the difference Vpg VigCN becomes larger for all B fields Solid black lines are guides to the eye The decrease in resistance in this Voge range increases as the perpendicular field is increased rising from 0 2kQ at B 0T to 1kO at B 2T be the only mode of transport as the bulk is localized and the resistance would be exactly h 2e For small
107. gnificantly Slices through the 2D conductance plot at fixed Vig are shown in Fig 3 2 c The slice at Vig 0 shows a single peak commonly observed in devices with only a global back gate 5 9 10 45 Using a Drude model away from the charge neutrality region mobility is estimated at 7000 cm Vs 5 The peak width height and back gate position are consistent with single layer graphene 9 10 45 and provides evidence that the electronic structure and degree of disorder of the graphene is not strongly affected by the oxide Slices at finite Vig reveal a doubly peaked structure The weaker peak which remains near Vbg 2 5 V at all Vig corresponds to the Dirac point of region 1 The stronger peak which moves linearly with Vig is the Dirac point for region 2 The difference in peak heights is a consequence of the different aspect ratios of regions 1 and 2 Horizontal slices at fixed Vpg corresponding to the horizontal lines in Fig 3 2 a are shown in Fig 3 2 b These slices show a single peak corresponding to the Dirac point of region 2 This peak becomes asymmetric away from the charge neutrality point in region 1 We note that the Vig dependence of the asymmetry is opposite to that observed in Ref 47 where the 26 B 0 10 25 0 0 Vac V V mV Figure 3 2 a Two terminal differential resistance R as a function of the top gate voltage Vig and back gate voltage Vig
108. graphene B 6 Example I 070 A semiconducting carbon nanotube was synthesized by methane CVD and was configured for initial conductance characterization in a pristine state A source drain dc transport measurement was made by contacting ends of the nanotube Fig 8A is a plot of differential conductance g as a function of backgate voltage V for the pristine nanotube 071 The carbon nanotube was then processed to form a functionalization layer and an oxide layer on the full circumference and length of the cylindrical sidewall of the nan otube The nanotube was inserted into an ALD reaction chamber and the chamber was 118 pumped down to a pressure of 0 3 torr 5 ALD cycles were then conducted at room tem perature to form a functionalization layer by the following process A 100 torr dose of NO2 gas was first introduced into the chamber for 0 5 seconds and then pumped out Following a 10 second purge under continuous flow of 20 sccm of N2 a 1 torr dose of tetrakis dimethylamido hafnium IV TDH vapor was pulsed into the chamber The cham ber was then purged for e g about 5 minutes before beginning the next cycle 072 The resulting functionalization layer was then capped and a layer of HfO2 formed by 5 ALD cycles employing a 1 torr pulse of H2O vapor and a 1 5 torr pulse of TDH vapor under continuous flow of N2 and with 20 seconds intervals between the pulses at room temperature With the oxide and functionalization layers formed a
109. graphene regions This two dimensional plot reveals a skewed cross like pattern that separates the space of top gate and backgate voltages into four quadrants of well defined carrier type in the two regions of the graphene The horizontal diagonal ridge corresponds to charge neutrality i e the Dirac point in region 1 The slope of the charge neutral line in region 2 along with the known distances to the top gate and back gate gives a dielectric constant 6 for the functionalized A1203 The center of the cross at VTG VBG 0 2 V 2 5 120 V corresponds to charge neutrality across the entire graphene layer Its proximity to the origin of gate voltages demonstrates that the functionalized oxide did not chemically dope the graphene significantly 078 Data for slices through this 2 D conductance plot at a fixed top gate voltage VTG are shown in the plot of Fig 9C The slice at VTG 0 shows a single peak commonly observed in devices with only a global back gate Using a Drude model away from the charge neutrality region mobility is estimated at 7000cm2 Vs The peak width height and back gate position are consistent with single layer graphene and provide evidence that the electronic structure and degree of disorder of the graphene was not strongly affected by the oxide Slices at finite VTG reveal a doubly peaked structure The weaker peak which remains near VBG 2 5V at all VTG corresponds to the Dirac point of region 1 The s
110. graphene device of the invention enables temporal electronic control of the graphene layer to form a single p type graphene region directly adjacent to a single n type graphene region with the carrier types of the two regions being reversible at will Only one p n junction is required and employed in this first example graphene device of the invention A local top gate is disposed over one of the two graphene regions and therefore is disposed over the device electrode that is positioned at that region This single p n junction device and the ability to control its doping profile temporally provide the foundation for a graphene based bipolar technology that can surpass the current silicon based bipolar technology in performance and application 025 In addition beyond the myriad applications for graphene based p n junction de vices in general such a graphene p n junction device is of great interest for studying many low dimensional condensed matter physics phenomena For instance recent theory predicts that a local step in potential would allow solid state realizations of relativistic i e Klein tunneling and a surprising scattering effect known as Veselago lensing comparable to scat tering of electromagnetic waves in negative index materials The graphene p n junction device of the invention thereby provides a platform for both device design as well as study of physical phenomena 026 The invention further provides graphene device and circuit
111. he rectangle in Fig 5 6 is replaced by a Hae strip extending indefinitely to the right a Next we map the domain shown in a onto a rectangle with contact 3 5 6 4 straightened out b Under this mapping the sample is slightly distorted as indicated by the grey polygon in b Because the deviation of the grey polygon boundary from the original sample boundary red line in b is fairly small it can be neglected giving a half infinite strip c Finally the domain c is mapped onto the upper half plane d which allows to find the cross ratio A1234 Eq 5 9 and evaluate the effective aspect ratio Eq 5 10 58 so that the removed rectangle has vertices 23 4 A 25 6 tA iA 5 4 These points correspond to the points w34 2 s 1 in the w plane The value of A ensures that the edge of the sample on the x axis remains on the x axis under the mapping 5 2 The distance between points 73 and 25 plane equals A as follows from Eq 5 2 and the identity V2 1 2 1 2 1 2 amp 1 J a f ns ve which can be proved by making the change of variables y2 x in the integral in the e 1 2 2 left hand side of Eq 5 5 and z in the integral in the right hand side of Eq 5 5 The removed rectangle has aspect ratio equal to 2 the same as that for the contact 3 5 6 4 however their dimensions differ by a factor of A Scaling and shifting both Z in w z A z 5
112. he sheet circulating in a direction determined by the direction of B and the carrier type The situation is somewhat more complicated when varying local density and carrier type across the sample A 2D color plot of differential conductance g 1 R as a function of Vig and Vig at B 4 T is shown in Fig 3 3 a A vertical slice at Vig 0 through the p p and n n quadrants Fig 3 3 b reveals conductance plateaus at 2 6 and 10 e h in both quadrants demonstrating that the sample is single layer and that the oxide does not significantly distort the Dirac spectrum QH features are investigated for differing filling factors v and v2 in regions 1 and 2 of the graphene sheet A horizontal slice through Fig 3 3 a at filling factor v 6 is shown in Fig 3 3 c Starting from the n n quadrant plateaus are observed at 6 e h and 2 e h at top gate voltages corresponding to filling factors vg 6 and 2 respectively Crossing over to the n p quadrant by further decreasing Vig a new plateau at 3 2 e h appears for v 2 In the vg 6 region no clear QH plateau is observed Another horizontal slice at v 2 shows 2 e h plateaus at both v2 6 and 2 see Fig 3 3 d Crossing into the n p quadrant the conductance exhibits QH plateaus at 1 e h for v 2 and near 3 2 e h for v 6 For v and 12 of the same sign n n or p p the observed conductance plateaus follow g min v2 x e h 3 1 This relation suggests that the
113. he sign of charge produces a change in the sign of the Lorentz force This creates classical trajectories that are shown in Fig 6 1 c resembling snake states observed in inhomogeneous magnetic fields in two dimensional electron gases 86 Carriers in these systems are confined to one dimensional channels and carrier motion occurs in these channels perpendicular to the magnetic field gradient The density gradient induced snake states in graphene PNJs have been predicted in Ref 87 where it was shown that classical trajectories similar to that of Fig 6 1 c can exist at the interface of p and n regions 6 2 Devices fabrication and measurement setup Graphene flakes are obtained via mechanical exfoliation of HOPG on an degenerately doped Si substrate 5 oxidized by 300nm of SiO2 Once potential single layer graphene sheets are identified by optical contrast electrical contacts 5nm Ti 40nm Au are defined and deposited by electron beam lithography and thermal evaporation A functionalized gate dielectric layer of 30nm TMA NO2g 2 nm Al203 28 nm see Ref 40 for details is grown on top of the graphene sheet and a local gate is deposited in the same manner as the electrical contacts The doped substrate is used as Vpbg and can control the density globally while the top gate affects the density only directly under where it is patterned A completed device similar to the one used in this study is shown in Fig 6 1 a Importantly cont
114. ical exfoliation similar 80 Onm height scale 50 nm Figure 7 6 a HeIM image of a dose variation test pattern in graphene lower to higher dwell times represent increased helium ion doses b AFM image with corresponding SEM image of a pattern etched with 20 100 and 200 nC cm line dose variation from left to right to the method described in Ref 5 with the modifications of the process as described in Ref 40 Next mono and multi layer graphene flakes were identified with an optical microscope 7 4 Results and discussions In an initial experiment the He ion beam was focused on freestanding graphene flakes resulting in small holes in the material Fig 7 5 shows a HeIM image of one such hole with a diameter of 15 nm Variations of this dose were performed to ascertain the optimal operation point for He ion etching Fig 7 6a shows a HeIM image of lines etched in graphene sample showing changes in the pattern with increasing beam dose from left to right at a measured probe current of 1 6 pA The dose was varied from 3 nC cm to 15 nC cm in 3 nC cm steps The result indicates that a suitable dose for etching a graphene sample with the HeIM NPGS settings used in this work is in the range of 10 15 nC cm A larger dose variation performed with 20 100 and 200 nC cm is shown in Fig 7 6b The SEM image 81 Figure 7 7 a AFM step profile analysis for the graphene cut in Fig 7 6b with a dose
115. ical microscope that contains single bi and multi layer graphene is shown in Fig A 5 96 Appendix B Graphene p n Junction Device Patent J R Williams School of Engineering and Applied Sciences Harvard University Cambridge Massachusetts 02138 H C Churchill C M Marcus Department of Physics Harvard University Cambridge Massachusetts 02138 Microfabrication Of Carbon Based Devices Such As Gate Controlled Graphene p n Junction Devices U S Provisional Application No 61 125 365 4 Prepared by Theresa Lober T A Lober Patent Services 97 B 1 Cross reference to related application 001 This application claims the benefit of U S Provisional Application No 61 125 365 filed April 24 2008 the entirety of which is hereby incorporated by reference B 2 Background of the invention 002 This invention relates to forms of carbon such as graphene and carbon nanotubes and more particularly relates to microfabrication of carbon based electronic devices 003 Graphene a single layer hexagonal lattice of carbon atoms has recently emerged as a fascinating system for fundamental studies in condensed matter physics as well as a candidate for novel sensors and post silicon electronics Carbon nanotubes CNTs and graphene are allotropes of carbon in which the carbon atomic orbitals rearrange to produce a solid in which electrical conduction is possible as either a metallic or a semiconducting material The diffe
116. ightforward to interpret as the corresponding multiterminal measurement 14 it is the simplest to perform and may be the only measurement possible for instance with very small samples The presence of non zero longitudinal conductivity causes quantum Hall plateaus measured in a two terminal configuration to not be as well quantized as in multiprobe measurement 7 As discussed in detail below plateaus exhibit a characteristic N shaped distortion arising from the finite longitudinal conductivity that depends on device geometry In this Article we systematically examine two terminal conductance in the QH regime for monolayer and bilayer graphene for a variety of sample aspect ratios Table 5 1 We especially focus on the features that can help to distinguish monolayer and bilayer graphene the conductance extrema in the N shaped distortions of the quantum Hall plateaus and at the CNP We find that these features depend on the sample aspect ratio and on the number 45 of graphene layers Results are compared to recent theory 75 in which two terminal conductance for arbitrary shape is characterized by a single parameter the effective device aspect ratio L W for rectangular samples where L is the length or distance between contacts and W is the device width The N shaped distortions of the plateaus arranged symmetrically around the CNP are consistently observed in the two terminal conductance measured as a function of carrier de
117. is indeed the case experimentally Transport mediated by such states would almost certainly change the conventional picture of local conduction Further studies are required to clarify the physical mechanism responsible for the observed behavior 5 8 Acknowledgements Research supported in part by INDEX an NRI Center the Harvard NSEC and the Harvard Center for Nanoscale Systems CNS a member of the National Nanotechnology Infrastructure Network NNIN which is supported by the National Science Foundation under NSF award no ECS 0335765 We thank Pablo Jarillo Herrero for helpful discussions 62 Chapter 6 Snake States in Graphene p n Junctions J R Williams School of Engineering and Applied Sciences Harvard University Cambridge Massachusetts 02138 C M Marcus Department of Physics Harvard University Cambridge Massachusetts 02138 We report measurements of the magnetoresistance locally gated graphene where carriers are injected at and travel parallel to the p n junction In the bipolar regime a reduction of the longitudinal resistance and enhancement of the transverse resistance are observed consistent with an additional conduction channel existing at the p n interface This con tribution to conductance is studied as a function of perpendicular magnetic field where the zero field contribution is found to evolve linearly into peak in the Hall resistance in the quantum Hall regime Further an electric field perpendicular
118. ition on graphene To achieve local control of carrier type and density in graphene via the electric field effect a local gate insulated from the graphene device must be fabricated It is trivial to place a metallic gate electrode in close proximity to a sheet of graphene It is not as trivial to insulate that gate from the device Here I will describe a method for producing a gate dielectric that preserves the unique properties of graphene and was an essential experimental step in obtaining the results of Chapters 2 3 and 6 Al2O3 is grown via ALD by successive deposition of trimethylaluminum TMA and water Many attempts were made to deposit Al203 on graphene by varying temperature deposition amount and pump time However most 95 devices had top gates that leaked that is when a voltage was applied to the top gate a current was measured proportional to 14 that voltage in the device The few devices that did not leak had very thin top gates and resulted in heavily electron doped graphene with a charge neutrality point of lt 30V Those that did leak had a leakage resistance of roughly 1kQ a value close to the resistance of the graphene Ti Au interface contact resistance suggesting that most of the top gate was in electric contact with the graphene sheet It was since discovered that on pristine graphene the ALD precursors preferentially nucleate at edges and defect sites not on the pristine graphene plane resulting in a disconti
119. itional conduction along the interface could be a source conductance that raises this theoretical value to those closer to the experimentally measured values 6 7 Acknowledgements We thank L S Levitov and D A Abanin for useful discussions Research supported in part by INDEX an NRI Center and Harvard NSEC 73 Chapter 7 Precision Etching of Graphene with a Helium Jon Beam D C Bell M C Lemme L A Stern J R Williamst C M Marcus 1 School of Engineering and Applied Sciences and the Center for Nanoscale Systems Harvard University Cambridge MA 02138 USA 2 Department of Physics Harvard University Cambridge Massachusetts 02138 USA 3 Carl Zeiss SMT Peabody MA USA 4School of Engineering and Applied Sciences Harvard University Cambridge MA 02138 USA We report on the use of a helium ion microscope as a potential technique for precise nanopatterning of graphene films Combined with an automated pattern generation system we demonstrate controlled etching and patterning of graphene giving precise command over the geometery of the graphene nanostructure After determination of suitable doses sharp edge profiles and clean etching of areas when cutting layers of graphene were observed This technique could be an avenue for precise materials modification for future graphene based device fabrication This chapter is being submitted to Nano Letters 74 7 1 Introduction Helium Ion Microscopy HeI
120. ization species comprises atomic layer deposition of a functionalization species on the carbon surface 12 The method of claim 11 further comprising forming a layer of oxide on the chemically functionalized carbon surface by atomic layer deposition 13 A method for forming a material layer on a graphene layer comprising exposing a surface of the graphene to at least one functionalization species that non covalently bonds to the graphene surface while providing chemically functional groups at the graphene surface forming a layer of oxide on the chemically functionalized graphene surface and exposing the layer of oxide and the chemically functionalized graphene surface to a beam of electrons to compensate for extrinsic doping of the carbon surface 14 A structure comprising a carbon material and a layer of HfO2 disposed on a surface of the carbon material wherein the carbon material is electrically undoped 15 The structure of claim 14 wherein the carbon material comprises a layer of graphene 16 The structure of claim 14 wherein the carbon material comprises a carbon nanotube 17 The structure of claim 14 further comprising a functionalization layer under the HfO2 layer that is non covalently bonded to the carbon material surface and that provides chemically functional groups bonded to the HfO2 layer 18 A graphene p n junction device comprising a graphene layer a backgate electrode connected to a first surface of the graphene layer
121. l Bryson in A Short History of Nearly Everything Broadway Books Random House p 251 1 1 Allotropes of carbon Two allotropes of carbon are commonly used in daily life The first and perhaps better known form is diamond While very useful for a variety of purposes diamond is a poor electrical conductor This is a direct result of the bonding configuration of carbon atoms In diamond all of the p orbitals of carbon are used in forming the bond called sp bonding As a result there are no free electrons and conduction is poor Graphite from the Greek word to write was discovered circa 1500 AD in England and was originally used to mark sheep Graphite is a layered material comprised of many two dimensional 2D layers of carbon atoms arranged in a hexagonal lattice While bonding in the 2D plane is strong perpendicular to the plane it is weak Graphite unlike diamond has only 2 of the 3 p orbitals tied up in bonds The one unpaired orbital the p orbital can be used in the transport of electrons Hence graphite is a much better conductor than diamond 1 It is commonly thought that the next allotrope of carbon were fullerenes in the 1980 s However a 2D version of graphite called graphene was first synthesized in the 1970 s on the surface of metals Using phase segregation of carbon doped nickel single crystal Eizenberg and Blakely 2 were able to controllably grow single layers of graphite Originally the potential of this materia
122. l band structure of single layer graphene makes it a zero gap semiconductor with a linear photon like energy momentum relation near the points where valence and conduction bands meet Carrier type electron like or hole like and density can be con trolled using the electric field effect 5 obviating conventional semiconductor doping for instance via ion implantation This feature doping via local gates would allow graphene based bipolar technology devices comprising junctions between hole like and electron like regions or p n junctions to be reconfigurable using only gate voltages to distinguish p hole like and n electron like regions within a single sheet While global control of car rier type and density in graphene using a single back gate has been investigated by several groups 9 10 45 local control 46 47 of single layer graphene has remained an important technological milestone In addition p n junctions are of great interest for low dimensional condensed matter physics For instance recent theory predicts that a local step in po tential would allow solid state realizations of relativistic Klein tunneling 17 16 and a surprising scattering effect known as Veselago lensing 48 comparable to scattering of electromagnetic waves in negative index materials 49 We report the realization of local top gating in a single layer graphene device which combined with global back gating allows individual control of ca
123. l traveling edge states For the case of complete mode mixing that is when current entering the junction region becomes uniformly distributed among the v1 v2 parallel traveling modes quantized plateaus are expected 50 at values v v2 2 h 3 2 PARI eaks oe A table of the conductance plateau values given by Eqs 3 1 and 3 2 is shown in Fig 3 3 e Plateau values at 1 e h for vy v 2 and at 3 2 e h for v 6 and v2 2 are observed in experiment Notably the 3 2 e h plateau suggests uniform mixing among four edge stages three from region 1 and one from region 2 All observed conductance plateaus are also seen at T 4 K and for B in the range 4 to 8 T We do find some departures between the experimental data and Eqs 3 1 and 3 2 as represented in the grid of Fig 3 3 e For instance the plateau near 3 2 e h in Fig 3 3 d is seen at a value of 1 4 e h and no clear plateau at 3 e h is observed for v v 6 We speculate that the conductance in these regions being lower than their expected values is an indication of incomplete mode mixing We also observe an unexpected peak in conductance at a region in gate voltage between the two 1 e h plateaus at vy r 2 This rise in conductance is clearly seen for Vig values between 1 and 2 V and Vpg values between 5 and 2 V This may result from the possible existence of puddles of electrons and holes near the charge neutrality points of
124. l was mainly the ability to repel adsorbates from its surface a phenomena discussed in Chapter 2 and it was thought that the nickel single layer graphite system would find a use as a liner for the inside of ultra high vacuum chambers Zero and one dimensional allotropes of carbon were discovered in the ensuing two decades First were Buckminster Fullerenes discovered in 1984 by Richard Smalley and coworkers 3 Fullerenes are a ball of carbon atoms and can contain a few 20 to many gt 1000 carbon atoms with C60 being the first and most common in experiment Carbon nanotubes are a one dimensional wire of carbon atoms and were discovered by Ijima in the early 1990 s 4 Carbon nanotubes are still a very active area of research in physics chemistry biology and engineering The common feature to graphite fullerenes and nanotubes is the hexagonal arrangement of carbon atoms From a single sheet of hexagonal carbon atoms all three of these allotropes can be obtained the sheet can be stacked to form graphite rolled into a tube to form a nanotube or bent into a ball to form a fullerene It is only recently that the unique structural and electronic properties of a single layer of graphite called graphene have been widely appreciated The electrical properties of a single sheet of graphene 5 on an insulating substrate were first measured about 100 miles from the place where graphite was discovered in Manchester England and have since led
125. lectrode conductivity Then using conventional lift off techniques the resist is removed and the device electrodes 18 20 are formed on the graphene With the device electrodes in place a blanket top gate oxide layer 24 in Fig 1A is to be provided over the electrodes and 112 the graphene to operate both as a gate oxide layer and as a layer of protection against the environment 052 As explained above in accordance with the invention prior to such oxide layer formation a functionalization layer is first formed over the graphene in a blanket fashion thereby also covering the device electrodes The functionalization layer provides chemically functional groups at the graphene surface to enable deposition of an oxide layer on the graphene surface Preferably the functionalization layer only non covalently bonds with the graphene surface while providing the chemically functional groups for enabling deposition of a material on the graphene surface 053 In one functionalization layer formation process in accordance with the invention the structure is cleaned e g with acetone and IPA and then inserted into an ALD reaction chamber e g a Cambridge Nano Tech Savannah Atomic Layer Deposition Tool Cambridge Nano Tech Inc www cambridgenanotech com An ALD process is then carried out to form a functionalization layer that is based on precursors for producing an upper oxide layer of Al203 054 In one example functionalization passivation pro
126. les the growth of a wide variety of top gate oxide layers including ferroelectric and ferromagnetic layers without altering the electronic properties of the undoped graphene The invention provides an electron beam rastering process to compensate for any extrinsic doping of a carbon surface that occurs during microfabrication processing The electron beam rastering process enables the production of carbon based structures such as graphene devices and circuits that are electrically robust 124 and exhibit reproducible performance characteristics It is recognized of course that those skilled in the art may make various modifications and additions to the devices circuits and microfabrication processes of the invention without departing from the spirit and scope of the present contribution to the art Accordingly it is to be understood that the protection sought to be afforded hereby should be deemed to extend to the subject matter of the claims and all equivalents thereof fairly within the scope of the invention B 8 Claims 092 We claim 1 A method for forming a material layer on a carbon structure comprising exposing a carbon surface of the carbon structure to at least one functionalization species that non covalently bonds to the carbon surface while providing chemically functional groups at the carbon surface and exposing the chemically functionalized carbon surface to a beam of electrons to compensate for extrinsic doping of the
127. ltage Vig The two gates allow independent control of charge densities in adjacent regions of the device see Fig 4 3 c inset In the bipolar regime the best fit F shows little density dependence and averages 0 38 equal to the average value deep in the unipolar regime and similar to results for the back gate only single layer 40 Sample D e7 0 3K 0 T 1 1K T 7 7 T T r x T T 30 uy a 9 60 30 Figure 4 4 a Differential resistance R left axis and conductivity o right axis of sample D as a function of Vig with Vga 0 at 0 3 K solid markers and at 1 1 K open markers b c Best fit Tw normalized to JNT calibrated Te and F to S Vsa data over Vsa lt 0 5 1 mV for Te 0 3 1 1 K Inset Sublinear dependence of S on Vsa is evident in data taken over a larger bias range Solid red curve is the two parameter best fit of Eq 4 1 over Veq lt 0 5 mV samples Al A2 and B Close to charge neutrality in either region though particularly in the region under the top gate S5 Vsq deviates from the form of Eq 4 1 data not shown This is presumably due to resistance fluctuation near charge neutrality probably due mostly to mobile traps in the AlgO3 insulator beneath the top gate 41 4 5 Shot noise in a multi layer device Measurements at 0 3 K and at 1 1 K for sample D of dimensions 1 8 1 0 um are shown in Fig 4 4 A 3 nm step height between SiO2 and carbon surfaces me
128. lustrated new physics that can be observed in systems confined to two dimensions 6 Since graphene is an ultra 2D system it is only one atom thick it is natural to ask what the quantum Hall effect looks like in this system The underlying band structure of graphene produces quantum Hall conductance values different from conventional semiconducting 2D materials 7 The low energy Hamiltonian for graphene is equivalent to that of massless Dirac fermions 8 In the presence of a magnetic field the Hamiltonian is altered using a Peirels substitution Figure 1 2 Electronic band structure of graphene obtained using a tight binding approxi mation for nearest neighbor hopping only For small values of wavevector k around the K and K points the energy E is linear in k i p p eA resulting in gt up p eA oy r Ey r 1 9 where vp is the Fermi velocity vr 10 m o are the Pauli matrices and Y F is a two component wavefuntion Working in the Landau gauge A ByZ the first component of the wavefunction 7 can be eliminated to give Up p gt 2eBype e B y heB w2 7 E pa F 1 10 This equation can be solved to find the eigen energies of the Landau levels LL En 4 2ehv2 n B 1 11 for n 0 1 2 Equation 1 11 can be compared to the dispersion obtained for conventional 2D materials 6 where En we n 1 2 The first difference is that in Eq 1 11 there is a L
129. me gapped Introducing con finement in one more dimension produces on a few allowed perpendicular wave vectors that cut through the Dirac cones resulting in the band gap in the constriction lower left inset of Fig 1 5 determine if there is a gap and the size of the separation in energy of the valence and conduction bands 1 A graphene nanoribbon transistor schematic is shown in Fig 1 5 The ability to control the gap from a top down approach i e etching away 2D graphene is a distinct advantage over carbon nanotubes where semiconducting and metallic tubes can be grown but in unpredictable way This top down method requires precise control at the atomic level over the width and edge termination of the nanoribbon Nanoribbons have been created synthetically 19 20 and by oxygen plasma etching 21 22 however the precise control of the edge termination remains an experimental challenge 1 6 Minimum conductivity in graphene In 2D semiconductors the conductivity is related to the density of electronic states 14 o e7 Er D 1 13 Exactly at the K and K points the density of states vanishes When the Fermi level is at these points called the Dirac points Eq 1 13 expected to be zero However a 10 quantum treatment results in a finite conductivity at the Dirac point 23 24 a result of the underlying inability to localize Dirac electrons in 2D For a clean system of graphene the expected minimum conductivity is 4 7
130. med under the third top gate electrode 39 producing an n p n arrangement for e g a transistor device The applied top gate bias voltages are to be understood to include a consideration of device 105 capacitances as in Figs 2B 2C 033 Note in this configuration that no device electrode is disposed under the third top gate electrode 39 The invention does not require that each and every top gate be paired with a corresponding device electrode For the graphene device 70 of Fig 4A if there is no need to make electrical contact to the third graphene region 43 then no device electrode need be provided at that region But with local top gating of all three regions the polarity of the two p n junctions 51 53 of the device can be reversed and one or both of the p n junctions can be eliminated 034 Referring to Fig 4B such control of the p n junctions can reconfigure the transistor device 70 of Fig 4A to a diode or other single junction device 72 as in Fig 4B Here the first top gate electrode 35 is biased with an appropriate positive voltage 66 and second and third top gate electrodes 37 39 are biased with appropriate negative voltage 68 69 With this top gate biasing an n type graphene region 40 is formed under the first top gate electrode 35 and two p type graphene regions 42 43 are formed under the second and third top gate electrodes 37 39 resulting in a single p n junction 45 under the three top gates that can be employed in
131. n above The functionalization layer was then stabilized by a 5 cycle ALD process of H2O and TMA at room temperature also in the manner given above An oxide layer of Al203 was then formed over the stabilized functionalization layer by 300 ALD cycles of pulsed H20 TMA at a temperature of about 225C yielding an oxide thickness of about 30 nm To complete the device a local top gate was formed as in Fig 1A by electron beam lithography and lift off with layers of titanium and gold of 5 nm and 40 nm in thickness respectively The top gate was located over one of the device electrodes just as in Fig 1A 076 The completed device was cooled in a 3He refrigerator and characterized at tem peratures of 250 mK and 4 2 K Differential resistance R dV dI where I is the current and V the source drain voltage was measured by standard lock in techniques with a current bias of 1 nArms at 95 Hz for T 250 mK 4 2K The voltage across the two device electrodes contacting the graphene layer was measured in a four wire configuration eliminating series resistance of the cryostat lines but not contact resistance Contact resistance was evidently low 1k and no background was subtracted from the data 077 A measurement of the differential resistance R as a function of back gate voltage VBG and top gate voltage VTG at magnetic field B 0 is provided in the plot of Fig 9A This plot demonstrated independent control of carrier type and density in the two
132. n device electrodes 27 The device of claim 18 wherein the first and second graphene regions form a single p n junction with one p type region adjacent to one n type region 28 The device of claim 18 wherein the graphene layer includes a plurality of p n junctions 29 The device of claim 18 further comprising a third device electrode connected to a third region of the graphene layer 30 The device of claim 18 further comprising at least three device electrodes connected to corresponding regions of the graphene layer 127 31 The device of claim 18 further comprising a plurality of top gate electrodes disposed on the dielectric layer over corresponding device electrodes 32 The device of claim 18 further comprising a third device electrode connected to a third region of the graphene layer and a second top gate disposed on the dielectric layer over a second one of the device electrodes B 9 Figures 128 1 1 11 JF 26 STIT 129 Ere 2B oe a 42 Pap wA le Veg lt O 5 Vag POF Ae Crp Vau gt O 3 Ve lt O G2 Vee 130 131 132 OTN eee ee WNT Des WIFI ty vi NB P Z tem LET TN Xn 133 Ere 5A SO Vear i Vie 7 nz 134 isi o on oc g e7h 5 0 5 Backgate voltage V after functionalized HfO2
133. nd having device electrodes formed on the graphene if desired in the manner described above is cleaned e g with acetone and IPA and the substrate is inserted into an ALD reaction chamber The chamber is pumped down to a suitable pressure e g about 0 3 torr A number of ALD cycles e g 50 cycles are then carried out at e g room temperature to form a function alization layer by the following process A 100 torr dose of NO2 gas is first introduced into the chamber for about 0 5 seconds and then pumped out Following a 10 second purge un der continuous flow of 20 sccm of N2 a 1 torr dose of tetrakis dimethylamido hafnium IV TDH vapor is pulsed into the chamber The chamber is then purged for e g about 5 minutes before beginning the next cycle The resulting functionalization layer is then capped in the manner described above to prevent desorption by performing 5 cycles of 1 torr pulses of H2O and 1 5 torr pulses of TDH deposited at room temperature 060 With this step a stable functionalization layer is formed on the graphene layer and is ready for formation of a top gate oxide layer Here e g a layer of HfO2 can be directly formed on the functionalization layer in the ALD chamber with the TDH precursor The 115 layer of HfO2 can be deposited with a selected number of cycles each employing a 1 torr pulse of H2O vapor and a 1 5 torr pulse of TDH vapor under continuous flow of N2 and with 20 seconds intervals between the
134. nelson I V Grigorieva S V Dubonos and A A Firsov Two dimensional gas of massless Dirac fermions in graphene Nature 438 197 2005 Y Zhang Y W Tan H L Stormer and P Kim Experimental observation of the quantum Hall effect and Berry s phase in graphene Nature 438 201 2005 V P Gusynin and S G Sharapov Unconventional integer quantum Hall effect in graphene Phys Rev Lett 95 146801 2005 N M R Peres F Ginea A H Castro Neto Electronic Properties of Disordered Two Dimensional Carbon Phys Rev B 73 125411 2006 K S Novoselov E McCann S V Morozov V I Falko M I Katsnelson U Zeitler D Jiang F Schedin and A K Geim Unconventional quantum Hall effect and Berry s Phase of 2n in bilayer graphene Nature Physics 2 177 2006 C W J Beenakker and H van Houten Quantum transport in semiconductor nanos tructures Solid State Phys 44 1 1991 O Klein Die reexion von elektronen an einem potentialsprung nach der relativistis chen dynamik von Dirac Z Phys 53 157 1929 V V Cheianov and V I Falko Selective transmission of Dirac electrons and ballistic magnetoresistance of n p junctions in graphene Phys Rev B 74 041403 R 2006 M I Katsnelson K S Novoselov and A K Geim Chiral tunnelling and the Klein paradox in graphene Nature Phys 2 620 2006 K Nakada M Fujita G Dresselhaus and M S Dresselhaus Edge state in graphene
135. net has been modified to accomodate the NOg lecture bottle 2 4 Deposition of the functionalization layer The surface of graphene is catalytically unsuitable for the formation of oxide using precursors TMA and water Before deposition of a top gate oxide the surface of graphene must be pretreated with a functionalization layer FL that ideally would accomplish three functions the FL should not affect the unique electronic properties of graphene it should chemically dope the graphene and should leave behind a surface that is catalytically suitable 18 for subsequent oxide growth via ALD To this end a FL comprised of successive pulses of NO g and TMA g are deposited at room temperature 30 C on the entire chip containing a graphene sheet with electrical contacts Before the chip is placed in the reaction chamber the NOs and TMA lines are attached to the Parker solenoid valves with a stainless steel VCR gasket The lines are then evacuated by running the recipe Purging the Lines Table 2 1 repeating the two step process 10 times The pressure in each line should fall to the chamber pressure within a few pulses Table 2 1 Purging the Lines Line Pulse Time sec Pump Time sec NOg 0 1 10 TMA 0 1 10 First the chip is placed in the reaction chamber at 160 C Once the chip is in the cham ber the heaters to the chamber are turned off and allowed it to cool to room temperature This should take about 4 h
136. ng multiple top gates in three different charge carrier arrangements in accordance with the invention 011 Figs 4A 4B are schematic side views of a further example graphene p n junction device provided by the invention having multiple top gates and multiple p n junctions in two different charge carrier arrangements in accordance with the invention 012 Figs 4C 4D are schematic side views of a further example graphene p n junction device provided by the invention having a single top gate and multiple p n junctions in two different charge carrier arrangements in accordance with the invention 013 Figs 5A 5B are schematic top views of a p n junction circuit arrangement pro vided by the invention in two different wiring configurations in accordance with the inven tion 014 Fig 6 is a schematic representation of molecular species forming functionalization 100 and dielectric layers on a graphene layer in accordance with the invention 015 Fig 7 is a schematic side view of an extrinsically undoped carbon nanotube includ ing functionalization dielectric and gate material layers in accordance with the invention 016 Figs 8A 8C are plots of differential conductance as a function of voltage of a carbon nanotube in a pristine state after functionalization with HfO2 and after electron beam exposure in accordance with the invention respectively 017 Figs 9A 9D are plots of resistance and current as a function of voltage for
137. nonconvalent functionalization layer is first provided on the surface of the graphene layer in a manner that provides functional species that can react with deposition precursors to form a blanket coating of a selected oxide Specifically functionalization layer is provided to impart a catalytically suitable surface for growth of oxides such as high k dielectrics via vapor processes such as ALD The functionalization layer also passivates the graphene surface such that an oxide formed on the functionalization layer does not impact the electronic properties of the graphene 045 The functionalization layer is compatible with a wide range of oxide type and deposition methods For ALD the functionalization layer allows for the deposition of e g Al203 HfO2 and ZnO all of which are commonly employed as high k dielectric layers The functionalization layer can also be employed for carrying out physical vapor deposition and chemical vapor deposition processes to form blanket oxide layers of e g silicon dioxide titanium oxide or ferroelectric materials like lead zirconate titanate PZT With the functionalization layer in place on the graphene prior to the dielectric formation the dielectric does not extrinsically dope the graphene or otherwise impact the electronic properties of the graphene layer 046 The functionalization layer and blanket oxide layer are formed in accordance with the invention on a graphene layer once such is provided in pla
138. ns by pressing c on the key board Fig 18 shows the recommended exposure conditions see page 43 of the manual for an explanation of all the fields For the Exposure Condition Theta Correction you need to type in the work theta to use the file called theta used to perform the Theta Correction e Second press I on the keyboard to insert a CON file into the Schedule List Under No Condition enter the CON file name For Position Shift enter the amount in mm that you want to shift the drawing from the coordinates you entered in Job 1 If you want to write the drawing exactly where you positioned it in Job 1 enter 0 0 for the x and y position shifts The position shifts become useful when you are doing 153 SCHEDULE ENT A Y lhomejusersicaduserelioninuser SeumyWeb0121 0075mm 60080 dots Exposure _ f a Conditions Schedule File Name Schedule List Command Explanation Figure C 17 The home screen of Job 3 Exposure IELD Correction COARSE oa Cc OFF theta NORMAL OFF FC PO0S OFF OFF OFF x mm DY mm Figure C 18 Enter the exposure conditions here a dose test and you want to make a matrix of dose the best way to make a matrix is by typing x and using the Matrix Schedule command Dose shift allows you to enter the dose in psec per dot You can calculate this using Job 5 and can enter the value 154 SCHEDULE lt NONAME FIELD Correction COARSE Figure C 19 Display after Field C
139. nsity both in the data presented in this paper and elsewhere 40 74 45 The overall behavior of the conductance is in good qualitative agreement with theoretical results 75 Table 5 1 Measured two terminal graphene devices Sample Layers Inferred L W wm s Eft Al Monolayer 1 3 1 8 07 17 A2 Monolayer 0 4 2 0 0 2 0 2 B1 Bilayer 2 5 1 0 2 5 0 8 B2 Bilayer 0 3 1 8 0 2 0 3 C Monolayer Asymmetric 0 9 0 9 In Ref 75 the positions of conductance extrema on the distorted plateaus were found to align with the incompressible densities where the centers of quantized plateaus occur in multiterminal devices In particular it was predicted that in short samples lt 1 the conductance minima are centered around the incompressible densities On the other hand for narrow samples gt 1 the maxima of the conductance are expected to occur at the incompressible densities Here we demonstrate that this relation can be used to distinguish monolayer and bilayer graphene devices even when the distortions of the plateaus are strong We find that the maxima or the minima line up with incompressible densities precisely in the way expected for the monolayer and bilayer graphene 46 The correlation between the maxima minima and incompressible densities is unam biguous it is supported by all measurements presented in the paper We analyze data for several rectangular two terminal samples as well as for one
140. nstrating that the CNP does not change over the B range explored b Sz2 Vig A drop in resistance of 0 3 0 5kQ is observed at the transition from p p regime to p n regime red dashed line indicating that an additional conduction channel has been introduced at the p n interface This resistance drop occurs for the entire B field range lower inset c Rey Vig Hall resistance measurement where all the contacts are under the top gate reveals curves that are antisymmetric with respect to the CNP In contrast Szy d has larger resistance on the p n side of the CNP than Rey consistent with an additional conduction channel present at the p n interface This additional amount is quantified in e where a plot of S Rzy shows its largest value on the bipolar regime for all B fields lower inset Measurements of Sp2 Vig for B between 2T Fig 6 2 b at Vig 20V produce resis tance traces that are different from R and longitudinal measurements of previous graphene PNJ Here as the PNJ is form there is a marked decrease in resistance of 0 3kQ produc ing a resistance curve that is lower on the p n side of the CNP This decrease in resistance happens even at B 0T The opposite effect is observed in PNJ where carriers approach the junction at mostly normal incidence creating an increase in resistance 40 47 in the bipolar regime The inset of Fig 6 2 b indicates that this drop in resistance persists throughout the entire low
141. nt in one or two dimensions produces nanoribbons or quantum dots Typically such structures are on the order of 5 to 50 nanometers and have been fabricated either by electron beam lithography and reactive ion etching 21 22 92 99 by chemical derivation including cutting of carbon nanotubes 19 20 100 While both methods are suitable to produce devices near the atomic limit they also have shortcomings Reactive ion etching typically involves oxygen plasma which tends to underetch the resist masks randomly creating very disordered edges Chemical derivation methods are limited in that they result in randomly shaped and distributed flakes and devices It has further been proposed to etch graphene at the nanoscale with a focused electron beam 93 This method however requires suspending graphene on specific trans mission electron microscope grids making it difficult to perform electrical measurements Helium Ion Microscopy HeIM has recently been introduced as an ultra high resolution imaging technology for nanostructures and materials 90 91 101 In this work we use a helium ion microscope Orion Carl Zeiss SMT as a tool to modify properties of graphene devices in a controlled manner The HeIM is particularly well suited for this purpose because it produces a high brightness low energy spread sub nanometer size beam The microscope benefits from Hes ultra short de Broglie wavelength which is approximately 100 times smaller than
142. ntum point contacts c f Ref 88 Measurements of these four quantities are presented in Fig 6 2 6 3 Low magnetic field properties of transport along p n junctions Measurements of Rrx as a function of Vig for B between 2T Fig 6 2 a at Vig 20V reveal curves commonly observed in unipolar graphene samples 5 At Vig 20V the entire device consists of p type carriers By identifying the peak in Rzz a voltage Vig DE 3 5V is given to the value of Vig at which the CNP occurs indicated as a red dashed line in Figs 6 2 a e for Region 1 For Vig lt VigONP the entire graphene sheet has a uniform carrier type but not necessarily density and is in the unipolar p p regime For Vig gt Vig NP a PNJ forms along contacts A B and the device is in the bipolar regime A 2D plot of Rix Vig B inset of Fig 6 2 a shows that while the resistance increases as a function of B the value of the CNP does not change 67 Rxx kQ Figure 6 2 Measurements of the four quantities Rrr S22 Rey and Szy as a function of Vig black traces offset intentional for B between 2T in 0 5T steps at a back gate voltage of 20V The measurement scheme is shown in the upper right inset black contacts are the current leads and grey are the voltage leads in each panel a Rer Vig The red dashed line locates the resistance maximum at all B fields and indicates the CNP for Region 1 Lower inset Rza Vig B demo
143. nuous film 38 In fact a similar phenomena was observed a year prior in carbon nanotubes 39 and it was found that a functionalization layer FL was needed to pretreat the surface of the nanotube before it was suitable for ALD growth of oxide The Marcus Lab has one of the first ALD machines created by a former Marcus Lab postdoc Douwe Monsma and former Prof Gordon Lab graduate student Jill Becker The Cambridge Nanotech www cambridgenanotech com Savannah 100 is shown in Fig 2 2 and the details of the system can be found at the company website Briefly the system consists the following components a gas cabinet that houses the ALD precursors and the NO used in the functionalization layer a reaction chamber where the precursor gases interact with the sample and a control computer Not shown is the wet pump Leybold Trivac 016B behind the wall The length of KF 25 bellow connecting the reaction chamber to the pump is 3 The base pressure of this setup is 0 4 torr with 20 sccm of N flowing into the reaction chamber 2 3 NO and gas cabinet modification A similar pretreatment is necessary for graphene and an approach similar to that for nanotubes 39 was undertaken The main ingredient of the FL is NOg A small lecture bottle of liquid dinitrogen tetroxide Fig 2 2 was purchased from Matheson TriGas Dini trogen tetroxide is a liquid that evaporates into NO and has a vapor pressure at room 15 T Reaction Chamber D
144. nvention provides a functionalization layer 25 that is preferably included on the graphene to fully enable formation of the gate oxide layer without impacting the electrical properties of the graphene Electrical connections 26 28 30 32 are provided to the back electrode 14 device electrodes 18 20 and local top gate 22 respectively 020 Fig 1B is a schematic cross sectional view of a further example graphene p n junction device 33 provided by the invention that is equivalent to the first example in Fig 1A This device similarly includes a layer of graphene 12 and a backgate electrode 14 that can be electrically insulated from the graphene 12 by an insulating layer 16 and device electrodes 18 20 that directly contact the graphene A local top gate 35 is here provided above the right device electrode 20 The top gate is electrically insulated from the graphene 12 and the device electrodes 18 20 by a gate oxide layer 24 and a functionalization layer 25 described in detail below Electrical connections 26 28 30 32 are provided to the back electrode 14 device electrodes 18 20 and local top gate 22 respectively 021 With these graphene arrangements the invention provides a temporally controllable graphene p n junction device in the manner shown in Figs 2A 2C In Fig 2A the graphene p n junction device 33 is represented highly schematically to focus on the voltage biasing for p n junction device operation With this arrangement a backga
145. ny shape can be reduced to that of an effective rectangle via a conformal mapping 78 79 80 which depends on the sample shape but not on the conductivity tensor the rectangular geometry is universal for two terminal conductance Thus the model of a conducting rectangle with an unspecified aspect ratio is suitable for describing systems in which current pattern is not precisely known 5 3 Sample fabrication and measurement Graphene devices were fabricated by mechanically exfoliating highly oriented pyrolytic graphite 5 onto a n Si wafer capped with 300 nm of SiOz Potential single and bilayer graphene flakes were identified by optical microscopy Source and drain contacts defined by electron beam lithography were deposited by thermally evaporating 5 40 nm of Ti Au The aspect ratio of each sample was measured using either optical or scanning electron microscopy after transport measurements were performed Devices were measured in a He refrigerator allowing dc transport measurements in a 48 10 O N Vol VAS N 00 g e h 8 TSA VA j 10 6 2 02 10 Filling factor v Figure 5 1 Theoretical 75 two terminal QH conductance g as a function of filling factor v for a single layer graphene b bilayer graphene and c gapped bilayer graphene for effective aspect ratios L W 2 black and 0 5 red Finite longitudinal conductivity due to the states in the middle of each Landau level di
146. of at least one of the adjacent regions As a result an arbitrary number of p n junctions including a single p n junction can be produced within a single graphene layer in accordance with the invention Each distinct charge carrier region produced in the graphene layer with a corresponding local top gate can also be individually contacted under the top gate for device biasing and operational device control 041 The invention provides specific processes for fabricating the graphene devices cir cuits and systems of the invention It is recognized in accordance with the invention that for any graphene based technology to succeed the graphene behavior must meet the demands of modern electronics including stability and reproducibility In general stable electronics require that the properties of a device remain static over time But graphene is known to interact with water in even only relatively humid environments causing electronic charge hole doping of an exposed graphene region The resulting hole charge carrier concentra tion in the graphene is related to the amount of water in the environment and therefore changes as the ambient humidity changes In pristine graphene i e graphene with no ex ternal doping there is no excess electron or hole charge carrier concentration The excess 108 charge carrier concentration in graphene caused by extrinsic doping due to environmental conditions gives rise to reduced mobility in a graphene device
147. on as g min 1 v2 x e h B 1 085 This relation suggests that the edge states common to both regions propagate from source to drain while the remaining 1 2 edge states in the region of highest absolute filling factor circulate internally within that region and do not contribute to the conductance This picture is consistent with known results on conventional 2D electron gas systems with inhomogeneous electron density 122 086 Recent theory addresses QH transport for filling factors with opposite sign in regions 1 and 2 n p and p n In this case counter circulating edge states in the two regions travel in the same direction along the p n interface as shown in Fig 10F which presumably facilitates mode mixing between parallel traveling edge states For the case of complete mode mixing that is when current entering the junction region becomes uniformly distributed among the v v2 parallel traveling modes quantized plateaus are expected 18 at values given by the expression v v2 2 h B 2 Ae Ba 087 A table of the conductance plateau values given by Expressions 1 and 2 is shown in Fig 10E Plateau values at le h for v 1 v 2 and at 3 2 e h for v 6 and n 2 are observed in experiment Notably the 3 2 e h plateau suggests uniform mixing among four edge stages three from region 1 and one from region 2 All observed conductance plateaus are also seen at T 4K and for B in the range 4 to 8 T
148. on with an optical microscope allows potential single layer regions of graphene to be identified by a characteristic coloration that arises from thin film 24 interference These micron scale regions are contacted with thermally evaporated Ti Au 5 40 nm and patterned using electron beam lithography Next a 30 nm layer of oxide is deposited atop the entire substrate As illustrated Fig 3 1 b the oxide consists of two parts a non convalent functionalization layer NCFL and AlgO3 This deposition technique is based on a recipe successfully applied to carbon nanotubes 39 The NCFL serves two purposes One is to create a non interacting layer between the graphene and the AlgO3 and the other is to obtain a layer that is catalytically suitable for the formation of Al2O3 by atomic layer deposition ALD The NCFL is synthesized by 50 pulsed cycles of NO and trimethylaluminum TMA at room temperature inside an ALD reactor Next 5 cycles of H2O TMA are applied at room temperature to prevent desorption of the NCFL Finally AlgO3 is grown at 225 C with 300 H2O TMA ALD cycles To complete the device a second step of electron beam lithography defines a local top gate 5 40 nm Ti Au covering a region of the device that includes one of the metallic contacts 3 3 Measurement setup A completed device similar in design to that shown in the optical image in Fig 3 1 a was cooled in a He refrigerator and characterized at temperatures T of 25
149. or is observed contrary to theoretical expectations Further an independence on device geometry is also observed The role of disorder on the measured Fano factor is discussed and comparison to recent theory for disordered graphene is made The effect of a two terminal geometry where the device aspect ratio is different from unity is measured experimentally and analyzed theoretically A method for extracting layer number from the conductance extrema is proposed A method for a conformal mapping of a device with asymmetric contacts to a rectangle is demonstrated Finally possible origins of discrepancies between theory and experiment are discussed Transport along p n junctions in graphene is reported Enhanced transport along the junction is observed and attributed to states that exist at the p n interface A correspon dence between the observed phenomena at low field and in the quantum Hall regime is iii observed An electric field perpendicular to the junction is found to reduce the enhanced conductance at the p n junction A corollary between the p n interface states and snake states in an inhomogeneous magnetic field is proposed and its relationship to the minimum conductivity in graphene is discussed A final pair of experiments demonstrate how a helium ion microscope can be used to reduce the dimensionality of graphene one further producing graphene nanoribbons The effect of etching on transport and doping level of the graphen
150. orrection is complete here Try to keep the dose time above 5 usec per dot to avoid exposure areas going below this can cause a burnout of some electronics that control the beam blanking Cmem No allows you to automatically change beam current for different lines in the schedule list If you would like the system to perform a field correction at any time enter a line of K in the file name with nothing else note if you change the beam current it will automatically perform a Field and Beam Position correction This allows for a field correction to be performed before continuing the write see page 84 of the manual for more To exit out of Insert Schedule mode press Esc e Perform a field correction by type F press f on the keyboard Before doing this write down the z position of the stage where your sample is focused The stage will drive to perform a field correction You will be prompted with the query Check Con trast and Brightness Exe Y N Enter Y The system will perform a field correction Once its done enter N if you don t want to repeat the field correction Hint if the values of Width ATTX and Y are greater than 10 percent away from 8000 you might want to repeat the field correction see Fig 19 e Manually set the z coordinate back to the correct value for your sample 155 H I C Pherne pseraicaduser ebcrvaniserJrrreyWcbOl21 A arera So Figure C 20 Two windows in the Exposure Display shown with
151. ou pressed LOAD for Marker A otherwise the system won t accept the LOAD button The system will then perform another field correction and move back to Marker A to repeat the process This continues until the alignment is so good that you no longer move the Track Ball any more to align the markers with the cross hairs If you move the ball AT ALL the system will repeat the process until you press LOAD without moving the Track Ball at all If at any time you want to stop the process press and hold the SCAN SPEED button for 3 seconds e Once the Registration is complete the program will continue and write the CON file you create in Job 1 e Once the Exposure is complete the stage will return the the FC 157 To unload the sample you should Make the the sample is in the Exchange EX Position and the the Exchange Position light in on Close the Isolation Valve e Make sure the loadlock is still at adequate transfer pressure by the green EVAC light is on and not flashing If it is not press the Vacuum Toggle Button to EVAC and wait for the green light to stop flashing Switch the Door Control Button to Open Push transfer rod in towards the sample Once it is all the way extended into the chamber screw in the rod to the transfer plate The upper white line in Fig 9 should disappear when the screw in all the way in Do not torque the plate at all Retract the transfer rod and sample plate completely Switch the
152. ours This step is like an anneal in an N background Water tapped under the FL and graphene at room temperature expands as the temperature is increased for the oxide deposition and causes bubbling of the graphene device Once the temperature of the chamber reaches 30 C the deposition of the FL can begin The FL is deposited repeating the Functionalization Recipe in Table 2 2 nine times Table 2 2 Functionalization Recipe Line Pulse Time sec Pump Time sec NO2 0 3 7 TMA 0 1 5 TMA 0 1 5 TMA 0 1 120 19 NO Pulse 10 TMA Pulses g 8 S 7 Bg L 6 5 dp 18 20 22 24 26 28 30 nM 4 Time sec p Q A TMA Pulses 0 10 20 30 40 50 Time sec Figure 2 5 Pulse heights for one step of the Functionalization Recipe A large NO2 pulse is followed by three smaller pulses of TMA The inset shows a zoom in of the three TMA pulses It is important to perform the extra TMA pulses There is a critical pressure magnitude of the NO pulse and a critical ratio between the NO2 and TMA If the NO pulse is too small then the functionaliztion layer will not fully cover the graphene sheet and the device will leak If the ratio is not correct the graphene sheet will be doped and the mobility will be very poor 100 cm V s72 A typical pulse sequence is shown in Fig 2 4 2 5 Deposition of Al O3 After performing the nine repetitions of the Functionalization recipe the NOg line from the 1 solenoid v
153. own in Fig 13 will open We actually start with Job 2 instead of the logical Job 1 Highlight Job 2 and click EXEC In Job 2 you can set the Chip size the same as the write field size on the Raith which sets the size of the write field that the system can expose without moving the stage Use small Chip sizes for high resolution lithography In 148 Figure C 12 In the Ref position use the Au island to set focus and stigmation addition you can set the Dot Map equivalent to the step size on the Raith which sets the number of points that the Chip size is broken up into If you set the Chip size to 300 and the Dot Map to 20000 your pattern will be exposed in dots that are separated by 15nm See Fig 14 for a screen shot of the Job 2 menu Once you ve highlighted the values you want to use click SAVE In Job 1 you will take your CEL file created in in the dxf to cel conversion and turn 149 v ELC JOB MENU Pattern Data Creation Chip Size Modification Exposure Maintenance Dose Timer Caicuiation v PARAMETER MODIFICATION CHIP SIZE DOTMAP 75 um 20000 dot 150 um 60000 dot 240000 dot 600 um FILER Figure C 14 In Job 2 you can set the Chip size and Dot Map for your write in into a file that can be used to do the actual exposure By the end you should have a CON file that has all the positions and geometries of the write you are about to perform e Go to the Home menu of the EL
154. pe region 43 As stated just above each of the three regions is individually contacted by device electrodes 18 20 23 that enable full control of the device before during and after the polarity reversal 037 This control of p n junction polarity and the formation and elimination of p n junctions can be extended to any arbitrary number of junctions and to both device and circuit arrangements For example referring now to Fig 5A there is schematically shown an example four terminal graphene circuit 80 in accordance with the invention To clarify this arrangement the circuit is represented in a top down view with the top gates not shown Each of the three identified p type graphene regions 82 84 86 and each of the three identified n type regions 88 90 92 have a top gate that is physically located over the region and is biased with an appropriate polarity voltage VTG p and VTG n in the manner described above to produce the indicated charge carrier type in that region Each of the regions further is connected to one of four device contacts 94 96 98 100 An arrangement of p type and n type regions such as this can only be achieved with the local top gating provided by the invention 038 This graphene circuit 80 enables reconfigurable wiring by exploiting so called snake states that exist at a p n interface Specifically enhanced electrical conduction at each p n interface effectively forms a one dimensional wire that is physically locate
155. phene has not yet been reported This chapter presents an experimental study of shot noise in graphene at low tempera tures and zero magnetic field Data for five devices including a locally gated p n junction are presented For three globally gated single layer samples we find F 0 35 0 37 in both electron and hole doping regions with essentially no dependence on electronic sheet density ns in the range ns lt 101 cm Similar values are obtained for a locally gated single layer p n junction in both unipolar n n or p p and bipolar p n or n p regimes In a multi layer sample the observed F evolves from 0 33 at the charge neutrality point to 35 Spectrum Figure 4 1 a Differential resistance R of sample A1 as a function of back gate voltage Vbg at electron temperature Te 0 3 K perpendicular field B 0 and source drain voltage Vsa 0 b Differential two terminal conductance g Vsq 0 as a function of By and Vpg in the quantum Hall regime after subtracting a quadratic fit at each B Lines of constant filling factors 6 10 14 and 18 dashed lines indicate a single layer sample c Equivalent circuit near 1 5 MHz of the system measuring current noise using cross correlation of two channels 66 Current bias J contains a 7 5 nArms 20 Hz part for lock in measurements and a controllable dc part generating the dc component of Vzq via the shunt resistance r 5 kQ False color scanning electron mic
156. posure We attribute this residual conductivity to contamination of the SiO2 surface with hydrocarbons 8 4 Conclusions and acknowledgements We demonstrated etching of graphene devices with a helium ion beam for the first time Suspended graphene has been etched conclusively with minimum feature sizes in the 10 nm range Graphene on SiO2 was etched with a lower dose compared to suspended graphene However these devices showed a residual conductivity attributed to contaminants on the 89 surface Helium ion etching can be considered an alternative nanofabrication method for suspended graphene devices and if contamination issues can be solved graphene on SiO2 substrates MCL gratefully acknowledges the support of the Alexander von Humboldt foundation through a Feodor Lynen Research Fellowship The authors thank S Nakaharai for fruitful discussions regarding the process 90 Appendix A Graphene Deposition by Mechanical Exfoliation This section describes the art of graphene deposition This method has changed sub stantially since I started trying to do this in 2005 compare the method described here to the one used in the Supplementary Material of chapter 3 on p n junctions in the Quan tum Hall Regime The current method has been the most fruitful quantified by the number and area of the resulting graphene flakes but I m sure that the method could be further improved and honed The starting material is very important I ve
157. pted from Ref 39 Immediately following a cleaning with acetone and IPA the substrate is inserted into the atomic layer deposition ALD reaction chamber The chamber is pumped down to a pressure of 0 3 torr Next NCFL is deposited at room temperature using 50 cycles of the following process A 100 torr dose of NOg gas is first introduced into the chamber for 0 5 s and then pumped out Following a 7 s purge under continuous flow of 20 sccm of nitrogen gas N2 a 1 torr dose of trimethylaluminum TMA vapor is pulsed into the chamber The chamber is then purged for 2 min before beginning the next cycle Ellipsometry measurements on trial runs show that the NCFL thickness remains constant for up to 125 cycles indicating that NCFL growth is self limiting with only a single or few layers deposited on the graphene The AlgO3 is then grown by 305 ALD cycles consisting of a 1 torr pulse of H2O vapor and a 1 5 torr pulse of TMA vapor under continuous flow 31 of Ng and with 5 s intervals between pulses The first 5 cycles are performed at room temperature to prevent desorption of the NCFL The remaining cycles are continued after heating the chamber to 225 C With each H2O TMA cycle adding 1 A of Al2O3 the total oxide thickness is 30 nm Supporting Text Measurements of differential conductance g as a function of top gate voltage Vig and back gate voltage Vp similar to those shown in Fig 3 3A were performed at other tem peratures T an
158. pulses 056 A top gate oxide layer of e g Al203 in this example is then grown on the stabilized functionalization layer In one example process the ALD temperature is raised to about 225C and a selected number of cycles e g 300 cycles of a 1 torr pulse of H2O vapor followed by a 1 torr pulse of TMA vapor under continuous flow of N2 with 5 second intervals provided between pulses are carried out In this process each H2O TMA cycle adds about 1 Angstrom of A1203 to the layer A 300 cycle process thereby produces a total oxide thickness of about 30 nanometers Given the precision of the ALD formation process a wide range of oxide thicknesses can be obtained as desired Oxide layers as thin as about 10 nm and as thick as desired e g 100 nm or more given that there is no upper limit on the oxide thickness can be provided with this formation method The method is also quite flexible in temperature ALD growth can be carried out at temperatures as low as about 80C and as high as about 225C 057 Referring to Fig 6 with this oxide formation complete a layer of A1203 24 is pro vided on a functionalization layer 25 that blanket coats the graphene 12 and any graphene region device electrodes which are not shown here for clarity The functionalization layer forms a non interacting layer between the graphene and the top gate oxide layer thereby preserving the electronic properties of the underlying graphene and provides a surface that is c
159. r an arbitrary number of layers is not available for comparison to noise results in the multi layer sample D we compare only to existing theory for ballistic bi layer graphene 73 It predicts F 1 3 over a much narrower density range than for the single layer and abrupt features in F at finite density due to transmission resonances A noise theory beyond the bi layer ballistic regime may thus be necessary to explain the observed smooth decrease of F with increasing density in sample D We thank C H Lewenkopf L S Levitov and D A Abanin for useful discussions Research supported in part by the IBM Ph D Fellowship program L D C INDEX an NRI Center and Harvard NSEC 43 Chapter 5 Quantum Hall conductance of two terminal graphene devices J R Williams D A Abanin L DiCarlo L S Levitov C M Marcus School of Engineering and Applied Sciences Harvard University Cambridge Massachusetts 02138 USA t Department of Physics Massachusetts Institute of Technology Cambridge Massachusetts 02189 USA Department of Physics Harvard University Cambridge Massachusetts 02138 USA Measurement and theory of the two terminal conductance of monolayer and bilayer graphene in the quantum Hall regime are compared We examine features of conductance as a function of gate voltage that allow monolayer bilayer and gapped samples to be distinguished In particular we analyze the distortions of quantum Hall plateaus and the cond
160. rate of 20 nC cm resulting in a depth of 4 nm b AFM image used for the step profile The profile was taken along the upper part of the image indicated by the two black lines Figure 7 8 HeIM image of a high resolution Harvard University logo etched into multi layer graphene shows that all doses lead to a cut in the graphene layers However the combination of SEM and AFM images further reveals that for very high doses the underlying substrate can swell up by at least 50 nm from the effect of ion knock on damage to the underlying silicon The detailed AFM analysis for the graphene cut with the low dose rate of 20 nC cm for test lines resulted in a measured depth of 4 nm Fig 7 7 In principle the pattern generation system allows etching of any pattern in graphene 82 This is demonstrated in Fig 7 8 with a Harvard University logo etched into multi layer graphene with line widths well below 50 nm The overall dimensions of the logo are about 4 um x 5 pm 7 5 Conclusions We have successfully shown that it is possible to precisely cut etch graphene with 30kV helium ions and have shown results for the patterning of single and multiple layers of graphene In conjunction with a pattern generation system the helium ion microscope can be routinely used to pattern graphene This research may lead to graphene nanoscale electronic devices that take advantage of the semi conducting properties and physics of nanoscale shaped graphene 8
161. rences in the electrical conduction properties of CNTs and graphene arise solely from the differences in their geometric structure CNTs are solids in which the carbon atoms are arranged in a hexagonal lattice of a structure that is cylindrical and hollow This structure is long in one direction hundreds to thousands of nanometers and short and confined in the other two directions a few to tens of nanometers This confinement is key to the CNT electronic properties Depending on the diameter of the CNT that is how the CNT is rolled up the electronic properties are either semiconducting or metallic Exactly two thirds of all CNT made are semiconducting while the remaining third are metallic with the state of the art CNT production technology unable to reliably make CNT of one type or the other 004 Although graphene is also a structure that is formed out of hexagonal lattices of carbon atoms graphene is long in two directions and short in the other direction resembling a sheet of chicken wire This two dimensional structure in contrast to the CNT structure is always metallic The unusual band structure of single layer graphene makes graphene a 98 zero gap semiconductor with a linear i e photon like energy momentum relation near the points where valence and conduction bands meet That is a graphene sheet as formed is always a metallic conductor 005 Graphene has the ability to carry electric current with either of the two electronic
162. rograph of a three lead pattern defining two devices similar to Al and A2 Purple indicates single layer graphene and gold indicates metallic contacts 0 25 at ns 6 x 10 2 cm7 4 2 Methods Devices were fabricated by mechanical exfoliation of highly oriented pyrolytic graphite 5 Exfoliated sheets were deposited on a degenerately doped Si substrate capped with 300 nm of thermally grown SiO2 Regions identified by optical microscopy as potential single layer graphene were contacted with thermally evaporated Ti Au leads 5 40 nm patterned by electron beam lithography Additional steps in the fabrication of the p n junction device are detailed in Ref 40 Devices were measured in two He cryostats one allowing de lock 36 in transport measurements in fields B lt 8 T perpendicular to the graphene plane and another allowing simultaneous measurements of dc transport and noise 66 near 1 5 MHz but limited to B 0 4 3 Shot noise in single layer devices Differential resistance R dV q dI I is the current and V q is the source drain voltage of a wide short sample A1 W L 2 0 0 35 um is shown as a function of back gate voltage Vg at Viq 0 and B 0 in Fig 4 1 a While the width of the peak is consistent with Al being single layer graphene 9 10 more direct evidence is obtained from the QH signature shown in Fig 4 1 b The grayscale image shows differential conductance g 1 R as a function of Vig and B_
163. rom the semicircle law We take An 1 for n 0 1 and An 2 for other LLs consistent with previous observations 82 54 5 5 Bilayer samples The black curve in Fig 5 3 shows measured g Vpg for sample B1 s 2 5 at B 8T and T 4K This sample has two features indicating that it is a bilayer sample plateaus in conductance appearing near 4 8 12 and 16e h and a conductance maximum at the CNP whose relative size is much larger than those at higher LLs The conductance values at the plateaus v 4 here are lower than the expected 4 e h for a bilayer sample falling to 2 7 3 1 e h on the electron hole side of the CNP The peak value in conductance at v 0 Vig 0 5V is 5e h At higher filling factors the plateaus exhibit two different behaviors showing a flat plateau at v 8 and a plateau followed by a dip at v 12 The small dips align with the filling factors v 12 16 20 for 5T lt B lt 8T see inset of Fig 5 3 using a 7 2 x 101 cm7 V 1 and Vogset 0 5 V Theoretical g curves for aspect ratios Es 2 5 dashed blue curve and amp 0 8 solid red curve are shown in Fig 5 3 Theoretical g Vpg curves for these two aspect ratios are similar at high density but differ for v 0 the curve for 2 5 has a dip in conductance at the CNP while g 0 8 has a peak similar to the experimental curve The curve for Ent 0 8 also agrees better with experiment at higher densities
164. rovided over the functionalization layer and a coaxial gate electrode 158 is 117 provided at a selected point along the cylindrical wall surface of the carbon nanotube 068 The functionalization layer 154 is formed on the nanotube in the manner described above preferably with an ALD process that employs a precursor that is also used for forming the gate oxide layer 156 e g A1203 or HfO2 or other selected gate oxide material After the gate oxide layer is formed the carbon nanotube is electrically contacted at its ends to determine if the nanotube has been extrinsically doped by the functionalization and or oxide layers If so then the electron beam rastering process described above is carried out to compensate for the extrinsic doping and to render the nanotube with the characteristics of that of a pristine carbon nanotube 069 After such electron beam rastering of the nanotube a gate electrode can be formed on the nanotube either at a specific point or coaxially around the circumference of the nanotube The electron beam rastering of the gate oxide enables the production of a gated carbon nanotube that is not extrinsically doped by the environment or the layers deposited on the nanotube This demonstrates that the functionalization and oxide layer formation processes of the invention in conjunction with the electron beam compensation process of the invention can be applied to carbon based structures in general and is not limited to
165. rrier type and density in adjacent regions of a single atomic layer Transport measurements at zero perpendicular magnetic field B and in the quantum Hall QH regime demonstrate that the functionalized aluminum oxide Al203 separating the graphene from the top gate does not significantly dope the layer nor affect its low frequency transport properties We study the QH signature of the graphene p n junction finding new conductance plateaus at 1 and 3 2 e h consistent 23 A B a o en oc H 305 Ho A cycles TMA 50 cycles Region 2 Back Gate Vas Figure 3 1 a Optical micrograph of a device similar to the one measured Metallic contacts and top gate appear in orange and yellow respectively Darker regions below the contacts are thicker graphite from which the contacted single layer of graphene extends b Illustration of the oxide deposition process A non covalent functionalization layer is first deposited using NO and TMA 50 cycles and Al2O3 is then grown by atomic layer deposition using H20 TMA 305 cycles yielding 30 nm thickness c Schematic diagram of the device measured in this experiment with recent theory addressing equilibration of edge states at the p n interface 50 3 2 Device fabrication Graphene sheets are prepared via mechanical exfoliation using a method similar to that used in Ref 5 Graphite flakes are deposited on 300 nm of SiO2 on a degenerately doped Si substrate Inspecti
166. rstanding how carriers move through this environment is critical to having a clear picture of what the minimum conductivity should be in graphene 11 Chapter 2 Functionalization of and Atomic Layer Deposition on Graphene 2 1 Atomic Layer Deposition Atomic Layer Deposition ALD is a process by which metals and multi component oxides can be grown layer by layer In particular high quality high materials like AlgO3 and HfO can be grown via ALD A resurgence of interest in this method has occured in the last decade due to the need for high dielectrics in silicon based transistors For example Intel recently began using AlgO3 grown by ALD as the gate dielectric in their 45nm technology A great review of the ALD process and its applications can be found in Ref 37 While the creation of designer precursor chemicals and the understanding of the surface chemistry of these precursors are difficult the idea behind ALD is relatively simple First a substrate is placed in an evacuated chamber where the ALD growth will occur Then a fixed amount of a precursor gas Precursor 1 in Fig 2 1 a is pulsed into the ALD chamber This precursor chemically reacts with the substrate surface and binds to the surface For the reaction to occur only specific sites indicated by the triangular shapes in the substrate in Fig 2 1 a on the surface must be catalytically suitable for this reaction to occur if the precursor cannot find these sites the
167. s have led to the observation of novel conductance quantization in the QH regime 40 There p and n type carriers move in edge states in the same direction along the junction and achieve full mode mixing pro ducing new plateaus in the QH conductance in the bipolar regime 50 Aside from these locally gated devices PNJs play an important role in conduction at the charge neutrality point CNP of disordered graphene samples At the CNP the graphene sheet breaks up into an interconnected series of electron and hole puddles 33 a result of the underlying disorder in the sample In such samples the PNJs are randomly oriented with respect to the motion of the carrier Whereas previous studies 40 47 74 of locally gated graphene samples have only investigated transport in geometries where the majority of carriers ap proach the p n interface at normal incidence here we report on transport studies where the majority of transport happens parallel to the PNJ In this letter charge transport is studied in a locally gated graphene PNJ where the p n 64 Figure 6 1 a Scanning electron micrograph of a device similar to the one studied here Electrical contacts A F yellow to graphene purple allow for measurements of the quan tities Rex Sex Rzy and Szy as a function of Vig Vig and B The carrier type and density of Region 1 is controlled by both Vig and Vig while Region 2 is controlled on by Vig b Schematic of the device Contacts A and
168. s observed to remain nearly constant for ns lt 101 cm Over this density range the average F is 0 35 with standard deviation 0 01 The estimated error in the best fit F at each Vig setting is 0 002 comparable to the marker size and smaller than the variation in F near Vp 0 which we believe results from mesoscopic fluctuations of F Nearly identical noise results not shown were found for a similar sample B with dimensions 2 0 0 3 um and a QH signature consistent with a single layer Transport and noise data for a more square single layer sample A2 patterned on the same graphene sheet as Al with dimensions 1 8 1 3 um at Te 0 3 K solid circles and Te 1 1 K open circles are shown in Figs 4 2 c e At both temperatures the conductivity shows Omin 1 5 e h and gives 25 nm away from the charge neutrality point That these two values differ from those in sample A1 is particularly notable as samples Al and A2 were patterned on the same piece of graphene Results of fitting Eq 4 1 to S5 Vsa for sample A2 are shown in Figs 4 2 d and 4 2 e To allow for possible broadening of the quadratic to linear crossover by series resistance and or inelastic scattering we treat electron temperature as a second fit parameter along with F and compare the best fit value Tw with the Te obtained from Johnson noise Figure 4 2 d shows Tw tracking the calibrated Te at both temperatures Small deviations of Tw Te from unit
169. sample with asymmetric con tacts extracting an effective sample aspect ratio via conformal mapping Best fit values of the aspect ratio ft obtained by fitting the theory to the experimental data are compared to the measured sample aspect ratio s Agreement between data and theory is relatively good for the samples of smaller lengths and less good for the longer L 2 1 um samples We speculate on possible causes of these discrepancies including inhomogeneous contact resistance electron and hole puddles and contributions of transport along p n interfaces 5 2 Phenomenology of conductance in two terminal graphene devices Representative theoretical plots of two terminal conductance for monolayer bilayer and gapped bilayer graphene as a function of filling factor v are shown in Fig 5 1 For both monolayers and bilayers the absence of an energy gap between the conduction and valence bands gives rise to a zero energy Landau level LL 11 which can either increase or decrease the two terminal conductance around the charge neutrality point depending on the aspect ratio of the sample The eightfold degeneracy of the zero energy LL in bilayer graphene 67 enhances the size of this feature relative to monolayer graphene A gap in the spectrum of bilayer graphene opens when the on site energy in one layer differs from the on site energy in the other 67 This may result for instance from asym metric chemical doping 76 or electrosta
170. storts the plateaus into N shaped structures which are of opposite sign for lt 1 and gt 1 Local extrema of g at filling factors v 2 6 10 for single layers and at v 4 8 2 for bilayers are either all maxima gt 1 or all minima lt 1 For gapless monolayer and bilayer samples a b g v 0 is a maximum for lt 1 and minimum for gt 1 for the gapped bilayer c g vanishes at v 0 for all magnetic field B lt 8T perpendicular to the graphene plane Unless otherwise noted all measurements were taken at base temperature T 250mK Differential conductance g dI dV where I is the current and V the source drain voltage was measured using a 49 current bias I chosen to keep eV lt kgT and standard lock in technique at a frequency of 93 Hz All samples show B 0 characteristics of high quality single layer and bilayer graphene 9 10 a CNP positioned at back gate voltage Vi OV and a change in g exceeding 20 e7 h over the Vig range of 40 V 5 4 Monolayer samples Figure 2 a shows the two terminal conductance g Vbg for sample Al s 0 7 at B 8T black trace Plateaus are seen at v 2 near but not equal to 2e h with values of 2 3 2 7 e h on the electron hole side of the CNP At the CNP Vig 2 3V obtained from g at B 0 g departs from the quantized values dropping to a minimum of 1 4e h At higher densities the
171. te voltage VBG is applied to the backgate electrode 14 A device voltage VD is applied between the device electrodes 18 20 for device operation A top gate voltage VTG is applied to the local top gate 35 Depending on the relative top gate and backgate voltages two distinct graphene regions 40 42 are defined one being n type and the other being p type with a junction 45 at the border of the two regions 022 Referring to Fig 2B with the backgate voltage set as VBGj0 and the top gate voltage set as VTG 10 CTG CBG VBG where CTG and CBG are the capacitances associated with the top gate and the backgate respectively the graphene region 42 under the top gate 35 is rendered n type and the opposing region 40 is rendered p type The junction 45 between the n type and p type regions is at some mid point between the device 102 electrodes 18 20 023 This p n junction arrangement can be reversed at will by applying the biasing of Fig 2C Here the backgate voltage is set as VBG 0 and the top gate voltage is set as VTG j0 CTG CBG VBG where CTG and CBG are the capacitances associated with the top gate and the backgate respectively With this biasing the graphene region 42 under the top gate 35 is reversed to p type and the opposing region 40 is reversed to n type The junction 45 between the n type and p type regions is again at some mid point between the device electrodes 18 20 024 With this example it is demonstrated that this
172. ted in the schematic in Fig 7 2 The size of the ion interaction volume in the substrate material depends on the elemental composition and density of the material and on the acceleration voltage applied to the 76 Primary He lon Sputtered lon Sputtered Substrate Implanted He lon Figure 7 2 Schematic of the interactions of primary energetic He ions with a graphene layer on SiO2 substrate ion source The primary advantage for HeIM that can be utilized for etching graphene layers is that the interaction volume of the Helium ion is intrinsically smaller than in a typical scanning electron beam or a FIB at the corresponding accelerating voltage The ion interaction volume in the top few nm of the material being the determining factor for ultimate patterning resolution of graphene TRIM calculations 95 96 have been used to simulate ion beam propagation and average sputtering yield in graphene on substrates Simulation for gallium ions for a graphene film on a typical substrate of 285 nm SiO2 on silicon is shown in Fig 7 3a The heavy ions deposit the majority of their kinetic energy in the upper most parts of the material While this makes them highly effective at milling and etching the resulting surface region interaction volume limits the possible feature size to values far larger than the actual beam diameter TRIM calculations for helium ions on an identical specimen in contrast show that 77 y0
173. tic gating 77 The gap splits the zero energy LL suppressing conductance at the CNP The qualitative effect of a gap in the bilayer spectrum can be seen in Fig 5 1 by comparing the gapped case Fig 5 1 c which always has a zero of conductance at v 0 to the gapless cases Figs 1 a b which has a non zero value of conductance at v 0 AT Also illustrated in Fig 5 1 is how the aspect ratio of the sample affects the two terminal conductance near quantum Hall plateaus for all three spectrum types Finite longitudinal conductivity leads to N shaped distortions of the plateaus 75 which are of opposite signs for aspect ratios lt 1 and gt 1 Note however that the extrema of conductance minima for lt 1 and maxima for gt 1 are aligned with the plateaus centers which coincide with the incompressible density values different for monolayers and bilayers Distorted plateaus thus remain useful for characterizing the number of layers and density The back gate dependence of conductance for the five samples reported are most similar to those in Figs 1 a b indicating that these samples are single layers and gapless bilayers only see Table 1 We use the model of Ref 75 to fit the conductance data treating the aspect ratio as a fit parameter In doing so our presumption is that the visible dimensions of the sample may not reflect the actual pattern of current flow Since the conductance problem for a sample of a
174. tirely The local top gating arrangement provided by the invention enables this control the charge carrier type of each region is reversed simply by reversal of a gate electrode voltage from V to V or from V to V While this procedure is here demonstrated for a single graphene p n junction device it is applicable to all graphene p n junction device and circuit arrangements provided by the invention 031 For example referring to Figs 4A 4B this paradigm is extended to a two junction graphene device 70 The graphene device here includes a graphene layer 12 having a first region 40 a second region 42 and a third region 43 each of which are formed with a selected carrier type by application of a selected voltage applied to a top gate electrode disposed atop that region For clarity a global backgate electrode 14 is here shown biased at ground Device electrodes 18 20 are biased with a selected device voltage VD applied between those electrodes 032 Local top gate electrodes 35 37 39 are provided over the graphene 12 separated from the graphene by a gate insulator 24 and a functionalization layer not here shown for clarity With the first and second top gate electrodes 35 37 biased with an appropriate positive voltage 66 68 and the third top gate electrode 39 biased with an appropriate negative voltage 69 n type graphene regions 40 42 are formed under the first and second top gate electrodes 35 37 and a p type graphene region 43 is for
175. to a dramatic increase in research in the field 1 2 Band structure of graphene The atomic layer of hexagonally arranged carbon atoms forming graphene is shown in Fig 1 1 a The unit cell indicated by the dashed lines in Fig 1 1 a is composed of two atoms labeled A and B and has lattice vectors di a 1 0 and a3 a w The reciprocal lattice is also hexagonal shown in Fig 1 1 b with the high symmetry points I K and M The essential low energy features of the band structure can be captured by a tight binding approximation The eigenfunctions of graphene can be written as a linear com bination of Bloch functions k F DS i DA eik Ry F R built up from the atomic wavefunctions xj at site j as Wi KF So cul kig kr 1 1 The eigen energies of this system can be obtained by oe Y Ys Djy 0 Ci Cig Sjj k Ui V Divo chew Har k z 1 2 where H k Y H Y and Sy k W Y The solution can be arrived at by minizing the above equation with respect to the coefficient cj resulting in the secular Figure 1 1 a Real space lattice of graphene Unit cell vectors aj and da designate the unit cell The unit cell indicated by the dashed lines is composed of two atoms b The reciprocal lattice and the high symmetry points T K and M There are two inequivalent points in the Brillouin zone K and K c Each A atom red is surrounded by 3 nearest neighbors B atoms blue
176. to the junction is found to reduce the effect of this interface state in the low magnetic field regime A correspon dence between this interface state and snake states in two dimensional electron gases is proposed and its effect on the minimum conductivity in disordered graphene is discussed This chapter is being submitted to Physical Review Letters 63 6 1 Introduction Graphene is an atomically thin sheet of carbon atoms arranged into a hexagonal lattice producing a band structure that resembles Dirac fermions The electron and hole bands meet at a point giving rise to a gapless energy spectrum In contrast an energy gap between the electron and hole bands is common in conventional two dimensional electron gases The interesting band structure of graphene has led to the prediction of anomalous charge transport properties Most notably are half interger values of the quantum Hall QH conductance of 4 n 1 2 e h 11 52 experimentally observed in Ref 9 10 and the finite minimum conductivity omin 4 7 e h 52 Recently the ability to control the carrier type locally 40 47 74 produced configura tions where electrons n type and holes p type reside spatially adjacent to one another producing a p n junction PNJ The lack of a band gap in single layer graphene permits carriers approaching at normal incidence to access any region near the junction which is not possible in gapped systems 16 Bipolar graphene device
177. tomatically open Insert the sample plate into the loadlock as shown in Fig 7 and screw the transfer rod into the sample plate Don t tighten the screw too much once it reaches its maximum pull 142 Figure C 5 Make sure the isolation valve is closed before venting the loadlock Figure C 6 o vent the loadlock turn the toggle switch to vent Make sure the Door Control Button is set to closed 143 Screw in Sample Plate Figure C 7 Load sample plate into the loadlock back 1 2 a turn Close the loadlock and switch the Vacuum Toggle Button to Evac Once the loadlock is pumped down to an appropriate pressure the Evac light will cease blinking and will remain solid green Then and only then can you switch the Door Control Button to Open While doing this place your hand on the transfer rod to prevent the sample plate from being pulled into the main chamber When you flip the Door Control Button wait for two sounds before attempting to insert the sample plate Once the gate valve has fully opened turn the transfer rod lock button 1 2 turn counterclockwise to release the rod see Fig 8 and move the transfer rod all the way in Insert the sample all the way into the chamber until the transfer rod is fully extended Turn the rod counterclockwise until the white stripe on the rod has the same width as the white stripe see Fig 9 Give the rod a few more turns to be sure the screw is not longer attached to the sample
178. tronger peak which moves linearly with VTG is the Dirac point for region 2 The difference in peak heights is a consequence of the different aspect ratios of regions 1 and 2 079 Horizontal slices through the 2 D plot of Fig 9A at fixed VBG corresponding to the horizontal lines in Fig 9A are shown in Fig 9B These slices show a single peak corresponding to the Dirac point of region 2 This peak becomes asymmetric away from the charge neutrality point in region 1 The changing background resistance results from the different density in region 1 at each VBG setting 080 Fig 9D is a plot of measured current I as a function of applied voltage V for the device measured throughout the VTG VBG plane This plot indicates no sign of rectification in any of the four quadrants or at either of the charge neutral boundaries between quadrants as expected for reflectionless Klein tunneling at the p n interface 081 A plot of differential conductance g 1 R as a function of VBG and VTG with an applied magnetic field of B 4T is shown in Fig 10A A vertical slice of data taken at VTG 0 through the p p and n n quadrants of the plot of Fig 10A is shown in Fig 10B This plot reveals conductance plateaus at 2 6 and 10 e h in both quadrants demonstrat ing conclusively that the sample was single layer and that the oxide did not significantly 121 distort the Dirac spectrum 082 In the quantum hall QH regime at large B the Dirac like en
179. uctance peaks and dips at the charge neutrality point which can be used to identify the incompressible densities These results are compared to recent theory and possible origins of the discrepancy are discussed This chapter was submitted to Physical Review B 44 5 1 Introduction Graphene monolayers and bilayers are recently discovered two dimensional gapless semimet als The Dirac spectrum of excitations in monolayer graphene gives rise to a number of novel transport properties including anomalous quantized Hall conductance with plateaus at 4 n 1 2 e h n 0 1 2 in multiterminal samples 9 10 Bilayer graphene has a quadratic electron hole symmetric excitation spectrum leading to quantized Hall conduc tance values 4n e h n 1 2 7 13 Both monolayer and bilayer graphene have a zeroth Landau level located at the charge neutrality point CNP which is eightfold degen erate in bilayers and fourfold degenerate in monolayers Other Landau levels are all fourfold degenerate in both types of graphene 11 52 67 The novel transport signatures not only reflect this underlying band structure but serve as an experimental tool for identifying the number of layers and characterizing sample quality 7 In recent work on graphene two terminal magnetoconductance has emerged as one of the main tools of sample characterization 40 45 74 While a two terminal measurement is not as stra
180. vention one example process for producing the devices of Figs 1A 1B is described below but the invention is not limited to such It will be readily apparent that this process is applicable to all of the graphene devices and circuits described above and indeed to any graphene device in which the layer of graphene is to be electrically connected for biasing and for device or circuit operation 051 Referring then back to Fig 1A in this example fabrication sequence with a graphene layer 12 provided on an oxide layer 16 of a silicon substrate 14 as described above electrically conducting device electrodes 18 20 are formed directly on the graphene It is preferred that the device electrodes be provided directly on the graphene not separated from the graphene by functionalization or oxide layers In one example process to form the device electrodes a resist e g PMMA is spin coated onto the graphene and lithography e g electron beam lithography is carried out to define in the resist specified locations of graphene device electrodes The electrode material is then deposited by e g a physical deposition process such as thermal evaporation In one example the electrode material is provided as a 40 nm thick layer of gold layered on top of a 5 nm thick layer of titanium Titanium can be preferred to ensure good electrical contact to the graphene and an upper gold layer can be preferred to prevent the titanium from oxidizing and to provide good e
181. wang S Das Sarma H L Stormer and P Kim Measurement of scattering rate and minimum conductivity in graphene Phys Rev Lett 99 246803 2007 E Rossi S Adam and S Das Sarma Effective medium theory for disordered two dimensional graphene available at http arxiv org abs 0809 1425 M M Fogler Neutrality point of graphene with coplanar charged impurities available at http arxiv org abs 0810 1755 Mikko Ritala Atomic layer deposition High k Gate Dielectrics p 17 2004 163 38 39 41 42 43 44 45 46 Xinran Wang Scott M Tabakman Hongjie Dai Atomic Layer Deposition of Metal Oxides on Pristine and Functionalized Graphene J Am Chem Soc 130 8152 2008 D B Farmer and R G Gordon Atomic layer deposition on suspended single walled carbon nanotubes via gas phase noncovalent functionalization Nano Lett 6 699 2006 J R Williams L DiCarlo and C M Marcus Quantum Hall effect in a gate controlled p n junction of graphene Science 317 638 2007 F Schedin A K Geim S V Morozov E W Hill P Blake M I Katsnelson and K S Novoselov Detection of individual gas molecules adsorbed on graphene Nat Mater 6 652 2007 E H Hwang S Adam S D Sarma and A K Geim Transport in chemically doped graphene in the presence of adsorbed molecules available at http arxiv org abs cond mat 0610834 C Berger Z Song X Li X Wu
182. y near the charge neutrality point at Te 0 3 K can be attributed to conductance variations up to 20 in the fit range Vsa lt 350 uV at these values of Vig As in sample Al F is found to be independent of carrier type and density over ns lt 101 cm averaging 0 37 0 36 with standard deviation 0 02 0 02 at Te 0 3 1 1 K Evidently despite its different aspect 39 Fi R kQ feeds Sample C b 40 8 yuaz Js T oO O 200 Vsd uV 2 0 Vbg V Figure 4 3 a Differential resistance R of sample C a single layer p n junction as a function of back gate voltage Vig and top gate voltage Viz The skewed cross pattern defines quadrants of n and p carriers in regions 1 and 2 Red lines indicate charge neutrality lines in region 1 dotted and region 2 dashed b S Vgq measured in n p regime with Vig Vig 5 4 V solid dots and best fit to Eq 4 1 red curve with F 0 36 c Main Best fit F along the cuts shown in a at which ns ns2 purple and ns 4 ns2 black Inset Schematic of the device The top gate covers region 2 and one of the contacts ratio A2 exhibits a noise signature similar to that of Al 4 4 Shot noise in a p n junction Transport and noise measurements for a single layer graphene p n junction 40 sample C are shown in Fig 4 3 The color image in Fig 4 3 a shows differential resistance R as a function of Vig and local top gate vo

Williams Thesis - Center for Quantum Devices

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