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1. simulations performed with the SVDP model of ATHENA 3 The improvement is evaluated by the Root Mean Square Relative Error where Yexpi ANA Ysimi are respectively the ith experimental and simulated concentration values of a n points discretization of the profile Influence on Device Characteristics It is often recognized in the TCAD word that an accurate simulation of electrical MOSFET characteristics is primarily due to a good process simulation This is illustrated as an example in the Figure 7 where we have made the same ATLAS simulation with two different ATHENA process simulation One using the default value of the moments of the SVDP model and the other one using the calibrated one HM SVDP Default E SVDP Calibrated File view Plot Tools Print Properties Help Id g Yd 0 050 Calibrated Simulation Default Simulation 0 8 1 2 Gate Voltage SILVACO Internationa Figure 7 Comparison of the use of calibrated profiles on a device characteristic Conclusion In this study we have presented an original and efficient methodology for global ion implantation modeling The advantages of this methodology are a lower number of experiments confidence in the values of the calibrated model parameters and the rapid implementation of new data within our process simulator ATHENA However it is of great importance to notice that the aim of this paper was to show a calibration methodology and not necessary to g2. Silvaco is NOT for sale and will remain fiercely independent Don t lose sleep as your investment and partnership with Silvaco will only grow CONTACTS Silvaco Japan INTERNATIONAL jpsales silvaco com USA HEADQUARTERS S A E Silvaco International Silvaco Taiwan 4701 Patrick Henry Drive twsales silvaco com Building 2 Silvaco Singapore Santa Clara CA 95054 sgsales silvaco com USA Silvaco UK Phone 408 567 1000 uksales silvaco com Fax 408 496 6080 Silvaco France sales silvaco com frsales silvaco com www silvaco com Silvaco Germany desales silvaco com ECAD Products Licensed through Silvaco or e ECAD Vendor Partner
3. we can also perform yield analysis directly upon the experimental output Continued on page 2 INSIDE New Model for Simulation of Exposure Process in Complex Nonplanar resist Substrate Structures Fast Physical Predictive and Calibrated Modeling of lon Implantation Calendar of Events Hints Tips and Solutions SILVACO INTERNATIONAL Scattergram peakgm E 3 12 00 15 00 18 00 21 00 24 00 27 00 30 00 33 00 36 00 vdbrk x vabrk y l Gaiden Device n A e Fit Linear j Fit Info Axes Annotate Hardcopy Help Quit Figure 3 Scatter plot showing Voy YS Mpk for both the nominal and optimized device structures Device Optimization When the results from the Monte Carlo experiment are investigated in SPAYN the user can identify good devices by visually inspecting the scatter plots In Figure 1 a device has been chosen with both high gm x and breakdown SPAYN then displays each of the input variables for that simulation in a pop up box A simple yet effective method of optimization is then to center the input values on this good device and re run the whole experiment Figure 3 displays the combined scatter plots for both experiments showing a marked improvement in both gm and Vpprk Histogram n P wj 2 795 03 x 1 150 034 sup x O 1 i86 03 x 6 522 x 0 000367 0 Mean 0 9978 Std vdeo Gunber of occurrences Gunber of cecurrences 2 9090 65
4. of Design of Experiments DoE Thus only a few extra experiments are needed to extend the ion implantation simulation domain in order to take into account the most advanced Current Errors A Total iterations Average iteration tim Total elapsed time sec 0 Current rms 0 1 7388 1 7e 16 a Average error 0 013 gt target results 0 0074 value 0 68 Optimization in progress 4 gt 3llowing implant parameters are found in the ting line 24 ATHENA n ee m EXIT E i ls Figure 2 View of the Optimizer windows during extraction procedure August 2000 Page 7 View Edit Find Main Control Commands go athena line x loc 0 00 spac 0 01 line x loc 0 50 spac 0 1 line y loc 0 00 spac 0 0002 line y loc 0 25 spac 0 0004 init silicon orientation 100 struct outfile tmp str init infil tmp str deposit oxide thick 0 0023 set ENERGY _CAL 6 5 set DOSE_CAL 2 55e 14 set TILT_CAL set ROTATION_CAL 2 moments silicon 1 BORON dose DOSE_CAL energy ENERGY_CAL range 0 0234234 std dev 0 0148224 garre0 453 kurto 10 srange 0 0391053 sstd dev 0 0366053 sgarm 0 3946 skurto 10 dratio 0 87786 implant Boron dose DOSE_CAL energy ENERGY_CAL tilt TILT_CAL ion ROTATION_CAL_ s oxide 0 0023 print mom curvetdepth impurity Boron material Silicon mat occno 1 e 10 dp4 Line 28 Stop None The following implant parameters are found in the standard t
5. original methodology has been proposed 1 The main idea is that a simulation can be considered as calibrated not only if the set of model parameters is fitted to particular experiments The Simulation Standard but also if the sensitivity of these parameters to the experi mental process parameters is determined With this aim the use of Design of Experiments DoE and Response Surface Modeling RSM permits the choice of the most significant experiments to finally generate an empirical model for the para meters of the implantation model Nowadays the parameters of the most advanced analytical ion implantation models like 39 7619975 4 60085255 17 202025 JET O 0 05 1445518 0 0084 s 254 O OOR 6S oE O O00 364 005 0 O044 4a O 7 BoSS E DS 0 00 126 5656 0 OA 02664 0 O04168205 0 40 0006 2146 0 021307672 0 005 0 0 O O S840 85995 O04 25 lA 0 26551 6364 0 OO La Se 5 O 0 0 11565 5 451451973 0 5e7 40 SRE ADS 0 O81 1 BA 0 01 4445048 0 105267 0 0 00 17508 0 the Dual Pearson 4 DP4 2 are linearly interpolated in lookup tables to produce fast and accurate simulation process parameters However these lookup tables suffer from several drawbacks i default values in TCAD software must be calibrated and extended over the whole interesting range to make the modeling results closer to the specific experimental conditions of ea
6. 00 78 00 32 00 104 9 1127 0 1309 9 143 0 156 9 peekom E 3 Awe Farulaln K tote J Jamii xl l renkim a Doamulen braspy Iwp tral predictor input variables gate length second recess length InGas channel thickness total recess depth recess fraction B A d1 cap doping density d2 supply doping density d3 1st 6 doping density d4 2nd doping density response target variables gMpk peak transconductance V Dbrk break down voltage Table 1 Input and response variables for the experiment Figure 4 shows histograms of both gm and Vpprk for the nominal and optimized cases The qualitative improvement in the parameters is immediately observ able with the mean gm increasing from 410 to 490 mS mm and Vp from 24 to 28 V Further there is no significant change in the standard deviation of either distribution Yield Analysis Since both experiments were performed using Gaussian distributions the output distribution functions can be evaluated directly to obtain the yield values In our example we choose an arbitrary fail point for the breakdown voltage and integrate both the nominal and optimized distributions to calculate the expected yield from a wafer Choosing a minimum of 20 Volts Histogram Gunber of occurrences Humber of occurrences now famotgte X falls j vih x Distdzuticn Hadcopy Hep Qt J Comeintve Custom Pict Figure 4 Distribution an
7. Delta2 Doping Figure 2 Double recessed double 5 doped pHEMT structure Volume 12 Number 8 August 2000 SCATTER POINT INFO Set Mommies 10 H velit E708 Y pekom 03345 ss Bealtargras On et onl aner a Dhe Wolu f EI EKIFENT cowl 7 ls 2 2052 H i i H j 1 2 E6EZ a ee F EET r ia h E zisa H i a i eee FH Ja zile oe ee ee ee a p 2 08393 i eee E ae a a aide i iiO Fa la PRIE fa He ere a J 3 303 Le Pop ane aiar L 35Eu LT tok ta Di Ai d Thee LE Hae t a f Leie le nia baa ath Ji 1 iliv Le SEE R ENE E E ERE pr oo EE T eee pon Sah m P atiii ti yeniil 2 gaa I a j a ge Fed E ia vwha La E 2i a7 ai j hhe a A why 1 03 ee cert oo vilick 2705 p u 4 ni I kig ag ii a A i Fa aah Hii a jade b imat E 4 2 ae aT ga A Y bi puai h D W i ih ae a as rane tear TA 7a ae Wee Laila SAn emaan R g Bi Paa k 1A af i A na H r i Hia a 1 peu a hi 7 1 1 ii 1 ae at 1 1 r H ad 1 1 ankon l i ru 1 1 ie mi 1 7 i 4 1 1 s b 1 i i i A 1 i i i i i 1 1 Fil Mw Figure 1 Scatter plot showing Von YS gM from Monte Carlo experiment There are two common distribution choices for Monte Carlo experimental design a uniform random distribution suits device optimization as the input parameter plane is more efficiently covered however by using a Gaussian profile which is more representative of natural variations in the device
8. Simulation Standard TCAD Driven CAD A Journal for Process and Device Engineers Yield Analysis and Performance Optimization Using FastBlaze and SPAYN Introduction In previous Simulation Standard articles Nov 97 amp Nov 98 FastBlaze has been presented as a new highly efficient approach to simulating advanced HEMTs and MESFETs Conventional device simulators often suffer from slow execution times leading to a trade off between mesh density and physical model complexity against CPU run time and convergence This requires engineers to compromise accuracy to achieve a reasonable throughput By focusing solely upon FET simulation FastBlaze has been able to greatly optimize the physical solution procedure enabling the use of the most sophisticated physical models while maintaining a fast execution typically less than 1 minute for a full set of DC Ip Vps curves This speed enables both complex and extensive experimental designs to be completed on a reasonable time scale permitting experiments that would be prohibitively expensive for more traditional device simulators Experimental Design In this exercise we illustrate the power of FastBlaze when coupled to SPAYN by implementing a simple but large experimental design We took a relatively complicated double recessed double delta doped pHEMT structure Figure 2 and randomly varied 9 of the physical input parameters see Table 1 Supply Doping Delta1 Doping
9. ables and used for MATERIAL oxide ION Boron energy 6 5 dose 2 55e 14 range 0 0222 std dev 0 01138 garma 0 0391 kurtosis 3 04351 Istd dev 0 01138 kurtt 3 The following implant parameters are found from the moments statements and used for MATERIAL silicon ION Boron S OXIDE THICKNESS 0 0023um energy 6 5 dose 2 55e 14 tilt rotation 2 range 0 0234234 std dev 0 0148224 garma 0 453 kurtosis 10 srange 0 0391053 sstd dev 0 0366053 sgarma 0 3946 idee alle dratio 0 87786 Istd dev 0 0148224 kurtt 3 1lsstd dev 0 00732106 skurtt 3 ATHENA Figure 1 Input deck used for Dual Pearson 4 moments extraction process conditions accurately Our methodology is carried out for low energy B and As implantation which is the case in practice for ultra shallow junction engineering Calibration of lon implantation modeling The results provided by a TCAD simulator are a function of both the experimental conditions and of the parameters of the used model parameters which may themselves depend on the experimental conditions In the case of analytic simulation of ion implantation the tuning of the parameters for example the moments of the statistical distribution is often necessary because they incorporate the experimental uncertainties On the contrary for MC computations parameters are purely physical so do not need to be adjusted The problem of predictive calibration of TCAD simulators has been previously addressed and an
10. alysis Here the mean value of both Vp and gm have been increased in the optimized structure with no significant change in the standard deviations The Simulation Standard August 2000 Source P val T j eye Nn N BE H 00 Ko oe Ww N Hw N Lg 1 Linear model v sig RL W oO N j Oo 2 Extra due to interactions xy terms v sig Ea hae v sig 73 not sig 78 E ca CW 0 49 H ee Ov 3 Extra due to quadratic x terms A 46 rf lt 11 4 Extra due to interactions xyz terms d1 35 d3 0 47 5 Extra due to interactions xy terms not sig gmpk 0 39 6 Extra due to cubic x terms Error residual 2 2 nD aad Table 3 Analysis of variance ANOVA for Vpp x not sig N N wB Bd N w ol N VDbrk 0 50 Table 2 A bridged correlation matrix for the combined nominal and optimized experimental data breakdown the yield from the nominal structure is 92 2 where as the optimized is greater than 99 If the minimum is shifted to 22 Volts the nominal structure s yield drops to 80 where as the optimized is still greater than 98 SPAYN Parameter Analysis The previous examples demonstrate a straight forward optimization technique however the inter dependencies of each input parameter have not been analyzed SPAYN provides the tools for investigating these relationships via the correlation matrix SPAYN can also be used to generate an a
11. ch fab in particular the dose loss ii the global consistency of the table is not maintained when further parameter values are incorporated iii a great number of experiments is required to obtain discrete sets of model parameters that cover the experimental domain with a sufficient accuracy The advantages of RSM could then fulfill the requirements of predictive calibration of ion implantation analytical models Application to Advanced Analytical Models We applied our strategy to the DP4 ion implantation modeling we attempted to find a quadratic modeling of the parameters Rp DRp skewness kurtosis of the DP4 models To do that we have applied the following strategy e DoE on which SIMS profile will be extracted The domain of variation is shown on Table 1 Dose As BF2 at cm Dose B at cm Tilt deg Twist deg Peper 31013 to 1015 11013 to 51014 Table 1 Experimental ranges for As BF2 and B e Use of the SILVACO OPTIMIZER to extract moments of DP4 from experimental SIMS profile Figure 1 and 2 e Modelisation RSM of the DP4 moments We found that the RSM of these models parameters as function of the experimental process condition are satisfactory Indeed the adjusted R_ criterion value which indicates the quality of the empirical models is rarely below 0 8 The Simulation Standard Figure 3 Coefficients of the analytical model for each SVDP model parameter as a function of the Re
12. co welcomes the opportunity Success Continues at Silvaco As summer comes to a close Silvaco is ramping up for another busy fall stacked with exciting conferences worldwide Life never slows at Silvaco as development continues at breakneck speeds and with the power to simulate the largest designs and the speed to keep users design flows moving Silvaco s pride lies in its customers successes If you would like more information or to register for one of our our workshops please check our web site at http www silvaco com The Simulation Standard circulation 18 000 Vol 11 No 8 Au st 2000 is copyrighted by Silvaco International If you or someone you know wants a subscription gu to this free publication please call 408 567 1000 USA 44 1483 401 800 UK 81 45 820 3000 Japan or your nearest Silvaco distributor Simulation Standard TCAD Driven CAD Virtual Wafer Fab Analog Alliance Legacy ATHENA ATLAS MERCURY VICTORY VYPER ANALOG EXPRESS RESILIENCE DISCOVERY CELEBRITY Manufacturing Tools Automation Tools Interactive Tools TonyPlot TonyPlot3D DeckBuild DevEdit DevEdit3D Interpreter ATHENA Interpreter ATLAS Interpreter Circuit Optimizer MaskViews PSTATS SSuprem3 SSuprem4 Elite Optolith Flash Silicides MC Depo Etch MC Implant S Pisces Blaze Blaze3D Device3D TFT2D 3D Ferro SiGe SiC Laser VCSELS Quantum2D 3D Luminous2D 3D Giga2D 3D MixedMode2D 3D FastBlaze FastLar
13. e influence of the dose effect on the developed profile Artificial conditions were simulated to outline the importance of the dose effect In Figure 1 and 2 the intensity distributions in the resist over a non planar substrate are shown for the cases of constant refraction index ny 1 4 7 0 02 Figure 1 and the index varied with dose from ny for unexposed resist to n 14 i 0 04 for completely exposed one Figure 2 The exposure level near the center of the substrate deepening differs substantially for these two cases In the both cases there is the local maximum of the intensity due to reflections from the slope walls However in the continued from page 3 The computational demands for evaluating a regression model are minimal when compared to a full physical simulation hence we chose model 4 from the ANOVA table After fitting the regression equation a residual analysis is performed to check the model This is accomplished by plotting the residuals against the estimated values and also individual predictor variables see Figure 5 A visual inspection of these plots should not reveal any discernible trends If any patterns were apparent this would indicate a poor model and further analysis would be required Finally the response surface was then used in place of FastBlaze to re generate the original Monte Carlo data Note 1000 samples were simulated in under 1 second on a Sun ULTRA 10 workstation Vpp x was then c
14. endai Japan 31 September 1 2 3 Japan Applied Physics Hokkaido Japan 4 Japan Applied Physics Hokkaido Japan 5 Japan Applied Physics Hokkaido Japan 6 Japan Applied Physics Hokkaido Japan SISPAD 2000 Seattle WA 7 Japan Applied Physics Hokkaido Japan SISPAD 2000 Seattle WA 8 SISPAD 2000 Seattle WA 9 10 11 ESSDERC Cork Ireland 12 ESSDERC Cork Ireland 13 ESSDERC Cork Ireland Int l w s on Power and Timing Opt and Sim Germany 14 Int l w s on Power and Timing Opt and Sim German 15 Int l w s on Power and Timing Opt and Sim Germany 16 17 18 19 20 21 22 23 24 25 BCTM BiPOLAR Minneapolis 26 BCTM BiPOLAR Minneapolis 27 BCTM BiPOLAR Minneapolis 28 29 30 Bulletin Board III V Compound Conference in Japan Silvaco is heading to Japan August 20th through 23rd for the 2000 Hetero Structure Microelectronics conference Held this year in the Kyoto Research Park our Japanese office will be introducing attendees to Silvaco products and answering questions about Silvaco s powerful suite of tools Solid State Device and Materials Conference in Japan August 28th through 31st Silvaco s Japanese office is headed to the Sendai International Center for the International Conference on Solid State Device and Materials With benchmarks in reliability and speed Silvaco tools enable developers to reduce the time spent on jobs and eliminate inefficiencies Silva
15. fied instead the old Ray Tracing Method will be used To simulate the dose effect on the resist optical properties the difference of the complex refraction index for exposed and unexposed resist has to be specified It is assumed that standard value of the refraction index corresponds to the case of unexposed resist The following OPTICAL statement optical name resist RESIST1 i line delta real 0 1 delta imag 0 03 specifies that the real part of the refraction index increases by 0 1 for completely exposed resist while the imaginary part of the refraction index absorption is reduced by 0 03 for completely exposed resist The Simulation Standard pa File View v Development profile n 1 4 i 0 02 dn 0 2 i 0 02 second case this maximum is visibly lower due to modification of the resist properties during the exposure These quantitative differences in the intensity distributions result in completely differ ent resist development profiles see Figure 3 4 In the first case the feature is unresolved Figure3 while in the sec ond case Figure4 the whole lithogra phy process was successful New capabilities of the Optolith simulator allow to determine the characteristics of actual resists as well as to optimize parameters of the technological process SILVACO International Figure 4 The resist development profile corresponding to the dose distribution in Figure2 4 Example The figures illustrat
16. geSignal FastMixedMode FastGiga FastNoise Mocasim Spirt Beacon Frontier Clarity Zenith Vision Radiant TwinSim UTMOST UTMOST II UTMOST II UTMOST IV PROMOST SPAYN UTMOST IV Measure UTMOST IV Fit UTMOST IV Spice Modeling SmartStats SDDL SmartSpice FastSpice Twister Blast MixSim SmartLib TestChip Promost Rel RelStats RelLib Harm Ranger Ranger3D Nomad QUEST EXACT CLEVER STELLAR HIPEX net HIPEX r HIPEX c HIPEX rc HIPEX crc EM Power IR SI Timing SN Clock Scholar Expert Savage Scout Dragon Maverick Guardian Envoy LISA ExpertViews and SFLM are trademarks of Silvaco International The Simulation Standard Page 10 August 2000 Hints Tips and Solutions William French Applications and Support Manager Q Can ATLAS be used to simulate advanced III V or II VI materials A Yes ATLAS now supports a wide range of materials in its database This database covers single elememt conductors binary compounds and quaternary compounds A complete list of all materials can be found in Appendix B of the ATLAS Users Manual Vol II It should be noted however that many of these materials are quite recent and do not have a comprehensive set of physical parameters or physical models yet available Atlas can still be used to simulate these devices but requires three contributions from the user First the user should ensure that a complete set of physical parameters are available To illustrate
17. highly significant hence our regression model should include all linear x interaction xy and quadratic terms x Adding extra parameters to the regression equation models 4 5 and 6 produce non significant p values indicating that it is not worth including them in the model As an alternative we can also use the adjusted R value as the selection criterion In this case model 4 should be used i e all linear x interaction xy quadratic x and interaction xyz terms Continued on page 6 Scattergram 5 55e 15 k 1 51le 13 000 000 6 4 000 2 0 000 000 MLResid I N 4 000 6 000 8 000 10 00 L 4 L L L 4 15 00 18 00 21 00 24 00 27 00 30 00 33 00 36 00 Estimate 1 K 2 74e 13 L 4 i l L 4 18 00 21 00 24 00 27 00 30 00 33 00 36 00 Estimate X Estimate y Geiden Device Y 1 vabrk y Y2 MLrResia y 3 y Fit Fit Info Axes Annotate Hardcopy Help Quit Figure 5 Residual analysis of model 4 The Simulation Standard New Model for Simulation of Exposure Process in Complex Nonplanar Resist Substrate Structures 1 Introduction Predictive and efficient lithography simulation is an important component of the semiconductor industry efforts to develop the next generation of deep submicron technologies Emerging technologies are based on elements with very small feature sizes and extremely complex and nonplanar to
18. is was used to confirm the device optimization and corresponding improvement in yield Further the correlation matrix revealed which input parameters are most significant An analysis of variance was performed to select an appropriate regression model which was checked with a residual analysis Figure 5 shows no discernible trends indicating a good model Finally the regression equation was used to predict new values for the response variables with good accuracy validating the model selection August 2000 Fast Physical Predictive and Calibrated Modeling of lon Implantation Introduction Ion implantation has become a critical step for controlling ultra shallow junctions in sub 0 lmm CMOS technology In a Research amp Development environment Technology Computer Aided Design TCAD is involved in the device optimization loop and requires efficient and predictive implantation modeling with frequent updating of the range of validity For this purpose semi empirical models using statistical distributions are mainly chosen because this kind of simulation is faster than the physically based Monte Carlo MC approach We propose a methodology which can be applied to ion implantation modeling with easy build up and which gives a predictive capability in the explored experimental domain This calibration strategy will enhance the efficiency of analytical modeling by the combination the use of SIMS profile and the statistical qualities
19. ive new parameters for the SVDP implant model Indeed it is not guaranty that replacing the default values by the values obtained from this work will give better results in all cases The rea son is that the confidence we have in the results done in this work could not be maintained if we take the values out of their context This is due to the high degree of dependency of the way of doing calibration DoE used optimizer setup making measurements and more important the Fab itself References 1 G Le Carval SISPAD 97 pp 177 180 2 A F Tash J Electrochem Soc 136 3 1989 pp 810 814 3 SILVACO International ATHENA User s Manual Figure 6 RMSRE for Arsenic and Boron which show the reduction after 4 SILVACO Simulation Standard May 2000 calibration of the difference between SIMS profile and simulation August 2000 The Simulation Standard Calendar of Events August CO Co NISKAAN AAT Go No 20 2000 Topical on Hetro Structure Microelectronics Kyoto Japan 21 2000 Topical on Hetro Structure Microelectronics Kyoto Japan 22 2000 Topical on Hetro Structure Microelectronics Kyoto Japan 23 2000 Topical on Hetro Structure Microelectronics Kyoto Japan 24 25 26 27 28 Intl Conf on Solid State Devices and Materials Sendai Japan 29 Intl Conf on Solid State Devices and Materials Sendai Japan 30 Intl Conf on Solid State Devices and Materials S
20. nalytical black box model of this data set through regression analysis This is more computationally efficient than FastBlaze however is strictly limited to this structure For more information on the techniques described below please refer to the SPAYN User s Manual Correlation SPAYN can be used to investigate the inter parameter dependencies through the correlation matrix An abridged matrix showing the most significant variables is presented in Table 2 This is useful when determining which parameters will have a larger influence in the regression models In this case we can see that the gate length second recess length and the total recess depth are highly correlated with Vpprk 1 gt 0 5 Regression Regression analysis can be performed within SPAYN to generate response surfaces for the target parameters These regression equations can then be used to predict new values for the response variables far more efficiently than by using any physical simulator Using Vpp as the response variable and the 9 predictor parameters from Table 1 an analysis of variance ANOVA was performed to identify the most suitable August 2000 model If a more complete ANOVA analysis was required an engineer might also add or remove individual parameters There are several model selection criterion available the most commonly used being p value and adjusted R From the ANOVA table table 3 all of the p values up to model 3 are
21. ndard Page 4 August 2000 In this model the Helmholtz Files View Plots Tools Print 7 Properties Help equation for the electric field E into the media with complex refractive index n x y z WE RrE 0 where k is the wave number is solved in two main stages 1 First the diffraction over a small spatial step along the propagation is calculated thus obtaining the new field amplitude distribution without absorption taken into account 2 Then the actual field distribu Development profile n 1 4 i 0 02 dn 0 SILVACO International tion is computed as a product of this amplitude distribution and the distribution of the com plex absorption over the step Let the wave is propagated along z axis We find the solution as a quasi plane wave E A x y z exp inkz with slowly varied amplitude A A is modified with z slower than phase term inkz In this case the Fourier image of current distribution A in the plane z Z is defined as Pak k A x y z exp i k x ky dxdy After propagating over a small step each component of obtains additional phase shift corresponded to the value of k 1 k k k Thus the amplitude distribution at z Zo Az without accounting for absorption can be written as A x Y Zy Az Fa ky k exp ik Az exp i k x k y dk dk Due to difference of actual optical properties from ones for vacuum the field at the new plane z z Az is comp
22. ompared between the two data sets the first generated by FastBlaze and the second via the SPAYN regression model A deviation of less than 5 was typically observed illustrating the validity of this approach The Simulation Standard References 1 J Van Roey J van der Donk P E Lagasse Beam propagation method analysis and assessment J Opt Soc Am Vol 71 No 7 July 1981 p 803 2 J Z Y Guo F Cerrina Modeling X ray proximity lithography IBM J Res Develop Vol 37 No 3 May 1998 p 331 3 A Erdmann C L Henderson C G Wilson W Henke Influence of optical nonlinearities of the photoresist on the photolithographic process basics SPIE Proc Vol 3051 1997 p 529 4 A Erdmann C L Henderson C G Wilson R R Dammel Some aspects of thick film resist performance and modeling SPIE Proc Vol 3333 1998 p 1201 Conclusions By looking at the input parameters from the simulated good devices we can draw some conclusions about general design criteria for this type of device First we have obvious changes decreasing the gate length and increasing the second recess length to increase gm and breakdown respectively The recess fraction the ratio of 1st and total recess depths should be fixed for this structure at 0 8 Finally the doping density of the 1st delta should be lowered to increase breakdown whilst raising the density of the 2nd delta to maintain gm The SPAYN statistical analys
23. pographies Therefore lithography processing has to provide high resolution with large depth of focus Simultaneously such effects as nonplanar reflections and notching as well as refractive index dependence on local absorbed dose are very critical for printing small mask ele ments using short wavelength radiation This work presents a new approach for sim ulating the exposure process which takes into account these effects in complex non planar resist substrate structures The method is based on numerical solution of the Helmholtz equation for the electric field in the media with complex refractive index n x y z where I is the dose previously absorbed at the point Propagation of initial electromag netic field and fields reflected from the material inter face elements are calculated using the Beam Propagation Method BMP 1 Because the method is very general it can be used for different types of radia tion UV EUV X ray as well as for multiexposure processes and multilayer and nonlinear resists The method is implemented as a separate module which is interfaced with imaging and developing modules of Optolith Complete exposure simulations for a typical 2D structure take 2 20 sec on a Sun Ultra 10 workstation Intensity distribution n 1 4 i 0 02 dn 0 SILVACO International Figure 1 The distribution of intensity dose in the resist over a non planar substrate The resist refraction index is not modified during the ex
24. posure 2 Model The exposure model previously implemented into Optolith is based on the Ray Tracing Method RTM RTM cannot accurately calculate diffraction on small features and does not allow to account for optical nonlinearities of the photoresist The new exposure model has been developed to achieve several goals 1 More accurate simulation of the exposure process by taking into account diffraction effects Files View v Plot 7 Tools Print Properties Help 7 Intensity distribution n 1 4 i 0 02 dn 0 2 i 0 02 SILVACO International 2 Include a capability to simulate non linear effect of the intensity distribution on the local optical properties of the E resist material 3 Improve the simulator performance The Beam Propagation Method BPM is used to solve the Helmholtz equation for electromagnetic field inside the structure During the simulation the field distribution is formed as the superposition of incident light all the reflections from all elements of the resist substrate interface and secondary reflection s from the upper resist surface The formal descriptions of the BPM can be found in 1 In 2 4 some applications using BPM are described too Figure 2 The distribution of intensity dose in the resist over a non planar substrate The resist refraction index is modified during the exposure from for unexposed resist to for completely exposed one The Simulation Sta
25. sults As already explained in 4 we have used the ability of DeckBuild to include any UNIX command inside any simulator input file This feature authorizes users to include their own external routines inside DeckBuild This is what we did in ATHENA to specify the values of the moments of the SIMS Verified Dual Pearson SVDP mode The external routine contains the polynomial model that describes the SVDP model parameter Rp for example as a function of the process parameters like dose and energy see Figure 3 Figure 4 and 5 are an illustration of the profile obtained using this methodology for respectively Arsenic and Boron SIMS profile was superimposed for comparison purpose In Figure 6 we show the global improvement over the whole As and B profile database as compared to the File View Plot Tools Print Properties Help Dual Pearson IV Calibration vad Ao r Arsenic 3 keV 5e14cm 2 v4 21 20 Concentration at cm 3 SYDP Calibrated 0 004 0 008 0 012 0 016 0 02 0 024 Depth um Figure 4 Arsenic profile in TonyPlot before and after calibration comparison with SIMS profile Page 8 August 2000 File View Plot Tools Print Properties Help Dual Pearson IV Calibration Boron 3 ke 7e13cm 2 SIMS Profile Concentration at cm 2 SVDP Default 0 0 01 0 02 0 03 0 04 0 05 0 06 0 07 O08 0 09 01 Depth Figure 5 Boron profile in Tonyplot before and after calibration comparison with SIMS profile
26. this the material InAlAs will be invoked within an input deck To check the required physical parameters are available before a simulation is started the following command should be written within the input deck MODEL PRINT This will then produce in the runtime output window of deckbuild the following table when two regions are pre sent GaAs and InAlAs REGIONAL MATERIAL PARAMETERS Region 1 2 Material GaAs InAlAs Type semicond semicond Epsilon 13 2 0 BAND PARAMETERS Eg eV 142 2 1 Chi eV 4 07 0 Ne per cc 4 35e 17 1 Nv per cc 8 16e 18 1 ni per cc 2 12e 06 2 29e 18 Gc 2 2 Gv 4 4 Ed eV 0 044 0 044 Ea eV 0 045 0 045 RECOMBINATION PARAMETERS Lifetime el 1e 09 1 Lifetime ho 2e 08 1 Augercn 5e 30 0 Augercp le 31 0 Augerkn 0 0 Auger kp 0 0 Copt doe 10 0 An 629 110 Ap 105 30 August 2000 IMPACT IONIZATION MODEL PARAMETERS SELBERHERR MODEL betan 1 82 1 betap o 175 1 egran 0 0 an1 1 9e 05 8 6e 06 bn1 5 75e 05 3 5e 06 an2 1 9e 05 8 6e 06 an2 5 75e 05 3 5e 06 ap1 2 22e 05 2 3e 07 bp1 6 57e 05 4 5e 06 ap2 2 22e 05 2 3e 07 bp2 6 57e 05 4 5e 06 SATURATION VELOCITIES Vsatn cm s 7 7e 06 1e 06 1e 06 Vsatp cm s 7 7e 06 1e 06 1e 06 As shown the material InAlAs does not have certain parameters predefined such as epsilon and Chi The user is required to define these parameters all the Band Parameters and any Recombina
27. tion and Impact Ionization Parameters required in the model definitions In this case the necessary ATLAS statement could be material material InAlAs _ permittivity 13 9 nc300 1 5e17 nv300 8 1e18 affinity 3 6 eg300 1 47 taun0 1 2e 9 taup0 1 2e 9 Second the physical parameters inbuilt into ATLAS Blaze cover GaAs AlGaAs InGaASP SiGe and SiC For advanced materials either constants values need to be used or the C interpreter is required For instance the bandgap in these materials is a function of either the x or y or both mole fractions If a graded mole fractions is required in a device the user has to use the C interpreter to define the variation of bandgap with the x or y mole fraction Third there are a limited set of physical models available within ATLAS Blaze such as for mobility The C interpreter should therefore be applied by the user to define relevent and accurate physical models for the material they are studying Call for Questions If you have hints tips solutions or questions to contribute please contact our Applications and Support Department Phone 408 567 1000 Fax 408 496 6080 e mail support silvaco com Hints Tips and Solutions Archive Check our our Web Page to see more details of this example plus an archive of previous Hints Tips and Solutions www silvaco com The Simulation Standard 9 Your Investment in Silvaco is SOLID as a Rock While others faltered Silvaco stood SOLID for 15 years
28. uted simply E x y Zpt Az A X y Zp Az exp ik n x y z 1 Az The algorithm is repeated recursively step by step over all simulation domain The same calculations are applied to reflections from all segments of the resist boundaries And the whole procedure is repeated NUM REFL times where NUM REFL is specified in the EXPOSURE statement This approach allows the dependence of the refraction index n on intensity I to be taken into account The following formula for n x y z I is implemented n x Y Z I Nunexposed t spaad Ninensosed 1 Mpac x Y Z I August 2000 Figure 3 The resist development profile corresponding to the dose distribution in Figure1 OMpac Here a CI x y z t Mpac where I x y z t is the current intensity distribution C is the Mack s C parameter This effect is calculated by accumulating the total dose in several steps so the intensity distribution is formed as the sum of distributions obtained for each step In this case the previously accumulated intensities are used to compute current values of the refractive index for each point inside the resist area 3 Changes in Optolith Syntax Several additional parameters have been included in the OPTOLITH syntax to control the new model The BPM parameter in the EXPOSURE statement specifies that Beam Propagation Method is to be used during exposure simulation This parameter is now default If the RTM parameter is speci
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