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Numerical Simulation of MOS Transistors

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Semiconductors

Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 59))

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Abstract

This contribution is intended to review the international state-of-the-art in numerical simulation of MOS devices. Much emphasis is laid on the discussion of recent refinements to carrier transport models, e.g. drift-diffusion model, enhanced drift-diffusion equations, hydrodynamic model, and Monte Carlo simulation. Adequate models for the physical parameters are reported with suitable parameter values, e.g. carrier mobilities taking into account the various scattering mechanisms, and carrier generation-recombination including impact ionization. Examples are presented for two different types of MOS devices: on the one hand, simulation results of miniaturized MOS transistors are discussed which have been obtained by our simulator MINIMOS 5.0 with additional extensions, and on the other hand, simulation results concerning a power MOS transistor are shown which has been investigated with our device simulation program BAMBI 2.1.

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References

  1. M. Ali-Omar and L. Reggiani, Drift and Diffusions of Charge Carriers in Silicon and Their Empirical Relation to the Electric Field, Solid-State Electron, 30, 7 (1987), pp. 693–697.

    Article  Google Scholar 

  2. M. Aoki, K. Yano, T. Masuhara, S. Ikeda, and S. Meguro, Optimum Crystallographic Orientation of Submicrometer CMOS Devices Operated at Low Temperatures, IEEE Trans. Electron Devices ED-34, 1 (1987), pp. 52–57.

    Article  Google Scholar 

  3. N. Arora, J. Hauser, and D. Roulston, Electron and Hole Mobilities in Silicon as a Function of Concentration and Temperature, IEEE Trans. Electron Devices ED-29 (1982), pp. 292–295.

    Article  Google Scholar 

  4. G. Baccarani, M. Rudan, R. Guerrieri, and P. Ciampolini, Physical Models for Numerical Device Simulation, In European School on Device Modeling (University of Bologna, Italy, March 1991), pp. 1–70.

    Google Scholar 

  5. G. Baccarani and M. Wordeman, An Investigation of Steady-State Velocity Overshoot in Silicon, Solid-State Electron, 28, 4 (1985), pp. 407–416.

    Article  Google Scholar 

  6. K. Blotekjaer, Transport Equations for Electrons in Two-Valley Semiconductors, IEEE Trans. Electron Devices ED-17, 1 (1970), pp. 38–47.

    Article  Google Scholar 

  7. E. Buturla, P. Cottrell, B. Grossman, K. Salsburg, M. Lawlor, and C. McMullen, Three-Dimensional Finite Element Simulation of Semiconductor Devices, In ISSC (1980), pp.76–77.

    Google Scholar 

  8. C. Canali, G. Majni, R. Minder and G. Ottaviani, Electron and Hole Drift Velocity Measurements in Silicon and Their Empirical Relation to Electric Field and Temperature, IEEE Trans. Electron Devices ED-22 (1975), pp. 1045–1047.

    Article  Google Scholar 

  9. C. Canali and G. Ottaviani, Saturation Values of the Electron Drift Velocity in Silicon between 300K and 4.2K, Physics Lett. 32A, 3 (1970), pp. 147–148.

    Article  Google Scholar 

  10. D. Caughey and R. Thomas, Carrier Mobilities in Silicon Empirically Related to Doping and Field, Proc. IEEE 52 (1967), pp. 2192–2193.

    Article  Google Scholar 

  11. S. Chamberlain and A. Husain, Three-Dimensional Simulation of VLSI MOSFET’s, In Proc. Int. Electron Devices Meeting (1981), pp. 592–595.

    Google Scholar 

  12. A. Chynoweth, Ionization Rates for Electrons and Holes in Silicon, Physical Review 109 (1958), pp. 1537–1540.

    Article  Google Scholar 

  13. P. Ciampolini, A. Pierantoni, M. Melanotte, C. Cecchetti, C. Lombardi, and G. Baccarani, Realistic Device Simulation in Three Dimensions, In Proc. Int. Electron Devices Meeting (1989), pp. 131–134.

    Google Scholar 

  14. S. Colak, B. Singer and E. Stupp, Lateral DMOS Power Transistor Design, IEEE Electron Device Lett. EDL-1 (1980), pp. 51–53.

    Article  Google Scholar 

  15. E. Conwell, High Field Transport in Semiconductors, Academic Press, 1967.

    Google Scholar 

  16. C. Growell and S. Sze, Temperature Dependence of Avalanche Multiplication in Semiconductors, Appl. Phys. Lett. 9 (1966), pp. 242–244.

    Article  Google Scholar 

  17. D. Decker and C. Dunn, Temperature Dependence of Carrier Ionization Rates and Saturated Velocities in Silicon, J. Electronic Mat. 4,3 (1975), pp. 527–547.

    Article  Google Scholar 

  18. P. Dhanasekaran and B. Gopalam, The Physical Behaviour of an n + p Silicon Solar Cell in Concentrated Sunlight, Solid-State Electron 25, 8 (1982), pp. 719–722.

    Article  Google Scholar 

  19. P. Dickinger, New models of high voltage DMOS devices for circuit simulation, Electrosoft 1, 4 (December 1990), pp. 298–308.

    Google Scholar 

  20. J. Dorkel and P. Leturcq, Carrier Mobilities in Silicon Semi-Empirically Related to Temperature, Doping and Injection Level, Solid-State Electron. 24 (1981), pp. 821–825.

    Article  Google Scholar 

  21. J. Dziewior and W. Schmid, Auger Coefficients for Highly Doped and Highly Excited Silicon, Appl. Phys. Lett. 31 (1977), pp. 346–348.

    Article  Google Scholar 

  22. A. Franz and G. Franz, BAMBI — A Design Model for Power MOSFET’s, IEEE Trans. Computer-Aided Design CAD-4, 3 (1985), pp. 177–189.

    Article  Google Scholar 

  23. F. Gaensslen, R. Jaeger, and J. Walker, Low-Temperature Threshold behavior of Depletion Mode Devices — Characterization and Simulation, In Proc. Int. Electron Devices Meeting (1976), pp. 520–524.

    Google Scholar 

  24. I. Gamba and M. Squeff, Simulation of the Transient Behavior of a One-Dimensional Semiconductor Device II, SIAM J. Numer. Anal. 26, 3 (1989), pp. 539–552.

    Article  MathSciNet  MATH  Google Scholar 

  25. H. Gummel, A Self-Consistent Iterative Scheme for One-dimensional Steady State transistor Calculations, IEEE Trans. Electron Devices ED-11 (1964), pp. 455–465.

    Article  Google Scholar 

  26. P. Habaš and S. Selberherr, Impact of the Non-Degenerate Gate Effect on the Performance of Submicron MOS-Devices, MIDEM — Electronic Components and Materials (December 1990), pp. 185–188.

    Google Scholar 

  27. W. Hänsch, Carrier Transport in Semiconductor Devices of Very Small Dimensions, In Two-Dimensional Systems: Physics and Devices (Berlin, 1986), vol. 67, Springer, pp. 296–303.

    Google Scholar 

  28. W. Hänsch and H. Jacobs, Enhanced Transconductance in Deep Submicrometer MOSFET, IEEE Electron Device Lett. EDL-10, 7 (1989), pp. 285–287.

    Article  Google Scholar 

  29. W. Hänsch and M. Miura-Mattausch, The Hot-Electron Problem in Small Semiconductor Devices, J. Appl. Phys. 60 (1986), p. 650.

    Article  Google Scholar 

  30. W. Hänsch, M. Orlowski, and E. Weber, The Hot-Electron Problem in Submicron MOSFET’s, In ESSDERC (1988), pp. 597–606.

    Google Scholar 

  31. W. Hänsch and S. Selberherr, MINIMOS 3: A MOSFET Simulator that Includes Energy Balance, IEEE Trans. Electron Devices ED-34, 5 (May 1987), pp. 1074–1078.

    Article  Google Scholar 

  32. W. Hänsch and W. Weber, The Effect of Transients on Hot Carriers, IEEE Electron Device Lett. EDL-10, 6 (1989), pp. 252–254.

    Article  Google Scholar 

  33. A. Henning, N. Chan, J. Watt, and J. Plummer, Substrate Current at Cryogenic Temperatures: Measurements and a Two-Dimensional Model for CMOS Technology, IEEE Trans. Electron Devices ED-34, 1 (1987), pp. 64–74.

    Article  Google Scholar 

  34. P. Heremans, G. VanDenBosch, R. Bellens, G. Groeseneken, and H. Maes, Temperature Dependence of the Channel Hot-Carrier Degradation of n-Channel MOSFET’s, IEEE Trans. Electron Devices ED-37, 4 (1990), pp. 980–993.

    Article  Google Scholar 

  35. K. Hess and G. Iafrate, Theory and Applications of Near Ballistic Transport in Semiconductors, Proc. IEEE 76, 5 (1988), pp. 519–532.

    Article  Google Scholar 

  36. W. Heywang and H. Pötzl, Bandstruktur and Stromtransport, Springer, 1976.

    Google Scholar 

  37. A. Hiroki, S. Odanaka, K. Ohe, and H. Esaki, A Mobility Model for Submicrometer MOSFET Device Simulations, IEEE Electron Device Lett. EDL-8, 5 (1987), pp. 231–233.

    Article  Google Scholar 

  38. R. Hori, H. Masuda, O. Minato, S. Nishimatu, K. Sato, and M. Subo, Short Channel MOS-IC Based on Accurate Two-Dimensional Device Design, Jap. J. Appl. Phys. 15 (1976), pp. 193–199.

    Article  Google Scholar 

  39. A. Husain and S. Chamberlain, Three-Dimensional Simulation of VLSI MOSFET’s: The Three-Dimensional Simulation Program WATMOS, IEEE J. Solid-State Circuits SC-17, 2 (1982), pp. 261–268.

    Article  Google Scholar 

  40. C. Jacoboni, Monte Carlo Techniques, In European School on Device Modeling (University of Bologna, Italy, March 1991), pp. 101–124.

    Google Scholar 

  41. C. Jacoboni and L. Reggiani, The Monte Carlo Method for the Solution of Charge Transport in Semiconductors with Applications to Covalent Materials, Review of Modern Physics 55, 3 (1983), pp. 645–705.

    Article  Google Scholar 

  42. D. Kahng and M. Atalla, Silicon-Silicondioxide Field Induced Surface Devices, In IRE-AIEE Solid-State Device Res. Conf. (1960).

    Google Scholar 

  43. W. Kausel, H. Pötzl, G. Nanz, and S. Selberherr, Two-Dimensional Transient Simulation of the Turn-Off Behavior of a Planar MOS-Transistor, Solid-State Electron 32, 9 (1989), pp. 685–709.

    Article  Google Scholar 

  44. M. Kinugawa, M. Kakumu, T. Usami, and J. Matsunaga, Effects of Silicon Surface Orientation on Submicron CMOS Devices, In Proc. Int. Electron Devices Meeting (1985), pp. 581–584.

    Google Scholar 

  45. H. Kosina and S. Selberherr, Coupling of Monte Carlo and Drift Diffusion Method with Applications to Metal Oxide Semiconductor Field Effect Transistors, Jap. J. Appl. Phys. 29, 12 (December 1990), pp. 2282–2285.

    Google Scholar 

  46. N. Kotani and S. Kawazu, A Numerical Analysis of Avalanche Breakdown in Short-Channel MOSFET’s, Solid-State Electron 24 (1981), pp. 681–687.

    Article  Google Scholar 

  47. S. Laux and M. Fischetti, Monte Carlo Simulation of Submicrometer Si n-MOSFET’s at 77 and 300K, IEEE Electron Device Lett. EDL-9 (1988), pp. 467–469.

    Article  Google Scholar 

  48. S. Li and W. Thurber, The Dopant Density and Temperature Dependence of Electron Mobility and Resistivity in n-Type Silicon, Solid-State Electron 20 (1977), pp. 609–616.

    Article  Google Scholar 

  49. T. Linton and P. Blakey, A Fast, General Three-Dimensional Device Simulator and Its Application in a Submicron EPROM Design Study, IEEE Trans. Computer-Aided Design CAD-8, 5 (1989), pp. 508–515.

    Article  Google Scholar 

  50. H. Loeb, R. Andrew, and W. Love, Application of 2-Dimensional Solutions of the Shockley-Poisson Equation to Inversion-Layer M. O. S. T. Devices, Electron Lett. 4 (1968), pp.352–354.

    Article  Google Scholar 

  51. C. Lu, J. Sung, H. Kirsch, S. Hillenius, T. Smith, and L. Manchanda, Anomalous C-V Characteristics of Implanted Poly MOS Structures in n+/p+ Dual-Gate CMOS Technology, IEEE Electron Device Lett. EDL-10, 5 (1989), pp. 192–194.

    Article  Google Scholar 

  52. M. Mock, A Two-Dimensional Mathematical Model of the Insulated-Gate Field-Effect Transistor, Solid-State Electron 16 (1973), pp. 601–609.

    Article  Google Scholar 

  53. M. Mock, A Time-Dependent Numerical Model of the Insulated-Gate Field-Effect Transistor, Solid-State Electron 24 (1981), pp. 959–966.

    Article  Google Scholar 

  54. C. Moglestue, A Monte Carlo Particle Model Study of the Influence of the Doping Profiles on the Characteristics of Field-Effect Transistors, In NASECODE II Conf. (1981), pp. 244–249.

    Google Scholar 

  55. D. Navon and C. Wang, Numerical Modeling of Power MOSFET’s, Solid-State Electron 26, 4 (1983), pp. 287–290.

    Article  Google Scholar 

  56. T. Nishida and C. Sah, A Physically Based Mobility Model for MOSFET Numerical Simulation, IEEE Trans. Electron Devices ED-34, 2 (1987), pp. 310–320.

    Article  Google Scholar 

  57. S. Oh, D. Ward, and R. Dutton, Transient Analysis of MOS Transistors, IEEE Trans. Electron Devices ED-27 (1980), pp. 1571–1578.

    Google Scholar 

  58. H. Oka, K. Nishiuchi, T. Nakamura, and H. Ishikawa, Two-Dimensional Numerical Analysis of Normally-Off Type Buried Channel MOSFET’s, In Proc. Int. Electron Devices Meeting (1979), pp. 30–33.

    Google Scholar 

  59. Y. Okuto and C. Crowell, Ionization Coefficients in Semiconductors: A Nonlocalized Property, Physical Review BIO (1974), pp. 4284–4296.

    Google Scholar 

  60. T. Ong, P. Ko, and C. Hu, 50-A Gate-Oxide MOSFET’s at 77K, IEEE Trans. Electron Devices ED-34, 10 (1987), pp. 2129–2135.

    Google Scholar 

  61. M. Orlowski and C. Werner, Model for the Electric Fields in LDD MOSFET’s — Part II: Field Distribution on the Drain Side, IEEE Trans. Electron Devices ED-36, 2 (1989), pp. 382–391.

    Article  Google Scholar 

  62. M. Orlowski, C. Werner, and J. Klink, Model for the Electric Fields in LDD MOSFET’s — Part I: Field Peaks on the Source Side, IEEE Trans. Electron Devices ED-36, 2 (1989), pp. 375–381.

    Article  Google Scholar 

  63. Y. Park, D. Navon, and T. Tang, Monte Carlo Simulation of Bipolar Transistors, IEEE Trans. Electron Devices ED-31, 12 (1984), pp. 1724–1730.

    Article  Google Scholar 

  64. P. Robertson and D. Dumin, Ballistic Transport and Properties of Submicrometer Silicon MOSFET’s from 300 to 4.2K, IEEE Trans. Electron Devices ED-33, 4 (1986), pp. 494–498.

    Article  Google Scholar 

  65. M. Rudan and A. Gnudi, The Hydrodynamic Model of Current Transport in Semiconductors, In European School on Device Modeling (University of Bologna, Italy, March 1991), pp.125–160.

    Google Scholar 

  66. G. Sai-Halasz, Processing and Characterization of Ultra Small Silicon Devices, In ESSDERC (1987), pp. 71–80.

    Google Scholar 

  67. E. Sangiorgi, B. Ricco, and F. Venturi, MOS2: An Efficient Monte Carlo Simulator for MOS Devices, IEEE Trans. Computer-Aided Design CAD-7, 2 (1988), pp. 259–271.

    Article  Google Scholar 

  68. J. Schroeder and R. Muller, IGFET Analysis Through Numerical Solution of Poisson’s Equation, IEEE Trans. Electron Devices ED-15, 12 (1968), pp. 954–961.

    Article  Google Scholar 

  69. A. Schütz, S. Selberherr, and H. Pötzl, Numerical Analysis of Breakdown Phenomena in MOSFET’s, In NASECODE II Conf. (1981), pp. 270–274.

    Google Scholar 

  70. M. Seavey, Private Communication, 1987.

    Google Scholar 

  71. S. Selberherr, Analysis and Simulation of Semiconductor Devices, Springer, 1984.

    Google Scholar 

  72. S. Selberherr, MOS Device Modeling at 77K, IEEE Trans. Electron Devices ED-36, 8 (1989), pp. 1464–1474.

    Article  Google Scholar 

  73. S. Selberherr, W. Fichtner, and H. Pötzl, MINIMOS — a Program Package to Facilitate MOS Device Design and Analysis, In NASECODE I Conf. (1979), pp. 275–279.

    Google Scholar 

  74. S. Selberherr and E. Langer, Low Temperature MOS Device Modeling, In Workshop on Low Temperature Semiconductor Electronics (Burlington, Vermont, 1989), pp. 68–72.

    Chapter  Google Scholar 

  75. S. Selberherr and E. Langer, Numerical Simulation of Semiconductor Devices, In European Simulation Multiconf. (Rome, Italy, 1989), pp. 291–296.

    Google Scholar 

  76. S. Selberherr and E. Langer, Three-Dimensional Process and Device Modeling, Microelectronics Journal 20, 1–2 (1989), pp. 113–127.

    Article  Google Scholar 

  77. S. Selberherr, A. Schütz, and H. Pötzl, MINIMOS — A Two-Dimensional MOS Transistor Analyzer, IEEE Trans. Electron Devices ED-27 (1980), pp. 1540–1550.

    Article  Google Scholar 

  78. M. Sever, Analysis of a Discretization Algorithm for Time-Dependent Semiconductor Models, Compel 6, 3 (1987), pp. 171–189.

    MathSciNet  MATH  Google Scholar 

  79. G. Shahidi, D. Antoniadis, and H. Smith, Electron Velocity Overshoot at Room and Liquid Nitrogen Temperatures in Silicon Inversion Layers, IEEE Electron Device Lett. EDL-9, 2 (1988), pp. 94–96.

    Article  Google Scholar 

  80. N. Shigyo, M. Konaka, and R. Dang, Three-Dimensional Simulation of Inverse Narrow-Channel Effect, Electron Lett. 18, 6 (1982), pp. 274–275.

    Article  Google Scholar 

  81. J. Slotboom and G. Streutker, The Mobility Model in MINIMOS, In ESSDERC (1989), pp. 87–91.

    Google Scholar 

  82. Y.-C. Sun, Y. Taur, R. Dennard, and S. Klepner, Submicrometer-Channel CMOS for Low-Temperature Operation, IEEE Trans. Electron Devices ED-34, 1 (1987), pp. 19–27.

    Article  Google Scholar 

  83. S. Svensson, Theoretical Analysis of the Layer Design of Inverted Single-Channel Heterostructure Transistors, IEEE Trans. Electron Devices ED-34, 5 (1987), pp. 992–1000.

    Article  Google Scholar 

  84. S. Sze, Physics of Semiconductor Devices, Wiley, 1969.

    Google Scholar 

  85. A. Tamer, K. Rauch, and J. Moll, Numerical Comparison of DMOS, VMOS and UMOS Power Transistors, IEEE Trans. Electron Devices ED-30, 1 (1983), pp. 73–76.

    Article  Google Scholar 

  86. M. Thurner and S. Selberherr, The Extension of MINIMOS to a Three-Dimensional Simulation Program, In NASECODE V Conf. (Dublin, 1987), Boole Press, pp. 327–332.

    Google Scholar 

  87. T. Toyabe, K. Yamaguchi, S. Asai, and M. Mock, A Numerical Model of Avalanche Breakdown in MOSFET’s, IEEE Trans. Electron Devices ED-25 (1978), pp. 825–832.

    Article  Google Scholar 

  88. T. Toyabe, K. Yamaguchi, S. Asai, and M. Mock, A Two-Dimensional Avalanche Breakdown Model of Submicron MOSFET’s, In Proc. Int. Electron Devices Meeting (1980), pp. 432–435.

    Google Scholar 

  89. C. Turchetti, P. Prioretti, G. Masetti, E. Profumo, and M. Vanzi, A Meyer-Like Approach for the Transient Analysis of Digital MOS IC’s, IEEE Trans. Computer-Aided Design 5, 4 (1986), pp. 499–507.

    Article  Google Scholar 

  90. D. Vandorpe, J. Borel, G. Merckel, and P. Saintot, An Accurate Two-Dimensional Numerical Analysis of the MOS Transistor, Solid-State Electron 15 (1972), pp. 547–557.

    Article  Google Scholar 

  91. A. Walker and P. Woerlee, A Mobility Model for MOSFET Device Simulation, In ESSDERC (1988), pp. 265–269.

    Google Scholar 

  92. C. Wilson and J. Blue, Two-Dimensional Finite Element Charge-Sheet Model of a Short Channel MOS Transistor, Solid-State Electron 25, 6 (1982), pp. 461–477.

    Article  Google Scholar 

  93. J. Woo and J. Plummer, Short Channel Effects in MOSFET’s at Liquid-Nitrogen Temperature, IEEE Trans. Electron Devices ED-33, 7 (1986), pp. 1012–1019.

    Article  Google Scholar 

  94. K. Yamaguchi, A Time Dependent and Two-Dimensional Numerical Model for MOSFET Device Operation, Solid-State Electron 26, 9 (1983), pp. 907–916.

    Article  Google Scholar 

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Authors and Affiliations

  1. Institute for Microelectronics, Technical University Vienna, A-1040, Wien, Austria

    Erasmus Langer

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  1. Erasmus Langer
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Editors and Affiliations

  1. AT&T Bell Laboratories, 600 Mountain Ave., Rm. 2T-502, Murray Hill, NJ, 07974-0636, USA

    W. M. Coughran Jr.

  2. Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY, 12180, USA

    Julian Cole

  3. Technology CAD, AT&T Bell Laboratories, 1247 S. Cedar Crest Blvd., Allentown, PA, 18103-6265, USA

    Peter Lloyd

  4. Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, 50 Vassar St., Rm. 36-880, Cambridge, MA, 02139, USA

    Jacob K. White

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Langer, E. (1994). Numerical Simulation of MOS Transistors. In: Coughran, W.M., Cole, J., Lloyd, P., White, J.K. (eds) Semiconductors. The IMA Volumes in Mathematics and its Applications, vol 59. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8410-6_14

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