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Mobility Model for Hydrodynamic Transport Equations

  • Andreas Schenk
Part of the Computational Microelectronics book series (COMPUTATIONAL)

Abstract

The hydrodynamic (HD) transport scheme [2.8, 2.56] has become a standard device simulation tool with the capability for describing nonlocal and nonstationary phenomena. Computation times compare favorably with those of Monte Carlo (MC) simulations [2.23] and methods based on a spherical-harmonics (SH) expansion of the Boltzmann transport equation (BTE) [2.59]. Thus, it is suitable also for more sophisticated applications like power-device, multi-device or 3D-device simulations.

Keywords

Monte Carlo Electron Mobility Mobility Model Hole Mobility Impurity Scattering 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [2.1]
    M. Abramowitz and I. A. Stegun. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Dover Publications, New York, 1972.MATHGoogle Scholar
  2. [2.2]
    J. Appel. Interband Electron-Electron Scattering and Transport Phenomena in Semiconductors. Phys. Rev., 125(6): 1815–23, 1961.MathSciNetCrossRefGoogle Scholar
  3. [2.3]
    M. Asche and O. G. Sarbei. Electric Conductivity of Hot Carriers in Si and Ge. phys. stat. sol., 33:9–57, 1969.CrossRefGoogle Scholar
  4. [2.4]
    H. D. Barber. Effective Mass and Intrinsic Concentration in Silicon. Solid-State Electronics, 10:1039–51, 1967.CrossRefGoogle Scholar
  5. [2.5]
    R. T. Bate, R. D. Baxter, F. J. Reid, and A. C. Beer. Conduction Electron Scattering by Ionized Donors in InSb at 80K. J. Phys. Chem. Solids, 26:1205–14, 1965.CrossRefGoogle Scholar
  6. [2.6]
    H. S. Bennett and J. R. Lowney. Caculated Majority-and Minority-Carrier Mobilities in Heavily Doped Silicon and Comparisons with Experiment. J. Appl. Phys., 71(5): 2285–96, 1992.CrossRefGoogle Scholar
  7. [2.7]
    F. J. Blatt. Scattering of Carriers by Ionized Impurities in Semiconductors. Journ. Phys. Chem. Solids, 1:262–69, 1957.CrossRefGoogle Scholar
  8. [2.8]
    K. Bløtekjær. Transport Equations for Electrons in Two-Valley Semiconductors. IEEE Trans. Electron Devices, ED-17(1):38–47, 1970.CrossRefGoogle Scholar
  9. [2.9]
    K. Bløtekjær and E. B. Lunde. Collision Integrals for Displaced Maxwellian Distributions. phys. stat. sol., 85:581–92, 1969.Google Scholar
  10. [2.10]
    W. Brauer and H.-W. Streitwolf. Theoretische Grundlagen der Halbleiterphysik. Akademie-Verlag, Berlin, 1977.CrossRefGoogle Scholar
  11. [2.11]
    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-22:1045–47, 1975.CrossRefGoogle Scholar
  12. [2.12]
    D. Chattopadhyay and H. J. Queisser. Electron Scattering by Ionized Impurities in Semiconductors. Reviews of Modern Physics, 53(4):745–77, 1981.CrossRefGoogle Scholar
  13. [2.13]
    E. M. Conwell. High Field Transport in Semiconductors, Vol. 9 of Solid State Physics. Academic Press, New York and London, 1967.Google Scholar
  14. [2.14]
    P. P. Debye and E. M. Conwell. Electrical Properties of N-Type Germanium. Phys. Rev., 93(4):693–706, 1954.CrossRefGoogle Scholar
  15. [2.15]
    M. V. Fischetti. Effect of the Electron-Plasmon Interaction on the Electron Mobility in Silicon. Phys. Rev., B 44:5527–34, 1991.Google Scholar
  16. [2.16]
    H. Fröhlich and V. Paranjape. Dielectric Breakdown in Solids. Proc. Phys. Soc. (London), B69:21–32, 1956.Google Scholar
  17. [2.17]
    M. A. Green. Intrinsic Concentration, Effective Densities of States, and Effective Mass in Silicon. J. Appl. Phys., 67(6):2944–54, 1990.CrossRefGoogle Scholar
  18. [2.18]
    D. A. Greenwood. The Boltzmann Equation in the Theory of Electrical Conduction in Metals. Proc. Phys. Soc. London, 71:585–96, 1957.MathSciNetGoogle Scholar
  19. [2.19]
    C. Herring and E. Vogt. Transport and Deformation-Potential Theory for Many-Valley Semiconductors with Anisotropic Scattering. Phys. Rev., 101(3):944–961, 1956.MATHCrossRefGoogle Scholar
  20. [2.20]
    K. Hess. Phenomenological Physics of Hot Carriers in Semiconductors. In D. K. Ferry, J. R. Barker, and C. Jacoboni, (eds.), Physics of Nonlinear Transport in Semiconductors, Vol. 52, pp. 1–42, New York, London, Plenum Press, 1980.CrossRefGoogle Scholar
  21. [2.21]
    K. Hess. Advanced Theory of Semiconductor Devices. Solid State Physical Electronics. Prentice Hall, Englewood Cliffs, N. J., 1988.Google Scholar
  22. [2.22]
    ISE Integrated Systems Engineering AG, Zurich, Switzerland. DESSIS 3.0: Manual, 1996.Google Scholar
  23. [2.23]
    C. Jacoboni and L. Reggiani. The Monte Carlo Method for the Solution of Charge Transport in Semiconductor with Applications to Covalent Materials. Rev. Modern Phys., 55(3):645–705, 1983.CrossRefGoogle Scholar
  24. [2.24]
    E. O. Kane. Thomas-Fermi Approach to Impure Semiconductor Band Structure. Phys. Rev., 131(1):79–88, 1963.MATHCrossRefGoogle Scholar
  25. [2.25]
    L. E. Kay and T. W. Tang. An Improved Ionized-Impurity Scattering Model for Monte Carlo Simulations. J. Appl. Phys., 70(3): 1475–82, 1991.CrossRefGoogle Scholar
  26. [2.26]
    R. W. Keyes. Effects of Electron-Electron Scattering on the Electrical Properties of Semiconductors. J. Phys. Chem. Solids, 6:1–5, 1958.CrossRefGoogle Scholar
  27. [2.27]
    D. B. M. Klaassen. A Unified Mobility Model for Device Simulation — I. Model Equations and Concentration Dependence. Solid-State Electronics, 35(7):953–959, 1992.CrossRefGoogle Scholar
  28. [2.28]
    M. Kohler. Behandlung von Nichtgleichgewichtsvorgängen mit Hilfe eines Extremal-prinzips. Z. Physik, 124:772–89, 1947.MathSciNetCrossRefGoogle Scholar
  29. [2.29]
    R. Kubo. Statistical-Mechanical Theory of Irreversible Processes. I. General Theory and Simple Applications to Magnetic and Conduction Problems. J. Phys. Soc. Japan, 12(6):570–86, 1957.MathSciNetCrossRefGoogle Scholar
  30. [2.30]
    P. T. Landsberg (ed.). Basic Properties of Semiconductors, Volume 1. North-Holland, Amsterdam New York London Tokyo, 1992.Google Scholar
  31. [2.31]
    J. E. Lang, F. L. Madarasz, and P. M. Hemeger. Temperature Dependent Density of States Effective Mass in Nonparabolic p-Type Silicon. J. Appl. Phys., 54(6):3612, 1983.CrossRefGoogle Scholar
  32. [2.32]
    R. A. Logan and A. J. Peters. Impurity Effects upon Mobility in Silicon. J. Appl. Phys., 31(1): 122–124, 1960.CrossRefGoogle Scholar
  33. [2.33]
    C. Lombardi, S. Manzini, A. Saporito, and M. Vanzi. A Physically Based Mobility Model for Numerical Simulation of Nonplanar Devices. IEEE Trans. on CAD, 7(11): 1164–71, 1988.Google Scholar
  34. [2.34]
    D. Long. Scattering of Conduction Electrons by Lattice Vibrations in Silicon. Phys. Rev., 120(6):2024–32, 1960.CrossRefGoogle Scholar
  35. [2.35]
    G. W. Ludwig and R. L. Watters. Drift and Conductivity Mobility in Silicon. Phys. Rev., 101(6): 1699–1701, 1956.CrossRefGoogle Scholar
  36. [2.36]
    F. L. Madarasz, J. E. Lang, and P. M. Hemeger. Effective Masses for Nonparabolic Bands in p-Type Silicon. J. Appl. Phys., 52(7):4646–48, 1981.CrossRefGoogle Scholar
  37. [2.37]
    G. Masetti, M. Severi, and S. Solmi. Modelling of Carrier Mobility Against Carrier Concentration in Arsenic-, Phosphorus-and Boron-Doped Silicon. IEEE Trans. Electron Devices, ED-30:764–69, 1983.CrossRefGoogle Scholar
  38. [2.38]
    B. Meinerzhagen and W. L. Engl. The Influence of the Thermal Equilibrium Approximation on the Accuracy of Classical Two-Dimensional Numerical Modeling of Silicon Submicrometer MOS Transistors. IEEE Trans. Electron Devices, 35(5):689–697, 1988.CrossRefGoogle Scholar
  39. [2.39]
    J. R. Meyer and F. J. Bartoli. Phase-Shift Calculations of Ionized Impurity Scattering in Semiconductors. Phys. Rev. B, 23(10):5413–27, 1981.CrossRefGoogle Scholar
  40. [2.40]
    K. Misiakos and D. Tsamakis. Electron and Hole Mobilities in Lightly Doped Silicon. Appl. Phys. Lett., 64(15):2007–09, 1994.CrossRefGoogle Scholar
  41. [2.41]
    S. N. Mohammad. Unified Model for Drift Velocities of Electrons and Holes in Semiconductors as a Function of Temperature and Electric Field. Solid-State Electronics, 35(10): 1391–96, 1992.CrossRefGoogle Scholar
  42. [2.42]
    T. N. Morgan. Broadening of Impurity Bands in Heavily Doped Semiconductors. Phys. Rev. A, 139(1):343–48, 1965.Google Scholar
  43. [2.43]
    F. J. Morin and J. P. Maita. Electrical Properties of Silicon Containing Arsenic and Boron. Phys. Rev., 96(1):28–35, 1954.CrossRefGoogle Scholar
  44. [2.44]
    B. R. Nag. Hot-Carrier d.c. Conduction in Elemental Semiconductors. Solid-State Electronics, 10:385–400, 1967.CrossRefGoogle Scholar
  45. [2.45]
    P. Norton, T. Braggins, and H. Levinstein. Impurity and Lattice Scattering Parameters as Determined from Hall and Mobility Analysis in n-Type Silicon. Phys. Rev. B, 8(12):5632–53, 1973.CrossRefGoogle Scholar
  46. [2.46]
    G. Ottaviani, L. Reggiani, C. Canali, F. Nava, and A. Alberigi-Quaranta. Hole Drift Velocity in Silicon. Phys. Rev. B, 12(8):3318–29, 1975.CrossRefGoogle Scholar
  47. [2.47]
    G. L. Pearson and J. Bardeen. Electrical Properties of Pure Silicon and Silicon Alloys Containing Boron and Phosphorus. Phys. Rev., 75(5):865–83, 1949.CrossRefGoogle Scholar
  48. [2.48]
    C. J. Rauch, J. J. Stickler, H. J. Zeiger, and G. S. Heller. Millimeter Cyclotron Resonance in Silicon. Phys. Rev. Letters, 4(2):64–66, 1960.CrossRefGoogle Scholar
  49. [2.49]
    H. G. Reik and H. Risken. Distribution Functions for Hot Electrons in Many-Valley Semiconductors. Phys. Rev., 124(3):777–84, 1961.MATHCrossRefGoogle Scholar
  50. [2.50]
    D. L. Rode. Electron Mobility in Ge, Si, and GaP. phys. stat. sol. (b), 53:245–54, 1972.CrossRefGoogle Scholar
  51. [2.51]
    A. G. Samoilovich, I. Y. Korenblit, and I. V. Dakhovskii. Anisotropic Electron Scattering by Ionized Impurities. Soviet Physics —Doklady, 6(7):606–08, 1962.Google Scholar
  52. [2.52]
    A. Schenk. Spatially Variable Drift Mobility Model for Hg 1-x Cd x Te Diodes. phys. stat. sol. (a), 122:413–25, 723–29, 1990.CrossRefGoogle Scholar
  53. [2.53]
    S. Selberherr. Analysis and Simulation of Semiconductor Devices. Springer-Verlag, Wien New York, 1984.CrossRefGoogle Scholar
  54. [2.54]
    H. Shichijo, J. Y. Tang, J. Bude, and P. D. Yoder. Full Band Monte Carlo Program for Electrons in Silicon. In Karl Hess, editor, Monte Carlo Device Simulation: Full Band and Beyond, Chapt. 10, pp. 285–307. Kluwer Academic Publishers, Boston, 1991.CrossRefGoogle Scholar
  55. [2.55]
    R. Stratton. The Influence of Interelectronic Collisions on Conduction and Breakdown in Covalent Semiconductors. Proc. Roy. Soc. (London), A242:355–73, 1957.Google Scholar
  56. [2.56]
    R. Stratton. Diffusion of Hot and Cold Electrons in Semiconductor Barriers. Phys. Rev., 126(6):2002–14, 1962.CrossRefGoogle Scholar
  57. [2.57]
    N. Takimoto. On the Screening of Impurity Potential by Conduction Electrons. Jour. Phys. Soc. Japan, 14(9): 1142–58, 1959.CrossRefGoogle Scholar
  58. [2.58]
    R. Thoma, A. Emunds, B. Meinerzhagen, H. J. Peifer, and W. L. Engl. Hydrodynamic Equations for Semiconductors with Nonparabolic Band Structure. IEEE Trans. Electron Devices, ED-38(6): 1343–53, 1991.CrossRefGoogle Scholar
  59. [2.59]
    D. Ventura, A. Gnudi, G. Baccarani, and F. Odeh. Multidimensional Spherical Harmonics Expansion of Boltzmann Equation for Transport in Semiconductors. Appl. Math. Lett., 5(3):85–90, 1992.MathSciNetMATHCrossRefGoogle Scholar
  60. [2.60]
    J. D. Wiley. Polar Mobility of Holes in III-V Compounds. Phys. Rev. B, 4(8):2485–93, 1971.CrossRefGoogle Scholar
  61. [2.61]
    P. D. Yoder. Integrated Systems Laboratory, ETH Zurich. Private communication.Google Scholar
  62. [2.62]
    P. D. Yoder. First Principle Monte Carlo Simulation of Charge Transport in Semiconductors. PhD thesis, University of Illinois, Urbana, Illinois, 1994.Google Scholar
  63. [2.63]
    R. Zimmermann. Many Particle Theory of Highly Excited Semiconductors. Texte zur Physik, Band 18. BSB Teubner Verlagsgesellschaft Leipzig, 1988.Google Scholar

Copyright information

© Springer-Verlag Wien 1998

Authors and Affiliations

  • Andreas Schenk
    • 1
  1. 1.Institut für Integrierte SystemeETH ZürichSchweiz

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