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Part of the book series: Computational Microelectronics ((COMPUTATIONAL))

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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.

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References

  1. M. Abramowitz and I. A. Stegun. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Dover Publications, New York, 1972.

    MATH  Google Scholar 

  2. J. Appel. Interband Electron-Electron Scattering and Transport Phenomena in Semiconductors. Phys. Rev., 125(6): 1815–23, 1961.

    Article  MathSciNet  Google Scholar 

  3. M. Asche and O. G. Sarbei. Electric Conductivity of Hot Carriers in Si and Ge. phys. stat. sol., 33:9–57, 1969.

    Article  Google Scholar 

  4. H. D. Barber. Effective Mass and Intrinsic Concentration in Silicon. Solid-State Electronics, 10:1039–51, 1967.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  7. F. J. Blatt. Scattering of Carriers by Ionized Impurities in Semiconductors. Journ. Phys. Chem. Solids, 1:262–69, 1957.

    Article  Google Scholar 

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

    Article  Google Scholar 

  9. K. Bløtekjær and E. B. Lunde. Collision Integrals for Displaced Maxwellian Distributions. phys. stat. sol., 85:581–92, 1969.

    Google Scholar 

  10. W. Brauer and H.-W. Streitwolf. Theoretische Grundlagen der Halbleiterphysik. Akademie-Verlag, Berlin, 1977.

    Book  Google Scholar 

  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.

    Article  Google Scholar 

  12. D. Chattopadhyay and H. J. Queisser. Electron Scattering by Ionized Impurities in Semiconductors. Reviews of Modern Physics, 53(4):745–77, 1981.

    Article  Google Scholar 

  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. P. P. Debye and E. M. Conwell. Electrical Properties of N-Type Germanium. Phys. Rev., 93(4):693–706, 1954.

    Article  Google Scholar 

  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. H. Fröhlich and V. Paranjape. Dielectric Breakdown in Solids. Proc. Phys. Soc. (London), B69:21–32, 1956.

    Google Scholar 

  17. M. A. Green. Intrinsic Concentration, Effective Densities of States, and Effective Mass in Silicon. J. Appl. Phys., 67(6):2944–54, 1990.

    Article  Google Scholar 

  18. D. A. Greenwood. The Boltzmann Equation in the Theory of Electrical Conduction in Metals. Proc. Phys. Soc. London, 71:585–96, 1957.

    MathSciNet  Google Scholar 

  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.

    Article  MATH  Google Scholar 

  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.

    Chapter  Google Scholar 

  21. K. Hess. Advanced Theory of Semiconductor Devices. Solid State Physical Electronics. Prentice Hall, Englewood Cliffs, N. J., 1988.

    Google Scholar 

  22. ISE Integrated Systems Engineering AG, Zurich, Switzerland. DESSIS 3.0: Manual, 1996.

    Google Scholar 

  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.

    Article  Google Scholar 

  24. E. O. Kane. Thomas-Fermi Approach to Impure Semiconductor Band Structure. Phys. Rev., 131(1):79–88, 1963.

    Article  MATH  Google Scholar 

  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.

    Article  Google Scholar 

  26. R. W. Keyes. Effects of Electron-Electron Scattering on the Electrical Properties of Semiconductors. J. Phys. Chem. Solids, 6:1–5, 1958.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  28. M. Kohler. Behandlung von Nichtgleichgewichtsvorgängen mit Hilfe eines Extremal-prinzips. Z. Physik, 124:772–89, 1947.

    Article  MathSciNet  Google Scholar 

  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.

    Article  MathSciNet  Google Scholar 

  30. P. T. Landsberg (ed.). Basic Properties of Semiconductors, Volume 1. North-Holland, Amsterdam New York London Tokyo, 1992.

    Google Scholar 

  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.

    Article  Google Scholar 

  32. R. A. Logan and A. J. Peters. Impurity Effects upon Mobility in Silicon. J. Appl. Phys., 31(1): 122–124, 1960.

    Article  Google Scholar 

  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. D. Long. Scattering of Conduction Electrons by Lattice Vibrations in Silicon. Phys. Rev., 120(6):2024–32, 1960.

    Article  Google Scholar 

  35. G. W. Ludwig and R. L. Watters. Drift and Conductivity Mobility in Silicon. Phys. Rev., 101(6): 1699–1701, 1956.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  40. K. Misiakos and D. Tsamakis. Electron and Hole Mobilities in Lightly Doped Silicon. Appl. Phys. Lett., 64(15):2007–09, 1994.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  42. T. N. Morgan. Broadening of Impurity Bands in Heavily Doped Semiconductors. Phys. Rev. A, 139(1):343–48, 1965.

    Google Scholar 

  43. F. J. Morin and J. P. Maita. Electrical Properties of Silicon Containing Arsenic and Boron. Phys. Rev., 96(1):28–35, 1954.

    Article  Google Scholar 

  44. B. R. Nag. Hot-Carrier d.c. Conduction in Elemental Semiconductors. Solid-State Electronics, 10:385–400, 1967.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  49. H. G. Reik and H. Risken. Distribution Functions for Hot Electrons in Many-Valley Semiconductors. Phys. Rev., 124(3):777–84, 1961.

    Article  MATH  Google Scholar 

  50. D. L. Rode. Electron Mobility in Ge, Si, and GaP. phys. stat. sol. (b), 53:245–54, 1972.

    Article  Google Scholar 

  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. 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.

    Article  Google Scholar 

  53. S. Selberherr. Analysis and Simulation of Semiconductor Devices. Springer-Verlag, Wien New York, 1984.

    Book  Google Scholar 

  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.

    Chapter  Google Scholar 

  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. R. Stratton. Diffusion of Hot and Cold Electrons in Semiconductor Barriers. Phys. Rev., 126(6):2002–14, 1962.

    Article  Google Scholar 

  57. N. Takimoto. On the Screening of Impurity Potential by Conduction Electrons. Jour. Phys. Soc. Japan, 14(9): 1142–58, 1959.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  MathSciNet  MATH  Google Scholar 

  60. J. D. Wiley. Polar Mobility of Holes in III-V Compounds. Phys. Rev. B, 4(8):2485–93, 1971.

    Article  Google Scholar 

  61. P. D. Yoder. Integrated Systems Laboratory, ETH Zurich. Private communication.

    Google Scholar 

  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. R. Zimmermann. Many Particle Theory of Highly Excited Semiconductors. Texte zur Physik, Band 18. BSB Teubner Verlagsgesellschaft Leipzig, 1988.

    Google Scholar 

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© 1998 Springer-Verlag Wien

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Schenk, A. (1998). Mobility Model for Hydrodynamic Transport Equations. In: Advanced Physical Models for Silicon Device Simulation. Computational Microelectronics. Springer, Vienna. https://doi.org/10.1007/978-3-7091-6494-5_2

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  • DOI: https://doi.org/10.1007/978-3-7091-6494-5_2

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