Advertisement

Mathematical Modeling of Semiconductor Devices

  • Peter A. Markowich
Part of the Computational Microelectronics book series (COMPUTATIONAL)

Abstract

In this Chapter we shall formulate the system of partial differential equations, which describes potential distribution, carrier concentrations and current flow in semiconductor devices. We shall supplement the system by boundary conditions representing the interaction of the device with the outer world and discuss the modeling of physical parameters appearing in the system. Also, various choices of dependent variables, which are useful for analytical purposes, will be presented. Finally, we shall scale the physical quantities and put the system of equations and the boundary conditions into a dimensionless form appropriate for further mathematical and numerical investigations.

Keywords

Carrier Concentration Semiconductor Device Schottky Contact Doping Profile Current Relation 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [2.1]
    Antoniadis, D. A., Hauser, S. E., Dutton, R. W.: SUPREM II: A Program for IC Process Modeling and Simulation. Report 5019–2, Stanford University, Cal., U.S.A., 1978.Google Scholar
  2. [2.2]
    Antoniadis, D. A., Dutton, R. W.: Models for Computer Simulation of Complete IC Fabrication Processes. IEEE J. Solid State Circuits SC-14, No. 2, 412–422 (1979).Google Scholar
  3. [2.3]
    De Mari, A.: An Accurate Numerical Steady State One-Dimensional Solution of the P—N Junction. Solid State Electron., 11, 33–58 (1968).CrossRefGoogle Scholar
  4. [2.4]
    De Mari, A.: An Accurate Numerical One-Dimensional Solution of the P—N Junction under Arbitrary Transient Conditions. Solid State Electron. 11, 1021–2053 (1968).CrossRefGoogle Scholar
  5. [2.5]
    Furikawa, S., Matsumura, H., Ishiwara, H.: Theoretical Considerations on Lateral Spread of Implanted Ions. Jap. J. Appl. Phys. 11, No. 2, 134–142 (1972).CrossRefGoogle Scholar
  6. [2.6]
    Franz, G. A., Franz, A. F., Selberherr, S.: Cylindrically Symmetric Semiconductor Device Simulation. Report, Institut für Allgemeine Elektrotechnik, Technische Universität Wien, Austria, 1983.Google Scholar
  7. [2.7]
    Hall, R. N.: Electron-Hole Recombination in Germanium. Physical Review 87, 387 (1952).CrossRefGoogle Scholar
  8. [2.8]
    Hofmann, H.: Das elektromagnetische Feld, 2. Aufl. Wien—New York: Springer 1982.CrossRefGoogle Scholar
  9. [2.9]
    Jüngling, W.: Hochdotierungseffekte in Silizium. Diplomarbeit, Technische Universität Wien, Austria, 1983.Google Scholar
  10. [2.10]
    Jüngling, W., Guerrero, E., Selberherr, S.: On Modeling the Intrinsic Number and Fermi Levels for Device and Process Simulation. COMPEL 3, No. 2., 79–105 (1984).Google Scholar
  11. [2.11]
    Lin, C. C., Segel, L. A.: Mathematics Applied to Deterministic Problems in the Natural Sciences. New York: Macmillan 1974.Google Scholar
  12. [2.12]
    Markowich, P. A.: A Qualitative Analysis of the Fundamental Semiconductor Device Equations. COMPEL 2, No. 3, 97–115 (1983).CrossRefGoogle Scholar
  13. [2.13]
    Markowich, P. A., Ringhofer, C.: A Singularly Perturbed Boundary Value Problem Modeling a Semiconductor Device. SIAM J. Appl. Math. 44, No. 2, 231–256 (1984).Google Scholar
  14. [2.14]
    Mock, M. S.: Analysis of Mathematical Models of Semiconductor Devices. Dublin: Boole Press 1983.Google Scholar
  15. [2.15]
    Schütz, A.: Simulation des Lawinendurchbruchs in MOS-Transistoren. Dissertation, Technische Universität Wien, Austria, 1982.Google Scholar
  16. [2.16]
    Selberherr, S.: Analysis and Simulation of Semiconductor Devices. Wien—New York: Springer 1984.CrossRefGoogle Scholar
  17. [2.17]
    Selberherr, S., Griebel, W., Pötzl, H.: Transport Physics for Modelling Semiconductor Devices, Proceedings, Conference “Simulation of Semiconductor Devices”, Swansea, 1984.Google Scholar
  18. [2.18]
    Shockley, W., Read, W. T.: Statistics of the Recombination of Holes and Electrons. Physical Review, 87, No. 5, 835–842 (1952).CrossRefGoogle Scholar
  19. [2.19]
    Smith, R. A.: Semiconductor, 2nd ed. Cambridge: Cambridge University Press 1978.Google Scholar
  20. [2.20]
    Sze, S. M.: Physics of Semiconductor Devides, 2nd ed. New York: J. Wiley 1981.Google Scholar
  21. [2.21]
    Van Roosbroeck, W. V.: Theory of Flow of Electrons and Holes in Germanium and Other Semiconductors. Bell Syst. Tech. J. 29, 560–607 (1950).Google Scholar
  22. [2.22]
    Vasileva, A. B., Butuzow, V. F.: Singularly Perturbed Equations in the Critical Case. MRC—TSR 2039, Math. Res. Center, University Wisconsin-Madison, U.S.A., 1980.Google Scholar
  23. [2.23]
    Vasileva, A. B., Stelmakh, V. G.: Singularly Disturbed Systems of the Theory of Semicon-ductor Devices. USSR Comput. Math. Phys. 17, 48–58 (1977).Google Scholar
  24. [2.24]
    Zimam, J. M.: Electrons and Phonons. London: Clarendon Press 1963.Google Scholar

Copyright information

© Springer-Verlag Wien 1986

Authors and Affiliations

  • Peter A. Markowich
    • 1
  1. 1.Institut für Angewandte und Numerische MathematikTechnische Universität WienViennaAustria

Personalised recommendations