Drift-Diffusion Systems: Variational Principles and Fixed Point Maps for Steady State Semiconductor Models

  • Joseph W. Jerome
Part of the The Springer International Series in Engineering and Computer Science book series (SECS, volume 113)


The mathematical semiconductor device model, consisting of the potential equation and the current continuity subsystem for the carriers, is studied from the standpoint of its decoupling fixed point map and the numerical approximate fixed point map. Variational principles will be discussed for this process and for discretizations achieved by use of generalized splines. By the choice of trial space, these capture the upwinding associated with Scharfetter-Gummel methods. An approximation calculus will be introduced in conjunction with the numerical fixed point map.


Variational Inequality Variational Principle Generalize Spline Flux Representation Recombination Term 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    H. K. Gummel. A self-consistent iterative scheme for one-dimensional steady-state transistor calculations. IEEE Trans. Electron Devices, ED-11:455–465, 1964.CrossRefGoogle Scholar
  2. [2]
    Joseph W. Jerome. On uniform approximation by certain generalized spline functions. J. Approximation Theory, 7:143–154, 1973.MathSciNetzbMATHCrossRefGoogle Scholar
  3. [3]
    Joseph W. Jerome. Consistency of semiconductor modeling: An existence/stability analysis for the stationary Van Roosbroeck system. SIAM J. Appl. Math., 45:565–590, 1985.MathSciNetzbMATHCrossRefGoogle Scholar
  4. [4]
    Joseph W. Jerome and Thomas Kerkhoven. The Steady State Drift-Diffusion Semiconductor Model. SIAM, 1991.Google Scholar
  5. [5]
    M. A. Krasnosel’skii, G. M. Vainikko, P. P. Zabreiko, Ya. B. Rutitskii, and V. Ya. Stetsenko. Approximate Solution of Operator Equations. Wolters-Noordhoff, 1972.Google Scholar
  6. [6]
    H. L. Scharfetter and H. K. Gummel. Large signal analysis of a silicon read diode oscillator. IEEE Trans. Electron Devices, ED-16:64–77, 1969.CrossRefGoogle Scholar
  7. [7]
    W. R. Van Roosbroeck. Theory of flow of electrons and holes in germanium and other semiconductors. Bell System Technical J., 29:560–607, 1950.Google Scholar

Copyright information

© Springer Science+Business Media New York 1991

Authors and Affiliations

  • Joseph W. Jerome
    • 1
  1. 1.Department of MathematicsNorthwestern UniversityEvanstonUSA

Personalised recommendations