On the Scharfetter-Gummel Box-Method

  • T. Kerkhoven


For a linear potential function one-dimensional constant current drift-diffusion equations can be integrated in closed form, yielding the Scharfetter-Gummel (SG) discretization. The box-method generalizes the insistence on exact current conservation to higher dimensions by imposing the exact balancing of Scharfetter-Gummel fluxes through box-faces.

It has long been recognized that the one-dimensional SG discretization defines a finite element method that yields the exact solution by employing closed form solutions as an approximant. Finite element analyses of the box-method tend to employ piecewise linear approximating functions and fail to incorporate the exact integration properties of the SG discretization.

Nevertheless, the current conservation validates for the SG box-method an analytical coupling limitation for the differential drift-diffusion equations.


Piecewise Linear Current Conservation Linear Interpolant Exact Balance Semiconductor Device Simulation 
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]
    Randolph E. Bank and Donald J. Rose. Some Error Estimates for the Box Method. SIAM J. on Numer. Anal., 24:777–787, 1987.MathSciNetMATHCrossRefGoogle Scholar
  2. [2]
    Randolph E. Bank, Donald J. Rose, and Wolfgang Fichtner. Numerical Methods for Semiconductor Device Simulation. SIAM J. on Scient. and Statist. Comp., 4(3):416–435, September 1983.MathSciNetMATHCrossRefGoogle Scholar
  3. [3]
    E.M. Buturla, P.E. Cottrell, B.M. Grossman, and K.A. Salzburg. Finite-Element Analysis of Semiconductor Devices: The Fielday Program. IBM J. Res. Develop., 25:218–231, July 1981.CrossRefGoogle Scholar
  4. [4]
    Walter L. Engl, Heinz K. Dirks, and Bernd Meinerzhagen. Device Modeling. Proceedings of the IEEE, 71(1):10–33, January 1983.Google Scholar
  5. [5]
    W. Hackbusch. On First and Second Order Box Schemes. Computing, 41:277–296, 1989.MathSciNetMATHCrossRefGoogle Scholar
  6. [6]
    Thomas Kerkhoven. Piecewise Linear Petrov-Galerkin Analysis of the Box-Method. SIAM J. Numer. Anal., 20 pages, submitted.Google Scholar
  7. [7]
    Thomas Kerkhoven. On the Effectiveness of Gummel’s Method. SIAM J. on Scient. & Statist. Comput.,9:48–60, January 1988.MATHCrossRefGoogle Scholar
  8. [8]
    Thomas Kerkhoven. A Computational Analysis Of The Steady State Drift-Diffusion Semiconductor Model. SIAM, Philadelphia, 1993.Google Scholar
  9. [9]
    D. Scharfetter and H.K. Gummel. Large signal analysis of a silicon read diode oscillator. IEEE Trans. Electron Devices, ED-20:64–77, 1969.CrossRefGoogle Scholar
  10. [10]
    Siegfried Selberherr. Analysis and Simulation of Semiconductor Devices. Springer-Verlag, New York, 1984.CrossRefGoogle Scholar
  11. [11]
    Jan W. Slotboom. Computer-Aided Two-Dimensional Analysis of Bipolar Transistors. IEEE TRans. Electron. Dev., ED-20(8):669–679, August 1973.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Wien 1993

Authors and Affiliations

  • T. Kerkhoven
    • 1
  1. 1.Department of Computer ScienceUniversity of Illinois at Urbana-ChampaigneUrbanaUSA

Personalised recommendations