Numerical Methods and their Application to Device Modelling

  • Eric A. B. Cole
Chapter

Abstract

The numerical modelling of devices involves the solution of sets of coupled partial differential equations, which in turn involve the solution of simultaneous nonlinear equations after discretisation has taken place. It is not possible in a single paper to fully describe all the numerical techniques involved in this process, and in this paper we will concentrate on the finite difference approach. Descriptions of the Finite Element method (Selberherr 1984, Mobbs 1989), the Boundary Element method and the Multigrid method (Ingham 1989) can be found elsewhere. Motivation for considering certain techniques will be given by examining the equations involved in the modelling of a two-dimensional MESFET. Finite differences are introduced in section 2, the solution of simultaneous equations discussed in section 3, and the discretisation of the current continuity equations and energy equation discussed in section 4. In section 5 we give details of the implementation for the case of the MESFET , and for a one-dimensional p-n junction. Finally in section 6 we discuss parameter determination.

Keywords

Boundary Element Method Spectral Radius Uniform Mesh Doping Profile Transient Solution 
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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Copyright information

© Springer-Verlag London Limited 1993

Authors and Affiliations

  • Eric A. B. Cole
    • 1
  1. 1.University of LeedsUK

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