Accession Number : ADA137970

Title :   Numerical Methods for Transient Semiconductor Device Modelling.

Descriptive Note : Technical summary rept.,

Corporate Author : WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s) : Ringhofer,C

PDF Url : ADA137970

Report Date : Dec 1983

Pagination or Media Count : 39

Abstract : A mixed system of parabolic and elliptic partial differential equations is used to describe the carrier transport and potential distribution in semi-conductor devices such as MOSFETs, diodes, etc. A singular perturbation analysis of the corresponding initial boundary value problem is carried out. Asymptotic expansions of the solution in powers of the minimal Debeye length are given. Based on this analysis a finite difference method for the numerical solution of these problems is developed. Here problems arise due to different time scales which are intrinsically present in the analytical problem. These different time scales do not occur in the physical solutions because of special (equilibrium-) initial conditions. Nevertheless they cause severe stability problems for finite difference methods. An unconditionally stable scheme is developed which minimizes computational effort. Numerical experiments on a test problem in one space dimension are presented. (Author)

Descriptors :   *Numerical methods and procedures, *Mathematical models, *Partial differential equations, *Semiconductor devices, Finite difference theory, One dimensional, Perturbations, Boundary value problems, Asymptotic series, Time dependence

Subject Categories : Electrical and Electronic Equipment
      Numerical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE