Numerical Methods for Transient Semiconductor Device Modelling

摘要

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)