Using Multigrid for Semiconductor Device Simulation in 1-D

ID
TR-88-13
Authors
Uri M. Ascher and Stephen E. Adams
Publishing date
September 1988
Abstract

This paper examines the application of the multigrid method to the steady state semiconductor equations in one dimension. A number of attempts reported in the literature have yielded only limited success in applying multigrid algorithms to this sensitive problem, suggesting that a more careful look in relatively simple circumstances is worthwhile.

Several modifications to the basic multigrid algorithm are evaluated based on their performance for a one-dimensional model problem. It was found that use of a symmetric Gauss-Seidel relaxation scheme, a special prolongation based on using the difference operator, and local relaxation sweeps near junctions, produced a robust and efficient code. This modified algorithm is also successful for a wide variety of cases, and its performance compares favourably with other multigrid algorithms that have been applied to the semiconductor equations.