Using Multigrid for Semiconductor Device Simulation in 1-D

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.