Shane Mulligan : February 5, 2003

Numerical methods for semiconductor device modelling.

Abstract

In this presentation we consider numerical methods for the solution of the semiconductor device equations. These consist of a system of three coupled partial differential equations, a Poisson equation and two continuity equations, which describe the electric potential and the flow of electron and hole currents in a semiconductor device.

The equations are discretised using a generalised finite difference control volume method. The resulting 3 equations may be solved in a decoupled manner, using a Gauss-Seidel like scheme, or in a fully coupled manner using a damped Newton iteration.

We compare some preconditioned iterative methods for the solution of these systems. Numerical results will be presented for a number of specific devices.