Steady State Semiconductor Device Modelling a State of the Art Report

In this paper we present a state-of-theart report on mathematical and numerical steady state semiconductor device modeling. As underlying device model we use the basic semiconductor device equations, which consist of Poisson's equation, the current relations and the continuity equations. By appropriate scaling we reformulate the device problem as singularly perturbed elliptic system with the characteristic Debye length A as perturbation parameter. Asymptotic analysis for A+O+ is used to analyse the structure of solutions. We employ the information obtained by the perturbation analysis to develop appropriate numerical simulation techniques and present simulation results for a MOS-transistor. 1. THE MATHEMATICAL MODEL The system of partial differential equations, which describes potential distribution and current flow in an arbitrary semiconductor device, is in the steady state case given by (see (8),(11)): (1.1) E~W = -q(p-n+C(x))