Semiconductor device modelling from the numerical point of view

In this paper mathematical and computational aspects of device modelling are treated. Four main subjects are discussed; the analytical model, the discretizations, the non-linear and the linear systems of equations. On the one hand the most commonly used numerical techniques are described; on the other hand several new techniques are presented. Noteworthy new techniques are the generalized upwind box scheme and the mixed variable approach. Aspects such as the choice of variables and the singularly perturbed nature of the problem are treated. Properties of the matrices involved are presented in a systematic way. Throughout the paper a standard one-dimensional diode is used to illustrate the concepts involved. Finally several realistic two-dimensional examples are given.