On the inclusion of the recombination term in discretizations of the semiconductor device equations

In this paper we consider the semiconductor device equations for stationary problems where the recombination term cannot be neglected. We illustrate our ideas by deriving systematically discretizations of the two continuity equations and of the Poisson equation in the case of one space dimension. This approach leads to finite difference schemes for the continuity equations which are related to the Scharfetter-Gummel scheme. For the Poisson equation we obtain a new finite difference scheme which reduces to a scheme of Mock if the mesh is uniform and the recombination is zero.