In recent years the mathematical modeling of charge transport in semi­ conductors has become a thriving area in applied mathematics. The drift diffusion equations, which constitute the most popular model for the simula­ tion of the electrical behavior of semiconductor devices, are by now mathe­ matically quite well understood. As a consequence numerical methods have been developed, which allow for reasonably efficient computer simulations in many cases of practical relevance. Nowadays, research on the drift diffu­ sion model is of a highly specialized nature. It concentrates on the explora­ tion of possibly more efficient discretization methods (e.g. mixed finite elements, streamline diffusion), on the improvement of