Stationary solutions to an energy model for semiconductor devices where the equations are defined on different domains

Abstract

We discuss a stationary energy model from semiconductor modelling. We accept the more realistic assumption that the continuity equations for electrons and holes have to be considered only in a subdomain Omega0 of the domain of definition Omega of the energy balance equation and of the Poisson equation. Here Omega0 corresponds to the region of semiconducting material, OmegasetminusOmega0 represents passive layers. Metals serving as contacts are modelled by Dirichlet boundary conditions. We prove a local existence and uniqueness result for the two-dimensional stationary energy model. For this purpose we derive a W1,p-regularity result for solutions of systems of elliptic equations with different regions of definition and use the Implicit Function Theorem.