Diffusion relaxation limit of a nonisentropic hydrodynamic model for semiconductors

In this paper, we discussed a general multidimensional nonisentropic hydrodynamical model for semiconductors with small momentum relaxation time. The model is self‐consistent in the sense that the electric field, which forms a forcing term in the momentum equation, is determined by the coupled Poisson equation. With the help of the Maxwell‐type iteration, we prove that, as the relaxation time tends to zero, periodic initial‐value problem of certain scaled multidimensional nonisentropic hydrodynamic model has a unique smooth solution existing in the time interval where the corresponding classical drift‐diffusion model has smooth solutions. Meanwhile, we justify a formal derivation of the drift‐diffusion models from the nonisentropic hydrodynamic models. Copyright © 2007 John Wiley & Sons, Ltd.