Semiclassical Limit of Solutions to an Ultra-Small Semiconductor Device Model

Abstract

The semiclassical limit of solutions to the initial Dirichlet-Neumann boundary value problem for bipolar isentropic quantum drift-diffusion model in one space dimension is investigated. It is shown that the solutions of the problem converge to the one of classical drift-diffusion model as the Planck constant approaches to zero by using interpolation technique and compactness theory.