Uniform Asymptotic Representation of Solutions of the Basic Semiconductor-Device Equations

Abstract

Abstract : In this paper the basic semiconductor device equations modelling a symmetric one-dimensional voltage-controlled diode are formulated as a singularly perturbed two point boundary value problem. The perturbation parameter is the normed Debye-length of the device. The authors derive the zeroth and first order terms of the matched asymptotic expansion of the solutions, which are the sums of uniformly smooth outer terms (reduced solutions) and the exponentially varying inner terms (layer solutions). The main result of the paper is that, if the perturbation parameter is sufficiently small then there exists a solution of the semiconductor device problem which is approximated uniformly by the zeroth order term of the expansion, even for large applied voltages. This result shows the validity of the asymptotic expansions of the solutions of the semiconductor device problem in physically relevant high-injection conditions.