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

In this paper we analyse the basic semiconductor-device equationsmodelling a symmetric one-dimensional voltage-controlled diodeunder the assumptions of zero recombination-generation and constantmobilities. Employing the singular-perturbation formulationwith the normed Debye length as perturbation parameter we derivethe zeroth-order terms of the matched asymptotic expansion ofthe solutions, which are sums of uniformly smooth outer terms(reduced solutions) and exponentially varying inner terms (layersolutions). The main result of the paper is that, if the perturbationparameter is sufficiently small, then there exists a solutionof the semiconductor-device problem which is approximated uniformlyby the zeroth-order term of the expansion, even for large appliedvoltages. This result shows the validity of the asymptotic expansionsof the solutions of the semiconductor-device problem in physicallyrelevant high-injection situations.