Uniform asymptotic representation of solutions of the basic semiconductor-device equations

In this paper we analyse the basic semiconductor-device equations modelling a symmetric one-dimensional voltage-controlled diode under the assumptions of zero recombination-generation and constant mobilities. Employing the singular-perturbation formulation with the normed Debye length as perturbation parameter we derive the zeroth-order terms of the matched asymptotic expansion of the solutions, which are sums of uniformly smooth outer terms (reduced solutions) and 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 situations.