Quasi-neutral Limit of the Drift-Diffusion Models for Semiconductors with PN-Junctions

The limit of vanishing Debye length in a bipolar drift-diffusion model for semiconductors with p-n junctions is studied in one space dimension. For general sign-changing doping profiles, the quasi-neutral limit (zero-Debye-length limit) is proved by using the asymptotic expansion methods of singular perturbation theory and the classical energy methods. An exact approximating solution with the 1st order term expansion is given, which takes into account the effects of initial and boundary layers. Then the structural stability of this approximate solution is established.