QUASINEUTRAL LIMIT OF THE MULTI-DIMENSIONAL DRIFT-DIFFUSION-POISSON MODELS FOR SEMICONDUCTORS WITH PN-JUNCTIONS

Abstract

In this paper the vanishing Debye length limit (space charge neutral limit) of bipolar time-dependent drift-diffusion models for semiconductors with p-n-junctions (i.e. with a fixed bipolar background charge) is studied in the multi-dimensional case. For generally smooth sign-changing doping profiles with good boundary conditions, the quasineutral limit (zero-Debye-length limit) is justified rigorously in the Sobolev's norm uniformly in time. The proof is based on the elaborate energy method and the relative entropy functional method which yields the uniform estimates with respect to the scaled Debye length.