Quasineutral Limit of the Multi-dimensional Drift-diffusion Models for Semiconductors With PN-junctions

The quasineutral limit of drift-diffusion models for semiconductors with PN-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 yield the uniform estimates with respect to the scaled Debye length.