带PN结的高维半导体漂流扩散方程组的拟中性极限

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

为了研究带PN结的高维半导体漂流扩散方程组的拟中性极限问题,使用能量方法和entropy方法在索伯列夫范数意义下严格证明了具有好边界的变号doping轮廓情形下的PN结高维半导体漂流方程组的拟中性极限。

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.