Quasineutral limit of a time-dependent drift–diffusion–Poisson model for p-n junction semiconductor devices
Quasineutral limit of a time-dependent drift–diffusion–Poisson model for p-n junction semiconductor devices
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DOI：
10.1016/j.jde.2006.01.022
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发表时间：
2006-06
影响因子：
2.4
通讯作者：
L. Hsiao;Shu Wang
中科院分区：
文献类型：
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作者：
L. Hsiao;Shu Wang
本文研究了具有p-n结的绝缘半导体器件(即具有固定的双极背景电荷)的双极时变漂移-扩散-泊松方程的消失德拜长度极限。对于具有“良好”边界条件的变号光滑掺杂分布，利用奇异微扰分析的多重尺度渐近展开式和仔细执行的经典能量方法，严格地实现了准中性极限(零德拜长度极限)。证明的关键是首先引入一个‘密度’变换和两个λ加权的Liapunov型泛函，然后建立关于标度德拜长度的一致估计的熵产生积分不等式。该方法的基本思想是通过熵和熵耗散的相互作用来控制强非线性振荡。
In this paper the vanishing Debye length limit of the bipolar time-dependent drift–diffusion–Poisson equations modelling insulated semiconductor devices with p-n junctions (i.e., with a fixed bipolar background charge) is studied. For sign-changing and smooth doping profile with ‘good’ boundary conditions the quasineutral limit (zero-Debye-length limit) is performed rigorously by using the multiple scaling asymptotic expansions of a singular perturbation analysis and the carefully performed classical energy methods. The key point in the proof is to introduce a ‘density’ transform and two λ-weighted Liapunov-type functionals first, and then to establish the entropy production integration inequality, which yields the uniform estimate with respect to the scaled Debye length. The basic point of the idea involved here is to control strong nonlinear oscillation by the interaction between the entropy and the entropy dissipation.