Uniform estimates and uniqueness of stationary solutions to the drift-diffusion model for
Uniform estimates and uniqueness of stationary solutions to the drift-diffusion model for
复制标题
漂移扩散模型平稳解的统一估计和唯一性
DOI：
10.1080/00036811.2018.1460820
复制
发表时间：
2018
影响因子：
1.1
通讯作者：
Toru Kan and Masahiro Suzuki
中科院分区：
文献类型：
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作者：
Suzuki Yukihito;Ohnawa Masashi;Mori Naofumi;Kawashima Shuichi;Toru Kan and Masahiro Suzuki
研究了具有混合边界条件的漂移扩散模型的定常问题。对于这个问题，在一般情况下建立了解的存在性，而唯一性仅在不完全涵盖半导体器件在集成电路中使用的特殊情况下被研究。在这篇文章中，我们证明了在物理相关的情况下的唯一性。证明的关键是推导出电子和空穴密度的双边一致估计。我们建立了一种新的技术来表示下界。这与Moser迭代法一起导致了上界。
We study the stationary problem of the drift–diffusion model with a mixed boundary condition. For this problem, the existence of solutions was established in general settings, while the uniqueness was investigated only in some special cases which do not entirely cover situations that semiconductor devices are used in integrated circuits. In this paper, we prove the uniqueness in a physically relevant situation. The key to the proof is to derive two-sided uniform estimates for the densities of the electron and hole. We establish a new technique to show the lower bound. This together with the Moser iteration method leads to the upper bound.