Steady hydrodynamic model of semiconductors with sonic boundary and transonic doping profile
Steady hydrodynamic model of semiconductors with sonic boundary and transonic doping profile
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具有声波边界和跨声速掺杂分布的半导体稳态流体动力学模型
DOI：
10.1016/j.jde.2020.06.022
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发表时间：
2020
影响因子：
2.4
通讯作者：
Zhang Kaijun
中科院分区：
文献类型：
--
作者：
Chen Liang;Mei Ming;Zhang Guojing;Zhang Kaijun
如文[17]、[18]所示，对于具有音速边界和亚/超音速掺杂剖面的Euler-Poisson方程所表示的半导体流体动力学模型，其定态解的结构非常复杂。它可以有各种解决方案，如亚音速/超音速/跨音速流动。在本文中，我们考虑了一种更具挑战性的情况，即掺杂是跨音速的，它被分为两种类型：亚音速主导和超音速主导。在亚音速占优的情况下，我们证明了在适当的假设下，系统存在唯一的内部亚音速解、至少一个内部超音速解和无限多个跨声速解。然而，与亚音速掺杂剖面的情况不同的是，当弛豫时间较小时，在特殊情况下可能不存在内部亚音速解和内部超音速解。在超音速占优的情况下，还得到了所有类型解的不存在性和存在性。所采用的方法是结合格林函数法的技术紧凑性分析。在这里，所获得的结果完美地发展了已有的研究。
As shown in [17], [18], for the hydrodynamic model of semiconductors represented by Euler-Poisson equations with sonic boundary and subsonic/supersonic doping profile, the structure of stationary solutions are very complicated. It may possess various solutions like subsonic/supersonic/transonic flows. In this paper, we consider a more challenging case where the doping profile is transonic, which is categorized into two types: subsonic-dominated and supersonic-dominated. In the subsonic-dominated case, we show that the system has a unique interior subsonic solution, at least one interior supersonic solution and infinitely many transonic solutions under the suitable assumptions. However, the difference with the case of subsonic doping profile is that the interior subsonic solution and interior supersonic solution may not exist in special cases when the relaxation time is small. In the supersonic-dominated case, the non-existence and existence of all types of solutions are also obtained. The approach adopted is the technical compactness analysis combining the Green's function method. Here, the results obtained perfectly develop the existing studies.