A Singularly Perturbed Boundary Value Problem Modelling a Semiconductor Device.
A Singularly Perturbed Boundary Value Problem Modelling a Semiconductor Device.
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DOI：
10.1137/0144018
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发表时间：
1982-05
影响因子：
1.9
通讯作者：
P. Markowich;C. Ringhofer
中科院分区：
文献类型：
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作者：
P. Markowich;C. Ringhofer
本文研究了偏压作用下半导体器件(即$pn$结)的静态一维模型。控制方程是描述半导体中载流子输运的众所周知的方程，它由一组常微分方程组组成，这些常微分方程组受到施加在接触处的边界条件的约束。由于边界处溶液分量的量级不同，我们分别对各分量进行定标，得到了一个奇异摄动问题，通过忽略空穴和电子的电流密度，分析了平衡情况(施加零偏压)，并建立了近似模型，假设为奇异摄动的二阶方程。这对于小的正向偏置和适度的反向偏置是有意义的。对于整个问题，我们证明了电子-空穴载流子对数目的先验估计，并通过建立约化系统和边界，导出了渐近展开式(当微扰参数趋于零时)。
This paper is concerned with the static, one-dimensional modelling of a semiconductor device (namely the $pn$-junction) when a bias is applied. The governing equations are the well-known equations describing carrier transport in a semiconductor which consist of a system of ordinary differential equations subject to boundary conditions imposed at the contacts. Because of the different orders of magnitude of the solution components at the boundaries, we scale the components individually and obtain a singular perturbation problem.We analyse the equilibrium case (zero bias applied) and set up approximate models, posed as singularly perturbed second order equations, by neglecting the hole and electron current densities. This makes sense for small forward bias and for moderate reverse bias.For the full problem we prove an a priori estimate on the number of electron-hole carrier pairs and derive asymptotic expansions (as the perturbation parameter tends to zero) by setting up the reduced system and the boundary ...