Uniform asymptotic representation of solutions of the basic semiconductor-device equations
Uniform asymptotic representation of solutions of the basic semiconductor-device equations
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基本半导体器件方程解的一致渐近表示
DOI：
10.1093/imamat/36.1.43
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发表时间：
1986
影响因子：
1.2
通讯作者：
C. Schmeiser
中科院分区：
文献类型：
--
作者：
P. Markowich;C. Schmeiser
摘要：本文将对称一维压控二极管的半导体器件基本方程表述为奇摄动两点边值问题。扰动参数是设备的规范德拜长度。导出了解的匹配渐近展开式的零阶项和一阶项，即均匀光滑的外项（约化解）和指数变化的内项（层解）的和。本文的主要结果是，如果扰动参数足够小，则存在一个半导体器件问题的解，即使在大的施加电压下，也可以用展开的零阶项均匀逼近。这一结果证明了半导体器件问题解的渐近展开式在物理相关的高注入条件下的有效性。
Abstract : In this paper the basic semiconductor device equations modelling a symmetric one-dimensional voltage-controlled diode are formulated as a singularly perturbed two point boundary value problem. The perturbation parameter is the normed Debye-length of the device. The authors derive the zeroth and first order terms of the matched asymptotic expansion of the solutions, which are the sums of uniformly smooth outer terms (reduced solutions) and the exponentially varying inner terms (layer solutions). The main result of the paper is that, if the perturbation parameter is sufficiently small then there exists a solution of the semiconductor device problem which is approximated uniformly by the zeroth order term of the expansion, even for large applied voltages. This result shows the validity of the asymptotic expansions of the solutions of the semiconductor device problem in physically relevant high-injection conditions.