用微扰理论方法模拟p - i - n二极管有源区载流子分布

A. Bomba, I. Moroz
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引用次数: 0

摘要

提出了扩散-融合-漂移近似中p-i-n二极管有源区(i区)电子-空穴等离子体平稳分布的数学模型。该模型以电子-空穴电流连续性方程组、泊松方程和相应的边界条件的非线性奇摄动边值问题的形式表示。基于解的渐近表示,对p-i-n二极管等离子体中载流子平稳分布建模的非线性边值问题进行了分解。该模型问题被简化为线性边值问题的序列,具有渐近的主要(正则)分量的特征分离和边界修正。研究发现,求渐近正则部分零项问题的公式与双极扩散近似(自洽静电场近似)中p-i-n-二极管特性建模问题的经典公式相吻合。所提出的数学模型及其线性化方法使确定扩散漂移过程中的主要成分并研究它们的作用成为可能。例如,可以研究(包括通过分析方法)等离子体在p-i, n-i接触区的行为。研究结果旨在开发设计p-i-n二极管结构的方法,特别是用作微波数据传输系统信号开关和相应保护装置的有源元件。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Simulation of the Charge Carriers Distribution in the Active Region of the P-I-N-Diodes by the Perturbation Theory Methods
A mathematical model of the electron-hole plasma stationary distribution in the active region (i-region) of p-i-n-diodes in the dif-fusion-drift approximation is proposed. The model is represented in the form of a nonlinear singularly perturbed boundary value prob-lem for the system of equations of the electron-hole currents conti-nuity, the Poisson equation and the corresponding boundary condi-tions. The decomposition of the nonlinear boundary value problem of modeling the stationary distribution of charge carriers in the plasma of p-i-n-diodes is carried out on the basis of the solutions asymptotic representation. The model problem is reduced to a se-quence of the linear boundary value problems with a characteristic separation of the main (regular) components of the asymptotics and a boundary corrections. It was found that the formulation of the problem for finding the zero term of the asymptotics regular part coincides with the classical formulation of the p-i-n-diodes charac-teristics modeling problem, which is carried out in the approxima-tion of the ambipolar diffusion (approximation of a self-consistent electrostatic field).The proposed mathematical model and the method of its linearization make it possible to determing the main components in the diffusion-drift process and to study their role. For example, it becomes possible to study (including by analytical methods) the behavior of plasma in the p-i-, n-i-contacts zones. The results of the study are aimed at developing methods for de-signing p-i-n-diode structures, used, in particular, as active ele-ments of the signals switches of a microwave data transmission systems and the corresponding protective devices.
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