用微扰理论方法建立了p-i-n二极管有源区中考虑加热和复合的扩散漂移过程的数学模型

A. Bomba, I. P. Moroz
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引用次数: 3

摘要

随着电流通过半导体器件的长时间传输,在特定的p-i-n二极管中,其有源区域的电子空穴等离子体被加热。本文给出了等离子体加热效应的理论研究结果,即在p-i-n二极管体积内的焦耳热释放和载流子复合能量释放对p-i-n二极管有源区等离子体浓度分布的影响。针对由载流子电流连续性方程、泊松方程和导热系数组成的方程组,提出了以给定区域内非线性边值问题的形式预测体p-i-n二极管i区电子-空穴等离子体稳态浓度分布和温度场的数学模型。结果表明,该模型的微分方程包含一个小参数,使得泊松方程为奇摄动,热传导方程为规则摄动。用相应的小参数幂渐近级数的形式得到了问题的近似解。该渐近序列描述了研究区域内等离子体浓度和电位的行为,包含近边界修正以确保边界条件的满足。这些级数的项是通过求解一系列边值问题而得到的,这些边值问题是对线性微分方程组的原问题进行拆分而得到的。将非线性热方程的边值问题简化为相应的线性非齐次方程的一系列问题。精炼解决方案的过程是迭代的。系统中负反馈的存在保证了过程的稳定性(随着温度的升高,载流子的迁移率降低)。
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THE DIFFUSION-DRIFT PROCESS WITH ACCOUNT HEATING AND RECOMBINATION IN THE p-i-n DIODES ACTIVE REGION MATHEMATICAL MODELING BY THE PERTURBATION THEORY METHODS
With prolonged transmission of an electric current through the semiconductor devices, in a particular p-i-n diodes, an electron-hole plasma of their active region is heated. This paper presents the theoretical studies results of the plasma heating effect by the Joule heat release in the p-i-n diode volume and the charge carriers recombination energy release on the plasma concentration distribution in the p-i-n diodes active region. The mathematical model is proposed for predicting the electron-hole plasma stationary concentration distribution and the temperature field in the i-region of the bulk p-i-n diodes in the form of a nonlinear boundary value problem in a given area for the equations system, which consist of the charge carrier current continuity equations, the Poisson and the thermal conductivity. It is shown that the differential equations of the model contain a small parameter in such a way that the Poisson equation is singularly perturbed and the heat conduction equation is regularly perturbed. An approximate solution of the problem posed is obtained in the form of the corresponding asymptotic series in powers of the small parameter. The asymptotic serieses, which describes the behavior of the plasma concentration and potential in the investigated region, containing near-boundary corrections to ensure the fulfillment of the boundary conditions. The terms of these series are found as a result of solving a sequence of boundary value problems, obtained as a result of splitting the original problem, for systems of linear differential equations. The boundary value problem for a nonlinear heat equation is reduced to a sequence of problems for the corresponding linear inhomogeneous equations. The process of refining solutions is iterative. The stabilization of the process is ensured by the existence of negative feedback in the system (as the temperature rises, the mobility of charge carriers decreases).
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