Prediction of the charge carriers stationary distribution in the active region of the p-i-n structures by the perturbation theory methods

Abstract

The p-i-n diode is an electronic device that is widely used for switching a microwave signals. The theory of the p-i-n diode is based on linear mathematical models that satisfactorily explain the diodes switching properties at low microwave power levels. The developed methods for modeling the corresponding devices on p-i-n diodes turned out to be untenable when studying the properties of diodes and diode structures under the with high-power microwave signals (typical for high-power switches and protective devices). Here are faced with the need to take into account the mutual influence of diffusion-drift, wave, thermal processes, in which the nonlinear components of the mathematical models will dominate. The development of the computer technology and the corresponding mathematical methods (for example, the perturbation theory methods) determines the possibility of improving the existing p-i-n diodes mathematical models and the possibility of the new approaches developing to the analysis of the nonlinear processes in p-i-n diodes and similar electronic devices. The goal of this paper is to improve the mathematical model and methods for predicting the electron-hole plasma stationary distribution in the active region of surface-oriented p-i-n structures based on the use of the boundary functions method. The mathematical model of the electron-hole plasma stationary distribution in the integrated surface-oriented p-i-n structures active region is constructed in the form of the nonlinear singularly perturbed boundary value problem for the system of equations of the charge carriers current continuity and Poisson. An approximate solution of the corresponding boundary value problem is found in the form of the asymptotic series leading terms in powers of a small parameter. A scheme for finding the problem solution is proposed, which automatically includes the classical formulations of problems for modeling the p-i-n structures characteristics and allows you to make significant amendments to the solution. This ensures an increase in the level of adequacy of modeling and understanding of the features of a number of physical processes (diffusion-drift, recombinant, injection) in the p-i-n diodes active region. We consider the proposed approach a promising tool for studying nonlinear thermal, diffusion-drift, generation-recombination stationary and non-stationary processes occurring in the p-i-n structures elements under the action of the external microwave radiation, and predicting new physical effects in the studied systems, for example, due to the influence of local surface and bulk defects on the p-i-n structures characteristics.