SIMULATION OF DYNAMIC PROCESSES IN A p - i - n DIODE BY THE METHODS OF PERTURBATION THEORY

Abstract

In the paper a mathematical model of the dynamic process of the electron-hole plasma formation in the active region ( i - region) of a semiconductor p - i - n - diode in the direct bias mode with a harmonic signal fed on the diode is developed. The basis of the model is a nonlinear nonstationary sin- gularly perturbed boundary value problem for a system of continuity equations of electron-hole currents and Poisson's equation. The algorithm for searching the charge carrier concentration distributions and the potential distribution is based on the asymptotic method of boundary functions and the Fourier method. In the course of the research, a technique for decomposing a nonlinear problem based on the development of perturbation theory me- thods was proposed. The initial nonlinear problem is reduced to a recurrent sequence of linear stationary boundary value problems, solved by classical and partially original analytical-numerical methods. The identification of the boundary functions in the solution of the problem provides, in particular, in contrast to the classical approximation of ambipolar diffusion, an adequate description of the electric field strength behavior in the active region of p - i - n - diodes. The obtained research results shed light on the peculiarities of the formation of the impedance characteristics of p - i - n - structures. The results of the work reveal more deeply the nature of the physical processes in the studied technical system and are aimed at improving the methodology for modeling and designing control semiconductor devices.