Projective approximation of the stochastic model of collective motion of minority charge carriers generated by a broad electron beam in semiconducting material

Abstract

The method of approximating the statistical characteristics (expectation and autocorrelation function) of the depth distribution of minority charge carriers (MCCs) generated by a broad electron beam in the homogeneous semiconducting material is described. This method developed for analyzing the model of collective motion of MCCs is based on the projective approach and the matrix operator theory. It is assumed that the electrophysical parameters (lifetime, diffusion coefficient, and surface recombination rate of MCCs) of a material are random quantities and obey the truncated normal distribution law. The influence of the variance of these parameters on the MCC distribution over depth is estimated. The potential of the method is illustrated by solving the problem of determining the statistical characteristics of the MCC distribution when MCCs are produced by a broad electron beam of moderate energy.