On the Simulation and Qualitative Analysis of the Diffusion Processes due to Wide Electron Beams in Homogeneous Semiconductor Targets

Abstract

Some aspects of mathematical modeling and qualitative analysis of steady-state diffusion processes caused by the interaction of wide beam electrons with homogeneous semi-infinite semiconductor targets are considered. The use of wide electron beams incident normally on the target surface makes it possible to reduce the problem of modeling the diffusion of nonequilibrium minority charge carriers to a one-dimensional one. Consideration is carried out for electron beams with energies from several units to several hundreds of keV. Two mathematical models are studied: the classical mathematical model of so-called collective diffusion and the so-called model of independent sources. The first model considers a differential diffusion equation, the solution of which is a function that describes the distribution of nonequilibrium charge carriers in the volume of a semiconductor. The second model considers a differential diffusion equation that describes the distribution of charge carriers generated in the volume of a semiconductor by an infinitely thin plane parallel to the target surface. For the second model, the desired depth distribution of charge carriers is found by summing the distributions obtained from each infinitely thin plane. For both mathematical models, it is shown that a small change in the experimental conditions leads to a small change in the distribution of minority charge carriers over the target depth. For both models, estimates are given for the influence of the experimental conditions on the distribution of nonequilibrium minority charge carriers as a result of their diffusion in the semiconductor.