The transport equation theory applied to the prediction of the spatial distribution of an electron beam in a target

Abstract

The author makes a contribution to the understanding of the phenomenon of the electron distribution under the circumstances of a beam-induced charge build-up in a target. Such phenomena are encountered in electron-beam-assisted microanalysis or in Auger electron analysis. The theoretical problem of the motion of a beam of charged particles in a solid is resolved by interpreting the transport equation in terms of an integro-differential equation. A treatment of the Boltzmann equation is developed for the energy dependence in order to predict the electron penetration in targets bombarded under the simultaneous influence of scattered and decelerated incident particles. The exact values of the specific moments of the electron distribution in a semi-infinite medium are calculated. The author suggests a procedure applied to the calculation of an analytic expression characterizing the asymptotic trend of the electron spatial distribution at very small residual energies. The perturbing effects of insulator irradiation are treated and charge deposition profiles near the surface are calculated for mixed alkali silica glasses. Results are compared with previous data; agreement is in most cases fairly good.