Scattering of Conduction Electrons by Localized Surface Charges

Abstract

The differential scattering probability ${w}_{s}$ for conduction electrons scattered by localized surface charges is calculated using the Born approximation. This is applied to a recently derived expression for the Fuchs reflectivity parameter $p$ in terms of ${w}_{s}$. In a typical (semiconductor) case, the reflectivity $p$ is an order of magnitude closer to unity than is the kinetic specularity ${W}_{0}$ (=probability of a specular reffection). A strong angular dependence of $p$ is shown to be a compromise between an "aspect effect" and a "termination effect," with the latter usually dominant. The "termination effect" is the partial suppression of the scattering matrix element produced by terminating the wave function at the crystal surface. The "aspect effect" is the increase in the number of surface scatterers seen by a de Broglie wave front of unit diameter when it is turned toward glancing incidence. The dominance of the "termination effect" produces unit reflectance $p$ at glancing angles.