Inverse dielectric function for a semi‐infinite solid

Abstract

Abstract An old problem is addressed being the description of the dielectric response of electrons near the surface of an infinite half space to perturbing potentials and external charges. Taking into account spatial dispersion, expressions are derived for the screened potential and the inverse dielectric function within the approximation of specular electron reflection. The expressions generalize former results in a way that spatial symmetries of the problem are properly reflected. The boundary conditions are shown to follow from the definition of the screened potential. The inverse dielectric function obtained in the treatment fulfils the orthogonality relation to the dielectric function and the f ‐sum rule.