Inelastic Effects in Photoemission: Microscopic Formulation and Qualitative Discussion

Abstract

The previous microcoscopic models of photoemission are developed and reformulated in order to include inelastic scattering effects. A general expression is given for the photocurrent and its energy distribution (EDC). The problem of inelastic scattering is more thoroughly discussed in the case of electron-phonon interaction for a pseudo-one-dimensional model. The approximations necessary for a random-walk description of the propagation of the electron in the final state to be valid are given. The microscopic formulation is then used to discuss phenomenological models such as the step model. It is shown that, in general, this model is not a good picture since one cannot separate simply the optical-transition step from the propagation of the excited electron and its escaping into the vacuum. In particular, even in the absence of inelastic effects, it is impossible to make a general prediction about the degree of accuracy with which the EDC may reproduce the optical joint density of states of the semi-infinite solid. Finally the paper discusses what type of information about the solid may be reasonably extracted from EDC measurements as a function of the energy of the primary excited state. It is concluded that the best conditions are met for uv and x-ray photoemission for which the elastic EDC should give information about the occupied surface states (uv) and bulk density of states (x ray).