Theory of Inelastic Scattering of Electrons from Solids

Abstract

The general properties of the single electron wave functions for a crystal are discussed, and an expression derived for the probability of excitation by electron bombardment as a function of the two electronic levels involved in the transition. When the excitation energy is small compared with the energy of the bombarding electron, the relative transitions probabilities approach those for excitation by radiation. A detailed calculation has been carried out for the case of solid copper, for which the energy levels are now known from other work. Approximate wave functions —of the atomic type for the lower state, free-electron-like for the upper state—were used to evaluate the transition integrals. The calculated distribution curve for the inelastically scattered electrons is in fair agreement with the experimental curve in the region of small energy losses: the rapid rise from small values and the following two maxima exhibited by the experimental curve are all reproduced in their proper positions. The departures for higher losses are attributed to the fact that the free-electron-like wave functions used are not a proper approximation to the actual functions in this region.