Theory of the Inelastic Scattering of Low-Energy Electrons from Crystal Surfaces by One-Phonon Processes

Abstract

In this paper, we present a theoretical discussion of the form of the differential cross section per unit solid angle, per unit energy shift for the inelastic scattering by one-phonon processes of low-energy electrons from the surface of a semi-infinite crystal. A number of general features of the cross section are discussed, with particular attention to a comparison with the results obtained from the kinematical theory of the scattering process. We have also carried out a series of numerical studies of the dependence of the shape of the energy loss spectrum on momentum transfer for an electron incident on the (100) surface of an fcc crystal. For a general value of the momentum transfer, the energy loss spectrum consists of one or more lines that arise from the scattering off surface modes, and a band that has its origin in scattering produced by bulk modes. The shape of the latter feature, as well as the position of the surface mode peaks, is found to be quite sensitive to the values of the atomic force ...