Imaging surface states in the electron microscope: a semiclassical model

A beam of electrons, grazing the surface of a semiconductor or insulator, can cause transitions between bands of localized surface states. When the scattered beam is focused in an energy-resolving transmission electron microscope, an image of the surface is obtained. This paper uses a semiclassical model to analyse inelastic electron-surface scattering and predict the brightness and shape of the surface image. The range of validity of the semiclassical model depends on the symmetries of the initial and final surface wavefunctions in a direction perpendicular to the surface.