Search

This work develops the semiclassical dielectric theory of energy loss, including retardation effects, for electrons travelling normal to a stratified slab. Starting from a transfer matrix formulation and using computer algebra, we obtain closed formulae for the dispersion relation, the Hertz vector and the energy-loss spectrum, valid for any finite number of layers. Our results are applied to multilayers of Al/Al2O3 and are used to investigate the validity of modelling a single interface by a sharp discontinuity in the dielectric function.

This paper develops the dielectric theory of energy loss, including retardation effects, for electrons travelling parallel to the interfaces of a stratified slab. A transfer matrix recurrence relation is introduced to implement the boundary conditions at surfaces and interfaces. This recurrence relation is solved exactly to provide closed formulae for the Hertz vector, the dispersion relation and the energy-loss probability, valid for any position of the beam and any number of layers. The non-retarded limits of these expressions are also examined and compared with the results of a simpler calculation based directly on Poisson's equation. Our final results are illustrated by numerical calculations applied to Al/Al2O3 multilayers and a InSb/GaP bilayer.

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.