Electron energy loss in multilayered slabs. II. Parallel incidence

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.