Electron energy loss in multilayered slabs

This paper extends the local dielectric theory of electron energy loss to stratified slabs. With the help of transfer matrices, computer algebra and mathematical induction, we have established closed-form solutions for dispersion relations and electron energy-loss spectra, valid for a wide class of multilayered structures. Our formulae apply to any number of layers and provide unified results for structures ranging from bulk media to superlattices. Both normal and parallel incidence are considered. For multilayers of isotropic media our calculations include the effects of retardation. For multilayers of anisotropic media we consider only the electrostatic, non-retarded limit. Our general results are illustrated by examples involving Al, Al2O3, Si, SiO2, InSb, GaP and graphite layers.