Dielectric response theory for electron energy loss in clad cylindrical systems

Abstract

Inelastic interactions between an electron and a clad cylindrical system were investigated using the dielectric response theory. By solving the Poisson equation and applying the boundary conditions, these interactions were formulated in terms of the surface, interface and volume excitations. Formulas of the differential inverse inelastic mean free path (DIIMFP) were derived for electrons moving parallel to the axis of such a cylindrical structure. A sum-rule-constrained extended Drude dielectric function with spatial dispersion was applied to the calculations of the DIIMFP for a Si cylindrical tube or a Si cylinder clad in a ${\mathrm{SiO}}_{2}$ film. For the Si tube, it was found that surface excitations occurred as electrons moved near either the inner or outer surface of the tube and either inside or outside Si. Whereas, volume excitations arose only for electrons moving inside Si. Surface excitations increased, or volume excitations decreased, as electrons moved closer to the surface. For the Si cylinder clad in the ${\mathrm{SiO}}_{2}$ film, inelastic interactions were contributed from volume, surface, and interface excitations. Calculated results showed that the relative importance of these excitations depended on the electron distance from the surface or interface of the cylindrical system, the radius of the Si cylinder, and the thickness of the ${\mathrm{SiO}}_{2}$ film.