Angular and energy dependences of the surface excitation parameter for electrons crossing a solid surface

When fast electrons cross a solid surface, surface plasmons may be generated. Surface plasmon excitations induced by electrons moving in the vacuum are generally characterized by the surface excitation parameter. This parameter was calculated for 200-1000 eV electrons crossing the surfaces of Au, Cu, Ag, Fe, Si, Ni, Pd, MgO and SiO₂ with various crossing angles. Such calculations were performed based on the dielectric response theory for both incident (from vacuum to solid) and escaping (from solid to vacuum) electrons. Calculated results showed that the surface excitation parameter increased with crossing angle but decreased with electron energy. This was due to the longer time for electron-surface interaction by glancing incident or escaping electrons and by slow moving electrons. The results were fitted very well to a simple formula, i.e. P_s = frac(aE^{- b}, (cos α)^c), where P_s is the surface excitation parameter, E is the electron energy, α is the angle between the electron trajectory and the surface normal, and a, b and c are material dependent constants.