Influence of the direction of motion on the inelastic interaction between electrons and solid surfaces

Theoretical derivations of the inelastic differential inverse mean free path (DIMFP) and inelastic mean free path (IMFP) for electrons crossing solid surfaces were made for different crossing angles and electron distances relative to the crossing point at the surface. Individual contributions from volume and surface excitations were separated and analyzed for electrons traveling inside and outside the solid. Extended Drude dielectric functions were employed to calculate the DIMFP and inverse IMFP for electrons incident into and escaping from Cu. It was found that the DIMFP and inverse IMFP for electrons moving inside the solid were approximately independent of crossing angle and position of electrons due to the compensation of volume and surface excitations. For electrons moving deep inside the solid, the DIMFP and inverse IMFP reduced to the values for electrons moving in an infinite solid. As electrons traveling in the vacuum, the DIMFP and inverse IMFP became greater for glancing incident and escaping angles since surface excitations were more probable. The surface excitation parameter (SEP) for electrons traveling in vacuum showed an angular dependence. The SEP of escaping electrons was found larger than that of incident electrons due to the attractive force exerted by the induced surface charges. The calculated SEP was found to follow a simple expression.