Electron differential inverse mean free path for surface electron spectroscopy

A new, general expression for the position-dependent differential inverse mean free path (DIMFP) of an electron penetrating into vacuum from a solid is derived. This DIMFP can be divided up into a bulk and a surface term. It is found that the surface effect is restricted to a surface layer extending on both sides of the vacuum-solid interface. An extended Drude dielectric function, which allows the characteristic oscillator strength, damping constant, and critical-point energy for each subband of valence electrons, is employed to estimate electron DIMFPs near Al and Au surfaces. Our results are relevant to the understanding of inelastic electron scattering near a solid surface.