Influence of elastic and inelastic scattering on energy spectra of electrons emitted from solids

We have investigated theoretically the spectrum of electrons emitted from a solid in the case of a primary excitation function corresponding to a narrow line as in Auger and photoelectron spectroscopy. We concentrate on the influence of elastic and inelastic electron scattering on the shape and intensity of the spectrum in the vicinity of the primary peak. A near-peak as well as an off-peak region is identified; the critical energy loss separating the two regions is shown to depend on the relative significance of angular deflection and inelastic scattering. A rigorous formula has been derived that allows the extraction of the primary spectrum from a measured electron current if the normalized energy-loss function is available. The physical significance of the escape depth extracted from experiments with overlayers is analyzed. We find that it is not justified in general to identify the escape depth measured by means of overlayers with the inelastic mean free path.