Mean Escape Depth of Signal Photoelectrons from Amorphous and Polycrystalline Solids

Escape depth of photoelectrons leaving a target without being scattered inelastically was submitted to extensive theoretical analysis. Dependence of the mean escape depth on the X-ray angle of incidence and the electron initial angular distribution inside the sample was considered. The Monte Carlo algorithm was developed basing on a differential elastic scattering cross-section calculated within the partial-wave expansion method and a realistic electron-atom interaction potential. The mean escape depth was evaluated by means of the depth distribution function found analytically by solving a kinetic equation and by the Monte Carlo technique. The agreement between the results obtained from two methods is excellent. Elastic scattering was found to reduce considerably the escape depth. This reduction may reach up to 25% in the case of heavy elements in the practical X-ray photoelectron spectroscopy analysis. It was shown that the mean escape depth expressed in units of the electron transport mean free path is a universal function of the ratio of the inelastic to the transport mean free paths, the asymmetry parameter and the X-ray angle of incidence. A simple explicit expression for this function is proposed.