Emission depth distribution function for photoelectrons emitted by laboratory hard X-ray radiation sources

Formalism of quantitative X-ray photoelectron spectroscopy is based on a function describing the probability that a photoelectron emitted at a certain depth leaves the solid without energy loss. Determination of this function called the emission depth distribution function (EMDDF) requires knowledge of the photoemission cross section for analyzed photoelectrons. Typically, this cross section estimated within the so-called dipole approximation (DA) is used in the relevant formalism. It is well known now that the DA approach is applicable to photoelectrons with kinetic energy below 2 keV. An attempt is made here to extend the analytical expression for the EMDDF to higher energies by taking into account the non-dipolar contributions to the photoemission cross section, i.e. the non-dipole approximation (NDA). Accuracy of the derived formalism has been analyzed by extensive comparisons with Monte Carlo simulations. It has been found that the EMDDFs derived from both theoretical models compare very well. This analysis has been performed for Si 2s1/2, Cu 2p3/2, Ag 3d5/2 and Au 4f7/2 photoelectrons emitted by Ti Kα radiation (4510 eV). It has been found that the photoelectron signal intensity was considerably affected by the NDA effects, by up to 30% depending on the experimental configuration. The EMDDFs derived for high energy photoelectrons were used in calculations of parameters describing the photoelectron transport, i.e. the information depth (ID) and the mean escape depth (MED). It has been found that both parameters are practically not affected by the NDA model. This is an unexpected result indicating that the IDs and MEDs determined in the past using the DA model are also valid for high kinetic energy photoelectrons.