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EN
As follows from the formalism of X-ray photoelectron spectroscopy, knowledge of the angular distribution of photoemission is crucial for certain applications of quantitative X-ray photoelectron spectroscopy analysis. In the present work, the experimental data on the relative angular distribution of photoemission from solid materials are reviewed and compared with theoretical predictions. Noticeable discrepancies are usually observed. It has been proved that major part of the observed discrepancies can be ascribed to elastic photoelectron scattering. The commonly used formalism, where the elastic collisions are neglected, may be of insufficient reliability for certain solids, or in certain experimental geometries. This formalism can be easily extended to account for elastic photoelectron collisions by introducing two correction factors, Q_{X} and β_{eff}. The second parameter, called the effective asymmetry parameter, describes the observed decrease in anisotropy of photoemission. Determination of the correction factors requires a reliable theory describing elastic electron scattering in the solid. A need arises for accurate differential and total elastic electron scattering cross-sections pertinent to kinetic energies of considered photoelectrons or the Auger electrons. The increasingly important role of electron transport in surface analysis has stimulated an effort to construct a complete database containing the differential and total atomic elastic scattering cross-sections.
EN
The photoelectron emission from solids irradiated by X-rays was described by the analytical theory of electron transport and simulated by the Monte Carlo technique. The medium energy electron transport problem is treated by means of a Boltzmann type kinetic equation satisfying appropriate boundary conditions. The solution of the transport equation was obtained in the transport approximation based on the generalized radiative field similarity principle. Simple and reliable formalism was derived for both the differential and the total photoelectron yields. The dependence of the photoelectron yield on the X-ray incidence angle and the "flattening" effect of multiple elastic scattering on the angular distribution of electrons leaving the target are analysed in detail. The photoelectron yields and angular distributions calculated by the Monte Carlo algorithm, based on a realistic differential elastic scattering cross-section, are in good agreement with the results found from analytical theory. It is shown that main characteristics of the photoelectron emission are determined primarily by two parameters: the inelastic and the transport mean free paths.
EN
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.
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