Towards a universal description of elastic scattering effects in X-ray photoelectron spectroscopy

Expressions predicting photoelectron intensities, within the common formalism of X-ray photoelectron spectroscopy (XPS), are derived on the assumption that the effects of elastic electron scattering are negligible. In recent years, this assumption has been frequently proved to be invalid. In the present work, a general analytical formalism for quantitative XPS analysis is proposed. This formalism accounts properly for both elastic and inelastic interactions of the signal electrons with one-element solids, and is applicable to any experimental configuration of XPS. The problem of elastic scattering is treated within the framework of the generalized radiative field similarity principle implying the validity of the so-called transport approximation. The dependence of the photoelectron yield on the X-ray incidence angle and the analyser position, derived within the analytical theory, is compared with the results of Monte Carlo simulations. Very good agreement is observed which proves the reliability of the proposed analytical model. The computational procedure, making use of the developed formalism, is described in detail. Extensive tabulation of parameters necessary for these calculations is provided.