Modern methods of transfer theory used for solution of signal identification problems of XPS

•We calculate exact numerical solutions for XPS elastic peak angular distributions.•XPS angular distributions were calculated for a finite thickness layer.•Numerical solution is compared to transport and straight line approximations.

Within the framework of the classical radiative transfer theory [1], [2] and [3], signal shaping of the most recently needed method of electron spectroscopy – X-ray Photoemission Spectroscopy (XPS) is analyzed. The boundary problem for the photoelectron transfer equation is solved on the basis of invariant embedding methods. Approximate analytical solutions of the derived equations are determined using the spherical harmonics method, straight line and transport approximations. The exact solutions are obtained by numerical matrix methods. The obtained results are analyzed comparing the calculation data to the results of MC simulation. High efficiency of the numerical matrix methods is shown for inverse problem solution in XPS. Errors of the straight line and transport approximations are estimated.