Quantitative Interpretation of Electron Spectroscopy Signals. Extracting the Differential Inverse Inelastic Mean Free Path and Differential Surface Excitation Probability in Solids

A method for extracting the differential inelastic scattering cross sections of electrons x in (Δ) from the energy spectra of electron spectroscopy is developed. The derived cross sections are verified by interpreting experimental data on electron-energy-loss spectra, X-ray photoelectron spectroscopy, and Auger spectroscopy. The paper highlights existing methods for determining the cross sections x in (Δ) using electron-energy-loss spectra. Inconsistency in analytical solution of the inverse problem (i.e., deconvolution) is shown for calculating the inelastic scattering cross section of electrons x in (Δ). In this paper, the solution of the mathematically ill-posed problem of cross-section retrieval is based on a fitting procedure consisting in multiple direct-problem calculations, i.e., calculations of the electron spectra taking into account both elastic and inelastic multiple scattering events. To implement an efficient fitting algorithm, a high-performance procedure for solving the direct problem of determining the energy spectra of electron spectroscopy is developed. The method for calculating the spectra is based on solution of the boundary problem for the transport equation by using the invariant imbedding method. The procedure developed in this work allows the energy-loss cross sections in the surface layer and in the sample homogeneous bulk layer remote from the surface to be reconstructed. The cross sections x in (Δ) retrieved from experimental data on the electron-energy-loss spectra satisfactorily reproduce the Auger spectroscopy and X-ray photoelectron spectroscopy signals and vice versa: the cross sections x in (Δ) retrieved from the X-ray photoelectron spectroscopy data satisfactorily reproduce the electron-energy loss and Auger spectroscopy spectra. It is shown that for the description of the X-ray photoelectron spectroscopy spectra of Be, Mg, Al, Nb, and W, it is not necessary to use additional mechanisms of energy losses, so-called “intrinsic excitations”.