GENERALIZATION OF THE TOUGAARD METHOD FOR INELASTIC-BACKGROUND ESTIMATION IN ELECTRON-SPECTROSCOPY - INCORPORATION OF A DEPTH-DEPENDENT INELASTIC MEAN FREE-PATH

A generalization of the Tougaard method for subtraction of the background of inelastically scattered electrons from an electron-energy spectrum is presented. Firstly, a depth dependence of the inelastic mean free path is introduced, which enables the analysis of electron-energy spectra from elements in inhomogeneous samples. The incorporation of the depth dependence of the inelastic mean free path also provides an equation for the calculation of peak intensities of electron-energy spectra from elements in inhomogeneous samples and the possibility of estimating the effect of elastic scattering of signal electrons. Secondly, it is shown that the Tougaard method allows the direct calculation of the background of inelastically scattered electrons from a known primary excitation spectrum for an arbitrary in-depth distribution of electron emitters. The validity of these generalizations is demonstrated for the case of an XPS model spectrum originating from a substrate covered with an overlayer, by comparing the results obtained in the present study with those reported previously.