Universality Classes of Inelastic Electron Scattering Cross-sections

Quantitative XPS and AES analysis of surfaces requires models to do fast calculations of the energy loss of electrons at any energy as they move in solids of general and non-uniform composition. This is possible with the Universal cross-section that was introduced a decade ago. A critical review is given of the Universal cross-section in the light of the results of research carried out since then. In particular its validity is compared to that of experimental cross-sections determined by analysis of reflected electron energy-loss spectroscopy (REELS) spectra. It is shown that for applications in quantitative surface analysis by XPS and AES, the solids can be divided into classes according to the full width at half-maximum of the dominating shape of the inelastic scattering cross-section. The Universal cross-section is quite accurate for solids with a cross-section width 20 eV. For solids with a cross-section width of 10–15 eV, the Universal cross-section is still fairly good for the description of the far-peak region (30 eV from the peak energy) but it is less accurate to account for the near-peak region (10 eV from the peak energy). For solids with a cross-section width 5 eV, the REELS cross-section is always more accurate than the Universal cross-section. A Three-parameter Universal cross-section was defined, which gives a good fit to narrow experimental cross-sections. Parameters for different solids were determied and it was shown that the polymers form a separate universality class. © 1997 by John Wiley & Sons, Ltd.