A universal algorithm for calculating the backscattering factor in Auger-electron spectroscopy

We describe a universal Monte Carlo algorithm that can be used for the efficient calculation of backscattering factors (BFs) for quantitative Auger-electron spectroscopy (AES). This algorithm makes use of the continuous slowing-down approximation and the electron stopping power instead of simulation of individual inelastic-scattering events. This approach is attractive because it can be applied to any material with an empirical formula for the stopping power, available data for differential elastic-scattering cross sections, and an empirical formula for inner-shell ionization cross sections. We report BFs for the Si KL23L23, Cu L3M45M45, Ag M5N45N45, and Au M5N67N67 Auger transitions in the corresponding elemental solids. These BFs were calculated for normal incidence of the primary beam, primary energies from near threshold for ionization of the relevant core levels to 20 keV, and Auger-electron emission angles of 10°, 60°, and 80°. We found satisfactory agreement between these BFs and values obtained from a more accurate algorithm in which individual inelastic-scattering events were simulated. Percentage deviations between BFs from the two algorithms were <2% for Au, <5% for Ag, <7% for Cu, and <10% for Si for primary energies likely to be used in practical AES. These deviations arise mainly from our use of stopping powers from the empirical formula rather than more reliable values calculated from experimental optical data.