Theory of the cross sections for inelastic scattering of electrons by core level excitations in solids

A calculation of cross sections for the inelastic scattering of electrons from core levels is carried out based on a model in which core level electrons are excited into a free-electron-like band state. A simplified model is also developed that assumes oscillator strengths appropriate to band-to-band excitations in solids. The results for Al L23 and Mo M45 cross sections are compared with a number of previous calculations. These previous calculations include: (a) the constant-oscillator-strength model, (b) the Rez model (based on exoitations to atomic-like states), and (c) the semi-empirical hydrogenic model proposed by Egerton. We have incorporated optical data into all of the models considered in this paper with the exception of Egertonʹs. Calculations are presented for incident electron energies of 100, 200 and 500 keV, collection angles of 1–41 mrad, and energy collection windows of 20–200 eV. Comparison is also made with experiment where possible and reasonable agreement is found.