Elastic and inelastic scattering of electrons reflected from solids: Effects on energy spectra

The effects of elastic and inelastic scattering on energy spectra of electrons reflected from solids have been investigated theoretically. The aim was to evaluate the spectrum in the vicinity of the elastic peak. Following Tougaard and Sigmund’s approach [Phys. Rev. B 25, 4452 (1982)], the elastic and inelastic scattering events are separated as independent when calculating the flux of reflected electrons. The influence of elastic scattering is considered here in detail within the $P_1$ approximation of the Boltzmann transport equation, and the inelastic scattering is described by the Landau formula. A general expression for the energy spectrum as well as expressions for discrete and continuous energy spectra are derived. Comparisons are made with the continuous part of measured spectra and a reasonable agreement is seen.