Monte Carlo calculations are used to obtain the energy loss and spatial distribution of electrons penetrating matter. For this purpose, reliable cross section for the inelastic collisions must be known. As an approximation valid for large energy losses, the Coulomb cross section can be used. It can be modified in a simple way to account for the binding of electrons and for the exchange effect. In the Gryzinski model, collisions with moving electrons are assumed. In the quantum mechanical Bethe approximation, σ is closely related to the dipole oscillator strength (DOS), and its extension to finite momentum transfers, the generalized oscillator strength (GOS). Therefore, the influence of the state of a material on DOS is shown for the example of gaseous and solid silicon. Some details of the Bethe model are given for Si. The Bethe asymptotic approximation to the stopping power is derived, and the reason for the shell corrections is demonstrated. Collision cross sections calculated with three different models are compared. In general, models based on a detailed knowledge of the GOS should be used for applications.
"Energy Loss of Electrons Below 10 keV,"
Scanning Microscopy: Vol. 1990
, Article 10.
Available at: https://digitalcommons.usu.edu/microscopy/vol1990/iss4/10