A method for solving the transport equation for the propagation of electrons in the primary energy range of interest in electron beam technology has been developed which is based on discretizing the related integral equation. The integral equation is solved by a collocation procedure yielding a system of linear equations.
The elementary scattering processes were described for elastic scattering by quantum mechanical differential cross sections and for inelastic scattering by Gryzinski type semi-empirical excitation functions for core and outer electrons separately.
From the electron flux density calculated, angular and energy distributions of transmitted and backscattered electrons were derived for various elements (Al, Cu, Ag, Au) and film thicknesses. The results agree with experimental data, including finer details as e.g. the dependence of the elastic backscattering peak on scattering angle and atomic number.
Hoffmann, Karl E. and Schmoranzer, Hans
"Inelastic and Elastic Multiple Scattering of Fast Electrons Described by the Transport Equation,"
Scanning Electron Microscopy: Vol. 1982
, Article 18.
Available at: https://digitalcommons.usu.edu/electron/vol1982/iss1/18