Interaction of low-energy electrons (1-30 eV) with condensed molecules: I. Multiple scattering theory

We derive a mathematical expression for the energy-loss spectrum or the energy distribution of electrons backscattered from a disordered film deposited on a substrate in terms of a primary scattering probability function corresponding to the elastic and inelastic scattering probabilities. Both single- and multiple-collision effects are included and can serve to describe electron scattering in the submonolayer- and multilayer-coverage regimes, respectively. The basic equations are derived from the equation of radiative transfer by using the Schuster-Schwarzschild approximation. Despite the presence of an energy-loss dependence in our formulation these equations can be reduced to simpler expressions by performing Fourier transforms on the energy, as long as the energy-loss range remains small. For small scattering angles they reduce to the Landau formula applicable to the transmission of electron through a solid. At large thicknesses, the amplitude of the energy distribution of backscattered electrons becomes independent of the thickness and nature of the substrate.