F. Yubero, N. Pauli, A. Dubus, S. Tougaard
Physical Review B, 77 (2008) 245405 (11)
doi: 10.1103/PhysRevB.77.245405

An electron reaching the detector after being backscattered from a solid surface in a reflection electron energy loss spectroscopy (REELS) experiment follows a so-called V-type trajectory if it is reasonable to consider that it has only one large elastic scattering event along its total path length traveled inside the solid. V-type trajectories are explicitly assumed in the dielectric model developed by Yubero et al.[Phys. Rev. B 53, 9728 (1996)] for quantification of electron energy losses in REELS experiments. However, the condition under which this approximation is valid has not previously been investigated explicitly quantitatively. Here, we have studied to what extent these REELS electrons can be considered to follow near V-type trajectories. To this end, we have made Monte Carlo simulations of trajectories for electrons traveling at different energies in different experimental geometries in solids with different elastic scattering properties. Path lengths up to three to four times the corresponding inelastic mean free paths have been considered to account for 80–90% of the total electrons having one single inelastic scattering event. On this basis, we have made detailed and systematic studies of the correlation between the distribution of path lengths, the maximum depth reached, and the fraction of all electrons that have experienced near V-type trajectories. These investigations show that the assumption of V-type trajectories for the relevant path lengths is, in general, a good approximation. In the rare cases, when the detection angle corresponds to a scattering angle with a deep minimum in the cross section, very few electrons have experienced true V-type trajectories. However, even in these extreme cases, a large fraction of the relevant electrons have near V-type trajectories.