Transport equation treatment of transmitted electrons through thin films of aluminium

A theoretical study of the transmission of electrons through thin films of aluminium of various thicknesses and for primary energy 1.5 to 3 keV is attempted using the Boltzmann equation treatment proposed by Bethe et al (Proc. Am. Phil. Soc.; 78:573 (1938)) and more recently applied to the penetration and backscattering of electrons in solids. Semi-empirical expressions for the energy loss on the basis of a continuous slowing-down approximation are improved. The results are compared with experimental measurements of the energy distribution and the transmission coefficient. The discrepancy in the energy distribution seems similar to that already pointed out using a Monte Carlo calculation with the continuous slowing-down approximation. The results obtained and a comparison between the theoretical and semi-empirical stopping powers suggest further modifications in order to obtain a satisfactory agreement and justify the validity of this treatment. (author)