Quantitative analysis in low-energy-electron transmission and reflection spectroscopy

A recent model of particle transport in plane-parallel media, including both quasielastic and inelastic scattering, has been proposed [Goulet et al., Phys. Rev. A 41, 6006 (1990)] which claims to be fully three dimensional, to include the effects of multiple scattering, and to avoid the normal difficulties associated with such problems. The present paper demonstrates that a transport problem is being solved and that the method used is of comparable accuracy to elementary diffusion theory. It is shown that the model, applied here to the low-energy-electron transmission and reflection spectroscopy problem, is valid only under a fairly stringent assumption on the interface scattering at the boundaries of the layer. The model is rederived for this case in terms of standard transport theory. A comparison of the two models points to an ambiguity in the interface reflectivity in the previous model. In addition the method presented here leads to a more satisfactory application of the Snell-Descartes law and a full solution in terms of known functions.