Simple model for electron inelastic mean free paths: Application to condensed organic materials

Abstract

A simple, ‘one-mode’ approximation for the wavevector- and frequency-dependent energy-loss function is employed to derive an expression for the electron inverse mean free path, λ v −1, including the effect of exchange between the incident electron and the electrons in the medium. Relation to optical data is made by averaging λ v −1, over the optical oscillator strength distribution, which is proportional to ωIm[— 1/ϵ(ω)]. For materials for which the optical oscillator strength distribution may be approximated by a single, Drude-type function, especially organic materials, the general results may be cast in a particularly simple form. Using a few constants derived from optical data for a given material, electron mean free paths in that material can be predicted for electron energies ≳ 150 eV. An approximate expression is also deduced for estimating electron mean free paths in materials for which no optical data are available. Mean free paths determined using this approximate expression agree well with those obtained in our earlier ‘universalcurve’ predictions. For polyethylene, the excellent agreement between results from the model presented here and those from a more detailed insulator model gives additional support for this simple theoretical approach. Agreement between theoretical predictions and experimental measurements of electron mean free paths in organic compounds, which in some cases is quite good, is on the whole less than satisfactory.