Inelastic Mean Free Paths of Low-Energy Electrons in Solids

We present a summary of recent calculations of the electron inelastic mean free paths (IMFPs) of 50-2000 eV electrons in 27 elements and 15 inorganic compounds. These calculations are based in part on experimental optical data to represent the dependence of the inelastic scattering probability on energy loss and the theoretical Lindhard dielectric function to represent the dependence of the scattering probability on momentum transfer. The calculated IMFPs for the elements were fitted to a modified form of the Bethe equation for inelastic electron scattering in matter and the four parameters in this equation were empirically related to other material parameters. The resulting formula, designated TPP-2, provides a convenient means for predicting IMFPs in other materials. We have used two powerful integral equations or sum rules to evaluate the optical data on which our IMFP calculations are based. While the optical data for the elements satisfied these sum rules to an acceptable degree, there were significant deviations in the data for the compounds. In addition, differences in IMFPs calculated from the optical data for the compounds and the values predicted by TPP-2 correlated with the average errors of the optical data as determined by the sum rules. IMFPs calculated from TPP-2 for these compounds are therefore believed to be more reliable than IMFPs obtained from the imperfect optical data.