The energy dependence of electron inelastic mean free paths

Abstract

AbstractAn analysis has been made of the dependence on electron energy of calculated inelastic mean free paths (IMFPs) for aluminum, copper, silver, and gold from four recent sources of data. The analysis was made using Fano plots which clearly show differences in energy dependences. In addition, the slopes of linear regions in the Fano plots can be compared with values calculated from experimental optical data and with values obtained from Fano plots made with experimental attenuation length (AL) data. It was found that the slopes of the Fano plots using IMFPs from calculations of Powell and Penn agreed well with the optical results; there was generally good agreement for the IMFPs of Ashley et al., but the slopes using the IMFP data of Szajman et al. exceeded the optical values by 9–40%. The slopes in the Fano plots using AL data for Al, Cu, and Au exceeded the optical values by 29–54 %; this result is similar to those found in other analyses and indicates that the electron energies for these AL measurements were not high enough to be in the asymptotic Bethe region. Analysis of the optical data also showed that a lower limit for the electron energy range over which the Fano plots could be expected to be linear (with their asymptotic slopes) was about 400 eV for Al and about 1000 eV for Cu, Ag, and Au. More extensive AL measurements over a wide electron energy range are needed to determine the shapes of the Fano plots for different types of materials.