Electron Inelastic Mean Free Paths for LiF, CaF₂, Al₂O₃, and Liquid Water from 433 keV down to the Energy Gap

We report new calculations, which include the influence of the band gap and exciton states, of the electron inelastic mean free path (IMFP) for liquid water, LiF, CaF₂, and Al₂O₃ from the band gap to 433 keV. Among compounds, liquid water is the most studied due to its role in radiobiological research, whereas LiF and CaF₂ are the most widely used thermoluminescent dosimeters in environmental monitoring and medical and space dosimetry. Due to its sensitivity, the optically stimulated luminescent dosimeter, Al₂O₃, has recently begun to be used for personnel monitoring. Previous treatments have modified the integration domain to consider the indistinguishability between the incident electron and the ejected one or the bandgap energy for nonconductors but not to accommodate exciton states within the band gap, and no published IMFP data are available for CaF₂. Our calculation was carried out using an electron-beam-solid-state interaction model through the relativistic full Penn algorithm. Integration limits that consider the band gap, the valence band width, and exciton interactions have been used. The results suggest that, at electron energies below 100 eV, the different choices of models for integration limits and the exciton interaction can affect the IMFP by 9-29%. At higher energies, the differences associated with the choice of energy-loss function and other input parameters are around 2.5-7.5%.