Determination of electron inelastic mean free path and stopping power of hafnium dioxide

We present inelastic mean free path (IMFP) and stopping power data of the hafnium dioxide applying the relativistic dielectric response theory. The energy loss function (ELF) derived from reflection electron energy loss spectroscopy spectrum with the reverse Monte Carlo method was used for the first time to obtain the IMFP and stopping power of HfO2. The probability of the energy loss is determined by the dielectric response function epsilon(q, omega) as a function of the frequency omega and the wavenumber q of the electromagnetic disturbance. Two algorithms, namely the full Penn algorithm (FPA) and the super-extended Mermin algorithm (SMA), were employed to expand the optical energy loss function, Im{-1/epsilon(0, omega)}, into the (q, omega)-plane. The results indicate that the IMFP and the stopping power obtained by using both algorithms are consistent at high electron energies, but show differences at low electron energies (less than similar to 70 eV). This discrepancy arises from the consideration of the finite plasmon lifetimes effect in the SMA model, while it is neglected in the FPA model. Additionally, we observed that the band gap has a significant influence on the IMFP and the stopping power at low electron energies. Typically, the inclusion of the band gap leads to an increase in the IMFP, because transition channels with energies larger than E - E-g - E-v are prohibited.

Automated summary

In this study, we used the relativistic dielectric response theory to obtain the inelastic mean free path (IMFP) and stopping power of hafnium dioxide (HfO2). The energy loss function derived from reflection electron energy loss spectroscopy spectrum was applied for the first time. Two algorithms were utilized to expand the optical energy loss function into the (q, omega)-plane. The results showed consistency at high electron energies, but differences at low electron energies due to the consideration of the finite plasmon lifetimes effect.