Kramers-Kronig analysis of reflection electron-energy-loss spectra measured with a cylindrical mirror analyzer

We have discussed a valence-electron energy-loss spectrum measured in reflection geometry using a cylindrical mirror analyzer (CMA) and derived the angular distribution of inelastic scattering, the momentum transfer, and the differential cross section per unit energy. If a critical inelastic-scattering angle is smaller than the angular aperture of the analyzer, the differential cross section no longer depends on momentum transfer. The reflection electron-energy-loss spectroscopy (REELS) spectra of ${\mathrm{MoS}}_2$ and graphite have been measured and the Kramers-Kronig analysis has been applied. The results are compared with those of the composite energy-loss function calculated from the energy-loss functions perpendicular and parallel to the c axis. It has been shown that the Kramers-Kronig analysis is still valid for the REELS spectra at higher incident energies than 500 eV and that the derived optical constants consist approximately of 80% of the perpendicular component and 20% of the parallel component.