Surface optical constants of silicon and germanium derived from electron-energy-loss spectroscopy

High-resolution electron-energy-loss spectra are reported for cleaved surfaces of silicon and germanium. The inelastic scattering has been observed with a small calibrated angular aperture spectrometer under various angles of incidence. Therefore absolute inelastic cross sections could be derived. For higher loss energies (>3.5 eV), where bulk transitions prevail, the cross sections are in agreement with a recent theory of Mills that relates the cross sections to a loss function $\mathrm{Im}\left[\frac{-1\mathrm{}}{(\epsilon +1)}\right]$ calculated from the bulk dielectric function $\epsilon \left(\omega \right)$. For smaller energies additional surface-state transitions are observed. These cross sections are described by assuming an optically active surface layer. The optical absorption of this layer is calculated from the loss spectra in an energy range up to 3 eV through use of an extension of the earlier theory. The result compares reasonably well to previously reported optical data.