Surface excitation in a semi-classical approach

We present a detailed semi-classical theoretical model of surface excitation to describe the electron differential inverse inelastic mean free path (DIIMFP) in the surface region. The formulation in the cylindrical coordinate system of momentum transfer allows the introduction of an explicit surface plasmon dispersion related to the parallel component of momentum transfer for the better description of surface plasmon excitation. With the bulk dielectric function represented by the Drude-Lindhard oscillator parameters, the associated surface dielectric function and its depth-dependent form are derived. This electron inelastic scattering modelling is integrated into the reverse Monte Carlo simulation model for the quantitative electron-beam analysis by the reflection electron energy loss spectroscopy (REELS) technique to extract the bulk dielectric function. Measurement of REELS spectra and numerical analysis have been performed for lead (Pb) at electron incident energies of 1 keV, 1.5 keV and 2 keV covering a wide energy loss range of 0-200 eV. The derived optical energy loss function reveals a pronounced bulk plasmon at 13 eV, exhibiting significantly higher intensity than previously reported, which agrees excellently with our time-dependent density functional perturbation calculation.