Determination of the effective surface region thickness and of Begrenzungs effect

The thickness, x s , of the effective surface region, defined as the region in which an electron travelling inside a material experiences surface excitations, as well as Begrenzungs effect, i.e. the variation of the bulk inelastic cross section in the surface region are theoretically determined for aluminium and silicon using the QUEELS- ε ( k , ω ) -REELS software. This software allows to determine the energy-differential inelastic electron scattering cross sections for reflection-electron-energy-loss spectroscopy (REELS) within the dielectric response theory. This study has been carried out for electron energies between 300 eV and 5000 eV. We find that the bulk inelastic cross section decreases exponentially with the distance to the surface, that x s is practically independent of electron incidence and exit angles and that x s = [ 2 ( v B ) 0.4 / ω s ] v 0.6 , where ω s is the surface plasmon frequency, v the electron velocity and v B the Bohr velocity ( v B = 2.19 × 10 6 m / s ).