Inelastic energy loss of light particles scattered by solid surfaces at low energy: influence of the `gap'

Abstract The energy spectra of particles scattered by solid surfaces are used to determine the inelastic energy loss at low energy. Assuming the binary collision approximation, a modified TRIM code provides length distributions which are converted to time-of-flight (TOF) spectra by using the friction coefficient as an adjustable parameter. Owing to the nonlinear effects occurring in this energy range, the theoretical value of the electronic stopping power is performed from electron-particle scattering cross-section using a screened potential and so, the phase shifts, obtained self-consistently in the framework of density functional theory (DFT). In the case of He/a:Si interaction at 4 keV, the standard model leads to a largely overestimated value. This fact has been attributed to the presence of the electron energy gap E G and to the structure of the valence band. We verify this assumption in a non-static model involving all electrons of the valence band with a threshold condition v e ′2 > v F 2 +2 E G , where v F is the Fermi velocity and v e the electron velocity after scattering (non-static extended collisional model). The theoretical results agree very well with the experimental ones for He colliding three targets: a:Si, a:Ge and polycrystalline Ni at 4 keV. The calculations performed for the velocity range below 1 a.u. confirm the important role of the gap and the band structure in the lowering of stopping power at low velocity.