The spatial extent of surface effects on electron inelastic scattering

We calculate the thickness of the surface scattering layer, defined as the region where electron inelastic scattering is affected by the surface, using the semi-classical treatment of electron energy loss provided by the Chen–Kwei theory. To this end, we consider the depth-dependent, surface-related contributions to the inverse inelastic mean free path, namely, the excitation of surface plasmons and the reduction in bulk plasmon excitation (Begrenzung effect). We find that surface effects extend further after electrons cross the surface than before they cross it. The ‘pre-surface thickness’ is given by the ratio of the electron velocity to the plasma frequency, the characteristic decay length for surface effects. All thickness estimates increase linearly with the electron velocity and decrease as (cosα)x with the angle α between the electron trajectory and the surface normal.