Surface excitation parameter for electrons crossing the AlN surface

Fast electrons crossing a solid surface induce surface excitations. The total probability of such excitations for electrons moving outside the solid, i.e. in vacuum, is characterized by the surface excitation parameter (SEP). In the present work, the SEP was calculated for either incident or escaping electrons with normal or glancing crossing angles over the surface of aluminum nitride (AlN), a wide-band-gap semiconductor. These calculations were performed based on the dielectric response theory using the sum-rule-constrained extended Drude dielectric function with parameters obtained from a fit of this function to experimental optical data and electron energy-loss data. Dependences of the SEP on electron energy and crossing angle were analyzed. A simple formula was proposed for the fitting of SEP as a function of electron energy and crossing angle.