Energy loss of electrons traveling parallel to the interface of a semi-infinite granular composite

The energy loss of an electron traveling above a semi-infinite granular composite consisting of randomly located spherical inclusions is investigated. We express this loss in terms of a surface response function which is then calculated using an effective medium theory for the bulk dielectric function of the system. Three different models are analyzed. The first two models correspond to local and nonlocal versions of a truncated bulk, and the third one includes the effects of the distribution of the spherical inclusions near the surface. We find that a correct treatment of this distribution is necessary in order to get meaningful results.