Excitation spectrum of mesoscopic proximity structures

We investigate one aspect of the proximity effect, viz., the local density of states of a superconductor-normal metal sandwich. In contrast to earlier work, we allow for the presence of an arbitrary elastic mean free path in the structure. The superconductor induces a gap in the normal-metal spectrum that is proportional to the inverse of the elastic mean free path lN for rather clean systems. For a mean free path much shorter than the thickness of the normal metal, we find a gap size proportional to lN that approaches the behavior predicted by the Usadel equation ~diffusive limit!. We also discuss the influence of interface and surface roughness, the consequences of a nonideal transmittivity of the interface, and the dependence of our results on the choice of the model of impurity scattering.