Generalized proximity effect model in superconducting bi- and trilayer films

This article presents a general model for calculating the density of states and the Cooper pair potential in proximity-coupled superconducting bi- and trilayer films. It is valid for any kind of bilayer S-1-S-2, whatever the quality of the materials S-1 and S-2, the quality of the S-1-S-2 interface, and the layer thicknesses. The trilayer model is valid for a thin S-3 laye r, whereas the other two layers have arbitrary thicknesses. Although the eq uations of the dirty limit are used, it is argued that the model stays vali d in clean bi-and trilayer films. The typical example of superconducting tu nnel junctions is used to show that existing models, which apply to very th in or very thick layers or to perfectly transparent S-1-S-2 interfaces, are too restrictive to apply to an arbitrary bilayer. The new model is applied to practical junctions, with layer thicknesses intermediate between the "t hick" and the "thin" approximation. (C) 2001 American Institute of Physics.