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The theory of superconductivity in thin SN sandwiches (bilayers) in thediffusive limit is developed within the standard Usadel equation method, withparticular emphasis on the case of very thin superconductive layers, d_S <<d_N. The proximity effect in the system is governed by the interlayer interfaceresistance (per channel) \rho_{int}. The case of relatively low resistance(which can still have large absolute values) can be completely studiedanalytically. The theory describing the bilayer in this limit is of BCS typebut with the minigap (in the single-particle density of states) E_g << \Deltasubstituting the order parameter \Delta in the standard BCS relations; theoriginal relations are thus severely violated. In the opposite limit of anopaque interface, the behavior of the system is in many respects close to theBCS predictions. Over the entire range of \rho_{int}, the properties of thebilayer are found numerically. Finally, it is shown that the results obtainedfor the bilayer also apply to more complicated structures such as SNS and NSNtrilayers, SNINS and NSISN systems, and SN superlattices.Comment: 15 pages (including 10 EPS figures), REVTeX. Version 2: minor  changes; added references, a note is added concerning applicability of our  results to SNINS and NSISN systems. To appear in Phys. Rev. B on March 1,  200

Superconductive properties of thin dirty superconductor–normal-metal bilayers