The Takahashi-Tachiki equations, describing the critical properties of proximity-effect systems in the dirty limit, are solved exactly using the full eigenfunction expansion. Both parallel and perpendicular critical fields are calculated. The theory is applied to experimental data of Kanoda et aI. for V/Ag and of Chun et aI. for Nb/Cu, using the T, of the superconducting material and the diffusion coefficients of both materials as fit parameters. For the three-dimensional (3D) systems the fits compare nicely with the experimental results, but for 2D systems this is not always the case. It is found that the V and Nb critical temperatures necessary to fit the data can be larger than the corresponding bulk critical temperatures. This contrasts with what has been observed for single V and Nb films. Attempts to remedy this by choosing unconventional system parameters and using boundary conditions for less transparent interfaces turn out to be only limitedly successful. In the light of these anomalies earlier less complete calculations are reconsidered. It turns out that several assertions are superficial and cannot be affirmed by the results of the present work.

An exact expression is derived for the matrix Green's function of a clean superconducting layered structure with an arbitrary number of interfaces. A multiple-scattering approach is employed, in which the interfaces act as the scattering centres. Some initial applications of the theory to systems with transverse dimensions which vary from narrow to wide are given. The local density of states is calculated for an SNS and for an SNSNS junction (‘S’ standing for a superconducting layer and ‘N’ for a normal layer). For certain critical transverse widths the exact theory shows remarkable features not seen in the Andreev approximation. If the gap function for the systems is calculated self-consistently it turns out that for transverse dimensions smaller than twenty per cent of the superconducting coherence length, superconductivity is suppressed.

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An improved description of the critical properties of metallic multilayers is obtained by introducing the concept of a scaled magnetic coherence length in the Takahashi-Tachiki theory. By that, the absolute magnitude of the upper critical fields and the position of the dimensional crossover are uncoupled and become independent quantities. Much better phase diagrams can be obtained by using this scaling procedure. Although this concept is inspired by the character of disagreement between the theory without scaling and experiment, the procedure lacks an external justification. The fact that it works might serve as an indication how the Takahashi-Tachiki theory has to be modified in order to give a realistic quantitative description of upper critical fields in real metallic multilayers. The theory is applied to the V/Cu, V/Ag, Nb/Cu, and Nb/Ag systems. ͓S0163-1829͑96͒06425-9͔

The Takahashi-Tachiki equations, describing the critical properties of proximity effect systems in the dirty limit, are solved exactly using the full eigenfunction expansion. Both parallel and perpendicular critical fields are calculated. The theory is applied to experimental data of Kanoda et al. for V/Ag and of Chun et al. for Nb/Cu, using the 7 of the superconducting material and the diffusion coefficients of both materials as fit parameters. For the 3D systems the fits compare nicely with the experimental results, but for 2D systems this is not always the case. It is found that the V and Nb critical temperatures necessary to fit the data can be larger than the corresponding bulk critical temperatures. This contrasts with what has been observed for single V and Nb films. Additionally, the diffusion coefficients resulting from the fit procedure are found to be much smaller than one would expect from resistivity measurements. In the light of these anomalies earlier less complete calculations are reconsidered. It turns out that several assertions are superficial and cannot be affirmed by the results of the present work.