This paper presents a general model for calculating the density of states and the Cooper pair potential in proximised 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 layer, whereas the other two layers have arbitrary thicknesses. Although the equations of the dirty limit are used, it is argued that the model stays valid in clean bi-and trilayer films. The typical example of superconducting tunnel junctions is used to show that existing models, applying to very thin or very thick layers, or to perfectly transparent S 1 -S 2 interfaces, are too restrictive to apply to any bilayer. The new model is applied to existing junctions, with layer thicknesses intermediate between the 'thick' and the 'thin' approximation.
1
I INTRODUCTIONUnderstanding the proximity effect in superconducting films is important for the development of practical devices such as superconducting tunnel junctions (STJ's). Depositing a superconductor S 1 onto another S 2 modifies the properties of both S 1 and S 2 materials. If both superconductors are thick enough (typically thicker than 10 ξ S 1 (S 2 ) , with ξ S 1 (S 2 ) the coherence length of S 1 (S 2 )), the extremities of the bilayer behave as bulk materials obeying the BCS theory, though not necessarily like bulk S 1 and bulk S 2 . The intermediate region around the S 1 -S 2 interface is characterised by a relatively sharp transition between the two bulk-like regions, and can be pretty far from a BCS-like description. If the layers are relatively thin, any BCS-like behaviour can be absent from the structure. Finally, in the case where the layers are extremely thin, as described by McMillan [1], each layer behaves again like a BCS superconductor.The physical quantities affected in a proximised bulk superconductor, are the Cooper pair potential ∆, the density of states for the Cooper pairs, P , and the density of states for the quasiparticles, N. As the density of states in both superconductors is modified due to the proximity effect, the resultant bandgap ∆ g lies at an intermediate value between the bulk values for S 1 and S 2 , ∆ g,S 1 and ∆ g,S 2 respectively. This feature has been fully described in the specific case, of a thin, low bandgap material S 2 next to a thick, high bandgap material S 1 , with both superconductors in the dirty limit [2,3].The goal of the present paper is to present the need for, and develop a model of, the proximity effect, which is not restricted to this very specific case.In particular section V shows that there are many situations where this special case does not apply, and for which the simple BCS approach does not provide a satisfactory description.Specifically, in the case of STJ's used as photon detectors, a more general description of the proximity effect is required to adequately address such issues as device performance.The general conditions for an ...