Josephson tunneling and the proximity effect

Josephson junctions containing one or two proximity systems (e.g., S_α-M_β-I-S_γ, S_α-M_β-I-M_γ-S_δ; M_β(γ) is a normal metal or superconductor) are studied. An analysis of the thickness and temperature dependences of the maximum dc Josephson current IM is carried out. The curvature of the function IM(L_β) is found to depend strongly on the ratio of energy gaps ε_γε_α and on the temperature. The analysis is based on the thermodynamic Green's-function method, and the effect of strong coupling is also taken into account. If the proximity system contains two superconductors S_α and S_β then it appears that the electron-phonon interaction described by the constant λ_β contributes noticeably even if T>T_cβ.