Modelling the energy gap in transition metal/aluminium bilayers

We present an application of the generalised proximity effect theory. The theory has been used to determine the energy gap (Δ_g) in proximised transition metal/aluminium bilayer structures such as Nb/Al, Ta/Al, V/Al and Mo/Al. These bilayers have different film thicknesses ranging from 5 to 260 nm. For the cases of Nb/Al, Ta/Al and V/Al bilayers, the interface parameters γ and γ_BN (here we define γ as the ratio of the products of normal state resistivity and coherence length in each film of the bilayer while γ_BN is the ratio of the boundary resistance between films 1 and 2 to the product of the resistivity and coherence length in the second film), which were used as input parameters to the model, were inferred experimentally from an existing bilayer of each kind and then suitably modified for different film thicknesses. This experimental assessment is therefore based on a comparison of measurements of the critical temperature and the energy gap at 300 mK with the predictions from the model for various values of γ, γ_BN. The energy gap of the bilayer was experimentally determined by using symmetrical superconducting tunnel junctions (STJs) of the form S–Al–AlO_x–Al–S, where each electrode corresponds to a proximised bilayer. However for the case of Mo/Al bilayers the interface parameters were determined theoretically since currently no STJ data for this configuration are available. The results for the Nb/Al, Ta/Al and V/Al bilayers have also then been compared to experimentally determined energy gaps found for a series of STJs with different film thicknesses. The correspondence between experiment and theory is very good.