Dependence of critical current density on oxygen exposure in Nb-AlOx-Nb tunnel junctions

We demonstrate that a large fraction of the available data relating the critical current density J_c of superconducting Nb-AlO_x-Nb tunnel junctions to oxidation parameters can be accounted for by a single, nearly universal dependence. For fixed oxidation temperature, J_c does not depend independently on oxygen partial pressure and oxidation time, but only on their product. There are two distinct regimes in this dependence, corresponding to high and low J_c