  We report low-temperature measurements of current-voltage characteristics for
highly conductive Nb/Al-AlOx-Nb junctions with thicknesses of the Al interlayer
ranging from 40 to 150 nm and ultra-thin barriers formed by diffusive oxidation
of the Al surface. In the superconducting state these devices have revealed a
strong subgap current leakage. Analyzing Cooper-pair and quasiparticle currents
across the devices, we conclude that the strong suppression of the subgap
resistance comparing with conventional tunnel junctions originates from a
universal bimodal distribution of transparencies across the Al-oxide barrier
proposed earlier by Schep and Bauer. We suggest a simple physical explanation
of its source in the nanometer-thick oxide films relating it to strong local
barrier-height fluctuations which are generated by oxygen vacancies in thin
aluminum oxide tunnel barriers formed by thermal oxidation.
