Tunneling properties of barriers in Nb/Al/AlO_x/Nb junctions

We have measured dc I-V curves of niobium-trilayer (Nb/Al/AlO _x/Nb) junctions with barriers thermally grown within a broad range of oxygen exposure E = Pt, from 2 × 10⁵ to 2 × 10 ⁹ Pa-s, and for applied electric fields ranging from zero all the way up to the breakdown - typically, above 10 MV/cm. The data can be reasonably well fitted by the direct theory assuming trapezoidal barrier profile and using the numerical solution of the Schrödinger equation. (The traditional WKB approximation gives considerable errors for barriers so thin and sharp.) The fitting has shown that with the increase of oxygen exposure, the effective oxide thickness d_ef ≡ (m/m₀)^α d (where m is the effective mass of the tunneling electron and (α ≈ 0.51) grows from 0.83 to 1.08 nm, while the average barrier height grows from 1.7 to 1.9 eV, and the zero-voltage conductance G₀ continues to drop as E^-1/2 through all the studied exposure range.