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Vertical stacks of up to five NbN/TiNx/NbN junctions were fabricated using an inductively coupled plasma etching technique. The spread in critical currents at junctions in the fabricated stacks was measured as a function of the number of junctions in a stack N and the thickness of the intermediate NbN electrodes. Stacks with thin intermediate electrodes (d = 20 nm) and N greater than 3 exhibited large spreads of critical currents, whereas stacks with thick intermediate electrodes (d = 50 nm) showed small spreads. The I - V curve for a stack of five NbN/TiNx/NbN junctions with 50-nm-thick intermediate electrodes indicated that the critical currents in those junctions were almost identical.