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We report fabrication and characterization of epitaxial NbN/TaN/NbN Josephson junctions grown by pulsed laser ablation. These SNS junctions can be used as elements of rapid-single-flux-quantum (RSFQ) logic, which is a promising technology for high speed digital electronic devices. The NbN/TaN/NbN trilayer films were prepared on a single crystal MgO substrate by pulsed laser ablation, and patterned into junctions using a novel process utilizing e-beam lithography, chemical vapor deposition and e-beam evaporation. The quality of junctions was tested by measuring the temperature dependence of the junctions' IcRn values, observed to be quite close to theoretical values.