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We have fabricated step-stack Josephson junctions based on high quality epitaxial BSCCO (2212 phase) thin films, deposited on Y-doped bismuth (Bi-22Y2) steps. Bi-2212 and Bi-22Y2 films were grown by a high oxygen pressure dc-sputtering technique. The structural characteristics have been analyzed by X-ray, transmission electron microscopy (TEM), and Rutherford backscattering spectrometry (RBS). Bi-22Y2 steps between 100 and 300 nm high were patterned by photolithography and non-aqueous chemical etching. Junctions were characterized by current-voltage (I-V) measurements under magnetic fields and microwave irradiation. I-V curves have shown a clearly hysteretic weak-link Josephson behavior at different temperatures. The temperature dependence of the critical current in these step-stack junctions has also been analyzed.