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We have fabricated high-T/sub c/ ramp-edge junctions with a Ga-doped YBa/sub 2/Cu/sub 3/O/sub 7-/spl delta// (YBCO) barrier in the trilayer geometry of YBa/sub 2/Cu/sub 3/O/sub 7-/spl delta///YBa/sub 2/Cu/sub 2.79/Ga/sub 0.21/O/sub 7-/spl delta///YBa/sub 2/Cu/sub 3/O/sub 7-/spl delta// on LaAlO/sub 3/ single crystals. Interface resistances of the junctions were drastically reduced by using in-situ RF plasma cleaning treatment. The cross-sectional images of the interface of the junctions were analyzed by high resolution transmission electron microscopy. The temperature dependences of critical currents and junction resistances were consistent with the behavior predicted by the conventional proximity effect. The critical currents of the Ga-doped junctions were less sensitive to the variation of the barrier thickness compared to those of the other junctions. The increase of the barrier resistivity by Ga-doping resulted in an enhancement of the I/sub c/R/sub n/ values, up to 320 /spl mu/V at 60 K.