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We fabricated ramp-edge junctions with an interface-modified barrier on YBa2Cu3Oy (YBCO) liquid phase epitaxy (LPE) thick films. The LPE thick films were used as ground-planes. For the insulating layer between the ground plane and base electrode, a SrTiO3 (STO)/(LaAlO3)0.3-(SrAl0.5Ta0.5O3)0.7 (LSAT)/STO multilayer with the dielectric constant of approximately 32 was employed. We fabricated ramp-edge junctions with La-doped YBa2Cu3Oy (La-YBCO) and La-doped YbBa2Cu3Oy (La-YbBCO) as base and counter electrodes, respectively. The fabricated junctions exhibited resistively and capacitively shunted junction (RCSJ)-like characteristics and typical IcRn products of 2.6 and 1.1 mV at 4.2 and 40 K, respectively. The 1 σ-spread in Ic as small as 8.1% was obtained for 100-junction series-arrays. The use of ground plane reduced the sheet inductance of electrodes to a value of 0.76-0.94 pH/square at 4.2 K.