  We study the electrical transport of vertically-stacked Josephson tunnel
junctions using GdBa$_2$Cu$_3$O$_{7-d}$ electrodes and a BaTiO$_3$ barrier with
thicknesses between 1 nm and 3 nm. The junctions with an area of 20 mm x 20 mm
were fabricated combining optical lithography and ion etching using
GdBa$_2$Cu$_3$O$_{7-d}$ (16 nm) / BaTiO$_3$ (1 - 3 nm) /
GdBa$_2$Cu$_3$O$_{7-d}$ (16 nm) trilayers growth by sputtering on (100)
SrTiO$_3$. Current-voltage measurements at low temperatures show a Josephson
coupling for junctions with BaTiO$_3$ barriers of 1 nm and 2 nm. Reducing the
barrier thickness bellow a critical thickness seems to suppress the
ferroelectric nature of the BaTiO$_3$. The Josephson coupling temperature is
strongly reduced for increasing barrier thicknesses, which may be related to
the suppression of the superconducting critical temperature in the bottom
GdBa$_2$Cu$_3$O$_{7-d}$ due to stress. The Josephson energies at 12 K are of
$\approx$ 1.5 mV and $\approx$ 7.5 mV for BaTiO$_3$ barriers of 1 nm and 2 nm.
Fraunhofer patterns are consistent with fluctuations in the critical current
due to structural inhomogeneities in the barriers. Our results are promising
for the development of Josephson junctions using high-T$_c$ electrodes with
energy gaps much higher than those usually present in conventional
low-temperature superconductors.
