Dispersion Relation of the Dielectric Constant of ${\rm YBa}_{2}{\rm Cu}_{3}{\rm O}_{7}$ Grain Boundary Josephson Junctions Tilted Around Different Axes

We have studied the frequency dependence of the dielectric constant of YBa
₂
Cu
₃
O
₇
Josephson junctions fabricated on bicrystalline substrates with different angles tilted around alpha and
c
axis. The ratio of the dielectric constant to the thickness of the barrier, epsiv/
t
, can be deduced by measuring the voltage of Fiske steps V
_eta
= etaOslash
₀
c macr
/
omega, where eta is the resonance number, omega the junction width and Oslash
₀
the magnetic flux quantum. Changing a technological parameter as omega we are modifying V
_eta
, so the resonant frequency
f

_n
=
V

_eta
/Oslash
₀
for each fixed eta . This makes possible to generate experimentally a dispersion relation of the dielectric constant of the barrier, epsiv(
f

_n
) = epsiv(omega) . For all the bicrystalline geometries investigated, data can be fitted to the expression of epsiv(omega) that describes the behavior of the dielectric constant close to a resonance in a dielectric medium with losses. Consistent with the analysis of transport parameters, the values deduced for the resonance frequency and damping constant show a tendency to a more semiconductive behavior with the increase of the misorientation angle. In terms of the equivalent circuit RLC, we can obtain additional information on the inductive response of the barrier.