Dispersion relation of the dielectric constant of YBa2Cu3O7 grain boundary Josephson junctions tilted around different axes

We have studied the frequency dependence of the dielectric constant of YBa2Cu3O7 Josephson junctions fabricated on bicrystalline substrates with different angles tilted around a and c axis. The ratio of the dielectric constant to the thickness of the barrier, epsilon/t, can be deduced by measuring the voltage of Fiske steps V-n = n phi(0)(c) over bar/omega, where n is the resonance number, omega the junction width and phi(0) the magnetic flux quantum. Changing a technological parameter as w we are modifying V-n, so the resonant frequency f(n) = V-n/phi(0) for each fixed n. This makes possible to generate experimentally a dispersion relation of the dielectric constant of the barrier, epsilon(f(n)) = epsilon(omega). For all the bicrystalline geometries investigated, data can be fitted to the expression of epsilon(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.