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 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 = etaOslash₀c macr/ omega, where eta is the resonance number, omega the junction width and Oslash₀ the magnetic flux quantum. Changing a technological parameter as omega we are modifying V_eta, so the resonant frequency f _n = V _eta/Oslash₀ 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.