The coplanar resonator technique for determining the surface impedance of YBa2Cu3O7-δ thin films

We describe how coplanar microwave resonators fabricated from patterned thin films of YBa₂Cu₃O₇(-δ) (YBCO) can he used to measure the ab-plane microwave surface impedance Z_s=R_s+jX_s of the films, in particular the absolute value and temperature dependence of the magnetic penetration depth λ. The current distribution of the resonator is calculated by modelling the resonator as a network of coupled transmission lines of rectangular cross-sections; this is then used to estimate the ab-plane λ(T) from the measurements of resonators of different geometries patterned onto the same film. We obtain values of λ(0) in the range 150-220 nm. The unloaded quality factors of the linear resonators at 7.95 GHz are around 45000 at 15 K and around 6500 at 77 K. We estimate the corresponding values of the intrinsic R_s at 7.95 GHz to be 23 μΩ and 110 μΩ at 15 K and 77 K, respectively. These values are comparable with those of other high quality unpatterned YBCO films reported in the literature. Z_s for the best optimised films appears to be insensitive to the effects of patterning