The coplanar resonator technique for determining the surface impedance of YBa/sub 2/Cu/sub 3/O/sub 7-δ/ thin films

Abstract

We describe how coplanar microwave resonators fabricated from patterned thin films of YBa/sub 2/Cu/sub 3/O/sub 7/(-/spl delta/) (YBCO) can he used to measure the ab-plane microwave surface impedance Z/sub s/=R/sub s/+jX/sub s/ of the films, in particular the absolute value and temperature dependence of the magnetic penetration depth /spl lambda/. 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 /spl lambda/(T) from the measurements of resonators of different geometries patterned onto the same film. We obtain values of /spl lambda/(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/sub s/ at 7.95 GHz to be 23 /spl mu//spl Omega/ and 110 /spl mu//spl Omega/ 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/sub s/ for the best optimised films appears to be insensitive to the effects of patterning.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>