The effective microwave surface impedance of high Tc thin films

The dependence of the effective surface impedance Zeff=Reff+iXeff of superconducting thin films on the film thickness d, on the magnetic field penetration depth λ, and on the dielectric properties of the substrate material is investigated theoretically by means of impedance transformations. It was found that the effective surface resistance Reff can be expressed by RSf(d/λ)+Rtrans where RS is the intrinsic surface resistance of the superconductor. The function f(d/λ) describes the altered current density distribution in the film. Rtrans arises from power transmission through the film. It depends on d and λ as well as on the dielectric properties of the substrate material and is significantly altered in the case of a resonant background. The effective surface reactance Xeff of a superconducting thin film can be expressed by XS cosh(d/λ) where XS=ωμ0λ is the intrinsic surface reactance. Measurements of Zeff at 87 GHz have been performed for YBa2Cu3O7-δ thin films grown epitaxially by laser ablation on SrTiO3, MgO, and LaAlO3. With the best films, Reff (77 K) values of 21 mΩ and RS (77 K) values of 8 mΩ were achieved. The temperature dependence of λ was found to be in good agreement to both weak-coupling BCS theory in the clean limit and the empirical two-fluid model relation with λ (0 K) values ranging from 140 to 170 nm and 205 to 250 nm, respectively