The effective microwave surface impedance of high T c thin films

Abstract

The dependence of the effective surface impedance Z_eff=R_eff+iX_eff 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 R_eff can be expressed by R_Sf(d/λ)+R_trans where R_S is the intrinsic surface resistance of the superconductor. The function f(d/λ) describes the altered current density distribution in the film. R_trans 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 X_eff of a superconducting thin film can be expressed by X_S cosh(d/λ) where X_S=ωμ₀λ is the intrinsic surface reactance. Measurements of Z_eff at 87 GHz have been performed for YBa₂Cu₃O_7−δ thin films grown epitaxially by laser ablation on SrTiO₃, MgO, and LaAlO₃. With the best films, R_eff (77 K) values of 21 mΩ and R_S (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.