The effective microwave surface impedance of high T c thin films

Abstract

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.

Recent developments in the characterization of superconducting films by microwaves

“…For instance, the strongly temperature dependent permittivity of SrTiO 3 leads to oscillations of Z eff (T) [26]. Present efforts aim at understanding the different microwave properties of bulk and thin film SrTiO 3 for device applications.…”

“…New aspects arise for t<λ, due to partial reflection and transmission at the additional film-substrate interface, e.g., in very thin films or near T c . The effective surface impedance follows from an implicit equation [5,26,27]:…”

Surface impedance measurements of single crystal MgB2films for radiofrequency superconductivity applications

“…P rf is the RF induced heat, k and M are geometry dependent coefficients and ω is the resonant circular frequency. The RF induced heat is calculated from the difference between the power from the heater required to keep a constant sample temperature without RF fields in the cavity and the power from the heater re- The penetration depth λ s is derived from the effective penetration depth using = coth ( / ) [21] with d the film thickness. The results are plotted in Figure 2.…”

Strong reduction of field-dependent microwave surface resistance in YBa2Cu3O7−δ with submicrometric BaZrO3 inclusions

“…The field induced change in the intrinsic thin film impedance, ∆R ′ s + i∆X ′ s = (∆ρ 1 + i∆ρ 2 )/d, was measured for T > 60 K and µ 0 H < 0.8 T by means of a sapphire dielectric resonator operating in the TE 011 mode at 47.7 GHz. 10 The STO substrate resonances 11,12 were removed with the introduction of an additional spacer to change the substrate impedance. 13 Here, ρ 1 + iρ 2 is the complex resistivity of the film.…”