Influence of films' thickness and air gaps in surface impedance measurements of high temperature super-conductors using the dielectric resonator technique

The dielectric resonator technique is commonly used for microwave surface resistance measurements of High Temperature superconducting (HTS) films. Thickness of super-conductors and its impact on measurement results has not been taken into consideration so far. A theoretical mode-matched solution analysis of a TE₀₁₁ 10 GHz sapphire resonator was performed. The results of this analysis demonstrate that the thickness of the films under test can significantly affect the resonant frequencies (f(res)) and quality factor Q of the resonant system, particularly when the thickness is less than three times the penetration depth (λ) of the films at the operating temperature. In such cases the microwave properties of the substrate affect f(res) and Q. For HTS films' thickness relatively small as compared to λ, measured quality factors and resonant frequency may also be affected by substrate thickness and the conductivity of the backing plates of the system. The presence of air gaps between the sapphire and the HTS films does not significantly influence surface resistance measurements. However they can markedly affect the surface reactance from which the penetration depth is calculated.