Calculations of the microwave conductivity of high-T c superconducting thin films from power transmission measurements

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Abstract
To calculate the complex conductivity σ=σ1−jσ2, and thus the surface resistance Rs and penetration depth λL, of high Tc superconducting thin films from microwave power transmission measurements, new expressions are derived taking into account the film thickness. Numerical examples are given to show that, compared with the calculations which neglect the film thickness, corrections in σ1, σ2, Rs, and λL are a few percent for film thickness ranging between 0.65 and 0.46 λL and that corrections in σ1 and σ2 are greater than those in Rs and λL. Using the newly derived expressions, maximum errors in Rs and λL are estimated to be about 30% and 3%, respectively, if errors between −10% and +10% are tolerated in the measurements of the magnitude and phase shift of microwave transmission.