Q factor and resonance amplitude of Josephson tunnel junctions

Abstract

The surface impedance of the superconducting films comprising the electrodes of Josephson tunnel junctions has been derived from the BCS theory in the extreme London limit. Expressions have been obtained for (i) the dependence of the penetration depth λ on frequency and temperature, and (ii) the quality factor Q of the junction cavity, attributable to surface absorption in the electrodes. The effect of thin electrodes (λ) is also included in the calculations. Comparison of the calculated frequency dependence of λ with resonance measurements on Pb-alloy and all-Nb tunnel junctions yields quite good agreement indicating that the assumptions made in the theory are reasonable. Measurements of the (current) amplitude of the resonance peaks of the junctions have been compared with the values obtained from inclusion of the calculated Q in the theory by Kulik. In common with observations on microwave cavities by other workers, we find that a small residual conductivity must be added to the real part of the BCS value. With its inclusion, good agreement is found between calculation and experiment, within the range determined by the simplifying assumptions of Kulik's theory. From the results, we believe the calculation of Q to be reasonably accurate for the materials investigated. It is shown that the resonance amplitude of Josephson junctions can be calculated direct from the material constants and a knowledge of the residual conductivity. © 1977 The American Physical Society.