Calculation of the Low-Temperature Microwave Resistance of a Thin Metal Film on a Bulk Substrate

A simple free-electron model is used to explain the experimentally observed low values of the effective resistivities derived from the low-temperature microwave absorption of metal films plated onto (normal-conducting) tin. In the limit of zero film thickness the calculation gives an effective resistivity of $\rho =\frac{{\rho }_1{l}_1}{2\delta }$, where ${\rho }_1{l}_1$ is a material constant of the material of the film and $\delta$ the anomalous skin depth in the base metal. Good agreement is obtained for gold films on tin. The experimental data for copper films on tin are much higher than expected from this model. The implications of these findings for the proximity effects in superconductivity, that is, for the influence of a normal metal on an adjoining superconductor and vice versa, are discussed.