Surface Impedance of Thin Superconducting Films
Theoretical analysis and experimental measurements have been made of the propagation of electromagnetic waves in a structure consisting of two planar superconductors which are of the order of a penetration depth apart. One superconductor is tantalum and is much thicker than a penetration depth; the other is a vacuum evaporated indium film and may be as thin as a penetration depth. It is shown that such a structure will propagate waves at a phase velocity less than the speed of light in the medium separating the superconductors, a phenomenon that is the result of an inductive component in the surface impedance of the superconductors. The exact velocity is shown to be a function of the thickness parameters in a manner which depends on the law relating the vector potential and the supercurrent in the indium. Experimental measurements indicate that the relationship between vector potential and current in the vacuum evaporated indium is characterized by a coherence distance which is considerably smaller than that found for pure metals by the measurements of Pippard and the theory of Bardeen, Cooper and Schrieffer. The penetration depth at zero temperature is deduced from dependence of phase velocity on the thicknesses of the indium and dielectric. For indium λ is found to be 650 ± 75Å, in good agreement with Lock's value of 640Å and Toxen's range from 625 to 725Å. For tantalum λ is found to be 500 ± 175Å. This is believed to be the first measurement. The value of λ for indium is also deduced from the dependence of phase velocity on temperature. It is found to be 704 ± 120Å. Surface resistance of the two superconductors is found to increase as ω^2, in good agreement with theory, and to depend on temperature according to an empirical law proposed by Pippard.
I should like to thank Dr. Roy W. Gould for his constant encouragement and advice during the progress of the research reported herein. I should also like to thank Dr. Carver Mead for much useful advice on experimental techniques, and Richard Carrouche for construction of much of the apparatus. And last, but not least, my thanks to Mrs. Ruth Stratton who did an excellent job of preparing the manuscript in a very short time.
Submitted - TR000357.pdf