Size Effects in Thin Superconducting Indium Films

Abstract

Measurements of residual resistivity, superconductive critical temperature, and critical magnetic field have been carried out on indium films ranging in thickness from 650 to 126 000 A. The thickest films had the bulk critical field and critical temperature. The variation of residual resistivity with thickness is consistent with Fuchs' model if one assumes an intrinsic resistivity ${\ensuremath{\rho}}_{0}$ of 1.31\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}8}$ ohm cm and an intrinsic mean free path ${l}_{0}$ of 152 000 A. The value of ${\ensuremath{\rho}}_{0}{l}_{0}$ so obtained was 2.0\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}11}$ ohm ${\mathrm{cm}}^{2}$. The critical temperature was found to be a systematic function of film thickness, increasing with decreasing thickness. The magnitude of this change in critical temperature is in good agreement with a simple model relating critical temperature to elastic stresses in the films. The penetration depth, as calculated from the critical field by means of the London theory or the Ginzburg-Landau theory, was found to increase with decreasing film thickness. This result is consistent with a nonlocal model and implies a coherence length of approximately 2600 A.