# Critical fields of thin superconducting films. II. Mean free path effects in indium-tin alloy films

## Abstract

In a previous paper, a theoretical model was presented from which the critical magnetic fields of thin superconducting films could be calculated. The model was worked out for the nonlocal model of Pippard, but only thickness effects were discussed in detail and compared to experimental data on pure indium films. In this paper, mean free path effects as well as thickness effects are discussed, and the results are found to be in good agreement with critical field measurements on thin alloy films of indium containing 0-4.6 at.% tin, if one assumes that ξ0λL2 is equal to 1.62×109 3 at 0.9Tc, ξ0 is equal to 2600, and ρl is approximately 2.0×10-11 Ω-cm2. For these values of ξ0 and ρl, the coherence length, ξ, has been calculated for each film from measurements of resistivity and thickness, and is found to vary from 2600 at 0 at.% Sn to 1000 at 4.6 at.% Sn. Also, the question of whether size effects in thin films are equivalent to mean free path effects is discussed in detail. It is concluded that size effects are not equivalent to mean free path effects, or more precisely, boundary scattering is not equivalent to scattering by randomly distributed defects. In fact, it is demonstrated that whereas the London or "local" limit obtains in the presence of high concentrations of randomly distributed defects, the Pippard or "nonlocal" limit obtains in very thin films, where boundary scattering predominates. © 1963 The American Physical Society.