Critical Fields of Thin Superconducting Films. I. Thickness Effects

A theoretical model is presented with which the critical magnetic fields of thin superconducting films can be calculated from any theory of superconductivity for which the kernel of the current-vector potential relationship is known. The model is worked out in detail for the nonlocal theory of Pippard with specular boundary conditions, and the critical field is shown to be a function of film thickness and the nonlocal parameters $\xi$ and ${\xi }_0{{\lambda }_L}^2$. The results are compared to critical-field data for pure indium films and are found to predict very well the observed thickness dependence of critical field. On the basis of reasonable assumptions, ${\xi }_0$ and ${\lambda }_L\mathrm{}\left(0\right)\mathrm{}$ are calculated from the indium critical field data to be 2600±400 Å and 350±30 Å, respectively.