Critical Fields of Thin Superconducting Films

The critical fields of thin superconducting films have been calculated on the basis of the Bardeen-Cooper-Schrieffer (BCS) theory of superconductivity following a method outlined by Schrieffer. It is shown that it is convenient to use the critical field formula postulated by London where the London penetration depth is replaced by an effective penetration depth which can be specified through the use of the BCS theory. The effective penetration depth, unlike the London penetration depth which, for a given material, varies only with the temperature, is found to vary, in the BCS theory, with both the film thickness and the electronic mean free path of the normal material. This paper attempts to show that the measured critical fields of thin tin films are in general qualitative agreement with the predictions of the BCS theory.