The critical magnetic field of thin superconducting films

In recent papers [1 to 4] on critical magnetic field of superconducting films the one‐electron state is treated almost in a “semiclassical” way. Though the motion of electrons in the direction of the film thickness is described by a quantum number n [2], the special features of electron pairing in thin films were not taken into account. Thus the results are valid only for thick metal films ( L ≧ 10 −5 cm). In this paper the quantization of electron motion in the direction of the film thickness is taken into account. This motion is described by a wave function Ψ( z ) and a quantum number n. Moreover Cooper pairs are built in a correct way [5]. H e is calculated for thin metal films. In the limiting case of thick films the result agrees with that of [2]. Furthermore, the approach used permits to study semi‐metal and semiconducting films too, where H c is calculated for the whole range of thicknesses (50 to 1000 Å). All results are valid near T c .