Free electron distribution in thin films

In this paper we analyze the electron states in metallic films. The first part of the paper is devoted to the study of the film where ion-ion interaction changes only in boundary layers. It was concluded that bulk states always appear in such film. Surface states appear only if the variation of the ion-ion interaction in the direction of the symmetry breaking in the boundary layer are neutralized. If the conditions for the creation of surface states are realized, one can obtain dense currents running along the film surface. In the second part of the paper we study the film where translational symmetry is broken in the whole volume. Symmetry breaking is treated as a perturbation. The perturbation was homogenously spatially distributed in the vicinity of the film boundary, while the central part was unperturbed. The analysis of the electron states in such a perturbed film has shown that the maximum of the electron density shift towards that part of the film where potential wells of the ion-ion interaction are shallower. Electrons in this part of the film have comparatively high population and increased chemical potential, which implies higher density of states. From the point of view of the BCS theory, these electrons might have a higher critical temperature compared to the electrons in the unperturbed metallic matrix.