Electron energy spectrum in thin films,taking into account an arbitrary one-dimensional internal field

A compact and accurate solution of the specified problem is obtained in the model of an infinitely deep potential well. The solution is expressed in terms of the one-dimensional Green's function for an electron in an arbitrary field in the absence of film boundaries. The one-dimensional problem may be generalized to the three-dimensional case when the three-dimensional field allows separation of variables along and perpendicular to the plane of the film. The case of a periodic field is examined in more detail. It is shown that in the forbidden band of a bulk crystal there arise permitted film subbands.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 7–11, May, 1977.Thanks are due to V. L. Boneh-Bruevich for discussion of the work and for useful comments.