Hypergeometric solution of the Stark-ladder effect in crystals

Abstract

The motion of electrons in a crystal subjected to a linear electric field is studied by means of the molecular orbital method. The field perturbation of the resonance integrals, as well as the Coulomb ones, results in the Schroedinger equation being expressed as a hypergeometric difference equation, whose solution gives rise to the well-known Stark-ladder picture of the tilted energy band. It is found that the part played by the resonance integral perturbation is just as important as that of the Coulomb integral perturbation and, therefore, cannot be neglected as in earlier investigations.