Electrons in Infinite One-Dimensional Crystals in a Uniform Electric Field

Abstract

The one-dimensional Schrödinger equation with the Kroning-Penny potential plus the electric-field potential eFx has been solved numerically. All the interband effects are included in the exact numerical calculation. Although an infinite crystal was considered, localized wave functions have been obtaind at energies which make a Stark ladder. One Stark ladder is associated with one band. When the probability of the Zener tunneling to the next band is appreciable for given values of parameters, the wave function necessarily penetrates into the region of the next band and is not localized.