Theory of the absorption edge in semiconductors in a high magnetic field

Abstract

A theory based on the effective mass approximation is given for hole-electron pairs in a semiconductor in a magnetic field. The intensity of the absorption edge is determined by the wave function of relative motion of the pair, so that essentially it becomes necessary to solve the Schrödinger equation for a hydrogen atom in a magnetic field. This is done in an approximation valid in high fields which assumes that the Coulomb term affects only the motion along the field, and uses a potential form which allows the solutions to be written in terms of confluent hypergeometric functions. The results show that the main intensity in each magnetic sub-band transition is thrown into the lowest exciton line and that the absorption in the continuum is reduced to an insignificant shoulder. The peaks observed in the so-called magneto-optic effect will all be exciton peaks.