THE SYMMETRY OF THE RELATIVE MOTION OF EXCITONS IN SEMICONDUCTOR HETEROSTRUCTURES

A theoretical model of excitonic states in semiconductor heterostructu res is presented. The approach employs the envelope function approxima tion, and involves a two parameter variational calculation in which th e symmetry of the component of the wave function representing the rela tive motion is allowed to vary between the two- and three-dimensional limits. Detailed calculations are described for a variety of single qu antum wells and superlattices. The results show that the excitons are neither 2D nor 3D like, but are intermediate in character. Furthermore , in the main, they assume the symmetry of a prolate spheroid. An exce ption to this occurs in the special case of an asymmetric double quant um well close to resonance, where two stable exciton states are found for the same one-particle states. One of these 'twin' exciton states i s an oblate spheroid. The results illustrate the need for accurate det ermination of excitonic properties if the dynamical evaluation of exci ton states, in for example, quantum well lasers, is to be readily dete rmined. (C) 1996 Academic Press Limited