WANNIER EXCITONS IN NONINTEGER DIMENSIONS - A SIMPLE ANALYTICAL EXPRESSION FOR THE COMPLEX DIELECTRIC-CONSTANT OF SEMICONDUCTOR STRUCTURES

Absorption spectra of low-dimensional structures such as quantum wells or wires have been strinkingly well reproduced by expressions based o n solutions of the Schrodinger equation for the Coulomb potential in n oninteger dimensions. The compact and analytical complex dielectric co nstant of Wannier excitons in fractional d dimensions is given, the va lue of d being deduced from the binding energy of the fundamental exci tonic bound state. We show that the influence of correlated electron-h ole pairs - the ''continuum states'' - to the dielectric constant must be taken into account for quantum wells, but not necessarily so in th e case of quantum wires. Our simple expression can be used to obtain a n accurate description of the optical properties of semiconductor stru ctures of reduced dimensionality in the vicinity of the absorption thr eshold.