Wannier Excitons in Noninteger Dimensions: A Simple Analytical Expression for the Complex Dielectric Constant of Semiconductor Structures

Abstract

Absorption spectra of low-dimensional structures such as quantum wells or wires have been strinkingly well reproduced by expressions based on solutions of the Schrodinger equation for the Coulomb potential in noninteger dimensions. The compact and analytical complex dielectric constant of Wannier excitons in fractional d dimensions is given, the value of d being deduced from the binding energy of the fundamental excitonic bound state. We show that the influence of correlated electron±hole pairs ± the acontinuum stateso ± to the dielectric constant must be taken into account for quantum wells, but not necessarily so in the case of quantum wires. Our simple expression can be used to obtain an accurate description of the optical properties of semiconductor structures of reduced dimensionality in the vicinity of the absorption threshold.