FRACTIONAL-DIMENSIONAL CALCULATION OF EXCITON BINDING-ENERGIES IN SEMICONDUCTOR QUANTUM-WELLS AND QUANTUM-WELL WIRES

We propose a fractional-dimensional approach of excitonic characteristics in semiconductor quantum wells and quantum-well wires with cylindrical or rectangular cross sections. This type of approach has proved to provide accurate and convenient methods for extracting excitonic binding energies, either from optical spectroscopy experiments, or from simple envelope function calculations. In this paper, we first try and extend the simple description previously developed for single quantum wells and superlattices. Next, we show how the accuracy of the model is dramatically improved by invoking microscopic considerations, in order to describe the anisotropy of the relative motion of confined electron-hole pairs. This original approach allows a rather simple and quick determination of eigenenergies of confined excitons, whatever the quantum numbers of the conduction and valence subbands, and whatever the shape of the confining medium. The results of our calculations compare favorably to those of available variational theories and to experimental findings.