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

We propose a fractional-dimensional approach of excitonic characterist ics in semiconductor quantum wells and quantum-well wires with cylindr ical or rectangular cross sections. This type of approach has proved t o provide accurate and convenient methods for extracting excitonic bin ding energies, either from optical spectroscopy experiments, or from s imple 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 i s dramatically improved by invoking microscopic considerations, in ord er to describe the anisotropy of the relative motion of confined elect ron-hole pairs. This original approach allows a rather simple and quic k determination of eigenenergies of confined excitons, whatever the qu antum numbers of the conduction and valence subbands, and whatever the shape of the confining medium. The results of our calculations compar e favorably to those of available variational theories and to experime ntal findings.