Excitons in semiconductor quantum discs

Abstract

The ground-state binding energy of the exciton in a finite-potential quantum disc setting is calculated variationally to study the change in dimensionality of the exciton within the limiting cases of the quantum well, wire, and dot, as well as the intermediate regime between these limiting geometries. Quantitative comparisons have been made with previous calculations using different trial wavefunctions to show the superiority of the present trial wavefunction in the quantum disc setting and to further illustrate the behaviour of the exciton in the quantum dot limit. Using the binding energy obtained from the present calculations, we further calculated the virial theorem number for the exciton is various confinement geometries, to disprove the recent claim of the existence of universal-constant virial theorem numbers for the quantum wells and wires. Also, the dimensionality parameter of the fractional-dimensionality model for confined excitons in the various confinement geometries has been calculated to facilitate discussion of its applicability to these structures, including the quantum dot limit.