Excitons in semiconductor quantum discs

The ground-state binding energy of the exciton in a finite-potential quantu m disc setting is calculated variationally to study the change in dimension ality of the exciton within the limiting cases of the quantum well, wire, a nd dot, as well as the intermediate regime between these limiting geometrie s. 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 beh aviour of the exciton in the quantum dot limit. Using the binding energy ob tained from the present calculations, we further calculated the virial theo rem number for the exciton in various confinement geometries, to disprove t he recent claim of the existence of universal-constant virial theorem numbe rs for the quantum wells and wires. Also, the dimensionality parameter of t he fractional-dimensionality model for confined excitons in the various con finement geometries has been calculated to facilitate discussion of its app licability to these structures, including the quantum dot limit.