Semi-analytical formulation for exciton in cuboidal semiconductor quantum dot with parabolic confinement: Hydrostatic pressure and temperature effects

The exciton properties in a cubical quantum dot (CQD), with parabolic confining potential, are theoretically investigated. We have used the two-band model, the effective mass approximation, and the variational method. An analytical formulation to be used for calculating exciton properties in a cubical quantum dot with a parabolic potential profile has been developed. The analytical expressions of the binding energy, the normalized photoluminescence energy transition, the spatial extension, and the oscillator strength of the exciton, in the ground state, have been obtained. The numerical calculations for the typical GaAs/AlxGa1-xAs CQD are presented. The effects of the side length of a cubic quantum dot, the hydrostatic pressure, and the temperature on the exciton properties are discussed. The results of the calculation illuminate that the hydrostatic pressure and the CQD length can make an important impact on the exciton binding energy and the photoluminescence peak energy.