Calculation of the ground-state energies in intermixed GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As cylindrical quantum dots

For the calculation of the ground-state energy in thin cylindrical quantum dots with an arbitrary radial potential, a theoretical approach has been developed. The results of the calculations are compared to the experimental observations of the photoluminescence energy of GaAs/${\mathrm{Al}}_{\mathit{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As quantum dots realized by the implantation-induced intermixing technique. For these structures an error-function-like radial potential is assumed and its steepness was estimated from the comparison with the calculations. It is concluded that the observed diameter-dependent luminescence blueshift is caused by the confinement in the radial potential, rather than by intermixing in the center of the quantum dots.