Hydrogenic impurities in GaAs-(Ga,Al)As quantum dots

The ground-state energy and the binding energy of shallow hydrogenic impurities in spherical GaAs-(Ga,Al)As quantum dots have been calculated as functions of the radius of the dot. The binding energy has been calculated following a variational procedure within the effective-mass approximation. We have used a finite confining potential well with depth determined by the discontinuity of the band gap in the quantum dot and the cladding. Calculations were also performed for an infinite confining potential. For the infinite potential well we found that the impurity binding energy increases as the dot radius decreases whereas in the finite potential-well situation, the binding energy reaches a peak value as the dot radius decreases and then diminishes to a limiting value corresponding to the radius for which there are no bound states in the well. We found that the strong electronic confinement in these quantum dots reflects itself in the ground-state energy and in the impurity binding energies, which are higher than those found in GaAs-(Ga,Al)As quantum wells and quantum-well wires.