Exciton bound to an ionized donor impurity in semiconductor spherical quantum dots

Abstract

The effect of the quantum confinement on the electronic and optical properties of an exciton bound to an ionized hydrogenic donor placed at the center of a semiconductor spherical microcrystal is studied theoretically as a function of the sphere radius $R$ and the effective mass ratio $\ensuremath{\sigma}$ of the electron and the hole. The valence-and conduction-band offsets are assumed to be infinite. The ground-state energy is determined by Ritz's variational method. The influence of the confinement on the dipole absorption of the bound exciton is discussed in relation to the exciton absorption. We show that the quantum confinement gives rise to a "giant" oscillator strength per impurity, contrary to what happens in bulk materials where a "giant" oscillator strength results only in the case of a high doping. The ratio between the exciton and the bound-exciton oscillator strengths may be close to unity in small microcrystals, contrary to the three-dimensional case where it is very small. Thus bound-exciton lines are expected to be easier to observe in the former case.