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 $\sigma$ 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.

We have studied the simultaneous effects of magnetic and electric fields on the ground-state energy of a donor impurity confined in a polar CdSe quantum nanocrystallite embedded in a nonpolar matrix. Calculations are performed in the framework of the effective-mass approximation using the Hassé variational approach. We describe the effect of the quantum confinement by a finite deep potential and we take onto account the interaction between the charge carriers (electron and ion) and the confined longitudinal optical phonons (LO phonons). It is found that the corrections due to the LO phonons on the binding energy, the diamagnetic coefficient, and the polarizability are very important and cannot be neglected or ignored.