The electronic structures of zero-dimensional quantum wells are studied with a spherical model in the framework of the effective-mass theory. The mixing effect of the heavy and light holes is taken into account, and the symmetry classification and the energy levels of hole states are obtained. The energies of the donor and acceptor states are calculated. The difference between the shallow-impurity states and the eigenstates for the small semiconductor sphere disappears. The selection rules for the optical transition between the conduction- and valence-band states are obtained. The Δn=0 selection rule is not followed strictly because of the mixing of the L- and (L+2)-orbital wave functions in the wave functions of the hole states. The exciton binding energies are calculated for the small GaAs spheres. The energy levels of the ZnSe spheres are given as functions of the radius and compared with the experiments.

• Received 22 May 1989

DOI:https://doi.org/10.1103/PhysRevB.40.8500