Quantized holes and the absorption edge in spherical semiconductor microcrystals with a complex valence band structure

Radial equations for the wave functions of holes moving in a spherically symmetric potential are obtained for diamond-like semiconductors with a finite spin-orbit splitting of their valence band described by a six-band Hamiltonian. The results are used to develop a theory of size quantization of holes in spherical microcrystals with a cubic lattice. The dependences of the positions of the lowest size-quantized levels of holes on the microcrystal radius are determined for cubic CdS. The forces of oscillator transitions to the lowest electron size-quantized level are discussed and it is shown that the absorption edge of CdS microcrystals is formed by several transitions of comparable intensities from various size-quantized levels of holes. It is shown that the lowest hole level in small CdS microcrystals is a state of the p symmetry and it does not participate in the optical transition to the lowest size-quantized level of electrons (s-type symmetry). This explains the observed low quantum efficiency of the luminescence emitted by small CdS microcrystals.