Electronic structure of quantum spheres with wurtzite structure

The hole effective-mass Hamiltonian for the semiconductors with wurtzite structure is given. The effective-mass parameters are determined by fitting the valence-band structure near the top with that calculated by the empirical pseudopotential method. The energies and corresponding wave functions are calculated with the obtained effective-mass Hamiltonian for the CdSe quantum spheres, and the energies as functions of sphere radius R are given for the zero spin-orbital coupling (SOC) and finite SOC cases. The energies do not vary as ${1/R}^2$ as the general cases, which is caused by the crystal-field splitting energy and the linear terms in the Hamiltonian. It is found that the ground state is not the optically active S state for the R smaller than $30\hspace{0.5em}\mathrm{\AA }\mathrm{},$ in agreement with the experimental results and the “dark exciton” theory.