Exciton states and optical spectra in CdSe nanocrystallite quantum dots

By using the hole effective-mass Hamiltonian for semiconductors with the wurtzite structure, we have studied the exciton states and optical spectra in CdSe nanocrystallite quantum dots. The intrinsic asymmetry of the hexagonal lattice structure and the effect of spin-orbital coupling (SOC) on the hole states are investigated. It is found that the strong SOC limit is a good approximation for hole states. The selection rules and oscillator strengths for optical transitions between the conduction- and valence-band states are obtained. The Coulomb interaction of exciton states is also taken into account. In order to identify the exciton states, we use the approximation of eliminating the coupling of ${\Gamma }_6\mathrm{}(X,Y)\mathrm{}$ with ${\Gamma }_1\mathrm{}\left(Z\right)\mathrm{}$ states. The results are found to account for most of the important features of the experimental photoluminescence excitation spectra of Norris et al. However, if the interaction between ${\Gamma }_6\mathrm{}(X,Y)\mathrm{}$ and ${\Gamma }_1\mathrm{}\left(Z\right)\mathrm{}$ states is ignored, the optically passive $P_x$ state cannot become the ground hole state for small CdSe quantum dots of radius less than 30 Å. It is suggested that the intrinsic asymmetry of the hexagonal lattice structure and the coupling of ${\Gamma }_6\mathrm{}(X,Y)\mathrm{}$ with ${\Gamma }_1\mathrm{}\left(Z\right)\mathrm{}$ states are important for understanding the “dark exciton” effect.