Excitons in CdSe quantum dots

Recent advances in material synthesis have provided samples with CdSe quantum dots with a degree of monodispersity high enough to allow for observation of excited exciton states and their size dependence [Norris et al., Phys. Rev. Lett. 72, 2612 (1994)]. Here we report theoretical results for these exciton states using the effective bond-orbital model (EBOM) for the hole and single-band effective-mass theory (EMT) for the electron in an iterative Hartree scheme including the Coulomb interaction and finite offsets. We present results for hole energies, exciton energies, and exciton oscillator strengths and compare with experiments and other theoretical results. Our results are found to account for most of the important features of the experimental absorption spectra by Norris et al. In particular, experimental states corresponding to the exciton ground state (1${\mathrm{\Gamma }}_8$-${1\mathrm{S}}_{\mathrm{e}}$), as well as the 2${\mathrm{\Gamma }}_8$-${1\mathrm{S}}_{\mathrm{e}}$ and 3${\mathrm{\Gamma }}_8$-${1\mathrm{S}}_{\mathrm{e}}$ excited states, have been identified. Also, a set of experimental exciton states observed lifted with an energy close to the spin-orbit splitting λ≈420 meV above the exciton ground state have been identified as ${\mathrm{\Gamma }}_7$-${1\mathrm{S}}_{\mathrm{e}}$ spin-orbit split-off states with large oscillator strengths. A nonperturbative study of the effects of the crystal-field splitting, which is inherent in hexagonal CdSe quantum dots, revealed patterns of avoided crossings, accompanied with redistribution of oscillator strengths, between different exciton states for increasing values of the crystal-field splittings. In CdSe where the crystal-field splitting is ≈25 meV, the splitting is not expected to have a significant effect on the present quantum dot absorption spectra.