Dark excitons due to direct Coulomb interactions in silicon quantum dots

Electron-hole exchange interactions can lead to spin-forbidden ''dark'' exc itons in direct-gap quantum dots. Here, we explore an alternative mechanism for creating optically forbidden excitons. In a large spherical quantum do t made of a diamond-structure semiconductor, the symmetry of the valence ba nd maximum (VBM) is t(2). The symmetry of the conduction band minimum (CBM) in direct-gap material is a(1), but for indirect-gap systems the symmetry could be (depending on size) a(1), e, or t(2). In the latter cases, the res ulting manifold of excitonic states contains several symmetries derived fro m the symmetries of the VBM and CBM (e.g., t(2) X t(2) = A(1) + E + T-1 + T -2 or t(2) X e = T-1 + T-2). Only the T-2 exciton is optically active or "b right," while the others A(1), E, and T-1 are "dark." The question is which is lower in energy, the dark or bright. Using pseudopotential calculations of the single-particle states of Si quantum dots and a direct evaluation o f the screened electron-hole Coulomb interaction, we find that, when the CB M symmetry is t(2), the direct electron-hole Coulomb interaction lowers the energy of the dark excitons relative to the bright T-2 exciton. Thus, the lowest energy exciton is forbidden, even without an electron-hole exchange interaction. We find that our dark-bright excitonic splitting agrees well w ith experimental data of Calcott et al., Kovalev et al., and Brongersma et al. Our excitonic transition energies agree well with the recent experiment of Wolkin et al. In addition, and contradicting simplified models, we find that Coulomb correlations are more important for small dots than for inter mediate sized ones. We describe the full excitonic spectrum of Si quantum d ots by using a many-body expansion that includes both Coulomb and exchange electron hole terms. We present the predicted excitonic spectra.