Excitonic exchange splitting and Stokes shift in Si nanocrystals and Si clusters

The size dependence of the electron-hole exchange interaction in Si nanocrystals is investigated and the excitonic exchange splitting is predicted to be as large as 300 meV in extremely small Si clusters. The exciton-phonon interaction in Si nanocrystals for acoustic phonon modes is formulated to calculate the Stokes shift and the Huang-Rhys factor. It is found that the observed onset energy of photoluminescence can be interpreted mainly in terms of the excitonic exchange splitting, although the contribution from the Stokes shift is not negligible. The importance of the self-consistent determination of the effective dielectric constant of Si clusters including the excitonic effect is demonstrated in view of the possibility of resolving the large discrepancy between theories and experiments concerning the size dependence of the exciton energy.