The electronic structure of nanocrystalline Si which shows visible photoluminescence is calculated using the density-functional approach for finite structures. Except for geometry this is the same theory as for first-principles band structures of semiconductors and other solids. Our results for clusters ranging up to 706 Si atoms suggest that the band gap scales linearly with ${\mathit{L}}^{\mathrm{-}1}$, where L is the cluster diameter. For such clusters it is found that dipole transitions across the gap are symmetry allowed. The finite structures thus show a direct band gap which is considerably larger than the one of bulk silicon. For larger clusters we find a strong decrease of oscillator strength, consistent with the occurrence of the indirect gap in the bulk limit.

• Received 17 September 1992

DOI:https://doi.org/10.1103/PhysRevB.47.1397