Quantum Confinement and Optical Gaps in Si Nanocrystals

Quasiparticle gaps, self-energy corrections, exciton Coulomb energies, and optical gaps in Si quantum dots are calculated from first principles using a real-space pseudopotential method. The calculations are performed on hydrogen-passivated spherical Si clusters with diameters up to 27.2 Å ( $\sim 800\mathrm{Si}$ and H atoms). It is shown that (i) the self-energy correction in quantum dots is enhanced substantially compared to bulk, and is not size independent as implicitly assumed in all semiempirical calculations, and (ii) quantum confinement and reduced electronic screening result in appreciable excitonic Coulomb energies. Calculated optical gaps are in very good agreement with absorption data.