Electron-hole interactions in silicon nanocrystals

We investigate the electron-hole interactions in spherical silicon nanocrystals by incorporating Coulomb, exchange, and spin-orbit couplings into a tight-binding model. We study the effect of the electron-hole attraction on the absorption spectra and on the dielectric constant, using a real-time propagation technique. Diagonalizing the full fine-structure Hamiltonian for two-particle states close to the band gap gives exchange splittings that range from $\sim 100$ to 7 meV for nanocrystals of radii 6–18 Å. The splittings persist in the presence of spin-orbit coupling for nanocrystals of radius up to 18 Å, suggesting that dark triplet states below the absorption threshold can be the origin of the Stokes shifts and temperature-dependent lifetimes observed in luminescence experiments.