Excitonic and Quasiparticle Gaps in Si Nanocrystals

Abstract

We present calculations of the one- and two-particle excitations in silicon nanocrystals. The one-particle properties are handled in the $\mathrm{GW}$ approximation, and the excitonic gap is obtained from the Bethe-Salpeter equation. We develop a tight binding version of these methods to treat clusters up to 275 atoms. The self-energy and Coulomb corrections almost exactly cancel each other for crystallites with radius larger than 0.6 nm. The result of this cancellation is that one-particle calculations give quite accurate values for the excitonic gap of crystallites in the most studied range of sizes.