Quasiparticle gaps and exciton Coulomb energies in Si nanoshells: First-principles calculations

Quasiparticle gaps and exciton Coulomb energies of H-passivated spherical Si nanoshells are computed using first-principles ΔSCF method and selectively comparing to GW computations. We find that the quasiparticle gap of a nanoshell depends on both its inner radius R1 (weakly) and outer radius R2 (strongly). These dependences on R1 and R2 are mostly consistent with electrostatics of a metallic shell. We also find that the unscreened Coulomb energy ECoul in Si nanoshells has a somewhat unexpected size dependence at fixed outer radius R2: ECoul decreases as the nanoshell becomes more confining, contrary to what one would expect from quantum confinement effects. We show that this is a consequence of an increase in the average electron-hole distance, giving rise to reduced exciton Coulomb energies in spite of the reduction in the confining nanoshell volume.