Quasiparticle Gaps and Exciton Coulomb Energies in Si Nanoshells

Quasiparticle gaps and exciton Coulomb energies are calculated in Si nanoshells passivated by H at the inner and outer surfaces. We consider spherical nanoshells with inner radii $R_1$ up to 1 nm and outer radii $R_2$ up to 1.6 nm. Quasiparticle gaps are calculated using $\Delta$SCF and GW methods. While the single-band effective mass approximation predicts that the gap should depend only on the thickness $t=R_2 - R_1$ of the nanoshell, we find from first principles calculations that it depends on both $R_1$ and $R_2$. The dependences of the quasiparticle gap on $R_1$ and $R_2$ are mostly consistent with electrostatics of a charged metallic shell. We also find that the (unscreened) Coulomb energy in Si nanoshells has a somewhat unexpected size dependence at fixed outer radius $R_2$. Namely, the exciton Coulomb energy {\em decreases} as the nanoshell becomes more {\em 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.