Electron affinities and ionization energies in Si and Ge nanocrystals

We present calculations for electron affinities, ionization potentials, and quasiparticle gaps for hydrogenated silicon and germanium nanocrystals (quantum dots) with radii up to $14\mathrm{\AA }$ or about 800 atoms using real-space ab initio pseudopotentials constructed within the local-density approximation. We show that electron affinities and ionization energies exhibit a strong size dependence characteristic of quantum confinement, and remain significantly different from corresponding bulk values even for the largest nanocrystals studied. Both Si and Ge nanocrystals have very close values of ionization and affinity energies, while quasiparticle and single-particle gaps for silicon dots are slightly larger $\left(\sim 0.2\mathrm{eV}\right)$ than those computed for germanium nanocrystals. Our calculated affinities and ionization potentials scale with radius R of the nanocrystal as $R^{-l},$ where $l=1.1\mathrm{}\pm 0.2,$ in contrast to the scaling factor $l=2\mathrm{}$ predicted by simple effective-mass models.