Optical Gaps and Screening in Quantum Dots

Semiconductor structures with reduced dimensionality often have optical properties that are quite different than the optical properties of crystalline matter. For example, silicon has a band gap of about 1.2 eV in the crystalline state whereas nanocrystalline dots of silicon have “band gaps” of ∼ 2 eV or larger. Until recently, the modification of the gap from quantum confinement has not been examined using ab initio methods owing to the large size of the dots; the smallest dots measured contain on the order of 500 atoms. Here we present results using ab initio pseudopotentials to investigate the optical gap as a function of cluster size. We consider clusters up to ∼30Å in diameter which contain over 1,000 atoms. The optical gaps are computed by adding the electron-hole Coulomb energy to the quasi-particle gap. We find excellent agreement between our calculations and the measured optical gap.