Ground states of group-IV nanostructures: Magic structures of diamond and silicon nanocrystals

We have developed an effective model to investigate the energetic stability of hydrogenated group-IV nanostructures, followed by validations from density-functional theory calculations. The Hamiltonian of XmHn (X = C, Si, Ge, and Sn) is expressed analytically by the atom numbers (m, n) and the magic numbers of diamond nanocrystals and silicon nanocrystals are determined. It is found that surface reconstructions would alter the morphology of silicon nanocrystals significantly and consequently induce dramatic modulation on their electronic properties.