Ab initioabsorption spectra of Ge nanocrystals

Ab initio absorption spectra and optical gaps for hydrogen-passivated Ge nanocrystals are calculated using time-dependent density functional theory within the adiabatic local density approximation. The results are compared to previous effective mass, tight-binding, empirical pseudopotential, and ``Δ self-consistent field'' calculations and shed light on the validity of the various approximations used. By comparing our results with calculations for hydrogen-passivated Si nanocrystals, we predict that the Ge optical gap is smaller than that of Si for any nanocrystal size.