Ab Initio Absorption Spectra and Optical Gaps in Nanocrystalline Silicon

The optical absorption spectra of ${\mathrm{Si}}_n{\mathrm{H}}_m$ nanoclusters up to $\sim 250$ atoms are computed using a linear response theory within the time-dependent local density approximation (TDLDA). The TDLDA formalism allows the electronic screening and correlation effects, which determine exciton binding energies, to be naturally incorporated within an ab initio framework. We find the calculated excitation energies and optical absorption gaps to be in good agreement with experiment in the limit of both small and large clusters. The TDLDA absorption spectra exhibit substantial blueshifts with respect to the spectra obtained within the time-independent local density approximation.