Size and hydrogen saturation effects on third-order polarizabilities of Si clusters

We report the frequency-dependent third-order polarizabilities (γ) of a series of hydrogen-capped silicon clusters obtained using time-dependent density functional theory. We find that the magnitude of γ increases with a decrease in silicon cluster size, while the sign of γ at low input photon energy changes from positive to negative when the ratio of hydrogen saturation increases. At higher input photon energy, the sign of γ is determined mainly by cluster size. Our results rationalize several recent experiments on the optical properties of silicon nanostructures and are helpful for designing opto-electronic devices based on them.