Density-functional studies of excited states of silicon nanoclusters

Abstract

The molecular structures of ${\mathrm{Si}}_{29}{\mathrm{H}}_{24}$, ${\mathrm{Si}}_{29}{\mathrm{H}}_{36}$, and ${\mathrm{Si}}_{35}{\mathrm{H}}_{36}$ clusters in the ground state as well as in the lowest singlet and triplet excited states have been studied at the density-functional theory level using the first-order linear-response-theory approach for the singlet excited state. Structural changes compared to the ground state due to Franck-Condon relaxation of the singlet excited state are small, whereas optimization of the lowest triplet state is found to result in a dissociation of a $\mathrm{Si}\mathrm{Si}$ bond. The electronic excitation spectra up to $5\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ for the ground-state and excited-state structures of the silicon nanoclusters are also reported. The obtained Franck-Condon shift for the first excited state of ${\mathrm{Si}}_{29}{\mathrm{H}}_{36}$ is $0.70\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$, yielding a luminescence energy of $3.14\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ which is in good agreement with experimental data. The Franck-Condon shifts for ${\mathrm{Si}}_{29}{\mathrm{H}}_{24}$ and ${\mathrm{Si}}_{35}{\mathrm{H}}_{36}$ are found to be 1.17 and $1.67\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$, yielding emission energies of 1.57 and $2.03\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$, respectively, which are significantly smaller than the experimental value of about $3\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$. Thus, the present study supports the notion that the silicon nanoclusters fabricated through electrochemical etching consist of 29 Si atoms surrounded by 36 hydrogen atoms.