First-principles calculations of the temperature dependence of the band gap of Si nanocrystals

Abstract

The temperature dependence of the band gap of hydrogen-passivated Si nanocrystals of radius $R=0.7$ and $1.1\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ has been calculated from first principles using constant-temperature molecular-dynamics simulations. The band-gap change with temperature $\mathrm{\ensuremath{\Delta}}{E}_{g}(R,T)={E}_{g}(R,T)\ensuremath{-}{E}_{g}(R,0)$ is obtained by averaging over the configurations sampled during the molecular-dynamics simulation. We find that $\mathrm{\ensuremath{\Delta}}{E}_{g}(R,T)$ depends strongly on the nanocrystal size. At room temperature, the calculated $\mathrm{\ensuremath{\Delta}}{E}_{g}(R,T)$ is approximately $\ensuremath{-}150\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$ for $R=1.1\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ nanocrystals, and $\ensuremath{-}210\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$ for $R=0.7\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ nanocrystals, significantly larger in magnitude than in the case of bulk Si. We also find that in Si nanocrystals the band-gap deformation potential is positive, but smaller than in bulk Si.