Dynamics of hydrogen in silicon at finite temperatures from first-principles

Hydrogen point defects in silicon still hold unsolved problems, whose disclosure is fundamental for future advances in Si technologies. Among the open issues is the mechanism for the condensation of atomic hydrogen into molecules in Si quenched from above $T\sim700\,^{\circ}$C to room temperature. Based on first-principles calculations, we investigated the thermodynamics of hydrogen monomers and dimers at finite temperatures within the harmonic approximation. The free energies of formation indicate that the population of H$^{-}$ cannot be neglected when compared that of H$^{+}$ at high temperatures. The results allow us to propose that the formation of molecules occurs during cooling processes, in the temperature window $T\sim700\textrm{-}500\,$K, above which the molecules collide with Si-Si bonds and dissociate, and below which the fraction of H$^{-}$ becomes negligible. The formation of H$^{-}$ and most notably of a fast-diffusing neutral species could also provide an explanation for the apparent \emph{accelerated} diffusivity of atomic hydrogen at elevated temperatures in comparison to the figures extrapolated from measurements carried out at cryogenic temperatures. We finally show that the observed diffusivity of the molecules is better described upon the assumption that they are nearly free rotors, all along the minimum energy path, including at the transition state.