  Thermal electron emission process of a hydrogen impurity is an important
topic of fundamental semiconductor physics. Despite of decades-long study,
theory is not established yet. Here, we study the process of $\mathrm{H}^{-}$
in silicon, $\mathrm{H^{-}} \to \mathrm{H^{0}} + e^{-}$, using a
first-principles calculation. Our calculation indicates that the process
consists of two steps: slow diffusion of H$^{-}$ from a tetrahedral site to a
bond-center site, which is the rate-limiting step, and faster nonradiative
transition from $\mathrm{H}^{-}$ to $\mathrm{H}^{0} + e^{-}$ that occurs
subsequently at the body-center site. The calculated rate is consistent with a
deep level transient spectroscopy experiment
