  The T-center in silicon is a well-known carbon-based color center that has
been recently considered for quantum technology applications. Using first
principles computations, we show that the excited state is formed by a
defect-bound exciton made of a localized defect state occupied by an electron
to which a hole is bound. The localized state is of strong carbon \textit{p}
character and reminiscent of the localization of the unpaired electron in the
ethyl radical molecule. The radiative lifetime for the defect-bound exciton is
calculated to be on the order of $\mu$s, much longer than other quantum defects
such as the NV center in diamond and in agreement with experiments. The longer
lifetime is associated with the small transition dipole moment as a result of
the very different nature of the localized and delocalized states forming the
defect-bound exciton. Finally, we use first principles calculations to assess
the stability of the T-center. We find the T-center to be stable against
decomposition into simpler defects when keeping the stoichiometry fixed.
However, we identify that the T-center is easily prone to (de)hydrogenation and
so requires very precise annealing conditions (temperature and atmosphere) to
be efficiently formed.
