Isotope effect in the vibrational lifetime of the CH$_{2}^{\ast}$ defect in Si

The CH$_{2}^{\ast}$ defect in Si has two metastable configurations with H bound at bond-centered (BC) or antibonding (AB) sites of Si and C: Si-H$_{BC}$...C-H$_{AB}$ or H$_{AB}$-Si...H$_{BC}$-C. Th IR absorption signature of this defect should consist of four sharp lines associated with the two Si-H and two C-H stretch modes, respectively. Yet, only three modes have seen by FTIR, and the fourth, very broad, line has only recently been reported by the highly sensitive multiple-internal-reflection FTIR. Further, the ``missing'' mode produces a very sharp line only for the deuterium substitution Si-H$_{BC}$...C-D$_{AB}$. Our calculations show that this is due to the isotope-dependence of the vibrational lifetime of this mode. The C-H mode decays very quickly into two phonons and the very short lifetime causes the IR line to be extremely broad. On the other hand, the C-D mode has a much longer lifetime and decays into at least three phonons, resulting in a much sharper IR line. We will report the calculations of these vibrational lifetimes.