Vibrational lifetimes and frequency-gap law of hydrogen bending modes in semiconductors.

Vibrational lifetimes of hydrogen and deuterium related bending modes in semiconductors are measured by transient bleaching spectroscopy and high-resolution infrared absorption spectroscopy. We find that the vibrational lifetimes follow a universal frequency-gap law; i.e., the decay time increases exponentially with increasing decay order, with values ranging from 1 ps for a one-phonon process to 265 ps for a four-phonon process. The temperature dependence of the lifetime shows that the bending mode decays by lowest-order multiphonon process. Our results provide new insights into vibrational decay and the giant isotope effect of hydrogen in semiconductor systems.