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 multi-phonon process. Our results provide new insights into vibrational decay and the giant isotope effect of hydrogen in semiconductor systems.