  We report a first principles study of the structure and the vibrational
properties of the Si(100)-H(2 \times 1) surface in an electric field. The
calculated vibrational parameters are used to model the vibrational modes in
the presence of the electric field corresponding to a realistic STM tip-surface
geometry. We find that local one-phonon excitations have short lifetimes (10 ps
at room temperature) due to incoherent lateral diffusion, while diffusion of
local multi-phonon excitations are suppressed due to anharmonic frequency
shifts and have much longer lifetimes (10 ns at room temperature). We calculate
the implications for current induced desorption of H using a recently developed
first principles model of electron inelastic scattering. The calculations show
that inelastic scattering events with energy transfer $n \hbar \omega$, where
n>1, play an important role in the desorption process.
