  We report STM-induced desorption of H from Si(100)-H(2$\times1$) at negative
sample bias. The desorption rate exhibits a power-law dependence on current and
a maximum desorption rate at -7 V. The desorption is explained by vibrational
heating of H due to inelastic scattering of tunneling holes with the Si-H
5$\sigma$ hole resonance. The dependence of desorption rate on current and bias
is analyzed using a novel approach for calculating inelastic scattering, which
includes the effect of the electric field between tip and sample. We show that
the maximum desorption rate at -7 V is due to a maximum fraction of
inelastically scattered electrons at the onset of the field emission regime.
