  We study the influence of the pulse energy and fluence on the thermalization
of photo-doped Mott insulators. If the Mott gap is smaller than the width of
the Hubbard bands, the kinetic energy of individual carriers can be large
enough to produce doublon-hole pairs via a process analogous to impact
ionization. The thermalization dynamics, which involves an adjustment of the
doublon and hole densities, thus changes as a function of the energy of the
photo-doped carriers and exhibits two timescales -- a fast relaxation related
to impact ionization and a slower timescale associated with higher-order
scattering processes. The slow dynamics depends more strongly on the gap size
and the photo-doping concentration.
