  We compute the transient dynamics of phonons in contact with high energy
"hot" charge carriers in 12 polar and non-polar semiconductors, using a
first-principles Boltzmann transport framework. For most materials, we find
that the decay in electronic temperature departs significantly from a
single-exponential model at times ranging from 1 ps to 15 ps after electronic
excitation, a phenomenon concomitant with the appearance of non-thermal
vibrational modes. We demonstrate that these effects result from the slow
thermalization within the phonon subsystem, caused by the large heterogeneity
in the timescales of electron-phonon and phonon-phonon interactions in these
materials. We propose a generalized 2-temperature model accounting for the
phonon thermalization as a limiting step of electron-phonon thermalization,
which captures the full thermal relaxation of hot electrons and holes in
semiconductors. A direct consequence of our findings is that, for
semiconductors, information about the spectral distribution of electron-phonon
and phonon-phonon coupling can be extracted from the multi-exponential behavior
of the electronic temperature.
