  The interplay between the illuminated excitation of carriers and subsequent
thermalization and recombination leads to the formation of non-equilibrium
distributions for the "hot" carriers and to heating of both electrons, holes
and phonons. In spite of the fundamental and practical importance of these
processes, there is no theoretical framework which encompasses all of them and
provides a clear prediction for the non-equilibrium carrier distributions.
Here, a self-consistent theory accounting for the interplay between excitation,
thermalization, and recombination in continuously-illuminated semiconductors is
presented, enabling the calculation of non-equilibrium carrier distributions.
We show that counter-intuitively, distributions deviate more from equilibrium
under weak illumination than at high intensities. We mimic two experimental
procedures to extract the carrier temperatures and show that they yield
different dependence on illumination. Finally, we provide an accurate way to
evaluate photoluminescence efficiency, which, unlike conventional models,
predicts correctly the experimental results. These results provide a starting
point towards examining how non-equilibrium features will affect properties
hot-carrier based application.
