Theory of Non-equilibrium Hot Carriers in Direct Band-gap Semiconductors Under Continuous Illumination

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 photo-luminescence 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.