Theory of hot carriers and carrier heating in a semiconductor under continuous illumination

The dynamics of the optically generated hot carriers in semiconductors are critically important to estimate the performance of electronic and optoelectronic devices. The interplay of optically generated carriers, their thermalization, and recombination leads to the formation of non-equilibrium distributions of hot carriers, and heating of carriers and phonons. Surprisingly, a theoretical framework, incorporating the non-equilibrium nature of the carriers and the carrier heating effect, is lacking to date. Here we present a semi-quantum coupled Boltzmann-heat equation formalism for calculating the non-equilibrium steady-state electron and hole distributions and temperatures. The formalism correctly accounts for energy and particle number conservation required for a physically-consistent solution of the Boltzmann equations. We show how the illumination energy splits between the different energy dissipation channels, and find a non-linear dependence of the electron and hole temperatures on illumination intensity, originating from the interplay between carrier-carrier interactions, carrier-phonon dissipation, and carrier recombination. These results are the first step towards a full estimation of hot-carrier generation on efficiency in solar cells and other optoelectronic devices.