The relaxation of high-energy hot carriers in semiconductors is known to involve the redistribution of energy between (i) hot and cold carriers and (ii) hot carriers and phonons. Over the past few years, these two processes have been identified in lead-halide perovskites (LHPs) using ultrafast pump-probe experiments, but the interplay between these processes is not fully understood. Here we present a comprehensive kinetic model to elucidate the individual effects of the hot and cold carriers in bulk and nanocrystal $CsPbBr_{3}$ films obtained from pump-push-probe measurements. In accordance with our previous work, we observe that the cooling dynamics in the materials decelerate as the number of hot carriers increases, which we explain through a hot-phonon bottleneck mechanism. On the other hand, as the number of cold carriers increases, we observe an acceleration of the cooling kinetics in the samples. We describe the interplay of these opposing effects using our model, and by using series of natural approximations, reduce this model to a simple form containing terms for the carrier-carrier and carrier-phonon interactions. The model can be instrumental for evaluating the details of carrier cooling and electron-phonon couplings in a broad range of LHP optoelectronic materials.
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