Temperature-dependent photoluminescence: A theoretical study

Photoluminescence (PL) is a light matter quantum interaction associated with the chemical potential of light formulated by the Generalized Planck's law. Without knowing the inherent temperature dependence of chemical potential, the Generalized Planck's law is insufficient in order to characterize PL vs. T. Recent experiments showed that PL at a critical temperature abruptly shifts from a conserved rate, accompanied by a blue-shift, to thermal emission. Here, we theoretically study temperature dependent PL by including phononic interactions in a detailed balance analysis. We show that in a three-level system, both chemical potential and T are defined in the case of fast thermalization. Our solution validates recent experiments and predicts new features, including an inherent relation between emissivity and external quantum efficiency of a system, a universal point defined by the pump and the temperature where the emission rate is fixed to any material, a new phonon induced quenching mechanism, and thermalization of the photon spectrum. Our high temperature luminescence solution is relevant to and important for all photonic fields where the temperature is dominant