Temperature-dependent evolution of photoluminescence

Photoluminescence (PL) is the process by which absorbed photons excite electrons, followed by thermalization and emission of light, playing an important role in science and engineering. Traditionally, PL is modeled using a nonzero chemical potential in Planck's law, describing its deviation from thermal emission. In this work, we establish a fundamental relationship that expresses the chemical potential as a function of the system's parameters: temperature, material properties, and excitation conditions. This formulation allows for the analysis of temperature-dependent PL characteristics, including spectral emission. It captures the transition from intense narrowband to broadband thermal emission, explaining the previously reported temperature-induced blueshift. These results provide potential insights into the thermodynamic and optical nature of PL, laying the foundations for designing temperature-tunable light sources.