A modified model for thermodynamics of localized-state luminescence in disordered materials

Carrier localization in semiconductor materials often arises from band fluctuations, causing energy minima that trap carriers. The anomalous luminescence behaviors of localized states in such materials are complex to investigate quantitatively. In this paper, we propose a novel and accessible method for analyzing the temperature dependence of localized-state luminescence by modifying the localized-state ensemble model. The thermal carrier redistribution effect on the temperature-dependent luminescence peak position is explained by a small energy shift near the density of states center of localized states, yielding a simple and physically intuitive expression. This method accurately reproduces the “S-shaped” temperature dependence of the luminescence peak position. Its validity is confirmed by fitting various systems, demonstrating good consistency with the previous models. Additionally, analytical formulas for the changes of entropy and enthalpy in the localized systems are derived, revealing that entropy and enthalpy peak at intermediate temperatures due to the carrier redistribution and delocalization effects. This thermodynamic analysis offers deeper insights into the microscopic properties of localized states. The modified model will provide a more accessible framework for the quantitative study of the thermodynamics of localized-state luminescence in disordered materials.