Multiple Linear Regression‐Enhanced Optical Thermometry via Phonon‐Assisted Back Energy Transfer in Tm3+‐Eu3+ Co‐Doped Phosphors

Abstract Optical thermometry utilizing the fluorescence intensity ratio (FIR) mode has garnered significant attention due to its notable benefits, such as non‐contact, high sensitivity, and fast response. However, the accuracy and precision of FIR thermometry limit its further applications. Herein, multiple linear regression (MLR) is developed to optimize these thermometry parameters of Tm 3+ ‐Eu 3+ co‐doped Y 3 TaO 7 phosphors. By adjusting the doping concentration of Tm 3+ and Eu 3+ , the energy transfer efficienc from Tm 3+ to Eu 3+ can reach 86.44%. Interestingly, the abnormal anti‐thermal quenching of Tm 3+ is found in the temperature range of 303–563 K, which is assisted by the phonon‐assisted back energy transfer from Eu 3+ to Tm 3+ at elevated temperatures. The maximum relative sensitivity (S r ) of Y 3 TaO 7 : Tm 3+ , Eu 3+ reaches 0.541% K −1 and 0.207% K −1 based on the single FIR and fluorescence lifetime mode, respectively. Importantly, the MLR model combined with FIR, fluorescence lifetime, and absolute emission peak intensity is developed, the S r can be increased to 1.78%–2.37% K −1 in the temperature range of 303–503 K, and the 10 −3 orders temperature uncertainty of magnitude is maintained. These results confirm that the back energy transfer mechanism and MLR can be extended as a new strategy to design and optimize optical thermometry materials.