Determination of radiative and multiphonon non-radiative relaxation rates of upconversion materials

The radiative and multiphonon non-radiative relaxation rates of lanthanide ions are intrinsic parameters to characterize the optical properties, which are the basic data for the theoretical model and numerical simulation of lanthanide upconversion systems. However, there are complex energy transfer processes, such as energy migration, energy transfer upconversion, and cross-relaxation in the lanthanide-doped upconversion materials, so it is difficult to accurately measure the intrinsic radiative and multiphonon relaxation rates. Therefore, a method to determine the relaxation rates of multi-level upconversion systems is proposed based on multi-wavelength excitation and level-by-level parameter calculations in this paper. For a dilute doped multi-level luminescence system excited at low powers, a model based on the measurements of steady-state emission spectra and luminescence decay curves is established through the macroscopic rate equations at multi-wavelength excitation, which can be used for the level-by-level calculation of the multi-level radiative and multiphonon relaxation rates. With the dilute doped β-NaYF₄:Er³⁺ six-level luminescence system as an example, the measurement method and the model are introduced in detail. Under the experimental conditions of neglecting the energy transfer effect between ions, the materials are excited by five lasers with central wavelengths of 1523 nm, 980 nm, 808 nm, 660 nm, and 520 nm to form five subsystems. The steady-state emission spectra and luminescence decay curves of the luminescence system excited by each wavelength were recorded. The intrinsic relaxation rates including 11 radiative relaxation rates and 4 multiphonon relaxation rates in the β-NaYF₄:Er³⁺ six-level system were determined based on the established model and method, which experimentally verified the applicability of the method proposed in this paper. This work will provide basic data for the analysis and regulation of the luminescence properties of lanthanide upconversion systems.