Absolute quantum yield for understanding upconversion and downshift luminescence in PbF₂:Er³⁺,Yb³⁺ crystals

The search for new materials capable of efficient upconversion continues to attract attention. In this work, a comprehensive study of the upconversion luminescence in PbF₂:Er³⁺,Yb³⁺ crystals with different concentrations of Yb³⁺ ions in the range of 2 to 7.5 mol% (Er³⁺ concentration was fixed at 2 mol%) was carried out. The highest value of upconversion quantum yield (ϕ_UC) 5.9% (at 350 W cm^-2) was found in the PbF₂ crystal doped with 2 mol% Er³⁺ and 3 mol% Yb³⁺. Since it is not always easy to directly measure ϕ_UC and estimate the related key figure of merit parameter, saturated photoluminescence quantum yield (ϕ_UCsat), a method to reliably predict ϕ_UCsat can be useful. Judd-Ofelt theory provides a convenient way to determine the radiative lifetimes of the excited states of rare-earth ions based on absorption measurements. When the luminescence decay times after direct excitation of a level are also measured, ϕ_UCsat for that level can be calculated. This approach is tested on a series of PbF₂:Er³⁺,Yb³⁺ crystals. Good agreement between the estimates obtained as above and the directly experimentally measured ϕ_UCsat values is demonstrated. In addition, three methods of Judd-Ofelt calculations on powder samples were tested and the results were compared with Judd-Ofelt calculations on single crystals, which served as the source of the powder samples. Taken together, the results presented in our work for PbF₂:Er³⁺,Yb³⁺ crystals contribute to a better understanding of the UC phenomena and provide a reference data set for the use of UC materials in practical applications.