Simulating Energy Transfer and Upconversion in β-NaYF 4 : Yb 3+ , Tm 3+

The design of upconversion phosphors with higher quantum yield requires a deeper understanding of the detailed energy transfer and upconversion processes between active ions inside the material. Rate equations can model those processes by describing the populations of the energy levels of the ions as a function of time. However, this model presents some drawbacks: energy migration is assumed to be infinitely fast, it does not determine the detailed interaction mechanism (multipolar or exchange), and it only provides the macroscopic averaged parameters of interaction. Hence, a rate equation model with the same parameters cannot correctly predict the time evolution of upconverted emission and power dependence under a wide range of concentrations of active ions. We present a model that combines information about the host material lattice, the concentration of active ions, and a microscopic rate equation system. The extent of energy migration is correctly taken into account because the energy transfer processes are described on the level of the individual ions. This model predicts the decay curves, concentration, and excitation power dependences of the emission. This detailed information can be used to predict the optimal concentration that results in the maximum upconverted emission.