Modeling blue to UV upconversion in β-NaYF₄:Tm³

Samples of 0.01% and 0.3% Tm³⁺-doped β-NaYF₄ show upconverted UV luminescence at 27 660 cm^-1 (361 nm) after blue excitation at 21 140 cm^-1 (473 nm). Contradictory upconversion mechanisms in the literature are reviewed and two of them are investigated in detail. Their agreement with emission and two-color excitation experiments is examined and compared. Decay curves are analyzed using the Inokuti-Hirayama model, an average rate equation model, and a microscopic rate equation model that includes the correct extent of energy transfer. Energy migration is found to be negligible in these samples, and hence the average rate equation model fails to correctly describe the decay curves. The microscopic rate equation model accurately fits the experimental data and reveals the strength and multipolarity of various interactions. This microscopic model is able to determine the most likely upconversion mechanism.