Understanding Yb³⁺-sensitized photon avalanche in Pr³⁺ co-doped nanocrystals: modelling and optimization

Among different upconversion processes where the emitted photon has higher energy than the one absorbed, photon avalanche (PA) is unique, because the luminescence intensity increases by 2-3 orders of magnitude in response to a tiny increase in excitation intensity. Since its discovery in 1979, PA has been observed in bulk materials but until recently, obtaining it at the nanoscale has been a significant challenge. In the present work, the PA phenomenon in β-NaYF₄ colloidal nanocrystals co-doped with Pr³⁺ and Yb³⁺ ions was successfully observed at 482 nm (³P₀ → ³H₄) and 607 nm (³P₀ → ³H₆) under excitation at 852 nm. The impact of Pr³⁺ ion concentration and pump power dependence on PA behavior was investigated, i.e. PA non-linearity slopes of luminescence intensity curves as a function of pump power density as well as PA thresholds. The highest slopes, namely 8.6 and 9.0, and the smallest thresholds equal to 286 kW cm^-2 and 281 kW cm^-2, observed for emission bands at 607 nm and 482 nm, respectively, were obtained for NaYF₄:0.5%Pr³⁺,15%Yb³⁺@NaYF₄ colloidal nanocrystals. Besides experimental research, simulations of PA behavior in Pr³⁺, Yb³⁺ co-doped materials were performed based on differential rate equations describing the phenomena that contribute to the existence of PA. The influence of different processes leading to PA, e.g. the rates of nonradiative and radiative transitions as well as energy transfers, on PA performance was simulated aiming to understand their roles in this complex sensitized system.