Explaining the Nanoscale Effect in the Upconversion Dynamics of β‑NaYF₄:Yb³⁺, Er³⁺ Core and Core–Shell Nanocrystals

Nanocrystals of β-NaYF₄:Yb³⁺, Er³⁺ generally have lower NIR-to-visible upconversion (UC) internal quantum efficiency, IQE, compared to high-quality bulk materials, and exhibit more rapid UC dynamics, typical of quenching, when excited with a pulsed source near 980 nm. The addition of a protective shell increases the IQE of the nanocrystals and slows the overall excited-state dynamics. Here, we show that an extension of a recently developed model for UC in powders of micron-sized β-NaYF₄:18%Yb³⁺, 2%Er³⁺ crystals correctly predicts the time-resolved luminescence curve shapes, relative intensities, and observed drop in IQE of the various emission lines for core and core–shell nanoparticles following pulsed excitation. The model clearly shows that the nanoscale effect on visible upconversion luminescence in these materials, with typical high-Yb³⁺ and low-Er³⁺ doping, is largely due to rapid energy migration among Yb³⁺(²F_5/2) and Er³⁺(⁴I_11/2) ions at the 1 μm energy level, such that an equilibrium is achieved between interior sites and rapidly relaxing surface sites. The faster kinetics observed in visible emission following pulsed NIR excitation is mainly a propagation of the effect of surface quenching of the 1 μm reservoir states and is not due to direct quenching of the visible emitting states themselves. For Er³⁺ ions contributing to UC emission, the relaxation rate constants for the blue (²H_9/2), green (²H_11/2, ⁴S_3/2), and red (⁴F_9/2) emitting states are essentially unchanged from their bulk values, indicating that Er³⁺ ions close to the nanoparticle surface are nearly silent with regard to UC. The addition of a passive β-NaYF₄ shell retards the drain of the 1 μm excitation reservoir and recovers the participation of outer Er³⁺ sites in UC. The dependence of IQE on shell thickness is well explained in terms of a Förster-type model describing an energy donor (Er³⁺, Yb³⁺) interacting with a thin plane layer of acceptors (oleate). The UC behavior of both the core and the core–shell nanocrystals can be modeled, almost quantitatively, solely on the basis of quenching at the 1 μm level, without separate consideration of a near-surface Er³⁺ population. However, a two-layer model for the core nanoparticles is revealing with regard to the modest extent to which near-surface ions do participate in UC and gives a better representation of the detailed dynamics of the NIR emitting states. A method is presented for allowing investigators to estimate the IQE for any nanosample (with 18% Yb³⁺, 2%Er³⁺ doping) as a function of excitation power density (cw) or pulse-energy density based on the low pulse energy measurement of the decay constant for the 1 μm emission