Volume and surface effects on two-photonic and three-photonic processes in dry co-doped upconversion nanocrystals

Despite considerable advances in synthesizing high-quality core/shell upconversion (UC) nanocrystals (NC; UCNC) and UCNC photophysics, the application of near-infrared (NIR)-excitable lanthanide-doped UCNC in the life and material sciences is still hampered by the relatively low upconversion luminescence (UCL) of UCNC of small size or thin protecting shell. To obtain deeper insights into energy transfer and surface quenching processes involving Yb³⁺ and Er³⁺ ions, we examined energy loss processes in differently sized solid core NaYF₄ nanocrystals doped with either Yb³⁺ (YbNC; 20% Yb³⁺) or Er³⁺ (ErNC; 2% Er³⁺) and co-doped with Yb³⁺ and Er³⁺ (YbErNC; 20% Yb³⁺ and 2% Er³⁺) without a surface protection shell and coated with a thin and a thick NaYF₄ shell in comparison to single and co-doped bulk materials. Luminescence studies at 375 nm excitation demonstrate back-energy transfer (BET) from the ⁴G_11/2 state of Er³⁺ to the ²F_5/2 state of Yb³⁺, through which the red Er^{3+ 4}F_9/2 state is efficiently populated. Excitation power density (P)-dependent steady state and time-resolved photoluminescence measurements at different excitation and emission wavelengths enable to separate surface-related and volume-related effects for two-photonic and three-photonic processes involved in UCL and indicate a different influence of surface passivation on the green and red Er³⁺ emission. The intensity and lifetime of the latter respond particularly to an increase in volume of the active UCNC core. We provide a three-dimensional random walk model to describe these effects that can be used in the future to predict the UCL behavior of UCNC.