Anomalous Diffusion and Decay of Clusters of Dopants in Lanthanide-Doped Nanocrystals

Upconversion (UC) luminescence in doped lanthanide nanocrystals is associated with the energy migration (EM) process within clusters of dopant ions. The process of the synthesis of core-shell nanocrystals occurs at elevated temperatures, promoting the diffusion of the dopants into the shell accompanied by the decay of dopant clusters. The details of this unwanted effect are poorly understood. In this paper, we theoretically study a model of the diffusion of dopant ions in a nanocrystal using Monte Carlo (MC) simulations. We characterize the diffusion, spatial neighboring relations and clustering of dopant ions regarding the function of reduced temperature and MC time of the heating process. The dopants undergo a weak subdiffusion caused by trapping effects. The main results of this study are as follows: (i) the phase diagram of the variables reduced the temperature and MC time, which separates the enhanced and limited cluster-driven EM regimes, and (ii) a dependence of the average nearest distance between Yb ions as a function of reduced temperature, the concentration of Yb ions and MC time was found. In both cases, the requirements for an effective EM are formulated.