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Vacancy clusters have been observed in ZnO by positron-annihilation spectroscopy (PAS), but detailed mechanisms are unclear. This is because the clustering happens in non-equilibrium conditions, for which theoretical method has not been well established. Combining first-principles calculation and kinetic Monte Carlo simulation, we determine the roles of non-equilibrium kinetics on the vacancies clustering. We find that clustering starts with the formation of Zn and O vacancy pairs (VZn-Vo), which further grow by attracting additional mono-vacancies. At this stage, vacancy diffusivity becomes crucial: due to the larger diffusivity of VZn compared to VO, more VZn-abundant clusters are formed than VO-abundant clusters. The large dissociation energy barriers, e.g., over 2.5 eV for (VZn-Vo), suggest that, once formed, it is difficult for the clusters to dissociate. By promoting mono-vacancy diffusion, thermal annealing will increase the size of the clusters. As the PAS is insensitive to VO donor defects, our results suggest an interpretation of the experimental data that could not have been made without the in-depth calculations. [ABSTRACT FROM AUTHOR]

We propose a phase field method to model consistently dislocation climb by vacancy absorption or emission. It automatically incorporates the exact balance between the vacancy flux and the phase field associated with the dislocation evolution, enforced by the conserved character of the total population of vacancies. One of its major advantage is the natural introduction of a dynamic coefficient controlling the kinetics of vacancy emission/absorption by the dislocation. We also derived a closed-form expression of the climb rate valid from the diffusion-limited to the attachment-limited regimes. [ABSTRACT FROM AUTHOR]