Vacancy-assisted migration of group-III impurities in ZnO*

Zinc oxide is a wide-band-gap material used as transparent conductor. As grown it often shows n-type conductivity, probably due to impurity contamination. High electron concentrations can be achieved by intentional doping with group-III elements, a process that usually involves annealing. It is thus important to understand the diffusion properties of the dopants. We perform first-principles calculations for the vacancy-assisted migration process of Al, Ga and In in ZnO, using both standard density functionals and hybrid functionals to correct the underestimated band gap. Indium induces the largest distortions in the lattice and has the highest formation energy. Its migration barrier to a neighboring Zn vacancy is the lowest. Al shows the highest barrier and thus has the best thermal stability. From the calculated migration barriers and formation energies, we determine diffusion activation energies and estimate annealing temperatures. The results are compared with recent experiments.