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Group-III elements act as donors in ZnO when incorporated on the Zn site. Their incorporation and behavior upon annealing is governed by diffusion, which proceeds mainly through a vacancy-assisted process. We report first-principles calculations for the migration of Al, Ga, and In donors in ZnO, based on density functional theory using a hybrid functional. From the calculated migration barriers and formation energies, we determine diffusion activation energies and estimate annealing temperatures. Impurity-vacancy binding energies and migration barriers decrease from Al to In. Activation energies for vacancy-assisted diffusion are lowest for In and highest for Al.