Atomistic modeling of As diffusion in ZnO

Ab initio methods are used to predict the diffusion coefficient of As dopants in ZnO as a function of Fermi level. Contributions to As diffusion from interstitial, simple substitutional, and cluster diffusion are considered. Formation and migration energies for Zn vacancies (V${}_{\mathrm{Zn}}$), As substituting on Zn lattice sites (As${}_{\mathrm{Zn}}$), complexes of As with up to two Zn vacancies (As${}_{\mathrm{Zn}}$-1V${}_{\mathrm{Zn}}$ and As${}_{\mathrm{Zn}}$-2V${}_{\mathrm{Zn}}$), and interstitial Zn and As (Zn${}_{\mathrm{I},\mathrm{oct}}$ and As${}_{\mathrm{I},\mathrm{oct}}$) are calculated using GGA $+$ $U$ and hybrid Hartree-Fock density-functional theory calculations. As${}_{\mathrm{Zn}}$ is the dominant As-containing donor and As${}_{\mathrm{Zn}}$-2V${}_{\mathrm{Zn}}$ is the dominant As-containing acceptor. At low Fermi levels, As is mostly immobile, while at high Fermi levels, As${}_{\mathrm{Zn}}$-2V${}_{\mathrm{Zn}}$ is mobile with a migration energy of 1.6 eV.