Influence of Fermi level position on vacancy-assisted diffusion of aluminum in zinc oxide

The influence of Fermi level position and annealing ambient on the zinc vacancy ${V}_{\mathrm{Zn}}$ generation and Al diffusion is studied in monocrystalline zinc oxide (ZnO). From secondary-ion mass spectrometry and positron annihilation spectroscopy results, a quadratic dependence between the concentrations of ${V}_{\mathrm{Zn}}$ and Al is established, demonstrating the Fermi level dependence of the formation of the electrically compensating $\ensuremath{-}2$ charge state of ${V}_{\mathrm{Zn}}$ in conductive $n$-type ZnO crystals. In contrast, thermal treatment in the zinc-rich ambient is shown to efficiently reduce the ${V}_{\mathrm{Zn}}$ concentration and related complexes. Using a reaction-diffusion model, the diffusion characteristics of Al at different donor background concentrations are fully accounted for by mobile (${\mathrm{Al}}_{\mathrm{Zn}}{V}_{\mathrm{Zn}}{)}^{\ensuremath{-}}$ pairs. These pairs form via the migration and reaction of isolated ${V}_{\mathrm{Zn}}^{2\ensuremath{-}}$ with the essentially immobile ${\mathrm{Al}}_{\mathrm{Zn}}⁺$. We obtain a migration barrier for the ${({\mathrm{Al}}_{\mathrm{Zn}}{V}_{\mathrm{Zn}})}^{\ensuremath{-}}$ pair of $2.4\ifmmode\pm\else\textpm\fi{}0.2$ eV, in good agreement with theoretical predictions. In addition to strongly alter the shape of the Al diffusion profiles, increasing the donor background concentration also results in an enhanced effective Al diffusivity, attributed to a reduction in the ${\mathrm{V}}_{\mathrm{Zn}}^{2\ensuremath{-}}$ formation energy as the Fermi level position increases.