The hydrogen interstitial and the substitutional ${\mathrm{Al}}_{\mathrm{Zn}}$, ${\mathrm{Ga}}_{\mathrm{Zn}}$, and ${\mathrm{In}}_{\mathrm{Zn}}$ are all shallow donors in ZnO and lead to $n$-type conductivity. Although shallow donors are expected to repel each other, we show by first-principles calculations that in ZnO these shallow donor impurities attract and form a complex, leading to a donor level deep in the band gap. This puts a limit on the $n$-type conductivity of (Al,Ga,In)-doped ZnO in the presence of hydrogen.

• Received 24 November 2011

DOI:https://doi.org/10.1103/PhysRevB.86.165207