Existing defect models for ${\mathrm{In}}_2{\mathrm{O}}_3$ and ZnO are inconclusive about the origin of conductivity, nonstoichiometry, and coloration. We apply systematic corrections to first-principles calculated formation energies $\Delta H$, and validate our theoretical defect model against measured defect and carrier densities. We find that (i) intrinsic acceptors (“electron killers”) have a high $\Delta H$ explaining high $n$-dopability, (ii) intrinsic donors (“electron producers”) have either a high $\Delta H$ or deep levels, and do not cause equilibrium-stable conductivity, (iii) the O vacancy $V_{\mathrm{O}}$ has a low $\Delta H$ leading to O deficiency, and (iv) $V_{\mathrm{O}}$ has a metastable shallow state, explaining the paradoxical coexistence of coloration and conductivity.

• Received 7 September 2006

DOI:https://doi.org/10.1103/PhysRevLett.98.045501