Origins of thep-type nature and cation deficiency inCu2Oand related materials

While most of crystalline wide gap oxides are both stoichiometric and insulating, a handful of them including ZnO and ${\mathrm{In}}_2{\mathrm{O}}_3$ are naturally anion-deficient and electron conductors. Even fewer of the oxides are naturally cation-deficient and hole conductors, the arch-type of which is ${\mathrm{Cu}}_2\mathrm{O}$. Based on first principles calculation of equilibrium nonstoichiometry and defect stability, we explain why the ${\mathrm{Cu}}^{\left(\mathrm{I}\right)}\left(d^{10}\right)$ oxide-based materials are both $p$-type and naturally cation-deficient, and why cation vacancies lead to delocalized, conductive states, whereas in other oxides (e.g., ZnO and MgO), they lead to localized, nonconductive states.