Understanding conduction in ${\mathrm{Cu}}_2\mathrm{O}$ is vital to the optimization of Cu-based $p$-type transparent conducting oxides. Using a screened hybrid–density-functional approach we have investigated the formation of $p$-type defects in ${\mathrm{Cu}}_2\mathrm{O}$ giving rise to single-particle levels that are deep in the band gap, consistent with experimentally observed activated, polaronic conduction. Our calculated transition levels for simple and split copper vacancies explain the source of the two distinct hole states seen in DLTS experiments. The necessity of techniques that go beyond the present generalized-gradient- and local-density-approximation techniques for accurately describing $p$-type defects in Cu(I)-based oxides is discussed.

• Received 7 July 2009

DOI:https://doi.org/10.1103/PhysRevLett.103.096405