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Description
Transparent conducting oxides (TCOs) are widely used for many applications. Typically, most of TCOs are intrinsically n-type semiconductors and are difficult to be doped for p-type conductivity. The spinel ZnRh$_2$O$_4$ has been recognized as a potential p-type TCO. In this work, we present energetics and electronic properties of native defects including vacancy, interstitial and antisite defects in ZnRh$_2$O$_4$ by mean of first-principles calculations. Computed pinned Fermi levels are closed to the valence band edge in any possible growth conditions. It is thus difficult to grow an n-type ZnRh$_2$O$_4$, which is consistent with experimental facts. Based on our calculated formation energies, we observe that the Zn vacancy (V$_{Zn}$) acts as a deep acceptor and has relatively high formation energy, and thus V$_{Zn}$ is unlikely to be responsible for the p-type conductivity. By contrast, we find that Zn substituting for Rh (Zn$_{Rh}$) acts as an acceptor forming a shallower transition level than that of V$_{Zn}$. Under O-rich/Rh-poor and Zn-rich/O-poor conditions, Zn$_{Rh}$ is found to be the major source of unintentional p-type conductivity in ZnRh$_2$O$_4$. To enhance hole concentration, we suggest experimentalists to grow ZnRh$_2$O$_4$ under high oxygen partial pressure with low Rh concentration.
