Control of Doping by Impurity Chemical Potentials: Predictions for $\mathit{p}$-Type ZnO

Theoretical work has so far focused on the role of host-element chemical potentials in determining defect formation energies that control doping levels in semiconductors. Here, we report on our analysis of the role of the dopant-impurity chemical potential, which depends on the source gas. We present first-principles total-energy calculations that demonstrate a wide variation in the possible effective chemical potential of N. We account in detail for the recent puzzling observations of doping ZnO using ${\mathrm{N}}_2$ and ${\mathrm{N}}_2\mathrm{O}$ and predict that the use of dilute NO or ${\mathrm{NO}}_2$ gas would resolve the long-standing problem of achieving p-type ZnO.