Impact of nitrogen and carbon on defect equilibrium in ZrO₂

We investigate the electronic properties of nitrogen and carbon impurities in ZrO₂ using density functional theory with a hybrid functional. It is commonly accepted that N substitutes on the O site and is stable in the −1 charge state (N_O⁻). The N_O⁻ acceptors are then compensated by donor defects such as O vacancies in the +2 charge state. We test the validity of this assumption by determining the formation energies of all relevant charge states of nitrogen and oxygen vacancies as a function of Fermi level. We also examine the effects of carbon, a common unintentional impurity in ZrO₂. We find that carbon impurities have relatively low formation energies and would indeed incorporate easily during growth of ZrO₂, but they do not affect the equilibrium between nitrogen and oxygen vacancies. Our results show that the Kröger-Vink picture is valid for common growth conditions and the dominant defects are N_O⁻ and V_O⁺².