Impact of nitrogen and carbon on defect equilibrium in ZrO2

Abstract 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 Kroger-Vink picture is valid for common growth conditions and the dominant defects are N O − and V O + 2 .