Theoretical Evaluation of Oxidation Rate of Zr

First principle calculations were performed to evaluate stress effect on the diffusion process of oxygen vacancy in ZrO2 film, and oxidation rate of Zr was evaluated by solving simple diffusion equations. Our calculation results have indicated that both the vacancy formation and migration energies of ZrO2 increase with increasing compressive applied stress. The energy increase causes a decrease in the diffusion coefficient of oxygen vacancy in ZrO2, leading to a decrease in oxidation rate of Zr. The stress effect on diffusion process may explain the experimental fact that Zr is oxidized in proportion to the cubic root of time.