Effect of electric field on defect generation and migration in HfO2

Abstract

Understanding the effect of electric fields on defect creation and diffusion in metal oxides is of fundamental importance for developing accurate models of oxide degradation in electronic devices and dielectric breakdown. We use the Berry phase operator method within density functional theory to calculate how an applied electric field affects barriers for the creation of oxygen vacancy-interstitial defect pairs (DPs) and diffusion of interstitial O ions in monoclinic ($m$-)${\mathrm{HfO}}_{2}$. The results demonstrate that even close to breakdown fields, barriers for DP generation exceed 6 eV in the perfect $m\ensuremath{-}{\mathrm{HfO}}_{2}$ lattice. Simulated injection of extra electrons from electrodes significantly lowers barriers for the creation of DPs, which are further reduced by the field to around 1 eV. Thus, bias application facilitates the injection of electrons into the oxide; these extra electrons reduce energy barriers for the creation of O vacancies, and these barriers as well as those for O ion diffusion are further lowered by the field. We find that, within a linear regime, the electric field modulates the barrier height by a dot product between the electric field and the electric dipole at the zero-field transition state to good accuracy.