Reduction of Monoclinic HfO₂: A Cascading Migration of Oxygen and Its Interplay with a High Electric Field

Using density functional theory, we investigated the formation of an extended Frenkel pair (EFP) in monoclinic m-HfO2 which we propose to be a prototype defect in oxide reduction by an intense electric field. We studied an emission mechanism that involves the cascading migration of 3-fold coordinated O atoms along the [001̅] direction leading to a well separated pair of oxygen vacancy (VO)/oxygen interstitial (Oi). For the neutral case, the calculated energy barrier at 5.2 eV is in good agreement with the activation energy value extracted from time to breakdown tests, supporting a thermochemical model for oxygen extraction from HfO2. An associated net dipole develops itself along the calculated emission path leading to an estimated critical electric field of 10 MV/cm. The role of charge injection on EFP formation and diffusion is also studied and shows a consequent lowering of the activation energy to 2.9 eV. The electroforming of an oxygen poor filament is commented in the framework of resistive random access memories.