The transport properties of oxygen vacancy-related polaron-like bound state in HfOx

The oxygen vacancy-related polaron-like bound state migration in HfOx accounting for the observed transport properties in the high resistance state of resistive switching is investigated by the density functional theory with hybrid functional. The barrier of hopping among the threefold oxygen vacancies is strongly dependent on the direction of motion. Especially, the lowest barrier along the <001> direction is 90 meV, in agreement with the experimental value measured from 135 K to room temperature. This hopping mainly invokes the z-directional motion of hafnium and threefold oxygen atoms in the vicinity of the oxygen vacancy resulted from the synergized combination of coupled phonon modes. In the presence of surface, the lowest barrier of hopping between the surface oxygen vacancies is 360 meV along the <101> direction, where the significant surface perpendicular motion of hafnium and twofold oxygen atoms surrounding the oxygen vacancy is identified to facilitate this type of polaron-like bound state migration. Thus, the migration on the surfaces could be more important at the high temperature.