Oxygen migration around the filament region in HfOx memristors

The exact composition and structure of conductive filaments in hafnia-based memristors are still not fully understood, but recent theoretical investigations reveal that hexagonal HfOx phases close to the h.c.p. Hf structure are probable filament candidates. In this work we list h.c.p. Hf, Hf6O, Hf3O and Hf2O as possible phases for the filament in hafnia memristors. Their differences in lattice parameters, electronic structures and O charge states are studied in details. Migration of O ions for both in-plane and out-of-plane directions in these phases is investigated using first-principles calculations. Both single-phase supercells and filament-in-dielectric models are used for migration barrier calculations, while the latter is proven to be more accurate for the c-direction. The migration of O ions is fastest in metal Hf, while slowest in Hf2O. The existence of O interstitials in Hf tends to hinder the transport of O.