Modelling of oxygen vacancy aggregates in monoclinic HfO2: can they contribute to conductive filament formation?

Formation of metal rich conductive filaments and their rearrangements determine the switching characteristics in HfO2 based resistive random access memory (RRAM) devices. The initiation of a filament formation process may occur either via aggregation of pre-existing vacancies randomly distributed in the oxide or via generation of new oxygen vacancies close to the pre-existing ones. We evaluate the feasibility of vacancy aggregation processes by calculating the structures and binding energies of oxygen vacancy aggregates consisting of 2, 3 and 4 vacancies in bulk monoclinic (m)-HfO2 using density functional theory (DFT). We demonstrate that formation of neutral oxygen vacancy aggregates is accompanied by small energy gain, which depends on the size and shape of the aggregate. In the most strongly bound configurations, vacancies are unscreened by Hf cations and form voids within the crystal, with the larger aggregates having larger binding energy per vacancy (-0.11 to  -0.18 eV). The negatively charged di-vacancy was found to have similar binding energies to the neutral one, while the positively charged di-vacancy was found to be unstable. Thus aggregation process of either neutral or negatively charged oxygen vacancies is energetically feasible.