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

Abstract

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.

Mechanisms of Oxygen Vacancy Aggregation in SiO2 and HfO2

“…The formation of pairs of O vacancies has been suggested in heavily thermochemically reduced MgO [18]. Recent simulations [19,20] have shed some light on the formation of O-vacancy clusters in SiO 2 and HfO 2 . Computational modeling was used to investigate the structures and binding energies of vacancy dimers and trimers in amorphous (a)-SiO 2 , the energy barriers for the diffusion of individual vacancies, and whether this diffusion can be stimulated by trapping of injected electrons at vacancies [19].…”

“…The calculations performed in Bradley et al [20] demonstrate that the formation of neutral oxygen vacancy dimers, trimers and tetramers in monoclinic HfO 2 is accompanied by an energy gain with respect to the separated vacancies, 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 energy gain per vacancy (0.11-0.18 eV).…”

Ab Initio Simulation of Ta2O5: A High Symmetry Ground State Phase with Application to Interface Calculation

“…At zero temperature, the structure of ground state Ta 2 O 5 crystal has been under debate for decades . On the other hand, the applied computational researches on Ta 2 O 5 /TaO x have been much rare, compared with HfO 2 /HfO x , though TaO x and HfO x share many properties in common and both are regarded as the most promising candidates for next‐generation memristors. This state of affairs is strongly related to the uncertainty regarding which model to use for the ground state of Ta 2 O 5 .…”

Stress Induced Vacancy Clustering Mechanism of Resistive Switching in Hafnium Oxides

“…+ may capture electrons tunneling from cathode to the middle part of the dielectric layer (it is described by the term (Fig.1a) which, in turn, can also trap electrons and transform to neutral vacancies, O V . Positively charged vacancies cannot form vacancy clusters with each other [8]. Furthermore, we assume, that vacancy clusters of any size may contain no more than single one-charged vacancy, otherwise they decompose.…”

“…Furthermore, we assume, that vacancy clusters of any size may contain no more than single one-charged vacancy, otherwise they decompose. This assumption is justified due to the Coulomb's repulsion energy of two elementary point charges separated by interatomic distance (~ 0.4 nm), which is about 3.6 eV, while the binding energy between lattice vacancies does not usually exceed 0.5 eV [8] (Fig. 1b), which may capture tunneling electron and transform to a neutral bi-vacancy.…”