Field-enhanced route to generating anti-Frenkel pairs in HfO2

The generation of anti-Frenkel pairs (oxygen vacancies and oxygen interstitials) in monoclinic and cubic ${\mathrm{HfO}}_{2}$ under an applied electric field is examined. A thermodynamic model is used to derive an expression for the critical field strength required to generate an anti-Frenkel pair. The critical field strength of ${\mathcal{E}}_{\mathrm{aF}}^{\mathrm{cr}}\ensuremath{\sim}{10}^{1}\phantom{\rule{0.16em}{0ex}}{\mathrm{GVm}}^{\ensuremath{-}1}$ obtained for ${\mathrm{HfO}}_{2}$ exceeds substantially the field strengths routinely employed in the forming and switching operations of resistive switching ${\mathrm{HfO}}_{2}$ devices, suggesting that field-enhanced defect generation is negligible. Atomistic simulations with molecular static (MS) and molecular dynamic (MD) approaches support this finding. The MS calculations indicated a high formation energy of $\mathrm{\ensuremath{\Delta}}{E}_{\mathrm{aF}}\ensuremath{\approx}8\phantom{\rule{0.16em}{0ex}}\mathrm{eV}$ for the infinitely separated anti-Frenkel pair, and only a decrease to $\mathrm{\ensuremath{\Delta}}{E}_{\mathrm{aF}}\ensuremath{\approx}6\phantom{\rule{0.16em}{0ex}}\mathrm{eV}$ for the adjacent anti-Frenkel pair. The MD simulations showed no defect generation in either phase for $\mathcal{E}<3\phantom{\rule{0.16em}{0ex}}{\mathrm{GVm}}^{\ensuremath{-}1}$, and only sporadic defect generation in the monoclinic phase (at $\mathcal{E}=3\phantom{\rule{0.16em}{0ex}}{\mathrm{GVm}}^{\ensuremath{-}1})$ with fast $({t}_{\mathrm{rec}}<4\phantom{\rule{0.16em}{0ex}}\mathrm{ps})$ recombination. At even higher $\mathcal{E}$ but below ${\mathcal{E}}_{\mathrm{aF}}^{\mathrm{cr}}$ both monoclinic and cubic structures became unstable as a result of field-induced deformation of the ionic potential wells. Further MD investigations starting with preexisting anti-Frenkel pairs revealed recombination of all pairs within ${t}_{\mathrm{rec}}<1\phantom{\rule{0.16em}{0ex}}\mathrm{ps}$, even for the case of neutral vacancies and charged interstitials, for which formally there is no electrostatic attraction between the defects. In conclusion, we find no physically reasonable route to generating point-defects in ${\mathrm{HfO}}_{2}$ by an applied field.