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

Abstract

The generation of anti-Frenkel pairs (oxygen vacancies and oxygen interstitials) in monoclinic and cubic 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 E cr aF ∼ 10 1 GVm −1 obtained for HfO 2 exceeds substantially the field strengths routinely employed in the forming and switching operations of resistive switching 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 E aF ≈ 8 eV for the infinitely separated anti-Frenkel pair, and only a decrease to E aF ≈ 6 eV for the adjacent anti-Frenkel pair. The MD simulations showed no defect generation in either phase for E < 3 GVm −1 , and only sporadic defect generation in the monoclinic phase (at E = 3 GVm −1) with fast (t rec < 4 ps) recombination. At even higher E but below E cr aF 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 rec < 1 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 HfO 2 by an applied field.

Generation of Frenkel defects above the Debye temperature by proliferation of phonons near the Brillouin zone edge

“…This idea remains to be worked out in the future. It should be noticed, however, that such a scenario is not in conflict with a recent calculation for the insulator HfO 2 that concluded that field-enhanced generation of point defects was negligible [31].…”

Silicon Oxide (SiOx): A Promising Material for Resistance Switching?

“…The experimental results also show different breakdown times for the same field in devices of different dielectric thicknesses . Describing oxide degradation as a purely field‐driven process is therefore an oversimplification …”

Electro-thermal transport in disordered nanostructures: a modeling perspective

“…17 Furthermore, it is energetically more favorable to form oxygen vacancies at HfO x interfaces rather than in the bulk. 22 In addition to lamentary type switching, VCM is also proposed to operate in a volume-type mode where the total amount of oxygen vacancies stays constant. 16 It relies on the redistribution of oxygen vacancies next to the active electrode during the switching process.…”

“…Their calculation takes either the form of an eigenvalue problem 86 or of a complex contour integral. 87 By incorporating the resulting phonon boundary self-energies P B into eqn (22) and by transforming the wave function expressions into GFs, we obtain the following system of equations to solve:…”

“…88 While eqn (23) and (24) have the same form as the equations for electrons, there is an important difference. Namely, eqn (22) does not depend on the phonon population, therefore eliminating the need for an iterative solution process and reducing the computational cost as compared to electrons. The procedure involved in atomistic thermal transport simulations is depicted in the right-hand side of Fig.…”