Computational and experimental studies of diffusion in monoclinic HfO2

Conference Dates

March 10-14, 2019


Research on hafnia and zirconia has received a boost in the last two decades, mainly because of their electrical properties. As materials with high dielectric permittivity and a wide band-gap, they can replace SiO2 in Si-based semiconductor devices as the gate dielectric, and they can be employed as the insulator in metal—insulator—metal structures, showing memristive behavior.[1,2] Anion, and possibly cation, transport is of fundamental importance for the annealing of such devices and the proposed mechanism of resistive switching (filament switching in the case of HfO2).[2,3] In this study, we investigated both cation and anion diffusion in HfO2 using diffusion experiments, with subsequent determination of the diffusion profiles by Secondary Ion Mass Spectrometry (SIMS). For the diffusion of oxygen in dense ceramics of monoclinic HfO2,, (18O/16O) isotope exchange anneals were performed in the temperature range 573 ≤ T / K ≤ 973 at an oxygen partial pressure of pO2 = 200 mbar.[4] All measured isotope profiles exhibited two features: the first feature, closer to the surface, was attributed to slow oxygen diffusion in an impurity silicate phase; the second feature, deeper in the sample, was attributed to oxygen diffusion in a homogeneous bulk phase. The activation enthalpy of oxygen tracer diffusion in bulk HfO2 was found to be ΔHD* ≈ 0.5 eV.

In contrast to oxygen diffusion, diffusion of cations in HfO2 and other oxide-ion conductors is experimentally much more challenging. It is slow, requiring, therefore, high temperatures and long diffusion times. In the case of HfO2, there is also the problem of Si impurities (see above), which are hard to get rid of in ceramic samples. To alleviate these problems somewhat, we directly investigated the diffusion of Zr in thin films of nanocrystalline, monoclinic HfO2, prepared by Atomic Layer Deposition (ALD) and coupled with a sputtered top layer of ZrO2 as a diffusion source. Diffusion experiments were performed in the temperature range 1173 ≤ T / K ≤ 1323 in air. All measured diffusion profiles exhibited bulk diffusion and fast grain-boundary diffusion. Using numerical simulations, we were able to describe the profiles and extract diffusion coefficients for Zr diffusion in bulk HfO2 and along its grain boundaries. The activation enthalpies of diffusion in both cases were, surprisingly, the same at ΔHDb/Dgb ≈ 2.1 eV. They are also much lower than activation energies predicted by static atomistic simulations.[5]

In order to aid the interpretation of the experimental data, we conducted atomistic simulations of cation diffusion in HfO2. Specifically we performed Molecular Dynamics (MD) simulations using the empirical pair potentials derived by Catlow and Lewis.[6,7] These potentials are suitable for describing defect behaviour in HfO2.[8,9] The activation enthalpy of Hf diffusion in bulk HfO2 we obtained from the MD simulations agrees exceedingly well with the experimental results: ΔHD* ≈ 2 eV. The reasons for this behaviour are discussed.

[1]: V. A. Gritsenko et al., Phys. Rep 613, 1 (2016).

[2]: R. Waser et al., Adv. Mater. 21, 2632 (2009).

[3]: S. Uhlenbruck et al., Solid State Ionics 180, 418 (2009).

[4]: M. P. Mueller, R. A. De Souza, Appl. Phys. Lett. 112, 051908 (2018).

[5]: S. Beschnitt et al., J. Phys. Chem. C 119, 27307 (2015).

[6]: C. R. A. Catlow, Proc. R. Soc. Lond. A. 353(1675), 533 (1977).

[7]: G. Lewis, C. R. A. Catlow, J. Phys. C: Solid State Phys. 18(6), 1149 (1985).

[8]: M. Schie et al., J. Chem. Phys. 146, 094508 (2017).

[9]: M. Schie et al., Phys. Rev. Mat. 2, 035002 (2018)

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