Ultrahigh Oxygen Ion Mobility in Ferroelectric Hafnia

Liyang Ma, Jing Wu, Tianyuan Zhu, Yiwei Huang, Qiyang Lu, and Shi Liu

Phys. Rev. Lett. 131, 256801 – Published 20 December 2023

Abstract

Ferroelectrics and ionic conductors are important functional materials, each supporting a plethora of applications in information and energy technology. The underlying physics governing their functional properties is ionic motion, and yet studies of ferroelectrics and ionic conductors are often considered separate fields. Based on first-principles calculations and deep-learning-assisted large-scale molecular dynamics simulations, we report ferroelectric-switching-promoted oxygen ion transport in ${HfO}_{2}$ , a wide-band-gap insulator with both ferroelectricity and ionic conductivity. Applying a unidirectional bias can activate multiple switching pathways in ferroelectric ${HfO}_{2}$ , leading to polar-antipolar phase cycling that appears to contradict classical electrodynamics. This apparent conflict is resolved by the geometric-quantum-phase nature of electric polarization that carries no definite direction. Our molecular dynamics simulations demonstrate bias-driven successive ferroelectric transitions facilitate ultrahigh oxygen ion mobility at moderate temperatures, highlighting the potential of combining ferroelectricity and ionic conductivity for the development of advanced materials and technologies.

Received 12 June 2023
Accepted 21 November 2023

DOI:https://doi.org/10.1103/PhysRevLett.131.256801

Physics Subject Headings (PhySH)

Ferroelectricity Ionic conductivity

Deep learning Density functional theory Molecular dynamics

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Liyang Ma ^1,*, Jing Wu^1,*, Tianyuan Zhu^1,2, Yiwei Huang³, Qiyang Lu^3,4, and Shi Liu ^1,2,†

¹Key Laboratory for Quantum Materials of Zhejiang Province, Department of Physics, School of Science, Westlake University, Hangzhou, Zhejiang 310024, China
²Institute of Natural Sciences, Westlake Institute for Advanced Study, Hangzhou, Zhejiang 310024, China
³School of Engineering, Westlake University, Hangzhou, Zhejiang 310030, China
⁴Research Center for Industries of the Future, Westlake University, Hangzhou, Zhejiang 310030, China

^*These authors contributed equally.
^†Corresponding author: liushi@westlake.edu.cn

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Vol. 131, Iss. 25 — 22 December 2023

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Images

Figure 1
Polarization switching pathways in ferroelectric ${HfO}_{2}$ . (a) $X_{2}^{-}$ mode in the unit cell of $P c a 2_{1}$ ${HfO}_{2}$ with outward- and inward-displaced oxygen atoms denoted by purple and salmon spheres, respectively. The polarization is along the $z$ axis. (b) Alternately arranged nonpolar oxygen ions ( $O^{np}$ ) and polar oxygen ions ( $O^{p}$ ) in $P c a 2_{1}$ ${HfO}_{2}$ . The gray shaded area marks the polar region. (c) Schematics of shift-inside (SI) and shift-across (SA) switching pathways driven by an external electric field ( $E$ ). The SA pathway has $O^{np}$ ions reversing the sign of the $X_{2}^{-}$ mode (colored in gray during the transition). The SI and SA pathways can start from the same configuration, which should be identified by polarization ( $P$ ) vectors (represented as green arrows) pointing in opposite directions to ensure compatibility with classical electrodynamics. (d) Calculated minimum energy paths for different switching pathways with DFT (lines) and a deep neural network-based force field (scatters). (e) Switching barrier as a function of field strength.
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Figure 2
Dual-valued remnant polarization and single-valued piezoelectric response in ${HfO}_{2}$ . (a) Polarization variation along SA and SI-1 switching pathways from the same starting configuration (the center insert) in response to opposing electric fields. The upward electric field aligned along the $- z$ direction is defined arbitrarily as $+ E$ . Configurations are labeled by the displacement ( $δ$ ) of the salmon-colored $O^{p}$ ion relative to the top Hf plane; $l$ is the distance between neighboring Hf planes along $z$ and $δ_{0}$ is the $O^{p}$ displacement at the ground state. Oxygen ions always move against $E$ . (b) Schematics of $P − E$ hysteresis loops for SA and SI and the corresponding switching currents. (c) Strain ( $η_{3}$ , empty circles) as a function of an electric field applied along the $z$ axis ( $E_{3}$ ) and the corresponding $O^{p}$ displacements ( $δ$ , filled squares) obtained with finite-field MD simulations at 300 K. The slop of $η_{3} − E_{3}$ gives the absolute value of $d_{33}$ whose sign depends solely on the arbitrary sign of $E_{3}$ .
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Figure 3
Oxygen ion transport coupled to the nucleation-and-growth mechanism of ferroelectric switching. (a) Polar-antipolar phase cycling arising from successive SI and SA ferroelectric transitions. The highlight $O^{np}$ in the initial configuration becomes $O^{p}$ with $δ = δ_{0}$ after SI-2 and then $O^{p}$ with $δ = - δ_{0}$ after SA. (b) Schematic illustration of stochastic nucleation events in a three-dimensional bulk. The nucleus is two dimensional within the $x z$ plane, featuring a thickness equivalent to half a unit cell of $P c a 2_{1}$ ${HfO}_{2}$ along the $y$ axis. (c) A 2D slim-diamond-shaped nucleus extracted from MD simulations using a $10 \times 10 \times 24$ supercell of 28 800 atoms. The nucleus profile is determined based on the $δ$ values of $O^{p}$ ions. (d) Line profiles of $δ$ along the $z$ and $x$ directions marked in (c).
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Figure 4
Ferroelectricity-promoted oxygen ion mobility in ${HfO}_{2}$ . (a) Mobility of oxygen ions ( $u_{O}$ ) in $P c a 2_{1}$ ${HfO}_{2}$ (without and with oxygen vacancies $V_{O}$ ) as a function of $E$ at different temperatures from MD simulations. The results in nonpolar $M$ phase at 600 K are shown for comparison. The shaded area indicates the transition region where the critical electric field $E_{t}$ is located. (b) Left: device structure of an electrochemical ionic synapse with $P c a 2_{1}$ ${HfO}_{2}$ as the electrolyte layer, which is sandwiched between a channel layer connected to source (S) and drain (D) electrodes and an oxygen-storing reservoir layer. The channel layer has its conductance depending on the oxygen ion concentration. Right: schematic showing the ultrafast oxygen ion transport in ${HfO}_{2}$ electrolyte layer under an electric field.
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