Unified Phase-Field Framework for Antiferroelectric, Ferroelectric and Dielectric Phases: Application to HZO Thin Films

TL;DR

This work tackles the challenge of designing hafnia-based thin-film capacitors that exhibit tunable ferroelectric, antiferroelectric, and dielectric behavior by explicitly resolving grain-scale microstructure. It introduces a unified grain-resolved 3-D phase-field model that evolves both macroscopic $P_m$ and staggered $P_s$ order parameters within a realistic Voronoi grain topology and layer-resolved vertical phase architectures, coupled to self-consistent electrostatics via Poisson’s equation. The study shows that phase fractions chiefly determine the hysteresis character, while vertically segregated AFE and FE regions enable substantial reductions in the coercive field $E_c$ through microstructure-assisted switching pathways and interlayer electrostatic coupling; remanent polarization $P_r$ is mainly set by the FE fraction. These insights yield design principles for FE–AFE hafnia heterostructures, demonstrating that interior placement of moderately AFE-rich layers in multilayer stacks can decrease $E_c$ while preserving FE-like $P_r$, with symmetric multilayers offering the strongest performance, and establishing a framework for predictive, microstructure-aware device design and potential data-driven surrogates for rapid screening.

Abstract

Polycrystalline hafnia-based thin films exhibit mixed ferroelectric (FE), antiferroelectric (AFE), and dielectric (DE) behavior, with switching characteristics strongly influenced by microstructure and phase distribution. Here, we develop a unified grain-resolved three-dimensional phase-field framework for metal-insulator-metal capacitors that simultaneously captures ferroic phase characteristics in realistic polycrystalline microstructures by explicitly incorporating grain topology and crystallographic orientation. Antipolar sublattice kinetics are represented via the coupled evolution of macroscopic and staggered polarization order parameters. All thermodynamic and kinetic parameters are calibrated to experimental P-E hysteresis loops and held fixed across all simulations. The results show that phase fractions primarily determine hysteresis character, while vertical segregation of AFE- and FE-rich regions systematically reduces the effective coercive field (Ec) under identical electrical loading. Grain-resolved analysis reveals that this reduction arises from microstructure-assisted switching pathways and electrostatic coupling between layers. These findings demonstrate that vertical phase arrangement provides a viable strategy to engineer switching behavior in hafnia-based ferroic capacitors and highlight the importance of explicit microstructural resolution for quantitative phase-field modeling.

Figures (10)

• Figure 1: Zero-field bulk free-energy density $f(P)$ versus polarization $P$ for the scalar Kittel--Landau model. Curves correspond to FE double-well ($a<0$), AFE/PE coexistence ($a=a_{\mathrm{coex}}$), and AFE triple-well ($a_{\mathrm{ord}}^{spn}>a>a_{\mathrm{coex}}$).
• Figure 2: Calibration of thermodynamic and kinetic parameters using experimental $P$--$E$ hysteresis loops of polycrystalline thin films. Solid lines denote TDGL simulations and dashed lines experimental data, obtained under identical electric-field loading conditions.
• Figure 3: TDGL switching trajectories compared with the quasi-static equilibrium reference (red/blue). The experimental sweep rate ($\nu=10~\mathrm{kHz}$, black) exhibits kinetic deviation from equilibrium, while slower sweeping (green, yellow) progressively restores antipolar order and converges to the thermodynamic hysteresis loop.
• Figure 4: Representative polycrystalline thin-film microstructures used in the TDGL simulations. (a) Single-layer AFE-dominated film with minority FE and DE grains. (b) Multilayer film with vertically segregated phase distributions, consisting of AFE-rich and FE-rich layers. Panels (a,b) show oblique 3-D views, while panels (c,d) show the corresponding $y$–$z$ cross-sectional views. Grain boundaries are indicated in black. The color scale denotes the phase-ID.
• Figure 5: Global-frame polarization microstructures in a 100% AFE single-layer polycrystalline film. Panels (a,b) show $P_{m,z}^G$ and $P_{s,z}^G$ at $E=+E_{\max}$, and panels (c,d) show the corresponding fields at $E=0$ after field reversal.