Defect- and Chemistry-Mediated Antiferroelectric-to-Ferroelectric Phase Conversion Under Electric-Field Cycling in HZO Thin Films: Coupling Explicit Defect Transport to Grain-Resolved Phase-Field Modeling

Polycrystalline Hf$_{1-x}$Zr$_x$O$_2$ (HZO) thin films in metal-insulator-metal capacitors contain coexisting ferroelectric (FE), antiferroelectric (AFE), and dielectric (DE) regions, and under repeated electric-field cycling they can undergo conversion of AFE material into FE material (experimentally seen as progressive merger of pinched double hysteresis sub-loops into a single loop with finite remanent polarization). A 2026 unified grain-resolved three-dimensional phase-field framework with coupled macroscopic and staggered polarization order parameters reproduces the switching response and shows that vertical segregation of AFE-rich and FE-rich layers systematically reduces the coercive field; however, because it contains no interface-, defect-, or chemistry-driven AFE$\to$FE conversion, it cannot generically enhance the remanent polarization $P_r$, and its authors defer 'explicit incorporation of defect-mediated electrostatic and transport effects' to future work. The open problem is to make cycling-induced AFE$\to$FE phase conversion in HZO films predictable from explicit microscopic mechanisms: couple charged-defect (oxygen-vacancy) transport, defect-mediated electrostatics, and chemistry-, dopant-, and interface-dependent phase-stabilization energetics to the grain-resolved antipolar phase-field dynamics on realistic polycrystalline microstructure, demonstrate reproduction of the observed cycling evolution from a defect-free architecture-only baseline, and answer the source study's design question of whether chemical design combined with vertical phase architecture can enhance $P_r$ beyond architecture-only effects.

Background

A ferroelectric (FE) material possesses a switchable spontaneous electric polarization; an antiferroelectric (AFE) instead forms two antiparallel sublattice polarizations that cancel at zero field, giving a characteristic double ('pinched') hysteresis loop with near-zero remanent polarization $P_r$ that can nevertheless be driven into a polar phase by a large enough electric field. Thin films of hafnium-zirconium oxide, Hf$_{1-x}$Zr$_x$O$_2$ (HZO), are fluorite-structure (calcium-fluoride-type crystal lattice) polymorphic oxides compatible with complementary metal-oxide-semiconductor (CMOS) processing and are studied for nonvolatile memories, negative-capacitance devices (which exploit a ferroelectric near its phase instability to amplify charge), and high-density energy-storage capacitors. Depending on composition, thickness, and processing they contain mixtures of a polar orthorhombic phase (FE), a nonpolar tetragonal phase that sublattice models treat as AFE-like, a monoclinic phase, and dielectric (DE) regions; the phase fractions largely determine whether the film responds as FE (single loop, finite $P_r$), AFE-like (double loop), or linear dielectric. A well-documented phenomenon is 'wake-up': under repeated field cycling, initially pinched or AFE-like hysteresis evolves — separated sub-loops progressively merge into a single FE-like loop with finite $P_r$ — indicating field-cycling-driven conversion of material into the polar phase, while charge defects such as oxygen vacancies (missing oxygen ions that act as mobile charged point defects in the lattice) redistribute through the film.

Phase-field modeling describes such films with continuous order parameters relaxed by time-dependent Ginzburg-Landau (TDGL) equations derived from a free-energy functional. For AFEs one uses the Kittel two-sublattice representation, with a macroscopic polarization $P_m$ (the spatial average of the sublattice polarizations, which couples to the applied field) and a staggered polarization $P_s$ (their difference, the antipolar order that vanishes in the FE phase), coupled through Landau bulk terms (polynomial free-energy expansions in the order parameters), gradient terms penalizing spatial variations, and self-consistent electrostatics (a Poisson equation) that generate depolarization fields — the internal fields arising from uncompensated bound charge. Pankaj and co-workers (2026) developed a unified grain-resolved three-dimensional phase-field framework for HZO metal-insulator-metal capacitors: it resolves the actual polycrystalline grain topology by Voronoi tessellation (a construction that partitions space into grains around seed points, here with roughly 30 nm grains), assigns FE/AFE/DE phase identity grain by grain, evolves both $P_m$ and $P_s$, treats depolarization fields self-consistently, and calibrates all thermodynamic and kinetic parameters to experimental polarization-electric-field (P-E) hysteresis loops. Its main findings are that phase fractions primarily determine hysteresis character, and that vertical segregation of AFE-rich and FE-rich layers systematically reduces the effective coercive field $E_c$ through earlier nucleation and accelerated percolation of reversed domains plus interlayer electrostatic coupling. Crucially, vertical stacking alone does not generically enhance $P_r$: in the model, $P_r$ is set by the volume fraction and connectivity of FE-rich layers because there is no interface- or chemistry-driven AFE$\to$FE phase conversion during cycling. The authors state that additional interface-, dopant-, or processing-induced phase-stabilization mechanisms are likely required for substantial $P_r$ enhancement beyond these architecture-only effects, and that explicit incorporation of defect-mediated electrostatic and transport effects 'will be addressed in future work'. They also acknowledge secondary simplifications: elastic energy is neglected (the Landau coefficients only implicitly absorb average substrate clamping), grain boundaries are treated as immobile with no microstructural evolution, and switching is approximated as uniaxial (out-of-plane polarization only).

Problem Statement

Make electric-field-cycling-induced antiferroelectric-to-ferroelectric phase conversion in polycrystalline Hf$_{1-x}$Zr$_x$O$_2$-based metal-insulator-metal capacitors predictable from explicit microscopic mechanisms, by extending the grain-resolved antiferroelectric phase-field framework of Pankaj et al. (2026) — in which time-dependent Ginzburg-Landau evolution of macroscopic and staggered polarization order parameters runs on an explicit three-dimensional Voronoi polycrystalline microstructure with self-consistent depolarization electrostatics and experimentally calibrated parameters — through the following coupled objective:

1. Formulate and solve a coupled model in which the antipolar/polar phase-field dynamics are coupled to explicit defect and chemistry physics: transport of charged defects (oxygen vacancies), defect-mediated electrostatics, and chemistry-, dopant-, interface-, and processing-dependent phase-stabilization energetics — with each new coupling term and parameter derived from or calibrated against identified atomistic calculations or experimental measurements, and with the coupled system thermodynamically consistent.
2. Demonstrate that the model reproduces the experimentally observed cycling evolution — the progressive merger of pinched AFE double-hysteresis sub-loops into a single FE-like loop with finite remanent polarization $P_r$, as documented for Hf$_x$Zr$_{1-x}$O$_2$ films — and that it reduces to the architecture-only behavior of the source framework (systematic $E_c$ reduction without generic $P_r$ enhancement) when the defect/chemistry terms are disabled.
3. Answer the design question posed by the source study: can chemical and defect design (dopant and vacancy control, interface and processing engineering), combined with vertical phase architecture, enhance $P_r$ beyond the architecture-only effects — in which $P_r$ is essentially set by the volume fraction and connectivity of FE-rich layers — and at what cost in coercive field, reversibility, and endurance?

The defect/chemistry coupling in items 1-3 is the load-bearing core: it is the only mechanism class absent from the source framework that can change the zero-field phase identity of material during cycling. Item 3 is resolved only when both of its parts are answered: the determination of whether chemical and defect design combined with vertical phase architecture can enhance $P_r$ beyond the architecture-only effects, and the assessment of the associated cost in coercive field, reversibility, and endurance, for which all three metrics are required. The Source study's further acknowledged simplifications — local elastic heterogeneity and substrate-induced stress, grain-boundary migration and microstructure evolution over long-term cycling, and full-vector (in-plane) polarization switching in less-textured films — are secondary coupled refinements of the same prediction targets and may be incorporated to the extent they materially affect the conversion and switching predictions; they are not separately required for the completion boundary above.

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