Zr Concentration-Dependent Sub-Lattice Phase-Field Model of Hf1-xZrxO2: Analysis of Phase Composition and Polarization Switching

Abstract

We develop a sub-lattice phase-field model of Hf1-xZrxO2 incorporating zirconium (Zr) concentration (x)-dependence. Our framework expands the time-dependent Ginzburg-Landau (TDGL) equation to the sub-lattice level and incorporates x-dependent interaction parameters and gradient coefficients. Our experimentally calibrated model captures the evolution of charge-voltage (Q-V) characteristics for x ranging from 0.5 to 1.0. The sub-lattice formulation explains the thermodynamic preference and kinetic transition barriers of competing orthorhombic phase (o-phase) and tetragonal phase (t-phase), while the phase-field framework enables spatially resolved analysis of polarization (P) and electric-field (E-field) profiles, allowing multi-domain (MD) polarization and mixed-phase states to emerge naturally. Our model reproduces the experimentally observed ferroelectric (FE)-to-anti-ferroelectric (AFE) transition as x increases from 0.5 to 1.0. At low Zr concentration (x = 0.5-0.6), the o-phase dominates, yielding distinct FE behavior. At high concentration (x = 0.9-1.0), the t-phase is stabilized, leading to AFE transitions. A key finding of our work is the unique behavior at intermediate Zr concentrations (x = 0.7-0.8). Here, the o- and t-phase energies are comparable, making the system strongly influenced by local variations in the electric field (E-field), which arise from stray fields near the domain walls. This non-uniform field distribution results in a mixed-phase composition and spatially staggered polarization reversal, which manifests as a more gradual Q-V evolution compared to other values of x. By linking energy landscapes to spatial field effects, the model provides insights into the FE-to-AFE crossover in Hf1-xZrxO2.