Thermodynamic scaling of coercive field in ferroelectric films: Single-domain and multi-domain switching competition

Abstract

The scaling of the coercive field Ec with ferroelectric thickness d is critical to device miniaturization. Here, we integrate Thomas–Fermi screening self-consistently into the Landau–Ginzburg–Devonshire framework via Gauss's and Kirchhoff's laws, thereby treating depolarization without resorting to an empirical background dielectric constant. By linking the d1/2 scaling of equilibrium domain size to the energy barrier of 180° multi-domain (MD) switching, we perform a comparative analysis of the Gibbs free energies for single-domain (SD) and MD reversal pathways to determine the energetically favored mechanism. We show that above a critical thickness (∼36 nm for PbZr0.2Ti0.8O3) the MD route dominates and Ec ∝ d−1/2, and below it the SD path prevails, leading to a monotonic decrease in Ec with reduced thickness until it vanishes in the ultrathin limit. Our work provides a unified thermodynamic description of Ec scaling across all thickness regimes, serving as a predictive tool for assessing ultrathin ferroelectrics.