Modified JKD Scaling for Thin Orthorhombic HfO2 Ferroelectric Films: The Effect of Anisotropic Crystal Structure

Ferroelectric hafnium oxide (HfO2) exhibits a thickness-dependent coercive field $\text {(}{E}_{c}\text {)}$ behavior that deviates from the trends observed in perovskites and the predictions of Janovec–Kay–Dunn (JKD) theory. Experiments show that, in thinner HfO2 films (<100 nm), ${E}_{c}$ increases with decreasing thickness but at a slower rate than predicted by the JKD theory. In thicker films, ${E}_{c}$ saturates and is independent of thickness. Prior studies attributed the thick film saturation to the thickness-independent grain size, which limits the domain growth. However, the reduced dependence in thinner films is poorly understood. In this work, we revisit the JKD theory and expound the reduced thickness dependence of ${E}_{c}$ in the lower thickness regime, attributing it to the anisotropic crystal structure of the polar orthorhombic (o) phase of $\textit {HfO}_{{2}}$ . The crystal structure of o-phase consists of continuous polar layers (CPLs) and alternating polar and spacer layers (APSLs) along the orthogonal in-plane directions. The spacer layers decouple adjacent polar layers along APSL, increasing the energy barrier for domain growth compared to the CPL direction. As a result, the polarization domains are confined to a single polar layer in HfO2, forming a half-prolate elliptical cylinder geometry rather than a half-prolate spheroid geometry observed in perovskites. Considering a single grain of o- HfO2, we model the nucleation and growth energetics of these confined anisotropic domains and derive a modified scaling law of ${E}_{c} \propto {d}^{-{1}/{2}}$ for HfO2 that deviates from the classical JKD dependence of ${E}_{c} \propto {d}^{-{2}/{3}}$ . The proposed scaling combined with depolarization-field correction for imperfect screening at ferroelectric–metal interfaces shows good agreement with the experimentally observed thickness scaling of coercive field in various ferroelectric HfO2 samples with thickness <100 nm.