Theoretical lower limit of coercive field in ferroelectric hafnia

The high coercive field ($E_c$) of hafnia-based ferroelectrics presents a major obstacle to their applications. The ferroelectric switching mechanisms in hafnia that dictate $E_c$, especially those related to domain nucleation in the Nucleation-Limited-Switching (NLS) model and domain wall motion in the Kolmogorov-Avrami-Ishibas (KAI) model, have remained elusive. We develop a deep-learning-assisted multiscale approach, incorporating atomistic insights into the critical nucleus, to predict both NLS- and KAI-type coercive fields. The theoretical NLS-type $E_c$ values agree with previous experimental results as well as our own measurements and also exhibit the correct thickness scaling for films between 3 and 20 nm. Combined theoretical and experimental investigations reveal that the giant $E_c$ in hafnia-based ferroelectrics arises from the ultra-thin geometry, which confines switching to the NLS mechanism. We predict that the theoretical lower limit for KAI-type $E_c$ is 0.1 MV/cm arsing from mobile domain walls. The activation of KAI-type switching to achieve lower $E_c$ is supported by our experimental demonstration of a low coercive field of 1 MV/cm in a 60 nm ferroelectric (HfO$_2$)$_n$/(ZrO$_2$)$_n$ ($n=3$ unit cells) superlattices. These findings establish a comprehensive framework for understanding ferroelectric switching in hafnia and highlight the potential of geometry and domain-wall engineering to achieve low-$E_c$ devices.