Device-area selection of memristive transport regimes in epitaxial $H{f}_{0.5}Z{r}_{0.5}{O}_2$-based ferroelectric devices

Ferroelectric memristive devices based on hafnia are promising systems for neuromorphic electronics, yet the interplay between polarization-modulated resistive changes and defect-mediated transport often leads to complex and debated switching mechanisms. Here, we investigate this competition in epitaxial Hf${}_{0.5}$Zr${}_{0.5}$O${}_2$/La${}_{0.67}$Sr${}_{0.33}$MnO${}_3$ heterostructures with Pt top electrodes by combining structural, ferroelectric, and memristive characterization with a statistical analysis across a broad range of device areas spanning three orders of magnitude. We identify two distinct memristive regimes with opposite resistance–voltage chiralities. Small devices exhibit a low-resistance state that scales inversely with area, consistent with area-distributed tunneling transport, while larger devices display an area-independent resistance indicative of localized conductive channels. A statistical nucleation model quantitatively captures this behavior and yields a crossover characteristic area $A^{\ast }\approx {10}^3\mu {\mathrm{m}}^2$. This crossover also correlates with the onset of ferroelectric wake-up in larger devices, linking conductive-channel nucleation and oxygen-vacancy redistribution within a unified physical picture. These results establish lateral device size as a key parameter controlling the dominant transport mechanism in epitaxial hafnia-based devices.