Device-area selection of memristive transport regimes in epitaxial $Hf_{0.5}Zr_{0.5}O_{2}$-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 electronic 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 $A^* \approx 10^3\,μ\mathrm{m}^2$. This crossover also correlates with the onset of ferroelectric wake-up for the 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.