Small-signal capacitance in ferroelectric hafnium zirconium oxide: mechanisms and physical insights†

This study presents a theoretical investigation of the physical mechanisms governing small-signal capacitance in ferroelectrics, focusing on hafnium zirconium oxide (Hf_0.5Zr_0.5O₂, HZO). We utilize a time-dependent Ginzburg–Landau formalism-based 2D multi-grain phase-field framework to simulate the capacitance of metal–ferroelectric–insulator–metal (MFIM) capacitors. Our simulation methodology closely mirrors the experimental procedures for measuring ferroelectric small-signal capacitance, and the outcomes replicate the characteristic butterfly capacitance–voltage behavior. Notably, this behavior can be obtained without invoking traps. We delve into the components of the ferroelectric capacitance associated with the dielectric response and polarization switching, discussing the primary mechanisms – domain bulk response and domain wall response – contributing to the butterfly characteristics. We explore their interplay and relative contributions to the capacitance, correlating them to the polarization switching mechanisms and domain configurations. Additionally, we investigate the impact of increasing domain density with ferroelectric thickness scaling, demonstrating an enhancement in the polarization capacitance component, in addition to the dielectric component. Furthermore, we analyze the contributions of the domain bulk and domain wall responses across ferroelectric thicknesses, relating the capacitive memory window (for memory applications) to the capacitance and revealing a non-monotonic dependence of the maximum memory window on the ferroelectric thickness.