Phase field modeling of domain dynamics and polarization accumulation in ferroelectric HZO

In this work, we investigate the accumulative polarization (P) switching characteristics in ferroelectric (FE) thin films under the influence of sequential sub-coercive electric-field pulses. Performing the dynamic phase-field simulation (based on time-dependent Landau-Ginzburg model) and experimental measurement on Hf_0.4Zr_0.6O₂ (HZO), we analyze the electric field induced domain-wall (DW) motion and the resultant P accumulation process in FE. According to our analysis, even in the absence of an applied electric field, the DW can potentially undergo spontaneous motion. Such a DW instability leads to spontaneous P-excitation and relaxation processes, which play a pivotal role in accumulative P-switching in an FE grain. We show that the extent of such P accumulation increases with the increase in the applied electric field, increase in excitation time and decrease in relaxation time. Finally, by considering an ensemble of grains with local and global coercive field distributions, we model the P-accumulation process in a large area HZO sample. In such a multi-grain scenario, the dependency of P accumulation on the applied electric field pulse attributes follows similar features as that of a single-grain, although the spontaneous processes (excitation/relaxation) are less prominent in large area sample.