Phase-field simulations of polarization variations in polycrystalline Hf_0.5Zr_0.5O₂ based MFIM: Voltage dependence and dynamics

In this work, we investigate the device-to-device variations in the remanent polarization of metal-ferroelectric-insulator-metal stacks based on ferroelectric hafnium-zirconium-oxide (HZO). Our study employs a 3D dynamic multi-grain phase-field model to consider the effects of the polycrystalline nature of HZO in conjunction with the multi-domain polarization switching. We explore the dependence of variations on various design factors, such as the ferroelectric thickness and voltage stimuli (set voltage, pulse amplitude, and width), and correlate the trends to the underlying polarization switching mechanisms. Our analysis reveals a non-monotonic dependence of variations on the set voltage due to the coupled effect of the underlying polycrystalline structure variations and the voltage dependence of polarization switching mechanisms. We further report that collapsing of oppositely polarized domains at higher set voltages can lead to an increase in variations, while ferroelectric thickness scaling lowers the overall device-to-device variations. Considering the dynamics of polarization switching, we highlight the key role of voltage and temporal dependence of domain nucleation in dictating the trends in variations. Finally, we show that using a lower amplitude pulse for longer duration to reach a target mean polarization state results in lower variations compared to using a higher amplitude pulse for shorter duration.