  In this work, we investigate the device-to-device variations in remanent
polarization of Hafnium-Zirconium-Oxide based
Metal-Ferroelectric-Insulator-Metal (MFIM) stacks. We consider the effects of
polycrystallinity in conjunction with multi-domain effects in HZO to understand
the dependencies of variations on static and dynamic voltage stimuli using our
3D dynamic multi-grain phase-field simulation framework. We examine the trends
in variations due to various design factors - set voltage, pulse amplitude and
pulse width and correlate them to the dynamics of polarization switching and
the underlying mechanisms. According to our analysis, variations exhibit a
non-monotonic dependence on set voltage due to the interplay between
voltage-dependent switching mechanisms and the polycrystalline structure. We
further report that towards the higher end of the set voltages, collapsing of
oppositely polarized domains can lead to increase in variations. We also show
that ferroelectric thickness scaling lowers the device-to-device variations. In
addition, considering the dynamics of polarization switching, we signify the
key role of voltage and temporal dependence of domain nucleation in dictating
the trends in variations. Finally, we show that to reach a target mean
polarization, using a pulse with lower amplitude for longer duration results in
lower variations compared to higher amplitude pulse for a shorter duration.
