  In this paper, the multi-domain nature of ferroelectric (FE) polarization
switching dynamics in a metal-ferroelectric-metal (MFM) capacitor is explored
through a physics-based phase field approach, where the three-dimensional
time-dependent Ginzburg-Landau (TDGL) equation and Poisson's equation are
self-consistently solved with the SPICE simulator. Systematically calibrated
based on the experimental measurements, the model well captures transient
negative capacitance in pulse switching dynamics, with domain interaction and
viscosity being the key parameters. It is found that the influence of pulse
amplitudes on voltage transient behaviors can be attributed to the fact that
the FE free energy profile strongly depends on how the domains are interacted.
This finding has an important implication on the charge-boost induced by
stabilization of negative capacitance in an FE + dielectric (DE) stack since
the so-called capacitance matching needs to be designed at a specific operation
voltage or frequency. In addition, we extract the domain viscosity dynamics
during polarization switching according to the experimental measurements. For
the first time, a physics-based circuit-compatible SPICE model for multi-domain
phase field simulations is established to reveal the effect of domain
interaction on the FE energy profile and microscopic domain evolution.
