  In this paper, we present the dynamics and modeling of multi-domains in the
ferroelectric FET (FeFET). Due to the periodic texture of domains, the
electrostatics of the FeFET exhibit an oscillatory conduction band profile. To
capture such oscillations, we solve coupled 2-D Poisson's equation with the net
ferroelectric energy density (gradient energy + free energy + depolarization
energy) equation. Multi-domain dynamics are captured by minimizing the net
ferroelectric energy leading to a thermodynamically stable state. Furthermore,
we show that the motion of domain walls originates local bound charge density
in the ferroelectric region, which induces the negative capacitance (NC)
effect. The strength of domain wall-induced NC is determined by the gradient
energy of the ferroelectric material. FeFET exhibits variability in the drain
current with domain period due to the inherent NC effect. Additionally, the
impact of domain wall transition (soft$\rightleftharpoons$hard) on the device's
electrostatic/transport is also analyzed. The model also accurately captures
both nucleations of a new domain and the motion of the domain wall.
Furthermore, the model is thoroughly validated against experimental results and
phase-field simulations.
