A Compact Model of Nanoscale Ferroelectric Capacitor

In this brief, we present a compact model of nanoscale ferroelectric (FE) capacitors. We first use the phase-field simulation to study the polarization switching of very small FE capacitor that contains only a few grains. We show that at higher applied voltage, the entire grain undergoes a single-domain-like switching, but at lower applied voltage, the domain wall growth mechanism dominates due to the difference between the domain wall energies of bulk and defect nuclei. To create a compact model that includes this voltage dependence, we use a time-dependent domain switching model for each discrete grain with empirical modifications capturing the two different switching mechanisms. In addition, a voltage-dependent dielectric model is included to represent the nonlinear capacitance of the FE capacitor. We verify this compact model by fitting the results of phase-field modeling results with excellent agreement.