A Compact Model for Ferroelectric Capacitors Based on Multidomain Phase-Field Framework

A generalized and fast multidomain phase-field-based compact model for the metal-ferroelectric-metal (MFM) capacitor is presented. Time-dependent Landau–Ginzburg (TDGL) and Poisson’s equations are solved self-consistently to model the polarization dynamics. Additionally, physics-based empirical relationships for voltage-dependent kinetic and gradient energy coefficients are formulated. It is also demonstrated how gradient energy coefficient needs to be modified to accurately capture the physics of the device when a coarse simulation grid is used for fast computation. The developed model is 30000 times faster than our prior multidomain phase-field model with no degradation in accuracy. Moreover, a further computational speedup has been achieved by decreasing the number of Poisson solver nodes with a slight compromise of accuracy. The model shows a good agreement with the experimental results of both transient characteristics and minor hysteresis loops. The proposed model has the potential to facilitate fast and accurate simulations of large-scale circuits containing ferroelectric capacitors.