Size-Dependent Switching in Thin Ferroelectric Films: Mathematical Aspects and Finite Element Simulation

The paper is devoted to the theoretical analysis and numerical implementation of a mathematical model of a nonlinear reaction–diffusion system on the COMSOL Multiphysics platform. The applied problem of the computer simulation of polarization switching in thin ferroelectric films is considered. The model is based on the Landau–Ginzburg–Devonshire–Khalatnikov thermodynamic approach and formalized as an initial-boundary value problem for a semilinear parabolic partial differential equation. The theoretical foundations of the model were explained. The user interface design application was developed with COMSOL Multiphysics. A series of computational experiments was performed to study the ferroelectric hysteresis and temperature dependences of polarization on the example of a ferroelectric barium titanate film.