Variational Phase Field Formulations of Polarization and Phase Transition in Ferroelectric Thin Films

TL;DR

This paper introduces new variational phase field formulations for modeling polarization and phase transitions in ferroelectric thin films, improving computational efficiency and clarity in electrostatic interactions.

Contribution

It develops hybrid real-Fourier variational formulations for electrostatic energy and polarization dynamics, addressing ambiguities in previous models.

Findings

Enhanced numerical simulation methods for ferroelectric polarization switching

More accurate modeling of electrostatic interactions in thin films

Demonstrated effectiveness through polarization switching examples

Abstract

Electric field plays an important role in ferroelectric phase transition. There have been numerous phase field formulations attempting to account for electrostatic interactions subject to different boundary conditions. In this paper, we develop new variational forms of the phase field electrostatic energy and the relaxation dynamics of the polarization vector that involves a hybrid representation in both real and Fourier variables. The new formulations avoid ambiguities appeared in earlier studies and lead to much more effective ways to perform variational studies and numerical simulations. Computations of polarization switching in a single domain by applying the new formulations are provided as illustrative examples.