A real-space non-local phase-field model of ferroelectric domain patterns in complex geometries

Ferroelectric perovskites are used in various transducer, memory and optical applications due to their attractive properties. In these applications, the ferroelectric materials often have complex geometries and electrode arrangements, and are subjected to domain switching. Therefore, it is important to understand the domain pattern that forms in these geometries. However, models of domain evolution often make assumptions like periodicity and complete shielding which make them unrealistic for these applications. In this paper, we develop a phase-field approach that can study domain patterns and domain evolution in complex geometries with no a priori assumption on geometry, electrode arrangement, and dielectric properties. The key idea is a boundary element method to resolve the electrostatic fields. We illustrate the method by examining the closure domains that form at a free surface and domain switching under cyclic electric field in a device with interdigitated electrodes.