Ferroelectric domain morphologies of (001) PbZr _1-xTi _xO ₃ epitaxial thin films

Ferroelectric domain morphologies in (001) PbZr _1-xTi _xO ₃ epitaxial thin films were studied using the phase-field approach. The film is assumed to have a stress-free top surface and is subject to a biaxial substrate constraint. Both the electrostatic open-circuit and short-circuit boundary conditions on the film surfaces were considered. The phase-field simulations indicated that in addition to the known tetragonal and rhombohedral phases, an orthorhombic phase becomes stable in films under large tensile constraints. The orthorhombic domain structure contains (100) and (010) 90° domain walls and (110) and (1-10) 180° domain walls. For the rhombohedral phase in a thin film, the domain walls are found to be along {101}, (100), and (010) of the prototypical cubic cell. It is shown that the short-circuit boundary condition and compressive substrate constraint enhance the out-of-plane polarization component while the open-circuit boundary condition and tensile substrate constraint suppress it. It is also shown that the depolarization field promotes the formation of herringbonelike morphology for the rhombohedral phase.