Compatible domain arrangements and poling ability in oriented ferroelectric films

The microstructure in single crystal ferroelectric films is significantly affected by the substrate conditions and the crystallographic orientation of the film. Domain arrangements form to minimize the total energy producing a stable state corresponding to the external boundary conditions. In order to find low energy domain arrangements, this study uses exact compatibility conditions for periodic laminate structures which ensure that all the adjacent domains fit together compatibly. These conditions are applied to films with various orientations and crystal systems, such as the rhombohedral and tetragonal crystal systems. A systematic search is used to discover exactly compatible structures for given states of macroscopic strain and polarization in the film. The theory is applied to [001], [011], and [111] oriented rhombohedral and tetragonal films. The results indicate poling paths along which the microstructure can evolve continuously while maintaining compatibility, to get from a state of zero through-thickness polarization to the state with the greatest value of through-thickness polarization. The evolution of the domain arrangement along these poling paths is shown, and the poling ability, or the limit on the maximum polarization achieved, is discussed. The influence of a strain state imposed by the substrate on the microstructure and poling ability is studied. The use of the model is illustrated by developing poling maps for a tetragonal [001] oriented film to show the set of polarization states that can be achieved as a function of the imposed substrate strain.