Stability and crossover of 71° and 109° domains influenced by the film thickness and depolarization field in rhombohedral ferroelectric thin films

The stability of domain patterns in rhombohedral ferroelectric films was studied using the minimum of free energy consisting of electrostatic and elastic energies. The converse piezoelectric effect due to the residual depolarization field was also considered. In the open-circuit condition, the 109° domain is more stable than the 71° one, which has a large depolarization field energy. By gradually decreasing the depolarization field energy, the stable domain pattern changes from 109° to 71° at a critical film thickness. This critical thickness of crossover from 109° to 71° domains is predicted to decrease with increasing residual depolarization field.