Influence of size-dependent electrostatic energy on the ferroelectric nanodot domain structure by phase field method

A three-dimensional phase field model is proposed to study the effects of size-dependent electrostatic energy on ferroelectric nanodots at room temperature. The simulation results demonstrate that three domain structures exist in different sizes of nanodots, i.e. vortex structure, 90 degrees domain structure and single domain. The periodic distributions of the electrostatic potential and its energy with positive and negative signs across the domain body are the main causes of the formation of the vortex structure. With decreasing nanodot size, the change in the competitiveness between the electrostatic energy and other intrinsic energies induces the formation of a 90 degrees domain structure or a single domain.