Size dependent domain configuration and electric field driven evolution in ultrathin ferroelectric films: A phase field investigation

Size dependent domain configuration and its evolution under an external electric field are investigated for ultrathin ferroelectric films using an unconventional phase field method. The simulation reveals a series of domain configurations at different thicknesses, including zigzag patterns with eight variants or four variants coexisting, a vortex pattern with four variants coexisting, and a stripe pattern with two variants coexisting. When the film thickness falls below a critical value of 2.8 nm, the polarization vanishes, indicating the suppression of ferroelectricity. The evolution of domain configuration under an alternating electric field is also investigated, and the reduction in remnant polarization and coercive field with respect to decreasing thickness is observed.