Influence of depolarization field on polarization states in epitaxial ferroelectric thin films with nonequally biaxial misfit strains

Depolarization field and misfit strain are two important factors that greatly influence the properties of ferroelectric thin films. The present work studies the effect of depolarization field on polarization states in a single-domain ferroelectric thin film with nonequally biaxial in-plane misfit strains. Three coupled Euler-Lagrange equations are derived from the minimization of the total free energy and solved numerically. Misfit-strain-misfit-strain phase diagrams are constructed to represent the polarization states. Under the short-circuit boundary condition, the depolarization field shifts the phase boundaries in the phase diagrams, leading to the contraction and expansion of the regions of out-of-plane and in-plane phases, respectively. Under the open-circuit boundary condition, there exists an out-of-plane electretlike state under high compressive misfit strains when a surface polarization Pm is included.