Theory of phase transitions in second-order ferroelectric films: effects of surfaces and surface-induced stresses on polarization

The Landau–Devonshire theory is used to study the inter-relationship between polarization and stress in a second-order ferroelectric thin film, where both polarization and stress are in-plane. The intrinsic effects of surfaces and surface-induced stresses on polarization are considered by the introduction of extrapolation lengths in the formulation. Numerical calculations are made for a freestanding ferroelectric film, which is symmetric with respect to mid plane. The study is performed under the assumption that the polarization is enhanced or suppressed near the film surface. For a film with polarization enhanced near the surface, it is assumed that the surface tends to expand thus inducing a surface-tensile stress (‘tensile’ surface). Surface-induced compressive stress is assumed to exhibit in surface with polarization suppressed near surface (‘compressive’ surface). It is shown that a diminishing film size (thickness) has a strong influence on polarization and stress.