Effect of out-of-plane misfit strain on phase diagrams and ferroelectric properties of ferroelectric films in vertical nanocomposite structures

A phenomenological thermodynamic Landau-Devonshire theory is developed to investigate phase diagrams of epitaxial ferroelectric films with out-of-plane misfit strain induced by vertical nanocomposites. The thermodynamic potential of ferroelectric films is obtained based on the boundary conditions of three-dimensional clamping induced by the vertical nanocomposites. Our calculated results indicate that the out-of-plane misfit strain modulates the transition temperature and spontaneous polarization of ferroelectric films in a wide range even the substrate does not provide an effective in-plane misfit strain control. An enhanced critical transition temperature up to 803 A degrees C in BaTiO3 films under a tensile out-of-plane misfit strain is predicted, which is consistent with the experimental result very well. The polarization properties of BaTiO3 films can also be effectively modulated by the out-of-plane misfit strain which is controlled by the volume fraction of nanopillars in the vertical nanocomposites. Our method provides a theoretical guide for the out-of-plane strain engineering of ferroelectric films.