Substrate-induced mechanical and dielectric properties of a ferroelectric thin film

We propose herein a phenomenological model for the dielectric and mechanical behavior of ferroelectric PbTiO3 film on an MgO oxide substrate. The model takes into account the superstructure imposed on the epitaxial film by the substrate, the dislocation formation mechanism, and the specific mechanical boundary conditions. It is shown that nonhomogeneous film–substrate coupling related to superstructure formation is one possible mechanism for elastic stress relaxation in thin films. Stability regions in the thickness–temperature plane are obtained for different ferroelectric states formed during the deposition process and the subsequent cooling to room temperature. In ultrathin films, the superstructure formation mechanism favors a phase with a nontrivial unit cell multiple as well as a polarization direction perpendicular to the substrate. For films with a thickness of greater than 100 nm, two-dimensional clamping serves to stabilize the typical c domains. For intermediate thicknesses, several a type states may become stable. Numerical modeling of the residual strain level in the film is performed for three qualitatively different thicknesses.