Effects of non-equally biaxial misfit strains on the phase diagram and dielectric properties of epitaxial ferroelectric thin films

The effects of non-equally biaxial in-plane misfit strains on the equilibrium polarization states and the dielectric properties of single-domain epitaxial ferroelectric thin films are investigated by a nonlinear thermodynamic theory. The “misfit strain-misfit strain” and “temperature-misfit strain” phase diagrams for single-domain BaTiO3 (BT) and PbTiO3 (PT) thin films grown on tetragonal substrates are developed by minimizing the Helmholtz free energy. The non-equally biaxial misfit strains cause the presence of two in-plane tetragonal ferreoelectric phases, 1 a ( 0 0 3 2 1 = = ≠ P P P , ) and 2 a ( 0 0 3 1 2 = = ≠ P P P , ), in both BT and PT thin films, which do not exist if the misfit strains are equally biaxial. * Corresponding author, Tel: (852) 2358-7192, Fax: (852) 2358-1543, E-mail: [email protected] 2 Ferroelectric thin films have been found wide applications in new generations of dynamic random access memories, nonvolatile memories, tunable microwave devices, and other microelectronic and electro-optic devices. The misfit strains between a ferroelectric thin film and its substrate are able to change the Curie temperature, the order of the paraelectric/ferroelectric phase transition, the equilibrium polarization states, and the dielectric properties of the material. Certainly, a deep understanding of the relationship between the misfit strains and the material properties will provide guidelines on how to control the material properties by manipulating the misfit strains, which might be crucial for applications of ferroelectric thin films. Great progress has been achieved in the theoretical study of the misfit strains effect, especially, by using the powerful thermodynamics theories, and the “misfit strain-temperature” phase diagrams have been constructed. However, the previous work has investigated only equally biaxial misfit strains, called the isotropic misfit strains also in the literature, which are induced when ferroelectric thin films are grown on cubic substrates. If ferroelectric thin films are grown on tetragonal substrates, the misfit strain along a crystalline axis will differ from the misfit strain along the other crystalline axis, which are called nonequally biaxial (or anisotropic) misfit strains, as illustrated by recent experimental studies. The non-equally biaxial misfit strains may induce new material properties and thus open up other possibilities for the design of electronic devices. In the present work, we study a single-domain ferroelectric thin film epitaxially grown on a thick tetragonal substrate and assume the film/substrate interface is coherent. Using the Voigt matrix notation of strains and the rectangular Cartesian coordinator system with the 3 x axis perpendicular to the film/substrate interface, we may define the non-equally biaxial in-plane