Phase diagrams and dielectric response of epitaxial barium strontium titanate films: A theoretical analysis

Abstract

We develop phase diagrams for single-domain epitaxial barium strontium titanate films on cubic substrates as a function of the misfit strain based on a Landau–Devonshire phenomenological model similar to the one developed by Pertsev et al. [Phys. Rev. Lett. 80, 1988 (1998)]. The biaxial epitaxy-induced internal stresses enable phase transformations to unusual ferroelectric phases that are not possible in single crystals and bulk ceramics. The dielectric response of the films is calculated as a function of the misfit strain by taking into account the formation of misfit dislocations that relieve epitaxial stresses during deposition. It is shown that by adjusting the misfit strain via substrate selection and film thickness, a high dielectric response can be obtained, especially in the vicinity of structural instabilities. Theoretical estimation of the dielectric constant of (001) ${\mathrm{Ba}}_{\text{0.7}}{\mathrm{Sr}}_{\text{0.3}}{\mathrm{TiO}}_3$ and ${\mathrm{Ba}}_{\text{0.6}}{\mathrm{Sr}}_{\text{0.4}}{\mathrm{TiO}}_3$ films on (001) Si, MgO, ${\mathrm{LaAlO}}_3,$ and ${\mathrm{SrTiO}}_3$ substrates as a function of misfit strain and film thickness is provided. An order-of-magnitude increase in the dielectric constant with increasing film thickness is expected for films on ${\mathrm{LaAlO}}_3$ and ${\mathrm{SrTiO}}_3$ substrates. A structural instability around 40 nm is predicted in films on MgO substrates accompanied by a substantial increase in the dielectric constant. For films on MgO substrates thicker than 40 nm, the analysis shows that the dielectric constant decreases significantly. We show that the theoretical approach not only predicts general trends but is also in good quantitative agreement with the experimental data reported in literature.