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 ͑1998͔͒. 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 ͑001͒ Ba 0.7 Sr 0.3 TiO 3 and Ba 0.6 Sr 0.4 TiO 3 films on ͑001͒ Si, MgO, LaAlO 3 , and 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 LaAlO 3 and 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.

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The tunability of epitaxial barium strontium titanate films is analyzed theoretically using a phenomenological model. The relative dielectric constant of Ba 0.5 Sr 0.5 TiO 3 ͑BST 50/50͒ films as a function of the applied external electric field is calculated and an electric field-misfit strain phase diagram is developed to assist in the interpretation of the behavior. On the basis of these results, the tunability of BST 50/50 films as a function of the misfit strain is provided and compared with the experimental data in the literature. Analysis shows that a high tunability can be achieved by adjusting the misfit strain especially in the vicinity of a structural phase transformation. The misfit strain in epitaxial films can be controlled with the selection of a substrate material or variations in the film thickness. The film thickness dependence is due to misfit dislocation formation at the film growth temperature. A critical thickness to attain the maximum tunability can be defined for BST 50/50 films on MgO ͑ϳ90 nm͒ and LaAlO 3 ͑ϳ120 nm͒ substrates. It is suggested that the selection of the substrate and/or the film thickness can be chosen as design parameters to manipulate the strain state in the film to achieve optimum tunability.

A thermodynamic formalism is developed to calculate the pyroelectric coefficients of epitaxial ͑001͒ Ba 0.6 Sr 0.4 TiO 3 ͑BST 60/40͒ and Pb 0.5 Zr 0.5 O 3 ͑PZT 50/50͒ thin films on ͑001͒ LaAlO 3 , 0.29 LaAlO 3 :0.35(Sr 2 TaAlO 6) ͑LSAT͒, MgO, Si, and SrTiO 3 substrates as a function of film thickness by taking into account the formation of misfit dislocations at the growth temperature. The role of internal stress is discussed in detail with respect to epitaxy-induced misfit and thermal stresses arising from the difference between the thermal expansion coefficients of the film and the substrates. It is shown that the pyroelectric coefficients steadily increase with increasing film thickness for BST 60/40 and PZT 50/50 on LSAT and SrTiO 3 substrates due to stress relaxation by misfit dislocations. Large pyroelectric responses ͑ϳ1.1 C/cm 2 K for BST 60/40 and ϳ0.3 C/cm 2 K for PZT 50/50͒ are theoretically predicted for films on MgO substrates at critical film thicknesses ͑ϳ52 nm for BST 60/40 and ϳ36 nm for PZT 50/50͒ corresponding to the ferroelectric to paraelectric phase transformation. Analysis shows that the pyroelectric coefficients of both BST 60/60 and PZT 50/50 epitaxial films on Si substrates are an order of magnitude smaller than corresponding films on LaAlO 3 , LSAT, MgO, and SrTiO 3 substrates.

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