A Study On Thermodynamic Properties Of Epitaxial Ba_xSr_1-xTiO₃ Thin Films

As a compound, the properties of Ba_xSr_1-xTiO₃ (BST) materials are determined by pure BaTiO₃ and SrTiO₃. Ferroelectricity appears when appropriate ferroelectric BaTiO₃ is added to quantum paraelectric SrTiO₃, which means dopant induces phase transition from paraelectric to ferroelectric. As a result, Ba_xSr_1-xTiO₃ may exhibit two structural phase with the variation of BaTiO₃ concentration. The ferroelectric phase transition is still not observed even near 0K in pure SrTiO₃ single crystals because of the large ground state quantum fluctuation of soft mode. However, the phase transition temperature of BaTiO₃ is 400K. Therefore, by varying Sr²⁺ and Ba²⁺ content, Ba_xSr_1-xTiO₃ films may be tailed and fabricated to meet different requirements. The Curie temperature(Tc=280K) of Ba_0.6Sr_0.4TiO₃ films is close to room temperature, which expects a large dielectric constant. However, the thermodynamic properties of epitaxial Ba_xSr_1-xTiO₃ films are greatly different from their bulk and single crystal samples which may be attributed to compositional and microstructural inhomogeneities, higher concentration of defect, internal stresses arising from lattice misfit and the difference of thermal expansion coefficient between substrates and films. Internal stresses, including normal stresses and shear stresses, are intrinsic mechanism to have effect on epitaxial ferroelectric films. The normal stresses comprise compressive stresses and tensile stresses. The compressive stresses appear when substrate lattice parameter is smaller than that of thin films. On the contrary, the tensile stresses occur. The shear stresses may be neglected when ferroelectric materials are epitaxially grown on thicker substrates. Epitaxial Ba_xSr_1-xTiO₃ thin films may have five stable low-temperature phases with reasonable stresses comparing with three phases in bulk samples. The phenomenon has also been found in epitaxial Pb(Zr_xTi_1-x)O₃ films because of internal stresses effect. Similarly, all possible eight stable phases exist in epitaxial SrTiO₃ films, including five ferroelectric phases, taking into account structural order parameter. For compositionally graded Ba_xSr_1-xTiO₃ films, the upgraded and downgraded films show different dielectric properties considering internal stresses. Furthermore, epitaxial films also exit other stress effect relating to order parameter with nonlinearly elastic approximation that comes from the difference of order parameters between epitaxial films and bulk one. In present paper, we discuss that the effect of stresses on dielectric nonlinear response of tetragonal single-domain Ba0.6Sr0.4TiO3 films(P1=P2=0, P3≠0) that are epitaxial deposited on thicker MgO and LaAlO3 substrates based on Landau-Devonshire(LD)-type phenomenological model considering internal stresses and stress relates to the polarization. Theoretical model contains the mutual-interaction term of ferroelectric order parameter and stresses and mechanical conditions in the films. The variation of stresses is the result of changing film thickness and growth temperature. Based on Landau-Ginsburg-Devonshire(LGD)-type phenomenological model, we investigate the low-temperature thermodynamic properties of SrTiO3 films in different phases by considering the coupling of ferroelectric order parameter, oxygen displacement and biaxial strain. The results exhibit epitaxial strain may induce ferroelectricity in quantum paraelectric SrTiO3 films and the existing of oxygen displacement is the reason to explain "weak peak"phenomenon, which has been observed in experiments. Based on the transverse-field Ising model(TIM) with the framework of mean field theory, the different dielectric properties of compositional upgraded/downgraded BaxSr1-xTiO3(x=0.0-0.15) films have been studied by taking into account stress distribution relaxed gradually σ= σ0 e ?z/Ï„. The random bond model of related parameters is applied to mimic doping. The tunability of corresponding graded films is also further discussed.