Effect of in-plane shear strain on phase states and dielectric properties of epitaxial ferroelectric thin films

Abstract

A modified thermodynamic potential based on the eight-order Landau-Devonshire polynomial is derived for ferroelectric thin films grown on dissimilar substrates that induce anisotropic tensile/ compressive strains and the shear strain in the film plane. The effect of the shear strain on the ferroelectric phase transition occurring in considered films is analyzed theoretically. It is shown that the application of the shear strain suppresses the formation of ferroelectric c phase and raises the temperature of aa ‫ء‬ phase formation. The directional dependence of in-plane dielectric permittivity of a ferroelectric film is also calculated and compared with the dependence observed in ͑Ba 0.60 Sr 0.40 ͒TiO 3 films deposited on NdGaO 3 .

Strain on ferroelectric thin films

“…The consequences on dielectric properties of films [131,134,136,137], their tunability [137] and pyroelectric properties [136,137] of such strain conditions have been calculated. These comparisons between the phenomenological predictions and the experimental measurements may lead to reasonable agreement as long as sufficient expansion of the Landau polynomial, appropriate electrical boundary conditions, available and reliable set of parameters have been used in the model and, as importantly, accurate measurement of the lattice parameters have been carried out [134].…”

“…See [134] and [139] in the case of BaTiO 3 , and [137] for Ba 0.7 Sr 0.3 TiO 3 . In addition, the use of an eight-order polynomial enables to address the question of the stability of the phase in which the three components of the polarization are not nil.…”

“…Taking into account this strain destabilizes the phase where P ¼ ðP 1 ¼ 0; P 2 ¼ 0; P 3 6 ¼ 0Þ [134], leading to a shift of the 180°f erroelectric domain walls compared to the hypothetical case where the film would be free from the substrate and therefore free to be strained in the z direction [140]. In addition, the use of an eight-order Landau polynomial leads to the complete destabilization, from a thermodynamic point of view, of the phase in which all components are not nil (P = (P 1 = 0, P 2 = 0, P 3 = 0)).…”

“…Experimental reports such as the one about lead titanate thin films deposited on orthorhombic DyScO 3 [138] showed that ac and r phases can be stabilized by anisotropic stress fields. One has to pay attention to the set of parameters used to calculate the phase diagrams as the use of an erroneous set leads to incorrect results (compare, for example, [134] and [132]). …”

“…The monodomain case is the simpler one to address and several misfit strain-misfit strain phase diagrams (at constant temperature) have been calculated by thermodynamic theory for PbTiO 3 [131][132][133][134][135], Pb(Zr 0.5 Ti 0.5 )O 3 [134], (Pb 0.35 Sr 0.65 )TiO 3 [131], BaTiO 3 [132][133][134], (Ba x Sr 1-x ) TiO 3 (x = 0.5 [136], 0.7 [137]). Experimental reports such as the one about lead titanate thin films deposited on orthorhombic DyScO 3 [138] showed that ac and r phases can be stabilized by anisotropic stress fields.…”