A Landau-Ginsburg-Devonshire-type nonlinear phenomenological theory is presented, which enables the thermodynamic description of dense laminar polydomain states in epitaxial ferroelectric thin films. The theory explicitly takes into account the mechanical substrate effect on the polarizations and lattice strains in dissimilar elastic domains (twins). Numerical calculations are performed for PbTiO 3 and BaTiO 3 films grown on (001)-oriented cubic substrates. The "misfit strain-temperature" phase diagrams are developed for these films, showing stability ranges of various possible polydomain and single-domain states. Three types of polarization instabilities are revealed for polydomain epitaxial ferroelectric films, which may lead to the formation of new polydomain states forbidden in bulk crystals. The total dielectric and piezoelectric small-signal responses of polydomain films are calculated, resulting from both the volume and domainwall contributions. For BaTiO 3 films, strong dielectric anomalies are predicted at room temperature near special values of the misfit strain.

Variations of the dielectric properties of ferroelectric thin films with the misfit strain S m in the film/substrate system and the associated biaxial stress inside the film are analyzed theoretically. Calculations are performed in a mean-field approximation for the dielectric response displayed in a plate-capacitor setup by single crystalline films epitaxially grown on tensile substrates (S m Ͼ0). It is shown that, in the absence of misfit-strain-induced phase transitions, the film dielectric susceptibility 33 obeys the Curie-Weiss-type law For many applications of ferroelectric thin films, such as cells for GBit dynamic random access memories, integrated decoupling capacitors, high-frequency transducers, etc., a high electric permittivity is required. 1 The dielectric properties of a thin film, however, depend not only on the ferroelectric substance itself, but also on the substrate material and other factors. In particular, these properties should be strongly affected by the lattice misfit between the film and substrate. [2][3][4] The misfit-strain changes directly manifest itself in the variation of the in-plane lattice parameter, which can be evaluated by the x-ray diffraction. 2 Even in the same film/ substrate system, the misfit strain S m may differ for films of different thicknesses because of the strain relaxation caused by the formation of misfit dislocations. 5 Strong changes of S m with increasing film thickness are evident in BaTiO 3 /Pt/MgO and BaTiO 3 /SrTiO 3 heterostructures. 2,6 The misfit strain can also be tuned to a certain extent by bending the substrate by an external load. Such a bending test was recently performed by Shaw et al. for Ba 0.7 Sr 0.3 TiO 3 films grown on platinum coated silicon substrates. 7 They evaluated the associated change of the in-plane biaxial stress in the film and attributed the observed variation of the capacitance to the stress effect. During the dielectric measurements, however, the film grown on a thick substrate is under a fixed strain, but not at constant stress. 3 Besides, in the presence of spontaneous polarization, the stress is not directly related to the strain. 2 Therefore, the stress effect is not equivalent to the underlying misfit-strain one.In this letter, we analyze the strain and stress effects on the dielectric response exhibited by perovskite ferroelectric films in a conventional plate-capacitor setup. For clarity, we consider only ferroelectric overlayers grown on cubic substrates providing positive misfit strains in the heterostructure.To describe the above effects theoretically, we will calculate the dielectric response of a single crystalline epitaxial film using the thermodynamic theory, which was developed recently. 3,4 In contrast with Refs. 3 and 4, a specific feature of the film dielectric properties will be reported here. Namely, our concept is to demonstrate that the reciprocal dielectric susceptibility of a ferroelectric thin film may be a linear function of the misfit strain S m ͑or internal stress ͒ even in the presence of a subst...

A Landau–Ginsburg–Devonshire-type thermodynamic theory is used to describe epitaxial ferroelectric films with dense laminar domain structures, where spontaneous polarizations in both domains are oriented in the film plane. For PbTiO3 films, it is found that, at positive misfit strains, the domain patterning transforms the orthorhombic aa phase, which is stable in single-domain films, into a pseudotetragonal a1/a2/a1/a2 polydomain state. In BaTiO3 films, the latter is further replaced at low temperatures by a polydomain aa1/aa2/aa1/aa2 state. With decreasing misfit strain, both a1/a2/a1/a2 and aa1/aa2/aa1/aa2 patterns become unstable with respect to the appearance of polarization component orthogonal to film surfaces. This results in the formation of polydomain states in BaTiO3 films, which do not exist in bulk crystals. The stability ranges of various states in the misfit strain-temperature phase diagram are determined.