Alexander L. Roytburd

We present a nonlinear thermodynamic formalism coupled with an electrostatic analysis of uniaxial n-layered compositionally graded heteroepitaxial ferroelectric films and extend this formalism to continuously graded ferroelectric films. We show that the domain morphology and its subsequent evolution in the presence of an electric field are determined by the spontaneous polarisation of the film induced through the compositional grading. The results for compositionally graded epitaxial (001) (Ba,Sr)TiO(3) and (001) Pb(Zr,Ti)O(3) films on (001)SrTiO(3) demonstrate that, while the domain morphologies in these two films are different in appearance, the dielectric displacement and the dielectric permittivity of such graded ferroelectric films exhibit a strong nonlinear behaviour which results in a high dielectric tunability. These findings indicate that it is possible to design specific domain structures that will yield desirable dielectric properties by controlling the strength of the compositional grading in the films.

Phase-field simulations were used to explore the effect of the characteristics of the Landau-Devonshire free energy and values of electrostatic and elastic interactions on the formation of different types of domain structures in ferroelectric thin films. Simulations were performed at different constant-applied electric fields and by using a cyclic continuously changing field. It is shown that the 180deg or 90deg domain structures can be produced depending on the relative strength of elastic interactions and the ratio of barrier heights that determine the energy of the 180deg and 90deg domain boundaries. It is shown that the applied field strength and the thickness of the dead layer can play a minor role in the transition between the 90deg and 180deg domain structures. It is also demonstrated that the poling history can affect the type of the domain structure.

The results of phase-field simulation of domain structures (DSs) in ferroelectric nanorods of different shapes and sizes are presented. It is shown that equilibrium DSs consist of an electrostatically compatible circuit of 180° and 90° domains. A DS in a thin rod contains 90° cubic elastic domains. The trend to minimize the residual stress and the stray field results in the formation of crater-shaped sets of closed circuits of 90° domains, which can be mechanically incompatible but able to maintain electrostatic compatibility during the evolution under an applied electric field.

Substrate clamping and inter‐domain pinning limit movement of non‐180° domain walls in ferroelectric epitaxial films thereby reducing the resulting piezoelectric response of ferroelectric layers. Our theoretical calculations and experimental studies of the epitaxial PbZr_xTi_1–xO₃ films grown on single crystal SrTiO₃ demonstrate that for film compositions near the morphotropic phase boundary it is possible to obtain mobile two‐domain architectures by selecting the appropriate substrate orientation. Transmission electron microscopy, X‐ray diffraction analysis, and piezoelectric force microscopy revealed that the PbZr_0.52Ti_0.48O₃ films grown on (101) SrTiO₃ substrates feature self‐assembled two‐domain structures, consisting of two tetragonal domain variants. For these films, the low‐field piezoelectric coefficient measured in the direction normal to the film surface (d₃₃) is 200 pm V^–1, which agrees well with the theoretical predictions. Under external AC electric fields of about 30 kV cm^–1, the (101) films exhibit reversible longitudinal strains as high as 0.35 %, which correspond to the effective piezoelectric coefficients in the order of 1000 pm V^–1 and can be explained by elastic softening of the PbZr_xTi_1–xO₃ ferroelectrics near the morphotropic phase boundary.

The equilibrium domain structure and its evolution under an electric field in ferroelectric bilayers and graded multilayers are considered. The equilibrium bilayer is self-poled and contains single-domain and polydomain (with 180° domains) layers. The polarization of a graded multilayer proceeds by movement of wedge-like domains as a result of progressive transformation of polydomain layers to a single-domain state. The theory provides the principal explanation of dielectric behavior of graded ferroelectric films.

The converse piezoelectric response of a thin film constrained by a substrate is analyzed in different geometries under various boundary conditions. We considerthe effects of elastic deformation of the substrate on the total displacement of thefilm surface induced by the electric field. The change of film thickness and the bending curvature of a film/substrate couple are calculated. For a thin film island clamped on a large thick substrate, the theoretical estimation of the piezoresponse, including a local bending in the vicinity of the island/substrate interface, is in agreement with the finite element calculation.