Recent Developments in Thermodynamic Theory of Ferroelectric Thin Films
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Recent Developments in Thermodynamic Theory of Ferroelectric Thin Films N. A. Pertsev Institut für Festkörperforschung, Forschungszentrum Jülich, D-52425 Jülich, GERMANY; A. F. Ioffe Physico-Technical Institute, 194021 St. Petersburg, RUSSIA ABSTRACT The nonlinear thermodynamic theory of epitaxial ferroelectric films has predicted several important strain-induced phenomena, which have been already observed experimentally. This justifies further development of this theory aiming at the better understanding of the structure/property relationships in thin-film ferroelectrics. To that end, a number of new theoretical studies have been performed recently. First, the thermodynamic formalism has been extended to epitaxial films grown on dissimilar substrates inducing anisotropic strains and a shear deformation in the film plane. Second, the polarization states and dielectric properties were calculated for polydomain Pb(Zr1-xTix)O3 films deposited on cubic substrates. Third, the effect of depolarizing field on the physical properties of strained single-domain films sandwiched between continuous electrodes was described. The results of these studies will be discussed in this paper. INTRODUCTION The nonlinear thermodynamic theory of ferroelectric thin films is based on the Landau theory of phase transitions [1] and the Devonshire theory of ferroelectric crystals [2]. This approach employs a polynomial expansion of the energy density in terms of the primary (electric polarization) and secondary (mechanical stress or strain) order parameters. For bulk crystals kept under constant (external) stresses, the equilibrium thermodynamic states can be determined via the minimization of the Gibbs free energy G. The thermodynamic coefficients involved in the expansion of G up to the sixth-order polarization terms are known for several perovskite ferroelectrics, including BaTiO3 [3], PbTiO3 [4], and Pb(Zr1-xTix)O3 [5]. For ferroelectric thin films grown on dissimilar substrates, the existence of a mechanical film/substrate interaction represents one of the main factors distinguishing them from bulk ferroelectric materials. The importance of this interaction for the physical properties of ferroelectric films was recognized in the first half of the 1990’s [6-9]. The initial theoretical studies, however, were based on the minimization of the Gibbs free energy G, which is not suitable for thin films since here the in-plane (internal) stresses are not constant but depend on the film polarization. The actual mechanical boundary conditions imposed on thin films result in constant in-plane strains and fixed out-of-plane stresses. Such mixed conditions can be properly ~ taken into account via the introduction of a modified thermodynamic potential G [10,11]. (In the absence of external stresses, the Helmholtz free energy F can be used as well [12]). The secondorder polarization terms in this potential depend on the misfit strain between the film prototypic ~ state and the substrate [10]. The minimization of G makes it possible to det
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