We present a quantitative study of the thickness dependence of the polarization and piezoelectric properties in epitaxial ͑001͒ PbZr 0.52 Ti 0.48 O 3 films grown on ͑001͒ SrRuO 3 -buffered ͑001͒ SrTiO 3 substrates. High-resolution transmission electron microscopy reveals that even the thinnest films ͑ϳ8 nm͒ are fully relaxed with a dislocation density close to 10 12 cm −2 and a spacing of approximately 12 nm. Quantitative piezoelectric and ferroelectric measurements show a drastic degradation in the out-of-plane piezoelectric constant ͑d 33 ͒ and the switched polarization ͑⌬P͒ as a function of decreasing thickness. In contrast, lattice-matched ultrathin PbZr 0.2 Ti 0.8 O 3 films that have a very low dislocation density show superior ferroelectric properties. Supporting theoretical calculations show that the variations in the strain field around the core of the dislocation leads to highly localized polarization gradients and hence strong depolarizing fields, which result in suppression of ferroelectricity in the vicinity of a dislocation.Understanding nanoscale ferroelectrics has become a topic of intense fundamental research. 1,2 Recent studies show that lattice engineering and internal stresses have a major role in the structural and physical properties of ultrathin ferroelectric films. [3][4][5] In lattice-matched ͑or epitaxial͒ films and heterostructures, the strain due to lattice mismatch between the film and the substrate can be relaxed during film growth. by the formation of orthogonal arrays of misfit dislocations at the film-substrate interface. 6-11 For epitaxial 10 nm high PbZr 0.52 Ti 0.48 O 3 ͓PZT ͑52/ 48͔͒ nanoislands on Nbdoped SrTiO 3 ͑STO͒, the strain field associated with the dislocation core was found to be propagating into the ferroelectric layer with a height of ϳ4 nm and a width of ϳ8 nm, a significant volume fraction of the islands. 4 Recent theoretical results 12 for an epitaxial PTO thin film with periodic misfit dislocations predict that the strong coupling of the dislocation strain field with the polarization leads to high local polarization gradients. This results in strong depolarizing fields around a dislocation in a region of 5-10 nm in diameter around the core, that ultimately suppress ferroelectricity. 13,14 Misfit dislocations should thus act as an extrinsic dominating factor in the scaling of polarization and all physical properties as a function of thickness. In this letter, we provide a systematic quantitative study on the role of dislocations on the stability ferroelectricity in epitaxial ferroelectric thin films.Epitaxial ͑001͒ PZT ͑52/ 48͒ films were grown on ͑001͒ SrRuO 3 ͑SRO͒-buffered ͑001͒ SrTiO 3 ͑STO͒ substrates. The thickness of the PZT ͑52/ 48͒ layer was varied from 200 nm down to 12 nm thickness. The details of the growth method and parameters are given elsewhere. 15 In order to compare and contrast the effect of misfit dislocations, very well lattice-matched PZT ͑20/ 80͒/SRO/STO heterostructures were also prepared from 80 nm down to 4 nm. In order to avoid complica...

A thermodynamic analysis has been carried out to investigate the role of dislocations in ferroelectric materials. Due to the coupling of the stress field of the dislocation and the polarization, there is a drastic variation in the polarization near the dislocation. These polarization gradients result in strong depolarizing fields that suppress the polarization in a region that extends over several nanometrers. In epitaxial ferroelectric films, these polarization gradients should result in the formation of dead layers that severely degrade ferroelectric properties. The detrimental effect of such regions will be enhanced in ultrathin ferroelectric thin films, and hence play a critical extrinsic role in size effect studies of ferroelectrics.

A theoretical model is developed for ferroelectric bilayers and multilayer heterostructures that employs a nonlinear Landau-Devonshire formalism coupled with a detailed analysis of the depolarizing fields arising from the polarization mismatch across interlayer interfaces and the electrical fields of localized space charges at such interfaces. We first present how space charges alter the free-energy curves of ferroelectrics and then proceed with a numerical analysis for heteroepitaxial ͑001͒ PbTiO 3-SrTiO 3 ͑PTO-STO͒ bilayers and ͑001͒ superlattice structures on ͑001͒ STO substrates. The switchable ͑ferroelectric͒ and nonswitchable ͑built-in͒ polarizations and the dielectric properties of PTO-STO bilayers and superlattices are calculated as a function of the planar space-charge density and the volume fraction of the PTO layer. Similar to the temperature dependence of a monolithic ferroelectric, there exists a critical volume fraction PTO below which the bilayer or the superlattice is in the paraelectric state. This critical volume fraction is strongly dependent on the density of trapped charges at the interlayer interfaces. For charge-free ͑001͒ PTO-STO heteroepitaxial bilayer and superlattices, the critical fraction is 0.40 for both constructs but increases to 0.6 and 0.72, for the bilayer and the superlattice, respectively, for a planar space-charge density of 0.05 C / m 2. Furthermore, our results show that close to the vicinity of ferroelectric-paraelectric phase transition, there is a recovery in ferroelectric polarization. The dielectric-response calculations verify that there is sharp ferroelectric phase transformation for charge-free bilayers and superlattices whereas it is progressively smeared out with an increase in the charge density. Furthermore, our analysis shows that the dielectric constant of these multilayers at a given volume fraction of PTO decreases significantly in the presence of space charges.

Structural characteristics of phase transformations in epitaxial ferroelectric films are analyzed via a Landau-Devonshire thermodynamic formalism. It is shown that the phase transformation temperature, the lattice parameters, and the order of the phase transformation are a strong function of the misfit strain and are considerably different compared to unconstrained, unstressed single crystals of the same composition. Depending on the internal stress state, it is possible that the structural aspects of the paraelectric-ferroelectric phase transformation may be completely obscured in the presence of epitaxial strains. The thickness dependence of epitaxial stresses due to relaxation by misfit dislocations during film deposition is incorporated into the model using an ''effective'' substrate lattice parameter. There is a good quantitative agreement between the theoretical analysis and experimental observations reported in the literature on the variations in the lattice parameters and the phase transformation temperature with film thickness in epitaxial BaTiO 3 films.

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Within the phenomenological Landau–Ginzburg–Devonshire theory, we discuss the paraelectric-ferrolectric transition in superstructures consisting of ferroelectric and paraelectric layers of equal thickness. The polar axis of the ferroelectric is perpendicular to the layer plane as expected in fully strained BaTiO3/SrTiO3 superstructures on SrTiO3 substrates with pseudomorphic electrodes. We concentrate on the electrostatic effects and do not take into account the boundary conditions other than the electrostatic ones. We find that when the ferroelectric phase transition in the superstructures is into a multidomain state, both its temperature and its character, i. e., the profile of the polarization appearing at the phase transition is strongly influenced by the nature of the near-electrode region. This is also the case for the layer thickness separating the single-and multidomain regimes of the transition. Such a finding makes us question the idea that these superstructures can be thought of as infinite systems, i.e., periodic superstructures similar to a crystal. The irrelevance of this idea in certain conditions is demonstrated by comparing the phase transitions in two different superstructures consisting of ferroelectric and paraelectric layers of the same thickness. In one of them, the ferroelectric layer is in immediate contact with an ideal metallic electrode, whereas at the other boundary, it is the paraelectric layer that is in contact with the electrode. In another superstructure, one paraelectric layer is split in two equal parts which are placed as the first and last layer between the electrodes and the ferroelectric layers which are closest to the electrodes. We show (with some formal reservations) that the phase transition temperature in the first superstructure can be over 100 °C more than in the second one if the material parameters of BaTiO3/SrTiO3 are used for the estimations. Moreover, the profile of the polarization arising at the phase transition is inhomogeneous along the superstructure and has the maximum amplitude in the ferroelectric layer contacting the electrode. We argue that this situation is general and results in smearing of the phase transition anomalies for the layer thicknesses corresponding to multidomain transitions. The work is mainly analyical but numerical methods have been used to support some statements that have been put forward as hypotheses.

Epitaxial antiferroelectric/ferroelectric PbZrO 3 / PbZr 0.8 Ti 0.2 O 3 multilayers were grown on SrRuO 3-electroded SrTiO 3 ͑100͒ substrates by pulsed laser deposition. Polarization-field and switching current-voltage curves show a mixed antiferroelectric-ferroelectric behavior of the multilayers with an individual layer thickness above 10 nm, whereas below 10 nm the multilayers show only ferroelectric behavior. Clearly the PbZrO 3 layers thinner than 10 nm experienced a transition into the ferroelectric state. X-ray diffraction reciprocal space mapping showed a corresponding orthorhombic-to-rhombohedral transition of the PbZrO 3 layers. The observations are discussed in terms of the influence of strain.

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