Thermodynamic theory of stress distribution in epitaxial Pb(Zr, Ti)O3 thin films

Kim, H. Joon; Oh, Seogil; Jang, Hyun M.

doi:10.1063/1.125275

Cited by 68 publications

(40 citation statements)

References 9 publications

(9 reference statements)

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“…oxygen content in the films) during film growth; they suggested that crystal volume expansion by oxygen vacancies (V O ) could suppress the degree of the strain gradient (figure 3b). According to a general model for the strain profile [38], independent of the actual relaxation mechanism, the strain u(z) in epitaxial thin films can be expressed as…”

Section: (B) Strain Gradient and Its Engineering At Nanoscalementioning

confidence: 99%

Giant flexoelectric effect through interfacial strain relaxation

Lee

Noh

2012

Phil. Trans. R. Soc. A.

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Interfacial strain gradients in oxide epitaxial thin films provide an interesting opportunity to study flexoelectric effects and their potential applications. Oxide epitaxial thin films can exhibit giant and tunable flexoelectric effects, which are six or seven orders of magnitude larger than those in conventional bulk solids. The strain gradient in an oxide epitaxial thin film can generate an electric field above 1 MV m −1 by flexoelectricity, large enough to affect the physical properties of the film. Giant flexoelectric effects on ferroelectric properties are discussed in this overview of recent experimental observations.

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Section: (B) Strain Gradient and Its Engineering At Nanoscalementioning

confidence: 99%

Giant flexoelectric effect through interfacial strain relaxation

Lee

Noh

2012

Phil. Trans. R. Soc. A.

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“…An exponential profile over the thickness for the stress has been considered in several models [147] and compared to experimental variation with thickness of the lattice parameters for Pb(Zr 0.4 Ti 0.6 )O 3 [147]. Catalan et al [148] have used this exponential decay of the strain and X-ray diffraction analysis to calculate the strain profile.…”

Section: Thickness Dependent Relaxationmentioning

confidence: 99%

Strain on ferroelectric thin films

Janolin

2009

J Mater Sci

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Strain engineering aims to take advantage of the stress field imposed by substrates on thin films. It requires an understanding of the consequences of stress fields on the physical properties of the deposited materials. This is achieved in ferroelectric thin films through the use of misfit-strain phase diagrams that show the stability regions for the possible phases. These encompass bulk phases as well as new ones exhibiting symmetries that are not present in the bulk. For the solid solution lead zirconate-lead titanate, Pb(Zr 1-x Ti x )O 3 , monoclinic phases found in the bulk morphotropic phase boundary region and associated to concentrations exhibiting the highest properties can be stabilized on a wider range of composition in thin films. In addition, phases of lower symmetry can be stabilized through the use of anisotropic biaxial stress fields, generated by orthorhombic substrates for example. Another crucial aspect of the influence of biaxial stress fields is the generation of domain structures. Theoretical tools as well as experimental verifications have provided much insight on the underlying physics. We, therefore, present here an overview of the influence of both iso-and anisotropic biaxial stress fields on the structures and properties of ferroelectric thin films exemplified on Pb(Zr 1-x Ti x )O 3 .

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“…If the stress relaxation due to the misfit dislocations is negligible, the strain profile can be written as ‫ץ‬u 1 / ‫ץ‬z =−u 10 / ␣ 2 and ‫ץ‬u 2 / ‫ץ‬z =−u 20 / ␣ 2 . 9,11 In this letter, the misfit dislocations are assumed to provide the main relaxation mechanism, and the strain profiles as a function of z are given bywhere ␣ 1 and ␣ 2 are decline parameters that measure the penetration depth of the strain. u 10 and u 20 are the strains at the upper and lower film-substrate interfaces, respectively.…”

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confidence: 99%

“…[9][10][11][12][13][14] In this letter, we report on our investigation of the effects of the strain gradient caused by the epitaxial stresses in ferroelectric thin films ͑FTFs͒ sandwiched between two different substrates. Following the Landau-Ginzburg-Devonshire ͑LGD͒ theory, a general model that includes effects of flexoelectricity and stress gradient is formulated and applied.…”

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Effects of strain gradient on charge offsets and pyroelectric properties of ferroelectric thin films

Zheng

Wang

Woo

2006

Applied Physics Letters

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The Landau-Ginzburg-Devonshire theory is used to study the effects of the strain gradient due to the epitaxial stresses in ferroelectric thin films sandwiched between two different substrates. The polarization in the film is found to be nonuniform, resulting in charge offsets and an asymmetric hysteresis response with characteristics similar to those in compositionally graded ferroelectric materials. The authors' results suggest that the charge offset and pyroelectric effects can also be produced with effect of the strain gradient in film. In addition, such effects are found to be sensitive to an applied load. © 2006 American Institute of Physics. ͓DOI: 10.1063/1.2335369͔Functionally graded ferroelectrics in the form of either bulk or thin films possess properties 1-8 different from those of homogeneous ferroelectrics. The distribution of the polarization in graded ferroelectric devices is asymmetric and graded, and there is a translation of the hysteresis loop along the polarization axis with an attendant charge offset. As a result of this asymmetry, other properties such as the effective pyroelectric response, temperature dependence of the dielectric behavior, etc., 1,3 are also affected.At the same time, a strain gradient in a uniform ferroelectric thin film may also produce similar effects. [9][10][11][12][13][14] In this letter, we report on our investigation of the effects of the strain gradient caused by the epitaxial stresses in ferroelectric thin films ͑FTFs͒ sandwiched between two different substrates. Following the Landau-Ginzburg-Devonshire ͑LGD͒ theory, a general model that includes effects of flexoelectricity and stress gradient is formulated and applied.The thickness of the FTF is L, and the thicknesses of the rigid substrates are assumed to be much larger than L, so that the system can be considered to remain flat. The polarization P due to the eigenstrain of the ferroelectric transformation ͑simply called self-polarization͒ is assumed to be perpendicular to the film surface and is homogeneous on the x-y plane. Using the LGD theory and the Legendre transformation, the total free energy per unit area of the film can be written as: 4,9,10,15where A, B, and C are the expansion coefficients of the Landau free energy and D can be approximated as 2 · ͉A͑T − T c0 ͉͒, where T c0 is the Curie-Weiss temperature of the bulk material and is the characteristic length along which the polarization varies. 1 ␥ and are the direct and converse flexoelectric coefficients, respectively. 9,10 Q 12 is the electrostrictive coefficient describing the coupling between the mechanical deformation and the self-polarization. P 0 and P L are the polarizations, and ␦ 0 and ␦ L are the extrapolation lengths at the upper and lower surfaces, respectively. s ij is the elastic compliance tensor. E d ͑z͒ is the depolarization field and E ext ͑z͒ is the external field, which have been defined in Refs. 1, 3, and 4. u is the total biaxial in-plane residual strain in the thin film. x 1 = x 2 = x 0 is the transformation strain given by x...

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Thermodynamic theory of stress distribution in epitaxial Pb(Zr, Ti)O3 thin films

Abstract: Reciprocal space mapping of phase transformation in epitaxial PbTiO 3 thin films using synchrotron x-ray diffraction

Cited by 68 publications

References 9 publications

Giant flexoelectric effect through interfacial strain relaxation

Giant flexoelectric effect through interfacial strain relaxation

Strain on ferroelectric thin films

Effects of strain gradient on charge offsets and pyroelectric properties of ferroelectric thin films

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