A study of flexoelectric coupling associated internal electric field and stress in thin film ferroelectrics

Ma, Wenhui

doi:10.1002/pssb.200743514

Cited by 99 publications

(79 citation statements)

References 31 publications

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“…has the same effect on polarization as the external electric field E. It is sometimes called the "flexoelectric field" and is a convenient concept when considering the strength of flexoelectric poling effects. For example, when discussing polarization switching or poling caused by strain gradients [22][23][24][25], it is this quantity that should be compared with the coercive or built-in electric fields.…”

Section: Constitutive Equationsmentioning

confidence: 99%

Flexoelectric Effect in Solids

Zubko

Catalán

Tagantsev

2013

Annu. Rev. Mater. Res.

921

663

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Piezoelectricity-the coupling between strain and electrical polarization, allowed 2 Zubko, Catalan, Tagantsev by symmetry in a restricted class of materials-is at the heart of many devices that permeate our daily life. Since its discovery in the 1880's by Pierre and Jacques Curie, the piezoelectric effect has found use in everything from submarine sonars to cigarette lighters. By contrast, flexoelectricity-the coupling between polarization and strain gradients, allowed by symmetry in all materials-was largely overlooked for decades since its first proposal in the late 1950's, due to the seemingly small magnitude of the effect in bulk. The development of nanoscale technologies, however, has renewed the interest in flexoelectricity, as the large strain gradients often present at the nanoscale can lead to dramatic flexoelectric phenomena. Here we review the fundamentals of the flexoelectric effect, discuss its presence in many nanoscale systems, and look at potential applications of this fascinating phenomenon. The review will also emphasize the many open questions and unresolved issues in this developing field.

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Section: Constitutive Equationsmentioning

confidence: 99%

Flexoelectric Effect in Solids

Zubko

Catalán

Tagantsev

2013

Annu. Rev. Mater. Res.

921

663

View full text Add to dashboard Cite

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“…In general, the flexoelectric coefficients of simple homogeneous insulating solids are quite small, but large flexoelectric coefficients have been reported in several ferroelectric materials [42,43]. In this analysis, the range of flexoelectric coefficients to be considered is obtained by transforming the flexoelectric polarization coefficients (μ 12 ) into flexoelectric strain coefficients (f 12 ) [44] and obtaining both the upper-and lower-bound values from Refs. [42,43].…”

Section: B Adapting the Formalism For Compositionally Graded Ferroelmentioning

confidence: 99%

Understanding order in compositionally graded ferroelectrics: Flexoelectricity, gradient, and depolarization field effects

Zhang

Damodaran

et al. 2014

Phys. Rev. B

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A nonlinear thermodynamic formalism based on Ginzburg-Landau-Devonshire theory is developed to describe the total free energy density in (001)-oriented, compositionally graded, and monodomain ferroelectric films including the relative contributions and importance of flexoelectric, gradient, and depolarization energy terms. The effects of these energies on the evolution of the spontaneous polarization, dielectric permittivity, and the pyroelectric coefficient as a function of position throughout the film thickness, temperature, and epitaxial strain state are explored. In general, the presence of a compositional gradient and the three energy terms tend to stabilize a polar, ferroelectric state even in compositions that should be paraelectric in the bulk. Flexoelectric effects produce large built-in fields which diminish the temperature dependence of the polarization and susceptibilities. Gradient energy terms, here used to describe short-scale correlation between dipoles, have minimal impact on the polarization and susceptibilities. Finally, depolarization energy significantly impacts the temperature and strain dependence, as well as the magnitude, of the susceptibilities. This approach provides guidance on how to more accurately model compositionally graded films and presents experimental approaches that could enable differentiation and determination of the constitutive coefficients of interest.

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“…Moreover, they also represent areas of intense strain gradients that can attract large concentrations of dopants or defects, which will also modify greatly and very locally the materials' properties [5]. In addition, the strain gradients associated to those walls can induce electrical dipoles, due to the so-called flexoelectric effect [6][7][8][9].…”

Section: Introductionmentioning

confidence: 99%

Local conductivity and the role of vacancies around twin walls of (001)−BiFeO3 thin films

Farokhipoor¹,

Noheda²

2012

Journal of Applied Physics

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BiFeO3 thin films epitaxially grown on SrRuO3-buffered (001)-oriented SrTiO3 substrates show orthogonal bundles of twin domains, each of which contains parallel and periodic 71 o domain walls. A smaller amount of 109 o domain walls are also present at the boundaries between two adjacent bundles. All as-grown twin walls display enhanced conductivity with respect to the domains during local probe measurements, due to the selective lowering of the Schottky barrier between the film and the AFM tip (see S. Farokhipoor and B. Noheda, Phys. Rev. Lett. 107, 127601 (2011)). In this paper we further discuss these results and show why other conduction mechanisms are discarded. In addition we show the crucial role that oxygen vacancies play in determining the amount of conduction at the walls. This prompts us to propose that the oxygen vacancies migrating to the walls locally lower the Schottky barrier. This mechanism would then be less efficient in non-ferroelastic domain walls where one expects no strain gradients around the walls and thus (assuming that walls are not charged) no driving force for accumulation of defects.

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A study of flexoelectric coupling associated internal electric field and stress in thin film ferroelectrics

Cited by 99 publications

References 31 publications

Flexoelectric Effect in Solids

Flexoelectric Effect in Solids

Understanding order in compositionally graded ferroelectrics: Flexoelectricity, gradient, and depolarization field effects

Local conductivity and the role of vacancies around twin walls of (001)−BiFeO3 thin films

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