Fundamentals of flexoelectricity in solids

Yudin, P. V.; Tagantsev, A. K.

doi:10.1088/0957-4484/24/43/432001

Cited by 602 publications

(453 citation statements)

References 103 publications

(425 reference statements)

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“…It is our hypothesis that a strain gradient can "orient" these tetragons in a preferential direction, resulting in a nonzero χ (2) .This hypothesis is based on well-known recent results that show silicon nitride films are known to possess both  (2) and a Pockels coefficient [19][20][21][22][23] whose origin has not yet been fully understood. We also make clear the connection between the strain-gradient induced χ (2) (SGI-χ (2) ) and flexo-electric effect [24][25], in support of our hypothesis. Our estimate shows that only "orientation" or "poling" of the Si-N bonds under the strain gradient can explain the order of magnitude of the SGI-χ (2) and SGI Pockels coefficients observed in all the experiments to-date.…”

Section: Introductionsupporting

confidence: 87%

On the origin of the second-order nonlinearity in strained Si–SiN structures

et al. 2015

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The development of efficient low-loss electro-optic and nonlinear components based on silicon or its related compounds, such as nitrides and oxides, is expected to dramatically enhance silicon photonics by eliminating the need for non-CMOS-compatible materials. While bulk Si is centrosymmetric and thus displays no second-order (χ (2) ) effects, a body of experimental evidence accumulated in the last decade demonstrates that when a strain gradient is present, a significant χ (2) and Pockels coefficient can be observed. In this work we connect a straingradient-induced χ (2) with another strain-gradient-induced phenomenon, the flexoelectric effect. We show that even in the presence of an extremely strong strain gradient, the degree by which a nonpolar material like Si can be altered cannot possibly explain the order of magnitude of observed χ (2) phenomena. At the same time, in a polar material like SiN, each bond has a large nonlinear polarizability, so when the inversion symmetry is broken by a strain gradient, a small (few degrees) re-orientation of bonds can engender χ (2) of the magnitude observed experimentally. It is our view therefore that the origin of the nonlinear and electro-optic effects in strained Si structures lies in not in the Si itself, but in the material providing the strain: the silicon nitride cladding.

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Section: Introductionsupporting

confidence: 87%

On the origin of the second-order nonlinearity in strained Si–SiN structures

et al. 2015

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“…The relative magnitude of these contributions is discussed in a recent review article. 1 It is also indicated in the review, that there exist the upper limits for the magnitude of the static bulk contribution to the flexoelectric effect in ferroelectrics, the contribution which was considered as the dominating one and now is considered as one of the leading contributions. Here, we provide mathematical frame work for obtaining such upper limits in different materials.…”

mentioning

confidence: 99%

Upper bounds for flexoelectric coefficients in ferroelectrics

Yudin

Ahluwalia

Tagantsev

2014

Applied Physics Letters

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Flexoelectric effect is the response of electric polarization to the mechanical strain gradient. At the nano-scale, where large strain gradients are expected, the flexoelectric effect becomes appreciable and may substitute piezoelectric effect in centrosymmetric materials. These features make flexoelectricity of growing interest during the last decade. At the same time, the available theoretical and experimental results are rather contradictory. In particular, experimentally measured flexoelectric coefficients in some ferroelectric materials largely exceed theoretically predicted values. Here, we determine the upper limits for the magnitude of the static bulk contribution to the flexoelectric effect in ferroelectrics, the contribution which was customarily considered as the dominating one. The magnitude of the upper bounds obtained suggests that the anomalously high flexoelectric coupling documented for perovskite ceramics can hardly be attributed to a manifestation of the static bulk effect. V C 2014 AIP Publishing LLC.[http://dx.doi.org/10.1063/1.4865208] Flexoelectric effect is the response of electric polarization to the mechanical strain gradient. It can be viewed as higher-order effect with respect to piezoelectricity, which is the response of polarization to strain itself. However at the nano-scale, where large strain gradients are expected, the flexoelectric effect becomes appreciable. Besides, in contrast to piezoelectric effect, flexoelectricity is allowed by symmetry in any material. Due to these features flexoelectricity has attracted growing interest during the last decade. On the other hand, the available theoretical and experimental results are rather contradictory, attesting to a limited understanding in the field. In particular, often experimentally measured flexoelectric coefficients largely exceed theoretically predicted values. It is important to distinguish different contributions to the effect: bulk and surface contributions; static and dynamic contributions. The relative magnitude of these contributions is discussed in a recent review article.

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“…The most widely used model for flexoelectricity is the linear continuum theory of flexoelectricity (see the recent reviews 18,22,23 ). In this theory, flexoelectricity is represented by a fourth-order flexoelectric coupling tensor, whose symmetry is well understood [24][25][26] .…”

Section: Introductionmentioning

confidence: 99%

Revisiting pyramid compression to quantify flexoelectricity: A three-dimensional simulation study

et al. 2015

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Flexoelectricity is a universal property of all dielectrics, by which they generate a voltage in response to an inhomogeneous deformation. One of the controversial issues in this field concerns the magnitude of flexoelectric coefficients measured experimentally, which greatly exceed theoretical estimates. Furthermore, there is a broad scatter amongst experimental measurements. The truncated pyramid compression method is one of the common setups to quantify flexoelectricity, the interpretation of which relies on simplified analytical equations to estimate strain gradients. However, the deformation fields in 3D pyramid configurations are highly complex, particularly around its edges. In the present work, using three-dimensional self-consistent simulations of flexoelectricity, we show that the simplified analytical estimations of strain gradients in compressed pyramids significantly overestimate flexoelectric coefficients, thus providing a possible explanation to reconcile different estimates. In fact, the interpretation of pyramid compression experiments is highly nontrivial. We systematically characterize the magnitude of this overestimation, of over one order of magnitude, as a function of the truncated pyramid configuration. These results are important to properly characterize flexoelectricity, and provide design guidelines for effective electromechanical transducers exploiting flexoelectricity.

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Fundamentals of flexoelectricity in solids

Cited by 602 publications

References 103 publications

On the origin of the second-order nonlinearity in strained Si–SiN structures

On the origin of the second-order nonlinearity in strained Si–SiN structures

Upper bounds for flexoelectric coefficients in ferroelectrics

Revisiting pyramid compression to quantify flexoelectricity: A three-dimensional simulation study

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