Strain–displacement relations for strain engineering in single-layer 2d materials

Midtvedt, Daniel; Lewenkopf, Caio

doi:10.1088/2053-1583/3/1/011005

Cited by 43 publications

(68 citation statements)

References 45 publications

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“…As we have shown, the simple Cauchy-Born relation -often employed in this context -is not a good approximation as it tends to overestimate the strain. Instead, we propose to use strain-displacement relations, which are obtained by minimizing the elastic energy [15]. This approach is easily combined with the microscopic TB model and yields good quantitative agreement.…”

Section: Discussionmentioning

confidence: 99%

“…We obtain a very good agreement between fully numerical results (TB and VFM) with analytical estimates resulting from continuum elasticity [16] combined with the derived strain-induced modification of the band-gap given by Eq. (15).…”

Section: Discussionmentioning

confidence: 99%

“…(10), from a VFM is given in Ref. 15. Here we revisit the theory to explain and provide further insight on some of the expressions used in Sec.…”

Section: Discussionmentioning

confidence: 99%

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Multi-scale approach for strain-engineering of phosphorene

Midtvedt

Lewenkopf

2017

J. Phys.: Condens. Matter

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A multi-scale approach for the theoretical description of deformed phosphorene is presented. This approach combines a valence-force model to relate macroscopic strain to microscopic displacements of atoms and a tight-binding model with distance-dependent hopping parameters to obtain electronic properties. The resulting self-consistent electromechanical model is suitable for large-scale modeling of phosphorene devices. We demonstrate this for the case of inhomogeneously deformed phosphorene drum, which may be used as an exciton funnel.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

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Multi-scale approach for strain-engineering of phosphorene

Midtvedt

Lewenkopf

2017

J. Phys.: Condens. Matter

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“…[12]. This approach relates the VFM to the elastic stretching energy-density in terms of the strain tensor via a minimization procedure.…”

Section: B Elastic Propertiesmentioning

confidence: 99%

“…When accurately parametrized, they can be used to extract the phonon dispersion and elastic properties. Moreover, VFMs can be used to connect the microscopic structure and macroscopic quantities such as strain [12]. In particular, atomic displacements can be related to the macroscopic strain applied to the material, which is a requirement for strain-engineering investigations [11].…”

Section: Introductionmentioning

confidence: 99%

Valence-force model and nanomechanics of single-layer phosphorene

Midtvedt

2016

Phys. Chem. Chem. Phys.

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In order to understand the relation of strain and material properties, both a microscopic model connecting a given strain to the displacement of atoms, and a macroscopic model relating applied stress to induced strain, are required. Starting from a valence-force model for black phosphorous (phosphorene) [Kaneta et al., Solid State Communications, 1982, 44, 613] we use recent experimental and computational results to obtain an improved set of valence-force parameters. From the model we calculate the phonon dispersion and the elastic properties of single-layer phosphorene. Finally, we use these results to derive a complete continuum model, including the bending rigidities, valid for long-wavelength deformations of phosphorene. This continuum model is then used to study the properties of pressurized suspended phosphorene sheets.

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Coupling of Piezo/Flexoelectricity and Its Effect on the Band Structure of Wrinkled ZnO Monolayers

Yin,

Jia,

et al. 2024

Adv Funct Materials

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Wrinkles are used in manufacturing stretchable electronics, soft materials, smart displays, and microstructures. The emerging 2D materials enable the investigation of the intertwined piezoelectric and flexoelectric coupling effect in wrinkled structures and their energy, sensing, and other applications. However, current studies of the electromechanical coupling effect often consider it one effect or even overlook one of the two effects. This oversimplification leads to inaccuracies in the analysis. Here, a theoretical model is proposed to separate the piezoelectric and flexoelectric coefficients by fitting polarization formulas with discrete polarization values calculated using density functional theory. Wrinkled ZnO monolayers are built to mimic the realistic situation, where six nonzero coefficients are successfully isolated, revealing that the coupling of piezo/flexoelectricity and the contribution of piezoelectric and flexoelectric polarizations to the total polarization vary in different directions. Combined with the dipole moment analysis, the relationship between the polarization, piezoelectric coefficient, flexoelectric coefficient, and wrinkle amplitude is established. This study demonstrates that increasing the wrinkle amplitude significantly decreases the energy gap of 560 meV. The separation and quantification of piezoelectric and flexoelectric effects advance the understanding of wrinkles' mechanical and electromechanical properties and lay the foundation for their future applications.

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Strain–displacement relations for strain engineering in single-layer 2d materials

Cited by 43 publications

References 45 publications

Multi-scale approach for strain-engineering of phosphorene

Multi-scale approach for strain-engineering of phosphorene

Valence-force model and nanomechanics of single-layer phosphorene

Coupling of Piezo/Flexoelectricity and Its Effect on the Band Structure of Wrinkled ZnO Monolayers

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