The elastic field of a surface step: The Marchenko–Parshin formula in the linear case

Connell, Cameron; Caflisch, Russel E.; Luo, Erding; Simms, Geoffrey

doi:10.1016/j.cam.2005.08.020

Cited by 10 publications

(9 citation statements)

References 12 publications

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“…The total elastic strain energy el E is calculated using an atomistic strain model 22,23 , which assumes harmonic potentials and includes nearest-neighbor (NN), next-NN (NNN), and bond-bending (BB) interactions ( ) ( ) ( ) valence force field results 25 .…”

Section: Simulation Methodsmentioning

confidence: 99%

Simulation of self-assembled compositional core-shell structures in InxGa1−xN nanowires

et al. 2012

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We report the simulation of compositional core-shell structure formation in epitaxial InGaN nanowires (NWs) and its dependence on kinetic growth mode and epitaxial relation to substrate, based on atomistic-strain-model Monte Carlo simulations. On a lattice mismatched substrate, the layer-by-layer growth results in self-assembled core-shell structures with the core rich in the unstrained component (relative to the substrate), while the faceted growth mode leads to the strained core component, and both are distinctively different from the equilibrium composition profiles. Our simulation results explain the reason that all the existing core-shell alloy NWs grown by vapor-liquid-solid experiments have cores rich in the unstrained (or less strained) components is because they have been grown via the layer-bylayer mode, and more importantly suggest a possible route towards controlling the NW core-shell composition by altering growth mode and/or selecting substrate.

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Section: Simulation Methodsmentioning

confidence: 99%

Simulation of self-assembled compositional core-shell structures in InxGa1−xN nanowires

et al. 2012

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“…At a step on a boundary or interface, there are deviations from the continuum boundary conditions which can be interpreted as force distributions on the boundary. Details of the energy density and the discrete force balance equations can be found in [14,39]. Computational solution of the strain equations can be computationally challenging.…”

Section: Numerical Simulations For Thin Filmsmentioning

confidence: 99%

Growth, Structure and Pattern Formation for Thin Films

Caflisch¹

2008

J Sci Comput

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An epitaxial thin film consists of layers of atoms whose lattice properties are determined by those of the underlying substrate. This paper reviews mathematical modeling, analysis and simulation of growth, structure and pattern formation for epitaxial systems, using an island dynamics/level set method for growth and a lattice statics model for strain. Epitaxial growth involves physics on both atomistic and continuum length scales. For example, diffusion of adatoms can be coarse-grained, but nucleation of new islands and breakup for existing islands are best described atomistically. In heteroepitaxial growth, mismatch between the lattice spacing of the substrate and the film will introduce a strain into the film, which can significantly influence the material structure, for example leading to formation of quantum dots. Technological applications of epitaxial structures, such as quantum dot arrays, require a degree of geometric uniformity that has been difficult to achieve. Modeling and simulation may contribute insights that will help to overcome this problem. We present simulations that combine growth and strain showing the structure of nanocrystals and the formation of patterns in epitaxial systems.

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“…The strain field produced by a surface step, on an epitaxial surface, interacting with a buried step, on the interface between an epitaxial thin film and the substrate has been successfully studied in [7] using discrete harmonic potentials developed in [2]. We now try to understand step relaxation in core-shell layered nanocrystal system in a way that is analogous to that in [7].…”

Section: Step Interactionsmentioning

confidence: 99%

Strain in layered nanocrystals

Bae

Caflisch²

2007

Eur. J. Appl. Math

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Layered nanocrystals consist of a core of one material surrounded by a shell of a second material. We present computation of the atomistic strain energy density in a layered nanocrystal, using an idealised model with a simple cubic lattice and harmonic interatomic potentials. These computations show that there is a critical size r * s for the shell thickness r s at which the energy density has a maximum. This critical size is roughly independent of the geometry and material parameters of the system. Interestingly, this critical size agrees with the shell thickness at which the quantum yield has a maximum, as observed in several systems and thus leads one to support the hypothesis that maximal quantum yield is strongly correlated with maximal elastic energy density.

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The elastic field of a surface step: The Marchenko–Parshin formula in the linear case

Cited by 10 publications

References 12 publications

Simulation of self-assembled compositional core-shell structures in InxGa1−xN nanowires

Simulation of self-assembled compositional core-shell structures in InxGa1−xN nanowires

Growth, Structure and Pattern Formation for Thin Films

Strain in layered nanocrystals

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