Elastic relaxation of a truncated circular cylinder with uniform dilatational eigenstrain in a half space

Glas, Frank

doi:10.1002/pssb.200301801

Cited by 16 publications

(6 citation statements)

References 27 publications

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“…This approximation was recently shown to be reliable for computing the strain fields sufficiently away from the QWR where the system is sensitive to the QWR geometry and interfacial mismatch, but relatively unaffected by the internal properties of the QWR. [9][10][11] Whether this approximation is valid for points inside and close to the QWR ͑the crucial locations from an electronic device standpoint͒ is suspect and is the motivation for the present investigation.…”

Section: Introductionmentioning

confidence: 99%

“…13 Investigations of homogeneous polygonal inclusions have been carried out for both isotropic and anisotropic elastic cases. 11,[14][15][16] More recently, general solutions to anisotropic Eshelby problems that account for electromechanical coupling have been derived. These solutions are based either on the analytical continuation and conformal mapping method 10,17,18 or on the Green's-function method using the equivalent body-force concept.…”

Section: Introductionmentioning

confidence: 99%

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Strain fields in InAs∕GaAs quantum wire structures: Inclusion versus inhomogeneity

Pan

Han

Albrecht

2005

Journal of Applied Physics

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Realization of highly uniform self-assembled InAs quantum wires by the strain compensating technique Appl. Phys. Lett. 87, 083108 (2005); 10.1063/1.2034118Strong charge carrier confinement in purely strain induced Ga As ∕ In Al As single quantum wires Appl. Phys. Lett. 85, 3672 (2004); 10.1063/1.1807948Inhomogeneous strain state in a rectangular InGaAs quantum wire/ GaAs barrier specimen prepared for cross sectional high-resolution transmission electron microscopy Strain analysis of a quantum-wire system produced by cleaved edge overgrowth using grazing incidence x-ray diffraction Appl.This paper studies the elastic fields in InAs/ GaAs quantum wire ͑QWR͒ structures arising from the lattice mismatch between InAs and GaAs. The present treatment is different from recent analyses based on the Eshelby inclusion approach where the QWR material, for simplicity, is assumed to be the same as the matrix/substrate. Here, a more complete treatment is developed taking into account the structural inhomogeneity using the boundary integral equation method. We implement our model using discrete boundary elements at the interface between the QWR and its surrounding matrix. The coefficients of the algebraic equations are derived exactly for constant elements using our recent Green's-function solutions in the Stroh formalism. For both ͑001͒ and ͑111͒ growth directions, our results show that while the elastic fields far from the QWR are approximated well by the homogeneous inclusion approach, for points within or close to the QWR, the differences between the fields computed with the simplified inclusion and complete inhomogeneity models can be as large as 10% for the test system. These differences in the strain fields will have strong implications for the modeling of the quantized energy states of the quantum wire nanostructures. Since the strain fields inside and close to the wire are more important than the exterior strain fields from the standpoint of the confined electronic states, we suggest that in the vicinity of the QWR, the inhomogeneity model be used with proper elastic constants, while the simple exact inclusion model be used in the bulk of surrounding medium.[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP: 128.235.251.160 On: Tue, 23 Dec 2014 01:18:35 013534-2 Pan, Han, and Albrecht J. Appl. Phys. 98, 013534 ͑2005͒ [This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP: 128.235.251.160 On: Tue, 23 Dec 2014 01:18:35 013534-3 Pan, Han, and Albrecht J. Appl. Phys. 98, 013534 ͑2005͒ [This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP: 128.235.251.160 On: Tue, 23 Dec 2014 01:18:35 013534-4 Pan, Han, and Albrecht J. Appl. Phys. 98, 013534 ͑2005͒ [This article is copyrighted as indicat...

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Strain fields in InAs∕GaAs quantum wire structures: Inclusion versus inhomogeneity

Pan

Han

Albrecht

2005

Journal of Applied Physics

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“…Second, these are fully analytical formulas, where the answer is expressed through elementary or special functions. Such formulas are available for three-dimensional inclusions in an infinite space or in half-space, which have the shape of an ellipsoid (Eshelby, 1957;Seo and Mura, 1979), and disk Du, 1995a,b, 1996;Glas, 2003).…”

Section: Introductionmentioning

confidence: 99%

Elastic and piezoelectric fields due to polyhedral inclusions

Kuvshinov

2008

International Journal of Solids and Structures

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We derive explicit, closed-form expressions describing elastic and piezoelectric deformations due to polyhedral inclusions in uniform half-space and bi-materials. Our analysis is based on the linear elasticity theory and Green's function method. The method involves evaluation of volume and surface integrals of harmonic and bi-harmonic potentials. In case of polyhedra, such integrals are expressed through algebraic functions. Our results generalize numerous studies on this subject, and they allow to obtain fully analytical solutions for a number of physical and engineering problems. In the limiting case of an infinite space, our relations have an essentially more compact form, than relations obtained by other authors. We present solutions to classical Mindlin and Cherruti problems. We describe the elastic relaxation of a misfitting polygonal quantum dot in bi-materials assuming isotropic and vertically isotropic properties. It is explained how to analyze nonhydrostatic and non-uniform inclusions. We also study piezoelectric fields induced by inclusions in materials with cubic and hexagonal lattices. Among other results, we have found that a cubic inclusion in an isotropic material reproduces fields of quantum dots in GaAs (0, 0, 1) and GaAs (1, 1, 1) depending on the orientation of the cube. This suggests that one can qualitatively model crystals with different lattices by choosing an appropriate inclusion shape.

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“…For the isotropic and anisotropic elastic case, various investigations on the Eshelby problems related to polygonal inclusion have been carried out (Rodin, 1996;Nozaki and Taya, 1997;Faux et al, 1997;Yu, 2001;Glas, 2003), including a very interesting application to the cracked composite repair using composite patches (Duong and Yu, 2003). For general anisotropy with PE, ME, or ME coupling, solutions to the Eshebly problems of polygonal inclusion have also been developed based on the analytical continuation and conformal mapping methods (Ru, 1999(Ru, , 2000Wang and Shen, 2003), and the Green's function method and the equivalent body-force concept (Pan and Jiang, 2003;Pan, 2004a,b).…”

Section: Introductionmentioning

confidence: 99%

Exact solution for 2D polygonal inclusion problem in anisotropic magnetoelectroelastic full-, half-, and bimaterial-planes

Jiang

Pan

2004

International Journal of Solids and Structures

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Elastic relaxation of a truncated circular cylinder with uniform dilatational eigenstrain in a half space

Cited by 16 publications

References 27 publications

Strain fields in InAs∕GaAs quantum wire structures: Inclusion versus inhomogeneity

Strain fields in InAs∕GaAs quantum wire structures: Inclusion versus inhomogeneity

Elastic and piezoelectric fields due to polyhedral inclusions

Exact solution for 2D polygonal inclusion problem in anisotropic magnetoelectroelastic full-, half-, and bimaterial-planes

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