Young's Modulus, Shear Modulus, and Poisson's Ratio in Silicon and Germanium

Wortman, J. J.; Evans, R.

doi:10.1063/1.1713863

Cited by 1,175 publications

(539 citation statements)

References 2 publications

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“…It has been recognized for a long time [13] that the (1 1 1) plane of a cubic crystal (in the present case, zincblende or diamond semiconductor) is isotropic -and the same property also holds for the (a, b) plane of the wurtzite structure.…”

Section: Discussionmentioning

confidence: 86%

“…Usual semiconductors have c < 0: they are harder against a trigonal stress, which directly involves a change of bond length, than against a tetragonal stress which is accommodated mainly by bond rotation. As a result, they are harder along a 1 1 1 direction and softer along a 0 0 1 direction, with 1 1 0 in between [13].…”

Section: Crystalline Semiconductor Nwsmentioning

confidence: 99%

“…It can be done on the c ijkl tensor, or directly in the Voigt notation using the rotation rules described in reference [13]. We take the basis defined by the three vectors x = [110], y = [112], z = [1 1 1], identical to that in reference [6] but different from reference [26].…”

Section: Calculationmentioning

confidence: 99%

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Strain in crystalline core-shell nanowires

Ferrand

Cibert

2014

Eur. Phys. J. Appl. Phys.

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Abstract. We propose a comprehensive description of the strain configuration induced by the lattice mismatch in a core-shell nanowire with circular cross-section, taking into account the crystal anisotropy and the difference in stiffness constants of the two materials. We use an analytical approach which fully exploits the symmetry properties of the system. Explicit formulae are given for nanowires with the wurtzite structure or the zinc-blende structure with the hexagonal/trigonal axis along the nanowire, and the results are compared to available numerical calculations and experimental data on nanowires made of different III-V and II-VI semiconductors. The method is also applied to multishell nanowires, and to core-shell nanowires grown along the 0 0 1 axis of cubic semiconductors. It can be extended to other orientations and other crystal structures.

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Section: Discussionmentioning

confidence: 86%

Section: Crystalline Semiconductor Nwsmentioning

confidence: 99%

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Strain in crystalline core-shell nanowires

Ferrand

Cibert

2014

Eur. Phys. J. Appl. Phys.

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“…They can be obtained from the usual transformation rules by considering the elastic constants C 0 11 , C 0 12 , and C 0 44 defined in the crystal axis coordinate system. 20 21 In cylindrical coordinates, these elastic moduli can be written as…”

Section: B Bulk and Surface Propertiesmentioning

confidence: 99%

Displacement field of a screw dislocation in a〈011〉Cu nanowire: An atomistic study

Gailhanou

Roussel

2013

Phys. Rev. B

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By performing atomistic calculations with a tight-binding potential, we study the displacement field induced by a screw dislocation lying along a free 011 Cu cylindrical nanowire. For this anisotropic orientation that is often encountered experimentally, we show that the displacement field u z along the nanowire can be seen as the superposition of three different fields: the screw dislocation field in an infinite medium, the warping displacement field caused by the so-called Eshelby twist, and an additional image field induced by the free surfaces. A Fourier series analysis of this latter image displacement and stress fields is given. For a circular cross section of the wire, this image field corresponds mainly to an additional warping displacement u z ∝ xy. The dissociation mechanism of the dislocation into partials and the surface stress effects being also captured in our simulations, the present study enables one to quantify the various contributions to the formation of the x-ray diffractograms.

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“…The average of five measurements yielded a value of 0.252 ± 0.002 for the Poisson ratio of Ge epitaxial films. The Poisson ratio of isotropic materials can be calculated from bulk elastic compliances using the expression m = C 12 / (C 11 + C 12 ), where C 11 (129.2 GPa) and C 12 (47.9 GPa) are the elastic compliances of bulk Ge at 300 K. 15 This gives a value of m = 0.27 for Ge. This study shows that the Poisson ratio of Ge thin films is approximately 7% lower than that of bulk Ge.…”

mentioning

confidence: 99%

Poisson Ratio of Epitaxial Germanium Films Grown on Silicon

Bharathan

Narayan

Rozgonyi

et al. 2012

Journal of Elec Materi

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An accurate knowledge of elastic constants of thin films is important in understanding the effect of strain on material properties. We have used residual thermal strain to measure the Poisson ratio of Ge films grown on Si h001i substrates, using the sin 2 w method and high-resolution x-ray diffraction. The Poisson ratio of the Ge films was measured to be 0.25, compared with the bulk value of 0.27. Our study indicates that use of Poisson ratio instead of bulk compliance values yields a more accurate description of the state of in-plane strain present in the film.

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Young's Modulus, Shear Modulus, and Poisson's Ratio in Silicon and Germanium

Cited by 1,175 publications

References 2 publications

Strain in crystalline core-shell nanowires

Strain in crystalline core-shell nanowires

Displacement field of a screw dislocation in a〈011〉Cu nanowire: An atomistic study

Poisson Ratio of Epitaxial Germanium Films Grown on Silicon

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