A finite element analysis of surface-stress effects on measurement of the Si lattice parameter

Quagliotti, Danilo; Mana, Giovanni; Massa, Enrico; Sasso, C.P.; Kuetgens, U.

doi:10.1088/0026-1394/50/3/243

Cited by 16 publications

(31 citation statements)

References 25 publications

(39 reference statements)

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“…In addition, a native oxide layer grows of the slab surfaces -which is expected from 1 nm to 2 nm thick, but nothing is known about its stoichiometry [21,22,23]. [13]. The red shaded area shows the interval of the stress values given in the literature [13], which ranges from −0.68 N/m to 0.76 N/m.…”

Section: Resultsmentioning

confidence: 99%

“…[13]. The red shaded area shows the interval of the stress values given in the literature [13], which ranges from −0.68 N/m to 0.76 N/m. In order to investigate the intrinsic surface stress of the oxidized (110) surface, we started by considering the pristine (110) surface.…”

Section: Resultsmentioning

confidence: 99%

“…Preliminary measurements carried out by using a purposely designed two-thickness interferometer might have evidenced some clue, but, in the case, the observed strain is more than an order of magnitude smaller than predicted by Eq. (5) [13,28]. For this reason the density functional computation was carefully assessed; we are confident that the result obtained is representative of the idealized model used.…”

Section: Discussionmentioning

confidence: 99%

“…As a test case to assess the reliability of our DFT calculations, we considered the silicon (100) 2 × 1 surface, for which several theoretical and experimental estimates of the surface stress are given in [13]. In detail, we simulated an infinite slab by using supercells having 8, 12, 16, 20, layers of 8 silicon atoms.…”

Section: Calculation Of the Surface Stressmentioning

confidence: 99%

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Density functional theory calculations of the stress of oxidised (1 1 0) silicon surfaces

et al. 2016

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Abstract. The measurement of the lattice-parameter of silicon by x-ray interferometry assumes the use of strain-free crystals. This might not be the case because surface relaxation, reconstruction, and oxidation cause strains without the application of any external force. In a previous work, this intrinsic strain was estimated by a finite element analysis, where the surface stress was modeled by an elastic membrane having a 1 N/m tensile strength. The present paper quantifies the surface stress by a density functional theory calculation. We found a value exceeding the nominal value used, which potentially affects the measurement accuracy.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Calculation Of the Surface Stressmentioning

confidence: 99%

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Density functional theory calculations of the stress of oxidised (1 1 0) silicon surfaces

et al. 2016

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“…These investigations did not prove that surface stresses due to oxidation, relaxation and reconstruction did not affect the lattice-parameter value (Kessler et al, 1999). The magnitude of this effect was estimated by a finite element analysis, where the surface stress (a fundamental property of the crystal interface with the environment) was modelled by an elastic membrane having a hypothetical 1 N m À1 tensile strength (Quagliotti et al, 2013). We also calculated the surface stress by density functional theory (Melis et al, 2016) and found a value exceeding 1 N m À1 , which potentially jeopardizes the measurement accuracy.…”

Section: Introductionmentioning

confidence: 97%

X-ray phase-contrast topography to measure the surface stress and bulk strain in a silicon crystal

et al. 2020

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The measurement of the Si lattice parameter by X-ray interferometry assumes the use of strain-free crystals, which might not be true because of intrinsic stresses due to surface relaxation, reconstruction and oxidation. X-ray phase-contrast topography was used to investigate the strain sensitivity to the finishing, annealing and coating of interferometer crystals. The topography capabilities were assessed by measuring the lattice strain due to films of copper deposited on the interferometer mirror crystal. A by-product has been the measurement of the surface stresses after complete relaxation of the coatings.

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Nanomechanical Modeling of the Bending Response of Silicon Nanowires

Zare Pakzad,

Nasr Esfahani,

Tasdemir

et al. 2023

ACS Appl. Nano Mater.

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Understanding the mechanical behavior of silicon nanowires is essential for the implementation of advanced nanoscale devices. Although bending tests are predominantly used for this purpose, their findings should be properly interpreted through modeling. Various modeling approaches tend to ignore parts of the effective parameter set involved in the rather complex bending response. This oversimplification is the main reason behind the spread of the modulus of elasticity and strength data in the literature. Addressing this challenge, a surface-based nanomechanical model is introduced in this study. The proposed model considers two important factors that have so far remained neglected despite their significance: (i) intrinsic stresses composed of the initial residual stress and surface-induced residual stress and (ii) anisotropic implementation of surface stress and elasticity. The modeling study is consolidated with molecular dynamics-based study of the native oxide surface through reactive force fields and a series of nanoscale characterization work through in situ three-point bending test and Raman spectroscopy. The treatment of the test data through a series of models with increasing complexity demonstrates a spread of 85 GPa for the modulus of elasticity and points to the origins of ambiguity regarding silicon nanowire properties, which are some of the most commonly employed nanoscale building blocks. A similar conclusion is reached for strength with variations of up to 3 GPa estimated by the aforementioned nanomechanical models. Precise consideration of the nanowire surface state is thus critical to comprehending the mechanical behavior of silicon nanowires accurately. Overall, this study highlights the need for a multiscale theoretical framework to fully understand the size-dependent mechanical behavior of silicon nanowires, with fortifying effects on the design and reliability assessment of future nanoelectromechanical systems.

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A finite element analysis of surface-stress effects on measurement of the Si lattice parameter

Cited by 16 publications

References 25 publications

Density functional theory calculations of the stress of oxidised (1 1 0) silicon surfaces

Density functional theory calculations of the stress of oxidised (1 1 0) silicon surfaces

X-ray phase-contrast topography to measure the surface stress and bulk strain in a silicon crystal

Nanomechanical Modeling of the Bending Response of Silicon Nanowires

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