What is the Young's Modulus of Silicon?

Hopcroft, Matthew A.; Nix, William D.; Kenny, Thomas W.

doi:10.1109/jmems.2009.2039697

Cited by 1,756 publications

(893 citation statements)

References 30 publications

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“…4b. If we consider the case e=2, which corresponds to "textbook" values of moduli for silicon in the frame of reference of a standard (100) silicon wafer [15], i.e., E=169 GPa, G=50.9 GPa, and a shear coefficient of k=5/6, Fig. 4b shows that the largest influence of the Timoshenko effects on the resonant frequency is a 17% decrease in λres (31% reduction in ωres), accessed by following the link in the citation at the bottom of the page.…”

Section: Resonant Frequencymentioning

confidence: 99%

Timoshenko Beam Model for Lateral Vibration of Liquid-Phase Microcantilever-Based Sensors

Schultz

Heinrich

Josse

et al. 2013

MEMS and Nanotechnology, Volume 5

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Abstract:Dynamic-mode microcantilever-based devices are potentially well suited to biological and chemical sensing applications. However, when these applications involve liquid-phase detection, fluid-induced dissipative forces can significantly impair device performance. Recent experimental and analytical research has shown that higher in-fluid quality factors (Q) are achieved by exciting microcantilevers in the lateral flexural mode. However, experimental results show that, for microcantilevers having larger width-tolength ratios, the behaviors predicted by current analytical models differ from measurements. To more accurately model microcantilever resonant behavior in viscous fluids and to improve understanding of lateral-mode sensor performance, a new analytical model is developed, incorporating both viscous fluid effects and "Timoshenko beam" effects (shear deformation and rotatory inertia). Beam response is examined for two harmonic load types that simulate current actuation methods: tip force and support rotation. Results are expressed in terms of total beam displacement and beam displacement due solely to bending deformation, which correspond to current detection methods used with microcantilever-based devices (optical and piezoresistive detection, respectively). The influences of the shear, rotatory inertia, and fluid parameters, as well as the load/detection scheme, are investigated. Results indicate that load/detection type can impact the measured resonant characteristics and, thus, sensor performance, especially at larger values of fluid resistance.

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Section: Resonant Frequencymentioning

confidence: 99%

Timoshenko Beam Model for Lateral Vibration of Liquid-Phase Microcantilever-Based Sensors

Schultz

Heinrich

Josse

et al. 2013

MEMS and Nanotechnology, Volume 5

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“…27 Nevertheless, for anisotropic crystal such as black P, prior knowledge of the crystal direction is required for fabricating specifically-orientated indentation samples that attempt to mechanically decouple the two crystal axes. 28 However, unlike in Si (where the crystal orientation is always indicated by the cuts on Si wafers with good precision), 5 such information is not readily available for 2D nanocrystals, and complete mechanical decoupling between the two axes has not yet been achieved. 28 In this work, enabled by the first demonstration of black P resonant nanostructures with multimode responses, we show that the spatial mapping of the multimode resonance mode shapes creates a new means for the precise determination of black P crystal orientation (i.e., the anisotropic zigzag and armchair axes).…”

mentioning

confidence: 99%

Resolving and Tuning Mechanical Anisotropy in Black Phosphorus via Nanomechanical Multimode Resonance Spectromicroscopy

et al. 2016

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Black phosphorus (P) has emerged asWang Z.H., Jia H., Zheng X.-Q., Yang R., Ye G.J., Chen X.H., Feng P.X.-L., Nano Letters 16, 5394-5400 (2016) [Accepted Version] DOI: 10.1021/acs.nanolett.6b01598, Online Publication: August 9, 2016-2-Efficiently exploiting anisotropic properties in crystals plays important roles in many areas in science and technology, ranging from timing and signal processing using a rich variety of crystalline cut orientations in quartz to the modulation and conversion of light using anisotropic crystals. In state-of-the-art miniature devices and integrated systems, crystalline anisotropy enables a number of important dynamic characteristics in microelectromechanical systems (MEMS) such as gyroscopes, rotation rate sensors, and accelerometers. 1,2,3,4 Single crystal silicon (Si), the hallmark of semiconductors and the most commonly used crystal in MEMS, possesses clear mechanical anisotropy that has been extensively characterized and utilized (e.g., Young's moduli in the <110> and <100> directions are E Y<110> = 169 GPa and E Y<100> = 130 GPa). 5 , 6 As devices continue to be scaled down to nanoscale, anisotropy in mechanical properties may not always be readily preserved at device level due to lattice defects or surface effects, 7 , 8 , 9 and thus remain largely unexplored in emerging nanoelectromechanical systems (NEMS) built upon conventional crystals.The recent advent of atomic-layer crystals offer exciting opportunities for building twodimensional (2D) NEMS using single-crystal layered materials, in which many desired material properties are preserved, or even intensified, as the crystal thickness approaches genuinely atomic scale. One unique crystal is black phosphorus (P), not only a single-element directbandgap semiconductor with bandgap depending on the number of atomic layers (covering a wide range from visible light to IR) and with high carrier mobility, but also hitherto the bestknown atomic-layer crystal with strong in-plane anisotropy. The intrinsically anisotropic lattice structure (Figure 1a) of black P dictates a number of anisotropic material properties. In particular, it is theoretically predicted to exhibit in-plane mechanical anisotropy ( Figure 1a) 10,11,12,13 much stronger than that of Si, which shall lead to previously inaccessible dynamic responses in resonant NEMS 14 and new opportunities for studying carrier-lattice interaction in atomic layers. 15,16,17,18,19 To date, while extensive and rapidly growing efforts have been devoted to studying optical and electrical properties of black P and anisotropic effects in such devices, experiments on black P mechanical devices and mechanical anisotropic effects therein have been lacking. It is therefore of both fundamental and technological importance to systematically investigate the mechanical anisotropy in black P crystal.In bulk materials, such as crystalline Si, mechanical anisotropy is often characterized by measuring the sound velocity in different directions, 20,21,22,23 and fitting data to the Christoff...

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“…This value of elastic modulus measured from the MD simulation is not only for a crystalline system, but also reflect a combination of film/substrate modulus due to 83% penetration depth. Elastic modulus measured from the MD simulation is higher than the experimentally measured value (153±4 GPa for DLC film, Section 3.1) or that of Si wafer (typically 130 GPa [44]). Authors would like to posit that the indentation in the MD simulation was performed in a crystalline carbon film.…”

Section: Simulation Analysismentioning

confidence: 60%

Influence of test methodology and probe geometry on nanoscale fatigue failure of diamond-like carbon film

Faisal

Ahmed

Goel

et al. 2014

Surface and Coatings Technology

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What is the Young's Modulus of Silicon?

Cited by 1,756 publications

References 30 publications

Timoshenko Beam Model for Lateral Vibration of Liquid-Phase Microcantilever-Based Sensors

Timoshenko Beam Model for Lateral Vibration of Liquid-Phase Microcantilever-Based Sensors

Resolving and Tuning Mechanical Anisotropy in Black Phosphorus via Nanomechanical Multimode Resonance Spectromicroscopy

Influence of test methodology and probe geometry on nanoscale fatigue failure of diamond-like carbon film

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