Measurement of the Anisotropy of Young's Modulus in Single-Crystal Silicon

Boyd, E.; Uttamchandani, Deepak

doi:10.1109/jmems.2011.2174415

Cited by 73 publications

(41 citation statements)

References 9 publications

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“…Circular and elliptical diaphragms' design parameters. 21 0), which are also proven experimentally by (Boyd and Uttamchandani 2012), were lied in COMSOL simulations. However, in the analytical calculations, values were used ming plate bending for <110> in (100) Silicon to simplify initial design calculations.…”

Section: Analytical Mechanical Analysissupporting

confidence: 62%

“…(5) and (6), where α Si and α SU−8 are the silicon and SU-8 coefficients of thermal expansion (CTEs) respectively. Provided that silicon is an anisotropic material, and that a silicon wafer orientation of (100) is the most common case of MEMS fabrication, silicon mechanical properties presented in Hopcroft et al (2010), which are also proven experimentally by Boyd and Uttamchandani (2012), were applied in COMSOL simulations. However, in the analytical calculations, values were used assuming plate bending for <110>in (100) silicon to simplify initial design calculations.…”

Section: Analytical Mechanical Analysismentioning

confidence: 99%

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A micro-capacitive pressure sensor design and modelling

Kubba

Hasson

Kubba

et al. 2016

J. Sens. Sens. Syst.

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Abstract. Measuring air pressure using a capacitive pressure sensor is a robust and precise technique. In addition, a system that employs such transducers lies within the low power consumption applications such as wireless sensor nodes. In this article a high sensitivity with an elliptical diaphragm capacitive pressure sensor is proposed. This design was compared with a circular diaphragm in terms of thermal stresses and pressure and temperature sensitivity. The proposed sensor is targeted for tyre pressure monitoring system application. Altering the overlapping area between the capacitor plates by decreasing the effective capacitance area to improve the overall sensitivity of the sensor ( C/C), temperature sensitivity, and built-up stresses is also examined in this article. Theoretical analysis and finite element analysis (FEA) were employed to study pressure and temperature effects on the behaviour of the proposed capacitive pressure sensor. A MEMS (micro electro-mechanical systems) manufacturing processing plan for the proposed capacitive sensor is presented. An extra-low power short-range wireless read-out circuit suited for energy harvesting purposes is presented in this article. The developed read-out circuitry was tested in terms of sensitivity and transmission range.

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Section: Analytical Mechanical Analysissupporting

confidence: 62%

Section: Analytical Mechanical Analysismentioning

confidence: 99%

A micro-capacitive pressure sensor design and modelling

Kubba

Hasson

Kubba

et al. 2016

J. Sens. Sens. Syst.

View full text Add to dashboard Cite

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“…This timescale was selected to properly resolve the MHz vibrational frequencies of stiff nano to microscale material specimens (e.g., Young's modulus of 130-170 GPa for single-crystal Si, according to recent measurements), 16 as demonstrated with previous UEM studies. [23][24][25][26][27][28][29][30] A Q-switched, diode-pumped Nd:YAG laser (Bright Solutions WEDGE HF 1064-SB), with a fundamental wave length of 1064 nm and pulse duration of 700 ps full-width at half-maximum (FWHM; effectively 1 ns with jitter) served as the source of probe photoelectron packets.…”

Section: B Ultrafast Electron Microscopymentioning

confidence: 99%

“…continue to be found. [16][17][18] Previous reciprocal-space UEM studies on single-crystal Si wedges have resolved shear-wave motion and ultrafast vibrational responses induced by coherent photoexcitation. [19][20][21] As we will demonstrate here, a multimodal approach-combining real-and reciprocalspace information-enables spatial localization of photoinduced vibrational eigenmodes, opening the way to resolving the effects of nanoscale heterogeneity on statistical variability and fluctuations.…”

Section: Introductionmentioning

confidence: 99%

Multimodal visualization of the optomechanical response of silicon cantilevers with ultrafast electron microscopy

2016

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The manner in which structure at the mesoscale affects emergent collective dynamics has become the focus of much attention owing, in part, to new insights into how morphology on these spatial scales can be exploited for enhancement and optimization of macroscopic properties. Key to advancements in this area is development of multimodal characterization tools, wherein access to a large parameter space (energy, space, and time) is achieved (ideally) with a single instrument. Here, we describe the study of optomechanical responses of single-crystal Si cantilevers with an ultrafast electron microscope. By conducting structural-dynamics studies in both real and reciprocal space, we are able to visualize MHz vibrational responses from atomic-to micrometerscale dimensions. With nanosecond selected-area and convergent-beam diffraction, we demonstrate the effects of spatial signal averaging on the isolation and identification of eigenmodes of the cantilever. We find that the reciprocal-space methods reveal eigenmodes mainly below 5 MHz, indicative of the first five vibrational eigenvalues for the cantilever geometry studied here. With nanosecond real-space imaging, however, we are able to visualize local vibrational frequencies exceeding 30 MHz. The heterogeneously-distributed vibrational response is mapped via generation of pixel-by-pixel time-dependent Fourier spectra, which reveal the localized highfrequency modes, whose presence is not detected with parallel-beam diffraction. By correlating the transient response of the three modalities, the oscillation, and dissipation of the optomechanical response can be compared to a linear-elastic model to isolate and identify the spatial threedimensional dynamics.

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“…Reference [9] showed that for a 50-μm-thick silicon fabric, the fracture stress is about 1.1 GPa. Substituting a (100) silicon Young's modulus of 128 GPa [10] in Equation (1), and the resulting strain value from Equation (2), we obtain a minimum bending radius for the 50-μm-thick flexible silicon fabric of approximately 3 mm, which decreases with a decreasing thickness. Therefore, a plain flexible silicon substrate that is 50-μm-thick or thinner with a bending radius of more than 3 mm will safely operate below the fracture stress level.…”

Section: A Silicon's Bending Ability and Limitationsmentioning

confidence: 99%