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

In (100) silicon wafers, the most commonly used in microelectromechanical systems (MEMS) fabrication, the value of Young's modulus of a MEMS structure can vary by over 20%, depending on the structure's orientation on the wafer surface. This anisotropy originates from the crystal structure...

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Bibliographic Details
Published in:Journal of microelectromechanical systems 2012-02, Vol.21 (1), p.243-249
Main Authors: Boyd, E. J., Uttamchandani, D.
Format: Article
Language:English
Subjects:
Anisotropic magnetoresistance
Anisotropy
Crystal structure
elastic modulus
elasticity
Equations
Exact sciences and technology
Frequency measurement
Instruments, apparatus, components and techniques common to several branches of physics and astronomy
Mathematical analysis
Mechanical instruments, equipment and techniques
micro-electromechanical systems (MEMS)
Microelectromechanical systems
Micromechanical devices
Micromechanical devices and systems
Modulus of elasticity
Orientation
Physics
Resonant frequency
Silicon
Wafers
Young's modulus
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Summary:In (100) silicon wafers, the most commonly used in microelectromechanical systems (MEMS) fabrication, the value of Young's modulus of a MEMS structure can vary by over 20%, depending on the structure's orientation on the wafer surface. This anisotropy originates from the crystal structure of silicon. We have directly measured the anisotropy of Young's modulus in the (100) plane of silicon from the measured resonance frequencies of a "wagon-wheel" test structure comprising an arc of identical microcantilevers fabricated in the structural layer of a (100) silicon-on-insulator wafer. The direction of the principal axis of the cantilevers increased from 0° to 180 ° in 10° steps with respect to the [110] direction, allowing the angular dependence of Young's modulus to be experimentally mapped out. The Young's modulus was measured to have a value of 170 GPa ± 3 GPa at 0° and 90 ° to the [110] direction and a value of 131 GPa ± 3 GPa at ±40° and ±50° to the [110] direction. The measured values of Young's modulus and their angular dependence agree very well with the theoretical values that were recently reported, thereby experimentally verifying the theoretical calculations.
ISSN:1057-7157
1941-0158
DOI:10.1109/JMEMS.2011.2174415