Mechanical properties of silicon nanobeams with undercut evaluated by combining dynamic resonance test and finite element analysis

doi:10.1088/1674-1056/21/8/086101

Abstract Mechanical properties of silicon nanobeams are of prime importance in nanoelectromechanical system applications. A numerical experimental method of determining resonant frequencies and Young's modulus of nanobeams by combining finite element analysis and frequency response tests based on an electrostatic excitation and visual detection by laser Doppler vibrometer is presented in this paper. Silicon nanobeams test structures are fabricated from silicon-on-insulator wafers by using a standard lithography and anisotropic wet etching release process, which inevitably generates the undercut of the nanobeam clamping. In conjunction with three-dimensional finite element numerical simulations incorporating the geometric undercut, dynamic resonance tests reveal that the undercut significantly reduces resonant frequencies of nanobeams due to the fact that it effectively increases the nanobeam length by a correct value Δ L, which is a key parameter that is correlated with deviations in the resonant frequencies predicted from the ideal Euler-Bernoulli beam theory and experimentally measured data. By using a least-square fit expression including Δ L, we finally extract Young's modulus from the measured resonance frequency versus effective length dependency and find that Young's modulus of silicon nanobeam with 200-nm thickness is close to that of bulk silicon. This result supports that the finite size effect due to surface effect does not play a role in mechanical elastic behaviour of silicon nanobeams with the thickness larger than 200 nm.

Keywords: silicon nanobeams with undercut mechanical properties mechanical testing finite element method

Received: 06 December 2011
Revised: 03 February 2012
Accepted manuscript online:

PACS:	61.46.Km	(Structure of nanowires and nanorods (long, free or loosely attached, quantum wires and quantum rods, but not gate-isolated embedded quantum wires))
	62.25.-g	(Mechanical properties of nanoscale systems)
	81.70.Bt	(Mechanical testing, impact tests, static and dynamic loads)
	02.70.Dh	(Finite-element and Galerkin methods)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 41075026 and 61001044), the Open Research Fund of Key Laboratory of Microelectromechanical System of Ministry of Education, Southeast University, China (Grant Nos. 2009-03 and 2010-02), the Special Fund for Meteorology Research in the Public Interest, China (Grant No. GYHY200906037), and the Priority Academic Program Development of Sensor Networks and Modern Meteorological Equipment of Jiangsu Provincial Higher Education Institutions.

Corresponding Authors: Zhang Jia-Hong
E-mail: zjhnuist@yahoo.cn

Cite this article:

Zhang Jia-Hong (张加宏), Mao Xiao-Li (冒晓莉), Liu Qing-Quan (刘清惓), Gu Fang (顾芳), Li Min (李敏), Liu Heng (刘恒), Ge Yi-Xian (葛益娴 ) Mechanical properties of silicon nanobeams with undercut evaluated by combining dynamic resonance test and finite element analysis 2012 Chin. Phys. B 21 086101

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Mechanical properties of silicon nanobeams with undercut evaluated by combining dynamic resonance test and finite element analysis

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