中国物理B ›› 2012, Vol. 21 ›› Issue (8): 86101-086101.doi: 10.1088/1674-1056/21/8/086101

• CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES • 上一篇    下一篇

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

张加宏a b, 冒晓莉a b, 刘清惓a b, 顾芳c, 李敏a b, 刘恒a b, 葛益娴a b   

  1. a Jiangsu Key Laboratory of Meteorological Observation and Information Processing, Nanjing University of Information Science & Technology, Nanjing 210044, China;
    b College of Electronic & Information Engineering, Nanjing University of Information Science & Technology, Nanjing 210044, China;
    c College of Physics & Opto-Electronic Engineering, Nanjing University of Information Science & Technology, Nanjing 210044, China
  • 收稿日期:2011-12-06 修回日期:2012-02-03 出版日期:2012-07-01 发布日期:2012-07-01
  • 基金资助:
    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.

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

Zhang Jia-Hong (张加宏)a b, Mao Xiao-Li (冒晓莉)a b, Liu Qing-Quan (刘清惓)a b, Gu Fang (顾芳)c, Li Min (李敏)a b, Liu Heng (刘恒)a b, Ge Yi-Xian (葛益娴 )a b   

  1. a Jiangsu Key Laboratory of Meteorological Observation and Information Processing, Nanjing University of Information Science & Technology, Nanjing 210044, China;
    b College of Electronic & Information Engineering, Nanjing University of Information Science & Technology, Nanjing 210044, China;
    c College of Physics & Opto-Electronic Engineering, Nanjing University of Information Science & Technology, Nanjing 210044, China
  • Received:2011-12-06 Revised:2012-02-03 Online:2012-07-01 Published:2012-07-01
  • Contact: Zhang Jia-Hong E-mail:zjhnuist@yahoo.cn
  • Supported by:
    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.

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摘要： 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.

关键词: silicon nanobeams with undercut, mechanical properties, mechanical testing, finite element method

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.

Key words: silicon nanobeams with undercut, mechanical properties, mechanical testing, finite element method

中图分类号:  (Structure of nanowires and nanorods (long, free or loosely attached, quantum wires and quantum rods, but not gate-isolated embedded quantum wires))

  • 61.46.Km
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)