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

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.