Effect of non-ideal clamping shape on the resonance frequencies of silicon nanocantilevers.

In this paper, we investigate the effects of non-ideal clamping shapes on the dynamic behavior of silicon nanocantilevers. We fabricated silicon nanocantilevers using silicon on insulator (SOI) wafers by employing stepper ultraviolet (UV) lithography, which permits a resolution of under 100 nm. The nanocantilevers were driven by electrostatic force inside a scanning electron microscope (SEM). Both lateral and out-of-plane resonance frequencies were visually detected with the SEM. Next, we discuss overhanging of the cantilever support and curvature at the clamping point in the silicon nanocantilevers, which generally arises in the fabrication process. We found that the fundamental out-of-plane frequency of a realistically clamped cantilever is always lower than that for a perfectly clamped cantilever, and depends on the cantilever width and the geometry of the clamping point structure. Using simulation with the finite-elements method, we demonstrate that this discrepancy is attributed to the particular geometry of the clamping point (non-zero joining curvatures and a flexible overhanging) that is obtained in the fabrication process. The influence of the material orthotropy is also investigated and is shown to be negligible.

[1]  M. Esashi,et al.  Energy dissipation in submicrometer thick single-crystal silicon cantilevers , 2002 .

[2]  Sorin Perisanu,et al.  Self-oscillations in field emission nanowire mechanical resonators: a nanometric dc-ac conversion. , 2007, Nano letters.

[3]  M. Blencowe.  Nanoelectromechanical systems , 2005, cond-mat/0502566.

[4]  Jaume Esteve,et al.  Monolithic integration of mass sensing nano-cantilevers with CMOS circuitry , 2003 .

[5]  H. Craighead,et al.  Selective vibrational detachment of microspheres using optically excited in-plane motion of nanomechanical beams. , 2007, Nano letters.

[6]  W. J. Venstra,et al.  Effect of undercut on the resonant behaviour of silicon nitride cantilevers , 2009 .

[7]  Harold G. Craighead,et al.  Measurement of nanomechanical resonant structures in single-crystal silicon , 1998 .

[8]  W. D. Heer,et al.  Electrostatic deflections and electromechanical resonances of carbon nanotubes , 1999, Science.

[9]  H. Craighead,et al.  Young's modulus and density measurements of thin atomic layer deposited films using resonant nanomechanics , 2010 .

[10]  H. Craighead,et al.  Optical excitation of nanoelectromechanical oscillators , 2005 .

[11]  Anja Boisen,et al.  Fabrication and characterization of nanoresonating devices for mass detection , 2000 .

[12]  Maxim Zalalutdinov,et al.  Frequency-tunable micromechanical oscillator , 2000 .

[13]  Harold G. Craighead,et al.  Fabrication of nanoelectromechanical systems in single crystal silicon using silicon on insulator substrates and electron beam lithography , 1997 .

[14]  H. Craighead,et al.  Dynamic characterization of nanoelectromechanical oscillators by atomic force microscopy , 2007 .

[15]  David Cornu,et al.  Mechanical properties of SiC nanowires determined by scanning electron and field emission microscopies , 2008 .

[16]  M. Roukes,et al.  Ultra-sensitive NEMS-based cantilevers for sensing, scanned probe and very high-frequency applications. , 2007, Nature nanotechnology.

[17]  Pascal Vincent,et al.  Driving self-sustained vibrations of nanowires with a constant electron beam , 2007 .

[18]  M. R. Freeman,et al.  Multifunctional Nanomechanical Systems via Tunably Coupled Piezoelectric Actuation , 2007, Science.

[19]  H. Craighead,et al.  Enumeration of DNA molecules bound to a nanomechanical oscillator. , 2005, Nano letters.

[20]  T. Kenny,et al.  What is the Young's Modulus of Silicon? , 2010, Journal of Microelectromechanical Systems.

[21]  J Verd,et al.  On the electromechanical modelling of a resonating nano-cantilever-based transducer. , 2004, Ultramicroscopy.