Pull-In Retarding in Nonlinear Nanoelectromechanical Resonators Under Superharmonic Excitation

In order to compensate for the loss of performance when scaling resonant sensors down to NEMS, a complete analytical model, including all main sources of nonlinearities, is presented as a predictive tool for the dynamic behavior of clamped-clamped nanoresonators electrostatically actuated. The nonlinear dynamics of such NEMS under superharmonic resonance of an order half their fundamental natural frequencies is investigated. It is shown that the critical amplitude has the same dependence on the quality factor Q and the thickness h as the case of the primary resonance. Finally, a way to retard the pull-in by decreasing the AC voltage is proposed in order to enhance the performance of NEMS resonators.

[1]  Sebastien Hentz,et al.  Dynamic range enhancement of nonlinear nanomechanical resonant cantilevers for highly sensitive NEMS gas/mass sensor applications , 2010 .

[2]  Zhonghe Jin,et al.  Electrostatic resonator with second superharmonic resonance , 1998 .

[3]  M. Belhaq,et al.  2:1 and 1:1 frequency-locking in fast excited van der Pol–Mathieu–Duffing oscillator , 2008 .

[4]  S.K. De,et al.  Full-Lagrangian schemes for dynamic analysis of electrostatic MEMS , 2004, Journal of Microelectromechanical Systems.

[5]  D. Greywall,et al.  Theory of amplifier-noise evasion in an oscillator employing a nonlinear resonator. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[6]  J. Casals-Terre,et al.  Resonant Pull-In Condition in Parallel-Plate Electrostatic Actuators , 2007, Journal of Microelectromechanical Systems.

[7]  Sebastien Hentz,et al.  Nonlinear phenomena in nanomechanical resonators: mechanical behaviors and physical limitations , 2010 .

[8]  Sébastien Baguet,et al.  Computational and quasi-analytical models for non-linear vibrations of resonant MEMS and NEMS sensors , 2011 .

[9]  Earl H. Dowell,et al.  Routes to escape from an energy well , 1995 .

[10]  M. Dahleh,et al.  Melnikov-Based Dynamical Analysis of Microcantilevers in Scanning Probe Microscopy , 1999 .

[11]  Ali H. Nayfeh,et al.  Dynamics of MEMS resonators under superharmonic and subharmonic excitations , 2005 .

[12]  D. Elata,et al.  On the dynamic pull-in of electrostatic actuators with multiple degrees of freedom and multiple voltage sources , 2006, Journal of Microelectromechanical Systems.

[13]  T. A. Roessig,et al.  Nonlinear mixing in surface-micromachined tuning fork oscillators , 1997, Proceedings of International Frequency Control Symposium.

[14]  M. Younis,et al.  A Study of the Nonlinear Response of a Resonant Microbeam to an Electric Actuation , 2003 .

[15]  Ali H. Nayfeh,et al.  Global Dynamics of MEMS Resonators under Superharmonic Excitation , 2004, 2004 International Conference on MEMS, NANO and Smart Systems (ICMENS'04).

[16]  H. Nishiyama,et al.  Capacitance of a strip capacitor , 1990 .

[17]  Woei Wan Tan,et al.  The nonlinearity cancellation phenomenon in micromechanical resonators , 2008 .

[18]  V. Kaajakari,et al.  Phase noise in capacitively coupled micromechanical oscillators , 2005, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[19]  A. Nayfeh,et al.  Secondary resonances of electrically actuated resonant microsensors , 2003 .

[20]  Lidija Sekaric,et al.  Parametric amplification in a torsional microresonator , 2000 .

[21]  Igor Mezic,et al.  Complex Dynamics in a Harmonically Excited Lennard-Jones Oscillator: Microcantilever-Sample Interaction in Scanning Probe Microscopes , 2000 .

[22]  S. Timoshenko,et al.  Theory of elasticity , 1975 .

[23]  Ali H. Nayfeh,et al.  Dynamic pull-in phenomenon in MEMS resonators , 2007 .

[24]  O. Thomas,et al.  Non-linear behaviour of free-edge shallow spherical shells: Effect of the geometry , 2006 .

[25]  S. Krylov,et al.  Pull-in Dynamics of an Elastic Beam Actuated by Continuously Distributed Electrostatic Force , 2004 .

[26]  W. H. Reid,et al.  The Theory of Elasticity , 1960 .

[27]  Sebastien Hentz,et al.  From MEMS to NEMS: Modelling and Characterization of the Non Linear Dynamics of Resonators, a Way to Enhance the Dynamic Range , 2008 .

[28]  D. Rugar,et al.  Mechanical parametric amplification and thermomechanical noise squeezing. , 1991, Physical review letters.

[29]  Ali H. Nayfeh,et al.  A reduced-order model for electrically actuated microbeam-based MEMS , 2003 .

[30]  Kristofer S. J. Pister,et al.  Analysis of closed-loop control of parallel-plate electrostatic microgrippers , 1994, Proceedings of the 1994 IEEE International Conference on Robotics and Automation.

[31]  N. C. MacDonald,et al.  Five parametric resonances in a microelectromechanical system , 1998, Nature.

[32]  L. Sekaric,et al.  Measurement of mechanical resonance and losses in nanometer scale silicon wires , 1999 .

[33]  B. Reig,et al.  Nonlinear dynamics of nanomechanical beam resonators: improving the performance of NEMS-based sensors , 2009, Nanotechnology.

[34]  W. P. Robins,et al.  Phase Noise in Signal Sources , 1984 .

[35]  J. Seeger,et al.  Stabilization of electrostatically actuated mechanical devices , 1997, Proceedings of International Solid State Sensors and Actuators Conference (Transducers '97).

[36]  Michael L. Roukes,et al.  Dynamic range of nanotube- and nanowire-based electromechanical systems , 2005 .

[37]  M. Roukes,et al.  Phase Noise and Frequency Stability of Very-High Frequency Silicon Nanowire Nanomechanical Resonators , 2007, TRANSDUCERS 2007 - 2007 International Solid-State Sensors, Actuators and Microsystems Conference.

[38]  Sebastien Hentz,et al.  Bifurcation topology tuning of a mixed behavior in nonlinear micromechanical resonators , 2009 .

[39]  A. Nayfeh Introduction To Perturbation Techniques , 1981 .