Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-24T20:32:25.589Z Has data issue: false hasContentIssue false
  • English
  • Français

Nonlinear phenomena in nanomechanical resonators: mechanicalbehaviors and physical limitations

Published online by Cambridge University Press:  03 February 2011

Najib Kacem ,
Sébastien Baguet ,
Sébastien Hentz  and
Régis Dufour
Najib Kacem*
Affiliation:
CEA/LETI, MINATEC, 17 rue des Martyrs, 38054 Grenoble, France Université de Lyon, CNRS, INSA-Lyon, LaMCoS UMR 5259, 69621 Villeurbanne, France
Sébastien Baguet
Affiliation:
Université de Lyon, CNRS, INSA-Lyon, LaMCoS UMR 5259, 69621 Villeurbanne, France
Sébastien Hentz
Affiliation:
CEA/LETI, MINATEC, 17 rue des Martyrs, 38054 Grenoble, France
Régis Dufour
Affiliation:
Université de Lyon, CNRS, INSA-Lyon, LaMCoS UMR 5259, 69621 Villeurbanne, France
*
a Corresponding author:[email protected]
Get access

Abstract

In order to overcome the loss of performances issue when scaling resonant sensors down toNEMS, it proves extremely useful to study the behavior of resonators up to largedisplacements and hence high nonlinearities. A comprehensive nonlinear multiphysics modelbased on the Euler-Bernoulli equation which includes both mechanical and electrostaticnonlinearities in the case of a capacitive doubly clamped beam is presented. This purelyanalytical model captures all the nonlinear phenomena present in NEMS resonatorselectrostatically actuated including bistability, multistability which can lead to severalphysical limitations such as noise mixing, frequency stability deterioration as well asdynamic pull-in. Moreover, close-form expressions of the critical amplitudes and pull-indomain initiation amplitude are provided which can potentially serve for NEMS designers asquick design rules.

Keywords

NEMS resonatornonlinear dynamicscritical amplitudepull-inmixed behaviorRésonateur NEMSdynamique non-linéaireamplitude critiquepull-incomportement mixte
Type
Research Article
Information
Mechanics & Industry , Volume 11 , Issue 6: VCB (Vibrations, Chocs et Bruits) , November 2010 , pp. 521 - 529
Copyright
© AFM, EDP Sciences 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Références

Ekinci, K.L., Roukes, M.L., Nanoelectromechanical systems, Rev. Sci. Instrum. 76 (2005) 061101 CrossRefGoogle Scholar
Huang, X.M.H., Ekinci, K.L., Roukes, M.L., Ultrasensitive nanoelectromechanical mass detection, Appl. Phys. Lett. 84 (2004) 4469–4471 Google Scholar
Jensen, K., Kim, K., Zettl, A., An atomic-resolution nanomechanical mass sensor, Nature Nanotechnol. 3 (2008) 533–537 CrossRefGoogle ScholarPubMed
C.T. Nguyen, Micromechanical components for miniaturized low-power communications, in 1999 IEEE MTT-S international Microwave Symposium FR MEMS Workshop, 1999, pp. 48–77
A.C.W. Nguyen, C.T.D. Hao, Tunable, switchable, high-q vhf microelectromechanical bandpass filters, in IEEE International Solid-State Circuits Conf., 1999, Vol. 448, p. 78
Cho, A., Physics-researchers race to put the quantum into mechanics, Science 299 (2003) 36–37 CrossRefGoogle ScholarPubMed
LaHaye, M.D., Buu, O., Camarota, B., Schwab, K.C., Approaching the quantum limit of a nanomechanical resonator, Science 304 (2004) 74–77 CrossRefGoogle ScholarPubMed
Kacem, N., Hentz, S., Pinto, D., Reig, B., Nguyen, V., Nonlinear dynamics of nanomechanical beam resonators: improving the performance of nems-based sensors, Nanotechnology 20 (2009) 275501 CrossRefGoogle ScholarPubMed
Kacem, N., Arcamone, J., Perez-Murano, F., Hentz, S., Dynamic range enhancement of nonlinear nanomechanical resonant cantilevers for high sensitive NEMS gas/mass sensors applications, J. Micromech. Microeng. 20 (2010) 04502 CrossRefGoogle Scholar
Sumpter, B.G., Noid, D.W., The onset of instability in nanostructures: the role of nonlinear resonance, J. Chem. Phys. 102 (1995) 6619–6622 CrossRefGoogle Scholar
X.L. Feng, Phase noise and frequency stability of very-high frequency silicon nanowire nanomechanical resonators, in 14th International Conference on Solid-State Sensors, Actuators and Microsystems, 2007, pp. 327–30
R.T. Howe, T.A. Roessig, A.P. Pisano, Nonlinear mixing in surface-micromachined tuning fork oscillators, in Frequency Control Symposium, 1997, Proc. IEEE Int., 1997, pp. 778–782
Kaajakari, V., Koskinen, J.K., Mattila, T., Phase noise in capacitively coupled micromechanical oscillators, IEEE Trans. Ultrason. Ferroelec. Freq. Contr. 52 (2005) 2322–2331 CrossRefGoogle ScholarPubMed
Seoánez, C., Guinea, F., Castro Neto, A.H., Dissipation in graphene and nanotube resonators, Phys. Rev. B 76 (2007) 125427 CrossRefGoogle Scholar
V. Sazonova, A tunable carbon nanotube resonator, Ph.D. Dissertation, Cornell University, Ithaca, New York, 2006
L.D. Landau, E.M. Lifshitz, Theory of Elasticity, Butterworth-Heinemann, Oxford, 3rd edition, 1986
Nishiyama, H., Nakamura, M., Capacitance of a strip capacitor, IEEE Trans. Compon. Hybrids Manuf. Technol. 13 (1990) 417–423 CrossRefGoogle Scholar
Nayfeh, A.H., Younis, M.I., Abdel-Rahman, E.M., Dynamic pull-in phenomenon in mems resonators, Nonlinear Dyn. 48 (2007) 153–163 CrossRefGoogle Scholar
Thouzé, C., Thomas, O., Non-linear behaviour of free-edge shallow spherical shells: Effect of the geometry, Int. J. Non-Linear Mech. 41 (2006) 678–692 CrossRefGoogle Scholar
N. Kacem, Nonlinear dynamics of M&NEMS resonant sensors: design strategies for performance enhancement, Ph.D. Dissertation, Insa-Lyon, CEA-LETI, Grenoble, 2010
Husain, A., Hone, J., Postma, H.W. Ch., Huang, X.M.H., Drake, T., Barbic, M., Scherer, A., Roukes, M.L., Nanowire-based very-high-frequency electromechanical resonator, Appl. Phys. Lett. 83 (2003) 1240–1242 CrossRefGoogle Scholar
A.H. Nayfeh, D.T. Mook, Nonlinear Oscillations, Wiley, 1979
C. Gui, R. Legtenberg, H.A.C. Tilmans, J.H.J. Fluitman, M. Elwenspoek, Nonlinearity and hysteresis of resonant strain gauges, in Micro Electro Mechanical Systems, 1995, MEMS ’95, Proc. IEEE, 1995, pp. 157–162
Shao, L.C., Palaniapan, M., Tan, W.W., The nonlinearity cancellation phenomenon in micromechanical resonators, J. Micromech. Microeng. 18 (2008) 065014 CrossRefGoogle Scholar
Kacem, N., Hentz, S., Bifurcation topology tuning of a mixed behavior in nonlinear micromechanical resonators, Appl. Phys. Lett. 95 (2009) 183104 CrossRefGoogle Scholar
Kaajakari, V., Mattila, T., Lipsanen, A., Oja, A., Nonlinear mechanical effects in silicon longitudinal mode beam resonators, Sens. Actuators A: Physical 120 (2005) 64–70 CrossRefGoogle Scholar
Osterberg, P.M., Senturia, S.D., M-test: A test chip for mems material property measurement using electrostatically actuated test structures, J. Microelectromech. Syst. 6 (1997) 107–118 CrossRefGoogle Scholar
N. Kacem, S. Hentz, H. Fontaine, V. Nguyen, P. Robert, B. Legrand, L. Buchaillot, From mems to nems: Modelling and characterization of the non linear dynamics of resonators, a way to enhance the dynamic range, in Int. Conf. Nanotech, Boston, Massachusetts, USA, 2008
Ouakad, H.M., Younis, M.I., Nonlinear dynamics of electrically-actuated carbon nanotube resonator, J. Comput. Nonlinear Dynam. 5 (2010) 011009 CrossRefGoogle Scholar