Effect of cubic nonlinearity on auto-parametrically amplified resonant MEMS mass sensor

Sensors and Actuators, A: Physical

Volumn 102, Issue 1-2, 2002, Pages 139-150

  Zhang, Wenhua ^a   Baskaran, Rajashree ^a   Turner, Kimberly L ^a  

^a University of California   (United States)

Author keywords

Chemical sensor; Damping; Mass sensor; Mathieu equation; MEMS; Nonlinearity; Parametric resonance

Indexed keywords

DAMPING; DYNAMIC RESPONSE; ELECTROSTATICS; FREQUENCY RESPONSE; MICROELECTROMECHANICAL DEVICES; PARAMETRIC OSCILLATORS; RESONANCE;

MASS SENSORS;

MICROSENSORS;

EID: 0036896806     PISSN: 09244247     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0924-4247(02)00299-6     Document Type: Article

References (34)

1. L. Ruby, Applications of the Mathieu equation, Am. J. Phys. 64 (1996) 39-44.
2. J.A. Burns, More on pumping a swing, Am. J. Phys. 38 (1970) 920-921.
3. J.W.S. Rayleigh, R.B. Lindsay, The Theory of Sound, Dover Publications, New York, 1st American, 1945, pp.
4. K.L. Turner, S.A. Miller, P.G. Hartwell, N.C. Macdonald, S.H. Strogartz, S.G. Adams, Five parametric resonances in a microelectromechanical system, Nature 396 (1998) 149-152.
5. K.L. Turner, W. Zhang, Design and analysis of a dynamic MEM chemical sensor, in: Proceedings of the 2001 American Control Conference, Arlington, VA, USA, 25-27 June 2001, pp. 1214-1218.
6. J.P. Raskin, A.R. Brown, B. Khuri-Yakub, G.M. Rebeiz, A novel parametric-effect MEMS amplifier, J. Microelectromech. Syst. 9 (2000) 528-537.
7. A. Olkhovets, D.W. Carr, J.M. Parpia, H.G. Craighead, Non-degenerate nanomechanical parametric amplifier, in: Proceedings of the 14th IEEE International Conference on Micro Electro Mechanical Systems, Interlaken, Switzerland, 21-25 January 2001, pp. 298-300.
8. M.K. Baller, H.P. Lang, J. Fritz, C. Gerber, J.K. Gimzewski, U. Drechsler, H. Rothuizen, M. Despont, P. Vettiger, F.M. Battiston, J.P. Ramseyer, P. Fornaro, E. Meyer, H.J. Guntherodt, A cantilever array-based artificial nose, in: Proceedings of the International Conference on Scanning Probe Microscopy, Cantilever Sensors and Nanostructures, Seattle, WA, USA, 30 May-1 June 1999, pp. 1-9.
9. T. Bachels, R. Schafer, Microfabricated cantilever-based detector for molecular beam experiments, Rev. Sci. Instrum. 69 (1998) 3794-3797.
10. T.D. Stowe, K. Yasumura, T.W. Kenny, D. Botkin, K. Wago, D. Rugar, Attonewton force detection using ultrathin silicon cantilevers, Appl. Phys. Lett. 71 (1997) 288-290.
11. T. Kenny, Nanometer-scale force sensing with MEMS devices, IEEE Sens. J. 1 (2001) 148-157.
12. P. Mohanty, D.A. Harrington, M.L. Roukes, Measurement of small forces in micron-sized resonators, in: Proceedings of the 22nd International Conference on Low Temperature Physics, Espoo, Finland, 4-11 August 1999, pp. 2143-2144.
13. M. Cartmell, Introduction to Linear, Parametric, and Nonlinear Vibrations, Chapman & Hall, London, 1990, pp. xii, 242.
14. K.L. Turner, P.G. Hartwell, F.M. Bertsch, N.C. Macdonald, Parametric resonance in a microelectromechanical torsional oscillator, in: ASME International Mechanical Engineering Congress and Exposition Proceedings of the Microelectromechanical Systems (MEMS), Anaheim, CA, USA, 15-20 November 1998, pp. 335-340.
15. R. Berger, C. Gerber, H.P. Lang, J.K. Gimzewski, Micromechanics: a toolbox for femtoscale science: towards a laboratory on a tip, in: Proceedings of the International Conference on Micro- and Nanofabrication, Glasgow, UK, 22-25 September 1996, pp. 373-379.
16. T. Thundat, P.I. Oden, R.J. Warmack, Microcantilever sensors, Microscale Thermophys. Eng. 1 (1997) 185-199.
17. T. Thundat, R.J. Warmack, G.Y. Chen, D.P. Allison, Thermal and ambient-induced deflections of scanning force microscope cantilevers, Appl. Phys. Lett. 64 (1994) 2894-2896.
18. B. Vu Thien, N. Garcia, A.L. Levanyuk, A mechanical nanosensor in the gigahertz range: where mechanics meets electronics, Surf. Sci. 301 (1994) L224-228.
19. R. Lifshitz, M.L. Roukes, Thermoelastic damping in micro- and nanomechanical systems, Phys. Rev. B, Condens. Matter 61 (2000) 5600-5609.
20. Z.J. Davis, G. Abadal, O. Kuhn, O. Hansen, F. Grey, A. Boisen, Fabrication and characterization of nanoresonating devices for mass detection, J. Vac. Sci. Technol. B, Microelectron. Nanometer Struct. 18 (2000) 612-616.
21. N.C. Macdonald, SCREAM microelectromechanical systems, Microelectron. Eng. 32 (1996) 49-73.
22. S.G. Adams, F.M. Bertsch, K.A. Shaw, N.C. Macdonald, Independent tuning of linear and nonlinear stiffness coefficients (actuators), J. Microelectromech. Syst. 7 (1998) 172-180.
23. ANSYS, Release 5.7.
24. Coulomb, Three-Dimensional Electrostatic Field Solver, Version 5.1 (2000).
25. R. Grimshaw, Nonlinear Ordinary Differential Equations, CRC Press, Boca Raton, FL, 1993, pp. viii, 328.
26. S. Evoy, D.W. Carr, L. Sekaric, A. Olkhovets, J.M. Parpia, H.G. Craighead, Nanofabrication and electrostatic operation of single-crystal silicon paddle oscillators, J. Appl. Phys. 86 (1999) 6072-6077.
27. M. Aikele, K. Bauer, W. Ficker, F. Neubauer, U. Prechtel, J. Schalk, H. Seidel, Resonant accelerometer with self-test, in: Proceedings of the EUROSENSORS, 14th European Conference, Copenhagen, Denmark, 27-30 August 2000, pp. 161-167.
28. R.H. Rand, Lecture Notes on Nonlinear Vibrations, Version 34a, Available online at http://www.tam.cornell.edu/randdocs/, 2000.
29. K.L. Turner, Multi-dimensional MEMS motion characterization using laser vibrometry, in: Transducers'99 The 10th International conference on solid-state Sensors and Actuators, Digest of Technical Papers, Sendai, Japan, 7-10 June 1999, pp. 1144-1147.
30. Polytec, Vibrometer User's Manual (1999).
31. L. Rong, B. Paden, K. Turner, MEMS resonators that are robust to process-induced feature width variations, in: Proceedings of the 2001 IEEE International Frequency Control Symposium and PDA Exhibition, Seattle, WA, USA, 6-8 June 2001, pp. 556-563.
32. M.T.A. Saif, N.C. Macdonald, Planarity of large MEMS, J. Microelectromech. Syst. 5 (1996) 79-97.
33. J.E. Mehner, L.D. Gabbay, S.D. Senturia, Computer-alded generation of nonlinear reduced-order dynamic macromodels. Part II. Stress-stiffened case, J. Microelectromech. Syst. 9 (2000) 270-278.
34. T.B. Gabrielson, Mechanical-thermal noise in micromachined acoustic and vibration sensors, IEEE Trans. Electron Devices 40 (1993) 903-909.