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TECHNICAL PAPERS

A Capacitive Microcantilever: Modelling, Validation, and Estimation Using Current Measurements

[+] Author and Article Information
Mariateresa Napoli, Bassam Bamieh, Kimberly Turner

Department of Mechanical Engineering, University of California, Santa Barbara, CA 93106

J. Dyn. Sys., Meas., Control 126(2), 319-326 (Aug 05, 2004) (8 pages) doi:10.1115/1.1767851 History: Received July 02, 2003; Revised November 03, 2003; Online August 05, 2004
Copyright © 2004 by ASME
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References

Indermhule,  P. , 1997, “Fabrication and Characterization of Cantilevers With Integrated Sharp Tips and Piezoelectric Elements for Actuation and Detection for Parallel AFM Applications,” Sens. Actuators, A, A60(1–3), pp. 186–190.
Despont,  M. , 2000, “VLSI-NEMS Chip for Parallel AFM Data Storage,” Sens. Actuators, A, A80(2), pp. 100–107.
Britton,  C. , 2000, “Multiple-Input Microcantilever Sensors,” Ultramicroscopy, 82(1–4), pp. 17–21.
Moulin,  A. , 2000, “Microcantilever-Based Biosensors,” Ultramicroscopy, 82, pp. 23–31.
Sarid, D., Scanning Force Microscopy, Oxford University Press, New York, 1994.
Binning,  G. , 1986, “Atomic Force Microscope,” Phys. Rev. Lett., 56(9), pp. 930–933.
Fritz,  J. , 2000, “Translating Biomolecular Recognition Into Nanomechanics,” Science, 288, pp. 316–318.
Raiteri,  R. , 1999, “Sensing of Biological Substances Based on the Bending of Microfabricated Cantilevers,” Sens. Actuators B, 61, pp. 213–217.
Chui,  B. , 1998, “Independent Detection of Vertical and Lateral Forces With a Sidewall-Implanted Dual-Axis Piezoresistive Cantilever,” Appl. Phys. Lett., 72(11), pp. 1388–1390.
Tortonese,  M., Barrett,  R., and Quate,  C., 1993, “Atomic Resolution With an Atomic Force Microscope Using Piezoresistive Detection,” Appl. Phys. Lett., 62(8), pp. 834–836.
Gaucher,  P. , 1998, “Piezoelectric Bimorph Cantilever for Actuation and Sensing Applications,” J. Phys. IV, 8, pp. 235–238.
Itoh, T., Ohashi, T., and Suga, T., “Piezoelectric Cantilever Array for Multiprobe Scanning Force Microscopy,” in Proc. of the IX Int. Workshop on MEMS, San Diego, CA, pp. 451–455, 1996.
Minne,  S., Manalis,  S., and Quate,  C., 1995, “Parallel Atomic Force Microscopy Using Cantilevers With Integrated Piezoresistive Sensors and Integrated Piezoelectric Actuators,” Appl. Phys. Lett., 67(26), pp. 3918–3920.
Huang,  Q., and Lee,  N., 2000, “A Simple Approach to Characterizing the Driving Force of Polysilicon Laterally Driven Thermal Microactuators,” Sens. Actuators, A, A80(3), pp. 267–272.
Attia,  P. , 1998, “Fabrication and Characterization of Electrostatically Driven Silicon Microbeams,” Microelectron. J., 29, pp. 641–44.
Blanc,  N. , 1996, “Scanning Force Microscopy in the Dynamic Mode Using Microfabricated Capacitive Sensors,” J. Vac. Sci. Technol. B, 14(2), pp. 901–905.
Shiba,  Y. , 1998, “Capacitive Afm Probe for High Speed Imaging,” Trans. of the IEE of Japan,118E(12), pp. 647–50.
Napoli, M., and Bamieh, B., “Modeling and Observer Design for an Array of Electrostatically Actuated Microcantilevers,” in Proc. 40th IEEE Conf. on Dec. and Cont., Orlando FL, December 2001.
Salapaka,  S. , 2002, “High Bandwidth Nano-Positioner: A Robust Control Approach,” Rev. Sci. Instrum., 73(9), pp. 3232–41.
Daniele, A. et al., “Piezoelectric Scanners for Atomic Force Microscopes: Design of Lateral Sensors, Identification and Control,” in Proc. of the 1999 American Control Conference, San Diego, CA, June 1999.
Turner, K., “Multi-Dimensional MEMS Motion Characterization Using Laser Vibrometry,” in Digest of Technical Papers Transducers’99, Sendai, Japan, 1999.
Arnold, V., Mathematical Methods of Classical Mechanics, Springer, 1988.
McLachlan, N., Theory and Applications of the Mathieu Functions, Oxford University Press, London, 1951.
Rand, R., Lecture Notes on Nonlinear Vibrations, available online http://www.tam.cornell.edu/randdocs/, 2001.
Vidyasagar, M., Nonlinear Systems Analysis, SIAM, 1993.
Zhang,  W. , 2002, “Effect of Cubic Nonlinearity on Auto-Parametrically Amplified Resonant MEMS Mass Sensor,” Sens. Actuators, A, A102(1–2), pp. 139–150.
Nagpal,  K., and Khargonekar,  P., 1991, “Filtering and Smoothing in an H Setting,” IEEE Trans. Autom. Control, 36(2), pp. 152–66.
Chen, T., and Francis, B., Optimal Sampled-Data Control Systems, Springer, 1995.
Bamieh,  B. , 1993, “Minimization of the l-Induced Norm for Sampled-Data Systems,” IEEE Trans. on AC,38(5), pp. 717–32.

Figures

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A schematic of an electrostatically driven cantilever
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SEM image of a polySi cantilever. The inset shows details of the mechanical connection to the base.
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Frequency response of the capacitive cantilever: the dashed line corresponds to measured data, the solid one is its least square fit
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Electrostatic resonance. The dots represent measured values of resonance frequency, the solid line is their linear fit.
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Mathieu equation: the shaded areas correspond to unstable behavior
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First instability region: experimental data points (circles) and curves with identified parameters. Inset: effect of damping visible on experimentally measured data, marked with circles.
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Cantilever response in parametric resonance (oscilloscope data)
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Exponential growth of oscillation following parametric excitation
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Frequency response above critical driving voltage amplitude (A=10 V). The solid and dashed lines have been added to the experimental data points (marked with o and +) to facilitate the reading.
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Phase portrait of Eq. (6). The labelling corresponds to the regions of Fig. 9.
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A schematic of the observer problem
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H-norm vs. frequency of excitation
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Performance of the observers in the presence of measurement noise and initial estimation error. The dashed line is the measured position signal, the solid line its estimate. a) Optimal observer b) Reduced order observer.
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Expected current signal from experimental velocity and position data
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Estimation error for different values of the observer gain: a) k>0 cos(ϕ)<0, b) k<0 cos(ϕ)>0

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