Research Papers

Simulation of Micromechanical Measurement of Mass Accretion: Quantifying the Importance of Material Selection and Geometry on Performance

[+] Author and Article Information
Michael James Martin

Department of Mechanical Engineering,
Louisiana State University,
Baton Rouge, LA 70803
e-mail: martinm2@asme.org

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received April 11, 2012; final manuscript received September 25, 2013; published online November 26, 2013. Assoc. Editor: Steven W Shaw.

J. Vib. Acoust 136(2), 021003 (Nov 26, 2013) (7 pages) Paper No: VIB-12-1098; doi: 10.1115/1.4025842 History: Received April 11, 2012; Revised September 25, 2013

Micro- and nanomechanical resonators operating in liquid have been used to measure the change in the mass of either cells or functionalized surfaces attached to the resonator. As the system accretes mass, the natural frequency of the system changes, which can be measured experimentally. The current work extends methods previously developed for simulation of an atomic force microscope operating in liquid to study this phenomenon. A silicon cantilever with a 10 micron width, an 800 nm thickness, and a length of 30 microns was selected as a baseline configuration. The change in resonant frequency as the system accretes mass was determined through simulation. The results show that the change in natural frequency as mass accretes on the resonator is predictable through simulation. The geometry and material of the cantilever were varied to optimize the system. The results show that shorter cantilevers yield large gains in system performance. The width does not have a large impact on the system performance. Selecting the optimal thickness requires balancing the increase in overall system mass with the improvement in frequency response as the structure becomes thicker. Because there is no limit to the maximum system stiffness, the optimal materials will be those with higher elastic moduli. Based on these criteria, the optimum resonator for mass accretion measurements will be significantly different than an optimized atomic-force microscopy (AFM) cantilever.

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Zhong, Q., Innisss, D., Kjoller, K., and Elings, V. B., 1993, “Fractured Polymer Silica Fiber Surface Studied by Tapping Mode Atomic-Force Microscopy,” Surf. Sci. Lett., 290(1–2), pp. L688–L692. [CrossRef]
Ashhab, M., Salapaka, M. V., Dahleh, M., and Mezic, I., 1999, “Dynamical Analysis and Control of Microcantilevers,” Automatica, 35(2), pp. 1663–1670. [CrossRef]
Fung, R.-F., and Huang, S.-C., 2001, “Dynamic Modeling and Vibration Analysis of the Atomic Force Microscope,” ASME J. Vib. Acoust., 123(4), pp. 502–509. [CrossRef]
Hansma, P. K., Cleveland, J. P., Radmacher, M., Walters, D. A., Hillner, P. E., Bezanilla, M., Fritz, M., Vie, D., Hansma, H. G., Prater, C. B., Massie, J., Fukunaga, L., Gurley, J., and Elings, V., 1994, “Tapping Mode Atomic Force Microscopy in Liquids,” Appl. Phys. Lett., 4(13), pp. 1738–1740. [CrossRef]
Tamayo, J., Humphris, A. D. L., Owen, R. J., and Miles, M. J., 2001, “High-Q Dynamic Force Microscopy in Liquid and Its Application to Living Cells,” Biophys. J., 81(1), pp. 526–537. [CrossRef] [PubMed]
Gaudó, M. V., Abadal, G., Verd, J., Teva, J., Perez-Murano, F., Costa, E. F., Montserrat, J., Uranga, A., Esteve, J., and Barniol, N., 2007, “Time-Resolved Evaporation Rate of Attoliter Glycerine Drops Using On-Chip CMOS Mass Sensors Based on Resonant Silicon Micro-Cantilevers,” IEEE Trans. Nanotechnol., 6(5), pp. 509–512. [CrossRef]
Park, K., Jang, J., Irimia, D., Sturgis, J., and Lee, J., 2008, “‘Living Cantilever Arrays for Characterization of Mass of Single Live Cells in Fluids,” Lab on Chip, 8(7), pp. 1034–1041. [CrossRef]
Park, K., Millet, L. J., Kim, N., Li, H., Jin, X., Popescu, G., Aluru, N. R., Hsia, K. J., and Bashir, R., 2010, “Measurement of Adherent Cell Mass and Growth,” Proc. Natl. Acad. Sci., 107(48), pp. 20691–20696. [CrossRef]
Kim, S., Yi, D., Passian, A., and Thundat, T., 2010, “Observation of an Anomalous Mass Effect in Microcantilever-Based Biosensing Caused by Adsorbed DNA,” Appl. Phys. Lett., 96(15), p. 153703. [CrossRef]
Ekinci, K. L., Huang, X. M. H., and Roukes, M. L., 2004, “Ultrasensitive Nanoelectromechanical Mass Detection,” Appl. Phys. Lett., 84(22), pp. 4469–4471. [CrossRef]
Lavrik, N. V., Sepaniak, M. J., and Datskos, P. G., 2004, “Cantilever Transducers as a Platform for Chemical and Biological Sensors,” Rev. Sci. Instrum., 75(7), pp. 2229–2253. [CrossRef]
Blom, F. R., Bouwstra, S., Elwenspoek, M., and Fluitman, J. H. J., 1992, “Dependence of the Quality Factor of Micromachined Silicon Beam Resonators on Pressure and Geometry,” J. Vac. Sci. Technol. B, 10(1), pp. 19–26. [CrossRef]
Sader, J. E., 1998, “Frequency Response of Cantilever Beams Immersed in Viscous Fluids With Applications to the Atomic Force Microscope,” J. Appl. Phys., 84(1), pp. 64–76. [CrossRef]
Bhiladvala, R. B., and Wang, Z. J., 2004, “Effect of Fluids on the Q Factor and Resonance Frequency of Oscillating Micrometer and Nanometer Scale Beams,” Phys. Rev. E, 69(3), p. 036307. [CrossRef]
Martin, M. J., and Houston, B. H., 2008, “Computation of Damping for Vibrating Micro-Machined Cantilevers in the Slip Flow Regime,” AIAA Paper No. 2008-0690. [CrossRef]
Martin, M. J., Fathy, H. K., and Houston, B. H., 2008, “Dynamic Simulation of Atomic Force Microscope Cantilevers Oscillating in Liquid,” J. Appl. Phys., 104(4), p. 044316. [CrossRef]
Martin, M. J., and Houston, B. H., 2008, “Frequency Response of Nanoelectromechanical Cantilevers Operating in Fluid,” 8th IEEE Conference on Nanotechnology (NANO'08), Arlington, TX, August 18–21. [CrossRef]
Basak, S., Raman, A., and Garimella, S. V., 2006, “Hydrodynamic Loading of Microcantilevers Operating in Viscous Fluids,” J. Appl. Phys., 99(11), p. 114906. [CrossRef]
Weaver, W., Timoshenko, S. P., and Young, D. H., 1990, Vibration Problems in Engineering, 5th ed., Wiley, New York.
Young, W. C., and Budynas, R. G., 2002, Roark's Formulas for Stress and Strain, McGraw-Hill, New York.
Thompson, W. T., 1993, Theory of Vibrations with Applications, Prentice-Hall, Englewood Cliffs, NJ.
Fletcher, C. A. J., 1991, Computational Techniques for Fluid Dynamics, Vol. II, Specific Techniques for Different Flow Categories, 2nd ed., Springer-Verlag, New York.
Peterson, K. E., 1982, “Silicon as a Mechanical Material,” Proc. IEEE, 70(5), pp. 420–457. [CrossRef]
Franklin, G. F., Powell, J. D., and Emani-Naeini, A., 2003, Feedback Control of Dynamic Systems, 4th ed., Prentice-Hall, Upper Saddle River, NJ.
Ali, S. M., Mantell, S. C., and Longmire, E. K., 2011, “Mechanical Performance of Microcantilevers in Liquids,” Microelectromech. Syst., 20(2), pp. 441–450. [CrossRef]
Walters, D. A., Cleveland, J. P., Thomson, N. H., Hansma, P. K., Wendman, M. A., Gurley, G., and Elings, V., “Short Cantilevers for Atomic Force Microscopy,” Rev. Sci. Instrum., 67(10), pp. 3583–3590. [CrossRef]
Shackelford, J. F., and Alexander, W., 2003, CRC Materials Science and Engineering Handbook, 3rd ed., CRC Press, Boca Raton, FL.
Philip, J., Hess, P., Feygelson, T., Butler, J. E., Chattopadhyay, S., Chen, K. H., and Chen, L. C., 2003, “Elastic, Mechanical, and Thermal Properties of Nanocrystalline Diamond Films,” J. Appl. Phys., 93(4), pp. 2164–2171. [CrossRef]


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Fig. 1

Resonator configuration

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Fig. 4

Displacement versus frequency for unloaded silicon resonators with varying lengths

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Fig. 5

Gain versus frequency for unloaded silicon resonators with varying lengths

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Fig. 6

Frequency shift versus accreted mass for silicon resonators with varying lengths

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Fig. 7

Gain versus frequency for unloaded silicon resonators with varying widths

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Fig. 8

Frequency shift versus accreted mass for silicon resonators with varying widths

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Fig. 9

Gain versus frequency for unloaded silicon resonators with varying thicknesses

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Fig. 10

Frequency shift versus accreted mass for silicon resonators with varying thicknesses

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Fig. 11

Displacement versus frequency for unloaded resonators with varying materials

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Fig. 12

Gain versus frequency for unloaded resonators with varying materials

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Fig. 13

Frequency shift versus accreted mass for resonators with varying materials



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