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Analysis of the Effect of Spatial Uncertainties on the Dynamic Behavior of Electrostatic Microactuators

Published online by Cambridge University Press:  21 July 2016

Aravind Alwan  and
Narayana R. Aluru
Aravind Alwan*
Affiliation:
Department of Mechanical Science and Engineering, Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, 405 N. Mathews Avenue, Urbana, IL 61801, USA
Narayana R. Aluru*
Affiliation:
Department of Mechanical Science and Engineering, Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, 405 N. Mathews Avenue, Urbana, IL 61801, USA
*
*Corresponding author. Email addresses:[email protected] (A. Alwan), [email protected] (N. R. Aluru)
*Corresponding author. Email addresses:[email protected] (A. Alwan), [email protected] (N. R. Aluru)
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Abstract

This paper examines the effect of spatial roughness on the dynamical behaviour of electrostatic microactuators. We develop a comprehensive physical model that comprises a nonlinear electrostatic actuation force aswell as a squeeze-film damping term to accurately simulate the dynamical behavior of a cantilever beam actuator. Spatial roughness is modeled as a nonstationary stochastic process whose parameters can be estimated from profilometric measurements. We propagate the stochastic model through the physical system and examine the resulting uncertainty in the dynamical behavior that manifests as a variation in the quality factor of the device. We identify two distinct, yet coupled, modes of uncertainty propagation in the system, that result from the roughness causing variation in the electrostatic actuation force and the damping pressure, respectively. By artificially turning off each of these modes of propagation in sequence, we demonstrate that the variation in the damping pressure has a greater effect on the damping ratio than that arising from the electrostatic force. Comparison with similar simulations performed using a simplified mass-spring-damper model show that the coupling between these two mechanisms can be captured only when the physical model includes the primary nonlinear interactions along with a proper treatment of spatial variations. We also highlight the difference between nonstationary and stationary covariance formulations by showing that the stationary model is unable to properly capture the full range of variation as compared to its nonstationary counterpart.

Keywords

Uncertainty quantificationmicroelectromechanical systems (MEMS)electrostatic actuationsqueeze-film dampingroughnessrandom processdamping ratio
Type
Research Article
Information
Communications in Computational Physics , Volume 20 , Issue 2 , August 2016 , pp. 279 - 300
Copyright
Copyright © Global-Science Press 2016 

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References

[1] De, S. K. and Aluru, N., “Full-Lagrangian schemes for dynamic analysis of electrostatic MEMS,” J. Microelectromech. Syst., vol. 13, no. 5, pp. 737–758, 2004.Google Scholar
[2] Shi, F., Ramesh, P., and Mukherjee, S., “Dynamic analysis of micro-electro-mechanical systems,” Int. J. Numer. Meth. Eng., vol. 39, no. 24, pp. 4119–4139, 1996.Google Scholar
[3] Nayfeh, A. H., Younis, M. I., and Abdel-Rahman, E. M., “Dynamic pull-in phenomenon in MEMS resonators,” Nonlinear Dynam., vol. 48, no. 1-2, pp. 153–163, 2007.Google Scholar
[4] De, S. K. and Aluru, N., “Coupling of hierarchical fluid models with electrostatic and mechanical models for the dynamic analysis of MEMS,” J. Micromech. Microeng., vol. 16, no. 8, p. 1705, 2006.Google Scholar
[5] Xiu, D. and Karniadakis, G., “Modeling uncertainty in flow simulations via generalized polynomial chaos,” J. Comput. Phys., vol. 187, pp. 137–167, May 2003.Google Scholar
[6] Agarwal, N. and Aluru, N. R., “Stochastic analysis of electrostatic MEMS subjected to parameter variations,” J. Microelectromech. Syst., vol. 18, pp. 1454–1468, Dec. 2009.CrossRefGoogle Scholar
[7] Han, J. and Kwak, B., “Robust optimal design of a vibratory microgyroscope considering fabrication errors,” J. Micromech. Microeng., vol. 11, no. 6, p. 662, 2001.Google Scholar
[8] Wittwer, J., Baker, M., and Howell, L., “Robust design and model validation of nonlinear compliant micromechanisms,” J. Microelectromech. Syst., vol. 15, no. 1, pp. 33–41, 2006.Google Scholar
[9] Martowicz, A. and Uhl, T., “Reliability-and performance-based robust design optimization of MEMS structures considering technological uncertainties,” Mech. Syst. Signal Pr., vol. 32, pp. 44–58, 2012.Google Scholar
[10] Senturia, S., Aluru, N., and White, J., “Simulating the behavior of MEMS devices: computational methods and needs,” IEEE Comput. Sci. Eng., vol. 4, pp. 30–43, Jan.-Mar. 1997.Google Scholar
[11] Aluru, N. and White, J., “An efficient numerical technique for electromechanical simulation of complicated microelectromechanical structures,” Sensor. Actuat. A-Phys., vol. 58, no. 1, pp. 1–11, 1997.CrossRefGoogle Scholar
[12] Li, G. and Aluru, N., “Efficient mixed-domain analysis of electrostatic MEMS,” IEEE T. Comput. Aid. D., vol. 22, pp. 1228–1242, Sept. 2003.Google Scholar
[13] Pandey, A. K. and Pratap, R., “Effect of flexural modes on squeeze film damping in MEMS cantilever resonators,” J. Micromech. Microeng., vol. 17, no. 12, p. 2475, 2007.CrossRefGoogle Scholar
[14] Duwel, A., Gorman, J., Weinstein, M., Borenstein, J., and Ward, P., “Experimental study of thermoelastic damping in MEMS gyros,” Sensor. Actuat. A-Phys., vol. 103, no. 1, pp. 70–75, 2003.Google Scholar
[15] Lepage, S., Stochastic finite element method for the modeling of thermoelastic damping in micro-resonators, PhD thesis, University of Liège, 2006.Google Scholar
[16] Patrikar, R. M., “Modeling and simulation of surface roughness,” Appl. Surf. Sci., vol. 228, no. 1, pp. 213–220, 2004.Google Scholar
[17] Palasantzas, G. and De Hosson, J.T.M., “Pull-in characteristics of electromechanical switches in the presence of Casimir forces: Influence of self-affine surface roughness,” Phys. Rev. B, vol. 72, no. 11, p. 115426, 2005.Google Scholar
[18] Palasantzas, G. and De Hosson, J.T.M., “Surface roughness influence on the pull-in voltage of microswitches in presence of thermal and quantum vacuum fluctuations,” Surf. Sci., vol. 600, no. 7, pp. 1450–1455, 2006.Google Scholar
[19] Broer, W., Palasantzas, G., Knoester, J., and Svetovoy, V. B., “Significance of the Casimir force and surface roughness for actuation dynamics of MEMS,” Phys. Rev. B, vol. 87, no. 12, p. 125413, 2013.Google Scholar
[20] Chandrasekharaiah, D. S. and Debnath, L., Continuum Mechanics, Academic Press, 1994.Google Scholar
[21] Parkus, H., Thermoelasticity, Blaisdell Publishing Company, New York, 1968.Google Scholar
[22] Jaswon, M. and Symm, G., Integral Equation Methods in Potential Theory and Elastostatics, Academic Press, New York, 1977.Google Scholar
[23] Shi, F., Ramesh, P., and Mukherjee, S., “On the application of 2D potential theory to electrostatic simulation,” Commun. Numer. Meth. En., vol. 11, no. 8, pp. 691–701, 1995.CrossRefGoogle Scholar
[24] Alwan, A. and Aluru, N., “Analysis of hybrid electrothermomechanical microactuators with integrated electrothermal and electrostatic actuation,” J. Microelectromech. Syst., vol. 18, pp. 1126–1136, Oct. 2009.Google Scholar
[25] Burgdorfer, A., “The influence of the molecular mean free path on the performance of hydrodynamic gas lubricated bearings,” Trans. ASME, Ser. D, vol. 81, pp. 94–100, 1959.Google Scholar
[26] Cressie, N. A., Statistics for Spatial Data, revised edition, vol. 928, Wiley, New York, 1993.CrossRefGoogle Scholar
[27] Williams, C. K. and Rasmussen, C. E., Gaussian processes for machine learning, MIT Press, 2006.Google Scholar
[28] Sampson, P. D. and Guttorp, P., “Nonparametric estimation of nonstationary spatial covariance structure,” J. Am. Stat. Assoc., vol. 87, no. 417, pp. 108–119, 1992.Google Scholar
[29] Alwan, A. and Aluru, N., “A nonstationary covariance function model for spatial uncertainties in electrostatically actuated microsystems,” Int. J. Uncertain. Quantif., vol. 5, no. 2, pp. 99–121, 2015.CrossRefGoogle Scholar
[30] Patil, A., Huard, D., and Fonnesbeck, C. J., “PyMC: Bayesian stochastic modelling in Python,” J. Stat. Softw., vol. 35, no. 4, p. 1, 2010.Google Scholar
[31] Poutous, M. K., Hosseinimakarem, Z., and Johnson, E. G., “Photoresist surface roughness characterization in additive lithography processes for fabrication of phase-only optical vortices,” J. Micro. Nanolithogr. MEMS MOEMS, vol. 11, no. 4, pp. 043009–043009, 2012.Google Scholar
[32] Perrin, O. and Meiring, W., “Identifiability for non-stationary spatial structure,” J. Appl. Probab., vol. 36, no. 4, pp. 1244–1250, 1999.CrossRefGoogle Scholar