Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-28T00:15:26.306Z Has data issue: false hasContentIssue false
  • English
  • Français

Extraction of Frequency Dependent Macromodels for Mems Squeezed-Film Damping Effects

Published online by Cambridge University Press:  05 May 2011

Yao-Joe Joseph Yang ,
Chih-Ming Chien ,
Mattan Kamon ,
Vladimir L. Rabinovich  and
John R. Gilbert
Yao-Joe Joseph Yang*
Affiliation:
Department of Mechanical Engineering, National Taiwan University, Taipei, Taiwan 10617, R.O.C.
Chih-Ming Chien*
Affiliation:
Department of Mechanical Engineering, National Taiwan University, Taipei, Taiwan 10617, R.O.C.
Mattan Kamon*
Affiliation:
Coventor, Inc., Cambridge, MA, U.S.A.
Vladimir L. Rabinovich*
Affiliation:
Coventor, Inc., Cambridge, MA, U.S.A.
John R. Gilbert*
Affiliation:
Coventor, Inc., Cambridge, MA, U.S.A.
*
*Associate Professor
** Graduate student
*** Project Manager
*** Project Manager
*** Chief Technology Officer
Get access

Abstract

In this paper, an efficient macromodel extraction technique for dynamical MEMS gas damping effects is presented. The technique applies an Arnoldi-based model-order-reduction algorithm to generate low-order macromodels from a FEM approximation of the governing equation of the squeeze-film fluidic damping effect, the Reynolds equation. We demonstrate that this approach is more than 100 times efficient than previous approaches, which solve the Reynolds equation using transient finite-element/finite-difference methods. The generated gas-damping macromodels can be easily inserted into system-level modeling packages, such as SPICE, Saber and Simulink, for transient and frequency coupled-domain analysis. We also demonstrated that the simulated results are in good agreement with experimental results for various MEMS devices.

Keywords

MacromodelSqueeze-film dampingMEMSModel order reduction
Type
Articles
Information
Journal of Mechanics , Volume 21 , Issue 4 , December 2005 , pp. 227 - 234
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2005

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

1.Senturia, S. D., Microsystem Design, Kluwer Academie Publishers, Boston (2001).CrossRefGoogle Scholar
2.Tang, W. C., Nguyen, T. H. and Howe, R. T., “Laterally Driven Polysilicon Resonant Microstructures,” Technical Digest of the IEEE Micro Electromechanical Systems Workshop, Salt Lake City, Utah, Feb 20–22, pp. 53–59 (1989).Google Scholar
3.Langlois, W. E. “Isothermal Squeeze Films,” Quar Applied Mathematics, XX(2), pp. 131–150 (1962).CrossRefGoogle Scholar
4.Blech, J. J., “On Isothermal Squeeze Films,” Journal of Lubrication Technology, 105, pp. 615–620 (1983).CrossRefGoogle Scholar
5.Yang, Y.-J. and Senturia, S. D., “Numerical Simulation of Compressible Squeezed-Film Damping,” Tech. Digest, Solid State Sensor and Actuator Workshop Hilton Head Island, SC, June (1996).Google Scholar
6.Veijola, T., et al., “Equivalent-Circuit Model of the Squeezed Gap Film in a Silicon Accelerometer,” Sensors and Actuators A, A48, pp. 239–248 (1995).CrossRefGoogle Scholar
7.Yang, Y-J., Gretillat, M-A. and Senturia, S. D., “Effects of Air Damping on the Dynamics of Nonuniform Deformations of Microstructures,” Transducers 97, II, Chicago, IL, U.S.A June 16–19, pp. 1093–1096 (1997)Google Scholar
8.Veijola, T., “Finite-Difference Large Displacement Gas-Film Model,” Transducers 99, Sendai, Japan, June 7–10, pp. 1152–1155 (1999).Google Scholar
9.da Silva, M., et al., “Gas Damping and Spring Effects on MEMS Devices with Multiple Perforations and Multiple Gaps,” Transducers 99, Sendai, Japan, June 7–10, pp. 1148–1151 (1999).Google Scholar
10.Gretillat, M-A., et al, “Electrostatic Polysilicon Micro-Relays,” Ph.D. Dissertation, DVIT, University of Neuchâtel, Switzerland (1997).Google Scholar
11.Coventorware 2003 Module Guide, Coventor Inc. (2003).Google Scholar
12.Odabasioglu, A., et al., “PRIMA,” IEEE Transaction on Computer-Aide d Design of Integrated Circuits and Systems, 17(8), Aug. (1998).Google Scholar
13.Yang, Y.-J. and Yu, C.-C., “Extraction of Heat-Transfer Macromodels for MEMS Devices,” Journal of Micromechanics and Microengineering, 14(4), pp. 587–596 (2004).CrossRefGoogle Scholar
14.Yang, Y.-J., Kamon, M., Rabinovich, V. L., Ghaddar, C., Deshpande, M., Greiner, K. and Gilbert, J. R., “Modeling Gas Damping and Spring Phenomena in MEMS with Frequency Dependent Macro-Models,” Proc. IEEE 14th International Conference on Micro Electro-Mechanical Systems Workshop (MEMS 2001), Interlaken, Switzerland, Jan, pp. 365–368, (2001).Google Scholar
15.Bechtold, T., Rudnyi, E. B., and Korvink, J. G., Automatic Generation of Compact Electro-Thermal Models for Semiconductor Devices, IEICE Transactions on Electronics, E86C(3), pp. 459–465 (2003).Google Scholar
16.Zaman, M. H., et al., “A Technique for Extraction of Macro-Models in System Level Simulation of Inertial Electro-Mechanical Micro Systems,” MSM ‘99, San Juan, PR., April 19–21, pp 163–167 (1999).Google Scholar
17.Saber User's Guide, Synopsys, Inc. (2003).Google Scholar
18.Ananthasuresh, G. K., et al., “An Approach to Macromodeling of MEMS for Nonlinear Dynamic Simulation,” ASME International Mechanical Engineering Congress and Exposition, Symposium on MEMS, Atlanta, GA, Nov., pp. 18–22 (1996).Google Scholar
19.Craig, R. R. Jr, Structural Dynamics: An Introduction to Computer Methods, Wiley (1981).Google Scholar
20.Salimbahrami, B. and Lohmann, B., “Krylov Subspace Methods in Linear Model Order Reduction: Introduction and Invariance Properties,” Scientific Report, Univ. of Bremen (2002).Google Scholar
21.Rewieński, M., and White, J., “A Trajectory Piecewise-Linear Approach to Model Order Reduction and Fast Simulation of Nonlinear Circuits and Micromachined Devices,” IEEE Transaction on Computer-Aided Design of Integrated Circuits and Systems, 22(2), Feb., pp. 155–170, (2003).CrossRefGoogle Scholar
22.Yang, Y.-J. and Shen, K.-Y., “Nonlinear Heat-Transfer Macromodeling for MEMS Thermal Devices,” Journal of Micromechanics and Microengineering, 15, pp. 408–418 (2005).CrossRefGoogle Scholar
23.Grey wall, D. S., “Phenomenological Model for Gas Damping of Micromechanical Structures,” Private Communication, Lucent Technologies, NJ (1998).Google Scholar
24.Minami, K., et al, “Simple Modeling and Simulation of the Squeeze Film Effect and Transient Response of the MEMS Device,” MEMS 99, pp. 338–343 (1999).Google Scholar