Skip to main content
SpringerLink
Log in

Numerical Modeling of the Electromechanical Interaction in MEMS

  • Conference paper
  • First Online:
Advanced Computational Methods in Science and Engineering

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 71))

Abstract

Microsystems or Micro–Electro–Mechanical Systems (MEMS) are small (micrometersize) machines usually built by lithographic technologies originally developed for microchips. MEMS are designed to integrate sensing and actuation (and evendata processing) on a single chip, therefore they often include moving and deforming parts. Currently microsystem technologies are used for a wide variety of purposes such as: read/write heads in hard-disk drives, ink-jet printheads, Digital Light Processing (DLP) chips in video projection systems and several types of sensors for pressure, flow, acceleration or bio-elements.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Adams, S., Bertsch, F., Shaw, K., Hartwell, P., Moon, F., MacDonald, N.: Capacitance based tunable resonators. Jounal of Micromechanics and Microengineering 8, 15–23 (1998)

    Article  Google Scholar 

  2. Aluru, N., White, J.: An efficient numerical technique for electrochemical simulation of complicated microelectromechanical structures. Sensors & Actuators: A. Physical 58(1), 1–11 (1997)

    Google Scholar 

  3. Bailey, C., Taylor, G., Cross, M., Chow, P.: Discretisation procedures for multi-physics phenomena. Journal of Computational and Applied Mathematics 103(1), 3–17 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  4. Bathe, K.: Finite element procedures. Prentice Hall, Englewood Cliffs, NJ (1996)

    Google Scholar 

  5. Bochobza-Degani, O., Elata, D., Nemirovsky, Y.: An efficient DIPIE algorithm for CAD of electrostatically actuated MEMS devices. Microelectromechanical Systems, Journal of 11(5), 612–620 (2002)

    Article  Google Scholar 

  6. Budianski, B.: Theory of buckling and post-buckling behavior of elastic structures. In: C. Yih (ed.) Advances in Applied Mechanics, vol. 14, pp. 1–65. Academic Press (1974)

    Google Scholar 

  7. Cervera, M., Codina, R., Galindo, M.: On the computational efficiency and implementation of block-iterative algorithms for nonlinear coupled problems. Engineering Computations 13(6), 4–30 (1996)

    Article  MATH  Google Scholar 

  8. Cheng, J., Zhe, J., Wu, X.: Analytical and finite element model pull-in study of rigid and deformable electrostatic microactuators. Journal of Micromechanics and Microengineering 14(1), 57–68 (2004)

    Article  Google Scholar 

  9. Crisfield, M.: A fast incremental/iterative solution procedure that handles snap-through. Computers and Structures 13(1–3), 55–62 (1981)

    Article  MATH  Google Scholar 

  10. Crisfield, M.: Non-Linear Finite Element Analysis of Solids and Structures, Volume 1: Essentials. John Wiley & Sons, New York (1991)

    Google Scholar 

  11. Dai, C., Yu, W.: A micromachined tunable resonator fabricated by the CMOS post-process of etching silicon dioxide. Microsystem Technologies 12(8), 766–772 (2006)

    Article  Google Scholar 

  12. Degani, O., Socher, E., Lipson, A., Lejtner, T., Setter, D., Kaldor, S., Nemirovsky, Y.: Pull-in study of an electrostatic torsion microactuator. Microelectromechanical Systems, Journal of 7(4), 373–379 (1998)

    Article  Google Scholar 

  13. Farhat, C., Lesoinne, M., Maman, N.: Mixed explicit/implicit time integration of coupled aeroelastic problems: three-field formulation, geometric conservation and distributed solution. International Journal for Numerical Methods in Fluids 21(10), 807–835 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  14. Ferziger, J., Perić, M.: Computational Methods for Fluid Dynamics. Springer (2002)

    Google Scholar 

  15. Fung, Y.: Foundations of Solid Mechanics. Prentice-Hall, Englewood Cliffs, NJ (1968)

    Google Scholar 

  16. Géradin, M., Rixen, D.: Mechanical Vibrations. John Wiley & Sons, New York (1997)

    Google Scholar 

  17. Gilbert, J., Legtenberg, R., Senturia, S.: 3D coupled electro-mechanics for MEMS: applications of CoSolve-EM. Micro Electro Mechanical Systems, 1995, MEMS'95, Proceedings. IEEE

    Google Scholar 

  18. Griffiths, D.: Introduction to Electrodynamics. Prentice-Hall, Englewood Cliffs, NJ (1999)

    Google Scholar 

  19. Gyimesi, M., Avdeev, I., Ostergaard, D.: Finite-element simulation of micro-electromechanical systems (MEMS) by strongly coupled electromechanical transducers. Magnetics, IEEE Transactions on 40(2), 557–560 (2004)

    Article  Google Scholar 

  20. Hannot, S., Rixen, D.: Determining pull-in curves with electromechanical FEM models. In L.J.Ernst et al. (eds.) Proceedings of the 9th International Conference on Thermal, Mechanical and Multiphysics Simulation and Experiments in Micro-Electronics and Micro-Systems, Freiburg, Germany, April 2008, pp. 528–535 (2008)

    Google Scholar 

  21. Hannot, S., Rixen, D., Rochus, V.: Rounding the corners in an electromechanical FEM model. In E. Onate et al. (Eds.) Proceedings of the Second International Conference on Computational Methods for Coupled Problems in Science and Engineering, Ibiza, Spain, May 2008 pp. 507–510 (2007)

    Google Scholar 

  22. Henneken, V., Tichem, M., Sarro, P.: In-package MEMS-based thermal actuators for micro-assembly. Journal of Micromechanics and Microengineering 16(6), S107–S115 (2006)

    Article  Google Scholar 

  23. Henneken, V., Tichem, M., Sarro, P.: Improved thermal U-beam actuators for micro-assembly. Sensors & Actuators: A. Physical 142(1), 298–305 (2008)

    Google Scholar 

  24. Hung, E., Senturia, S.: Generating efficient dynamical models for microelectromechanical systems from a few finite-element simulation runs. Microelectromechanical Systems, Journal of 8(3), 280–289 (1999)

    Article  Google Scholar 

  25. Jackson, J.: Classical Electrodynamics. John Wiley & Sons (1975)

    Google Scholar 

  26. Katsikadelis, J.: Boundary Elements: Theory and Applications. Elsevier (2002)

    Google Scholar 

  27. Kolesar, E., Allen, P., Howard, J., Wilken, J., Boydston, N.: Thermally-actuated cantilever beam for achieving large in-plane mechanical deflections. Thin Solid Films 355, 295–302 (1999)

    Article  Google Scholar 

  28. Kouhia, R., Mikkola, M.: Some aspects of efficient path-following. Computers and Structures 72(4–5), 509–524 (1999)

    Article  MATH  Google Scholar 

  29. Lee, K., Cho, Y.: A triangular electrostatic comb array for micromechanical resonant frequency tuning. Sensors & Actuators: A. Physical 70(1–2), 112–117 (1998)

    Google Scholar 

  30. Lee, W., Kwon, K., Kim, B., Cho, J., Youn, S.: Frequency-shifting analysis of electrostatically tunable micro-mechanical actuator. Journal of Modeling and Simulation of Microsystems 2(1), 83–88 (2001)

    Google Scholar 

  31. Majumder, S., McGruer, N., Adams, G., Zavracky, P., Morrison, R., Krim, J.: Study of contacts in an electrostatically actuated microswitch. Sensors & Actuators: A. Physical 93(1), 19–26 (2001)

    Google Scholar 

  32. Mukherjee, S., Bao, Z., Roman, M., Aubry, N.: Nonlinear mechanics of MEMS plates with a total Lagrangian approach. Computers & Structures 83, 758–768 (2005)

    Article  Google Scholar 

  33. Nadal-Guardia, R., Dehe, A., Aigner, R., Castaner, L.: Current drive methods to extend the range of travel of electrostatic microactuators beyond the voltage pull-in point. Microelectromechanical Systems, Journal of 11(3), 255–263 (2002)

    Article  Google Scholar 

  34. Nathanson, H., Newell, W., Wickstrom, R., Davis Jr, J.: The resonant gate transistor. Electron Devices, IEEE Transactions on 14(3), 117–133 (1967)

    Article  Google Scholar 

  35. Riks, E.: An incremental approach to the solution of snapping and buckling problems. International Journal of Solids and Structures 15(7), 529–551 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  36. Rochus, V.: Finite element modeling of strong electro-mechanical coupling in MEMS. Université de Liège, PhD Thesis, Belgium (2006)

    Google Scholar 

  37. Rochus, V., Rixen, D., Golinval, J.: Monolithic modelling of electro-mechanical coupling in micro-structures. International Journal for Numerical Methods in Engineering 65(4), 461–493 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  38. Seeger, J., Boser, B.: Charge control of parallel-plate, electrostatic actuators and the tip-in instability. Microelectromechanical Systems, Journal of 12(5), 656–671 (2003)

    Article  Google Scholar 

  39. Slone, A., Pericleous, K., Bailey, C., Cross, M.: Dynamic fluid–structure interaction using finite volume unstructured mesh procedures. Computers and Structures 80(5–6), 371–390 (2002)

    Article  Google Scholar 

  40. Tang, W., Nguyen, T., Howe, R.: Laterally driven polysilicon resonant microstructures. Sensors & Actuators: A. Physical 20(1–2), 25–32 (1989)

    Google Scholar 

  41. Thompson, J., Hunt, G.: Elastic instability phenomena. John Wiley & Sons (1984)

    Google Scholar 

  42. Versteeg, H., Malalasekera, W.: An Introduction to Computational Fluid Dynamics: The Finite Volume Method. Longman Scientific & Technical, Harlow, Essex (1995)

    Google Scholar 

  43. Wautelet, M.: Scaling laws in the macro-, micro-and nanoworlds. European Journal of Physics 22(6), 601–611 (2001)

    Article  Google Scholar 

  44. Zhang, L., Zhao, Y.: Electromechanical model of RF MEMS switches. Microsystem Technologies 9(6), 420–426 (2003)

    Article  Google Scholar 

  45. Zhulin, V., Owen, S., Ostergaard, D.: Finite element based electrostatic-structural coupled analysis with automated mesh morphing. Proceedings of the International Conference on Modeling and Simulation of Microsystems MSM pp. 501–504 (2000)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Mechanical Maritime and Materials Engineering, Delft University of Technology, Mekelweg 2, 2628 CD, Delft, The Netherlands

    S. D. A. Hannot & D. J. Rixen

Authors
  1. S. D. A. Hannot
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. D. J. Rixen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. D. A. Hannot .

Editor information

Editors and Affiliations

  1. Scientific Computing &, Centrum Wiskunde & Informatica, Science Park 123, Amsterdam, 1098 XG, Netherlands

    Barry Koren

  2. Inst. Applied Mathematics, Delft University of Technology, Mekelweg 4, Delft, 2628 CD, Netherlands

    Kees Vuik

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Hannot, S.D.A., Rixen, D.J. (2009). Numerical Modeling of the Electromechanical Interaction in MEMS. In: Koren, B., Vuik, K. (eds) Advanced Computational Methods in Science and Engineering. Lecture Notes in Computational Science and Engineering, vol 71. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03344-5_11

Download citation

Publish with us

Policies and ethics

Search

Navigation