Skip to main content

Uncertainty-Based Design Optimization of MEMS/NEMS

  • Chapter
  • First Online:

Abstract

In designing micro-electromechanical systems (MEMS), model-based design and design optimization is inevitable. This is due to the complexity of the working principles and the manufacturing technology associated with high initial costs for experimental investigations. Uncertainty-based design optimization enables stochastic variables, such as scattering material properties, manufacturing tolerances, stochastic time dependent loads, aging, or wear, to be considered in the design. In this chapter, the fundamental concept of reliability or failure probability is introduced and probabilistic approximation and simulation methods are described. These methods are used for robust design optimization (RDO) and reliability-based design optimization (RBDO) as well. Applications and examples for of both approaches are also provided.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   89.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   119.99
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

Learn about institutional subscriptions

References

  1. Adams, B.M., Eldred, M.S., Wittwer, J.W.: Reliability-based design optimization for shape design of compliant micro-electro-mechanical systems. In: 11th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, Portsmouth, Virginia 6–8 Sep 2006

    Google Scholar 

  2. Agarwal, N., Aluru, N.R.: Stochastic analysis of electrostatic MEMS subjected to parameter variations. J. Microelectromech. Syst. 18(6), 1454–1468 (2009)

    Article  Google Scholar 

  3. Allen, M., Raulli, M., Maute, K., Frangopol, D.M.: Reliability-based analysis and design optimization of electrostatically actuated MEMS. Comput. Struct. 82, 1007–1020 (2004)

    Article  Google Scholar 

  4. Ang, A.H.S., Tang, W.: Probability Concepts in Engineering Planning and Design, vol. II Decision, Risk, and Reliability. Wiley, New York (1984)

    Google Scholar 

  5. Beyer, H.G., Sendhoff, B.: Robust optimization—a comprehensive survey. Comput. Method Appl. M. 196, 3190–3218 (2007)

    Google Scholar 

  6. Bucher, C.: Computational Analysis of Randomness in Structural Mechanics, Structures and Infrastructures Book Series, vol. 3. Taylor& Francis Ltd, Leiden (2009)

    Google Scholar 

  7. Bucher, C.G.: Adaptive sampling—an iterative fast Monte Carlo procedure. Struct. Saf. 5(2), 119–126 (1988)

    Article  Google Scholar 

  8. Canumalla, S.: Robust design of third level packaging in portable electronics: solder joint reliability under dynamic mechanical loading. In: 58th Electronic Components and Technology Conference ECTC 2008, May 27–30 2008

    Google Scholar 

  9. Chase, K.W., Parkinson, A.R.: A survey of research in the application of tolerance analysis to the design of mechanical assemblies. Res. Eng. Des. 3, 23–37 (1991)

    Article  Google Scholar 

  10. Cornell, C.A.: A probability-based structural code. J. Am. Concr. Inst. 66, 974–985 (1969)

    Google Scholar 

  11. Dehnad, K. (ed.): Quality Control, Robust Design, and the Taguchi Method. Wadsworth& Broos/Cole Advanced Books& Software Pacific Grove, California (1989)

    Google Scholar 

  12. Eldred, M.S., Adams, B.M., Copps, K.D., Carnes, B., Notz, P.K., Hopkins, M.M., Wittwer, J.W.: Solution-verified reliability analysis and design of compliant micro-electro-mechanical systems. In: 48th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Honolulu, April 23–26 2007

    Google Scholar 

  13. Fiessler, B., Rackwitz, R., Neumann, H.J.: Quadratic limit states in structural reliability. J. Eng. Mech. Div. 105(4), 661–676 (1979)

    Google Scholar 

  14. Gurav, S., Kasyap, A., Sheplak, M., Cattafesta, L., Haftka, R., Goosen, J., van Keulen, F.: Uncertainty-based design optimization of a micro piezoelectric composite energy reclamation device. In: 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, Albany, Aug 30–1, 2004

    Google Scholar 

  15. Gurav, S.P., Goosen, J.F.L., vanKeulen, F.: Bounded-but-unknown uncertainty optimization using design sensitivities and parallel computing: application to MEMS. Comput. Struct. 83, 1134–1149 (2005)

    Google Scholar 

  16. Haldar, A., Mahadevan, S. (eds.): Probability, Reliability and Statistical Methods in Engineering Design. John Wiley& Sons, New York (2000)

    Google Scholar 

  17. Hansen, L.P.: Large sample properties of generalized method of moments estimators. Econometrica 50, 1029–1054 (1982)

    Article  Google Scholar 

  18. Harik, V.M., Luo, L.S. (eds.): Micromechanics and Nanoscale Effects. Kluwer Academic Publishers, Amsterdam (2004)

    Google Scholar 

  19. Hsiung, K.L.: Design of microelectromechanical systems for variability via chance-constrained optimization. J. Phys. Conf. Ser. 34, 162–167 (2006). International MEMS Conference 2006

    Google Scholar 

  20. Huang, B., Du, X.: Analytical robustness assessment for robust design. Struct. Multidiscip. Optim. 34, 123–137 (2007)

    Google Scholar 

  21. Jung, H.S., Cho, S.: Reliability-based topology optimization of geometrically nonlinear structures with loading and material uncertainties. Finite Elem. Anal. Des. 41(3), 311–331 (2004)

    Article  Google Scholar 

  22. Jurecka, F.: Robust design optimization based on metamodeling techniques. Ph.D. thesis, Fakultät für Bauingenieur und Vermessungswesen der Technischen Universität München (2007)

    Google Scholar 

  23. Karpat, F., Ekwaro-Osire, S., Khandaker, M.P.H.: Probabilistic analysis of MEMS asymmetric gear tooth. J. Mech. Des.130, 042306-1–042306-6 (2008)

    Google Scholar 

  24. Katzan, H.j.: Managing Uncertainty: A Pragmatic Approach. Van Nostrand Reinhold, New York (1992)

    Google Scholar 

  25. Khandaker, M., Ekwaro-Osire, S.: Sensitivity based optimum design process for MEMS devices. In: 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, Albany, Aug. 30–1, 2004

    Google Scholar 

  26. Kim, C., Choi, K.K.: Reliability-based design optimization using response surface method with prediction interval estimation. J. Mech. Des. 130, 121401–121412 (2008)

    Google Scholar 

  27. Kim, C., Wang, S., Hwang, I., Lee, J.: Parallel computed reliability-based topology optimization using response surface method. In: 6th World Congresses of Structural and Multidisciplinary Optimization, Rio de Janeiro, 30 May–03 June 2005

    Google Scholar 

  28. Kim, C., Wang, S., Hwang, I., Lee, J.: Application of reliability-based topology optimization for microelectromechanical systems. AIAA J. 45(12), 2926–2934 (2007)

    Article  Google Scholar 

  29. Kleppmann, W.: Taschenbuch Versuchsplanung, 6th edn. Hanser Verlag München Wien (2009)

    Google Scholar 

  30. Kong, J.S., Frangopol, D.M., Raulli, M., Maute, K., Saravanan, R.A., Liew, L.A., Raj, R.: A methodology for analyzing the variability in the performance of a MEMS actuator made from a novel ceramic. Sens. Actuators, A 116, 336–344 (2004)

    Google Scholar 

  31. Lee, O.S., Park, Y.C., Kim, D.H.: Reliability estimation of solder joints under thermal fatigue with varying parameters by using form and mcs. J. Mech. Sci. Technol. 22, 683–688 (2008)

    Article  Google Scholar 

  32. Leondes, C.T. (ed.): MEMS/NEMS Handbook Techniques and Applications, vol. 1 Design Methods. Springer Science+Business Media, New York (2006)

    Google Scholar 

  33. Liu, N., Manoochehri, S.: Reliability-based MEMS system modeling and optimization. In: Proceedings of the 44th Annual Reliability Physics Symposium, San Jose, March 26–30 2006. pp. 403–409, ISBN: 0-7803-9498-4

    Google Scholar 

  34. Liu, P.L., Kiureghian, A.: Multivariate distribution models with prescribed marginals and covariances. Probab. Eng. Mech. 1, 105–112 (1986)

    Article  Google Scholar 

  35. Luo, R.C., Lin, C.F.: A review of mechatronics and bio-inspired mechatronics systems. J. Biomechatron. Eng. 1, 1–36 (2008)

    Google Scholar 

  36. Maute, K., Frangopol, D.M.: Reliability-based design of MEMS mechanisms by topology optimization. Comput. Struct. 81, 813–824 (2003)

    Article  Google Scholar 

  37. Melchers, R.E.: Structural Reliability Analysis and Prediction, 2nd edn. John Wiley& Sons, New York (1999)

    Google Scholar 

  38. Neubert, H., Fleischer, D., Kamusella, A., Pham, T.Q.: Optimization of bipolar magnetic actuators for microvalves with regard to the tolerances. In: Proceeding of the 11th International Conference and Exhibition on New Actuators and Drive Systems ACTUATOR 2008, pp. 1038–1041, Bremen, June 9–11, (2008)

    Google Scholar 

  39. Neubert, H., Kamusella, A., Pham, T.Q.: Uncertainly design analysis and optimization of LTCC based accelerometers in COMSOL Multiphysics with OptiY. In: Proceeding of the European COMSOL Conference, Grenoble, Oct 22–23, 2007

    Google Scholar 

  40. Neubert, H., Partsch, U., Fleischer, D., Gruchow, M., Kamusella, A., Pham, T.Q.: Thick film accelerometers in LTCC-technology design optimization, fabrication, and characterization. JMEP 5(4), 150–155 (2008)

    Google Scholar 

  41. Nikolaidis, E., Ghiocel, D.M., Singhal, S. (eds.): Engineering Design Reliability Handbook. CRC Press LLC, New York (2005)

    Google Scholar 

  42. Oberkampf, W.L., DeLand, S.M., Rutherford, B.M., Diegert, K.V., Alvin, K.F.: Error and uncertainty in modeling and simulation. Reliab. Eng. Syst. Safe. 75, 333–357 (2002)

    Article  Google Scholar 

  43. Pfingsten, T., Herrmann, J., Rasmussen, C.E.: Model-based design analysis and yield optimization. IEEE Trans. Semiconduct. M. 19, 475–486 (2006)

    Google Scholar 

  44. Pham, T.Q., Kamusella, A.: Zuverlässigkeitsanalyse und zuverlässigkeitsbasierte Optimierung mit probabilistischen Methoden am Beispiel eines Magnetantriebes. In: VDI-Tagung Technische Zuverlässigkeit, Leonberg, April 29-30, (2009)

    Google Scholar 

  45. Pham, T.Q., Neubert, H., Kamusella, A.: Design for reliability and robustness through probabilistic methods in COMSOL Multiphysics with OptiY. In: Proceedings of the 2nd European COMSOL Conference, Hannover, Nov 4–6, (2008)

    Google Scholar 

  46. Press, W.H., Teukolsky, S.A., Vetterling, W.T. (eds.): Numerical Recipes, 3rd edn. Cambridge University Press, New York (2007)

    Google Scholar 

  47. Rackwitz, R., Fiessler, B.: Structural reliability under combined random load sequences. Comput. Struct. 9, 489–494 (1978)

    Article  Google Scholar 

  48. Radhakrishnan, S., Subbarayan, G., Nguyen, L., Mazotte, W.: Optimization and stochastic procedures for robust design of photonic packages with applications to a generic package. In: Proceedings of the 53rd Electronic Components and Technology Conference, pp. 720–726, May 27–30 2003

    Google Scholar 

  49. Raulli, M., Maute, K.: Reliability based design optimization of MEMS considering pull-in. J. Mech. Des. 131, 061014-1–10 (2009)

    Google Scholar 

  50. Raulli, M., Subramanyaswamy, R.P., Maute, K.: Reliability based design optimization of analog micro-mirrors using pull-in criteria. In: The 9th International Conference on Structural Safety and Reliability - ICOSSAR 2005, June 19-23, Rome, pp. 2041–2048 (2005)

    Google Scholar 

  51. Roos, D.: Approximation und Interpolation von Grenzzustandsfunktionen zur Sicherheitsbewertung nichtlinearer Finite-Elemente-Strukturen. Ph.D. thesis, Bauhaus-Universität Weimar (2002)

    Google Scholar 

  52. Roos, D.: Advanced methods of stochastic and optimization in industrial applications. In: Proceedings of the 7th international Conference and Workshop on Numerical Simulation of 3D Sheet Metal Forming Processes, Interlaken, Sept 1–5 2008

    Google Scholar 

  53. Roos, D., Adam, U., Bayer, V.: Design reliability analysis. In: 24th CAD-FEM Users Meeting 2006 International Congress on FEM Technology, Stuttgart, Oct 26–27, 2006

    Google Scholar 

  54. Roos, D., Adam, U., Bucher, C.: Robust design optimization. In: Weimarer Optimierungs- und Stochastiktage 3.0, Weimar, Nov 23–24, 2006

    Google Scholar 

  55. van Roosmalen, A.J., Zhang, G.Q.: Reliability challenges in the nanoelectronics era. Microelectron. Reliab. 46, 1403–1414 (2006)

    Article  Google Scholar 

  56. Rubinstein, R.Y., Kroese, D.P.: Simulation and the Monte Carlo Method, 2nd edn. John Wiley& Sons, New York (2008)

    Google Scholar 

  57. Taguchi, G.: System of Experimental Design: Engineering Methods to Optimize Quality and Minimize Costs. Kraus International, New York (1987)

    Google Scholar 

  58. Tsompanakis, Y., Lagaros, N., Papadrakakis, M. (eds.): Structural Design Optimization Considering Uncertainties. Taylor& Francis, London (2008)

    Google Scholar 

  59. Wang, G.G., Dong, Z., Aitchison, P.: Adaptive response surface method—a global optimization scheme for approximation-based design problems. Eng. Optim. 33(6), 707–734 (2001)

    Google Scholar 

  60. Wittwer, J.W.: Simulation-based design under uncertainty for compliant microelectromechanical systems. Ph.D. thesis, Department of Mechanical Engineering, Brigham Young University Provo (2005)

    Google Scholar 

  61. Wu, Y.T.: Methods for efficient probabilistic analysis of models with large numbers of randamo variables. In: 7th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization. paper 98–4908, St. Louis, September 1998

    Google Scholar 

  62. Zang, T.A., Hemsch, M.J., Hilburger, M.W., Kenny, S.P., Luckring, J.M., Maghami, P., Padula, S.L., Stroud, W.J.: Needs and opportunities for uncertainty-based multidisciplinary design methods for aerospace vehicles. Technical Report Nr. TM-2002-211462, NASA (2002)

    Google Scholar 

  63. Zhao, Y.G., Ang, A.H.S.: System reliability assessment by method of moments. J. Struct. Eng. 129(10), 1341–1349 (2003)

    Article  Google Scholar 

  64. Zhao, Y.G., Ono, T.: Moment methods for structural reliability. Struct. Saf. 23, 47–75 (2001)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Holger Neubert .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Neubert, H. (2012). Uncertainty-Based Design Optimization of MEMS/NEMS. In: Gerlach, G., Wolter, KJ. (eds) Bio and Nano Packaging Techniques for Electron Devices. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28522-6_6

Download citation

Publish with us

Policies and ethics