Managing Parameter Variations in Microsystems Device Design

  • Michael Huff
Part of the Microsystems and Nanosystems book series (MICRONANO)


The information covered from the previous chapters is brought together in this chapter to explain various techniques used in the microsystems design to manage the parameter variations resulting from use of microsystems manufacturing. Design for manufacturability (DfM) of microsystems is covered followed by some general recommendations for developing microsystems designs that adhere to DfM principles for MEMS devices. A review of the design techniques to manage device parameter variations is then provided including design centering: device parameter variation reduction; device size scaling; acceptance region increase; and best practices for layout. These techniques allow the variation region to be better aligned with the acceptance region. Each of these techniques is substantiated with examples in a one-dimensional parameter space, followed by how these techniques are used in multidimensional space. The use of Monte Carlo analysis techniques for design methods is then discussed including specific methods such as the centers of gravity algorithm; correlated sampling; and the common points method. The confidence of correct yield ranking is included in this discussion. Subsequently, sensitivity analysis for manufacturing or performance function improvement is outlined in both one- and multidimensional spaces. Lastly, a method for optimization of the manufacturing cost function is given.


Design for manufacturability Device partitioning Design centering Parameter variation reduction Device size scaling Acceptance range increase Best practices for mask layout design Sensitivity analysis Manufacturing cost function optimization 


  1. 1.
    S.P. Vudathu, K.K. Duganapalli, R. Laur, D. Kubalinska, A.B. Gerstner, Parametric Yield Analysis of MEMS VIA Statistical Methods. DTIP of MEMS and MOEMS, Stresa, IT, Apr. 26–28, (2006)Google Scholar
  2. 2.
    L. Gao, Q.-A. Huang, Modeling of the effect of process variations on a micromachined doubly-clamped beam. Micromachines J. 8, 81 (2017). Scholar
  3. 3.
    L. Rong, B. Paden, K. Turner, MEMS resonators that are robust to process-induced variations. J. Microelectromech. Syst. 11, 505–511 (2002)CrossRefGoogle Scholar
  4. 4.
    Z. Luo, X. Wang, M. Jin, S. Liu, MEMS gyroscope yield simulations based on Monte Carlo method. Proceeding of 2012 IEEE 62nd Electronic Components and Technology Conference, May 29 – June 1, (2012), pp. 1636–1639Google Scholar
  5. 5.
    S.D. Senturia, Microsystems Design (Springer, New York, 2001)Google Scholar
  6. 6.
    R. Dutton, “CRC Electronic Design Automation for IC Handbook. Vol II, Chapter 25, 2016Google Scholar
  7. 7.
    R.B. Bird, W.E. Stewart, E.N. Lightfoot, Transport Phenomena (Wiley, New York, 1960)Google Scholar
  8. 8.
    A. Ttimoshenko, S. Woinowky-Krieger, Theory of Plates and Shells, 2nd edn. (McGraw-Hill, New York, 1959)Google Scholar
  9. 9.
    P.R. Gray, P.J. Hurst, S.H. Lewis, R.G. Meyer, Analysis and Design of Analog Integrated Circuits, 5th edn. (Wiley, New York, 2009)Google Scholar
  10. 10.
    R.S. Soin, R. Spence, Statistical exploration approach to design centering. Proc. IEEE, Pt. G 127(6), 260–269 (1980)Google Scholar
  11. 11.
    I.R. Ibbotson, E. Compton, D. Boardman, Improved statistical design centering for electrical networks. Electron. Lett. 20(19), 757–758 (1984)CrossRefGoogle Scholar
  12. 12.
    R. Spence, R.S. Soin, Tolerance Design of Electronic Circuits (Imperial College Press, London, 1997)CrossRefGoogle Scholar

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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Michael Huff
    • 1
  1. 1.Corporation for National Research InitiativesMEMS & Nanotechnology ExchangeRestonUSA

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