Analysis of damping optimization through perforations in proof-mass of SOI capacitive accelerometer

  • S. KalaiselviEmail author
  • L. Sujatha
  • R. Sundar


MEMS capacitive accelerometers are ubiquitously used in wide-ranging applications. Different applications require a trade-off between design parameters to realize either high sensitivity or precision or wide-dynamic range or speed of response. Planar MEMS structures for sensors usually have a large area compared to thickness or gap. In such structures, squeeze film damping properties of the gas (or air) in the narrow gap significantly affect the dynamic performance of the device. Schemes to reduce the damping effect normally include perforations in the structure to reduce path-lengths of air movement in the narrow gap. But perforations in the structure decrease the mass of the structure leading to a reduction in sensitivity. Therefore, the structural design requires selection of perforation parameters that can provide an optimal trade-off between sensitivity and damping coefficient. This paper discusses our studies through numerical computation when using different configurations of perforations on a typical SOI-based capacitive square accelerometer structure with 1 µm air gap. Both static analysis and analysis at first resonant frequency were carried-out on a range of structures to characterize sensitivity and damping coefficients. The ratio of perforation size versus perforation pitch, η, is used as a basis for sensitivity normalization and studies were carried out to compute damping coefficients for structures with different values of η and count of perforations. Studies reveal a reduction in damping coefficient by 90% to 97% for the η range 0.3 <  η < 0.55. The corresponding reduction in effective change in capacitance of the device is limited to the range of 10–25%.


SOI capacitive accelerometer Squeeze film damping Perforated proof mass Solid fluid interaction 



We thank DRDOs (Grant No. GTRE/GATET/SM02/1516/088/16/01) Gas Turbine Research Establishment (GTRE) for providing financial support under GATET program for design and development of this MEMS capacitive accelerometer.


  1. 1.
    Andrews, M., Harm, I., & Turner, G. (1993). A comparison of squeeze-film theory with measurements on a microstructure. Sensors and Actuators A,36, 79–81.CrossRefGoogle Scholar
  2. 2.
    Veijola, T., Kuisma, H., Lahenpera, J., & Ryhanen, T. (1995). Equivalent-circuit model of the squeezed gas film in a silicon accelerometer. Sensor and Actuator A,48, 239–248.CrossRefGoogle Scholar
  3. 3.
    Bao, M. (2000). Micro mechanical transducers—pressure sensors, accelerometers, and gyroscope. Amsterdam: Elsevier.Google Scholar
  4. 4.
    Veijola, T. (2006). Analytic damping model for an MEM perforation cell. Microfluidics and Nanofluidics,2, 249–260.CrossRefGoogle Scholar
  5. 5.
    Veijola, T. (2006b). Analytic damping model for a square perforation cell. In Proceedings of the 9th international conference on modeling and simulation of microsystems, pp. 554–557. Boston.Google Scholar
  6. 6.
    Veijola, T. (2006). Analytical model for perforated squeezed film dampers (pp. 1–6). Grenoble: DTIP, TIMA Edition.Google Scholar
  7. 7.
    Bao, M., Yang, H., Sun, Y., & French, P. J. (2003). Modified Reynolds’ equation and analytical analysis of squeeze-film air damping of perforated structures. Journal of Micromechanics and Microengineering,13, 795–800.CrossRefGoogle Scholar
  8. 8.
    Skvor, Z. (1967). On acoustical resistance due to viscous losses in the air gap of electostatic transducers. Acustica,19, 295–297.Google Scholar
  9. 9.
    Veijola, T., & Mattila, T. (2001). Compact squeezed-film damping model for perforated surface. In Proceedings of transducers ’01, pp. 1506–1509. Mu¨nchen.Google Scholar
  10. 10.
    Homentcovschi, D., & Miles, R. N. (2005). Viscous damping of perforated planar micromechanical structures. Sensors and Actuators A,119, 544–552.CrossRefGoogle Scholar
  11. 11.
    Kwok, P. Y., Weinberg, M. S., & Breuer, K. S. (2005). Fluid effects in vibrating micromachined structures. Journal MicroElectro Mechanical Systems,14(4), 770–781.CrossRefGoogle Scholar
  12. 12.
    Pandey, A. K., Pratap, R., & Chau, F. S. (2007). Analytical solution of modified Reynolds equation in perforated MEMS structures. Sensors and Actuators A,135, 839–848.CrossRefGoogle Scholar
  13. 13.
    Sattler, R., & Wachutka, G. (2004). Compact models for squeeze-film damping in the slip flow regime. In Proceedings 7th international conference on modeling and simulation of microsystems (MSM2004) (Boston), pp. 243–246.Google Scholar
  14. 14.
    Feng, C., Zhao, P., & Liu, D. Q. (2007). Squeeze-film effects in MEMS devices with perforated plates for small amplitude vibration. Microsystem Technologies,13, 623–633.Google Scholar
  15. 15.
    Veijola, T. (2007). Methods for solving gas damping problems in perforated microstructures using a 2D finite-element solver. Sensors,7, 1069–1090.CrossRefGoogle Scholar
  16. 16.
    Nigro, S., Pagnotta, L., & Pantano, M. F. (2012). Analytical and numerical modeling of squeeze-film damping in perforated microstructures. Microfluid Nanofluid,12, 971–979.CrossRefGoogle Scholar
  17. 17.
    Veijola, T., De Pasquale, G., & Soma, A. (2009). Experimental validation of compact damping models of perforated MEMS devices. Microsystem Technologies,15, 1121–1128.CrossRefGoogle Scholar
  18. 18.
    De Pasquale, G., Veijola, T., & Soma, A. (2010). Modelling and validation of air damping in perforated gold and silicon MEMS plates. Journal of Micromechanics and Microengineering,20, 015010.CrossRefGoogle Scholar
  19. 19.
    Pandey, A. K., & Pratap, R. (2008). A comparative study of analytical squeeze film damping models in rigid rectangular perforated MEMS structures with experimental results. Microfluid Nanofluid,4, 205–218.CrossRefGoogle Scholar
  20. 20.
    Dias, R. A., & Rocha, L. A. (2014). Improving capacitance/damping ratio in a capacitive MEMS transducer. Journal of Micromechanics and Microengineering,24, 015008.CrossRefGoogle Scholar
  21. 21.
    Ghemari, Z., & Saad, S. (2017). Parameters improvement and suggestion of new design of capacitive accelerometer. Analog Integrated Circuits Signal Processing,92(3), 443–451.CrossRefGoogle Scholar
  22. 22.
    Ghemari, Z., & Saad, S. (2019). The use of mechanical sensitivity model to enhance capacitive sensor characteristics. Analog Integrated Circuits Signal Processing,99(2), 349–357.CrossRefGoogle Scholar
  23. 23.
    Veijola, T. (2015). Handbook of silicon based MEMS materials and technologies, micro and nano technologies (2nd ed., pp. 354–373). Norwich: William Andrew Publishing.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Centre for Excellence in MEMS and MicrofluidicsRajalalakshmi Engineering CollegeChennaiIndia

Personalised recommendations