Out-of-plane deformation and pull-in voltage of cantilevers with residual stress gradient: experiment and modelling

  • Anna Persano
  • Jacopo Iannacci
  • Pietro Siciliano
  • Fabio Quaranta
Technical Paper


The out-of-plane deformation and the pull-in voltage of electrostatically actuated cantilevers with a residual stress gradient, is investigated in the length range 100–300 µm. Measured pull-in voltages are compared with calculations, which are obtained using previously proposed analytical expressions and a finite element method (FEM) modelling. In particular, a simplified model of the residual stress distribution inside cantilevers is formulated that enables FEM simulation of measured out-of-plane deformations and pull-in voltages for all lengths of fabricated cantilevers. The presented experimental results and FEM model are exploitable in the design of cantilever-based microelectromechanical systems, in order to provide a reliable prediction of the influence of residual stress gradient on device shape and pull-in voltage.



The authors thank M.C. Martucci for performing surface profilometry measurements.


  1. Baek C-W, Kim Y-K, Ahn Y, Kim Y-H (2005) Measurement of the mechanical properties of electroplated gold thin films using micromachined beam structures. Sens Actuators A 117:17–27CrossRefGoogle Scholar
  2. Ballestra A, Brusa E, De Pasquale G, Munteanu MGh, Soma A (2010) FEM modelling and experimental characterization of microbeams in presence of residual stress. Analog Integr Circ Sig Process 63:477–488CrossRefGoogle Scholar
  3. Chowdhury S, Ahmadi M, Miller WC (2005) A closed-form model for the pull-in voltage of electrostatically actuated cantilever beams. J Micromech Microeng 15:756–763CrossRefGoogle Scholar
  4. De Coster J, Tilmans H A C, den Toonder JMJ, van Beek JTM, Rijks ThGSM, Steeneken PG, Puers R (2005) Empirical and theoretical characterisation of electrostatically driven MEMS structures with stress gradients. Sens Actuators A 123–124:555–562CrossRefGoogle Scholar
  5. Denhoff MW (2003) A measurement of Young’s modulus and residual stress in MEMS bridges using a surface profiler. J Micromech Microeng 13:686–692CrossRefGoogle Scholar
  6. Fang W, Wickert JA (1996) Determining mean and gradient residual stresses in thin films using micromachined cantilevers. J Micromech Microeng 6:301–309CrossRefGoogle Scholar
  7. Huang S, Zhang X (2007) Gradient residual stress induced elastic deformation of multilayer MEMS structures. Sens Actuators A 134:177–185CrossRefGoogle Scholar
  8. Huang J-M, Liew KM, Wong CH, Rajendran S, Tan MJ, Liu AQ (2001) Mechanical design and optimization of capacitive micromachined switch. Sens Actuators A 93:273–285CrossRefGoogle Scholar
  9. Iannacci J (2013) Practical Guide to RF-MEMS, 1st ed. Wiley-Interscience, New YorkCrossRefGoogle Scholar
  10. Iannacci J (2018) RF-MEMS technology as an enabler of 5G: low-loss ohmic switch tested up to 110 GHz. Sens Actuators A 279:624–629CrossRefGoogle Scholar
  11. Iannacci J, Tschoban C (2017) RF-MEMS for future mobile applications: experimental verification of a reconfigurable 8-bit power attenuator up to 110 GHz. J Micromech Microeng 27:1–11CrossRefGoogle Scholar
  12. Iannacci J, Gaddi R, Gnudi A (2010) Experimental validation of mixed electromechanical and electromagnetic modeling of RF-MEMS devices within a standard IC simulation environment. J Microelectromech Syst 19:526–537CrossRefGoogle Scholar
  13. Iannacci J, Serra E, Sordo G, Bonaldi M, Borrielli A, Schmid U, Bittner A, Schneider M, Kuenzig T, Schrag G, Pandraud G, Sarro PM (2018) MEMS-based multi-modal vibration energy harvesters for ultra-low power autonomous remote and distributed sensing. Microsyst Technol 24:1–10CrossRefGoogle Scholar
  14. Majumdar R, Paprotny I (2017) Configurable post-release stress-engineering of surface micro-machined MEMS structures. J Microelectromech Syst 26(3):671–678CrossRefGoogle Scholar
  15. Matrecano M, Memmolo P, Miccio L, Persano A, Quaranta F, Siciliano P, Ferraro P (2015) Improving holographic reconstruction by automatic Butterworth filtering for microelectromechanical systems characterization. Appl Opt 54(11): 3428–3432CrossRefGoogle Scholar
  16. Mulloni V, Giacomozzi F, Margesin B (2010) Controlling stress and stress gradient during the release process in gold suspended micro-structures. Sens Actuators A 162:93–99CrossRefGoogle Scholar
  17. Mulloni V, Colpo S, Faes A, Margesin B (2013) A simple analytical method for residual stress measurement on suspended MEM structures using surface profilometry. J Micromech Microeng 23:025025CrossRefGoogle Scholar
  18. Osterberg PM, Senturia SD (1997) M-TEST: a test chip for MEMS material property measurement using electrostatically actuated test structures. J Microelectromech Syst 6(2):107–118CrossRefGoogle Scholar
  19. Ou K-S, Chen K-S (2014) Pull-in voltage estimation of micro cantilever beams with effects of residual stress gradients and capacitance fringing. IEEE Trans Device Mater Reliab 14(1):577–579CrossRefGoogle Scholar
  20. Ou K-S, Chen K-S, Yang T-S and Lee S-Y (2011) A novel semianalytical approach for finding pull-in voltages of micro cantilever beams subjected to electrostatic loads and residual stress gradients. J Microelectromech Syst 20(2):527–537CrossRefGoogle Scholar
  21. Pamidighantam S, Puers R, Baert K, Tilmans HAC (2002) Pull-in voltage analysis of electrostatically actuated beam structures with fixed–fixed and fixed–free end conditions. J Micromech Microeng 12:458–464CrossRefGoogle Scholar
  22. Peroulis D, Pacheco SP, Sarabandi K, Katehi LPB (2003) Electromechanical considerations in developing low-voltage RF MEMS switches. IEEE Trans Microw Theory Tech 51(1):259–270CrossRefGoogle Scholar
  23. Persano A, Quaranta F, Martucci MC, Siciliano P, Cola A (2015) On the electrostatic actuation of capacitive RF MEMS switches on GaAs substrate. Sens Actuators A 232:202–207CrossRefGoogle Scholar
  24. Persano A, Quaranta F, Capoccia G, Proietti E, Lucibello A, Marcelli R, Bagolini A, Iannacci J, Taurino A, Siciliano P (2016) Influence of design and fabrication on RF performance of capacitive RF MEMS switches. Microsyst Technol 22:1741–1746CrossRefGoogle Scholar
  25. Rabinov VL, Gupta RJ, Senturia SD (1997) The effect of release etch-holes on theelectromechanical behavior of MEMS structures. Int Conf Solid-State Sens Actuators. pp. 1125–1128Google Scholar
  26. Rebeiz G M (2003) RF MEMS: Theory, Design, and Technology. Wiley-Interscience, New YorkCrossRefGoogle Scholar
  27. Rottenberg X, De Wolf I, Nauwelaers BKJC, De Raedt W, Tilmans HAC (2007) Analytical model of the DC actuation of electrostatic MEMS devices with distributed dielectric charging and nonplanar electrodes. J Microelectr Syst 16(5):1243–1253CrossRefGoogle Scholar
  28. Shekhar S, Vinoy KJ, Ananthasuresh GK (2017) Surface-micromachined capacitive rf switches with low actuation voltage and steady contact. J Microelectromech Syst 26(3):643–652CrossRefGoogle Scholar
  29. Tai Y-C, Muller RS (1990) Measurement of Young’s modulus on microfabricated structures using a surface profiler Proc. IEEE Micro Electro Mechanical Systems Workshop (Napa Valley, CA) pp 147–52Google Scholar
  30. Yang H-H, Seo M-H, Han C-H, Yoon J-B (2013) A new approach to control a deflection of an electroplated microstructure: dual current electroplating methods. J Micromech Microeng 23:055016CrossRefGoogle Scholar
  31. Zhang W-M, Yan H, Peng Z-K, Meng G (2014) Electrostatic pull-in instability in MEMS/NEMS: A review. Sens Actuators A 214:187–218CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Anna Persano
    • 1
  • Jacopo Iannacci
    • 2
  • Pietro Siciliano
    • 1
  • Fabio Quaranta
    • 1
  1. 1.IMM-CNR, Institute for Microelectronics and Microsystem-Unit of Lecce, National Council of ResearchLecceItaly
  2. 2.CMM–FBK, Center for Materials and Microsystems, Fondazione Bruno KesslerTrentoItaly

Personalised recommendations