analysis and fabricatiON of curved multimorph actuators

  • Straight bimorphs [1] and multimorphs [2] are well understood and have been widely used for achieving out-of-plane bending in thermal and piezoelectric MEMS devices.
  • Unlike straight bimorphs that only undergo bending, curved bimorphs bend and twist during deformation.
  • Analysis of curved bimorphs will greatly increase the design space available to MEMS engineers.

Figure 1: Bimorph actuator (a) Undeformed (b) deformed. The out-of-plane displacement and twist-angle and z and φ respectively.

  • Analysis of curved bimorphs and multimorphs for small deformation
  • Fabrication of curved multimorphs
  • Validation of analysis using experiments and simulations
  • Application of curved multimorphs
  • The three components of curved multimorph analysis are
    • Strain produced in the thin-film layers by thermal/piezoelectric effects [2]
    • Deformation equations for curved beams [3]
    • Strain continuity at the interface between thin-films
  • Curved bimorphs and multimorphs with in-plane radius of curvature in the range 25 -500 microns were fabricated. A laser beam reflected from a rigid mirror plate attached to the multimorph was used to track its deformation at different ambient temperatures.

Figure 2: Fabricated curved multimorph structures.


 Figure 3: (a) Tip-deflection (b) Beam-twist of a 50 microns long, 6 microns wide, singly-clamped multimorph with the following layers — 0.15 microns SiO2 - 0.6 microns W - 0.2 microns SiO2 - 0.7 microns Al — for a temperature change of 100 K.

Figure 4: Experimental, analytical and simulation results for structure shown in Fig. 2. Discrepancies at large deformation may be attributed to the small-deformation assumptions used during analysis.

Qualitative study for large deformations:

Video: A circular bimorph clamped at one end is simulated for a 200 K temperature increase. The two layers of the bimorph are 1 micron Aluminum (top) and 0.4 microns Tungsten (bottom).

  • S. Pal, H. Xie, "Analysis simulation and fabrication of curved multimorph microactuators ," submitted to Transducers 2011, Beijing, June 5-9, 2011.
  • S. Pal, H. Xie, Analysis and Simulation of Curved Bimorph Microactuators," Microtech Conference and Expo, Anaheim, CA, USA, June 21-24, 2010.
Patents Pending:
  • S. Pal, H. Xie and K. Zawoy "MEMS Designs Based on Curved Multimorph Microactuators that Generate Combined Bending and Twisting", invention disclosure #UF13407.

[1] S. Timoshenko, "Analysis of bi-metal thermostats," Journal of Optical Society of America, vol. 11, pp. 233-256, 1925.
[2] M. S. Weinberg, "Working equations for piezoelectric actuators and sensors," Microelectromechanical Systems, Journal of, vol. 8, pp. 529-533, 1999.

[3] A. Blake, Handbook of Mechanics, Materials, and Structures. New York: Wiley, 1985.


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