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Reducing Pull-In Voltage by Adjusting Gap Shape in Electrostatically Actuated Cantilever and Fixed-Fixed Beams
Department of Electrical and Computer Engineering, University of Saskatchewan, 57 Campus Drive, Saskatoon, Saskatchewan, S7N 5A9, Canada
TRLabs, 111-116 Research Drive, Saskatoon, Saskatchewan, S7N 3R3, Canada
Karlsruher Institut für Technologie, Institut für Mikrostrukturtechnik (IMT), Postfach 3640, D-76021 Karlsruhe, Germany
* Author to whom correspondence should be addressed.
Received: 26 May 2010; in revised form: 9 July 2010 / Accepted: 26 July 2010 / Published: 28 July 2010
Abstract: A gap with variable geometry is presented for both cantilever beam and fixed-fixed beam actuators as a method to reduce the pull-in voltage while maintaining a required displacement. The method is applicable to beams oriented either in a plane parallel to or perpendicular to a substrate, but is most suitable for vertically oriented (lateral) beams fabricated with a high aspect ratio process where variable gap geometry can be implemented directly in the layout. Finite element simulations are used to determine the pull-in voltages of these modified structures. The simulator is verified against theoretical pull-in voltage equations as well as previously published finite element simulations. By simply varying the gap in a linear fashion the pull-in voltage can be reduced by 37.2% in the cantilever beam case and 29.6% in the fixed-fixed beam case over a structure with a constant gap. This can be reduced a further 4.8% by using a polynomial gap shape (n = 4/3) for the cantilever beam and 1.2% for the fixed-fixed beam by flattening the bottom of the linearly varying gap.
Keywords: electrostatic; actuator; gap shape; finite element; MEMS; pull-in voltage; high aspect ratio; LIGA
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Cite This Article
MDPI and ACS Style
Haluzan, D.T.; Klymyshyn, D.M.; Achenbach, S.; Börner, M. Reducing Pull-In Voltage by Adjusting Gap Shape in Electrostatically Actuated Cantilever and Fixed-Fixed Beams. Micromachines 2010, 1, 68-81.
Haluzan DT, Klymyshyn DM, Achenbach S, Börner M. Reducing Pull-In Voltage by Adjusting Gap Shape in Electrostatically Actuated Cantilever and Fixed-Fixed Beams. Micromachines. 2010; 1(2):68-81.
Haluzan, Darcy T.; Klymyshyn, David M.; Achenbach, Sven; Börner, Martin. 2010. "Reducing Pull-In Voltage by Adjusting Gap Shape in Electrostatically Actuated Cantilever and Fixed-Fixed Beams." Micromachines 1, no. 2: 68-81.