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Research Papers

Input and Design Optimization Under Uncertainty to Minimize the Impact Velocity of an Electrostatically Actuated MEMS Switch

[+] Author and Article Information
M. S. Allen1

Department of Engineering Physics, University of Wisconsin-Madison, 535 Engineering Research Building, 1500 Engineering Drive, Madison, WI 53706msallen@engr.wisc.edu

J. E. Massad, R. V. Field

Applied Mechanics Development, Sandia National Laboratories, Albuquerque, NM 87185

C. W. Dyck

RF/Optoelectronics, Sandia National Laboratories, Albuquerque, NM 87185

1

Corresponding author.

J. Vib. Acoust 130(2), 021009 (Feb 06, 2008) (9 pages) doi:10.1115/1.2827981 History: Received April 18, 2007; Revised September 14, 2007; Published February 06, 2008

The dynamic response of a radio-frequency (RF) microelectromechanical system to a time-varying electrostatic force is optimized to enhance robustness to variations in material properties and geometry. The device functions as an electrical switch, where an applied voltage is used to close a circuit. The objective is to minimize the severity of the mechanical impact that occurs each time the switch closes because severe impacts have been found to significantly decrease the life of these switches. Previous works have demonstrated that a classical vibro-impact model, a single-degree-of-freedom oscillator subject to mechanical impact with a single rigid barrier, captures the relevant physics adequately. Certain model parameters are described as random variables to represent the significant unit-to-unit variability observed during fabrication and testing of a collection of nominally identical switches; these models for unit-to-unit variability are calibrated to available experimental data. Our objective is to design the shape and duration of the voltage waveform so that impact kinetic energy at switch closure is minimized for the collection of nominally identical switches, subject to design constraints. A voltage waveform designed using a deterministic model for the RF switch is found to perform poorly on the ensemble. An alternative waveform is generated using the proposed optimization procedure with a probabilistic model and is found to decrease the maximum impact velocity by a factor of 2 relative to the waveform designed deterministically. The methodology is also applied to evaluate a design change that reduces the impact velocity further and to predict the effect of fabrication process improvements.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematic of RF MEMS switch

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Figure 2

Optical microscope image of RF MEMS switch

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Figure 3

PDFs of and histograms of available data for (a) elastic modulus of plate, (b) electrostatic gap, (c) plate thickness, and (d) travel distance

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Figure 4

One thousand sample histograms and PDF estimates of correlated variables, (a) effective mass and (b) effective stiffness, generated from the distributions shown in Fig. 3

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Figure 5

Sample actuation voltage waveform and parameter definitions

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Figure 6

Present design with a deterministic model: voltage waveform optimized for a deterministic switch model and the ensemble displacement and velocity response

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Figure 7

Present design with a deterministic model: histogram of the maximum contact velocity for the ensemble of switches using a waveform optimized for a deterministic switch model

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Figure 8

Present design with a probabilistic model: voltage waveform optimized under uncertainty and ensemble displacement and velocity responses

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Figure 9

Present design with a probabilistic model: histogram of the maximum contact velocity for the ensemble of switches after waveform OUU

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Figure 10

Modified design with a probabilistic model: voltage waveform optimized under uncertainty and resulting ensemble displacement and velocity responses

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Figure 11

Modified design with a probabilistic model: histogram of the maximum contact velocity for the ensemble of switches after waveform OUU

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Figure 12

Present design with process repeatability improved: histogram of the maximum contact velocity for the ensemble of switches for the present design after waveform OUU

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Figure 13

Estimates of the PDFs of contact velocity for the ensemble of switches using (1) waveform optimized for deterministic model, (2) the waveform optimized under uncertainty for the present design, and (3) waveform optimized under uncertainty after modifying the switch design

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