2axis MEMS mirror for rasterscanning displays

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2-axis MEMS mirrorfor raster-scanning displays

• Greg Horn and Jay Longson
• EE 215

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Design Goals
Proof of Concept
Raster-scanning display with the following
criteria
Laser

• Project 200 x 200 pixels
• Spanning an area of 0.5m2 from a projection
  distance of 4m
• Refresh rate of 30 fames per second

0.5m
2-axis mirror
4m
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Design Goals
Sweep Angle and Frequency
For 0.5m by 0.5m at 4m, need sweep of 1degree
For 200 x 200 pixels at 30fps, need one mode at
30Hz and other mode at 3KHz.
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Analytical Analysis
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Analytical Analysis
Electrostatic Torque
Assumptions -Field parallel to each surface
-Boundary conditions mirror ground and
electrode at V0 -Field magnitude invariant
along field lines
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Analytical Analysis
Electrostatic Torque
Apply boundary conditions
Solve for E
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Analytical Analysis
Electrostatic Torque
E Field!!!
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Analytical Analysis
Electrostatic Torque
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Analytical Analysis
Electrostatic Torque
(so take derivative)
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Analytical Analysis
Sprint Constant - Torsional Mode
Spring Constant (torsional)
2 Liu, Chang, "Foundations of MEMS", Upper
Saddle River, NJ, Pearson Prentice Hall, 2006
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Analytical Analysis
Pull-in Values - Torsional Mode
Matlab script
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Analytical Analysis
Pull-in Values - Torsional Mode
Matlab script
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Analytical Analysis
Pull-in Values - Torsional Mode
Values Pull in Voltage 14.1 V (FEA 14V -
15V) Pull in Angle 0.81 degrees (FEA 0.75-.95
degrees)
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Analytical Analysis
Resonant Frequency - Torsional Mode
Resonant Frequency
f 2.407KHz (FEA 2.517KHz)
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Analytical Analysis
Spring Constant - Cantilever Mode
(Beam theory goes out the window)
5 Young, W.C., Roark's Formulas for Stress and
Strain, 6th ed. McGraw-Hill. 1989
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Analytical Analysis
Spring Constant - Cantilever Mode
Extrapolate from FEA resonant frequency value
k? 10.3 10-9
In Matlab code, this implies pull in voltage of
19.1V, angle of 0.91 degrees -gtClose to FEA
result of 17V 18V, 0.6 0.8 degrees
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Finite Element Analysis
What FEA told us that we didnt already know
-Sag in the mirror may reduce the pull-in
voltage, although not apparent though voltage vs
displacement FEA analysis.
-New mode of resonance (trampoline mode) may
cause mode coupling problem between trampoline
mode and cantilever mode.
Resonant frequency Mode 1, torsional 2.52KHz
Mode 2, trampoline 4.86KHz Mode 3,
cantilever 5.09KHz
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Finite Element Analysis
Cantilever Mode
FEA Results
Pull-in voltage 17 - 18V Pull-in angle 0.6 0.8
degrees
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Finite Element Analysis
Torsional Mode
FEA Results
Pull-in voltage 14 - 15V Pull-in angle 0.8 0.95
degrees
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Finite Element Analysis
Convergence Issues
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Test Structures
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Proposed Test Procedure
Driver Circuit Schematic
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Proposed Test Procedure
Driver circuit waveform
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Conclusion
Torsional Mode
Cantilever Mode
-Frequency exceeds requirement for 100 x 100
pixel resolution, 30fps
-Tilt angel and pull-in voltage are reasonable
for proof of concept
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References
1 Senturia Stephen D., "Microsystem design",
Boston, Kluwer Academic, 2002 2 Liu, Chang,
"Foundations of MEMS", Upper Saddle River, NJ,
Pearson Prentice Hall, 2006 3 Kubby, Joel. EE
215 lectures. UC Santa Cruz, 2007 4 PolyMUMPS
Design Handbook, MEMSCap Inc. 5 Young, W.C.,
Roark's Formulas for Stress and Strain, 6th ed.
McGraw-Hill. 1989
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Layout!!