repulsive-force electrostatic actuated micromirror for vector-based display systems

147 Pages·2011·14.05 MB·English

REPULSIVE-FORCE ELECTROSTATIC ACTUATED
MICROMIRROR FOR VECTOR-BASED DISPLAY
SYSTEMS
by
James Chong
A thesis submitted in conformity with the requirements
for the degree of Masters of Applied Science
Graduate Department of Mechanical and Industrial Engineering
University of Toronto
© Copyright by James Chong, 2011
REPULSIVE-FORCE ELECTROSTATIC ACTUATED
MICROMIRROR FOR VECTOR-BASED DISPLAY SYSTEMS
James Chong
Masters of Applied Science
Graduate Department of Mechanical and Industrial Engineering
University of Toronto
2011
Abstract
This thesis presents the design and development of a novel two-axis micromirror utilizing
electrostatic, repulsive-force rotational actuators for laser scanned vector display systems. The
micromirror consists of a 1.0 mm reflective mirror plate that can be rotated at high speeds to
steer a laser beam to generate images. Fabricated using PolyMUMPs, the micromirror is
operated in a non-resonant mode between 0 V and 200 V and can achieve a maximum optical
scanning angle of ±2.6° in each axis with a settling time as fast as 2.75 ms and a first resonant
frequency of 1400 Hz. Open-loop control methods were developed for image correcting and
improving image quality. The micromirror was integrated into a portable, handheld vector
display device which included designing and developing driving circuits, device firmware,
mechanical components and optical components.
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Acknowledgments

I would like to extend my acknowledgment to my supervisors Professor Ridha Ben Mrad and
Professor Siyuan He for giving me the invaluable knowledge, support, and opportunity to pursue,
survive, and succeed in my M.A.Sc. program. Throughout my program, they have consistently
pushed my knowledge to the limits with their guidance and encouragement.
I would also like to thank Peng Yang and CMC Microsystems for their technical help and
support with PolyMUMPs and providing financial support through their Integration, Packaging
and Assembly programs. Without offering subsidized PolyMUMPs services and technology
programs, none of the work would have been possible.
I would also like to thank Ontario Graduate Scholarship Program (OGS), University of Toronto,
and Ryerson University for their financial support.
I would also like to show my appreciation to my fellow labmates at the Mechatronics and
Microsystems Design Laboratory (MMDL), Vainatey Kulkarni, Jalal Ahamed, Paul Chairot,
Mike Schertzer, Sergey Gubarenko, and Chakemeh Shafii and labmates at Ryerson Mechatronics
Research Facility, Soonho Park, Terry Xu, Chao Fan, and Zewdu Hailu for their expert help
when I needed.
Finally, I send my greatest gratitude and appreciation to my parents who have continuously
supported me through everything I have done in life.
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Table of Contents

Chapter 1 Introduction..................................................................................................................1 
1.1  Motivation ............................................................................................................................1 
1.2  Literature Review.................................................................................................................3 
1.2.1  Thermal Actuation ...................................................................................................4 
1.2.2  Electromagnetic Actuation .......................................................................................6 
1.2.3  Electrostatic Actuation .............................................................................................7 
1.3  Literature Review Summary ..............................................................................................13 
1.4  Thesis Outline ....................................................................................................................13 
1.5  List of Contributions ..........................................................................................................13 
Chapter 2 Conceptual Design .....................................................................................................15 
2.1  Constant Finger Width Design...........................................................................................16 
2.1.1  Designing the repulsive actuator ............................................................................17 
2.1.2  Design Considerations ...........................................................................................27 
2.1.3  Model Verification .................................................................................................28 
2.2  Varying Finger Width Designs ..........................................................................................32 
2.2.1  Establishing a Mathematical Procedure .................................................................33 
2.2.2  Optimizing using Newton-Raphson Method .........................................................36 
2.2.3  Designing the Micromirror ....................................................................................41 
2.3  Back-Etching Designs ........................................................................................................42 
2.3.1  Introducing the Back-Etching Step ........................................................................42 
2.3.2  Designing the Micromirror ....................................................................................44 
2.4  Chapter Summary ..............................................................................................................47

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Chapter 3 Analysis .......................................................................................................................49 
3.1  Principle of Operation ........................................................................................................49 
3.2  Experimental Analysis .......................................................................................................51 
3.2.1  Static Performance .................................................................................................53 
3.2.2  Dynamic Performance ...........................................................................................54 
3.3  Chapter Summary ..............................................................................................................56 
Chapter 4 Control Methods ........................................................................................................57 
4.1  Look-up-table .....................................................................................................................57 
4.2  Dwelling Method ...............................................................................................................62 
4.3  Scan Speed Control Method ..............................................................................................65 
4.4  Chapter Summary ..............................................................................................................66 
Chapter 5 Integration ..................................................................................................................67 
5.1  The First Design .................................................................................................................67 
5.1.1  Driving Circuitry ....................................................................................................67 
5.1.2  Control Program.....................................................................................................72 
5.1.3  Optical Components...............................................................................................73 
5.1.4  Fixtures and Enclosure ...........................................................................................76 
5.1.5  Assembly................................................................................................................77 
5.2  The Second Design ............................................................................................................79 
5.2.1  Driving Circuitry ....................................................................................................79 
5.2.2  Programming..........................................................................................................83 
5.2.3  Optical Components...............................................................................................84 
5.2.4  Fixtures and Enclosure ...........................................................................................84 
5.3  Chapter Summary ..............................................................................................................88 
Chapter 6 Conclusions and Recommendations .........................................................................89 
6.1  Conclusions ........................................................................................................................89 
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6.2  Recommendations ..............................................................................................................91 
References .....................................................................................................................................93 
Appendix A Micromirror Mask Designs ...................................................................................99 
Appendix B Repulsive Actuators Optimization Formulas .....................................................107 
Appendix C Electrical Schematic of Vector Display System .................................................111 
Appendix D Mechanical Drawings of Vector Display System ...............................................117 

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List of Tables

Table 2-1. Spring Dimensions. ..................................................................................................... 23 
Table 2-2. Parameters for Back-Etching micromirrors. ................................................................ 47 
Table 5-1. Bill of materials for vector display device. ................................................................. 70 
Table 5-2. Bill of materials for portable handheld vector display device. .................................... 80 

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List of Figures

Figure 1-1. Illustration of a simplified bimorph actuator. .............................................................. 5 
Figure 1-2. Illustration of a simplified single bent-beam actuator. ................................................. 5 
Figure 1-3. Illustration of a simplified parallel-plate actuator. ....................................................... 7 
Figure 1-4. Illustration of a simplified combdrive actuator. ........................................................... 8 
Figure 1-5. Illustration of a simplified repulsive-force actuator. .................................................... 9 
Figure 1-6. Electric field lines generated from the repulsive-force actuator. ............................... 10 
Figure 2-1. Conceptual micromirror design. ................................................................................. 17 
Figure 2-2. Conceptual actuator design. ....................................................................................... 18 
Figure 2-3. Side view of a finger being repelled. ......................................................................... 18 
Figure 2-4. Dimensioning the fingers for N=7 & N=9 using g . ............................................... 21 
max
Figure 2-5. Typical serpentine spring. .......................................................................................... 23 
Figure 2-6. Coventor mesh model of actuator to simulate stiffness. ............................................ 24 
Figure 2-7. Simulation results of actuator stiffness at T = 200 μN·μm. ....................................... 25 
Figure 2-8. Solutions to finger width optimization problem. ....................................................... 26 
Figure 2-9. Strengthened areas of repulsive-force actuator. ......................................................... 27 
Figure 2-10. Widths for repulsive-force actuator. ........................................................................ 28 
Figure 2-11. Plot of the rotation angle at an applied voltage. ....................................................... 29 
Figure 2-12. Mesh model for multi-physics simulation................................................................ 30 
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Figure 2-13. Coventor results at V = 100V. .................................................................................. 31 
Figure 2-14. Displacement results from analytical model and Coventor simulation. .................. 32 
Figure 2-15. Actuator with varying finger lengths and widths. .................................................... 34 
Figure 2-16. PolyMUMPs with two layers and back-etching....................................................... 44 
Figure 2-17. Dimensioned serpentine springs. ............................................................................. 44 
Figure 3-1. SEM graphic of the two-axis micromirror (a) no voltage is applied (b) rotation is
exhibited when voltage is applied. ................................................................................................ 49 
Figure 3-2. Two-axis micromirror driven by four repulsive-force actuators. ............................... 50 
Figure 3-3. Apparatus setup for performance testing. .................................................................. 51 
Figure 3-4. Photograph of micromirror wire bonded in a DIP40 packaged chip. ........................ 52 
Figure 3-5. Alignment of main optical components for performance tests. ................................. 53 
Figure 3-6. Static performance of the micromirror. ...................................................................... 54 
Figure 3-7. Dynamic performance in the time domain. (a) Step input of 200 V to 0 V. (b) Step
input of 0 V to 200 V. ................................................................................................................... 55 
Figure 3-8. Dynamic performance in the frequency domain. (a) Magnitude response. (b) Phase
response......................................................................................................................................... 56 
Figure 4-1. Points for the look-up-table. ....................................................................................... 58 
Figure 4-2. Vector based display setup for testing control methods. ............................................ 59 
Figure 4-3. Alignment of main optical components for displaying images. ................................ 60 
Figure 4-4. Voltage waveform patterns for a cross pattern. ......................................................... 61 
Figure 4-5. Demonstrated shapes created using the micromirror (a) partial butterfly curve (b)
rhodonea curve (c) star pattern ..................................................................................................... 62 
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Figure 4-6. Voltage waveform for cross pattern with dwelling implemented. ............................. 63 
Figure 4-7. Test patterns for assessing techniques to reduce ringing. .......................................... 64 
Figure 4-8. Result of patterns with different dwell times (35 fps). ............................................... 64 
Figure 4-9. Voltage waveform for cross pattern with scan speed control implemented. ............. 65 
Figure 4-10. Result of patterns with scan speed controlled (35 fps). ........................................... 66 
Figure 5-1. Portable laser scanned vector display device. ............................................................ 67 
Figure 5-2. PCB driving control board (left) top side (right) bottom side. ................................... 68 
Figure 5-3. Block diagram of control circuitry. ............................................................................ 70 
Figure 5-4. Circuit board design of first design (top) component side (bottom) solder side. ....... 71 
Figure 5-5. Micromirror wire bonded and mounted on PCB........................................................ 74 
Figure 5-6. Estimating maximum laser beam diameter. ............................................................... 75 
Figure 5-7. Fixtures supporting the optical components. ............................................................. 76 
Figure 5-8. 3D prototyped top and bottom enclosures. ................................................................ 77 
Figure 5-9. Solidworks model of handheld vector display device. ............................................... 77 
Figure 5-10. Demonstration of handheld vector display device. .................................................. 78 
Figure 5-11. Circuit board design of second design (top) component side (bottom) solder side. 81 
Figure 5-12. Block diagram of control circuitry. .......................................................................... 83 
Figure 5-13. Optical alignment of main components. .................................................................. 84 
Figure 5-14. Miniature stage concept. .......................................................................................... 85 
Figure 5-15. Exploded assembly and assembly of micromirror adjustable fixture. ..................... 86 
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