MetalMUMPs Processâ submitted in Journal of Mechanical Design. ...... The resonant frequency of the 1-DoF oscillator is designed to overlap the flat region of the 2-DoF ..... A ring, supported by semicircular rings, was built on top of CMOS chips. ...... Psd Voigt Fit ...... [16] http://www.intellisensesoftware.com/modules/sme.html.
DESIGN, FABRICATION AND CHARACTERIZATION OF METALMUMPs BASED MEMS GYROSCOPES
Rana Iqtidar Shakoor
A DISSERTATION SUBMITTED TO THE DEPARTMENT OF CHEMICAL AND MATERIALS ENGINEERING PAKISTAN INSTITUTE OF ENGINEERING AND APPLIED SCIENCES IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY.
2010
Declaration I declare that all material in this thesis which is not my own work has been identified and that no material has previously been submitted and approved for the award of a degree by this or any other university.
Signature: _________________________________ Author‟s Name:
Rana Iqtidar Shakoor
It is certified that the work in this thesis is carried out and completed under my supervision.
Supervisor:
Dr. Muhammad Masood ul Hassan Pakistan Institute of Engineering and Applied Sciences, Nilore, Islamabad.
Co-Supervisor:
Dr. Shafaat A. Bazaz GIK Institute of Engineering Sciences and Technology, Topi, Distt. Swabi.
ii
Abstract This Ph.D. dissertation reports dynamical systems and structural designs for an efficient 3-DoF non-resonant as well as 2-DoF resonant micromachined vibratory gyroscopes. All prototypes are fabricated using low-cost commercially available standard MEMS fabrication processes, MetalMUMPs. The proposed non-resonant designs are half the size of the previously available designs in this category. Mainly a 3-DoF design concept has been explored in this dissertation to achieve a dynamical system with wide bandwidth frequency responses in the drive-mode while the sense-mode frequency response is aimed to be overlapped without active control. Conventional comb drive based electrostatic actuator has been employed to drive the microgyroscope. Active and passive mass configuration has been implemented to achieve dynamic amplification of drive mass for higher drive displacements thus improving the sensitivity of the microgyroscopes. A detailed FEA based simulation methodology has been developed for drive as well as sense-mode characterization of the microgyroscope. A chevron-shaped thermal actuator has been introduced to drive the proof mass of 3-DoF non-resonant and 2-DoF resonant microgyroscopes for higher drive displacements at lower applied voltage. The characterization results of thermally actuated resonant gyroscope shows high drive direction amplitude of 7.36µm at low actuation static voltage of 0.7V. When the device is operated using a 1.3Vac signal, a peak-to-peak drive displacement of 4.2µm is achieved with a power consumption of 0.36W. The results of this work introduce and demonstrate a new paradigm in MEMS gyroscopes, where conventional comb drive actuator may be replaced with thermally actuated chevronshaped actuators in future. These actuators have low damping compared to electrostatic comb drive actuators which may result in high quality factor microgyroscopes operating at atmospheric pressure. These types of microgyroscopes are expected to yield reliable measurements of angular rate, thus enhancing their applications in automotive to aerospace and consumer electronics markets. iii
List of Publications This disseration is based on the following Journal as well as international conference publications. [1] Rana I. Shakoor, Shafaat A. Bazaz, M. Kraft, Y. Lai, M.M. Hasan “Thermal actuation based 3-DoF Non-resonant Microgyroscope using MetalMUMPs.” Sensors, 2009, pp. 2389-2814. [2] R. I. Shakoor, S.A. Bazaz, M. Burnie, Y. Lai M.M. Hasan “Electrothermally Actuated Resonant Rate Gyroscope Fabricated using the MetalMUMPs” accepted for publication in Microelectronics Journal. [3] R. I. Shakoor, S.A. Bazaz, Mubasher Saleem, M.M. Hasan “Mechanically Amplified 3-DoF Non-Resonant MEMS gyroscope Fabricated in Low Cost MetalMUMPs Process” submitted in Journal of Mechanical Design. [4] M. Burnie, Y. Lai, Rana I. Shakoor, Shafaat A. Bazaz, “Design and Simulation of Thermally Drive Gyroscopes” proceeding of 2nd IEEE Microsystems and Nanoelectronics Research Conference, Ottawa, Canada, October 13-14, 2009. [5] Rana I. Shakoor, Shafaat A. Bazaz, M. M. Hasan, “Design, Modeling and Simulation of Electrothermally Actuated Microgyroscope Fabricated using the MetalMUMPs” proceeding of THERMINIC 2009, Leuven Belgium. October 7-9, 2009. [6] Rana I. Shakoor, Shafaat A. Bazaz, M. M. Hasan. “3-DoF Dual-Mass Nickel MEMS
Gyroscope
utilizing
Chevron-Based
Actuation”
proceedings
of
International Conference of the Chinese Society of Micro/Nano Technology (CSMNT 08), Beijing, China. November 20-22, 2008 [7] Rana I. Shakoor, Shafaat A. Bazaz, M. M. Hasan. “Design of Dual-Mass MEMS Gyroscope with 2-DoF Drive Mode Oscillator” proceedings of IEEE International Conference on Semiconductor Electronics (ICSE 2008), Johor Bahru, Malaysia. November 25-27, 2008
iv
[8] Rana I. Shakoor, Shafaat A. Bazaz, Y. Lai and M. M. Hasan “Comparative Study on Finite Element Analysis & System Model Extraction for Non-Resonant 3-DoF Microgyroscope” proceedings of 2008 IEEE International Behavioral Modeling and Simulation (BMAS) Conference, San Jose, California, USA. September 25-27, 2008. [9] Rana I. Shakoor, Imran R. Chughtai, Shafaat A. Bazaz, Muhammad J. Hyder, M. M. Hasan “Numerical Simulations of MEMS Comb-Drive using Coupled Mechanical and Electrostatic Analyses” proceedings of 17th International Conference on Microelectronics 2005 (ICM 05), Islamabad, Pakistan. pp 344349.
v
Acknowledgments I would like to express my deepest gratitude to Dr. Muhammad Masood-ul-Hassan at Pakistan Institute of Engineering & Applies Sciences (PIEAS) for introducing me the amazing field of MEMS. I cannot thank enough to Dr. Shafaat A. Bazaz at GIK Institute of Engineering Sciences & Technology (GIKI) for his continuous guidance, encouragement and support. Both of my supervisors provide me an ideal environment to explore ideas in this emerging field of MEMS. I would also like to thank Prof. Yongjun Lai at MEMS Labs, Queens University, Kingston, ON Canada and Prof. Michael Kraft at Nanoscale System Integration Group, Southampton University, UK for invaluable discussions and advice, and sharing their expertise with me during my research attachments for six months each at the respective universities. I‟m grateful to Mr. Dan Gale and Bob Stevenson at CMC Microsystem and Dr. Noureldin at Royal Military College of Canada (RMC), Kingston, ON Canada for allowing me to have hands-on experience on the MEMS characterization equipment present in their test labs. Again thanks to Dr. Bazaz for helping me in establishing these collaborations through his network of MEMS professionals in Europe and North America. Furthermore, I would like to thank Higher Education Commission, Islamabad, Pakistan and Dr. Steve Jones, Scientific Advisor, The Canon Foundation for Scientific Research, Oxford, UK. Without their financial support, my PhD studies as well as the research attachments at Queens and Southampton University could have not been possible. I am thankful to Dean, Faculty of Electronics Engineering, GIKI, Dr. Junaid Mughal to provide me the administrative support to access the MEMS design and test lab established by Dr. Bazaz at GIKI. I cannot leave unmentioned the support of Dr. Badar Suleman, Dr. Javed Akhtar and Mr. Ikram-ul-Haq at my office for relieving me from my duties for my PhD studies. Without their logistic support, this journey would not have been completed. vi
Friendship is one of the things that make graduate studies affordable and enjoyable and for that I had Amjad, Arshad, Basit, Raffi, Rashid, Rauf, Waheed and Zahid with whom I spent many tough days and tense nights at PIEAS D-hostel during course work, exams and qualifiers. During my research attachments at Queens, I enjoyed the company of Mathew, Peng and Tom in the lab and Bill, Gwen and little Morgan at my residence Kings Street West, Kingston. At Southampton, I had the company of Prasanna, Zak, Ibrahim and John Zeimpekis. How can I forget to mention all Pakistanis at Kingston (for wonderful Aftars during whole month of Ramadan‟07 at Queens Musalah) and Southampton? Here I would like to mention especially Ponam Bhai & his family at Mississauga, ON for their generous hospitality whenever I visited Toronto (which I did very frequently, mostly because of home sickness); and Dildar, Shakeel, Asim and Surtaj( Queens as well as Aftar fellows) during my attachment at Queens University. Furthermore I extremely enjoyed the company of Mohsin, Babar, Shahzad, Tasawer, Aly Hassan, Ali, Fasih, Imran, Irfan, Saffan and Fahad at Southampton. I am also very grateful to the family of Dr. Shafaat at GIK Institute, Topi and their kids for accommodating me during my GIKI visits to discuss my research project with Dr. Bazaz. I would also like to thank Abdul Ghaffar, Afzal and Rasheed at Department of Chemical & Materials Engineering for their cooperation during my five year stay at PIEAS. Finally and foremost, I greatly appreciate the life-long support of my dear parents. Without them, none of my achievements would have been possible. I am deeply thankful to my beloved wife Rubina, my cute daughter Easha and my wonderful son Ahmed for bringing joy and meaning into my life. Without their never ending encouragements, sacrifices and steady support this dream would have not been realized.
vii
Dedication To my dear parents, beloved wife Rubina, cute daughter Easha & wonderful son Ahmed
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Table of Contents List of Figures ................................................................................................................. xiv List of Tables ................................................................................................................... xx 1. Introduction ................................................................................................................... 1 1.1
Vibratory Microgyroscopes .................................................................................... 1
1.2
Classification of Vibratory Microgyroscopes ......................................................... 3
1.3
Applications of Vibratory Microgyroscopes .......................................................... 5
1.4
Development of Micromachined Gyroscope .......................................................... 6
1.4.1
Contribution by Academia and R&D Institutes: ................................................. 6
1.4.2
Contribution by MEMS Industry: ..................................................................... 10
1.5
Research Motivation ............................................................................................. 12
1.6
Research Objective ............................................................................................... 13
1.7
Outline of Dissertation .......................................................................................... 15
References ......................................................................................................................... 17 2. Design Implementation of Micromachined Vibratory Gyroscopes ....................... 23 2.1
Introduction ........................................................................................................... 23
2.2.
Dynamics of Vibratory Microgyroscope .............................................................. 24
2.2.1 2.3
Rotating Coordinate Systems ........................................................................... 25 Mechanical Design Implementation ..................................................................... 27 ix
2.4.1
Microsuspension Design ................................................................................... 27
2.3.2
Damping Estimation ......................................................................................... 29
2.4
Actuation Mechanisms.......................................................................................... 31
2.4.1
Electrostatic Actuation Mechanism .................................................................. 31
2.4.2
Electrothermal actuation Mechanism ............................................................... 34
2.5
Sensing Mechanisms ............................................................................................. 35
2.5.1 2.6
Capacitive Sensing ............................................................................................ 36 Fabrication of Prototypes ...................................................................................... 37
2.6.1
Fabless Strategy ................................................................................................ 37
2.6.2
Proposed MUMPs Process................................................................................ 39
Conclusion ........................................................................................................................ 40 References ......................................................................................................................... 41 3. 3-DoF Electrostatic Microgyroscope ......................................................................... 45 3.1
3-DoF Design Concept ......................................................................................... 45
3.1.1
3-DoF System with 2-DoF Drive-Mode ........................................................... 46
3.1.2
Gyroscope Dynamics ........................................................................................ 48
3.1.3
Mechanical Design Implementation: ................................................................ 50
3.1.3.1
Suspension Design .................................................................................... 50
3.1.3.2
Damping Estimations ................................................................................ 52
3.1.4 3.2
The Coriolis Response ...................................................................................... 54 Prototype Modeling and Fabrication .................................................................... 54 x
3.2.1
Parametric optimization .................................................................................... 54
3.2.2
Dynamic Amplification: ................................................................................... 56
3.2.3
Prototype Fabrication ........................................................................................ 57
3.2.4
Prototype Design:.............................................................................................. 59
3.3
Simulation Results ............................................................................................... 60
3.4
Experimental Results ............................................................................................ 63
3.4.1
Drive-mode Characterization ............................................................................ 64
3.4.2
Sense-mode Characterization............................................................................ 66
3.4.3
Overall System Response ................................................................................. 68
Conclusion ........................................................................................................................ 68 References ......................................................................................................................... 70 4. Parametric Modeling of Microgyroscope using Model Order Reduction ............. 71 4.1
Introduction ........................................................................................................... 72
4.2
System Model Extraction (SME) .......................................................................... 73
4.2.1
SME Methodology ............................................................................................ 74
4.2.2
Systematic Implementation ............................................................................... 76
4.3
Simulation Methodology ...................................................................................... 76
4.3.1
Parametric Modeling of Comb Drive Actuator Through SME ........................ 77
4.3.2
FEM Results...................................................................................................... 83
4.3.3
SME Results..................................................................................................... 87
xi
Conclusion ........................................................................................................................ 91 References ......................................................................................................................... 93 5. Electrothermally Actuated Non-Resonant Microgyroscope ................................... 96 5.1
Introduction ........................................................................................................... 97
5.2
Design Concept and its Implementation ............................................................... 98
5.2.1
Non-resonant 3-DoF Micromachined Vibratory Gyroscopes (MVG).............. 98
5.2.2
Suspension Design Implementation:............................................................... 100
5.2.3
Damping Estimation: ...................................................................................... 101
5.3
Prototype Modeling and Fabrication .................................................................. 101
5.3.1
Design parameters and considerations ............................................................ 101
5.3.2
Prototype Fabrication ...................................................................................... 104
5.4
FEM Methodology .............................................................................................. 106
5.4.1
Modal Analysis ............................................................................................... 106
5.4.2
Static Analysis ................................................................................................ 110
5.4.3
Dynamic Analysis ........................................................................................... 113
5.4.4
Coriolis Response: .......................................................................................... 117
5.4.5
Capacitive Detection using Parallel Plates ..................................................... 119
5.4.6
Estimated Power Consumption ....................................................................... 119
Conclusion ...................................................................................................................... 121 References ....................................................................................................................... 123
xii
6. Electrothermally Actuated Resonant Microgyroscope ......................................... 126 6.1
Introduction ......................................................................................................... 126
6.2
Microgyroscope Design and Simulations ........................................................... 127
6.2.1
Suspension Design .......................................................................................... 128
6.2.2
FEM Simulations ............................................................................................ 129
6.3
Prototype Fabrication .......................................................................................... 131
6.4
Implementation and Test Results ........................................................................ 133
6.4.1
Design Implementation .................................................................................. 133
6.4.2
Testing Methodology ...................................................................................... 135
6.5
Experimental Evaluation ..................................................................................... 136
6.5.1
Static Characterization .................................................................................... 136
6.5.2
Sense-mode Characterization......................................................................... 138
6.5.3
Drive-mode Characterization .......................................................................... 140
6.5.4
Power Analysis ............................................................................................... 142
Conclusion ...................................................................................................................... 143 References ....................................................................................................................... 144 7. Conclusions ................................................................................................................ 146 7.1
Future Recommendations ................................................................................... 148
xiii
List of Figures Figure 1.1: Operating principle of Micromachined Vibratory Gyroscope …………..… 2 Figure 1.2: Classification of the Micromachined Vibratory Gyroscopes. ......................... 4 Figure 2.1: Representation of a particle moving in non-inertial frame B with respect to inertial frame A. ................................................................................................................ 24 Figure 2.2: Some commonly implemented microsuspension designs in MEMS ............ 28 Figure 2.3: Fixed-Guided beam under translational deflection. ...................................... 28 Figure 2.4: Illustration of couette flow damping ............................................................. 29 Figure 2.5: Squeeze-film damping................................................................................... 30 Figure 2.6: Model of comb drive showing movable comb with 30 fingers, fixed comb, folded flexure spring, shuttle mass and its anchor points. ................................................ 32 Figure 2.7: (a) Schematic diagram of a typical finger pair showing the details of fixed and movable fingers. Thickness (t) of the comb is 2 µm, length of the finger is 15 µm width (w) is 2 µm, whereas “l” is the initial finger overlap which is variable in our Comb drive-model. Voltage V is applied at fixed Comb where as movable comb is grounded.(b): SEM image of comb drive. ........................................................................ 33 Figure 2.8: An illustration of parallel plate electrostatic actuator. .................................. 34 Figure 2.9: Schematic of Chevron-shaped thermal actuator (a) top View (b) cross section B-B view. .......................................................................................................................... 36 Figure 2.10: Implementation of the differential sense capacitors for response sensing. . 37 Figure 2.11: Cross sectional view of a microrelay fabricated using all layers of the MetalMUMPs process (Figure not to scale) [31]. ............................................................ 39 Figure 3.1: 3-DoF design concept with 2-DoF drive and 1-DoF sense-mode oscillators. ........................................................................................................................................... 46 Figure 3.2: Micromachined Vibratory Gyroscopes with 2-DoF sense-mode. ................. 47 Figure 3.3: Representation of position vectors of the proof masses m1 and m2 of the gyroscope relative to the rotating gyroscope frame B. ..................................................... 48 Figure 3.4: Lumped mass-spring model of microgyroscopes.......................................... 49 xiv
Figure 3.5: SEM illustration of the folded flexures attached with the drive as well as sense mass. ........................................................................................................................ 51 Figure 3.6: (a) Lumped mass-spring-damper model for 2-DoF drive-mode oscillator (b) lumped mass-spring-damper model for 1-DoF sense-mode oscillator of 3-DoF gyroscope. ........................................................................................................................................... 55 Figure 3.7: Microgyroscope fabricated through MetalMUMPs process using L-Edit of MEMSPro ......................................................................................................................... 57 Figure 3.8: A-A‟ Cross sectional views of a microgyroscope ......................................... 58 Figure 3.9: Process flow for the fabrication of microgyroscope using MetalMUMPs in MEMSPro (a) N-type silicon wafer, (b) 2µm thick isolation oxide layer, (c) patterning of 0.35µm thick silicon nitride layers,(d) patterning of 0.7µm thick Polysilicon layer and (e) patterning of anchor metal layer (f) patterning of 20µm electroplated structural layer of Ni and trench etch in the substrate. ..................................................... 58 Figure 3.10: (a) First drive direction mode at 1.16kHz (b) second drive-mode at 2.31kHz and (c) sense-mode at 1.63kHz.. ....................................................................................... 62 Figure 3.11: Microsystem Analyzer MSA-400, utilized to characterize the microgyro at Nanoscale System Integration Group, University of Southampton, UK... ....................... 63 Figure 3.12: Drive-mode response of the microgyroscope from 700Hz to 850Hz showing the active and passive mass resonant peak at 754Hz ........................................................ 65 Figure 3.13: Drive-mode response of the gyroscope from the 2.0kHz to 2.5kHz range showing active and passive mass resonance peak at 2.17kHz... ....................................... 65 Figure 3.14: Frequency response of the isolated passive mass in drive-mode showing its resonant frequency at 1.508kHz instead of analytically calculated 1.308kHz. ................ 66 Figure 3.15: Frequency response of the 1-DoF sense-mode oscillators showing the resonant peak 1.868kHz instead of 1.639kHz. ................................................................. 67 Figure 4.1: Overview of the SME approach for the MEMS. N is the number of free nodes in the model. ........................................................................................................... 75 Figure 4.2: Outline of our initial 3-DoF Microgyroscope without actuator to extract macromodel....................................................................................................................... 78 xv
Figure 4.3: Schematic of SYNPLE to optimize the comb drive parameters using the macromodel of the gyroscope. .......................................................................................... 78 Figure 4.4: (a)-(e): Results of simulations in SYNPLE to predict the effect of different comb drive performance parameters like number of fingers, applied voltages and thickness upon the generated force and drive displacements……………………………81 Figure 4.5: Proposed Gyroscope design with comb drive actuator having parameters listed in Table 4.1. ............................................................................................................. 82 Figure 4.6: FEA simulation showing drive displacement of 0.060µm when 50Vdc is applied. .............................................................................................................................. 85 Figure 4.7: FEA simulation showing drive displacement of 0.11µm in response to a rotation rate of 10 rad/sec. The drive-mode was excited with a 50Vac +50Vdc at 1.65kHz. ........................................................................................................................................... 86 Figure 4.8: 2-DoF Drive-mode response showing two resonant frequencies located at 1.18kHz and 2.33kHz. ...................................................................................................... 86 Figure 4.9: 1-DoF sense-mode oscillator response showing a resonant peak located at 1.65kHz ............................................................................................................................. 86 Figure 4.10: SYNPLE model used to verify static analysis results. Dialogue box showing a drive displacement of 0.0577µm, closely in agreement with FEA based simulation results of 0.060µm. ........................................................................................................... 87 Figure 4.11: Model used to verify dynamic analysis results. Dialogue box shows a drive displacement of 0.108µm, closely in agreement with FEA based dynamic simulation results of 0.110µm when 50Vac is applied at sense-mode frequency of 1.65kHz. ........... 88 Figure 4.12: Full schematic of SYNPLE model for 3-DoF non-resonant Micromachined Vibratory Gyroscope. ........................................................................................................ 89 Figure 4.13: Coriolis feedback loop. ............................................................................... 89 Figure 4.14: SME transient results: response of drive direction at 1.65kHz . ................. 90 Figure 4.15: SME transient results: response of sense direction at 1.65kHz .................. 90 Figure 4.16: SME transient results: response of differntial capacitance at 1.65kHz . ..... 91
xvi
Figure 5.1: Proposed Gyroscope model with 2-DoF Drive-mode and 1-DoF sense-mode oscillator............................................................................................................................ 99 Figure 5.2: Lumped mass-spring model of the 3-DoF MVG. ......................................... 99 Figure 5.3: Suspension system configuration that forms the 2-DoF drive and 1-DoF sense-mode oscillators. ................................................................................................... 100 Figure 5.4. Microgyroscope fabricated through MetalMUMPs process using L-Edit of MEMSPro. ...................................................................................................................... 104 Figure 5.5: Cross sectional views of a microgyroscope (a) A-A‟ and (b) B-B‟ ............ 105 Figure 5.6: Process flow for the fabrication of microgyroscope using MetalMUMPs in MEMSPro (a) N-type silicon wafer, (b) 2µm thick isolation oxide layer, (c) patterning of 0.35µm thick silicon nitride layers, (d) patterning of 0.7µm thick Polysilicon layer, (e) patterning of anchor metal layer and (f) patterning of 20µm electroplated structural layer of Ni and trench etch in the substrate. .............................. 105 Figure 5.7: FEM methodology for sequential thermoelectromechanical analysis. Red arrows show the input parameters whereas blue arrows show the output of the respective analysis. ........................................................................................................................... 107 Figure 5.8. (a) Modal analysis results showing resonant frequencies. For better visualization of these oscillations, modal animations were carried out at a scale factor of 100 (b) first drive direction mode at 2.32kHz (c) second drive-mode at 4.43kHz and (d) sense-mode at 3.54kHz. .................................................................................................. 110 Figure 5.9: Drive direction displacement and maximum temperature when a static voltage is applied. ........................................................................................................... 111 Figure 5.10: The predicted drive displacement and temperature at an input of 0.12Vdc (a) shows the drive displacement of 7.64µm and (b) shows 52.06oC temperature achieved by the device.. ...................................................................................................................... 112 Figure 5.11: (a) 2-DoF Drive-mode oscillator frequency response: showing the 1st and 2nd resonant frequency peak at 2.32kHz and 4.43kHz respectively. (b) Combined response of 3-DoF gyroscope with 2-DoF Drive and 1-DoF sense-mode oscillator xvii
demonstrating that the sense-mode resonant frequency is located inside the drive-mode flat region. ....................................................................................................................... 115 Figure 5.12: Displacement profile of the 3-DoF micromachined vibratory gyroscope excited by a sinusoidal voltage of 0.5Vac amplitude and a frequency of 1.77kHz. Due to mechanical amplification, the passive mass m f m2 (blue) achieves a displacement of 4.07μm keeping the active mass m1 (yellow) at a displacement of 1.5μm. .................... 116 Figure 5.13: Temperature profile of the 3-DoF micromachined vibratory gyroscope when excited by a sinusoidal voltage of 0.5Vac amplitude and a frequency of 1.77kHz. ......................................................................................................................................... 117 Figure 5.14: 1-DoF Sense-mode oscillator frequency response when 1 o/s rotation rate is applied along with 0.5Vac. Resonance peak at 3.54kHz with amplitude of 1.70μm is in close agreement with the analytically estimated sense displacement. ............................ 118 Figure 5.15: Capacitive detection mechanism using parallel plates ............................. 119 Figure 6.1: The layout of the electrothermally actuated microgyroscope ..................... 128 Figure 6.2: The suspension system configuration ......................................................... 129 Figure 6.3: Modal analysis results (a) drive-mode at 5.37kHz and (b) sense-mode at 5.2kHz. ............................................................................................................................ 131 Figure 6.4: Microgyroscope fabricated through MetalMUMPs process using L-Edit of MEMSPro. ...................................................................................................................... 132 Figure 6.5: Cross sectional views of a microgyroscope (a) 3D view and (b) 2D view. 132 Figure 6.6: Process flow for the fabrication of microgyroscope using MetalMUMPs in N-type silicon wafer, (b) 2µm thick isolation oxide layer, (c) patterning of Oxide 1 layers, (d) patterning of 0.7µm thick Polysilicon layer, (e) patterning of anchor metal layer and (f) patterning of 20µm electroplated structural layer of Ni and trench etch in the substrate. ......................................................................................................................... 133 Figure 6.7: The scanning electron microscope (SEM) images of the fabricated microgyroscope. The overall size of the device is 1.8×2.0mm2 excluding the bonding pads. ................................................................................................................................ 134 xviii
Figure 6.8: (a): SEM image of chevron-shaped thermal actuator as well as the sense mass with the varying-gap type sense combs. (b): close-up of the sense combs............ 135 Figure 6.9: Microsystem Analyzer MSA-400, utilized to characterize the Microgyroscope at MEMS Laboratory, Queens University, Kingston, ON, Canada..... 136 Figure 6.10: Static analysis response showing a quadratic relationship between the applied voltage and the achieved displacement. ............................................................. 137 Figure 6.11: Static analysis response showing a quadratic relationship between the applied current and the achieved displacement. ............................................................. 137 Figure 6.12: The measurement of the sense-mode resonance characteristics for the fabricated gyroscope using PMA-400 showing a resonant peak at 5.98kHz. ................ 139 Figure 6.13: Schematic illustration of the setup used for the drive-mode characterization. ......................................................................................................................................... 141 Figure 6.14: Part of the chevron-shaped thermal actuator under the microscope in PMA400 showing the evaluation window............................................................................... 141 Figure 6.15: The time wave form of the thermal actuator operating at 2.99kHz. A pure sinusoidal peak-peak displacement of 4.21µm is achieved at 1.3Vac. ............................ 142 Figure 6.16: Power analysis graph of the fabricated device showing a power consumption of 0.36W while operating at the device operating frequency. .................. 142
xix
List of Tables Table 3.1: Comparison of simulated and analytical results for natural frequencies for drive and sense-modes. ..................................................................................................... 61 Table 4.1: Optimal comb drive parameters with dimension optimized using SYNPLE . 83 Table 4.2: Comparison of simulated and analytical results for natural frequencies for 2DoF drive-mode oscillators............................................................................................... 84 Table 5.1: Comparison of simulated and analytical results for natural frequencies for drive and sense-modes. ................................................................................................... 108 Table 5.2: Comparison of the proposed gyroscope the models developed by Alper et al. at Middle East Technical University, (METU) Turkey [21] and by Acar et al. at University of California, Irvine (UCI), USA, [22]. ........................................................ 121
xx
Chapter 1 Introduction In this chapter, an introduction to vibratory microgyroscope is presented including its types and applications. The detailed survey of the previous research carried out by the academia and the Microelectromechanical Systems (MEMS) industry in the area of the conventional as well as non-conventional micromachined gyroscopes is followed by the motivation and objective of the research. In the end, a general layout of this dissertation is presented.
1.1
Vibratory Microgyroscopes
A gyroscope is a device for measuring or maintaining orientation, based on the principles of angular momentum. Conventional gyroscopes like rotating wheel, fiber optic or ring laser are all too bulky and too expensive which limit their use in recent emerging applications. Using the recent developments in micromachining technology, the size of these bulky conventional gyroscopes can be shrinked by an order of magnitude reducing their fabrication cost considerably. The microfabrication also allows the designers to integrate the electronics on the same chip, further reducing the overall size of the packaged device [1]. Almost all microgyroscopes use a vibrating mechanical element to sense angular rate. This sensing element of the microgyroscope can be represented as inertia element with elastic suspension having two degrees of freedom (DoF). This inertia element is often called proof mass which is suspended over the substrate by a suspension system consisting of flexible beams. This proof mass is forced to vibrate in one of the vibrating modes with prescribed amplitude using some actuation mechanism. This mode is usually called primary or drive-mode. When, the proof mass experiences a rotation about a 1
predefined rotational axis i.e. sensitive axis, the resulting Coriolis force causes this proof mass to move in a direction orthogonal to both drive and rotational axes. This vibrating mode is usually referred as secondary or sense-mode. The overall dynamical system usually consists of 2-DoF mass-spring-damper system. The rotation induced Coriolis force causes energy transfer to sense-mode in proportion to the angular rate input. Such microgyroscopes are generally driven at resonance in the drive-mode using electrostatic or electromagnetic actuators. When the gyroscope experience an angular rotation, a sinusoidal Coriolis force at the driving frequency is induced in the direction orthogonal to the drive-mode oscillation. Fig.1.1 demonstrates the operating principle of the resonant Micromachined Vibratory Gyroscope.
Figure 1.1: Operating principle of resonant Micromachined Vibratory Gyroscope In order to achieve maximum possible response gain, it is generally desired to utilize resonance in both the drive and the sense-modes. One approach to achieve this is to design and tune the resonant frequencies of both drive and sense-mode to match. Alternatively, the sense-mode resonant frequency is designed to be slightly shifted from the drive-mode resonant frequency to improve robustness and thermal stability, while sacrificing gain and sensitivity [2]. However such gyroscopes with exact or close mode matching are extremely sensitive to fluctuations in the operating conditions as well as parametric variations in the oscillatory system due to fabrication imperfections. These
2
fabrication tolerances shift the natural frequencies causing mode mismatch and introduce anisoelasticity and quadrature error. Such errors then require compensation by advanced control architectures.
1.2
Classification of Vibratory Microgyroscopes
Micromachined Vibratory Gyroscopes (MVGs) are mainly classified into two types namely angle gyroscope and rate gyroscopes as shown in Fig. 1.2. The angle gyroscopes measure orientation angle directly whereas rate gyroscopes measure rotational rate. Numerical integration of rotation rate is then required to get the information of the object orientation. Most MVG implementations to date are found exclusively in angular rate measuring variety. Angle gyroscopes are considered to be the highest performance gyroscopes [3]. On the basis of the shape and type of the proof mass, these angle gyroscopes are further subdivided into vibrating ring, hemispherical resonating shell or symmetric vibratory shell gyroscopes. Among all angle gyroscopes, only vibrating cylinder and hemispherical resonating gyroscopes showed the potential for the inertial grade gyroscopes. The implementation of the microscale shell type angle gyroscope can be an interesting option but because of microfabrication limitations, it seems difficult in recent times. Since high precisions is required for inertial grade gyroscopes which is really difficult to achieve with the existing lithography based techniques, therefore a 3-DoF high precision shell are difficult, if not impossible, to implement at the microscale [3]. Rate gyroscopes are used to measure the angular rotation rate. These rate gyroscopes have a defined drive axis along which these are continually driven at constant amplitude of oscillations usually by the electrostatic force. The rotation induced Coriolis force is then sensed along the sensing axis, defined orthogonal to the drive axis. In conventional resonant rate gyroscopes the resonant frequencies of drive and sense axes are designed to match to get maximum possible gain and hence the sensitivity. But mode matching requirement in such conventional resonant microgyroscopes makes the system
3
response very sensitive to the fabrication imperfections and fluctuations in the operating conditions. So to get a desired degree of mode matching in such gyroscopes, the designers have to implement advance control system techniques.
Figure 1.2: Classification of the Micromachined Vibratory Gyroscopes. The resonant gyroscope is generally design to operate at or near their resonant peak. At high quality factor, the gain response becomes high. However, the operating bandwidth becomes very narrow. So a dynamical system with high bandwidth can be achieved by expanding the system design space. This expansion in the system design space can be achieved by increasing the DoF of the drive or sense-mode oscillatory system i.e. by designing non-resonant multi-DoF system instead of 2-DoF dynamical system used in conventional rate microgyroscope. This design concept aims to utilize the resonance in either the drive-mode or sense-mode to improve the sensitivity, while maintaining the robust operational characteristics. 3-DoF non-resonant dynamical system consists of structurally decoupled 2-DoF and 1-DoF oscillators in drive and sense-mode respectively. The frequency response of the 2-DoF oscillator consists of two peaks with a flat region between them. This flat region defines the operating frequency region of the 4
gyroscope. The resonant frequency of the 1-DoF oscillator is designed to overlap the flat region of the 2-DoF oscillator. The device is operated at the resonant frequency of the 1DoF oscillator while the amplitude response of the 2-DoF oscillator is inherently constant within the same frequency band.
1.3
Applications of Vibratory Microgyroscopes
Although the conventional rotating wheel, fiber optic and ring laser gyroscope are still dominant in many applications but their size, power hungry mechanism and cost limit their usage in a wider range of industries like automobiles, video games, hand held positioning systems and satellites. However the recent breakthroughs in the development of MEMS and micromachining technologies have made fabrication of miniature sized, low-cost microgyroscopes and their applications possible in that broader market. Moreover, advances in the microfabrication techniques allow the designer to integrate detection and control electronics on the same silicon chip together with the mechanical sensor elements. Thus, miniature vibratory gyroscope designs with innovative microfabrication processes may be an attractive solution to the current inertial sensing market needs. With their extraordinarily reduced size, cost, and weight, microgyroscopes have their potential application in the aerospace industry, military, automotive industry and consumer electronics market. The consumer electronics applications include image stabilization in video cameras, virtual reality products, inertial pointing devices, and computer gaming industry. The automotive industry is using microgyroscopes particularly in automotive chassis control systems (e.g. electronic stability programs and control), high performance navigation and guidance systems and advanced automotive safety systems (e.g. yaw and tilt control, roll-over detection and prevention), and next generation airbag systems and anti-lock brake systems. Miniaturization of gyroscopes has also opened some higher-end applications avenues including micro-satellites, microrobotics, and even implantable devices to cure vestibular disorders.
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1.4
Development of Micromachined Gyroscope
Micromachined inertial sensors have been the subject of intensive research for over three decades since Roylance et al. [4] reported the first micromachined accelerometer in 1979. Since then many authors have published work on various types of MEMS accelerometer. In this section, a comprehensive review of the contribution made by academia as well as MEMS industry in the field of Micromachined Vibratory Gyroscope is presented.
1.4.1
Contribution by Academia and R&D Institutes:
The first MEMS gyroscope was reported by Draper Labs in 1991 utilizing doublegimbals single crystal silicon structure suspended by torsional flexures and demonstrated a resolution of 4o/s/√Hz
over 60Hz bandwidth [5]. Since then different available
fabrication technologies like surface micromachining, bulk micromachining, metal electroforming, LIGA (German acronym for Lithographie, Galvanoformung, Abformung means Lithography, Electroplating, and Molding respectively) and hybrid surface-bulk micromachining have been successfully utilized for the development of various micromachined gyroscopes designs. Draper Labs also reported tuning fork gyroscope with 1 o/s/√Hz resolution at 60Hz bandwidth in 1993 using silicon-on-glass fabrication technique to reduce stray capacitances. The tuning fork is a classical example of the vibratory gyroscope. The tuning fork perforated proof masses are driven out of phase electrostatically with interdigitated comb drives to achieve large amplitude of 10μm. The rotation then excites the out-of-plane rocking mode which is capacitively monitored. The reported device size was 700×700μm2 [6]. Improved version of tuning fork gyroscope was introduced by Draper Labs in 1998 with temperature compensation and better control techniques. The resolution was improved to 0.003o/s/√Hz at 60Hz bandwidth using 10μm thick surface-micromachined polysilicon [7]. In 1994, University of Michigan developed first vibrating ring gyroscope with 0.5o/s/√Hz resolution using metal electroforming technique [8]. This device consisted of a ring, 6
supported by semicircular springs. Drive, sense and balance electrode were located around the structure. The ring was electrostatically excited into an in-plane elliptically shaped primary mode and the transfer of energy to the secondary flexural mode due to the Coriolis force was detected. In 2002, University of Michigan reported another high performance 150μm thick bulk micromachined single crystal silicon vibrating ring gyroscope. The ring was 2.7mm in diameter having high quality factor (Q), good nonlinearity and large sensitivity with 0.003 o/s/√Hz resolutions [9]. In 1994, British Aerospace Systems reported a single crystal silicon ring gyroscope fabricated on glass substrate by Deep Reactive Ion Etching (DRIE) of a 100μm silicon wafer. Later on Silicon Sensing Systems and Sumitomo Precision Products commercialized this sensor with a resolution of 0.5o/s/√Hz over a 100Hz bandwidth [10]. Berkeley Sensor and Actuator Center (BSAC) developed its first integrated z-axis Vibratory Rate Gyroscope in 1996 with a resolution of 1 o/s/√Hz utilizing the integrated surface micromachining process, iMEMS offered by Analog Devices Inc [2]. This z-axis gyroscope had a single proof mass driven in-plane at resonance. Electrostatic frequency tuning of sense-modes was successfully demonstrated to enhance the sensitivity by minimizing the mode mismatching. Furthermore, the quadrature error nullifying technique was employed to compensate the structural imperfections due to fabrication tolerances. Later in 1997, BSAC developed an x-y dual input axis gyroscope with a 2μm quad symmetric circular oscillating polysilicon rotor disc. This gyroscope utilizes torsional drive-mode excitation and two orthogonal torsional sense-modes to achieve a resolution of 0.24o/s/√Hz with cross axis sensitivity ranging from 3% to 16%. Upon the subsequent electrostatic tuning the device showed a performance of 0.05 o/s/√Hz but at the expense of high cross axis sensitivity [11]. In 2000, a z-axis vibratory gyroscope having parallel-plate electrostatic actuation and digital output was developed at BSAC. The structural layer of the proposed device was 2.25µm thick and was developed by the CMOS-compatible IMEMS process by Sandia National Laboratories. Parallel plates provide low actuation voltages with limited drive-mode amplitude. Device showed a resolution of 3o/s/ √Hz at atmospheric pressure [12]. Using the same IMEMS process, 7
another integrated micromachined gyroscope with resonant sensing was reported in 2002 by BSAC. This device was based on frequency modulation of double-ended tuning forks (DETF) due to the generated Coriolis force. A resolution of 0.3o/s/√Hz was demonstrated with the on-chip integrated electronics [13]. In 2003 BSAC developed another vibratory z-axis gyroscope with “Inside Sense Outside Drive (ISOD) suspension configuration using 6µm thick polysilicon structural material co-fabricated with 0.8 CMOS process. This surface micromachined z-axis ISOD frame gyroscope showed a resolution of 0.01o/s/√Hz and scale factor of 1.5mV/o/s at 70milli-Torr pressure [14]. Jet Propulsion Laboratory (JPL) together with University of California, Los Angeles (UCLA) developed a clover-leaf shaped bulk micromachined gyroscope in 1997. The device had a size of 7×7mm2 with a metal post epoxied inside a hole on the silicon resonator to enhance the rotational inertia of the sensing element. This device showed a resolution of 0.02o/s/√Hz with a scale factor of 24mV/o/s and an angle random walk of 6.3o/ √hr [15]. In 2000, Seoul National University reported a hybrid surface-bulk micromachining (SBM) process with DRIE to fabricate high aspect ratio structure with large sacrificial gaps, in a single wafer. New isolation method using sandwiched oxide, Polysilicon and metal films was developed for electrostatic actuation and capacitive sensing. This 40μm thick single crystal silicon micromachined gyroscope demonstrated a resolution of 0.0025o/s/√Hz at 100Hz bandwidth [16]. Carnegie-Mellon University (CMU), in 2001, demonstrated a lateral-axis integrated gyroscope using a maskless post-CMOS micromachining process with a resolution of about 0.5o/s/√Hz [17]. The lateral-axis gyroscope with 5μm thick structure had out of plane actuation and fabricated using Agilent three-metal 0.5μm CMOS process. Residual stress and thermal expansion coefficient mismatch caused curling in the structure and thus limited the device size. CMU also developed a 8μm thick z-axis integrated gyroscope was fabricated using six copper layer 0.18μm CMOS process with dimensions 410×330μm2 [18]. This device showed a sensitivity of 0.8μV/o/s and a resolution of 0.5o/s/ √Hz. In 2003, CMU demonstrated a DRIE CMOS-MEMS lateral axis gyroscope 8
having size a of 1×1 mm2 with a measured resolution of 0.02 o/s/√Hz at 5Hz. This device was fabricated by post-CMOS micromachining using interconnect metal layers to mask the structural etch steps. The device with on-chip CMOS circuitry had in-plane vibration and out of plane Coriolis acceleration detection [19]. In 2004, Middle East Technical University (METU), Turkey presented a symmetrical and decoupled surface micromachined gyroscope fabricated by electroforming thick Nickel on a glass substrate. A capacitive interface circuit which was fabricated in a 0.8μm CMOS process was hybrid connected to the gyroscope, where the circuit had an input capacitance lower than 50fF and a sensitivity of 33mV/fF. Calculations on measured resonance values suggested that the fabricated gyroscope with 16μm-thick structural layer provides a resolution of 0.004o/s/√Hz [20]. In 2005, a single-crystal silicon symmetrical and decoupled (SYMDEC) gyroscope was implemented using the dissolved wafer MEMS process on an insulating substrate at METU. The 12–15μm-thick singlecrystal silicon structural layer with an aspect ratio of about 10 using DRIE patterning provided a high sense capacitance of 130fF, while low parasitic capacitance of only 20fF was achieved due to the insulating substrate. Calculation showed a rate resolution around 0.56o/s with slightly mismatched modes, which revealed that the gyroscope can provide a rate resolution of 0.030o/s/√Hz in 50Hz bandwidth at atmospheric pressure and 0.017o/s/√Hz in 50Hz bandwidth at vacuum operation with matched modes [21]. In 2006, METU demonstrated another rate grade gyroscope using CMOS compatible Ni electroforming process. This gyroscope used 18µm thick Ni structural layer with 2.5µm capacitive gaps for enhanced sense capacitance. This device showed an estimated resolution of 0.05o/s/√Hz in a narrowed response bandwidth of 10Hz in vacuum [22]. In 2005, University of California, Irvine, (UCI) introduced structurally decoupled micromachined gyroscope with increased actuation and detection capacitances beyond the fabrication process limitations. Bulk micromachined prototype gyroscopes with assembled comb drives and detection electrodes exhibited a sensitivity of 0.91mV/o/s, excellent linearity and a resolution of 0.25o/s/√Hz at 50Hz bandwidth at atmospheric pressure [23]. In 2006 UCI demonstrated another micromachined gyroscope with 2-DoF 9
sense-mode oscillator which showed improved robustness to variation in temperature, damping and structural parameters solely by mechanical system design. Bulk micromachined gyroscope showed 5.8μm amplitude with 25Vdc and 3Vac drive signal. The prototype gyroscope exhibited a measured resolution of 0.64o/s/√Hz over 50Hz bandwidth [24].
1.4.2
Contribution by MEMS Industry
Industry always plays a vital role to bridge the gap between R&D and commercialization of any product. Without industrial support it becomes difficult for R&D organizations and academia to work effectively in any field. There are a number of industrial organizations who are striving to commercialize MEMS product through their close liaison with researchers in academia and R&D organizations. In this section, product review of the few micromachined gyroscopes that have been successfully commercialized and available in the market for their use. In 1995, Murata developed a lateral axis surface-micromachined polysilicon gyroscope having sensing electrodes underneath the thin perforated 400×800μm2 polysilicon resonator. This gyroscope was fabricated by diffusing phosphorus into the substrate and driven in lateral axis by electrostatic force. The output signal was detected by the change in capacitance between resonator and the substrate. A resolution of 2o/s/√Hz was reported with high mechanical quality factor (Q-factor) of 2,800 and 16,000 in both drive and sense-mode at pressure below 0.1 Pa [25]. In 1999, Murata reported another DRIE-based 50μm thick bulk micromachined single crystal silicon gyroscope. This device has independent beams for drive and detection modes to minimize the undesired coupling between the drive and sense-modes. A resolution of 0.07o/s/√Hz was demonstrated at 10Hz bandwidth with the device size 800×1200 μm2 [26]. A vibratory ring gyroscope was reported by Delphi in 1997 with an electroplated metal ring structure. A ring, supported by semicircular rings, was built on top of CMOS chips. The measured resolution was 0.1o/s/√Hz over 25Hz bandwidth [27].
10
In 1997, Samsung presented a tunable 7.5μm thick low-pressure chemical vapor deposited polysilicon vibratory microgyroscope with 0.3μm polysilicon sensing electrodes underneath the perforated proof mass [28]. The device, having size 1220x450 μm2 exhibited 0.1o/s/√Hz resolution after vacuum-packaging. In the same year Samsung introduce another in-plane device made from 6.5μm thick polysilicon, fabricated by 5 mask process having four fish-hook spring suspensions. This device demonstrated a resolution of 0.007 o/s/ √Hz at the bandwidth 100 Hz with the dynamic range of +/- 90o/s [29]. In 2000, Samsung demonstrated another bulk micromachined single crystal silicon sensor with mode decoupling. A 40μm thick, wafer-level vacuum packaged sensor exhibited a resolution of 0.013o/s/√Hz [30]. In 1997 Robert Bosch Gmbh, reported first silicon micromachined yaw rate sensor, DRSMM1 that utilized electromagnetic drive and capacitive sensing for automotive applications, with a resolution of 0.4o/s/√Hz [31]. The sensing elements were manufactured by using a mixed bulk and surface micromachining technology. Drivemode amplitude of 50μm was achieved by using permanent magnet inside the sensor package. In 1999 Robert Bosch Gmbh, developed another micromachined angular rate sensor with 11μm thick polysilicon structural layer. This device was fabricated by utilizing silicon surface micromachining with several new process steps. The device demonstrated a 0.4 o/s/√Hz resolution at 10Hz bandwidth [32]. Robert Bosch Gmbh introduced second generation of micromachined angular rate sensors, DRS-MM2 for roll over detection and vehicle navigation system in 2002. The sensor was fabricated in standard silicon surface micromachining technology and packaged under vacuum conditions using a silicon micromachined cap wafer. When an angular rate is applied, tilt movement of an electrostatically driven oscillating disk was detected capacitively by electrodes on the substrate underneath the oscillating disk [33]. The third generation of micromachined angular rate sensors, the DRS-MM3 was introduced by Robert Bosch, Gmbh, in 2007. This surface micromachined gyroscope exhibited a resolution of 0.004o/s/√Hz at 60Hz bandwidth [34].
11
Daimler Benz reported a silicon angular rate sensor with new architecture for automotive applications in 1997. It was a SOI-based bulk-micromachined tuning-fork gyroscope having piezoelectric drive and piezoresistive detection. A thin film of piezoelectric Aluminum Nitride was deposited on one of the tines as an actuator layer. Then the rotation induced shear stress in the step of the tuning fork was piezoresistively detected [35]. Allied Signal developed bulk-micromachined single crystal silicon sensors in 1998, and demonstrated a resolution of 0.005o/s/√Hz at 100Hz bandwidth [36]. HSG-IMIT reported in 2002, reported a 10μm thick polysilicon structural layer gyroscope with an excellent structural decoupling of drive and sense-modes using standard Bosch fabrication process. A resolution of 0.007o/s/√Hz with 100Hz bandwidth was reported [37]. In the same year, Analog Devices Inc. (ADI) developed a dual-resonator z-axis gyroscope having 4μm thick polysilicon structural layer. This device was fabricated by self developed iMEMS process. Two identical proof masses were used to be driven into resonance in opposite directions so that external linear accelerations could be rejected. This first commercial integrated micromachined gyroscope had a measured resolution of 0.05o/s/√Hz at 100Hz bandwidth [38].
1.5
Research Motivation
The flaws in the mechanical structure of the microgyroscope affect its performance, stability and robustness drastically. The main reason behind these flaws is the limited tolerances of the existing photolithography processes. Furthermore, the available microfabrication techniques are not efficient enough to produce the high performance inertial grade sensors. Thus the production of the highly sensitive and reliable microgyroscope with existing microfabrication techniques has become extremely challenging. In conventional microgyroscopes, resonance is used to enhance the response gain and hence the sensitivity of the device by matching the resonant frequencies of the drive and the sense-mode. But the variations in the system parameters due to fabrication tolerances
12
and fluctuations in the operating conditions do not allow a perfect mode matching. The slight variations in the fabrication processes (e.g. photolithography, etching and deposition) and residual stresses affect both the geometry as well as the material properties causing a mismatch between the drive and sense-mode frequencies. Furthermore, the slight temperature variations in the structure also introduce perturbation to the system parameters due to thermally induced localized stresses and temperature dependence of the Young‟s modulus. Extensive research has been carried out to address these issues in conventional resonant gyroscopes. Different designs of symmetric suspensions and resonator systems have been introduced to overcome mode matching and temperature dependence issues. However, in the presence of above mentioned perturbations, none of these symmetric designs can provide the required degree of mode-matching with active tuning and feedback control. The mechanical interference between the modes and mode coupling are other issues which need to be addressed for a stable microgyroscope. In view of the above mentioned issues, current states of the vibratory rate microgyroscopes require an order of magnitude improvement in performance, stability and robustness. All these errors and perturbations have to be compensated by advance control architectures. To eliminate such limitations, complexity of the control electronics can be shifted to the complexity in the dynamical system.
1.6
Research Objective
The objective of this research is to develop new dynamical systems and structural designs for such an efficient non-resonant as well as resonant Micromachined Vibratory Gyroscope using low-cost commercially available standard MEMS processes having low operation voltage which smaller in size compared to previously available designs. Mainly a 3-DoF design concept has been explored in this dissertation to achieve a dynamical system with wide bandwidth in the drive-mode while the sense-mode frequency response is aimed to be overlapped without active control. A detailed modeling
13
and Finite Element Analysis (FEA) based simulation methodology has been developed for the microgyroscope. A novel actuation technique has also been implemented in one of the 3-DoF microgyroscope instead of most commonly used electrostatic comb drive actuator. A thermal actuation based Chevron-shaped actuator has been introduced to achieve higher drive displacements at lower applied voltage in comparison with conventional comb drive based electrostatic actuator. MEMS fabrication is the outcome of highly expensive methods of Integrated Circuit (IC) manufacturing. MEMS and IC fabrication facilities require advanced, highly sophisticated and very expensive equipment starting from few hundreds of thousand and can go to few tens of million dollars. Therefore adopting the fabless manufacturing model, a detailed study of currently available standard MUMPs processes with a special emphasis on MetalMUMPs for the fabrication of our proposed microgyroscope prototypes have also been carried out. MetalMUMPs is a low-cost commercially available MEMS process developed by MEMSCap Inc. USA. This fabless approach focuses on in-house prototype designing and its characterization while using the external processing and manufacturing infrastructures which are commercially available in the market for prototype fabrication. This approach has been implemented successfully in the area of microelectronics/VLSI chip development. MetalMUMPs is a repeatable MUMPs process for known process tolerances as well as characteristics defined process design rules. It ideally suits to the smaller companies and the research institutions with design and characterization expertise but lack of in-house processing and fabrication capabilities. So this research focuses more on design optimization of the proposed prototypes around given constraints and design rules minimum feature size, feature space, layer gap, thickness etc. of MetalMUMPs.
1.7
Outline of Dissertation
In chapter 1, the working principle, types and applications of vibratory microgyroscope along with the prior research work on both conventional and non-conventional
14
micromachined gyroscopes carried out by academia and commercial organizations has been comprehensively covered. Chapter 2 comprehensively covers the dynamics of Micromachined Vibratory Gyroscope with its systematic design implementation. This implementation includes both mechanical as well as electrical components of the microgyroscope. In mechanical design implementation, different suspension designs along with the damping estimations have been discussed whereas different actuation and sensing mechanisms have been discussed in electrical part. After analyzing the drive and sense components towards end of the chapter, the sensing electronics and gyroscope testing and characterization is briefly discussed. Chapter 3 presents non-resonant 3-DoF design approach for microgyros with its systematic design implementation and prototype modeling. Main emphasis of this work is to demonstrate the optimization of gyroscope within the design rules of standard MetalMUMPs. A comprehensive optimization as well as simulation methodology in IntelliSuite has also been developed in this chapter for the proposed device. In the end the experimental setup to test microgyroscopes is described along with the test results of the fabricated device using Microsystem Analyzer, MSA400. Chapter 4 covers the basics of model order reduction (MOR) based system model extraction (SME) technique. This introduces an additional time efficient approach of the gyroscope design optimization. The systematic implementation for the parametric modeling of the comb drive actuator for a microgyroscope in system level simulator of IntelliSuite called SYNPLE is included in this chapter. Using the extracted macromodel, modal, static and dynamic simulations have been carried in SYNPLE. To make a comparison of SME technique with FEA, we repeated the set of simulations for the proposed model in FEA based Thermoelectromechanical module of IntelliSuite. On the basis of the predicted results by both techniques, a comparative study has also been presented in the end. In chapter 5, a novel Nickel based 3-DoF micromachined gyroscope, utilizing Chevronshaped thermal actuators, is proposed. Analytical derivations and finite element 15
simulations are carried out to predict the performance of the proposed device using the thermo-physical properties of the electroplated Nickel. Active-passive mass configuration has been used to improve the sensitivity by utilizing the dynamical amplification. A comprehensive theoretical description, dynamics and mechanical design considerations of the proposed gyroscopes model are also discussed in detail. Finally the prototype modeling and fabrication using MetalMUMPs has also been investigated. In chapter 6, an electrothermally actuated resonant microgyroscope fabricated using MetalMUMPs is presented. A Chevron-shaped thermal actuator has been used to drive the proof mass, whereas parallel plate electrodes have been used for sensing the rotation induced Coriolis force. The proposed model consists of three coupled proof masses that are driven together using a frame. A brief theoretical description of the resonant microgyroscope and mechanical design considerations of the proposed model are discussed. Prototype fabrication using MetalMUMPs has also been investigated in this study. Microsystem Analyzer MSA-400 has been used to test the prototype device at atmospheric pressure. A testing methodology has been devised in this chapter for the test of the microgyroscope. In the end, a comparison is made between the predicted and the experimental results. The last chapter of this dissertation (Chapter 7) concludes this research work on nonresonant as well as resonant microgyroscope and proposes future work in this area.
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Microelectromechanical Systems Workshop (MEMS‟97), Japan, 1997, pp. 272277. [29] K. Y. Park, C. W. Lee, Y. S. Oh, and Y. H. Cho. “Laterally Oscillated and Forcebalanced Micro Vibratory Rate Gyroscope Supported by Fish-hook Shape Springs” Proc. IEEE Microelectromechanical Systems Workshop (MEMS‟97), Japan, 1997, pp. 494-499.
20
[30] K. Y. Park, H. S. Jeong, S. An, S. H. Shin, C.W. Lee, “Lateral Gyroscope Suspended by Two Gimbals through High Aspect Ratio ICP Etching” Proc., IEEE 1999 Int. Conf. on Solid State Sensors and Actuators (Transducers ‟99), Sendai, Japan, June 1999, pp. 972-975. [31] M. Lutz, W. Golderer, J. Gerstenmeier, J. Marek, B. Maihofer, S. Mahler, H. Munzel, and U. Bischof. “A Precision Yaw Rate Sensor in Silicon Micromachining” Transducers 1997, Chicago, IL, June 1997, pp. 847-850. [32] K. Funk, H. Emmerich, A. Schilp, M. Offenberg, R. Neul, F. Larmer, “A Surface Micromachined Silicon Gyroscope using A Thick Polysilicon Layer” Proc., Twelfth IEEE Int. Conf. on Microelectromechanical Systems (MEMS ‟99), Orlando, FL, Jan. 1999, pp. 57-60. [33] T. R. Schellin, M. Lang, W. Bauer, J. Mohaupt, G. Bischopink, L. Tanten et al. “A Low-Cost Angular Rate Sensor in Si-Surface Micromachining Technology for Automotive Application” SAE 1999 World Congr. Detriot, MI, March 1999, Technical paper 1991-01-1931. [34] R. Neul, U. M. Gomez, K. Kehr, W. Bauer, et al. “ Micromachined Angular Rate Sensors for Automotive Applications” IEEE Sensors Journal, Vol. 7, No. 2, February 2007. pp 302-309. [35] R. Voss, K. Bauer, W. Ficker, T. Gleissner, W. Kupke, M. Rose, S. Sassen, J. Schalk, H. Seidel, and E. Stenzel. “Silicon Angular Rate Sensor for Automotive Applications with Piezoelectric Drive and Piezoresistive Read-out” Tech. Dig. 9th Int. Conf. Solid-State Sensors and Actuators (Transducers‟97), Chicago, IL, June 1997, pp. 879-882. [36] R. Hulsing. “MEMS Inertial Rate and Acceleration Sensor” IEEE AES Systems Magazine. November 1998, pp. 17-23. 21
[37] W. Geiger, W.U. Butt, A. Gaisser, J. Fretch, M. Braxmaier, T. Link, A. Kohne, P. Nommensen, H. Sandmaier, and W. Lang. “Decoupled Microgyros and the Design Principle DAVED” Sensors and Actuators A. Physical, Vol. A95, No.23, Jan. 2002, pp. 239-249. [38] J. A. Geen, S. J. Sherman, J. F. Chang, and S. R. Lewis. “Single-Chip Surface Micromachining Integrated Gyroscope with 50deg/hour Root Allan Variance” Dig. IEEE Int. Solid-State Circuits Conf., San Francisco, CA, Feb. 2002, pp. 426427.
22
Chapter 2 Design Implementation of Micromachined Vibratory Gyroscopes In this chapter dynamics of Micromachined Vibratory Gyroscope have been discussed. It is followed by a systematic design implementation of vibratory microgyroscope. This implementation
includes
both
mechanical
and
electrical
components
of
the
microgyroscopes. In mechanical design implementation, different suspension designs along with the damping estimations have been discussed. In electrical part, different actuation as well as sensing mechanisms available for microgyroscopes has been described in detail. After describing the basics of electrostatic and thermal actuations, a detailed
analysis
of
drive
and
sense
components
commonly
employed
in
microgyroscopes have been presented. This chapter concludes with a brief discussion on the fabless fabrication strategy and the proposed fabrication MUMPS process i.e. MetalMUMPs for the fabrication of the proposed microgyroscopes prototypes.
2.1
Introduction
Various Micromachined Vibratory Gyroscopes employ a wide range of the mechanical structures as well as actuation and sensing mechanisms. During the development of micromachined gyroscopes, various actuation mechanisms have been explored to oscillate the vibrating structure in the primary drive-mode. The most common ones include electrostatic, piezoelectric and electromagnetic means [1-4]. Electrostatic actuation using a comb drive design is the currently prevailing approach [1,2] as they can excite high frequency resonant modes. The background theory including the operating 23
principle and types of the thermal actuators has also been included in this chapter as the device proposed in chapter 5 has a Chevron-based thermal actuation mechanism. For the detection of the Coriolis-induced vibrations in the secondary sense-mode, the capacitive, piezoresistive or piezoelectric pick-off mechanisms are used. Among these, the capacitive sensing is the most commonly utilized mechanism. A brief introduction to this capacitive sensing mechanism has also been made in the end with the fabless strategy as well as proposed MetalMUMPs process.
2.2.
Dynamics of Vibratory Microgyroscope
Fig. 2.1 shows a particle having mass m and position vector
in an inertial frame of
reference A. Consider a non-inertial frame B whose position relative to the inertial one is given by X
. Since B is non-inertial, we must have that d2X/dt2 (the acceleration of
frame B with respect to frame A) is non-zero. Let the position of the particle in frame B be
.
B
xb (t )
A
xa (t ) X(t )
Figure 2.1: Representation of a particle moving in non-inertial frame B with respect to inertial frame A. Then
xa (t ) xb (t ) X(t )
(2.1)
24
Taking two time derivatives, this gives: d 2 xa d 2 xb d 2 X 2 dt 2 dt 2 dt
(2.2)
By Newton's Second Law F=ma where m is mass and a is the applied acceleration. Thus true force in frame A is Ftrue m
d 2 xa dt 2
(2.3)
But the apparent force in frame B is given by: Fapparent m
d 2 xb d 2 xa d2X d2X m m F m true dt 2 dt 2 dt 2 dt 2
(2.4)
Therefore, Ffictitious m
d2X dt 2
(2.5)
So the apparent force in frame B will be: Fapparent Ftrue Ffictitious
2.2.1
(2.6)
Rotating Coordinate Systems
A non-inertial frame of reference is useful when the reference frame is rotating. Since such rotational motion is non-inertial, due to the acceleration present in any rotational motion, a fictitious force can always be raised by using a rotational frame of reference. Despite this complication, the use of fictitious forces often simplifies the calculations involved.
25
The relationship between acceleration in an inertial frame and that in a coordinate frame rotating with angular velocity
, having velocity vin in inertial frame can be expressed
as:
dv dv ain in in vin dt in dt rot
(2.7)
We have used the relationship for the time derivative of a vector in rotating coordinates
dB dB B , for any vector B. dt in dt rot If r denotes the position vector, then vin v rot r , in such case the acceleration becomes:
d v rot r ain v rot r dt rot
(2.8)
or,
d dr dv ain rot r v rot r dt dt rot dt since
(2.9)
dv rot dr d a rot , and rot v rot so the above expression can be simplified dt dt dt
as below:
ain arot r 2 v rot r
(2.10)
The acceleration in the rotating frame then equals:
arot ain r 2 v rot r
(2.11)
Since the force in the rotating frame is Frot marot and, by definition, Frot Fin Ffict , the fictitious force equals: 26
Ffict 2m v rot m r m r
(2.12)
On R.H.S. of the Eq. 2.12, the terms involved are the Coriolis, Centrifugal and Euler forces respectively. This Coriolis acceleration term is of special interest. This term can be used to calculate the angular rate of the non inertial frame. Hence a rate gyroscope can be viewed as an accelerometer measuring the Coriolis acceleration to calculate the rotation rate.
2.3
Mechanical Design Implementation
This section mainly covers the different mechanical elements used in generic MEMS gyroscope design. This includes microsuspension designs and damping estimations. The theoretical models for these components are developed so that a comparison can be made with the tested results.
2.4.1
Microsuspension Design
Most commonly used microsuspension systems are beam, bent beam or crab leg springs, serpentine springs and U-shaped double folded flexures [5-9] shown in Fig. 2.2. Springs having an approximate shape of letter “U” (called here U-shaped double folded flexure) are mainly used for translatory motion of the rigid body along any of the desired axis. Due to symmetry about the axial (motion) direction the proof mass can translate about that axis. When this type of spring is implemented with the frame, it provides better mode decoupling characteristics, and minimizes the quadrature error and suspension anisoelasticities [6]. Thus, this flexure type of suspension has been implemented in the Micromachined Vibratory Gyroscope designs proposed in chapter 3, 5 and 6. In double folded flexures, each single beam can be modeled as two fixed-guided beams, which deform orthogonally to the axis of the beam. For a single fixed-guided beam as shown in Fig. 2.3, the translational stiffness for the motion in the orthogonal direction to the beam axis is given by [10]:
27
ksinglebeam
1 3EI Etw3 2 L 3 L3 2
(2.13)
E is the Young‟s modulus and I =
tw3 is second moment of inertia, whereas t, w and L 12
are thickness, width and length of the beam respectively.
Figure 2.2: Some commonly implemented microsuspension designs in MEMS.
Figure 2.3: Fixed-Guided beam under translational deflection. In micromachined gyroscopes, the proof mass is suspended over the substrate via anchors by two sets of four double folded flexures. These two sets of flexures provide the desired 28
spring stiffness in both drive and sense directions. In one double folded flexure, two fixed-guided beams deform translationally in series, whereas the four double folded flexures defines the overall stiffness of the device in the desired direction by: koverall
2.3.2
4 1 3EI 2 Etw3 2 2 L 3 L3 2
(2.14)
Damping Estimation
Damping of proof mass oscillation is a fundamental consideration in the design of the microgyroscopes. The major damping in the gyroscope structure comes from the viscous effects of the air surrounding the vibrating structures as well as confined between the proof mass and stationary surfaces. The structural damping is generally ignored because it is usually low in orders of magnitude in comparison to the viscous damping. Generally two damping models are used to capture the viscous damping effects: Couette flow damping and squeeze film damping. Steady viscous flow between the two plates when one plate is moving parallel to the other causes Couette flow damping. Fig. 2.4 illustrates this situation where two plates of area A separated by a distance y slide parallel to each other. Assuming the Newtonian gas, the Couette flow damping coefficient can be approximated as [11]: cCouette p p
A y
(2.15)
where µp=3.7×10-7 kg/m2.s.torr is the viscosity of the air, p is the air pressure, A is the overlap area of the plate and y is the plate separation.
Figure 2.4: Illustration of the couette flow damping
29
Another situation that arises in MEMS devices is shown in Figure 2.5 where a fluid fills the space between the two parallel plates. When these parallel plates approach each other, the fluid film is squeezed and causes squeeze film damping.
Figure 2.5: Squeeze-film damping This squeeze film damping effects are more complicated and can exhibit both damping and stiffness effects depending on the compressibility of the fluid. Using the HagenPoiseuille law, squeeze film damping can be modeled as [11]:
cSqueeze
7 Az 2 p p 3 y
(2.16)
Utilizing the above mentioned damping models, the total damping in drive and sensemode can be the sum of damping due to both Couette flow as well as squeeze film damping. In case of comb drive based actuation, total damping in the drive-mode will be the sum of damping due to Couette flow between the proof mass and substrate as well as between the fixed and moving comb fingers. Whereas, in parallel plates sense gap capacitors used for sensing the rotation induced Coriolis force, the total damping will be the sum of the Couette flow damping between the proof mass and substrate and squeeze film damping between the moving and fixed parallel plates. The accuracy of the damping models can be improved by using computational fluid dynamics (CFD) simulations where non-linear effects of the squeeze film damping can also be incorporated [12].
30
2.4
Actuation Mechanisms
Mainly six actuation mechanisms are available for the design and development of MEMS based devices and sensors. Depending upon the applications, these distinct actuation mechanisms are widely used in the development of various RF and Optical MEMS, best suited for commercial, industrial, military and space sensors applications [13-19]. 1. Electrostatic actuation 2. Piezoelectric actuation 3. Electromagnetic actuation 4. Electrothermal actuation 5. Electrodynamic actuation 6. Electrochemical actuation A brief introduction to critical elements of only two of these six actuation mechanisms (i.e. electrostatic and electrothermal actuation) and their structural requirement has been included in this thesis as all of the proposed microgyroscopes designs described in chapters 3, 4 and 5 utilize these two actuation mechanisms.
2.4.1
Electrostatic Actuation Mechanism
Electrostatic (ES) actuation mechanism is being widely used for actuating RF and optical MEMS devices. The design flexibility, moderate power consumption and displacementindependent forces for high stability has made ES actuation very popular in RF-MEMS switches, MEMS-phase shifters and MEMS based inertial sensors including microaccelerometers and microgyroscopes. Actuators utilizing ES force are based on the fundamental principle that the two plates having opposite charge always attract each other. Interdigitated comb drives shown in Fig. 2.6, introduced during last decade by Tang and Howe are one of the most common actuation structures used to implement ES actuation mechanism in MEMS devices [20]. Comb drives are used as transducing elements and offer a nearly constant force over a large range of displacements. Combined with
31
capacitive (electrostatic) detection, the comb drive based electrostatic excitation has become an attractive approach for silicon microstructures because of the simplicity and compatibility with micromachining technology such as surface micromachining [21]. The design introduced by Tang in [20] is still widely used in its original form, and its availability through foundry processes has enabled its broad use.
Figure 2.6: Model of comb drive showing movable comb with 30 fingers, fixed comb, folded flexure spring, shuttle mass and its anchor points [22]. Comb drive actuators consist of two interdigitated finger structures, where one comb is fixed and the other is connected to a compliant suspension. Applying a voltage difference between the comb structures will result in a deflection of the movable comb structure by electrostatic forces [22]. The geometry of the comb drive is such that the thickness of the fingers is smaller than the lengths and the widths. Therefore the attractive forces are mainly due to fringing field in the later direction x-direction as shown in the Fig. 2.7. The electrostatic force generated by the comb drive is given by the expression [23] Fel _ comb
1 t N 0 V 2 2 y
(2.17)
where 0 8.854 1012 F / m is the dielectric constant, N is the number of the fingers of the comb drive, t and y is the thickness and gap of the comb fingers and V is the applied voltage across the comb fingers.
32
(b) Figure 2.7: (a) Schematic diagram of a typical finger pair showing the details of fixed and movable fingers. Thickness (t) of the comb is 2 µm, length of the finger is 15 µm width (w) is 2 µm, whereas “l” is the initial finger overlap which is variable in our Comb drive-model. Voltage V is applied at fixed Comb where as movable comb is grounded.(b): SEM image of comb drive [22]. The applied voltage to the opposing comb sets of a comb drive actuator plays a vital role in achieving the linearized drive force along the drive x-axis. A combination of Vdc+Vac to one set of the fixed comb and Vdc- Vac to the other set can be a balanced interdigitated comb drive voltage imposing scheme where Vdc is a constant bias voltage whereas Vac is a time varying voltage. Assuming a negligible deflection along y-axis, the net electrostatic force reduces to [23]: Fel _ comb 4 N 0
t VdcVac y
(2.18)
It is noteworthy that net force along the drive axis (x-axis) is independent of the drive displacement and overlap length “l”. The force is directly proportional to drive voltages and the device thickness “t” and inversely proportional to the gap between the fingers “y”. Parallel plate actuator can also be used to implement ES actuation mechanism in many MEMS devices. The simplest form of parallel plate actuator consists of two parallel plate electrodes where one electrode is fixed and the other either moves towards or away from the fixed electrode as shown in the Fig. 2.8. 33
Figure 2.8: An illustration of parallel plate electrostatic actuator. Parallel plate actuation provides much larger force per unit areas as compared to comb drives but its stable actuation range is very limited with non-linear actuation force. The motion of the movable electrode is restrained by one or more springs. When the voltage across the electrodes is zero, the electrostatic force between the electrodes is also zero, resulting in a rest electrode separation distance, x0, also called the rest gap distance. As the voltage between the two electrodes is increased from zero, the resulting electrostatic force between the two electrodes pulls the movable electrode toward the fixed electrode until the electrostatic force equals the spring force. The net force generated by the parallel plate actuator is [24];
Fp
0Vdc2 A
(2.19)
2( x0 x) 2
Where 0 8.854 1012 F / m , A is the total actuation area and Vdc is the DC bias voltage.
2.4.2
Electrothermal actuation mechanism
Electrothermal (ET) actuators or heatuators are important actuating structures in MEMS which utilize the expansion of the metal due to increase in temperature. Among the various methods available for MEMS actuation, ET actuators are popular for their large deflection, large force and low driving voltage.
ET actuators are activated by the
resistive heating, generally called Joule heating. The internal heating (Joule heating) is 34
caused by the flow of electrical current to generate the thermal strains causing the desired mechanical deflection. Two types of ET actuators are very common these days: “U” shaped hot/cold arm thermal actuators [25-29] and “V” or Chevron-shaped actuators. The basics of only Chevron-shaped thermal actuator will be discussed here as this ET actuator has been used in some of our proposed designs discussed in chapter 5 and 6. The Chevron-shaped thermal actuator as shown in Fig. 2.9 consists of two thin hot arms at a small angle
with respect to each other. The heat generated by the current passing
through the constrained beam subjects it to both compression and lateral bending moment. This bending moment finally results in lateral displacement. Such beams can be modeled as the beam-column since they support both axial and lateral loads [30]. The Chevron or “V” shaped actuator provides rectilinear motion and allow stacking to achieve more force and hence the greater displacement. Further, Chevron-shaped actuators are more efficient than hot/cold arm actuators as there is no cold arm to reduce the net expansion [30]. The toggle mechanism provides large motion amplification, proportional to 1
for small angles. The displacement is proportional to the square of the
applied voltage and maximum displacement is limited by buckling of the hot arm at high temperature [25, 28, 30].
2.5
Sensing Mechanisms
Various microsensing mechanisms have been developed for MEMS and microdevices. These mechanisms include piezoresistive, piezoelectric and capacitive sensing. Of these, electrostatic capacitive sensing is most widely used in MEMS devices. There are number of other methods available to measure the position in MEMS, for example, inductance change, optical methods and scanning probe tips. Inductance change is very popular among macro-sensors but hasn‟t yet been explored for micro-sensors. Likewise, optical position sensing is quite new in MEMS and microdevices.
35
Figure 2.9: Schematic of Chevron-shaped thermal actuator (a) top view (b) cross-section B-B view.
2.5.1
Capacitive Sensing
Electrostatic capacitance sensing is a popular transduction technique for the MEMS. Any physical variable excitation (acceleration, pressure or rotation) can move parallel plate capacitors either with vertical motion of movable plate, modifying the gap or by transverse motion of one plate relative to another, modifying the effective area of the capacitor. Capacitance modification can also be achieved by out of plane motion of one of the electrode but this configuration is not very commonly used. In a microgyroscope, parallel plate sense capacitors are attached with the moving proof mass. As the proof mass moves in the sense direction in response to rotation induced Coriolis force, the gap between the parallel plate electrode changes and resulting capacitance change is detected. Differential capacitance is generally introduced to linearize the capacitance change with the proof mass deflection as shown in Fig. 2.10. When proof mass is displaced in positive direction, the gap between the moving electrode and stationary electrode A is decreased, increasing the capacitance. This increase in capacitance can be expressed as: C pp N
0tl
(2.20)
y0 y
where t and l is the thickness and length of the finger and y0 is the finger separation. 36
Direction of motion Figure 2.10: Implementation of the differential sense capacitors for response sensing.
While moving towards stationary electrode A, the moving electrode „B‟ moves away from the stationary electrode „A‟ thus decreasing the capacitance. C pp N
0tl
(2.21)
y0 y
By making the differential bridge shown in Fig. 2.10, the deflection is translated to a change in capacitance ΔC as follows C C( pp ) C( pp ) 2 N
( 0tly ) ( y02 y 2 )
(2.22)
From this expression, it is observed that change in capacitance is inversely proportional to the square of the initial separation between the fingers. Thus the performance of the device (resolution, sensitivity and signal to noise ratio) can be enhanced by decreasing the electrode gap.
2.6
Fabrication of Prototypes
2.6.1
Fabless Strategy
Fabless strategy is an alternate approach to develop MEMS products in house. This strategy is being successfully implemented in many universities and research institutes in 37
North America and Europe. This approach focuses on the design and characterization of the MEMS devices and product, while using entirely external processing and manufacturing infrastructure. Before making a commitment for the production of MEMS device, a complete validation of MEMS concept is crucial. In this validation, design and test of the MEMS device play a very vital role. This approach greatly emphasizes designing to specifications, and statistical understanding of process variations by separating the design from process development. The approach is well suited for universities, research institutes and small companies that posses design expertise but lack in in-house processing and fabrication facilities. The larger companies can establish external design groups which can also contribute to reduce the product development costs. This approach most importantly, can validate not just the technical viability of the new design, but also the producibility of a new product in a relatively short time. Thus, it may provide a realistic estimation to the design engineers about the development time and cost. The fabless approach significantly reduces the number of potential iterations simply because of designing to mature and standardized processes. These standard processes have established design rules (DRs) and the designers have to adhere to those DRs to ensure the structural integrity much like the integrated circuit designers to follow the design rules for CMOS or Bipolar processes. Today numbers of MEMS processing foundries are offering their wafer processing services. Although there is still a lack of process standardization across the MEMS industry, a few processes like MUMPS by MEMSCap Inc., SUMMIT by Sandia Lab, and Micragem by Micralyne have been developed. These standard processes are now widely used and have become “de-facto” standards. Thus fabless companies can help the designers to complete product development in short time with lower capital investment by eliminating expensive and time consuming process development than companies with concurrent process development.
38
2.6.2 Proposed MUMPs Process Metal Multi User MEMS Processes (MUMPs) are being used extensively by the designer in MEMS industry. The MUMPs fabrication processes like PolyMUMPs, MetalMUMPs and SOIMUMPs are available to designers making it is possible for them to find among these processes the one, most suitable to their designs. In this dissertation, all proposed microgyroscope designs have been fabricated using MetalMUMPs. MetalMUMPs is designed for general purpose electroplated Nickel micromachining of MEMS devices. Fig. 2.11 shows the layer used in MetalMUMPs.
Figure 2.11: Cross sectional view of a microrelay fabricated using all layers of the MetalMUMPs process (Figure not to scale) [31]. The MetalMUMPs has the following general features [31].
Electroplated Nickel is used as the primary structural material and electrical interconnect layer.
Doped polysilicon can be used for resistors, additional mechanical structures, and/or cross-over electrical routing.
Silicon nitride is used as an electrical isolation layer.
Deposited oxide, PhosphoSilicate Glass (PSG) is used for the sacrificial layers.
A trench layer in the silicon substrate can be incorporated for additional thermal and electrical isolation. 39
Gold overplate can be used to coat the sidewalls of Nickel structures with a low contact resistance material.
Conclusion In this chapter we presented a brief theoretical introduction of micromachined vibratory rate gyroscope with its dynamics. A comprehensive description of mechanical design implementation including microsuspension design and its damping estimation is also a part of this chapter. We further discussed different actuation mechanism used to drive microgyroscopes with a special emphasis on electrostatic and electrothermal actuations. An overview of MEMS capacitive sensing is also included in this chapter. In the end, a brief discussion on the fabless methodology adopted for the development of the proposed prototype MEMS devices is given. Finally a short description of MetalMUMPs process used to fabricate all of the proposed microgyroscope prototypes presented in this dissertation has also been included.
40
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MEMS
Actuator,”
Journal
of
Micromechanics
and
Microengineering. 16 (2006) 2067–2070. [30] E. T. Enikov, S. S. Kader, K. V. Lazarov, “Analytical Model for Analysis and Design of V-Shaped Thermal Microactuator” Journal of Microelectromechanical Systems, 2005, 14(4), pp 788-798. [31] A. Cowen, B. Dudley, E. Hill, M. Walters, R. Wood, S. Johnson, H. Wynands, and B. Hardy, “MetalMUMPs Design Hand book” (MEMSCap Inc. USA.) http://www.memscap.com/mumps/documents/MetalMUMPs.DR.2.0.pdf
44
Chapter 3 3-DoF Electrostatic Microgyroscope This chapter introduces the design concept of 3-DoF micromachined gyroscopes. In contrast to conventional gyroscopes having 2-DoF, this proposed microgyroscope design has 3-DoF dynamic system. Increased DoF allows shaping up the dynamic response of the microgyroscope by increasing the design parameter space at a minimal compromise in performance. This chapter demonstrates a successful implementation of 3-DoF microgyroscope in standard MetalMUMPs while enhancing its performance as well as reducing the size from previously proposed designs by other researchers using their inhouse customized micromachining process [1]. Starting from 3-DoF design concept, this chapter further describes lumped model for the proposed gyroscope along with its dynamics and equation of motions. In order to achieve dynamic amplification of mechanical motion, two vibrating proof masses are used in active and passive mass configuration in our proposed gyroscope model.
A
comprehensive optimization as well as simulation methodology has also been devised in this chapter for a non-resonant 3-DoF gyroscope. A prototype model and its fabrication using MetalMUMPs are also included in this chapter. In the end, experimental setup used to test microgyroscope is discussed along with the experimental test results of the fabricated prototype.
3.1
3-DoF Design Concept
Fig. 3.1 illustrates the 3-DoF design concept, which aims to utilize resonance in either drive-mode or sense-mode to improve the sensitivity while maintaining the robust operational characteristics. This could be achieved by forming structurally decoupled 245
DoF and 1-DoF oscillators. The 2-DoF oscillator has two resonant peaks with a flat region between them. This region normally defines the operational frequency region of the microgyroscope. The 1-DoF oscillator has one resonant peak that should lie within the flat region of the 2-DoF oscillator. Thus the device is operated at resonant frequency of the 1-DoF oscillator for improved sensitivity, while 2-DoF is inherently constant with the same frequency band. In the 3-DoF system with 2-DoF drive-mode, the wide band region is achieved in the drive-mode frequency response. By utilizing the dynamic amplification in the drivemode, large oscillation amplitude of the sense element is achieved with the small actuation amplitudes providing improved linearity and stability even with parallel plate actuation.
Figure 3.1: 3-DoF design concept with 2-DoF drive and 1-DoF sense-mode oscillators.
3.1.1
3-DoF System with 2-DoF Drive-Mode
Such types of Gyroscopes are operated at resonance in the sense-mode to achieve maximum sense-mode amplitudes and the wide bandwidth frequency region is achieved in the drive-mode. The overall 3-DoF Micromachined Vibratory Gyroscopes consist of
46
two interconnected proof masses m1 and m2 as shown in Fig. 3.2. Mass m1 is excited in the drive direction (x-axis) whereas it is constrained not to oscillate in sense direction. For the driving purpose of the gyroscope, a standard comb drive actuation mechanism is being used. This is very well proven mechanism to obtain large linear displacements. However large drive voltages are required and the resultant force of comb drive is low. Mass m2 can oscillate both in drive and sense direction (y-axis). In this way the gyroscope dynamical system consists of a 2-DoF drive-mode oscillator along with 1-DoF sense-mode oscillator. Mass m2, thus forms the passive mass of the 2-DoF drive-mode oscillator and acts as the vibration absorber of mass m1.
Figure 3.2: Micromachined Vibratory Gyroscopes with 2-DoF sense-mode. In the sense direction m2 defines a resonant 1-DoF oscillator. When an external angular rate is applied about the z-axis, the Coriolis force is induced on m2 and only m2 responds to this Coriolis force. This response of the sense-mode is detected by the parallel plate sensing electrode. Since the dynamical system is 1-DoF resonator in the sense direction,
47
the frequency response of the device has a single resonance peak in the sense-mode. For the purpose of defining the operational frequency region of the system, sense direction resonance frequency should lie within the flat region of the 2-DoF drive oscillator. This allows the operation at resonance in sense direction for improved sensitivity, while the drive direction amplitude is inherently constant in the same frequency band, in spite of parameter variations or perturbation.
3.1.2
Gyroscope Dynamics
3-DoF gyroscope dynamical system is analyzed in the non-inertial frame of reference associated with the gyroscope. Each of the interconnected proof masses are assumed to be a rigid body with a position vector r attached to a gyroscope reference frame rotating with an angular velocity of , resulting in an absolute acceleration in inertial frame.
arot ain r 2 vrot r
(3.1)
Figure 3.3: Representation of position vectors of the proof masses m1 and m2 of the gyroscope relative to the rotating gyroscope frame B.
Thus the equation of motion of m1 and m2 can be expressed in Inertial Frame as:
m1a1 F1 Fd Fr 2m1 v1 m1 ( r1 ) m1 r1 m2a2 F2 Fr 2m2 v 2 m2 ( r2 ) m2 r2 48
(3.2)
where Fd is the driving force applied to
m1, F1 is the net external force applied to m1
including elastic and damping forces from the substrate, F2
is the net external force
applied to m2 including damping force from the substrate and Fr is the elastic reaction force between m1 and m2 . In the gyroscope frame, r1 and r2 are the position vectors, and
v1 and v1 are the velocity vectors of m1 and m2. There are few constraints applied on the dynamical system so that the equation of motion of m1 and m2 can be further simplified and decomposed into the drive and sense directions.
The structure is stiff in out of plane direction;
The position vector of m1 and the decoupling frame are forced to lie along the drive direction i.e. y1 (t ) 0 ;
The decoupling frame and the sense mass m2 move together in drive direction;
m2 oscillates purely in sense direction relative to the decoupling frame.
Figure 3.4: Lumped mass-spring model of microgyroscopes. Fig. 3.4 shows the lumped mass spring model of the proposed gyroscope. Thus the equations of motion of m1 and m2 when subjected to an angular rate of z about the z-axis become:
49
m1 x1 c1x x1 k1x x1 k2 x ( x2 x1 ) m1 z 2 x1 Fd (t ) (m2 m f ) x2 c2 x x2 k2 x ( x2 x1 ) (m2 m f ) z 2 x2
(3.3)
m2 y2 c2 y y2 k2 y y2 m2 z 2 y2 2m2 z x2 m2 z x2 mf is the mass of decoupling frame, Fd (t ) is the driving electrostatic force applied to the active mass through the comb drive mechanism at the driving frequency d and z is the angular velocity applied to the gyroscope about the z-axis. It is assumed that there is no anisoelasticity or anisodamping in the system. The Coriolis force that excites the mass m2 in the sense direction is 2m2 z x2 and the Coriolis response of m2 in the sense direction ( y2 ) is detected for angular rate measurement.
3.1.3
Mechanical Design Implementation:
In this section, the main mechanical elements of a micromachined gyroscope, i.e. suspension design and damping components have been discussed in detail. Theoretical models of those components will be derived so that a comparison could be made with the experimental results. 3.1.3.1 Suspension Design Almost all existing Micromachined Vibratory Gyroscopes operate on the principle of detection of rotation induced Coriolis force in the presence of an angular rate input. So the proof mass should be free to oscillate in two orthogonal directions, and desired to be constrained in other vibration modes. Therefore suspension system design plays an important and critical role in achieving these objectives. The complete suspension system of the device is designed such that the first mass, m1 having 1-DoF is fixed in the sense direction and free to oscillate in Drive direction only. The second mass m2 having 2-DoF is free to oscillate in both drive and sense direction. The mass m2 is nested inside a drive-mode frame. The sense direction oscillations of the frame are constrained, where as the drive direction oscillations are automatically forced 50
to be in the designed drive direction. Thus the mass m2 is free to oscillate only in the sense direction with respect to the frame, and the sense-mode response will be perfectly orthogonal to the drive direction minimizing the manifestation of anisoelasticities as a quadrature error. Fig.3.5 illustrates the folded flexures attached with the drive as well as sense mass.
L2 x
L2 y
m2 mf
m1
L1x
Figure 3.5: SEM illustration of the folded flexures attached with the drive as well as sense mass. The suspension that connects the mass m1 with the substrate via anchors is comprised of four, double-folded flexures. Eeach beam of length L1x in the folded flexure can be modeled as a fixed-guided beam deforming in the orthogonal direction to the axis of the beam, leading to an overall stiffness of [2]:
4 1 3EI 2 Etw3 k1 x 2 2 L1x 3 L1x 3 2
(3.4)
51
where E is the Young‟s Modulus, I=tw3/12 is the second moment of inertia of the beam cross section, t is the beam thickness and w is the beam width. Possible anisoelasticities due to manufacturing flaws are suppressed by driving the mass m1 purely along the geometrical drive axis by this suspension and constraining m1 in the sense direction. Decoupling frame having mass m f is connected to m1 via four double-folded flexure, (each beam with length of L2 x ) that can be deformed in the drive direction resulting in the drive direction stiffness values of:
4 1 3EI 2 Etw3 k2 x 2 2 L2 x 3 L2 x 3 2
(3.5)
Sensing mass m2 is connected to decoupling frame with four five-folded flexures, each having beam length of L2 y . Since these flexures are stiff in drive direction and deform only in sense direction, instability due to dynamical coupling between drive and sensemode in the sensing element m2 is eliminating, minimizing zero rate drift of the gyroscope. So the overall stiffness with the length of L2 y for each beam is: 4 1 3EI 4 Etw3 k2 y 5 2 L2 y 3 5 L2 y 3 2
(3.6)
3.1.3.2 Damping Estimations Damping is a dominant energy dissipation mechanism in the gyroscope structures which is because of internal friction of the fluid confined between the proof mass surface and the stationary surface. Since the damping of the structure material is usually low as compare to the viscous damping so it is generally neglected. The c1x , c2 x and c2 y are the damping coefficient of drive as well as sense masses in x and y axes. These are due to viscous effect of the air between the masses and the substrate and in between the comb
52
drive and sense capacitor fingers. For the drive mass m1 , the total damping in the drivemode can be approximated as the combination of the slide film damping between the mass and the substrate, and the slide film damping between the integrated comb fingers. Slide film damping can be modeled as a Couette flow, leading to [3]: c1x e
2 Ncomblcombt A1 e z0 ycomb
(3.7)
where A1 is the area of the active mass, z0 is the elevation of the proof mass from the substrate, t is the thickness of the structure, Ncomb is the number of comb drive fingers,
ycomb is the distance between the fingers, and lcomb is the overlapping length of the fingers. The effective viscosity is e p p , where p is the ambient pressure within the cavity of the packaged device, and p =3.710 kg/m2.s.torr ( 2.78 10 [(kg/m2.s.Pa)] is the viscosity constant for air. Since there are no actuation and sensing capacitors attached to the decoupling frame, the damping coefficient in the drive is only due to the Couette flow between the proof mass and the substrate.
c2 x e
Af
(3.8)
z0
Damping on m2 in the sense-mode can be estimated as the combination of Couette flow between the proof mass and the substrate, and the squeeze-film damping between the airgap capacitor fingers [3]: c2 y e
7 Ncap lcapt A2 e z0 ycap
(3.9)
where A2 is the area of the passive mass, N cap is the number of air-gap capacitors, ycap is the distance between the capacitor fingers, and lcap is the overlapping length of the fingers.
53
3.1.4
The Coriolis Response
The design concept suggests that this gyroscope should be operated at the resonance frequency of the 1-DoF sense-mode oscillator so that maximum possible oscillation amplitude may be gained in response to the Coriolis force. The frequency response of the drive-mode oscillator has 2-DoF and two resonance peaks with a flat region between both peaks. When this drive-mode oscillator is excited in the flat frequency band, amplitudes of the drive-mode oscillations are insensitive to the parameter variations due to any change in the operation condition of the device Thus if we want to operate the sensemode resonator at resonance keeping the operation of drive-mode resonator into flat region frequency band, this flat frequency region should be overlapped with the sense direction resonance peak. So a flat frequency region with wider bandwidth can be easily overlapped precisely with the resonance peak of the sense-mode resonator without feedback control in the presence of manufacturing flaws and variation in operation conditions.
3.2
Prototype Modeling and Fabrication
3.2.1
Parametric Optimization
Sense direction deflection of sense mass m2 due to rotation induced Coriolis force is an important mechanical factor determining the performance of gyroscope. Therefore, the parameters of dynamical system must be optimized to maximize the sense direction amplitude of the mass m2. For the parametric optimization of the dynamical system, 3-DoF gyroscope system has been decomposed into the 2-DoF drive and 1-DoF sense-mode oscillator. Main objective of the parametric optimization in the 2-DoF drive-mode is to maximize the rotation induced Coriolis force Fc 2m2z x2 generated by mass m2 to excite 1-DoF sense-mode oscillator and is proportional to sensor sensitivity. 2-DoF drive-mode oscillator consists of drive mass m1 (active mass). The sinusoidal force is applied to this mass by Chevron thermal actuator. The combination of frame and 54
sense masses (mf+m2) comprises the vibration absorber (passive mass) of this 2-DoF oscillator. Approximating the gyroscope by a lumped mass-spring-damper model in Fig. 3.6(a), the equation of motion in the drive direction can be expressed as:
m1 x1 c1x x1 k1x x1 k2 x ( x2 x1 ) Fd (t )
(3.10)
(m2 m f ) x2 c2 x x2 k2 x ( x2 x1 ) 0
Figure 3.6: (a) Lumped mass-spring-damper model for 2-DoF drive-mode oscillator (b) lumped mass-spring-damper model for 1-DoF sense-mode oscillator of 3-DoF gyroscope. The equation of motion of the lumped mass-spring-damper model of the 1-DoF sensemode Fig. 3.6(b) becomes: m2 y2 c2 y y2 k2 y y2 2m2 z x2
(3.11)
When a constant-amplitude sinusoidal force Fd is applied on active mass m1, the steady state response of the 2-DoF system will be [4]:
X1
X2
F0 k1x
F0 k1x
1 2 x
c2 x j k2 x 2 2 k c1x c2 x k2 x 2x 1 j 1 j k1x 2 x k2 x k1x k1x 1x 1 2 2 k c1x c2 x k2 x 2x 1 j 1 j k1x 2 x k2 x k1x k1x 1x
55
(3.12)
where 1x k1x
m1
and 2 x k2 x
(m f m2 )
are the resonant frequencies of isolated
active and passive mass-spring system, respectively. When the driving frequency,
d 2 x the passive mass moves to exactly cancel out the applied input force Fd on the active mass, and maximum dynamic amplification is achieved. Maximization of the Coriolis force Fc generated by the proof mass m2 requires a large value of m2, and large drive direction amplitude x2. However m2 m f should be minimized for high oscillation amplitudes of the passive mass if drive direction response of the passive mass is observed for varying m2 values with m1 being fixed. 2 x is determined according to gyroscope operating frequency specifications, noting that larger Coriolis forces are induced at higher frequencies, but oscillation amplitudes become larger at lower frequencies [4]. As mass ratio x (m2 m f ) / m1 decreases, the resonant frequency separation of the 2DoF drive-mode oscillator decreases. However resonant frequencies should be far enough such that variations in the drive frequency away from 2 x don‟t cause significant changes in the passive mass amplitude [4]. Mechanical amplification depends upon the frequency ratio of isolated active and passive mass namely, x 2 x / 1x which should be high enough for high mechanical amplification, and high oscillation amplitude of the passive mass [4].
3.2.2
Dynamic Amplification:
To achieve maximum possible response of the gyroscope, amplitude of the drivedirection oscillation of the passive mass should be maximized. The active mass m1 is electrostatically forced to oscillate in drive direction by comb drive structure. There is no electrostatic force applied on the passive mass m2 and the only forces acting on this mass are the elastic coupling and damping forces in drive direction. In 3-DoF micromachined gyroscope, passive mass m2 acts as the vibration absorber of the active mass m1. While absorbing the oscillations of the active mass m1, the proof mass m2 56
itself achieves much larger drive-mode amplitude than m1 and generates larger Coriolis force in response to the rotation. The response of the passive mass in the sense direction to the rotation induced Coriolis force is monitored by air gap capacitors built around the passive mass providing angular rate information.
3.2.3
Prototype Fabrication
A prototype 3-DoF gyroscope is designed to fabricate in the Metal-Multi User MEMS Processes (MetalMUMPs) [5] for the design concept verification. MEMSPro available at GIK Institute of Engineering Sciences and Technology (GIKI) is used for the design rule checks and process simulations for MetalMUMPs. MetalMUMPs is a low-cost, commercially available, general purpose electroplated Nickel micromachining process. This is a popular process for the fabrication of the poly/Nickel powered grippers, the thermal-actuator based bistable micro-relays and MEMS variable capacitors. This process consists of a 20μm thick electroplated Nickel layer used as the primary structural material and electrical interconnect layer. The proposed microgyroscope model fabricated through MetalMUMPs after process simulation in MEMSPro is shown in Fig. 3.7. Cross sectional views are given in Fig. 3.8 to illustrate different layer used during prototype fabrication.
Figure 3.7: Microgyroscope fabricated through MetalMUMPs process using L-Edit of MEMSPro. 57
Figure 3.8: A-A’ Cross sectional views of a microgyroscope
Figure 3.9: Process flow for the fabrication of microgyroscope using MetalMUMPs in MEMSPro (a) N-type silicon wafer (b) 2µm thick isolation oxide layer (c) patterning of 0.35µm thick silicon nitride layers (d) patterning of 0.7µm thick Polysilicon layer (e) patterning of anchor metal layer (f) patterning of 20µm electroplated structural layer of Ni and trench etch in the substrate. Step by step fabrication of the gyroscope in MetalMUMPs has been shown in Fig. 3.9. The overall size of the device is 2.2×2.6mm2. The movable parts of the MVG like proof masses and folded flexure are defined using the 20µm thick Nickel layer. The anchors and fixed parts are formed by the isolation oxide, nitride layers, anchor metal and Nickel layers. 58
3.2.4
Prototype Design:
A prototype 3-DoF gyroscope was designed for experimental demonstration of the design concept with the following dynamical system parameters. The proof mass values are m1 3.86 107 kg and
m2 1.346 107 kg and the decoupling frame mass is
m f 4.8 108 kg. The spring constants for folded flexure are k1x 65.10 N/m, k2 x 12.32 N/m and k2 y 14.45 N/m calculated by finite element method (FEM) using Thermoelectromechanical (TEM) Analysis module of MEMS Design software IntelliSuite. These spring constants can be approximated analytically by the formulae explained in the mechanical design implementation of suspension design. For example for k1x 65.10 N/m, we can approximate this stiffness by putting the relevant values in:
4 1 3EI k1 x 2 2 L1x 3 2
3 2 Etw L1x 3
(3.13)
where t 20 m is the beam thickness, w 8 m is the beam width and L1x 410 m is the length of beam whereas Young‟s Modulus
E 214GPa was assumed for the
MetalMUMPs Ni structural layer. The calculated k1x 63.59 N/m is close to the
k1x 65.10 N/m predicted by IntelliSuite. Thus for drive-mode Oscillator, the active and passive proof mass values become 7 m1x 3.86 107 kg and m2 x (m2 m f ) 1.826 10 kg.
In the drive-mode, the
resonant frequencies of the isolated active and passive mass-spring systems are
1x k1x / m1x 2.068kHz and 2 x k2 x /(m2 m f ) 1.308kHz , respectively. The resulting frequency ratio will be
x 2 x / 1x 0.632 and a mass ratio of
x (m2 m f ) / m1 0.47 . With these parameters, the location of the two expected resonance peaks in the drive-mode frequency response were calculated as f x n1 1.16kHz and f x n2 2.34kHz based on the relation [5]:
59
f x n1 1/ 2(1 x 1/ x 2 (1 x 1/ x 2 ) 2 4 / x 2 ) 2 x f x n2 1/ 2(1 x 1/ x 2 (1 x 1/ x 2 ) 2 4 / x 2 ) 2 x
3.3
(3.14)
Simulation Results
In this section, device level, Finite Element Analysis (FEA) based simulation methodology
for
the
proposed
microgyroscope
design
is
devised.
Thermoelectromechanical (TEM) analysis module of the MEMS Design software IntelliSuite has been utilized for this purpose. The results of these TEM analyses will verify the design concept and parameters of the proposed model, which are discussed in design implementation section. Before starting FEA, IntelliSuite 3D Builder Module is used to build and mesh the threedimensional model of the MEMS device. This model is then transferred to TEM module where user assigns material properties, loads and boundaries to this model. Modal analysis was performed to predict the natural frequencies and their respective mode shape for the proposed gyroscope. In MetalMUMPs, the structural layer of electroplated Nickel has a residual stress of 100 MPa [6]. Therefore, while calculating natural frequencies and associated mode shapes of the device, this value of residual stress was used for accurate results. A nonlinear analysis assumption results in nonlinear stiffness terms of the system which modifies the stiffness matrix. This modified stiffness matrix is used to solve the eigenvalue problem to obtain the natural frequencies [7]. The resulting resonant frequencies from the modal analysis of the device are listed in Table 3.1 and their associated mode shapes are shown in Fig. 3.10(a)-(d). Two resonance frequencies for the 2-DoF drive-mode oscillator are observed at 1.168kHz and 2.312kHz, which compares well to the theoretically calculated values of 1.160kHz and 2.340kHz. The sense-mode frequency of 1.639kHz is located inside the drive-mode flat region as
60
desired, allowing the gyroscope to be operated at resonance in the sense-mode and within the flat region in the drive-mode. Table 3.1: Comparison of simulated and analytical results for natural frequencies for drive and sense-modes. Mode
Simulated Resonant
Analytical Resonant
No
Frequency (kHz)
Frequency (kHz)
1
1.168
1.16
1st Drive Mode
3
1.639
1.649
Sense Mode
5
2.312
2.34
2nd Drive Mode
(a)
61
Remarks
(b)
(c) Figure 3.10: (a) First drive direction mode at 1.16kHz (b) second drive-mode at 2.31kHz and (c) sense-mode at 1.63kHz.
62
3.4
Experimental Results
The frequency responses of 2-DoF drive-mode oscillator and 1-DoF sense-mode oscillator of the prototype 3-DoF Micromachined Vibratory Gyroscope were characterized at Nanoscale System Integration Group, Southampton University, UK. All measurements were taken at atmospheric pressure. Since accurate characterization of drive and sense-mode frequency response is very vital to ensure the design quality, a Polytec Microsystem Analyzer, MSA-400 was used. MSA400 can dynamically characterize the “in-plane” as well as “out-of-plane” vibrations using Planar Motion Analyzer, PMA-400 and Microscope Scanning Vibrometer, MSV400. PMA-400 measures vibrations utilizing stroboscopic video microscopy whereas MSV-400 uses laser-Doppler vibrometry with nanometer and micrometer displacement range respectively [8].
Figure 3.11: Microsystem Analyzer MSA-400, utilized to characterize the Microgyroscope at Nanoscale System Integration Group, University of Southampton, UK. The stroboscopic video microscopy, PMA-400 for in-plane motion detection is a special kind of image processing in which short light pulses synchronized with the objects 63
motion capture the position at precise phase angles. Motion is kept frozen during the illumination time. By shifting the timing of these pulses by phase angle increments, the motion of a moving object can be sampled and reconstructed. The internal signal generator periodically excites the component with a sine or a pulse signal. A “pattern generator” uses a green LED to generate ultra-short flashes of light (>80 ns) synchronously with the phase position of the excitation signal. This means that a high degree of phase accuracy is attained, even with high frequency excitation. The electronic camera shutter in turn is synchronized with the excitation. It remains open until enough light at the same phase of the periodic motion has been collected. This procedure is repeated to extract the amplitude and phase data of the vibrating object [8].
3.4.1
Drive-mode Characterization
Using Polytec MSA-400, the frequency response of the 2-DoF Drive-mode oscillator was characterized at atmospheric pressure. For drive-mode characterization, two probes were used to apply +/- DC bias voltage on the fixed comb drives on either sides of the microgyroscope whereas one probe was used to apply AC signal to the proof mass through the anchor. Fig. 3.12 presents the frequency response of the active mass m1 and passive mass m2+mf from 700Hz to 850Hz whereas Fig. 3.13 presents the frequency response of the active mass and passive mass from 2kHz to 2.5kHz. The first resonant frequency was observed at 754Hz where the passive mass was observed to reach a displacement of 658nm at 100Vdc and 60Vac achieving a 3 times dynamic amplification of the active mass. In drive-mode frequency response, a flat region of 1.416kHz was experimentally demonstrated. The two resonance peaks in the drive-mode frequency response was observed as
f x n1 754 Hz and
f x n2 2.17 kHz instead of
f x n1 1.16 kHz and
f x n2 2.34 kHz. At the second resonant frequency of 2.17kHz, the passive mass was
observed to reach a displacement of 460nm at 100Vdc and 60Vac achieving a 9 times dynamic amplification of the active mass having a displacement of 55nm.
64
3-DoF Microgyrscope Drive-Mode Response 1.0x10
Amplitude(m)
8.0x10
6.0x10
4.0x10
2.0x10
-6
(B) m2+mf Passive Mass
Equation
(E) m1 Active Mass
Adj. R-Squar
-7
-7
-7
725
750
0.76249
0.95767 Value
-7
0.0 700
y=y0 + (A/(w*sqrt(PI/2)))*exp(-2*((x-xc)/w)^ 2) Standard Erro
B
y0
7.58341E-
7.07771E-9
B
xc
754.52402
0.27006
B
w
8.85538
0.55663
B
A
7.31107E-
4.20606E-7
B
sigma
4.42769
B
FWHM
10.42642
B
Height
6.5874E-7
E
y0
1.02737E- 7.94588E-10
E
xc
754.83675
E
w
6.245
0.14933
E
A
1.8429E-6
3.9654E-8
E
sigma
3.1225
E
FWHM
7.35292
E
Height
2.35456E-
775
800
825
0.07316
850
Frequency (Hz)
Figure 3.12: Drive-mode response of the microgyroscope from 700Hz to 850Hz showing the active and passive mass resonant peak at 754Hz. 3-DoF Microgyroscope Drive-Mode Reponse 5.0x10
-7
4.0x10
-7
3.0x10
-7
(B) m2+mf Passive Mass Respose (E) m1Active Mass Response
Amplitude (m)
Equation
y=y0+A*exp(-0.5 *((x-xc)/w)^2)
Adj. R-Square
0.97271
0.20464 Value
2.0x10
1.0x10
-7
-7
0.0 2000
2100
Standard Error
B
y0
7.72023E-9
B
xc
2170.6578
B
w
3.55875
0.04841
B
A
4.6085E-7
5.4094E-9
E
y0
2.51673E-8
8.3691E-10
E
xc
2173.60574
E
w
4.24297
0.72589
E
A
5.56693E-8
8.20542E-9
2200
2300
2400
4.58559E-10 0.04815
0.72026
2500
Frequency (Hz)
Figure 3.13: Drive-mode response of the gyroscope from the 2.0kHz to 2.5kHz range showing active and passive mass resonance peak at 2.17kHz.
65
5.0x10
-6
4.0x10
-6
3-DoF Microgyroscope Isolated Passive Mass Drive-Mode Response
Psd Voigt Fit
Amplitude (m)
Equation
3.0x10
-6
y = y0 + A * ( mu * (2/PI) * (wL / (4*(x-xc)^2 + wL^2)) + (1 - mu) * (sqrt(4*ln(2)) / (sqrt(PI) * w G)) * exp(-(4*ln(2)/wG^2)*(x-xc)^2) )
Adj. R-Square
2.0x10
-6
1.0x10
-6
0.98139 y0 xc A wG wL mu
Value Standard Error 8.61125E-8 6.25985E-9 1506.86421 0.13227 7.82051E-5 1.59571E-6 15.9367 0.67025 12.26854 0.33126 1.49811 0.03914
0.0 1300 1350 1400 1450 1500 1550 1600 1650 1700
Frequency (Hz)
Figure 3.14: Frequency response of the isolated passive mass in drive-mode showing its resonant frequency at 1.508kHz instead of analytically calculated 1.308kHz. Figure 3.14 shows the frequency response of the isolated passive mass in drive-mode. The resonant frequency is observed at 1.508kHz instead of analytically calculated 1.308kHz.
3.4.2
Sense-mode Characterization
Similar voltage applying methodology was adopted to characterize sense-mode as was adopted for the drive-mode characterization. Now two probes were used to apply +/60VDC bias voltage on the fixed sides of the sensing parallel plate electrodes, whereas one probe was used to apply sinusoidal 45VAC on the proof mass through the anchor. Fig. 3.15 shows the frequency response of the 1-DoF sense-mode oscillators. The location of the peak was observed at 1.868Hz instead of 1.639Hz, which was calculated using FEA based Modal analysis.
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6.0x10
3-DoF Microgyroscope Sense-Mode Response
-6
PsdVoigt Fit
Amplitude (m)
Equation
4.0x10
2.0x10
-6
y = y0 + A * ( mu * (2/PI) * (wL / (4*(x-xc)^2 + wL ^2)) + (1 - mu) * (sqrt(4*ln(2)) / (sqrt(PI) * wG)) * exp(-(4*ln(2)/wG^2)*(x-xc)^2) )
Adj. R-Square
0.97814 Value
Standard Error
y0
1.02154E-7
xc
1868.77173
1.61548E-8 0.19382
A
2.03767E-4
6.75394E-6
wG
13.04961
0.53942
wL
56.50903
4.62198
mu
0.76672
0.01386
-6
0.0 1600
1700
1800
1900
2000
Frequency (Hz)
Figure 3.15: Frequency response of the 1-DoF sense-mode oscillator showing the resonant peak 1.868kHz instead of 1.639kHz. The experimental verification of drive as well sense-mode frequency responses demonstrated a difference, although not very big, between the predicted and tested resonant frequencies. The plausible causes for these variations among the tested and predicted results could be the simulation issues as well as the fabrication challenges. While simulating the device, the predicted results primarily depend upon the physical properties of the material used as the structural layer to fabricate the MEMS device. Generally, the thin film properties of the material are required when microdevices are simulated for their FEA based electromechanical analyses. Polysilicon has been widely used for the fabrication of the MEMS devices for decades. Therefore, an extensive research has already been carried to measure its physical properties in thin film form and these are easily available in the literature. But the proposed device in this chapter was fabricated through MetalMUMPs using structural layer of electroplated Nickel. The thin film properties of the electroplated Nickel were not available in the literature. Therefore, bulk properties of the electroplated Nickel were used for FEA based analyses to predict 67
its resonant frequencies. This may be one of the reasons for the difference between the predicted and tested resonant frequencies as the bulk properties remain no longer applicable and change drastically for the micro as well as the nano regimes. Fabrication imperfections are also unavoidable. These imperfections badly affect material properties as well as the geometry of MEMS devices. In surface micromachined gyroscopes, thin film deposition process determines the thickness of the structural layer including its microsuspension elements, whereas etching process affects its width. Additionally, deposition conditions affect the Young‟s Modulus of the deposited structural layer [1]. Lateral over-etching often cause variation in the width and crosssection of the suspension beams in bulk-micromachined devices. These parametric variations drastically affect the dynamic response of micromachined gyroscopes causing the error in predicted and tested results.
3.4.3
Overall System Response
When the drive and sense-mode frequency responses of the 3-DoF microgyroscope prototype were investigated together, a flat region of 1416 Hz in the drive-mode response was overlapped by the sense-mode resonant frequency, defining the operating frequency of the proposed device. These experimental test results demonstrate and verify the feasibility of the design concept.
Conclusion The major advantage of 3-DoF system is to achieve larger drive-mode amplitudes of the passive mass while keeping the drive amplitude of active mass very low. In this chapter this operational principle has been successfully demonstrated. A 3-DoF microgyroscope having 2-DoF drive-mode oscillator was fabricated. A low-cost commercially available MetalMUMPs process was utilized to fabricate a 20μm thick Nickel based Micromachined Vibratory Gyroscope with an overall device size of 2.2mm × 2.6mm. A detailed optimization and test methodology has been devised to test the 3-DoF microgyroscope. Using MSA-400 our fabricated prototype devices was characterized and 68
the test results were compared with the estimated resulted achieved by simulating the model in TEM module of IntelliSuite. The test results were found in good agreement with the simulated results. The passive mass achieved a dynamic amplification of the 3 times at first resonant peak of 754Hz and 8 times at the second resonant peak of 2170Hz in comparison with the active mass.
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References [1] C. Acar, “Robust Micromachined Vibratory Gyroscope” PhD thesis, University of California, Irvine, 2004 [2] W.C. Young. “Roark’s Formulas for Stress and Strain” McGraw-Hill, Inc., pp. 93-156, 1989. [3] N.C. Tsai ,C.Y. Sue, C.C. Lin, “Design and Dynamics of an Innovative Microgyroscope Against Coupling Effects” Microsystem
Technologies 14,
pp.295–306, (2008) [4] C. Acar, A. M. Shkel “Non-resonant Micromachined Gyroscopes with Structural Mode-Decoupling” IEEE Sensor journal , Vol 3, No.4, August 2003, pp 497-506. [5] C. W. Dyck, J. J. Allenand, R. J. Huber, “Parallel-Plate Electrostatic Dual-Mass oscillator” Proceeding of SPIE, SOE, CA, 1999. [6] A. Cowen, B. Dudley, E. Hill, M. Walters, R. Wood, S. Johnson, H. Wynands, and B. Hardy, “MetalMUMPs Design Hand book” (MEMSCap Inc. USA.) http://www.memscap.com/mumps/documents/MetalMUMPs.DR.2.0.pdf IntelliSuite Technical Reference Manual 8.2, 2007, IntelliSense Inc. USA. [7] http://www.polytec.com/eur/158_6392.asp
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Chapter 4 Parametric Modeling of Microgyroscope using Model Order Reduction The reduce-order macromodeling methodology for the microgyroscope has been developed in this chapter. Often, the design engineers require fast design and analysis cycle. Model order reduction (MOR) generates a reduce order model which allows a system level simulation and analysis. A MOR based system model extraction (SME) technique has been implemented for the parametric modeling of the comb drive actuator for the proposed dual mass, non-resonant microgyroscope. This chapter covers some basics of SME technique and its systematic implementation for the proposed 3-DoF microgyroscope in IntelliSuite system level simulator called SYNPLE. Then a comprehensive simulation methodology has been devised with the parametric modeling of the comb drive actuator for the gyroscope in SYNPLE. In the end, A system level model for the proposed device using this technique has been developed and finally comparative study of these results has been carried out with the FEA based electromechanical simulations results. This comparison concludes that both of these techniques are equally effective for MEMS gyroscope design and analyses, however the later is far less time consuming as compare to the former.
4.1
Introduction
Modeling of complex, multi-physical domain micro-electro-mechanical systems (MEMS) with a high degree of accuracy often involves higher order models comprising thousands of differential equations to represent the exact dynamics of such systems. For example, a 71
model of a micro-thruster used as a propellant for a microsatellite consists of 1071 ordinary differential equations [1-2]. Similarly, the matrix dimension of a typical model of electrostatically actuated beams, which are used to drive MEMS based RF Switches, is 16000 [3]. Modeling of these microsystems employed FEA discretization in ANSYS. Due to the large number of equations the modeling process is cumbersome and time consuming. The computational time usually exceeds reasonable limits if one attempts to simulate the full system behavior of which the MEMS device is a part. It may therefore result into an incorrect solution as the permissible time interval for the dynamic simulation may not be sufficient to capture the true response of the model. Thus, to save time and money in case of failure, macromodels of these systems having almost the same response characteristics as that of original model are developed using different model order reduction techniques. These model order reduction techniques include balanced truncation, Guyan and Krylov subspace methods [4]. These macromodels are then used for system level simulations with the control and interface circuitry using a circuit level simulator without losing too much accuracy in an efficient manner. Researchers have attempted to implement different model order reduction techniques for MEMS during the last decade. Betchtold et al. used a Krylov Subspace based Arnoldi algorithm and balanced truncation to produce a macromodel of MEMS based microignition unit [5]. They have also compared the results generated by these techniques with the original model response. They observed that the macromodel developed by the balanced truncation technique produced better matching results than the Arnoldi method. However, the computational cost of balanced truncation increases rapidly as the order of the system increases. They also used Guyan and Krylov subspace techniques to develop the macromodel of the same micro-ignition unit [6]. Wang et al. used an Arnoldi algorithm to develop the macromodel of the MEMS based micro-switch [7].
A
macromodel is developed for a capacitively driven micro-beam and micro-mirror while Chen et al. generated a macromodel for a micro-switch using extended Krylov subspace methods for weakly non-linear systems [8,9].
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Rewienski et al. developed a
computationally efficient technique, Trajectory Piecewise linear (TPWL) based on Krylov subspaces and applied it to the model of the micro-switch [10]. Arnoldi algorithm is extensively used to develop reduced order models (ROM) of the FEM models of various categories of MEMS such as electro-thermal MEMS devices [11, 12], structural mechanics problems [13], RF-MEMS devices [14] and fluidic interaction based MEMS problems [15]. Computational results shown in [5-15] confirm and verify that model order reduction is fast and efficient way to perform transient and harmonic analysis of large scale systems like MEMS without losing much accuracy. In this chapter an order reduction technique developed by IntelliSense, USA called system model extraction (SME) has been utilized to generate macromodels of highly nonlinear microgyroscope in an automatic and efficient way [16]. This SME technique is based on the Krylov subspace methods suitable for non-linear models. SYNPLE is used as a circuit simulator to perform system level simulations of macromodels of MEMS devices with the interface electronic circuitry.
4.2
System Model Extraction (SME)
System model extraction (SME) is a model order reduction technique, used to generate an analytical macromodel of a full 3D meshed finite element (FE) model of a multiconductor electromechanical device considering its damping dissipation. This macromodel is then inserted as a black-box element into any system level simulator to co-simulate the device with the CMOS control circuitry. This SME process is based upon an energy method approach. This approach constructs analytical models for each of the energy domain of the system and all forces are determined as the gradients of the energy. So this approach makes this process modular where the designer can incorporate other energy domains into the models at any stage of design and analysis. Another advantage of energy methods is that the models are guaranteed to be energy conserving, since each of the stored energies is constructed as an analytical function, and all forces are computed directly from analytically computed gradients. The SME process also has the benefit of being able to be performed almost 73
entirely automatically, requiring the designer only to construct the model, run a few full three-dimensional numerical computations, and set a few preferences a priori. Above all, this process has the ultimate benefit of constructing models that are computationally efficient, allowing their use in a dynamical simulator [17].
4.2.1
SME Methodology
Fig. 4.1 demonstrates a general overview of the SME approach for MEMS device. The first task is to minimize the system complexity by reducing the degree of freedom of the system. Ananthasuresh et al. demonstrated that only a few modal shapes are necessary to capture the motion of the MEMS devices [18]. So the motion of the system is constrained to a linear superposition of a selected set of deformation shapes rather than allowing each node in a FE model to be free to move in any direction. This set will act as the basis set or transformation matrix of motion. The positional state of the system will hence be reduced to a set of generalized coordinates, each coordinate being the scaling factor by which its corresponding basis shape will contribute. Next, analytical macromodels of each of the energy domains of the system are constructed. In case of conservative capacitive electromechanical systems, these consist of electrostatic, elastostatic, and kinetic energy domains. These macromodels will be analytical functions of the generalized coordinates. Then Lagrangian mechanics is used to construct the equation of motion for the system in terms of its generalized coordinates. Finally, these equations of motions are translated into an analog hardware description language, thereby constructing a black-box model of the electromechanical system that can finally be inserted into an analog circuit simulator.
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Figure 4.1: Overview of the SME approach for the MEMS. N is the number of free nodes in the model. In general, the deformation state and dynamics of the mechanical system can be accurately described as the linear combination of mode shape functions or modal superposition [17]: m
ui (t , xi , yi , zi ) ueq q j (t ). j (xi , yi , zi )
(4.1)
j 1
where ui represents the deformed state of the structure, ueq represents the initial equilibrium state (derived from the residual stress conditions without external loads), j represents the displacement vector for the jth mode, qj represents the coefficients for the jth mode, which is referred as “scaling factor for mode j”. In general, Eq. 4.1 describes a coordinate transformation of finite element displacement coordinates to modal coordinates of the macromodel. The deformation state of the structure given by n nodal displacements ui (i=1,2,…,n) is now represented by a linear combination of m modes weighted by their amplitudes qj (i=1,2,…,n) where m
