Whole-Angle MEMS Gyroscopes

Doruk Senkal, PhD, has been working on the development of Inertial Navigation Technologies for Augmented and Virtual Reality applications at Facebook since 2018. Before joining Facebook, he was developing MEMS Inertial Sensors for mobile devices at TDK Invensense. He received his Ph.D. degree in 2015 from University of California, Irvine, with a focus on MEMS Coriolis Vibratory Gyroscopes. Dr. Senkal 's research interests, represented in over 20 international conference papers, 9 peer-reviewed journal papers, and 16 patent applications, encompass all aspects of MEMS inertial sensor development, including sensor design, device fabrication, algorithms, and control. Andrei M. Shkel, PhD, has been on faculty at the University of California, Irvine since 2000, and served as a Program Manager in the Microsystems Technology Office of DARPA. His research interests are reflected in over 250 publications, 40 patents, and 2 books. Dr. Shkel has been on a number of editorial boards, including Editor of IEEE/ASME JMEMS and the founding chair of the IEEE Inertial Sensors. He was awarded the Office of the Secretary of Defense Medal for Exceptional Public Service in 2013, and the 2009 IEEE Sensors Council Technical Achievement Award. He is the IEEE Fellow.

• List of Abbreviations ixPreface xiAbout the Authors xiiiPart I Fundamentals of Whole-Angle Gyroscopes 11 Introduction 31.1 Types of Coriolis Vibratory Gyroscopes 31.1.1 Nondegenerate Mode Gyroscopes 41.1.2 Degenerate Mode Gyroscopes 51.2 Generalized CVG Errors 51.2.1 Scale Factor Errors 71.2.2 Bias Errors 71.2.3 Noise Processes 71.2.3.1 Allan Variance 71.3 Overview 92 Dynamics 112.1 Introduction to Whole-Angle Gyroscopes 112.2 Foucault Pendulum Analogy 112.2.1 Damping and Q-factor 122.2.1.1 Viscous Damping 132.2.1.2 Anchor Losses 142.2.1.3 Material Losses 152.2.1.4 Surface Losses 162.2.1.5 Mode Coupling Losses 162.2.1.6 Additional Dissipation Mechanisms 162.2.2 Principal Axes of Elasticity and Damping 162.3 Canonical Variables 182.4 Effect of Structural Imperfections 182.5 Challenges of Whole-Angle Gyroscopes 203 Control Strategies 233.1 Quadrature and Coriolis Duality 233.2 Rate Gyroscope Mechanization 243.2.1 Open-loop Mechanization 243.2.1.1 Drive Mode Oscillator 243.2.1.2 Amplitude Gain Control 263.2.1.3 Phase Locked Loop/Demodulation 263.2.1.4 Quadrature Cancellation 263.2.2 Force-to-rebalance Mechanization 273.2.2.1 Force-to-rebalance Loop 273.2.2.2 Quadrature Null Loop 293.3 Whole-Angle Mechanization 293.3.1 Control System Overview 303.3.2 Amplitude Gain Control 323.3.2.1 Vector Drive 323.3.2.2 Parametric Drive 333.3.3 Quadrature Null Loop 343.3.3.1 AC Quadrature Null 343.3.3.2 DC Quadrature Null 343.3.4 Force-to-rebalance and Virtual Carouseling 353.4 Conclusions 35Part II 2-D Micro-Machined Whole-Angle Gyroscope Architectures 374 Overview of 2-D Micro-Machined Whole-Angle Gyroscopes 394.1 2-D Micro-Machined Whole-Angle Gyroscope Architectures 394.1.1 Lumped Mass Systems 394.1.2 Ring/Disk Systems 404.1.2.1 Ring Gyroscopes 404.1.2.2 Concentric Ring Systems 414.1.2.3 Disk Gyroscopes 424.2 2-D Micro-Machining Processes 424.2.1 Traditional Silicon MEMS Process 434.2.2 Integrated MEMS/CMOS Fabrication Process 434.2.3 Epitaxial Silicon Encapsulation Process 445 Example 2-D Micro-Machined Whole-Angle Gyroscopes 475.1 A Distributed Mass MEMS Gyroscope – Toroidal Ring Gyroscope 475.1.1 Architecture 485.1.1.1 Electrode Architecture 495.1.2 Experimental Demonstration of the Concept 495.1.2.1 Fabrication 495.1.2.2 Experimental Setup 505.1.2.3 Mechanical Characterization 515.1.2.4 Rate Gyroscope Operation 525.1.2.5 Comparison of Vector Drive and Parametric Drive 535.2 A Lumped Mass MEMS Gyroscope – Dual Foucault Pendulum Gyroscope 545.2.1 Architecture 565.2.1.1 Electrode Architecture 575.2.2 Experimental Demonstration of the Concept 575.2.2.1 Fabrication 575.2.2.2 Experimental Setup 585.2.2.3 Mechanical Characterization 605.2.2.4 Rate Gyroscope Operation 605.2.2.5 Parameter Identification 60Part III 3-D Micro-Machined Whole-Angle Gyroscope Architectures 656 Overview of 3-D Shell Implementations 676.1 Macro-scale Hemispherical Resonator Gyroscopes 676.2 3-D Micro-Shell Fabrication Processes 696.2.1 Bulk Micro-Machining Processes 696.2.2 Surface-Micro-Machined Micro-Shell Resonators 746.3 Transduction of 3-D Micro-Shell Resonators 796.3.1 Electromagnetic Excitation 796.3.2 Optomechanical Detection 806.3.3 Electrostatic Transduction 817 Design and Fabrication of Micro-glassblown Wineglass Resonators 877.1 Design of Micro-Glassblown Wineglass Resonators 887.1.1 Design of Micro-Wineglass Geometry 907.1.1.1 Analytical Solution 907.1.1.2 Finite Element Analysis 927.1.1.3 Effect of Stem Geometry on Anchor Loss 947.1.2 Design for High Frequency Symmetry 967.1.2.1 Frequency Symmetry Scaling Laws 977.1.2.2 Stability of Micro-Glassblown Structures 1017.2 An Example Fabrication Process for Micro-glassblown Wineglass Resonators 1027.2.1 Substrate Preparation 1037.2.2 Wafer Bonding 1037.2.3 Micro-Glassblowing 1047.2.4 Wineglass Release 1057.3 Characterization of Micro-Glassblown Shells 1067.3.1 Surface Roughness 1077.3.2 Material Composition 1088 Transduction of Micro-Glassblown Wineglass Resonators 1118.1 Assembled Electrodes 1118.1.1 Design 1118.1.2 Fabrication 1128.1.2.1 Experimental Characterization 1138.2 In-plane Electrodes 1158.3 Fabrication 1158.4 Experimental Characterization 1188.5 Out-of-plane Electrodes 1238.6 Design 1238.7 Fabrication 1268.8 Experimental Characterization 1299 Conclusions and Future Trends 1339.1 Mechanical Trimming of Structural Imperfections 1339.2 Self-calibration 1349.3 Integration and Packaging 135References 137Index 149