LEAD ZIRCONATE TITANATE PIEZOELECTRIC CANTILEVERS FOR MULTIMODE VIBRATING MICROELECTROMECHANICAL SYSTEMS by XUQIAN ZHENG Submitted in partial fulfillment of the requirements For the degree of Master of Science Thesis Advisor: Dr. Philip Feng Department of Electrical Engineering and Computer Science CASE WESTERN RESERVE UNIVERSITY May, 2015 CASE WESTERN RESERVE UNIVERSITY SCHOOL OF GRADUATE STUDIES We hereby approve the thesis of Xuqian Zheng Candidate for the Degree of Master of Science Committee Chair Philip Feng Committee Member Soumyajit Mandal Committee Member Francis Merat Date of Defense March 27, 2015 i Table of Contents List of Figures ................................................................................................................. v List of Tables ................................................................................................................ vii Abstract ........................................................................................................................... 1 Acknowledgement ........................................................................................................... 2 Chapter 1 Introduction ..................................................................................................... 3 1.1 Motivation ............................................................................................................. 3 1.2 Research Object and Thesis Structure..................................................................... 5 Chapter 2 Review of Related Literature and Studies ........................................................ 7 2.1 Piezoelectric Materials ........................................................................................... 7 2.1.1 Quartz.............................................................................................................. 7 2.1.2 Polyvinylidene Fluoride ................................................................................... 7 2.1.3 Zinc Oxide....................................................................................................... 8 2.1.4 Aluminum Nitride ........................................................................................... 8 2.1.5 Lead Zirconate Titanate ................................................................................... 9 2.2 PiezoMEMS Device Structures and Applications ................................................... 9 2.2.1 Actuators ......................................................................................................... 9 2.2.2 Energy Harvesters ......................................................................................... 10 2.2.3 Sensors .......................................................................................................... 11 2.3 Future of PiezoMEMS ......................................................................................... 12 Chapter 3 Device Structure and Fabrication Process ...................................................... 13 3.1 Device Fabrication Process .................................................................................. 13 3.2 Device Structures ................................................................................................. 15 3.2.1 Fabrication Induced Positive Curvature ......................................................... 15 3.2.2 Stacking of Composite Beam ......................................................................... 16 ii Chapter 4 Static Mechanical and Piezoelectric Characteristics ....................................... 18 4.1 Mechanical Characteristics ................................................................................... 18 4.1.1 Mechanical Properties of Composite Cantilever ............................................. 18 4.1.2 Pre-Stress Induced Curvature of Cantilever.................................................... 19 4.1.3 Pre-Stress Analysis ........................................................................................ 23 4.1.4 Radius of Curvature Measurement ................................................................. 25 4.2 Piezoelectric Characteristics ................................................................................. 26 4.2.1 Piezoelectric Coefficients .............................................................................. 26 4.2.2 Piezoelectric Coefficients Extracting ............................................................. 28 Chapter 5 Dynamic Mechanical and Piezoelectric Characteristics.................................. 32 5.1 Cantilever Dynamics ............................................................................................ 32 5.1.1 Resonance Frequencies .................................................................................. 32 5.1.2 Simulation ..................................................................................................... 34 5.1.3 Vibrational Energy ........................................................................................ 36 5.2 Dynamic Piezoelectric Characteristics .................................................................. 37 5.2.1 Equivalent Circuit .......................................................................................... 37 5.2.2 Electrical Energy ........................................................................................... 38 5.3 Measurements and Results ................................................................................... 38 5.3.1 Optical Measurement ..................................................................................... 38 5.3.2 Insertion Loss Measurement .......................................................................... 42 5.4 Conclusions ......................................................................................................... 44 Chapter 6 Multimode Resonant Energy Conversion....................................................... 46 6.1 Reverse Piezoelectric Effect ................................................................................. 46 6.1.1 Electrical Power Analysis .............................................................................. 46 6.1.2 Mechanical Energy Analysis.......................................................................... 46 6.2 Direct Piezoelectric Effect .................................................................................... 48 6.2.1 Measurement System ..................................................................................... 48 6.2.2 Measurement Results ..................................................................................... 50 iii Chapter 7 Conclusions and Future Work ....................................................................... 52 7.1 Conclusions ......................................................................................................... 52 7.2 Future Work ......................................................................................................... 54 References ..................................................................................................................... 55 iv List of Figures Figure 3-1. SEM images of PZT cantilevers with positive curvature induced by pre-stress in fabrication process. Scale bars in (a) and (b) are 100µm and 400µm, respectively. ... 15 Figure 3-2. Composite cantilever structure. (a) SEM image of composite cantilever tip. Scale bar is 5μm. (b) Illustration of composite cantilever structure stacking with thickness of each layer. .................................................................................................. 16 Figure 4-1. (a) Schematic cantilever with positive curvature induced by a moment on tip. (b) Infinitesimal of the curved cantilever. ...................................................................... 20 Figure 4-2. Longitudinal strain distribution along y axis in the composite beam. ........... 21 Figure 4-3. (a) Schematic infinitesimal of the simplified cantilever beam composite structure with approximately defined pre-stress-induced forces. (b) Schematic infinitesimal of pre-stress induced curvature with force and moment analysis on the right ...................................................................................................................................... 24 Figure 4-4. (a) Optical microscopic image of Device #1 and #2 with color lines indicating the sections of profile measurements. Scale bar is 100µm. (b) SEM image of the same devices. Scale bar is 100µm. (c) & (d), curvature profile of relaxed Device ... 26 Figure 4-5. Schematic illustration of piezoelectric effects. (a) Direct piezoelectric effect. (b) Reverse piezoelectric effect. ..................................................................................... 27 Figure 4-6. Photos of white light profilometer with static voltage supply system for cantilever bending curvature measurement. (a) Whole system. (b) Device supported by a customized holder under profilometer............................................................................ 29 Figure 4-7. Relation of cantilever radius of curvature and voltage applied between PZT layer. (a) Device #1. (b) Device #2. ............................................................................. 30 Figure 5-1. Lumped model of damped simple harmonic oscillator. ............................... 33 Figure 5-2. Shape of first 7 transverse resonance modes of Device #1 from COMSOL Multiphysics simulation. ..............................................................................................