VOLTAGE TUNABLE RADIO FREQUENCY MICROELECTROMECHANICAL RESONATORS AND
FILTERS
A Dissertation Presented to the Faculty of the Graduate School
of Cornell University in Partial Fulfillment of the Requirements for the Degree of
Doctor of Philosophy
by Hengky Chandrahalim
August 2009

c 2009 Hengky Chandrahalim ALL RIGHTS RESERVED

VOLTAGE TUNABLE RADIO FREQUENCY MICROELECTROMECHANICAL RESONATORS AND FILTERS
Hengky Chandrahalim, Ph.D. Cornell University 2009
Advanced radio technology demands for low power consumption and compact architecture that operate at the global range of frequency standards. Using discrete components based on traditional surface acoustic wave (SAW) or thin film bulk acoustic resonator (TFBAR) technology to manufacture quad-band and 7-band radios presently requires an enormous number of power-hungry and large-size filters fabricated on different substrates. On the other hand, employment of Micro Electromechanical Systems (MEMS) technology to create radio front-ends facilitates reductions in size, weight, cost, and power in radio communications.
Several research groups from academia and industry have recently demonstrated electrostatically and ferroelectrically transduced microelectromechanical resonators and filters that operate at high frequency and exhibit low insertion loss as potential substitutes for conventional quartz and ceramic devices. However, the modern radio architecture today also requires the ability to discern bandwidths between 0.1 MHz and 5 MHz. This requires frequency-agile intermediate-frequency filters, generating a strong demand for narrow-bandwidth channel-select filters with very high quality factors (Q), which can be formed using high-Q MEMS resonators. This dissertation presents the state of the art transduction mechanisms of MEMS resonators and filters with key innovations in DC voltage tuning schemes, packaging technology and system integration.
Electrically coupled, high-Q, tunable channel-select ladder filters comprised

of dielectrically transduced thickness shear mode resonators are presented using integrated circuit compatible bulk micromachining technology. The ladder filter consists of shunt and series resonators operating in the half-wave thickness shear vibration mode. Each constituent resonator of the filter can be excited at above 810 MHz resonant frequency with Q of 7, 800 in air and a motional impedance (RX ) of 59 Ω. The ladder filter demonstrates a center frequency tuning range of 8 MHz at 817 MHz and an adjustable bandwidth from 600 kHz to 2.8 MHz, while maintaining an insertion loss < 4 dB, stop-band rejection > 30 dB and pass-band ripple < 2 dB. By having a tunability feature, radio frequency (RF) MEMS filters can accommodate various signal waveforms with bandwidth range of 0.1 MHz and 5 MHz. In addition, errors due to fabrication can be compensated and capacitive loading in receiver architecture can be minimized.
Multi-frequency and multi-band filters on-chip has motivated the design and fabrication of a center frequency and bandwidth tunable RF MEMS filter using a series-coupled array of dielectrically-transduced square-extensional contour mode resonators. The proposed digital tuning scheme provides channel-agility and bandwidth granularity for analog spectral processors and RF spectrum analyzers. A 512 MHz overtone square-extensional mode resonator is demonstrated with a Q of 1, 800 in air and RX of 3.1 kΩ. An array of four such resonators is coupled mechanically to form a channel-select filter with 1.4 MHz bandwidth at 509 MHz center frequency. By switching the DC-biasing scheme, the filter is split into narrower high and low sub-bands, each 700 kHz wide.
Despite of the advances in device performance, packaging technology for MEMS resonators and filters remains a critical challenge. Because of the extreme sensitivity to environment, MEMS resonators and filters need a good vacuum encapsulation technology. The promising on-chip applications also require a CMOS

compatible packaging process. The first successful combination of a dielectricallytransduced 200 MHz width-extensional contour mode resonator with the epi-silicon encapsulation process is demonstrated. The fabricated encapsulated-resonator exhibits a resonant frequency of 207 MHz and a Q of 6, 400. The high f ×Q (1.2×1012 Hz) makes this encapsulated resonator an excellent candidate for applications in local oscillators for RF front-ends and frequency references.
Dielectric transduction is not only limited to solid dielectric transduction. Lateral contour-mode resonators in which the transduction gaps are filled with a liquid dielectric having much higher permittivity than air are presented. Aqueous transduction is more efficient than air-gap transduction and has a higher frequency tuning range compared to solid dielectric transduction. A 42 MHz poly-SiGe disk resonator with de-ionized (DI) water confined to the electrode gaps is demonstrated. The resonator has a measured Q of 3, 800, RX of 3.9 kΩ and 3% series frequency tuning range.
Ferroelectric materials like lead zirconate titanate (PZT) is of interest because it offers a large electromechanical coupling coefficient (kt2) and electric field dependent permittivity and modulus of elasticity. In this effort, PZT transduced resonators with the same lateral dimensions are designed and fabricated with and without a silicon device layer to explore the insertion loss, linearity, tunability and Q trade-offs between the two types of resonators. A novel air-bridge fabrication technology is developed to minimize the pad capacitances and enables the frequency excitation of PZT transduced resonators above 1.8 GHz.
PZT transduced fully-differential filters are designed by mechanically coupling two high-overtone width-extensional mode resonators. The fully-differential filter configuration cancels the feed-through capacitance and improves the stop-band floor of the filter. The demonstrated electric field tuning provides channel-agility

and bandwidth adjustability for incorporation of analog spectral processors in state of the art radio receiver architectures. The filter demonstrates a center frequency tuning range of 7 MHz at 260 MHz and an adjustable bandwidth from 3 MHz to 6.3 MHz, while maintaining a maximum frequency shift due to hysteresis effects below 0.14% and a stop-band rejection floor of −60 dB. In order to improve immunity to hysteresis and realize the narrow bandwidth channel-select filter, the PZT transduced fully-differential filters are integrated with silicon device layer. A 206.3 MHz high-overtone width-extensional filter is demonstrated with 653 kHz bandwidth, −25 dB insertion loss and −62 dB stop-band rejection in air. Uncompensated temperature coefficient of frequency (TCF) of −16 ppm/◦C and third-order input intercept point (IIP3) of +29 dBm are demonstrated by the filter.
The monolithic integration of RF components has long been a goal of researchers and will enable not only more compact and lower cost systems but previously unachievable signal processing functions. This dissertation provides the first experimental demonstration of monolithically integrated piezoelectric RF MEMS switches with contour mode filters. PZT thin films are utilized to enable both low-voltage switch operation and filter tunability. This research leverages previous work using PZT actuators for low-voltage, wide-band switches and PZT transduced silicon resonators. The two device technologies are combined using a hybrid fabrication process that combines the key components of each device fabrication into a single unified process using silicon-on-insulator (SOI) substrates. The voltage tunable and switchable filter array provides a drop-in solution for frequency-agile channel selectivity required in tranceiver front-ends.

BIOGRAPHICAL SKETCH Hengky Chandrahalim was born and brought up in Parakan, Central Java, Indonesia. He studied at Loyola High School in Semarang, Indonesia. After graduating from high school, he moved to Columbus, Ohio, to attend the Ohio State University. He completed his undergraduate education with the degree of Bachelors of Science in Electrical and Computer Engineering in 2000. After finishing his undergraduate degree, he spent three years working as an integrated circuit design engineer at Integrated Circuit Systems, Inc. in San Jose, California.
In 2003, he joined the Master of Engineering program in electrical and computer engineering at Cornell University in Ithaca, New York. He worked under supervision of Professor Amit Lal in designing on-chip PZT actuation circuits for micro-atomizers. Soon after receiving his master’s degree he decided to further pursue a doctoral degree in electrical and computer engineering at Cornell University. He then worked under the guidance of Professor Sunil A. Bhave and Professor Amit Lal in the field of radio frequency microelectromechanical systems.
iii

To my beloved family iv

ACKNOWLEDGEMENTS
The successful completion of this thesis relies upon innumerable contributions from people throughout the multiple phases my life. I am forever in debt to many individuals who provided me with friendship and companionship whom I cannot acknowledge by their names here.
First and foremost, I would like to express my deepest appreciation to my research advisor, Professor Sunil A. Bhave, for his continuous advice, support and friendship during my graduate years. He has been a very understanding advisor, wonderful friend and genuine source of guidance to me during the last five years at Cornell. I thank him for strongly coupling me into multifarious aspects of research and teaching. I have always been impressed with his resourcefulness in the technical area. His understanding and benevolence to students are always the supreme virtues to me. I am thankful to my research co-advisor Professor Amit Lal who first introduced me to MEMS and supported my early research at Cornell. His futuristic engineering wisdom always enlightens me of bountiful research possibilities in MEMS area. I really appreciate his valuable feedback from time to time throughout my Ph.D. years. I am also grateful to Professor Ephrahim Garcia for serving as members of my dissertation committee, reviewing this manuscript and providing constructive critique and advice, and to Professor Clifford R. Pollock and Professor Tsuhan Chen for their enlightening discussions and encouragement.
I would like to thank Professor Paul L. McEuen and his group for supporting our experiments with nanotubes and graphene in his laboratory. Special thanks for Arend van der Zande, Zhaohui Zhong and Scott Bunch who assisted me to grow the carbon nanotubes and deposited graphene on our devices.
v

I am indebted to many former and current members of OxideMEMS and SonicMEMS laboratories. I would like to particularly thank Shankar Radhakrishnan, who thought me most of my micro-fabrication skills, Serhan Ardanuç, who is always willing to share his technical wisdom in acoustics and MEMS in general, Dana Weinstein for deriving the electrical equivalent model of thickness shear mode resonator, Lih Feng Cheow for running extensive simulations on the ladder filter, Chen Chen for providing spontaneous entertainments to the group , Venkata Siva Prasad Pulla, Steven Tin and Norimasa Yoshimizu for plenty of helpful technical and non-technical discussions. I ought to thank all the OxideMEMS and SonicMEMS members whose companionship made my life in Phillips Hall more exciting and stimulating - Dana Weinstein, Chen Chen, Eugene Hwang, Suresh Sridaran, Tiffany Cheng, Susmita Bhandari, Laura Fegely, David Hutchison, Wenzhe Zhou, Muhammet Kürşad Araz, Kwame Amponsah, Serhan Ardanuç, Alper Bozkurt, Venkata Siva Prasad Pulla, Abhishek Ramkumar, Janet Shen, Steven Tin, Norimasa Yoshimizu, Xi Chen, Rajesh Duggirala, Hang Guo, Hui Li, Pietro Toscano, Shankar Radhakrishnan and Shyi-Herng Kan.
My time spent at Cornell was made special through the social and academic interactions with my fellow students. I am very fortunate to have these people as friends. In no particular order, I wish to thank Wei Min Chan, Tchefor Tumasang Ndukum, Manoj Pandey, Song Peng, Christianto Liu, Georgios Lilis, Onimisi Ojeba, Khye Suian Wei, Udayan Ganguly, Shriram Shivaraman, Sasikanth Manipatruni, Jaegoo Lee, Alex Tuohung Hou, Rajeev Kumar Dokania, Xiao Wang, Haining Wang, Navin Mallavarpu, Ali Gokirmak, An-swol Hu, Kwok Loon Chan, Jonathan Aaron Winter, Keith Lyon, Justin Seo, Raymond Hyun Chull Kim, Yunju Sun and Joon Young Kwak.
vi

I thank all the past and present members of the Cornell Badminton Club, for the camaraderie and thrill I enjoyed on the courts of Helen Newman Hall. My life in Ithaca will not be the same without all of you: Professor Anil Netravali, who is the faculty advisor to the club, Xiaoshi Jin, Siew Ann Cheong, Chuan Lee, Archit Lal, Shengfeng Shen and I-Ho Chang, Ram Narayan, Mike Hsu, Chula Watugala, Winson Lin, Zhongtao Fu, Yuping Zhou, Seung Jin Oh, Peeyush Bhargava, Charlie Chuan-Che Wang and Nai-Ying Chang, Ivan Han, Suntao Wang, Xujie Zhang, Jian Zhang, Yong Sheng Khoo, Sebastien Lavoue, Peng Zhao, Quan Zhang, Venkat Krishnan and Shrut Kirti.
I also cannot forget the administrative support of present and former ECE department staff including Sue Bulkley, Lisa Gould, Sally Bird, Cheryl Francis, Dorothy Palladino, Linda Struzinsky and Daniel Richter. Special thanks to Jamie Dal Cero, who helped me a lot with the "shipping business" and always made sure I got prompt reimbursement for expenses during business travels and to Scott Coldren, who is our department manager of student services for his kind assistance in writing departmental letters, and for reminding us with all the important deadlines throughout the Ph.D. years.
I feel grateful to my former colleagues at ICS, who remain good friends until now. This includes Teck Chuan Ng, Eugene Chin, Kah Suan Seah, Deanna Luu, Vince Tat, Bruce Lo, Kristen Chen, Toai Nguyen, Pouran Asadipour, Allen Su, David Chiu, Tacettin (Taji) Isik, Michel Charbonnier and Chau Nguyen. Special thanks to Hoang Tran, who was my team manager for being a very understanding and supportive manager, and to Linda Wheeler, who gave me the opportunity to handle the duty of an integrated circuit design engineer despite of my lacking of relevant experience at that time.
vii

I am fortunate to meet friends from MEMS community in various conferences and had wonderful discussions with them. Their comments, critiques and suggestions are very beneficial for my research and in writing this manuscript. In no prticular order, I would like to thank Jonathan Hammond, Jagan Rao, Bongsang Kim, Maryam Ziaie-Moayyed, Yang Lin, Cheng Jie Zuo, Gavin Ho, Gianluca Piazza, Phil Stephanou, Tomohiro Ishikawa, Chiung Cheng Lo, Chuan-Yu Shao, Shih-Wei Lee, Franklin Chiang, Gaurav Shah, Jon Lovseth, Wen-Lung Huang, Jan Kuypers, Sheng-Shian Li and Yu-Wei Lin.
The fabrication of solid dielectrically transduced devices was made possible through kind assistances of Rob Ilic, Meredith Metzler, Vince Genova, Phil Infante, Garry J. Bordonaro, Michael Skvarla, Jerry Drumheller and the rest of the staff of the Cornell Nanoscale Science and Technology Facility. Special thanks to Rob Illic for his help in the clean room especially during odd hours, and to Meredith Metzler and Vince Genova who developed and characterized the etch recipe for hafnia. I am grateful for the support of Cornell Center for Materials Research and Center for Nanoscale Systems staff. Special thanks to Dr. Jonathan Shu, who assisted me with RF testing before our testing facility in Phillips Hall was ready, and to Mick Thomas, who has been always helpful with FIB.
Thanks to all Analog Spectral Processors (ASP) team members whose expertise has greatly helped me in completing this thesis. I would like to especially thank Professor Roger T. Howe and Professor Thomas W. Kenny at Stanford University for providing constructive comments and suggestions with the encapsulated resonators. Thanks to Kuan-Lin Chen and Shasha Wang at Stanford University who worked on the packaging process our dielectrically transduced contour-mode resonators.
viii

I would also like to thank the outstanding researchers and scientists with whom I have collaborated on various projects. Special thanks to Dr. Ronald Polcawich and Jeff Pulskamp at U.S. Army Research Laboratories for their assistance in fabricating PZT transduced devices, to Dr. Emmanuel Quévy for providing poly-SiGe samples, to Dr. Jennifer Sigman, Dr. Jon Ihlefeld and Dr. Paul Clem at Sandia National Laboratories for their assistance in fabricating ferroelectrically transduced devices, to Dr. Graham Cameron at Mayo Clinic, who assisted ASP program with device verification, to Dr. Christian Rembe and Sebastian Boedecker at Polytec, who helped with optical characterization of our resonators, to Dr. Kushal Bhattacharjee at RF Micro Devices, Inc. and Dr. Robert Potter at Rockwell Collins, Inc. for technical discussions, help, and encouragement.
Most of all, I would like to thank my parents for their love and support and to my sister Yulia that I love very much. I would like to thank Imelda Friska who has assisted me tremendously by providing many useful illustrations to complete this dissertation, and to Candra Alisiswanto a great friend who has always been there for me.
This research was funded by the DARPA ASP program, by Cornell Center for Nanoscale Systems (an NSF/Industry/University Research Center), by a grant from RF Micro Devices, Inc., and by a grant from the Charles Stark Draper Laboratory, Inc.
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TABLE OF CONTENTS

Biographical Sketch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii Dedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv

1 RF MEMS and the New Paradigms in Modern Wireless Commu-

nications

1

1.1 Analog Spectral Processors . . . . . . . . . . . . . . . . . . . . . . . 7

1.2 Previous Electromechanical Resonators . . . . . . . . . . . . . . . . 10

1.2.1 Quartz Crystal Resonators . . . . . . . . . . . . . . . . . . . 10

1.2.2 Surface Acoustic Wave Resonators . . . . . . . . . . . . . . 13

1.2.3 Bulk Acoustic Wave and FBAR Resonators . . . . . . . . . 15

1.2.4 Contour-Mode Resonators . . . . . . . . . . . . . . . . . . . 17

1.3 Contributions of this Dissertation . . . . . . . . . . . . . . . . . . . 22

1.4 Dissertation Organization . . . . . . . . . . . . . . . . . . . . . . . 22

2 High-Q MEMS Thickness Shear Resonators and Analog Voltage

Tunable Electrically-coupled Channel-Select RF Filters

24

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

2.2 Quarter-wave Thickness Shear Resonator . . . . . . . . . . . . . . . 26

2.2.1 Electrical Equivalent Impedances of a Quarter-wave TSM

Resonator . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

2.2.2 Fabrication Process . . . . . . . . . . . . . . . . . . . . . . . 31

2.2.3 Measurement Results . . . . . . . . . . . . . . . . . . . . . . 33

2.3 Half-wave Thickness Shear Resonator . . . . . . . . . . . . . . . . . 36

2.3.1 Motional Impedance of a Half-wave TSM Resonator . . . . . 37

2.3.2 Fabrication Process . . . . . . . . . . . . . . . . . . . . . . . 39

2.3.3 Measurement Results . . . . . . . . . . . . . . . . . . . . . . 39

2.4 Electrically Coupled RF MEMS Ladder Filters . . . . . . . . . . . . 41

2.5 RF MEMS Channel-select Filters with Tunable Center Frequency

and Bandwidth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

2.5.1 Orthogonal Frequency Tuning . . . . . . . . . . . . . . . . . 46

2.5.2 Pole-Zero Seperation Tuning . . . . . . . . . . . . . . . . . . 47

2.5.3 Filter Tuning Algorithm . . . . . . . . . . . . . . . . . . . . 49

2.5.4 Fabrication Process . . . . . . . . . . . . . . . . . . . . . . . 49

2.5.5 Measurement Results . . . . . . . . . . . . . . . . . . . . . . 51

2.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

x

3 High-overtone Square-extensional Resonators and Digitally Pro-

grammable Mechanically-coupled Frequency-agile Filters

58

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

3.2 High-overtone Square-extensional Mode Resonator . . . . . . . . . . 59

3.2.1 Effective mass, Damping ratio and Effective spring constant 61

3.2.2 Electromechanical Coupling Constant . . . . . . . . . . . . . 63

3.2.3 Electrical Equivalent Impedances of a High-overtone Square-

extensional Resonator . . . . . . . . . . . . . . . . . . . . . 64

3.3 Digitally Programmable Filters . . . . . . . . . . . . . . . . . . . . 65

3.4 Fabrication Process . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

3.5 Calibration and De-embedding Techniques . . . . . . . . . . . . . . 74

3.6 Characterization of a High-overtone Square-extensional Mode Res-

onator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

3.7 Characterization of a Digitally Programmable Filter . . . . . . . . . 76

3.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

4 Vacuum-encapsulated CMOS-compatible Packaging Technology

for Contour-mode Resonators

81

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

4.2 Width-extensional Mode Resonator . . . . . . . . . . . . . . . . . . 82

4.3 Epitaxy-silicon Microshell Packaging . . . . . . . . . . . . . . . . . 83

4.4 Fabrication Process . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

4.5 Measurement Results . . . . . . . . . . . . . . . . . . . . . . . . . . 87

4.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

5 Aqueous Transduction of Contour-Mode RF MEMS Resonators 92 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 5.2 Aqueous Transduction of a Contour-mode Poly-SiGe Disk Resonator 93 5.2.1 Measurement of a Poly-Sige Disk Resonator in Air . . . . . . 94 5.2.2 Measurement of Poly-Sige Disk Resonators with DI Water . 97 5.2.3 Series Frequency Tuning of Poly-Sige Disk Resonators . . . . 100 5.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

6 PZT Transduced Voltage Tunable Resonators

103

6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

6.2 Length Extensional Mode Resonator . . . . . . . . . . . . . . . . . 104

6.2.1 Effective mass, Damping ratio and Effective spring constant 106

6.2.2 Electromechanical Coupling Constant . . . . . . . . . . . . . 108

6.2.3 Electrical Equivalent Impedances of a PZT Transduced LEM

Resonator . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

6.3 Fabrication Process . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

6.4 Measurement Results . . . . . . . . . . . . . . . . . . . . . . . . . . 113

6.4.1 Resonance Frequency, Motional Impedance, and Quality Fac-

tor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

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6.4.2 DC Voltage Tuning . . . . . . . . . . . . . . . . . . . . . . . 115 6.4.3 Linearity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 6.4.4 Hysteresis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 6.5 High-overtone Width-extensional Mode Resonators . . . . . . . . . 117 6.6 Air-bridge Fabrication Process . . . . . . . . . . . . . . . . . . . . . 119 6.7 Measurement Results . . . . . . . . . . . . . . . . . . . . . . . . . . 122 6.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

7 PZT Transduced Mechanically-coupled Frequency-agile Filters 126 7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 7.2 PZT-only Mechanically-coupled Filters . . . . . . . . . . . . . . . . 127 7.2.1 Fully-differential High-overtone Width-extensional Filters . . 127 7.2.2 Measurement Results . . . . . . . . . . . . . . . . . . . . . . 129 7.3 PZT-on-silicon Mechanically-coupled Filters . . . . . . . . . . . . . 133 7.3.1 Measurement Results . . . . . . . . . . . . . . . . . . . . . . 135 7.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139

8 Monolithically Integrated Piezo-MEMS Switches and Contour-

mode Filters

141

8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

8.2 Design of Integrated PZT transduced Switches and Filters . . . . . 143

8.3 Fabrication Process . . . . . . . . . . . . . . . . . . . . . . . . . . . 146

8.4 Measurement Results . . . . . . . . . . . . . . . . . . . . . . . . . . 147

8.4.1 Frequency Domain Measurement . . . . . . . . . . . . . . . 147

8.4.2 Time Domain Measurement . . . . . . . . . . . . . . . . . . 150

8.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

9 Future Research Directions

152

9.1 Solid Dielectrically Transduced Devices . . . . . . . . . . . . . . . . 152

9.1.1 Transduction Efficiency . . . . . . . . . . . . . . . . . . . . . 152

9.1.2 On-chip Fully-differential Configuration . . . . . . . . . . . . 152

9.1.3 Long-term Stability . . . . . . . . . . . . . . . . . . . . . . . 153

9.1.4 Post-MEMS CMOS Integrated Systems . . . . . . . . . . . . 154

9.2 Liquid Dielectrically Transduced Devices . . . . . . . . . . . . . . . 156

9.3 PZT Transduced Devices . . . . . . . . . . . . . . . . . . . . . . . . 158

9.3.1 High-Q SHF PZT Transduced Resonators . . . . . . . . . . 158

9.3.2 Monolithically-integrated PZT Based Microsystems . . . . . 159

A Fabrication Process of Thickness Shear Resonators and Filters 160

B Calibration and De-embedding Techniques

166

Bibliography

168

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LIST OF TABLES 1.1 Quartz crystal mode of vibration and frequency range . . . . . . . 11 1.2 Quartz crystal cut and frequency range . . . . . . . . . . . . . . . 12 2.1 The measured characteristics of electrically coupled TSM filters . . 43 3.1 Design parameters of the high-overtone square-extensional resonator 67 3.2 Design parameters and measured data of the high-overtone square-
extensional resonator . . . . . . . . . . . . . . . . . . . . . . . . . . 76 3.3 Performance summary of the digitally programmable filter . . . . . 80 6.1 The measured characteristics of PZT-on-silicon resonators . . . . . 114 6.2 The measured characteristics of PZT-only resonators . . . . . . . . 114 6.3 The measured characteristics of PZT-on-silicon resonator with dif-
ferent bias voltages . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 6.4 The measured characteristics of PZT-only resonator with different
bias voltages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 6.5 The measured characteristics of high-overtone WEM resonators
with different silicon thicknesses . . . . . . . . . . . . . . . . . . . 125 7.1 The measured frequency response of a PZT transduced high-overtone
WEM filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 7.2 The measured frequency response of a PZT-on-silicon high-overtone
WEM filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
xiii

LIST OF FIGURES

1.1 Schematic illustrating the Hybrid Insect MEMS (HIMEMS). . . . . 2

1.2 Super-heterodyne Radio Architecture. . . . . . . . . . . . . . . . . 3

1.3 Mechanically-coupled resonant gate transistors (RGT) (a) Device

geometry, (b) Microphotogrpah of a device with cantilever length

of 240 μm, (c) Frequency response of a mechanically-coupled RGT

with fC of of 22 kHz and BW of 300 Hz, and (d) Frequency response of a mechanically-coupled RGT with fC of of 132 kHz and BW of 1 kHz. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5

1.4 Receiver architecture of Analog Signal Processors. . . . . . . . . . 9

1.5 Quartz crystal resonators: (a) Flexural/Length-extensional resonator,

(b) Face-shear resonator, (c) Thickness-shear resonator, (d) Pack-

aged quartz crystal resonator. . . . . . . . . . . . . . . . . . . . . . 12

1.6 A typical SAW device consists of two sets of interdigital transduc-

ers. The input transducer converts electric field energy into me-

chanical wave energy, and the output transducer senses the propa-

gated surface waves and converts the mechanical energy back into

an electric field. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

1.7 Packaged SAW resonators and filters with various frequency ranges. 14

1.8 Cross-section of bulk acoustic wave (BAW) resonators: (a) Solidly

mounted resonators (SMR), (b) Membrane bulk acoustic wave res-

onator (FBAR). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

1.9 Air-gap contour-mode resonators: (a) A radial-contour mode disk

resonator, (b) A polysilicon hollow-disk ring resonator, (c) An ex-

tensional wine-glass-mode resonator, (d) A nanocrystalline diamond

disk resonator, (e) A square-extensional mode resonator, and (f) A

Poly-SiGe contour-mode disk resonator. . . . . . . . . . . . . . . . 18

1.10 Piezoelectrically transduced contour-mode resonators: (a) An AlN

transduced ring-shaped contour-mode resonator, (b) An AlN trans-

duced square-ring-shaped contour-mode resonator, and (c) A ZnO

on silicon contour-mode resonator, (d) A ZnO-on-nanocrystalline

diamond resonator, and (e) An AlN transduced mechanically-coupled

contour-mode filter. . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.1 X-displacement contour plot from Ansys simulation of the symmetric quarter-wave thickness shear mode. . . . . . . . . . . . . . . 27
2.2 The schematic of an unreleased thickness shear bar. . . . . . . . . . 28 2.3 2-D cross-section schematic of the conversion of transverse electro-
static stress in the silicon nitride thin film to thickness shear mode in the half-length (A-A’ in Figure 2) bar resonator. . . . . . . . . . 29 2.4 Fabrication process flow of quarter-wave thickness shear mode resonators. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 2.5 SEM of a silicon nitride-on-silicon unreleased bar resonator. . . . . 33

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2.6 Measured transmission of the thickness shear mode of the unreleased resonator in air. . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.7 A partially released quarter-wave thickness shear mode resonator. . 34 2.8 Measured transmission of the partially released shear mode res-
onator in air. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 2.9 ANSYS contour plot of the symmetric half-wave thickness shear
mode. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 2.10 Schematic of a fully released half-wave thickness shear bar resonator. 37 2.11 ANSYS simulation of length (L) vs resonant frequency (fC) of the
3.2 μm thick half-wave shear mode resonator. . . . . . . . . . . . . 38 2.12 (a) SEM of a hafnium dioxide-on-silicon fully released bar res-
onator. (b) SEM of the 30 nm hafnium dioxide layer on the top of the silicon resonator. . . . . . . . . . . . . . . . . . . . . . . . . . . 39 2.13 Measured transmission response of a half-wave TSM resonator in air. 40 2.14 (a) Electrically coupled ladder filter configuration. (b) Bandpass frequency response of the ladder filter. . . . . . . . . . . . . . . . . 41 2.15 SEM of an array of ladder configuration electrically coupled thickness shear filters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 2.16 Measured transmission response showing two 650 kHz channelselect filters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 2.17 Measured filter transmission response over a wide frequency range. 44 2.18 The distorted bandpass response of the filter due to fabrication tolerances. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 2.19 Longitudinal cross-section of a deflected half-wave thickness shear mode resonator due to the orthogonal biasing configuration. . . . . 47 2.20 Electrical equivalent circuit of a dielectrically transduced MEMS resonator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 2.21 (a) The 3-D model of tunable ladder filter. (b) The device crosssection with isolated resonator and substrate for applying independent tuning voltages. . . . . . . . . . . . . . . . . . . . . . . . . . . 50 2.22 Microphotograph of tunable ladder filter with a gold wirebond bridge. 51 2.23 (a) The uncalibrated frequency characteristic of the resonator. (b) The measured frequency characteristic of the resonator after Cascade substrate calibration. . . . . . . . . . . . . . . . . . . . . . . . 52 2.24 (a) Measured frequency characteristic of the resonator after SOI calibration. (b) Measured series resonance tuning for VS = 5 V and VS = (i) 12 V, (ii) 8 V, and (iii) 5 V. (c) Resonant frequency tuning vs. substrate voltage. . . . . . . . . . . . . . . . . . . . . . . . . . 53 2.25 (a,b,c) Measured transmission response demonstrating pole-zero separation of a thickness shear mode resonator as DC bias VP increases from 5 V to 10 V. (d) Measured pole-zero separation vs. DC bias voltage of the resonator. . . . . . . . . . . . . . . . . . . . 54
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2.26 (a) Measured transfer function of ladder filter with no tuning. (b)
Measured transmission of ladder filter with fC tuning from 817 MHz to 809 MHz with (i) no tuning, and (ii) series resonator: VP = 5 V, VS = 15 V; shunt resonator: VP = 5 V, VS = 12 V. (c) Measured transmission of ladder filter with BW tuning from 0.6 MHz to 2.8 MHz with (i) no tuning, (ii) series resonator: VP = 12 V, VS = 12 V; shunt resonator: VP = 13 V, VS = 16 V. (d) Measured transfer function of ladder filter with BW tuning from 0.6 MHz to 1.4 MHz and fC tuning from 817 MHz to 811 MHz with (i) no tuning, and (ii) series resonator: VP = 10 V, VS = 19 V; shunt resonator: VP = 9 V, VS = 17 V. . . . . . . . . . . . . . . . . . . . . . . . . . . .

55

3.1 (a) Schematic of a 2-port high-overtone square-extensional mode resonator. (b) Cross-section of the device showing various layers that are deposited to build the resonator. (c) ANSYS mode shape of a high-overtone square-extensional resonator. . . . . . . . . . . . 60
3.2 Electrical equivalent circuit of a dielectrically transduced high-overtone square-extensional resonator. . . . . . . . . . . . . . . . . . . . . . 65
3.3 Simulated performance of a 500 MHz high-overtone square-extensional resonator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
3.4 Schematic of a digitally programmable filter composed of four series mechanically-coupled checkered-electrode resonators. Each resonator has individually addressable RF + DC lines. The silicon device layer is an RF ground to prevent substrate losses. . . . . . . 68
3.5 Four vibration modes of a 4-pole filter consisting of overtone squareextensional mode resonators. . . . . . . . . . . . . . . . . . . . . . 69
3.6 Simulated performance of a digitally programmable filter composed of four series mechanically-coupled checkered-electrode resonators. (a) Simulated 4-pole frequency response of the filter. (b) Simulated lower sub-band filter response. The biasing scheme forces the left two resonators to vibrate out of phase and sums the out-of-phase motional current of the right two resonators. (c) Simulated higher sub-band filter response. The biasing scheme forces the left two resonators to vibrate in phase and sums the in-phase motional current of the right two resonators. . . . . . . . . . . . . . . . . . . . . . . 71
3.7 Fabrication process flow of high-overtone square-extensional mode resonators and digitally programmable filters. . . . . . . . . . . . . 72
3.8 SEM image of a high-overtone 2-D square-extensional mode resonator with checkered electrodes for transduction. The resonator consists of a 55 nm SiN transducer sandwiched between poly electrodes and 2.75 μm thick silicon device layer. An oxide pedestal layer is implemented to elevate the RF signal lines off the ground plane. Pt/Au metal traces and pads are introduced to improve RF signal integrity and reduce noise during probing. . . . . . . . . . . 73

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3.9 SEM image of a digitally programmable filter composed of four series mechanically-coupled checkered-electrode resonators. Each resonator has individually addressable RF + DC lines. The silicon device layer is an RF ground to prevent substrate losses. All RF paths are metalized, routed on an elevated oxide bridge to reduce capacitance and de-embedded to the edge of DRIE trench. . . . . . 73
3.10 (a) Testing configuration for a 2-port high-overtone square-extensional mode resonator. (b) Measured series resonance response of a 2-port high-overtone square-extensional mode resonator in air at room temperature and pressure. . . . . . . . . . . . . . . . . . . . . . . . 75
3.11 Performance of a 50 Ω terminated filter with three different bias configurations in air. (a) Measured 4-pole frequency response of the filter. (b) Measured lower sub-band filter response. The biasing scheme forces the left two resonators to vibrate out of phase and sums the out-of-phase motional current of the right two resonators. (c) Measured higher sub-band filter response. The biasing scheme forces the left two resonators to vibrate in phase and sums the in-phase motional current of the right two resonators. . . . . . . . . 78
3.12 Transmission response of the filter with three different bias configurations after termination using the PNA’s pole-Z conversion function. The attenuated modes are clearly visible in the transmission response of the lower sub-band filter. The filter stop-band floor is high because electrical resistance in the ground plane leads to large capacitive feedthrough between drive and sense ports. . . . . . . . 79
4.1 (a) Schematic diagram of the dielectrically transduced, width-extensional mode resonator. (b) ANSYS contour plot of the width-extensional bar mode shape. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
4.2 Epi-silicon microshell encapsulation process for dielectrically transduced resonators. Vertical epi-vias to the poly electrodes provide RF input/output while the vias to the silicon device layer provide a micro RF -cage providing a shielded micro-environment. . . . . . 84
4.3 SEM of the fabricated resonator. The zoomed-in picture on the right shows the thin poly electrode on top of the resonator bar. The zoomed-in picture on the left shows the electrical contact between the epi-silicon and the device layer. . . . . . . . . . . . . . . . . . . 86
4.4 Transmission response using the 2-port measurement. Capacitive feedthrough masks the electromechanical resonance, resulting in a sharp dip at the target frequency. . . . . . . . . . . . . . . . . . . . 87
4.5 (a) Schematic of the pseudo-differential measurement setup, and (b) The equivalent circuit of pseudo-differential measurement to cancel the capacitive feedthrough current. . . . . . . . . . . . . . . 89
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4.6 Transmission responses of the simple 2-port measurement and pseudodifferential measurement. It is clearly shown that the resonance peak matches the sharp dip shown in the 2-port measurement. . . . 90
5.1 SEM image of a poly-SiGe disk resonator: (a) Cross-section of the resonator showing the 60 nm lateral air-gap (b) Close-up of anchor, and (c) Top view. . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
5.2 (a) Transmission measurement setup, and (b) Transmission response in air. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
5.3 (a) Schematic illustrating the experiment. The water wicks the 60 nm gap and is left under the structure. (b) Photograph of water droplet placed on resonator and then moved to the edge. (c) Measured transmission response after water drop is rolled away from the resonator: Q of 430 at 36 MHz. . . . . . . . . . . . . . . . . . . 97
5.4 (a) Schematic of water droplet rolled across the resonator; wicking the transducer gap but minimizing the water left underneath the resonator. (b) Transmission response: Q of 3, 800 at 42 MHz with RX = 3.9 kΩ. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
5.5 Transmission response of a resonator with repeated rolls of the DI water droplet. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
5.6 (a) 0.1% center frequency tuning of the air-gap transduced disk resonator before anchor failure. (b) In DI water, the resonator center frequency is tuned up to 3%, before the onset of electrolysis. 101
6.1 A 3-D schematic of PZT-on-Silicon length-extensional mode resonator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
6.2 An ANSYS mode shape of a length-extensional mode resonator. . . 105 6.3 The cross-section of a length-extensional mode resonator. . . . . . 106 6.4 Electrical equivalent circuit of a PZT transduced LEM resonator. . 109 6.5 Fabrication process-flow for PZT-on-silicon and PZT-only resonators.111 6.6 (a) SEM of a released PZT-only resonator. (b) SEM of a released
PZT-on-silicon resonator. The isotropic pit due to the XeF2 etch can be seen in the background. . . . . . . . . . . . . . . . . . . . . 112 6.7 Measured transmission response of PZT-only and PZT-on-silicon resonators with the exact same lateral dimensions in air at room temperature and pressure. . . . . . . . . . . . . . . . . . . . . . . . 113
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6.8 (a) Measured transmission of a 190 μm x 40 μm PZT transduced resonator on 10 μm silicon with different bias voltages in air at room temperature and pressure. 0.2% frequency tuning capability is observed due to DC bias dependent Young’s modulus and density of PZT thin film. (b) Measured transmission of a 90 μm x 20 μm PZT-Only resonator with five different bias voltages in air at room temperature and pressure. 5.1% frequency tuning capability is observed due to DC bias dependent Young’s modulus and density of PZT thin film. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
6.9 Measured IIP3 of (a) a 90 x 20 μm2 PZT-only, and (b) a 190 x 40 μm2 PZT on 10 μm silicon resonator with 0 V DC bias in air at room temperature. . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
6.10 (a) Measured hysteresis effect in the relative permittivity of a PZT thin film. (b) A PZT-on-silicon resonator shows imperceptible hysteresis, while a PZT-Only resonator shows a maximum of 0.17% center frequency (fC) shift. . . . . . . . . . . . . . . . . . . . . . . 118
6.11 (a) Schematic of a PZT-only high-overtone width-extensional mode resonator. (b) Schematic of a PZT-on-silicon high-overtone widthextensional mode resonator. (c) ANSYS mode shape of a highovertone width-extensional mode resonator. . . . . . . . . . . . . . 120
6.12 Air-bridge process cross-section of PZT-only and PZT-on-silicon high-overtone width-extensional mode resonators fabricated on the same wafer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
6.13 SEM of the fabricated high-overtone width-extensional mode resonator. The zoom-in picture shows the air-bridge routing that isolates the resonator from the bonding-pads. . . . . . . . . . . . . . . 123
6.14 (a) Measured transmission response of PZT-only and PZT on 3 μm, 5 μm and 10 μm silicon resonators with the exact same lateral dimensions in air at room temperature and pressure. All measurements were performed using termination impedances (RL) of 50 Ω. (b) A plot of silicon thickness (tSi) vs the calculated, simulated and measured resonance frequency (fC). . . . . . . . . . . . . . . . . . 124
7.1 (a) ANSYS modal analysis showing in-phase and out-of-phase mode of vibrations of a mechanically-coupled high-overtone width extensional filter. (b) SEM image of a PZT transduced high-overtone mechanically-coupled width-extensional filter with differential electrodes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
7.2 Testing configuration for a 2-pole mechanically-coupled high-overtone fully-differential filter. . . . . . . . . . . . . . . . . . . . . . . . . . 129
7.3 Measured transmission of a PZT transduced 2-pole high-overtone WEM filter with electric field tuning. Input and output terminals were terminated with 50 Ω termination impedances (RL) for all measurements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
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7.4 Measured third-order input intercept point (Δf = 400 kHz) of the filter demonstrates IIP3 of +21 dBm. . . . . . . . . . . . . . . . . 131
7.5 Measured frequency shifts in PZT transduced high-overtone width extensional filter due hysteresis effect in PZT. A maximum frequency shift of 0.14% was recorded. . . . . . . . . . . . . . . . . . 133
7.6 (a) Schematic of a mechanically-coupled PZT-on-silicon filter. (b) SEM image of a PZT-on-silicon high-overtone mechanically-coupled width-extensional filter with differential electrodes. . . . . . . . . . 134
7.7 Measured transmission of a PZT-on-silicon 2-pole high-overtone WEM filter with electric field tuning. Input and output terminals were terminated with 50 Ω termination impedances (RL) for all measurements. . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
7.8 Measured third-order input intercept point (Δf = 400 kHz) of the filter demonstrates IIP3 of +29 dBm. . . . . . . . . . . . . . . . . 138
7.9 Measured frequency shifts in PZT-on-silicon high-overtone width extensional filter due hysteresis effect in PZT. An imperceptible frequency shift of 0.013% was recorded. . . . . . . . . . . . . . . . 139
8.1 SEM image of an integrated single pole dual throw (SP2T) PZTMEMS switch and two PZT transduced width-extensional contourmode filters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
8.2 (a) SEM image of the air-bridge used for switch operation, and (b) reduced large pad capacitances in the filters. . . . . . . . . . . . . . 144
8.3 (a) SEM image of the width-extensional contour-mode filter. (b) Anti-symmetric and symmetric ANSYS mode shapes of a fundamental width-extensional mode filter. . . . . . . . . . . . . . . . . . 145
8.4 (a) S21 data at 0 V and 7 V for the PZT-MEMS switch co-fabricated with the PZT transduced width-extensional contour-mode filters. (b) S21 response of an integrated SP2T switch and filter with the switch in the Off-state (0 V), (c) S21 response for the left switch and filter with the switch On (7 V) and with 10 V VDC applied to the filter, and (d) S21 response for the right switch and filter. . . . 148
8.5 S21 response for a stand-alone PZT transduced contour-mode filter and an integrated PZT transduced switch + contour-mode filter with the DC bias at 10 V for both devices. The switch increases insertion loss (IL) by 0.4 dB. . . . . . . . . . . . . . . . . . . . . . 149
8.6 Time domain measurements of the switch + filter highlighting the 7 V switching actuation pulses and the ring-up response of the filter with the switch in the On-state. . . . . . . . . . . . . . . . . . . . 151
9.1 Estimated values of motional resistance (RX ) versus DC bias voltage for different dielectric materials. . . . . . . . . . . . . . . . . . 153
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9.2 (a) Pseudo-differential measurement setup to characterize the vacuumencapsulated resonator. (b) On-chip fully-differential configuration to eliminate parasitic capacitances. . . . . . . . . . . . . . . . . . . 154
9.3 Open-loop long-term stability measurement of a silicon nitride transduced vacuum-encapsulated resonator. (a) Measured quality factor as a function of time, and (b) Measured frequency as a function of time. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
9.4 (a) Hybrid-integration of a super-regenerative CMOS-MEMS transceiver. (b) Post-MEMS CMOS monolithically integrated system. . . . . . 155
9.5 (a) Four fundamental fluidic operations considered essential to build digital microfluidic circuits, which can be used for lab-on-a-chip or micro total analysis system all by electrowetting. (b) Lateral photographs of light-driven motion of an olive oil droplet. (c) Top-view of a liquid droplet moving along a liquophilic microstripe. The array of Ti-resistors (shown in light gray) beneath the liquophilic stripes locally heat the droplet thereby modifying the surface tension and propelling the liquid toward the colder regions of the device surface. The dark gray stripes represent the leads and contacts (Au) for the heating resistors. (d) Time shots of droplets moving on ratchet-tracks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
9.6 (a) ANSYS modal analysis of a high-overtone thickness-mode resonator. (b) Measured frequency response of a 50 Ω terminated PZT transduced high-overtone thickness-mode resonator in air at room temperature and pressure. . . . . . . . . . . . . . . . . . . . . . . . 158
9.7 Applications within the radio frequency spectrum. . . . . . . . . . 159 B.1 SOT de-embedding (a) schematic (b) equivalent circuit to cancel
pad capacitance and sheet resistance without canceling out any parasitic elements inherent to the resonators and filters. . . . . . . 167
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CHAPTER 1 RF MEMS AND THE NEW PARADIGMS IN MODERN
WIRELESS COMMUNICATIONS
Wireless communication systems have evolved rapidly with the advancements of radio engineering during the recent years. Since the first broadcast of the human voice was transmitted through the air on Christmas Eve of 1906 by Reginald Fessenden, there has been a surge of research activities in wireless telegraphy. Applications in this area have grown tremendously, allowing ubiquitous communication among people and devices. Cellular phones, wireless networks, wireless internet, sensor networks, and wireless entertainments are just to name a few. Apart from commercial applications, the wireless radio frequency (RF) communication has seen futuristic targets desired by armed forces. There is a growing military interest in developing a handheld radio operating from 20 MHz to 6 GHz with the ability to discern bandwidths between 0.1 MHz and 5 MHz.
The recent progress in Bio Micro Electro Mechanical Systems (Bio-MEMS) also has created a space for ultra low-power wireless transceivers. The U.S. Defense Advanced Research Projects Agency (DARPA) has been trying to develop tightly coupled machine-insect interfaces by placing micro-mechanical systems inside the insects during the early stages of metamorphosis as shown in Figure 1.1. The ultimate goal of this research project is to develop insect cyborgs, which could carry one or more sensors, such as a microphone or a gas sensor, to relay back information gathered from the target destination. The goal of the MEMS, inside the insects, will be to control the locomotion by obtaining motion trajectories from global positioning system (GPS) coordinates. The shrinkage in dimensions and reduction in power consumption have been the commonly recognized challenges in any integrated systems. An ultra low-power on-chip GPS radio system is necessary
1

Figure 1.1: Schematic illustrating the Hybrid Insect MEMS (HIMEMS).
in these integrated microsystems on insect because the tiny insects must be able to lift and carry the implanted microsystems including the power source to electrify the embedded electronics.
Almost all wireless devices use a transceiver to receive and transmit information. A significant amount of research has been focused on smart system architectures or other circuit-level innovations to improve the performance of radio transceivers [1–4]. However, the conventional super-heterodyne radio architecture has been commonly recognized to realize wireless transceivers today because of its reliable performance [5]. Figure 1.2 introduces the typical super-heterodyne radio architecture. The scaling law in integrated circuits over years has benefited wireless gadgets in reducing the area consumed by the active components. Unfortunately, not all the functionality in the transceiver can be implemented using transistors, especially the channel-select filtering at RF front end. As a matter of fact, presently
2

Figure 1.2: Super-heterodyne Radio Architecture.
most radio transceivers depend on a large number of discrete frequency-selection components, such as RF band-pass filters, intermediate-frequency (IF) channelselection filters, RF voltage-controlled oscillators (VCOs) and quartz crystal oscillators to perform the necessary analog signal processing as shown in Figure 1.2. These off-chip devices occupy a large portion of transceiver architecture, expensive in terms of price and the active electronics required to interface with them consume considerable amount of power.
The recent development in utilizing integrated circuit (IC) compatible lithography to micromachine mechanical structures has created an emerging field called Micro Electro Mechanical Systems (MEMS). This new field allows a new way of viewing electrical circuits and mechanical structures as an integrated system that can perform multiple of functions, including actuation, sensing and signal processing. The novel technology to fabricate microscale mechanical parts integrated with electronics has resulted vibrant research in this area. Earlier research works in MEMS since 1980s have been geared toward micro-sensors. A high-sensitivity capacitive pressure transducer with active processing circuit on the chip was demon-
3

strated [6]. The electrostatically resonated microbridge was fabricated and its vibration was detected capacitively using an integrated NMOS circuit [7]. Two novel processes for fabricating silicon piezoresistive pressure sensors were reported [8]. A surface micromachined capacitive accelerometer was designed and fabricated with on-chip detection circuitry [9].
The history of micromachining high quality factor (Q) vibrating structure was dated back in 1965, when Nathanson and Wickstrom from Westinghouse Research Laboratories fabricated mechanically resonating cantilevers over a semiconductor surface [10]. The further development of these devices resulted an electrostatically excited tuning fork that employs field effect transistor to read the output [11]. A bandpass filter response was excited by mechanically coupling two adjacent resonant gate transistors (RGT). Two adjacent RGT’s were fabricated with a coupling spring near the clamped end. Input electrodes were patterned underneath the first RGT to excite it electrostatically. The vibrations of the first RGT are mechanically transmitted to the second RGT via the coupling web, causing the second RGT to vibrate. The motional output current is detected by the electrodes underneath the second RGT. Figure 1.3 (a) and (b) show the schematic and microphotograph of a 2-pole mechanically-coupled resonant gate transistors fabricated by H. C. Nathanson et al. Frequency response of the filter exhibits center frequency (fC) of 22 kHz and filter bandwidth (BW ) of 300 Hz as shown in Figure 1.3 (c). In this work Nathanson et al was able to demonstrate a mechanically-coupled RGT filter with maximum fC of 132 kHz and BW of 1 kHz as shown in Figure 1.3 (d).
The research in resonant gate transistors at that time encountered several technical barriers and did not proceed any further. The most severe technical problems that researchers encountered thereupon were reproducibility and predictability of resonant frequencies, temperature stability and potential limitations on lifetime
4

Figure 1.3: Mechanically-coupled resonant gate transistors (RGT) (a) Device geometry, (b) Microphotogrpah of a device with cantilever length of 240 μm, (c) Frequency response of a mechanically-coupled RGT with fC of of 22 kHz and BW of 300 Hz, and (d) Frequency response of a mechanically-coupled RGT with fC of of 132 kHz and BW of 1 kHz.
5

due to fatigue [12]. Surface micromachining started to gain back the attention since Howe and Muller successfully demonstrated the resonant-microbridge vapor sensor [7]. The advancement in surface micromachining in the recent years has attracted a number of scientists to investigate more reliable, stable and reproducible micromechanical resonators and filters. Interdigitated finger (comb) structures were demonstrated to be effective for exciting electrostatically the resonance of polysilicon microstructures parallel to the plane of the substrate [13]. Resonance was observed visually, with frequencies ranging from 18 kHz to 80 kHz and quality factors from 20 to 130. Microelectromechanical filters based on coupled, lateral microresonators were succesfully fabricated [14]. This class of device has potential signal-proceessing applications for filters which require narrow bandwidth (highQ), good signal-to-noise ratio (SNR) and stable temperature and aging characteristics. The filter has a measured center frequency of 18.7 kHz and a bandwidth of 1.2 kHz in atmospheric pressure. Further research in surface micromachining of polysilicon has resulted the MEMS based monolithic high-Q oscillator, fabricated via a combined CMOS plus surface micromachining technology [15].
Early experiments at AT&T Bell Laboratories in etching bulk silicon have been developed to become another popular process of micromachining beside surface micromachining. Bulk micromachining is a fabrication technique to build mechanical structures by starting with a bulk silicon wafer, and then etching away unwanted parts, and being left with the desired mechanical devices. Bulk micromachining has been adopted strongly by MEMS community and became another prominent method to realize microelectromechanical resonators and filters. Bulk micromachining was used to back-etched a silicon wafer and released thin film bulk acoustic resonators (FBARS) with measured Q’s of over 1000 and resonant frequencies (fC) as low as 1.5 GHz and as high as 7.5 GHz [16]. The availability of high quality
6

single crystalline silicon device on insulator (SOI) wafers in combination with bulk micromachining technique has motivated several research groups to investigate the performance of SOI based MEMS resonators. Single-crystal silicon (SCS) capacitive resonators with operating frequencies in the high frequency (3 − 30 MHz) and very high frequency (30 − 300 MHz) range were successfully fabricated and characterized [17]. A bulk acoustic mode silicon micromechanical resonator with the first eigen frequency at 12 MHz and the Q of 180, 000 was demonstrated [18]. By using a low-noise preamplifier, a high spectral purity oscillator constructed using the same resonator was reported with phase noise less than −115 dBc/Hz at 1 kHz offset from the carrier.
The demand for ultra low-power, light weight and highly integrated Systemon-Chip (SoC) solutions has been placing accumulating pressure on the conventional RF circuit technology to reduce the number of off-chip and bulky passive components including the power-hungry electronic circuitry. On the other hand, the recent progress and development in micromachining through surface and bulk micromachining processes have promised innovative solutions to integrate RF electronics and MEMS technology. The "demand" factor from one research field and "availability" factor from another research area have strongly bridge the engagement between RF and MEMS as a new promising integrated technology to answer many of the unsolved problems in wireless communications.
1.1 Analog Spectral Processors
Wireless communications and microprocessing have greatly motivated the research of RF MEMS resonators and filters today. As the communication industry moves towards quad-band and 7-band technology, there is a growing demand for lightweight, low-power consumption and compact cellular phones that operate at the global range of frequency standards. Using traditional surface acoustic wave (SAW)
7

technology for these quad-band and 7-band radios, 10 −15 large and power-hungry filters fabricated on different substrates are required. On the other hand, filter banks composed of high-Q micromechanical resonators can be fabricated onchip in silicon, reducing size, weight, cost, and power in radio communications. This fact has driven several research groups to target their investigation to fit the performance of MEMS resonators or filters for a certain industry standard transceiver architecture or for a particularly allocated frequency spectrum and bandwidth [19–21].
Apart from commercial motivation, there is a growing Military interest in developing a handheld radio operating from 20 MHz to 6 GHz. This high performance radio is expected to aid battlefield communication by enabling a cognitive system that can find less-crowded frequencies to operate. In order to realize this class of radio, we need to constitute a compact, low-power handheld device that combines a spectrum analyzer and a truly powerful communication device. The spectrum analyzer would scan the frequency spectrum all the way from 20 MHz to 6 GHz to find empty spots channels that are receiving less use. Such a wide-band spectral processor would help soldiers switch channels quickly to avoid enemy jamming measures at military-use frequencies, while also enhancing military and civilian communications at other frequencies. The simplified receiver architecture of the Analog Signal Processors (ASP) is shown in Figure 1.4.
In contrast to the traditional super heterodyne receiver architecture, this receiver architecture requires the existence of high performance tunable filters to discern signals with dynamic waveforms and bandwidths between 0.1 MHz and 5 MHz. This requires frequency-agile RF filters, generating a strong demand for narrow-bandwidth channel-select filters with very high quality factors, which can be formed using high-Q MEMS resonators.
8

Figure 1.4: Receiver architecture of Analog Signal Processors. 9

The focus of this dissertation is to investigate different transducer materials, transduction mechanisms and device designs to realize these frequency tunable radio frequency channel-select filters using the currently available micro-fabrication technology.
1.2 Previous Electromechanical Resonators
A resonator is the basic building block for filters and oscillators in radio architecture. A resonator array can be electrically coupled in a ladder or lattice configuration to form a band-pass filter [22]. In mechanical domain, an array of mechanical resonator can be mechanically coupled with coupling springs to excite a band-pass filter response [23]. High-Q constituent resonators are the essential ingredients for designing narrow-bandwidth band-pass filters. In electrical engineering world, the resonator tank can be realized with electrical components such as inductor (L) and capacitor (C). However, filter designers will find the practical Q for L − C filter is very limited to achieve the channel-select filtering requirement for radio front-end. A vast amount of research efforts have been done to produce resonators with high quality factors. At this point, it is informative to review high-Q resonators that people have designed and fabricated over the years.
1.2.1 Quartz Crystal Resonators
Piezoelectricity has found various applications since it was discovered by Curie brothers in 1880. Early research on exploiting piezoelectric properties of quartz crystal for resonator application was done by Professor Walter Cady in 1921. He developed the first quartz crystal resonator and proposed to use quartz crystals to constitute a filter [24]. Even though there are a variety of materials that exhibit
10

Table 1.1: Quartz crystal mode of vibration and frequency range

Mode

Frequency Range

Flexural

0.4 - 100 kHz

Extensional 40 kHz - 15 MHz

Shear

0.1 - 200 MHz

piezoelectric effect, however, quartz has become a primary choice to construct narrow bandwidth filter because it is well known to have an excellent long term stability, superior temperature coefficient of frequency (TCF) and high quality factor.
Frequency of operation of quartz crystal resonators is determined by the mode of vibrations. Low-frequency of operation is normally attained by exciting flexural or length-extensional mode of vibrations. A typical low-frequency quartz crystal construction is shown in Figure 1.5 (a) and (b) [22]. The resonance frequency for this class of resonator is determined primarily by the blank length and width dimensions. The blank is supported by headed wires attached at nodal points so as not to dampen the mechanical resonance. These wires are then attached to posts in the crystal base. Higher-frequency crystals are of the thickness shear type, where the resonance frequency is determined by the blank thickness as shown in Figure 1.5 (c). The common packaging of quartz crystal resonator is shown in Figure 1.5 (d). Depending on the frequency of operation the length dimension of a packaged quartz crystal resonator may range from 1.3 − 6.4 cm. The frequency ranges of typically used modes for quartz crystals are summarized in Table 1.1 [25].
During manufacturing process quartz bar must be cut according to a specific orientation with respect to the crystallographic axes of the quartz. A particular cut will define the optimum frequency of operation, frequency drift over time,
11

Figure 1.5: Quartz crystal resonators: (a) Flexural/Length-extensional resonator, (b) Face-shear resonator, (c) Thickness-shear resonator, (d) Packaged quartz crystal resonator.
Table 1.2: Quartz crystal cut and frequency range Cut Frequency Range (kHz) X 40 - 20, 000 Y 1, 000 - 20, 000 AT 500 - 200, 000 BT 1, 000 - 75, 000 GT 100 - 550
quality factor, and temperature coefficient of frequency of the resonator. Some of the more common crystal cuts used are summarized, along with frequency ranges, in Table 1.2 [26, 27].
Quartz crystal resonators have been the prima donna for frequency reference and electromechanical signal processing in wireless communications since 1930s due to their superior quality factor, frequency and temperature stability up to very high frequency (VHF) range of operation. However, as the demand in ultra high frequency (UHF) filtering increases, a new class of device is necessary to
12

Figure 1.6: A typical SAW device consists of two sets of interdigital transducers. The input transducer converts electric field energy into mechanical wave energy, and the output transducer senses the propagated surface waves and converts the mechanical energy back into an electric field.
extend the frequency domain coverage of quartz crystal resonators.
1.2.2 Surface Acoustic Wave Resonators
The existence of surface acoustic wave (SAW) was first discovered by Lord Rayleigh in 1885 [28]. However, engineering community has not given too much attention until White and Voltmer from University of California, at Berkeley initiated the use of interdigital transducer (IDT) on piezoelectric substrates to excite SAW [29]. The schematic of a SAW resonator is illustrated in Figure 1.6. As a varying electric field is applied to the input transducer, the piezoelectric effect of the substrate induces mechanical displacements. The strongest coupling to surface waves happens when the transducer period matches with the SAW wavelength. The transmitted surface waves across the substrate are detected by the output transducer and converted into electrical output signal. SAW devices normally are fabricated on piezoelectric materials such as quartz, gallium arsenide (GaAs), lithium niobate (LiNbO3) or lithium tantalate (LiTaO3).
SAW devices operate well up to 2.5 GHz frequency range [30]. They are widely
13

Figure 1.7: Packaged SAW resonators and filters with various frequency ranges. used for UHF filtering in communication industry [31]. The commonly packaged SAW resonators and filters are shown in Figure 1.7. Despite of the ability to perform excellent filtering at UHF range and ubiquitously used in today’s wireless gadgets, SAW devices suffer from poor power handling and frequency shifting due to changes in temperature [32]. The accumulating pressure for miniaturized RF components in wireless communication with superior performance and minimum cost has fueled research activity in development of more integrated, silicon integrated circuit (IC) compatible, micro/nanoscale solutions for signal processing.
14

1.2.3 Bulk Acoustic Wave and FBAR Resonators
Bulk acoustic wave (BAW) and thin film bulk acoustic resonators (FBAR) have been dominating the wireless market hand in hand since early 1990s. BAW [33–39] and FBAR [40–42] possess lucrative features such as smaller dimensions, higher frequency of operation, better power handling and temperature coefficient compared to SAW devices. They can also be fabricated with traditional IC fabrication process. These two technologies today capture the market for US-PCS duplexers and transmit filters which are needed between the power amplifier and antenna in mobile phone applications [38]. Unlike SAW resonators, both BAW and FBAR devices are transduced by exciting the standing bulk acoustic waves across the thickness of an acoustically isolated piezoelectric thin-film. Aluminum nitride (AlN) and zinc oxide (ZnO) are the commonly used piezoelectric transducer materials for BAW or FBAR devices.
BAW resonators or commonly recognized as solidly mounted resonators (SMR) are normally fabricated on the a stack of acoustic mirror to achieve acoustic isolation from the substrate as shown in Figure 1.8 (a). The more straightforward way to build a bulk acoustic standing wave resonator is by fabricating a membrane BAW or FBAR as shown in Figure 1.8 (b) [36]. The SMR configuration has the advantage of the better mechanical robustness and the simpler process control. Wafer-handling, dicing and packaging of SMR are considerably easy as compared to FBAR. However, the acoustic behavior of FBAR is easier to model and fabrication efforts to accurately deposit the mirror layers can be eradicated.
SMR and FBAR have been conquering wireless market for nearly two decades for their excellent performance in filtering and processing signals at UHF range. The drawback of bulk acoustic wave resonators is they only have single frequency of operation for each deposited layer of transducer. Research efforts have been done
15

Figure 1.8: Cross-section of bulk acoustic wave (BAW) resonators: (a) Solidly mounted resonators (SMR), (b) Membrane bulk acoustic wave resonator (FBAR).
16

to introduce frequency tuning in FBAR [43]. However, the recent demand for integrated ultra low-power multi-frequency signal processors on a single chip has motivated researchers to investigate a new generation of devices with alternative modes of vibrations.
1.2.4 Contour-Mode Resonators
Contour mode resonators and filters are of interest because their frequency of operation is determined by the lateral dimensions. Thus, this class of resonators has a large frequency design space that enables the next generation of integrated analog signal processors on a single chip. A resonance frequency above UHF range can be attained by properly scaling the lateral dimensions and excite the device at high-overtone modes of vibrations.
Air-Gap Electrostatically Transduced Resonators
The recent advancement in surface micromachining has facilitated the rapid development of MEMS contour-mode resonators. Since the comb-drive era [13–15], the air-gap surface micromachined electrostatic resonators have aggressively evolved to catch the performance of SAW, BAW and FBAR resonators. A fabrication process has been demonstrated that combines polysilicon surface micromachining, metal electroplating, and a sidewall sacrificial-spacer technique, to achieve high-aspect-ratio, submicron, lateral capacitive gaps between a micromechanical structure and its metal electrodes, without the need for advanced lithographic and etching technology [44]. Using similar fabrication process, radial-contour mode disk resonators were fabricated and reported a resonance frequency as high as 829 MHz and with Q as high as 23, 000 at 193 MHz [45]. A vibrating polysilicon micromechanical "hollow-disk" ring resonator has been demonstrated in several vi-
17

Figure 1.9: Air-gap contour-mode resonators: (a) A radial-contour mode disk resonator, (b) A polysilicon hollow-disk ring resonator, (c) An extensional wineglass-mode resonator, (d) A nanocrystalline diamond disk resonator, (e) A squareextensional mode resonator, and (f) A Poly-SiGe contour-mode disk resonator.
18

bration modes spanning frequencies from HF (24.4 MHz), to VHF (72.1 MHz), to UHF (1.169 GHz), with Qs as high as 67, 519, 48, 048, and 5, 846, respectively [46]. Vibrating polysilicon micromechanical ring resonators, using a unique extensional wine-glass-mode shape to achieve lower impedance, have been designed and characterized at frequencies as high as 1.2 GHz with a Q of 3, 700, and 1.52 GHz with a Q of 2, 800 [47]. The first CVD nanocrystalline diamond micromechanical disk resonator with material-mismatched stem has been demonstrated with a recorded resonance frequency of 1.51 GHz with a Q of 11, 555 [48]. A micromechanical 13.1 MHz 2-D plate bulk acoustic mode (BAW) silicon resonator was reported with Q of 130, 000 [49]. Investigations to integrate air-gap contour-mode resonators with SiGe BiCMOS electronics based process have also been performed [50]. Figure 1.9 illustrated several of the previously fabricated air-gap contour-mode resonators.
Despite of the high frequency and high-Q that air-gap electrostatically transduced resonators perform, they suffer from a relatively large motional impedance (RX ), due to reduced transducer area [51] and inefficient electrostatic transduction (compared to lateral d31 piezoelectric transduction [52, 53]).
Piezoelectrically Transduced Resonators
Piezoelectric materials such as aluminum nitride or quartz offer larger electromechanical coupling coefficients that facilitate an efficient electromechanical transduction. In order to accommodate multiple-frequency resonators on a single chip with low motional impedance, a number of research teams have explored the development of piezoelectrically transduced contour-mode MEMS resonators and filters. Rectangular plates and rings resonators with an aluminum nitride layer as a transducer sandwiched between the bottom platinum electrode and top aluminum electrode have been fabricated and characterized up to frequency of 236 MHz. These devices were electrically cascaded to form a low insertion-loss (IL) bandpass filter
19

at 93 MHz [54]. The next generation devices were fabricated and exhibit frequency from 19 to 656 MHz [55]. Zinc oxide transduced contour-mode resonators have been developed and reported fC of 90 MHz, maximum Q of 3, 400 and RX of 600 Ω [56]. Piezoelectric on nano-crystalline diamond composite contour-mode resonators were fabricated. These resonators benefit from the large elastic modulus of the nano-crystalline diamond to boost the resonance frequency up to 1.2 GHz [57]. Contour-mode resonators can be mechanically-coupled to realize a bandpass filter. The development of narrow bandwidth, post-CMOS compatible aluminum nitride transduced MEMS filters operating in the VHF and UHF bands have been reported [58]. Figure 1.10 illustrated several of the previously fabricated piezoelectrically transduced contour-mode resonators.
The state of the art piezoelectrically transduced contour-mode resonator has been experimentally measured at frequency of 8.5 GHz [59]. Even though AlN transduced devices are able to attain super high frequency (SHF) range, however, they do not exhibit any frequency tuning capability.
Dielectrically Transduced Resonators
Internal dielectric transduction enhances both the force density of the actuator as well as the sense capacitance [60]. It has been previously proposed and experimentally verified using an aluminum nitride FBAR resonator in non-linear electrostatic mode [61]. Bhave et al successfully demonstrated a 121 MHz 3rd harmonic lateral bar resonator with internal electrostatic actuation and sensing of the mechanical motion, by depositing silicon nitride on the top surface of a silicon bar. In this dissertation we will explore more on dielectrically transduced high-Q RF MEMS resonators and investigate the device design for voltage tunable filters.
20

Figure 1.10: Piezoelectrically transduced contour-mode resonators: (a) An AlN transduced ring-shaped contour-mode resonator, (b) An AlN transduced squarering-shaped contour-mode resonator, and (c) A ZnO on silicon contour-mode resonator, (d) A ZnO-on-nanocrystalline diamond resonator, and (e) An AlN transduced mechanically-coupled contour-mode filter.
21

1.3 Contributions of this Dissertation
This thesis identifies crucial key features in RF MEMS field that have never been addressed before such as analog and digital frequency and bandwidth tuning of MEMS resonators and filters. The properties of high permittivity solid dielectric transducers such as silicon nitride and hafnia are exploited to demonstrate high-Q MEMS resonators and voltage tunable filter. This thesis also introduces a liquid dielectric to enhance the transduction efficiency and enable the voltage tuning of contour-mode resonators. A novel packaging technology for dielectrically transduced contour-mode resonators and filters that enables the post-MEMS CMOS integrated process is reported.
The properties of ferroelectric materials such as lead zirconate titanate (PZT) are examined and utilized to realize center frequency and bandwidth tunable resonators and filters. The monolithic integration of RF components on-chip has long been a goal of researchers and will enable not only more compact and lower cost systems but previously unachievable signal processing functions. This dissertation successfully demonstrated for the first time monolithically integrated piezoelectric MEMS RF switches with contour-mode filters.
1.4 Dissertation Organization
Chapter 2 demonstrates the design, fabrication and characterization of high-Q thickness shear mode resonators and analog voltage tunable filters. Chapter 3 presents the performances of high-overtone square extensional resonator and digitally programmable filter. Chapter 4 provides an overview of a wafer level packaging technology for MEMS contour-mode resonators. Chapter 5 discusses the aqueous transduction of contour-mode resonators. Chapter 6 explores the study
22

on PZT transduced resonators. Chapter 7 exploits the properties of PZT transduced resonators to realize voltage tunable bandpass filters. Chapter 8 presents the monolithically integrated PZT MEMS switches and contour-mode filters. Chapter 9 looks ahead on research possibilities that can be performed in the near future based on results that have been accomplished in this thesis.
Appendices of this dissertation will cover the fabrication technologies for thickness shear mode resonators and filters and the calibration and de-embedding methods to characterize RF MEMS resonators and filters.
23

CHAPTER 2 HIGH-Q MEMS THICKNESS SHEAR RESONATORS AND ANALOG VOLTAGE TUNABLE ELECTRICALLY-COUPLED
CHANNEL-SELECT RF FILTERS
2.1 Introduction
A great number of applications in cellular transceivers and sensor networks have mobilized the growth of on-chip, high-Q MEMS resonators and filters to substitute the present off-chip SAW, ceramic and quartz resonators in direct conversion transceivers. Multi-band, multi-standard radio receivers have narrow channels and are susceptible to nearby strong interferers. Channel-select filtering requires small bandwidth, superior stopband rejection, and excellent shape factor to filter out undesired frequencies. MEMS resonators with high-Q, high resonant frequency, and low RX can be coupled electrically in a ladder configuration to form a channelselect filter that operates at radio frequency.
Radio receivers require a large array of channel-select filters connected in parallel that causes the input capacitance of the filter array to load individual filters and worsening their stop-band rejection. For reconfigurable radios the front-end filters must also handle encoded waveforms with different bandwidth specifications. A filter that facilitates dynamic tuning of filter center frequency and bandwidth will not only overcome fabrication tolerances and performance degradation due to thermal drift, but will also reduce capacitive loading at the filter input, enable handling of multiple waveforms, and substantially decrease the number of filters in next-generation receivers.
The desired filter characteristics are defined by the MEMS resonators as the building blocks of the filter. Minimum insertion loss can be satisfied by decreasing
24

RX , while the resonators’ Q determines the shape factor. Air-gap electrostatically transduced MEMS resonators have Q > 10, 000 but are limited by their large motional impedance (RX > 10 kΩ) [48]. In lieu, piezoelectric FBARs have small motional impedance (RX > 10 Ω) but relatively low Q ( 2, 000) [41].
The thickness shear mode resonator is a suitable nominee to construct a MEMS filter for a number of reasons. Its high-Q mode has been demonstrated successfully in quartz resonators. Furthermore, it has a high frequency and low motional impedance. The thickness shear mode resonator also presents a frequency tuning capability which is useful for compensation of frequency shift due to fabrication errors. Dielectric transduction is accomplished here by sandwiching a thin film high-κ dielectric material between the silicon bar resonator and polysilicon electrodes. This enhances both the force density of the actuator as well as the sense capacitance, thereby improving the resonator’s motional impedance by a factor of κ2 [60].
High frequency resonators were fabricated by reducing the air gap and increasing the transducer area of bulk-mode bar resonators [62]. In spite of their high frequency, the huge RX of these resonators will produce a high insertion loss filter. An effort to decrease RX by filling the air gap of a wine-glass disk resonator with silicon nitride is presented in [63], resulting in a resonant frequency of 165 MHz with a Q of 21, 400 and an RX of 8.5 kΩ. Alternatively, contour-mode aluminum nitride piezoelectric resonators with 656 MHz resonant frequency and an RX of 170 Ω have been reported. However, the ladder filter comprised of these low-Q piezoelectric resonators exhibited a 20 dB shape factor of 2.7 [55].
This Chapter will first discuss the quarter-wave thickness shear mode (TSM) silicon bar resonator. The silicon bar resonator is capable to reach 723 MHz resonant frequency with a Q of 4, 400 and an RX of 2.4 kΩ using silicon nitride dielectric
25

transduction. Furthermore, the superior Q half-wave thickness shear mode of a fully-released bar resonator will be demonstrated. The motional impedance of the half-wave thickness shear bar resonator is significantly reduced by substituting silicon nitride (κ ∼ 9) with hafnium dioxide (κ ∼ 28), reducing dielectric thickness, and increasing the electrode area. The high-Q and low RX of this resonator facilitate the design of high quality channel-select filters. High performance MEMS resonators can be coupled electrically to form a bandpass filter that operates at radio frequency. The discussion will turn into the design and performance of electrically coupled thickness shear filters. Electrically coupled channel-select filters with 814 MHz center frequency, 600 kHz bandwidth, −4 dB insertion loss (IL) and < 1 dB pass-band ripple will be demonstrated. The next section of this Chapter will present the design of a reconfigurable ladder filter using RF MEMS resonators with voltage-tunable series and parallel resonance frequencies. We will introduce a voltage biasing scheme capable of independently tuning the series resonance and pole-zero separation of the filter’s constituent resonators [64]. Coupled with orthogonal frequency tuning, we can construct the filter with desired pass-band characteristic in real time. Finally, this Chapter will be concluded with a concise summary.
2.2 Quarter-wave Thickness Shear Resonator
The quarter-wave thickness shear mode (TSM) bar resonator is excited in a very similar way to quartz resonators. The asymmetric thickness shear mode is common in quartz resonators, excited by the application of an AC signal across electrodes on opposing faces of a quartz crystal [65]. In contrast to the quartz thickness shear mode, the electrode configuration of the dielectrically transduced silicon bar induces a symmetric mode, as shown in Figure 2.1.
26

Figure 2.1: X-displacement contour plot from Ansys simulation of the symmetric quarter-wave thickness shear mode.
2.2.1 Electrical Equivalent Impedances of a Quarter-wave

TSM Resonator

A one-dimensional thickness shear mode is derived for an unreleased silicon bar

transduced by a thin dielectric film. The film, deposited on top of the bar, is

sandwiched between the silicon bar and conducting top electrodes as shown in

Figure 2.2. The bottom face of the bar is fixed to an effectively infinite oxide

layer, imposing a zero-displacement boundary condition at the base of the bar. In

this configuration, the silicon bar is biased to a DC voltage VDC while a small alternating voltage vAC is applied to the top electrode. The voltage drop across the electrode-bar parallel plate capacitor induces a normal force on the dielectric

film, transferring to a lateral strain in the dielectric. Though the strain is in fact

uniform in both lateral directions, we consider a long narrow bar, approximating

a one dimensional model of the strain. This strain is distributed between the

film and silicon bar, inducing a quarter-wave thickness shear resonant mode. The

lateral displacement ux for the one-dimensional thickness shear mode is given by

ux(x, z, t) = Ax sin ω

ρ z ejωt G Si

(2.1)

for the quarter-wave thickness shear resonant frequency of

ω

=

π 2b

ρ G Si

(2.2)

27

Figure 2.2: The schematic of an unreleased thickness shear bar.

A voltage VDC + vAC applied across the dielectric film generates a normal force

fz

≈

−VDC

κf 0wL 2hf 2

vAC

(2.3)

for a bar of width w and length L, where κf and hf are the relative permittivity and thickness of the dielectric film, respectively. Here, we make the approximation

that vAC << VDC. The factor of 2 in the denominator arises from a configuration in which the drive electrode covers half the width of the bar, and the sense electrode

occupies the other half. The laterally transferred strain in the film is

x,f

= νf

z

=

νf fz Ef wL

and the lateral stress in the film is

(2.4)

σ0

=

Ef ∗

x,f

=

νf fz (1 − νf ) wL

(2.5)

28

Figure 2.3: 2-D cross-section schematic of the conversion of transverse electrostatic stress in the silicon nitride thin film to thickness shear mode in the half-length (AA’ in Figure 2) bar resonator.

where Ef ∗ is the axial Young’s modulus of the dielectric film. This initial lateral stress σ0 functions like an effective residual stress in the film, consequently distributing itself in both film and bulk silicon, as illustrated in Figure 2.3. We assume that the electrode’s thickness is negligible with respect to the thickness of the silicon bar resonator. The one-dimensional approximation holds true for resonators with L >> w, b. The shear stress in the silicon is approximated to be distributed linearly through the bar due to the displacement boundary condition imposed by the oxide anchor. This yields a maximum shear stress in the silicon of

σ0,b

=

Gf

GSihf

hf

+

1 2

GSib

σ0

≈

2hf b

σ0

(2.6)

29

in the approximation that hf << b. The maximum displacement of the bar can then be approximated as

ux,max

=

b GSi σ0,b

=

νf κf 0VDC vAC (1 − νf ) GSihf

(2.7)

With the first-order determination of the quarter-wave thickness shear mode, we calculate the motional impedance RX, inductance LX , and capacitance CX of the resonator. The change in the sensed capacitance over time is approximated as

∂C ∂t

≈

Qωκf 2hf

0wL
2

Δhmax

(2.8)

The quality factor Q is introduced here to account for effective displacement am-

plification at resonance. The film is laterally expanded and contracted as the bar

resonates, causing the thickness of the film to change with a Poisson efficiency

factor. The maximum change in the film thickness is given by

Δhmax = νf ux,max

(2.9)

The output current is

IOut

=

∂C VDC ∂t

=

Qπ (νf κf 0√VDC )2 4 (1 − νf ) GSiρ

wL hf 3b vAC

giving a motional impedance of

RX

=

vAC IOut

=

√ 4 GSiρ
Qπ

(1 − νf ) (νf κf 0VDC)2

hf 3b wL

The effective mass for the thickness shear mode is

ME f f

=

ρw L2

x2 sin2

ω

ρ z
GSi

dxdz

=

1 6 ρwLb

and the effective spring constant is

KE f f

=

MEff ω2

=

π2 GSiwL 24 b

(2.10) (2.11) (2.12) (2.13)

30

From equations 2.11 to 2.13, for

RX =

KEff MEff Qη2

The electromechanical coupling constant η is given by

η2

≈

(πwLνf κf 0VDC )2 24 (1 − νf ) hf 3b

The motional capacitance CX is

CX

=

η2 KE f f

=

(νf κf 0VDC )2 wL (1 − νf ) GSi hf 3

and the motional inductance LX is

LX

=

ME f f η2

=

4 (1 − νf ) ρ b2hf 3 π2 (νf κf 0VDC )2 wL

(2.14) (2.15) (2.16) (2.17)

2.2.2 Fabrication Process
A 68 nm low stress silicon nitride thin film is first deposited by LPCVD at 850◦C on an n-type low resistivity silicon on insulator (SOI) wafer with a 1.8 μm thick single crystal silicon (SCS) device layer. The silicon nitride is patterned to open contact holes to bias the silicon resonator as shown in Figure 2.4 (a). A 120 nm layer of n-doped polysilicon is then deposited by LPCVD at 620◦C, annealed at 1, 000◦C for 40 minutes, and patterned to form the electrodes as shown in Figure 2.4 (b). This is followed by a deep reactive ion etch (DRIE) step to define the resonator into the silicon device layer as shown in Figure 2.4 (c). The unreleased SEM image of a quarter-wave thickness shear mode resonator is shown in Figure 2.5. Appendix A will discuss a detail fabrication process flow for thickness shear mode resonators.

31

Figure 2.4: Fabrication process flow of quarter-wave thickness shear mode resonators.
32

Figure 2.5: SEM of a silicon nitride-on-silicon unreleased bar resonator.
2.2.3 Measurement Results
An unreleased 80 μm long by 40 μm wide bar resonator was characterized using a Desert Cryo microwave probe station. The resonator body was grounded and a DC bias was applied to both the drive and sense electrodes with bias-Ts from MiniCircuits. Transmission measurements were performed using an Agilent 8753ES Network Analyzer and the quality factor and insertion loss were extracted from the measured data. The motional impedance of the resonator was determined from the insertion loss data after adjusting for the attenuation losses at the drive pad. The quarter-wave thickness shear vibration mode of the unreleased silicon resonator was measured with a resonant frequency of 713 MHz, an RX of 10.5 kΩ and Q of 1, 517. Transmission response of the measured device is shown in Figure 2.6.
It has previously been shown that quality factor improves with reduced anchor area. By performing a timed etch of the buried oxide in HF as shown in Figure 2.7,
33

Figure 2.6: Measured transmission of the thickness shear mode of the unreleased resonator in air.
Figure 2.7: A partially released quarter-wave thickness shear mode resonator. 34

Figure 2.8: Measured transmission of the partially released shear mode resonator in air.

the overall contact area between the oxide and bottom surface of the resonator was

reduced to approximately 30 μm x 5 μm. This partially released bar had a resonant

frequency of 723 MHz, RX of 2.4 kΩ and Q of 4, 400 in air. Transmission response of

the measured device is shown in Figure 2.8. The large acoustic mismatch of the air

gap reduces leakage of the shear standing wave into the anchor, thereby decreasing

the quarter wavelength of the vibration mode. This explains the increased resonant

frequency of the partially released bar relative to the unreleased bar. The electromechanical coupling factor of the quarter-wave TSM resonator (kt2)

was measured using

kt2

=

fS fP

−1

≈

CX Cf t

(2.18)

where fS and fP are the series and parallel resonances of the device and Cft is the

feedthrough capacitance between input and output ports. The resonator exhibits

35

Figure 2.9: ANSYS contour plot of the symmetric half-wave thickness shear mode. kt2 of 0.03. This value is comparable to the coupling factor of quartz crystals [51].
Although a quarter-wave thickness shear mode resonator using dielectric transduction can achieve a high resonant frequency with low motional impedance, however, the relatively inadequate quality factor of the resonator constrains us from coupling the resonators to build a MEMS filter with a good shape factor. Hence, an attempt to enhance the quality factor of the resonator was done by exciting a half-wave thickness shear mode in the fully released silicon bar.
2.3 Half-wave Thickness Shear Resonator
The half-wave thickness shear bar resonator is excited in the same way as the quarter-wave thickness shear bar resonator. The electrode configuration of the dielectrically transduced silicon bar induces the symmetric half-wave thickness shear mode, as shown in Figure 2.9. This mode causes the tether suspension at the nodal plane to move along the Z-axis, as indicated by the down arrows.
36

Figure 2.10: Schematic of a fully released half-wave thickness shear bar resonator.
2.3.1 Motional Impedance of a Half-wave TSM Resonator
A one-dimensional quarter-wave thickness shear mode model was derived for an unreleased silicon bar transduced by a thin dielectric film in the previous section. In order to excite the half-wave thickness shear mode, the oxide layer of the SOI wafer is fully etched, leaving a free displacement boundary condition on the bottom face of the bar. The schematic of a fully released bar resonator is shown in Figure 2.10.

The resonant frequency of the half-wave thickness shear mode resonator is

two times of its quarter-wave counter part. Therefore, the first-order motional

impedance of the half-wave thickness shear bar resonator is also twice of the

quarter-wave thickness shear mode resonator’s motional impedance. The motional

impedance of the half-wave thickness shear bar resonator at resonant is given by

RX

=

√ 8 GSiρ (1 − νf )
Qπ (νf κf 0VDC )2

hf 3b wL

(2.19)

Pure half-wave thickness shear mode resonance of a bar depends only on thick-

ness b, with frequency

fC

=

1 2b

GSi ρSi

(2.20)

37

Figure 2.11: ANSYS simulation of length (L) vs resonant frequency (fC) of the 3.2 μm thick half-wave shear mode resonator.

where GSi and ρSi are the shear modulus and mass density of the silicon resonator, respectively. In reality, the resonator exhibits a small-amplitude flexure mode coupled to the shear mode. This coupling can be observed in the ANSYS modal analysis in Figure 2.9. The Southwell-Dunkerley formula [66] approximates the combined shear-flexure frequency as

1 fT otal2

=

1 fS hear 2

+

1

fF

2 lexure

(2.21)

Therefore, the silicon bar’s lateral dimensions affect the resonant frequency, giving layout design flexibility covering a 30 MHz range below 840 MHz. Figure 2.11 shows the bar’s simulated resonant frequency as a function of the bar length. The pure shear mode resonant frequency of the bar is 844 MHz. This property is exploited to fabricate multiple frequency resonators and filters on the same chip.

38

Figure 2.12: (a) SEM of a hafnium dioxide-on-silicon fully released bar resonator. (b) SEM of the 30 nm hafnium dioxide layer on the top of the silicon resonator.
2.3.2 Fabrication Process
The resonator is fabricated in a 4-mask SOI process similar to the fabrication process explained in the previous section. The silicon nitride layer is replaced with a 30 nm hafnium dioxide film (κ ∼ 28, and acoustic velocity (VA) ∼ 8, 500 m/s) on a low resistivity SOI wafer with a 3.2 μm thick SCS device layer. An SEM of the resonator is shown in Figure 2.12 (a). A high-resolution SEM revealing the 30 nm hafnium dioxide layer is shown in Figure 2.12 (b).
2.3.3 Measurement Results
A 100 μm x 40 μm bar resonator was tested in a Desert Cryo microwave probe station at room temperature and pressure. In order to simplify the microwave frequency measurement, the resonator device layer was grounded and both drive and sense electrodes were biased to 5 V using bias-Ts. SLOT (short-load-open-
39

Figure 2.13: Measured transmission response of a half-wave TSM resonator in air. through) characterization and transmission measurements were performed using an Agilent 8720ES network analyzer and the Q and insertion loss were determined from the measured S21 response. As expected, the motional impedance decreases with area of the resonator. In addition, the cubic dependence of RX on dielectric film thickness hf and its inverse square dependence on dielectric constant κf improve motional impedance to values close to 50 Ω. The half-wave thickness shear mode of the released silicon resonator was measured with a resonant frequency of 809 MHz, a Q of 7, 800 and an RX of 59 Ω in air. Transmission response of the measured device is shown in Figure 2.13. The calculated f x Q product of the resonator is 6.2 x 1012 Hz. MEMS resonators with the performance shown by the half-wave thickness shear mode resonator can be coupled electrically to form a channel-select RF MEMS filter that has both excellent shape factor and low insertion loss.
40

Figure 2.14: (a) Electrically coupled ladder filter configuration. (b) Bandpass frequency response of the ladder filter.
2.4 Electrically Coupled RF MEMS Ladder Filters
Electrical coupling is achieved by routing the electrical signal from successive resonators in a ladder configuration. The design flexibility afforded by the frequency dependence on lateral dimensions enables the design of series and parallel resonators of the ladder without the need for additional mass-loading or electroetching steps to reduce the shunt resonator frequency [32, 54]. The ladder filter configuration and its bandpass frequency response are shown in Figure 2.14 (a) and (b) respectively.
Five electrically coupled ladder filters were designed with 1 MHz separation in center frequency and 3 dB bandwidth of ∼ 600 kHz. Figure 2.15 shows an SEM of two ladder filters. The series resonators are 280 μm x 100 μm and the shunt
41

Figure 2.15: SEM of an array of ladder configuration electrically coupled thickness shear filters.
42

Table 2.1: The measured characteristics of electrically coupled TSM filters

Ladder filter 1 Ladder filter 2

IL

−3.5 dB

−4 dB

3dB BW

630 kHz

680 kHz

fc Ripple

813.6 MHz < 1 dB

814.5 MHz < 1.1 dB

Stop Band Rejection −24 dB

−25.2 dB

20dB Shape Factor

1.43

1.5

RL

712 Ω

750 Ω

resonators are 300 μm x 100 μm. Figure 2.16 provides the frequency response of the filters and Table 2.1 summarizes the filters performance in air with termination resistance RL. In order to verify that there are no spurious responses in the vicinity of the filter passband region, frequency was swept over a wide range. The wide spectrum swept of the channel-select filters in search of spurious responses is shown in Figure 2.17.
Pole-zero alignment in an electrically coupled ladder filter is a very critical factor to acquire the desired bandpass response. Fabrication errors can reallocate the pole and zero of the filter, hence the bandpass response of the filter may be distorted as shown in Figure 2.18. In order to overcome this problem a reconfigurable ladder filter using high performance MEMS resonators that can dynamically tune the pole and zero of the filter is necessary.

43

Figure 2.16: Measured transmission response showing two 650 kHz channel-select filters.
Figure 2.17: Measured filter transmission response over a wide frequency range. 44

Figure 2.18: The distorted bandpass response of the filter due to fabrication tolerances.
2.5 RF MEMS Channel-select Filters with Tunable Center
Frequency and Bandwidth
Low frequency filters comprised of electrostatically-coupled resonators have been demonstrated with 10x bandwidth tunability [67]. However, it is challenging to implement electrostatic coupling springs at GHz frequencies even with 100 nm airgaps. Galayko et al presented a tunable bandwidth filter using clamped-clamped beam resonators in a ladder configuration [68]. The first transmission zero (and hence filter bandwidth) was tuned by controlling the series resonance frequency of the shunt resonator, though large parasitic capacitance prevented implementation and tunability of the second transmission zero of the filter.
In a typical ladder filter configuration, the parallel resonance frequency of the shunt resonator (ωP ), which defines the filter center frequency fC, is matched to the series resonance frequency of the series resonators (ωS). Filter bandwidth
45

(BW ) is determined by notches on either side of the pass-band and is 2x the pole-zero separation of the series and shunt resonators. The key to tunable ladder filters is the ability to change fC and to dynamically tune the pole-zero separation (ωP - ωS) of the resonators. In the previous section we have demonstrated high performance channel-select ladder filters with 600 kHz bandwidth, 25 dB stop-band rejection, excellent shape factor, and low insertion loss (IL) using dielectricallytransduced thickness shear mode resonators. In this section, we introduce a voltage biasing scheme capable of independently tuning the series resonance and pole-zero separation of the filter’s constituent resonators. Coupled with orthogonal frequency tuning, we can configure the filter with desired pass-band characteristic in real time.
2.5.1 Orthogonal Frequency Tuning
The series resonance of low frequency resonators can be tuned by electrostatic spring tuning. However, the stiffness of high frequency resonators is quite large (a 1 GHz bulk-mode resonator has a stiffness on the order of 1 MN/m in the resonant direction) and would require considerable electrostatic force to tune the stiffness and the series resonance frequency.
In contrast, orthogonal frequency tuning deforms the resonator in a direction perpendicular to the direction of vibration. The resonators are generally less stiff in the orthogonal direction and can be deformed with substantially less force. The symmetric half-wave thickness shear mode resonator exhibits a small-amplitude flexure mode coupled to the shear mode as discussed in the previous section. The Southwell-Dunkerley formula approximates the combined shear-flexure frequency is given by equation 2.21. When a polarization voltage VP is applied to the resonator and a voltage VS is applied to the substrate, the tuning voltage VP - VS generates an electrostatic force that deflects the structure towards the substrate, as illustrated
46

Figure 2.19: Longitudinal cross-section of a deflected half-wave thickness shear mode resonator due to the orthogonal biasing configuration.
in Figure 2.19. Bending the structure will soften the flexural mode stiffness, hence the series resonance frequency will be reduced.

2.5.2 Pole-Zero Seperation Tuning

A dielectrically transduced MEMS resonator can be represented by an electrical equivalent series LCR circuit in parallel with a feedthrough capacitance Cft, as shown in Figure 2.20. For a given transduction efficiency η ≡ VP ∂C/∂X, RX = b/η2, CX = η2/K and LX = M /η2, where b, K and M denote the damping constant, effective spring stiffness and effective mass of the resonator. The feedthrough capacitance in a two-port resonator originates from electric field coupling from the input electrode to the output electrode and is a function of electrode geometry. The series resonance frequency is given by

ωS

=

√1 LX CX

=

K M

(2.22)

47

Figure 2.20: Electrical equivalent circuit of a dielectrically transduced MEMS resonator.

An expression for the parallel resonance frequency is obtained through a first-order Taylor’s expansion

ωP =

1 = ωS L CX Cft
X CX +Cf t

1+

CX Cf t

≈

ωS

1

+

CX 2Cf t

(2.23)

ωP

−

ωS

≈

ωS

CX Cf t

(2.24)

Δ (ωP − ΔωS

ωS )

≈

CX Cf t

(2.25)

For electrostatic transduction, the ratio of CX to Cft is very small (10−4 − 10−2).

Therefore, the separation between the series and parallel resonances is largely

independent of the series resonance frequency shifts due to changes in the spring

constant K. The pole-zero separation can be modeled as a function of structure

bias voltage VP .

ωP − ωS =

2A√2 2d4Cft KM

VP 2

(2.26)

In other words, the parallel resonance frequency is simply a voltage-controlled

offset from the series resonance frequency.

48

2.5.3 Filter Tuning Algorithm
A ladder filter consists of a shunt resonator and two series resonators. For minimum insertion loss and pass-band ripple, the parallel resonance frequency of the shunt resonator is matched to the series resonance frequency of the series resonators. Ladder filters can be cascaded to provide higher stop-band rejection at the expense of insertion loss. To achieve the desired center frequency and bandwidth, we use the following filter synthesis method: 1. Fix VP and change VS for the series and shunt resonators such that the desired series resonance frequencies are obtained (orthogonal frequency tuning). 2. Tune VP - VS separately for each resonator to obtain the desired pole-zero offset. Since VP - VS remains constant, the bending of the resonators does not change so the series resonance frequency remains fixed.
2.5.4 Fabrication Process
Filter T-sections consisting of one shunt and two series resonators shown in Figure 2.21 (a) were fabricated on an SOI wafer with a 3 μm heavily doped device layer and 0.5 μm buried oxide. The resonators are 310 μm (and 300 μm) x 100 μm x 3.1 μm released silicon bars with 20 nm of hafnium dioxide and 50 nm of polysilicon layers on top for dielectric transduction. Orthogonal frequency tuning was achieved by applying a substrate bias voltage to bend the resonators in the vertical direction. A back-side etch was added to the previous fabrication process to create substrate islands for independent tuning of the resonators. A front-side trench etch allowed isolated DC bias voltages to be applied to the resonators as shown in Figure 2.21 (b). Process limitations prevented polysilicon connections between the series and shunt resonators, so a small gold bondwire was implemented
49

Figure 2.21: (a) The 3-D model of tunable ladder filter. (b) The device crosssection with isolated resonator and substrate for applying independent tuning voltages.
50

Figure 2.22: Microphotograph of tunable ladder filter with a gold wirebond bridge.
as seen in Figure 2.22. Care must be taken to ensure that the wirebond does not damage the oxide under the pads and short the devices.
2.5.5 Measurement Results
Due to parasitics feedthrough, several calibrations are compulsory to extract the mechanical properties of the filter. The resonators and filters were characterized using a Desert Cryo microwave probe station. The resonator proof-mass was grounded and a DC bias VP was applied to both the drive and sense electrodes with MiniCircuits bias-Ts. Quality factor characterization and S21 transmission measurements were performed using an Agilent 8722ES Network Analyzer with 32 averaging steps. The resonators and filters were terminated with 50 Ω and 500 Ω impedances, respectively. The uncalibrated frequency characteristic of the res-
51

Figure 2.23: (a) The uncalibrated frequency characteristic of the resonator. (b) The measured frequency characteristic of the resonator after Cascade substrate calibration.
onator is shown in Figure 2.23 (a). Cascade substrate calibration cancels the cables and probes capacitances. The measured frequency characteristic of the resonator after Cascade substrate calibration is shown in Figure 2.23 (b). In addition, SOI substrate calibration is also necessary to minimize the effect of pad capacitance, electrical resistance of electrodes and nominal capacitance (VP = 0). The measured frequency response of the resonator after SOI substrate calibration is shown in Figure 2.24 (a). Measurement results demonstrating orthogonal frequency tuning are shown in Figure 2.24 (b) and (c). Keeping VP constant at 5 V and varying the substrate bias VS from 5 V to 17 V, we can tune the series resonance frequency of a single resonator from 816 MHz to 802 MHz, while maintaining a quality factor Q > 7, 000. The parallel and series resonance separation does not change during orthogonal frequency tuning.
Figure 2.25 shows that the pole-zero separation of the resonator varies from 0.6 MHz to 1.6 MHz when VP is changed from 5 V to 12 V. The substrate bias VP was held at VP during this measurement to prevent orthogonal forces acting on the resonator.
A bias voltage VP = 5 V yields a pass-band with fC = 817.2 MHz, 0.6 MHz
52

Figure 2.24: (a) Measured frequency characteristic of the resonator after SOI calibration. (b) Measured series resonance tuning for VS = 5 V and VS = (i) 12 V, (ii) 8 V, and (iii) 5 V. (c) Resonant frequency tuning vs. substrate voltage.
53

Figure 2.25: (a,b,c) Measured transmission response demonstrating pole-zero separation of a thickness shear mode resonator as DC bias VP increases from 5 V to 10 V. (d) Measured pole-zero separation vs. DC bias voltage of the resonator.
54

Figure 2.26: (a) Measured transfer function of ladder filter with no tuning. (b) Measured transmission of ladder filter with fC tuning from 817 MHz to 809 MHz with (i) no tuning, and (ii) series resonator: VP = 5 V, VS = 15 V; shunt resonator: VP = 5 V, VS = 12 V. (c) Measured transmission of ladder filter with BW tuning from 0.6 MHz to 2.8 MHz with (i) no tuning, (ii) series resonator: VP = 12 V, VS = 12 V; shunt resonator: VP = 13 V, VS = 16 V. (d) Measured transfer function of ladder filter with BW tuning from 0.6 MHz to 1.4 MHz and fC tuning from 817 MHz to 811 MHz with (i) no tuning, and (ii) series resonator: VP = 10 V, VS = 19 V; shunt resonator: VP = 9 V, VS = 17 V.
bandwidth, and IL of 3.2 dB as demonstrated in Figure 2.26 (a). Applying VS = 12 V and 15 V to the shunt and series resonators respectively, the center frequency is tuned from 817 MHz to 809 MHz without degradation in IL (3.5 dB) and shape factor (1.3), as shown in Figure 2.26 (b). Figure 2.26 (c) shows the bandwidth tuning from 0.6 MHz to 2.8 MHz while maintaining a constant center frequency at 817.2 MHz. Finally, a combination of bandwidth and center frequency tuning is shown in Figure 2.26 (d). A pass-band with fC = 811 MHz and 1.4 MHz bandwidth is obtained.
55

2.6 Conclusion
Thickness shear mode resonators that inherit the high resonant frequency and highQ from Quartz resonators have been successfully fabricated using integrated circuit compatible process in SOI wafers. The partially released quarter-wave thickness shear bar resonator’s f x Q product of 3.2 x 1012 Hz is within a factor of five of the f x Q product for quartz resonators. Quarter-wave thickness shear mode resonators using silicon nitride thin film as a dielectric transducer achieve high frequencies with greatly improved motional impedance. The lateral electrode design causes a Poisson ratio inefficiency in the transfer of vertical strain into lateral strain. However, this transfer is necessary to induce a shear resonance. Furthermore, this configuration allows for a large electrode area, significantly decreasing the resonator’s motional impedance.
In addition, half-wave thickness shear mode resonators with frequencies greater than 800 MHz and Q > 7, 000 have been fabricated. Dielectric transduction by a high-κ hafnium dioxide thin film reduces the motional impedance of the resonators more than 40 times relative to the previously design quarter-wave thickness shear mode resonator. Their 59 Ω motional impedance is the lowest reported to date for any silicon-based electrostatic VHF MEMS resonator design. An array of ladder filters with 600 kHz bandwidth, < 4 dB insertion loss, and < 1 dB pass-band ripple has been demonstrated.
Voltage tunability is more versatile than one-time modifications like laser trimming and mass loading, and enables us to overcome process tolerance and temperature variation frequency shifts. The frequency dependence of the thickness shear mode resonators on lateral dimensions provides the ability to fabricate resonators of various frequencies on a single chip. We have demonstrated bandwidth and center frequency tunability in an RF MEMS filter with IL < 4 dB and stop-band
56

rejection > 30 dB. With process tolerance and temperature variation frequency shifts of ±1.2 MHz and −14 ppm/◦C, respectively, this tuning capability not only overcomes these variations, but also enables channel agility and adaptability in multi-mode radio receivers.
57

CHAPTER 3 HIGH-OVERTONE SQUARE-EXTENSIONAL RESONATORS AND
DIGITALLY PROGRAMMABLE MECHANICALLY-COUPLED FREQUENCY-AGILE FILTERS
3.1 Introduction
Multi-band, multi-standard radio receivers such as next generation 7-band cellular phones and the Joint Tactical Radio System (JTRS) require a large array of channel-select filters connected in parallel. The input capacitance of the filter array will ’load’ individual filters, deteriorating their stop-band rejection. Therefore, such frequency agile radios need multi-octave tunable band-select radio frequency (RF) filters and bandwidth tunable channel-select intermediate frequency (IF) filters with good shape factor and excellent stop-band rejection. An RF filter with dynamically tunable bandwidth will enable handling of multiple waveforms, eliminate out-of-channel interferers, and substantially decrease the number of filters in next-generation receivers.
Dielectrically-transduced thickness shear-mode resonators with analog voltage tunable center frequency and bandwidth are suitable candidates for channel-select RF filters [69]. The resonators require a back-side etch of the SOI substrate to pattern orthogonal frequency tuning electrodes and eliminate parasitic pad capacitance and resistive ground loops. However, such back-side processing is not compatible with the high-vacuum, ultra-clean epi-Silicon encapsulation technology [70] necessary for field deployment of these filters. Contour-mode MEMS resonators with Q > 5, 000, low motional impedance (RX), compatibility with epiSilicon encapsulation and CAD-defined resonance frequencies from 10 MHz - 1 GHz are excellent candidates for designing channel-select filter arrays [71]. But unlike
58

thickness shear mode resonators, the frequency expressions for contour modes and flexural vibration modes do not directly couple. It is therefore difficult to perform orthogonal frequency tuning of contour-mode resonators. Since extensional mode resonators cannot be tuned at device-level (without excessive heating [72] or using liquid dielectric [73]), we implemented a tunable filter using a novel DC-biasing strategy in mechanically-coupled resonator array. This method does not require any frequency off-set between constituent resonators. As a result, lithography challenges are minimized, spatial distortion is greatly reduced and spurs in filter transmission are attenuated [74].

3.2 High-overtone Square-extensional Mode Resonator

MEMS resonators vibrating in a bulk-mode have superior linearity and high quality factors [75, 76]. Significant reductions in motional impedance of MEMS resonators have been achieved by mechanically coupling and exciting a parallel array of corner-coupled polysilicon square plate resonators [77]. By strongly coupling identical resonators in two dimensions a larger area can be acquired to further reduce the motional impedance. In addition, two-dimensional modal excitation causes less mode dispersion by averaging out the stochastic resonator characteristics [78]. The bulk-extensional mode resonance of a square resonator depends on L, with frequency of operation (fC) given by:

fC

=

n 2L

E ρ

(3.1)

where n is the overtone order, E is the effective elastic modulus for two-dimensional expansion, ρ is the effective density and L is the length of the resonator. Higher frequency overtone modes are selectively excited by patterning electrodes in checkerboard configuration on top of the resonator using dielectric transduction [79]. The

59

Figure 3.1: (a) Schematic of a 2-port high-overtone square-extensional mode resonator. (b) Cross-section of the device showing various layers that are deposited to build the resonator. (c) ANSYS mode shape of a high-overtone square-extensional resonator.
60

schematic of a 2-port dielectrically transduced high-overtone square-extensional mode resonator is illustrated Figure 3.1 (a) and (b). The resonator is modeled and simulated using finite element method in ANSYS. The ANSYS modal analysis of a high-overtone square-extensional resonator is shown in Figure 3.1 (c).
The 50 nm thin film silicon nitride film deposited on top of the resonator is sandwiched between the 2.75 μm thick silicon device layer and the 100 nm thick conducting top electrodes. A 50 V DC bias is superimposed to the AC signal at both input and output ports using bias-Ts and the silicon device layer is connected to RF ground. This time-varying voltage causes a squeezing force on the dielectric thin film. Due to the Poisson effect, the dielectric layer experiences a lateral strain. As the strain distributes through the resonator, the overtone square-extensional mode is excited.

3.2.1 Effective mass, Damping ratio and Effective spring
constant
The overtone square-extensional resonator can be treated as a parallel two-dimensional array of mechanically-coupled smaller square-extensional resonators with length LEL as shown in Figure 3.1 (a). The wave equation for a two-dimensional vibrating square-extensional mode resonator including the damping factor and external forces is

ρtEf

f

∂2u ∂t2

(x,

y,

t)

−

btEf

f

∂ ∂t

∂2u ∂x2

(x,

y,

t)

+

∂2u ∂y2

(x,

y

,

t)

−E tE f f

∂2u ∂x2

(x,

y,

t)

+

∂2u ∂y2

(x,

y

,

t)

=

∂f ∂t

(x,

y,

t)

(3.2)

61

By the method of separation of variables, we assume equation 3.2 has solutions of

the form

u(x, y, t) = g(t) sin

nπ x

+ sin

nπ y

LEL

LEL

Substituting 3.3 into 3.2 gives

(3.3)

ρtE f f

sin

xnπ
LEL

+ sin

ynπ
LEL

∂ 2 g (t) ∂t2

+btE f f

nπ LEL

2

sin

xnπ
LEL

+ sin

ynπ
LEL

∂g(t) ∂t

(3.4)

+E tE f f

nπ LEL

2

sin

xnπ
LEL

+ sin

ynπ
LEL

g(t) =

∂f ∂t

(x,

y

,

t)

Multiply 3.4 by sin

xnπ
LEL

+ sin

ynπ
LEL

and integrate over the area yields

L/2 −L/2

L/2 −L/2

ρtEf

f

sin

xnπ
LEL

+ sin

ynπ
LEL

2 ∂2g(t) ∂t2

+btE f f

nπ LEL

2

sin

xnπ
LEL

+ sin

ynπ
LEL

2 ∂g(t) ∂t

(3.5)

+E tE f f

nπ LEL

2

sin

xnπ
LEL

+ sin

ynπ
LEL

2
g(t)dxdy

=

F (t)

where F (t) is

L/2 L/2 ∂f (x, y, t) sin nπ x + sin nπ y dxdy

−L/2 −L/2 ∂t

LEL

LEL

(3.6)

Equation 3.5 can be simplified as

ρtE f f

LE

2 L

∂2g(t) ∂t2

+

btE f f

nπ LEL

2

LEL2

∂g(t) ∂t

+

E tE f f

nπ LEL

2
LEL2g(t) = F (t)

(3.7)

From equation 3.7, we can recognize the effective mass, damping ratio and effective

spring constant of a square-extensional resonator with length LEL are given by

ME f f

=

ρ

tEf

f

LE

2 L

(3.8)

62

ζ = b tEff

nπ LEL

2
LEL2 = b tEff (nπ)2

KEff = E tEff

nπ LEL

2

LE

2 L

=

E

tE f f

(nπ)2

(3.9) (3.10)

3.2.2 Electromechanical Coupling Constant

A voltage VDC + vAC applied across the dielectric film generates a normal force

fZ ≈ VDC

f

LEL2 tf 2

vAC

(3.11)

Here, we make the approximation that vAC « VDC. The laterally transferred strain

in the film is

x,f =

y,f

=

νf fZ Ef LEL2

(3.12)

and the lateral stress in the film is

σx,f

=

σy,f

=

(1

−

νf νf )LEL2

f

LEL2 tf 2

VDC

vAC

(3.13)

This initial lateral stress σx,f acts like an effective residual stress in the film and consequently distributing itself across the thickness of dielectric thin film and bulk

silicon. The distributed lateral strain in the structure is approximated as

x=

y

=

tf σx,f

Ef tf

+

1 2

ESitSi

This yields the distributed lateral stress in the bulk silicon

(3.14)

σx,Si

=

σy,Si

=

tf ESiσx,f

Ef tf

+

1 2

ESi

tSi

(3.15)

Assuming the thickness of the structure is dominated by the bulk silicon (tf « tSi),

we have a lateral force

Fx,f

=

Fy,f

=

2tf tSi

(1

νf − νf

)

f
tf 2

tSiLELVDC vAC

(3.16)

63

The efficiency of electromechanical transduction is indicated by the electromechan-

ical coupling constant η.

η = Fx,f = Fy,f vAC vAC

(3.17)

From 3.16 and 3.17, we recognize the transduction electromechanical coupling con-

stant

η

=

2LEL νf tf (1 − νf )

f VDC

(3.18)

3.2.3 Electrical Equivalent Impedances of a High-overtone

Square-extensional Resonator

The effective mass, damping ratio and effective spring constant can be related in

to

electrical

circuit

parameters.

By

substituting

∂g(t) ∂t

in

3.7

by

i(t) η

,

we

obtain

MEff ∂i(t) + ζ i(t) + KEff i(t)dt = F (t)

η ∂t η

η

(3.19)

or

ME f f η2

∂i(t) ∂t

+

ζ η2

i(t)

+

KE f f η2

i(t)dt = v(t)

(3.20)

From 3.20 we can define the motional resistance, capacitance and inductance of the

resonator in Figure 3.2. The feedthrough capacitance in a two-port resonator origi-

nates from electric field coupling from the input electrode to the output. The small

signal electrical equivalent impedances a resonator consist of j number of smaller

square-extensional resonators vibrating in fundamental mode (n = 1) connected

in parallel are

RX =

KEff MEff Qη2

=

π 4jQ

(1 − νf ) 2 tf 2tEff ρE 1

νf

LEL

2 f

VDC 2

CX

=

η2 KE f f

=

4j π2

νf (1 − νf )

2

2 f
E

LEL2 tf 2tEff

VDC 2

(3.21) (3.22)

64

Figure 3.2: Electrical equivalent circuit of a dielectrically transduced high-overtone square-extensional resonator.

LX

=

ME f f η2

=

1 4j

(1 − νf ) νf

2

ρ
2 f

tf

2 tE f f

1 VDC

2

(3.23)

The high-overtone square-extensional resonator is designed using the RLC electri-

cal equivalent circuit models and simulated in Agilent Advanced Design System

(ADS) software. The resonator design parameters are summarized in Table 3.1

and the simulation result is shown in Figure 3.3.

3.3 Digitally Programmable Filters
Electrically-coupled filters using AlN overtone-mode resonators have been recently demonstrated with narrow-bandwidth and low IL [80]. However, the electrical losses in the shunt capacitors and the patterned ground-plane degrade the shapefactor of the filter. These losses are more severe in electrically-coupled differential lattice configurations. Mechanically-coupled devices demand smaller area since the coupling spring is small. Furthermore, they do not suffer from energy losses since the coupling spring is made of crystalline material. In multi-pole mechanically-coupled filters the resonators are coupled using quarter-wavelength suspensions with stiffness ks at low-velocity nodes. The quarter-wavelength springs
65

Figure 3.3: Simulated performance of a 500 MHz high-overtone square-extensional resonator.
66

Table 3.1: Design parameters of the high-overtone square-extensional resonator

Parameter Value Unit

LEL tf tSi tP oly n

8.5 μm 50 nm 2.75 μm 80 nm 1—

j 72 —

Q 2, 000 —

RX 3.3 kΩ LX 5.36 mH CX 18.8 aF RL 50 Ω fC 500 MHz

minimize mass-loading of the resonators and low-velocity coupling enables narrow-

bandwidth filter design with standard lithography tools. However, as we scale

to radio frequencies KEff and MEff of overtone mode resonators scale with the overtone order, minimizing filter distortion due to mass-loading and simplifying

narrow-bandwidth filter design with coupled resonators at maximum-velocity lo-

cations. The schematic mechanically coupled four-pole filter consisting of overtone

square-extensional resonators is shown in Figure 3.4. The four vibration modes of

the filter are [21]:

fC1

=

1 2π

KE f f ME f f

fC2

=

1 2π

KEff + KS ME f f

(3.24) (3.25)

67

Figure 3.4: Schematic of a digitally programmable filter composed of four series mechanically-coupled checkered-electrode resonators. Each resonator has individually addressable RF + DC lines. The silicon device layer is an RF ground to prevent substrate losses.

fC3

=

1 2π

KEff + 2KS ME f f

(3.26)

fC4

=

1 2π

KEff + 3KS ME f f

(3.27)

The four vibration modes of a 4-pole filter composed by four mechanically cou-

pled overtone square-extensional resonators are shown in Figure 3.5. Only the first

and last resonators of multi-pole mechanically-coupled filters need to be electro-

statically transduced. The intermediate resonators are mechanically coupled and

DC biasing is not an absolute requirement. We retain individual control of the

DC bias (VDC) for each resonator and exploit this property to implement digitally-

tunable bandwidth channel-select filters. The programmable filter is configured as

follows:

1. [DC1 = +VDC, DC2 = DC3 = OFF, DC4 = +VDC] - excites all four vibration modes and enables 4-port filter response.

2. [DC1 = DC3 = +VDC, DC2 = DC4 = −VDC ] - excites the first two resonators

68

Figure 3.5: Four vibration modes of a 4-pole filter consisting of overtone squareextensional mode resonators.
69

out-of-phase. The system still has four vibration modes, however the DC bias configuration attenuates the excitation of modes #3 and #4. In addition, the DC bias configuration of the last two resonators sums the out-of-phase motion of the resonators while nulling in-phase modes (and motional currents). The configuration results in a 2-pole lower sub-band filter. 3. [DC1 = DC2 = DC3 = DC4 = +VDC] - excites the first two resonators in-phase. This leads to exact inverse of the above configuration and results in a 2-pole higher sub-band filter.
The filter is modeled as a network of mechanically coupled mass-spring-damper and simulated in MATHEMATICA. The simulation results demonstrate the filter frequency response with digitally programmable center frequency and bandwidth as shown in Figure 3.6.
3.4 Fabrication Process
The fabrication process of the high-overtone square-extensional resonators and digitally programmable filters is summarized in Figure 3.7. A 1 μm thick undoped oxide is initially deposited by plasma-enhanced chemical vapor deposition (PECVD) on an n-type low resistivity SOI wafer with 2.75 μm thick single-crystal silicon (SCS) device layer. The oxide layer is patterned using fluorine based reactive ion etcher as shown in Figure 3.7 (a). This oxide pedestal is patterned everywhere under the signal pad to reduce the pad capacitance. Next, a 55 nm layer of low-stress silicon nitride thin film is deposited by low-pressure chemical vapor deposition (LPCVD) at 850◦C. A 75 nm layer of n-doped polysilicon is then deposited by LPCVD at 620◦C, annealed at 1000◦C for 40 minutes, and patterned to form the top electrodes as shown in Figure 3.7 (c). This is followed by a deep reactive ion etch (DRIE) step to define the resonators and filters into the silicon
70

Figure 3.6: Simulated performance of a digitally programmable filter composed of four series mechanically-coupled checkered-electrode resonators. (a) Simulated 4pole frequency response of the filter. (b) Simulated lower sub-band filter response. The biasing scheme forces the left two resonators to vibrate out of phase and sums the out-of-phase motional current of the right two resonators. (c) Simulated higher sub-band filter response. The biasing scheme forces the left two resonators to vibrate in phase and sums the in-phase motional current of the right two resonators.
71

Figure 3.7: Fabrication process flow of high-overtone square-extensional mode resonators and digitally programmable filters. device layer. The silicon nitride is patterned to open contact holes to bias the resonators and filters. Partial metal routing is done by evaporating and patterning 80 nm layer of Pt/Au. Finally, the devices are released by performing a timed-etch of the buried oxide in hydrofluoric acid (HF) as shown in Figure 3.7 (f). The key innovations of this process include implementation of a pedestal oxide underneath each signal pad to minimize the pad capacitance and employment of partial metal routing to improve electrical conductivity. The Pt/Au layer is used to carry electrical input signals from input pads to the degenerately-doped polysilicon electrodes on the devices and to deliver the output signals from the devices to output pads. The released SEM images of a high-overtone square-extensional resonator and a 4-pole digitally programmable filter are shown in Figure 3.8 and 3.9 respectively.
72

Figure 3.8: SEM image of a high-overtone 2-D square-extensional mode resonator with checkered electrodes for transduction. The resonator consists of a 55 nm SiN transducer sandwiched between poly electrodes and 2.75 μm thick silicon device layer. An oxide pedestal layer is implemented to elevate the RF signal lines off the ground plane. Pt/Au metal traces and pads are introduced to improve RF signal integrity and reduce noise during probing.
Figure 3.9: SEM image of a digitally programmable filter composed of four series mechanically-coupled checkered-electrode resonators. Each resonator has individually addressable RF + DC lines. The silicon device layer is an RF ground to prevent substrate losses. All RF paths are metalized, routed on an elevated oxide bridge to reduce capacitance and de-embedded to the edge of DRIE trench.
73

3.5 Calibration and De-embedding Techniques
The resonators and filters are characterized in a Cascade RF probe station in a 2-port configuration using high-performance RF coaxial wires, GSG probes and bias-Ts. In order to characterize the 4-pole filters, additional in-phase and outof-phase power-splitters are necessary. Parasitics up to the probe tips are first cancelled with Short-Open-Load-Thru (SOLT) RF measurements on a standard calibration substrate. De-embedding is then performed with Cascade WinCal software, using Short-Open-Thru (SOT) structures fabricated on-chip, but separate from the resonators [81]. Appendix B will discuss in more detail the calibration and de-embedding techniques to measure the high-overtone square-extensional mode resonators and the digitally programmable filters.
3.6 Characterization of a High-overtone Square-extensional
Mode Resonator
The 2-port high-overtone square-extensional mode resonator is characterized using the measurement setup illustrated in Figure 3.10 (a). DC voltage is superimposed to the AC signal using Bias-Ts to introduce resonance at both input and output ports while the silicon device layer is connected to ground. Agilent E8364B PNA microwave vector network analyzer is used to measure the transmission and quality factor of the resonator. The measured frequency response of a high-overtone square-extensional mode resonator in air at room temperature and pressure has a resonance frequency of 512 MHz, motional impedance (RX) of 3.1 kΩ and Q of 1, 800 as demonstrated in Figure 3.10 (b). For comparative study, the designed and measured data for the resonator are summarized and tabulated in Table 3.2.
74

Figure 3.10: (a) Testing configuration for a 2-port high-overtone square-extensional mode resonator. (b) Measured series resonance response of a 2-port high-overtone square-extensional mode resonator in air at room temperature and pressure.
75

Table 3.2: Design parameters and measured data of the high-overtone squareextensional resonator
Parameter Designed Value Measured Value Unit

LEL 8.5 8.5 μm

tf 50 50 nm

tSi 2.75 2.75 μm

tP oly

80

80 nm

n 1 1—

j 72 72 —

Q

2, 000

1, 800

—

RX 3.3 3.1 kΩ RL 50 50 Ω fC 500 512 MHz

3.7 Characterization of a Digitally Programmable Filter
The 4-pole digitally programmable filter is characterized in 2-port configuration according to the measurement setup illustrated in Figure 3.4. In order to retain individual control of each transducer and reduce RF losses to the substrate, the silicon device layer is maintained at an RF ground and each RF I/O port has a superimposed independent DC supply. Calibration and de-embedding procedures to eliminate excessive probe-pad and substrate parasitics is again performed prior to all RF measurements. The power-splitters and bias-Ts (DC = GN D) for RFIN and RFOUT signals are included during de-embedding process. The programmable filter is configured and characterized as follows: 1. [VDC1 = 50 V, VDC2 = VDC3 = 0 V, VDC4 = 50 V ] - enables a 4-pole filter with

76

1.4 MHz bandwidth at 508.7 MHz center frequency. 2. [VDC1 = VDC3 = 40 V, VDC2 = VDC4 = −40 V] - preferentially excites and senses the first two vibration modes which results in a 720 kHz bandwidth lower sub-band filter. 3. [VDC1 = VDC2 = VDC3 = VDC4 = 40 V] - preferentially excites and senses the last two vibration modes which results in a 660 kHz bandwidth higher sub-band filter.
The 50 Ω terminated frequency response of the filter for each case of bias voltage configuration measured in air at room temperature and pressure is presented in Figure 3.11. In order to maximize the power transfer from input to output, the termination impedance of the filter is adjusted. Figure 3.12 and Table 3.3 summarize the filter response of each configuration with adjusted termination impedance. The DC bias for the sub-band filters was reduced to 40 V to compensate for increased transducer area and ensure all filters have the same impedance for characterization.
3.8 Conclusion
In this work we demonstrated the design, modeling, simulation, fabrication and characterization of high-overtone square-extensional resonators and digitally programmable filters. The center frequency and filter bandwidth are digitally tunable by controlling the DC bias voltages of individual resonators in a series coupled array. Using tri-state polarization voltage control (−VDC, GN D, +VDC), the programmable filter provides bandwidth granularity for next generation frequencyagile radios. Although square-extensional and other contour-mode MEMS resonators are excellent candidates for designing channel-select filter arrays, they cannot be tuned significantly at the device level. By using the system-level digital-
77

Figure 3.11: Performance of a 50 Ω terminated filter with three different bias configurations in air. (a) Measured 4-pole frequency response of the filter. (b) Measured lower sub-band filter response. The biasing scheme forces the left two resonators to vibrate out of phase and sums the out-of-phase motional current of the right two resonators. (c) Measured higher sub-band filter response. The biasing scheme forces the left two resonators to vibrate in phase and sums the in-phase motional current of the right two resonators.
78

Figure 3.12: Transmission response of the filter with three different bias configurations after termination using the PNA’s pole-Z conversion function. The attenuated modes are clearly visible in the transmission response of the lower sub-band filter. The filter stop-band floor is high because electrical resistance in the ground plane leads to large capacitive feedthrough between drive and sense ports.
79

Table 3.3: Performance summary of the digitally programmable filter

Parameter

4-pole filter Lower sub-band Higher sub-band

filter

filter

IL

−2.4 dB

−2 dB

−3.1 dB

3dB BW

1.4 MHz

720 kHz

660 kHz

fC Ripple

508.7 MHz < 2 dB

508.3 MHz < 1 dB

509.1 MHz < 3 dB

Stop Band Rejection −14 dB

−14 dB

−20 dB

VDC

50 V 40 V and −40 V

40 V

RL

4.1 kΩ

2.8 kΩ

2.9 kΩ

tuning scheme we have demonstrated a 4-pole filter consisting of four overtone square-extensional mode resonators at 509 MHz with 1.4 MHz bandwidth. By switching the DC polarization voltage of the individual resonators, the filter is split into narrower high and low sub-bands, each approximately 700 kHz wide. Due to limitations of the SOI fabrication process and resistive losses through the device layer, we were limited to four resonators and each RF I/O port had a superimposed independent DC supply. However, this can be easily resolved by switching to a surface-micromachining process [82]. Adding more resonators to the array will provide finer bandwidth granularity, however the maximum possible bandwidth is still limited by the coupling efficiency of the transducer.

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CHAPTER 4 VACUUM-ENCAPSULATED CMOS-COMPATIBLE PACKAGING
TECHNOLOGY FOR CONTOUR-MODE RESONATORS
4.1 Introduction
Wireless communication has greatly impacted our daily lives since the first radio system was invented. Applications, such as cellular phones, satellite television, GPS navigation, and wireless internet networks, are driving the development of RF components in the direction of being smaller, more inexpensive and requiring less power, and thus this topic has been one of the hottest research areas. MEMS resonators have great potential for replacing conventional resonators used in portable wireless applications because of their merits of small size, high quality factor (Q), and low power consumption [83]. There is also great interest in using coupled micro-resonators as band-pass filters and exciting results have been demonstrated in Chapter 2 and Chapter 3 of this dissertation.
Despite the advances in device performance, packaging for MEMS resonators remains a critical challenge. Because of their extreme sensitivity to the environment, MEMS resonators need vacuum encapsulation to enable real applications and post-MEMS CMOS integration. The promising on-chip application also requires a CMOS compatible packaging process. Due to the stringent RF requirements, the electrical properties and hermeticity of the packaging are also very important.
This Chapter presents the design, fabrication, packaging design, and measurement of a dielectrically transduced, width-extensional mode resonator encapsulated in an epitaxial-grown silicon package. The major challenges of merging two technologies into a promising solution of a high frequency MEMS-based device will also be discussed.
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4.2 Width-extensional Mode Resonator

Dielectrically-transduced silicon bar resonators vibrating in the bulk-mode have

superior linearity and high quality factors [60, 79]. The width-extensional mode

resonance of a bar resonator depends on the width, W , with frequency (fC) given

by

nE fC = W ρ

(4.1)

where n is the mode number (n = 1, 3, ...), and E and ρ are the effective elastic

modulus for 2-D expansion and the density of silicon, respectively. The width-

extensional mode is excited by patterning electrodes in plate configuration on top

of the resonator using dielectric transduction, as shown in Figure 4.1 (a). The

main resonator bar consists of three layers - a 100 nm polysilicon electrode layer, a

100 nm silicon nitride transducer layer, and a 3 μm single-crystal silicon resonator

layer. As shown in Figure 4.1, the input and output electrodes are patterned on

polysilicon and the silicon nitride layer is used as a high-κ dielectric to enhance the

transduction (compared to an air-gap). The quarter-wavelength anchoring scheme

is designed to minimize mass-loading of the resonator. A DC bias is superimposed

on a small AC voltage using a Bias-T and applied to the drive electrode, while

the silicon device layer is connected to RF ground. This time-varying voltage

causes a squeezing force on the dielectric thin film. Due to the Poisson effect,

the dielectric layer experiences a lateral strain. Since the silicon nitride layer is

structurally integrated with the silicon bar, the lateral strain is transferred from

the dielectric film to the silicon resonator layer. As the strain distributes through

the resonator, the width-extensional mode is excited and the motional current is

sensed through the sense electrode. The ANSYS fundamental mode shape of the

width-extensional resonator is shown in Figure 4.1 (b).

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Figure 4.1: (a) Schematic diagram of the dielectrically transduced, widthextensional mode resonator. (b) ANSYS contour plot of the width-extensional bar mode shape.
4.3 Epitaxy-silicon Microshell Packaging
The fabrication process is the fusion of two technologies developed at Cornell and Stanford [60, 84]. The wafer-level encapsulation packaging developed at Stanford University has the advantage of a small foot-print, superior long-term stability, and CMOS compatibility [85–87]. The epitaxial-grown silicon allows CMOS circuitry to be built on top of the package to be integrated with the MEMS device packaged inside.
Previously, there have been accelerometers and resonators working at 1.2 - 1.4 MHz or below, encapsulated in this packaging. However, there has not been an attempt to encapsulate devices with resonant frequencies higher than 20 MHz using this silicon package. A thorough study of the electrical performance of the packaging was investigated [88]. The paper indicates that the silicon vertical interconnect has less than 1 dB attenuation up to 6 GHz, which extends the utility of this packaging for intermediate frequency to high frequency resonator applications.
83

Figure 4.2: Epi-silicon microshell encapsulation process for dielectrically transduced resonators. Vertical epi-vias to the poly electrodes provide RF input/output while the vias to the silicon device layer provide a micro RF -cage providing a shielded micro-environment.
84

4.4 Fabrication Process
As shown in Figure 4.2, the fabrication begins with a silicon-on-insulator (SOI) wafer with a device layer of 3 μm. A stack of 100 nm stoichiometric silicon nitride and 100 nm heavily doped n+ polysilicon was deposited using low pressure chemical vapor deposition (LPCVD). The polysilicon layer was patterned to create electrodes. Part of the silicon nitride layer was etched to create electrical contact to the device layer, as shown in Figure 4.2 (b). The resonator was then patterned and etched through the nitride/silicon stack using deep reactive ion etching (DRIE). Low temperature oxide (LTO) was deposited as the sacrificial layer to create a cavity on top of the resonator. The LTO was then patterned and etched to create electrical contacts.
The main challenge is in creating low-loss vertical interconnects making contact to two different layers of the resonator. As shown in Figure 4.2 (d), the LTO was patterned and etched to create an electrical connection to the polysilicon layer as well as the device layer. Due to the thickness variation from the LTO deposition, stopping the etch on two different layers is extremely challenging using an academic-grade plasma etcher (insufficient etching selectivity, non-uniform etching across the wafer, etc.) However, this challenge can be greatly reduced with an industry-grade etcher.
Another challenging issue is the resistivity of the epi-polysilicon interconnects. A lot of characterization was done to ensure the resistivity of the epi-polysilicon was less than 10 mΩ-cm. Highly phosphorus doped epi-silicon was then grown on the top of the wafer to encapsulate the resonators. Vent holes were patterned to open access to the sacrificial LTO. A custom made HF vapor etcher in the Stanford Nanofabrication Facility was used to release the resonator. After releasing, vent holes were again sealed by LTO in a low pressure environment to vacuum-
85

Figure 4.3: SEM of the fabricated resonator. The zoomed-in picture on the right shows the thin poly electrode on top of the resonator bar. The zoomed-in picture on the left shows the electrical contact between the epi-silicon and the device layer.
86

Figure 4.4: Transmission response using the 2-port measurement. Capacitive feedthrough masks the electromechanical resonance, resulting in a sharp dip at the target frequency.
encapsulate the resonators. Finally, an aluminum layer was used for electrical interconnects and bond pads. An SEM picture of a fabricated width-extensional mode resonator is shown in Figure 4.3.
4.5 Measurement Results
As shown in Figure 4.4, a simple two-port measurement gives a clear sharp dip in S21, indicating the electromechanical resonance is masked by the parasitic feedthrough. To overcome the capacitive feedthrough, the resonator was characterized using a differential measurement technique, inspired by [89, 90]. An RF signal from the network analyzer first goes into a splitter to create in-phase and out-of-phase signals, represented by +RFin and −RFin, respectively. In order to
87

induce resonance of the resonator, a DC bias, VDC, was added into +RFin using a Bias-T. Two identical resonators were driven by +RFin and −RFin. While +RFin + VDC was driving the resonator, the pure AC signal (−RFin) was driving the dummy resonator, with only its parasitic capacitance being driven. The outputs from both structures were then mixed together, where the out-of-phase current from the parasitic capacitance cancels out the parasitic component in the signal from the resonator. The exact differential measurement setup and equivalent electrical circuit used in this work is express in Figure 4.5 . Although it would be ideal to have two identical resonators side-by-side when the differential measurement is conducted, the fabricated wafer only has a similar resonator by its side. Therefore, although the improvement of the signal to noise ratio is already greatly enhanced by using a similar structure as the dummy resonator, the feedthrough cancellation is not yet optimized.
From the SEM picture, one can observe that the vertical interconnect is firmly connected to the device layer, providing electrical ground to the resonator beam. One can also note that the thin (∼ 13 μm) epi-silicon is enough to provide mechanical stability for the low-pressure hermetic packaging. It is important to keep this layer thin because of the electrical requirements [88].
The fabricated resonator was measured using the differential measurement setup explained in the previous section. Figure 4.6 shows the response using feedthrough cancellation on top of the response from the 2-port measurement. The resonant frequency is 207 MHz and the quality factor is 6, 400. This is the highest reported frequency for a MEMS resonator packaged in a microshell. One can also note that there is a −13 dB noise reduction due to the implementation of the differential measurement.
88

Figure 4.5: (a) Schematic of the pseudo-differential measurement setup, and (b) The equivalent circuit of pseudo-differential measurement to cancel the capacitive feedthrough current.
89

Figure 4.6: Transmission responses of the simple 2-port measurement and pseudodifferential measurement. It is clearly shown that the resonance peak matches the sharp dip shown in the 2-port measurement.
90

4.6 Conclusion
A fully encapsulated, width-extensional mode resonator was successfully fabricated with an f x Q product of 12 x 1011 Hz, making it an excellent candidate for drop-in insertion in local oscillator and RF spectrum analyzer applications. The performance of the epitaxial-silicon packaging is also verified to sufficiently package VHF devices. In the future, we plan to introduce Hafnium dioxide (HfO2) as the dielectric film to reduce the motional impedance. Furthermore, the length of the width-extensional mode resonator can be increased to enlarge the transduction area. Hence, the motional impedance of the encapsulated resonator could be reduced and alleviate the challenge of impedance matching.
91

CHAPTER 5 AQUEOUS TRANSDUCTION OF CONTOUR-MODE RF MEMS
RESONATORS

5.1 Introduction

The increasingly crowded radio spectrum and the impending arrival of next gen-

eration 7-band cellular phones and the joint task force radio system (JTRS) has

necessitated front-end filter arrays capable of eliminating both out-of-band and

out-of-channel interferers. The filters will require extremely narrow bandwidth,

good stop-band rejection and excellent shape factor. Dielectrically-transduced

contour-mode MEMS resonators with quality factor Q > 10, 000, low motional

impedance RX and CAD-defined resonance frequencies from 40 MHz - 2 GHz are excellent candidates for designing channel-select filter arrays [63,71,91]. But unlike

thickness shear mode resonators, the frequency expressions for contour modes and

flexural vibration modes do not directly couple. It is therefore difficult to perform

orthogonal frequency tuning of contour-mode resonators [64].

Electrostatically transduced RF MEMS resonators have very high (Q) which

will enable design of narrow-bandwidth channel-select filters with steep shape-

factor. However, to date the high (RX ) of these resonators leads to large insertion loss (IL) in the filters when connected directly to 50 Ω RF systems. Therefore,

it is essential to minimize the motional impedance, while retaining high quality

factors.

In lateral-gap contour-mode resonators, the motional impedance is given by

KEff MEff R =X VDC 2 2A2
Q g4

(5.1)

where KEff and MEff are the effective spring constant and mass of the resonator.

RX can be reduced by decreasing the transducer gap (g), increasing the bias voltage

92

(VDC), electrode area (A) or dielectric constant ( ) of the transducer. This work focuses on increasing the dielectric constant of the transducer, by replacing vacuum or air-gap with DI-water.
The high permittivity of DI water (κW ater = 80.1) relative to air or vacuum enhances the efficiency of the transducer, thereby enabling operation at low DC bias voltage. Moreover, water has a low acoustic velocity (1, 500 m/s) compared to silicon, poly-SiGe and poly-SiC. The large acoustic mismatch between water and silicon allows the resonators to achieve a relatively large displacement in lateral direction. In addition, the high-κ dielectric liquid increases the electrostatic force between the electrodes and the resonator, which facilitates a larger electrostatic frequency tuning capability.
Sournart et al demonstrated that by using a local oscillator (LO) signal that is faster than the response time of a polar fluid, it is possible to prevent electrode polarization and double-layer formation [92]. Electrostatic actuators and viscosity sensors operating in water have been demonstrated using this technique [93, 94]. In this chapter, we demonstrate that the same approach enhances the performance of contour-mode poly-SiGe disk resonators by constraining DI water to the lateral transducer gaps.
5.2 Aqueous Transduction of a Contour-mode Poly-SiGe Disk
Resonator
Lateral dielectrically transduced thickness shear mode resonators with 0.8% tunable center frequency (fC)have been demonstrated in Chapter 2 of this thesis. However, the frequency of operation of these resonators is limited by the device thickness. Contour-mode air-gap poly-SiGe disk resonators are exceptionally at-
93

tractive choice for radio frequency filtering because their frequency of operation is defined lithographically. Furthermore, they have low anchor-loss, high-Q in air and can be integrated with CMOS electronics. However, since air is not a very efficient transducer (κAir = 1), these devices have high motional impedances and ppm/V tuning range.
5.2.1 Measurement of a Poly-Sige Disk Resonator in Air
In order to verify the feasibility of using DI water for aqueous transduction of MEMS resonators, we used a previously fabricated 50 nm air-gap poly-SiGe contour mode disk resonator shown in Figure 5.1 [95]. Figure 5.2 (a) shows the measurement setup and experimental result of the first radial mode air-gap polySiGe resonator. The superimposed LO signal prevents bi-layer formation [92] and enables aqueous transduction. Even though the LO signal might not be necessary on the actuation side since the actuation frequency is considerably high, it is required on the sense side. Care is taken to attenuate harmonics of the LO signal and prevent unintentional actuation of the resonator through non-linear electrostatic force. Before characterizing the resonator, we performed two standard RF calibrations. The first calibration is the Short, Load, Open, and Through (SLOT) substrate calibration up to the probe tips to remove parasitics associated with the cable and probe assembly. The second calibration is the Short, Open, and Through (SOT) de-embedding using Cascade WinCal software to cancel the large pad capacitances. Appendix B will discuss in more detail the calibration and de-embedding techniques for MEMS resonators and filters. The resonator has a transmission response with Q = 5, 300 and RX = 517 kΩ in air with a 5 V polarization voltage as shown in Figure 5.2 (b).
94

Figure 5.1: SEM image of a poly-SiGe disk resonator: (a) Cross-section of the resonator showing the 60 nm lateral air-gap (b) Close-up of anchor, and (c) Top view.
95

Figure 5.2: (a) Transmission measurement setup, and (b) Transmission response in air.
96

Figure 5.3: (a) Schematic illustrating the experiment. The water wicks the 60 nm gap and is left under the structure. (b) Photograph of water droplet placed on resonator and then moved to the edge. (c) Measured transmission response after water drop is rolled away from the resonator: Q of 430 at 36 MHz.
5.2.2 Measurement of Poly-Sige Disk Resonators with DI
Water
In our experiments, we used high resistivity DI water specially acquired to minimize the leakage current down to < 1 μA. Water has high loss tangent at frequencies above 2 GHz [96], which should be sufficient for most RF MEMS application frequencies. The initial trial was to immerse the resonator in a water droplet and measure the transmission response. However, after submerging the resonator under a water droplet, we could not measure a transmission response due to excessive mass-loading and Q losses resulting from viscous drag.
The subsequent attempt was done by coating the resonator with a hydrophobic self-assembled monolayer (SAM) to eliminate mass-loading and viscosity effects of
97

the water droplet on the resonator. The SAM layer is non-conformal, coating the top surface of the poly-SiGe disk resonator, while leaving the 50 nm transducer gaps hydrophilic. A drop of DI water was placed on the resonator and then the chip was slowly tipped to one side to let the water droplet roll-off the structure as shown in Figure 5.3 (a,b). The DI water ’wicked’ the electrostatic transducer gaps and a transmission response with a Q of 430 at 36 MHz was measured due to the reduced mass-loading and viscous damping on top of the resonator (Figure 5.3 (c)).
The Q was low because water got under the resonator through the space between the resonator and the CMP fill-pattern. Even though the gap under the disk was < 2 μm, the water underneath the resonator causes viscous damping and degrade the resonator’s quality factor. In order to reduce this effect, the water droplet was initially placed further away from the resonator on the SAM-coated fill pattern. The chip was slowly tipped, ensuring that the water droplet rolled over both the transducer gaps of the resonator as illustrated in Figure 5.4 (a). The short time that the water droplet overlapped the resonator was sufficient to wick the transduction gaps but greatly reduced the chance of water seeping under the resonator.
The hydrophobic SAM-coated CMP fill-pattern enabled the droplet to ’roll’ rather than drag along the chip surface. This allowed repetitive measurements with reasonable control over droplet roll-over. The transmission response of the resonator was measured with Q > 3, 500 and RX = 4.2 kΩ near 42 MHz as shown in Figure 5.4 (b).
As the water droplet is rolled back and forth, the capacitive floor increases and RX improves as shown in Figure 5.5. This phenomena happened because the water did not entirely ’wick’ the transduction gaps during the first-pass. Subsequent rolls
98

Figure 5.4: (a) Schematic of water droplet rolled across the resonator; wicking the transducer gap but minimizing the water left underneath the resonator. (b) Transmission response: Q of 3, 800 at 42 MHz with RX = 3.9 kΩ.
99

Figure 5.5: Transmission response of a resonator with repeated rolls of the DI water droplet.
allow more DI water to enter the gaps, however, the measured Q dropped from 4, 000 to 200 due to viscous damping as shown in Figure 5.5.

5.2.3 Series Frequency Tuning of Poly-Sige Disk Resonators

Non-linearity in air-gap parallel-plate electrostatic transducers introduces a DC

bias-dependent resonant frequency shift. This electrical spring stiffness is given by

KE

=

VDC 2C0 g2

(5.2)

where C0 is the nominal capacitance between the electrode area and the resonator body. KE directly subtracts from the mechanical spring stiffness KM . The electrical spring constant provides DC-bias controlled, post-fabrication tuning of elec-

trostatically transduced resonators:

Δf fM ech

=

−

1 2

VDC 2C0 KM g2

=

−

1 2

VDC 2 A KM g3

(5.3)

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Figure 5.6: (a) 0.1% center frequency tuning of the air-gap transduced disk resonator before anchor failure. (b) In DI water, the resonator center frequency is tuned up to 3%, before the onset of electrolysis.
The tuning range of low frequency (< 10 MHz) bending-mode beam resonators using electrostatic spring softening is on the order of 5 - 10 %. This facilitates resonator designs which not only overcome fabrication tolerances and temperature drift, but also enables frequency-agile filter and oscillator design. However, because tunability relies on the ratio of KE to KM , the relatively large effective stiffness of air-gap contour mode resonators limits their tuning range < 0.05% [97]. Other tuning techniques such as tuning the series capacitance and heating the resonator, de-Q the resonator [43] and cost excessive power consumption [98] respectively. Replacing air in the sub-micron transducer gap with DI water enhanced the electrostatic spring by >50 x and extended the tuning range to 3% - the highest tuning-range reported to date for electrostatically transduced contour-mode resonators as shown in Figure 5.6.
5.3 Conclusion
Aqueous transduction is an excellent alternative to solid-dielectric transduction due to the high permittivity and low acoustic velocity of water. However, the operating
101

frequency is limited up to 2 GHz as water has a significant loss tangent above that frequency [96]. It also facilitates a large frequency tuning capability. The 3% limit of electrostatic tuning capability was mainly due to electrolysis of water and bubble formation, which suggests that using an alternate low loss-tangent liquid such as dielectric oil [99] will enable high resonant frequency operation and wide tuning range. In addition to RF applications, aqueous transduction can be used for thermal cooling and isolation, single-molecule mass detection in liquid media and frequency-domain dielectric spectroscopy.
102

CHAPTER 6 PZT TRANSDUCED VOLTAGE TUNABLE RESONATORS
6.1 Introduction
Numerous applications in wireless communications and sensor networks have motivated the development of on-chip, high-Q MEMS resonators and filters to realize portable radios that consume low power and operate at the global range of frequency standards. Dielectrically transduced thickness shear mode and contourmode resonators have the capability to reach high frequency of operation while maintaining high Q and low motional impedance as presented in Chapter 2 and Chapter 3 of this dissertation. A band-pass filter can be constructed by electrically or mechanically coupling an array of these resonators. However, the inadequate effective coupling efficiency of the dielectrically transduced resonators limits the bandwidth of the filter, creating a demand for transducers with high electromechanical coupling coefficient.
Aluminum Nitride (AlN) is a popular material for fabrication of thin film bulk acoustic wave (BAW) and contour-mode resonators and filters because it possesses a high acoustic velocity, high quality factor and post-CMOS integration capability [54, 100]. However, intermediate frequency applications have driven the investigations for new piezoelectric or/and ferroelectric materials for resonators. At low frequencies, ferroelectrics like lead zirconate titanate (PZT) are better suited as they avoid thick film requirements and reduce the area required for the filters. Furthermore, PZT exhibits larger electromechanical coupling coefficient than AlN, enabling the design of larger % bandwidth filters [101].
A resonator with dynamically tunable center frequency will not only overcome fabrication tolerances and thermal drift, but will also facilitate filter design that
103

Figure 6.1: A 3-D schematic of PZT-on-Silicon length-extensional mode resonator.
has the ability to discern bandwidths between 0.1 MHz to 5 MHz, enabling a handheld analog spectral processor with voltage dependent dynamic frequency trimming and tuning. PZT has been previously shown to have frequency tuning capabilities [102, 103]. However, PZT-only resonators are well known to have low quality factor (Q < 300) [101, 104]. In order to overcome the low quality factor of PZT-only resonators, we developed a new fabrication technology to integrate PZT transduction with single-crystal silicon (SCS) resonators.
6.2 Length Extensional Mode Resonator
Previous results have shown that length-extensional mode (LEM) vibrations can be excited by sandwiching a piezoelectric transducer (AlN, Zinc Oxide, PZT, etc.) between metal electrodes [54,105]. However, due to poor crystallinity and repeatability of the piezoelectric thin-films, several research groups have chosen to use the piezoelectric material for actuation and sensing, while utilizing single-crystal silicon as the resonating structure [52, 106]. The schematic of a PZT transduced length-
104

Figure 6.2: An ANSYS mode shape of a length-extensional mode resonator.

extensional mode resonator on single-crystal silicon is presented in Figure 6.1. The

ANSYS mode shape of the designed LEM resonator is demonstrated in Figure 6.2.

In this effort, PZT transduced resonators were fabricated with and without a 10

μm thick silicon device layer to explore the insertion loss and Q trade-offs between

the two types of resonators. The bulk-extensional mode resonance of a length-

extensional mode resonator depends on L, with frequency of operation (fC) given

by:

fC

=

n 2L

E ρ

(6.1)

where L is the length of the resonator, E and ρ are effective elastic modulus for

2-D expansion and density of the resonator respectively, and n is the harmonic

order. The frequency independent motional impedances of the fundamental mode

of PZT transduced length-extensional mode two-port resonators will be derived in

the next subsections.

105

Figure 6.3: The cross-section of a length-extensional mode resonator.

6.2.1 Effective mass, Damping ratio and Effective spring

constant

The cross-section of a length-extensional mode resonator with length, L and thickness, t is shown in Figure 6.3. The resonator vibrates in the direction normal to area, A (not shown in the picture).
From Newton’s law of motion, the sum of forces that act on the resonator can be expressed as

ΣF

=

m

a

→

(σ(x, t) − dσ(x, t)) A − σ(x, t)A

=

∂2u(x, t) ρAdx ∂t2

(6.2)

Equation 6.2 can be written as

∂σ(x, t) A
∂x

=

∂2u(x, t) ρA ∂t2

A

∂E

∂u(x,t) ∂x

∂x

=

ρA

∂2u(x, ∂t2

t)

→

EA

∂2u(x, ∂x2

t)

=

ρA

∂2u(x, ∂t2

t)

(6.3) (6.4)

where E is the Young’s modulus of the structure. The wave equation for a one-

dimensional vibrating length-extensional mode resonator including the damping

106

factor and external forces is

ρA

∂2u ∂t2

(x,

t)

−

∂ bA
∂t

∂2u ∂x2

(x,

t)

−

EA

∂2u ∂x2

(x,

t)

=

∂f ∂t

(x, t)

(6.5)

By the method of separation of variables, we assume equation 6.5 has solutions of

the form

u(x, t) = g(t) sin

nπ x

L

(6.6)

Substituting 6.6 into 6.5 gives

ρA sin

nπ x L

∂

2g(t) ∂t2

+bA

nπ L

2
sin

nπ x L

∂g(t) +EA ∂t

nπ L

2
sin

nπ x L

g(t) = ∂f (x, t) ∂t

(6.7)

Multiply 6.7 by sin

nπ L

x

and integrate over the length yields

L/2 −L/2

ρA

sin

nπ L

x

2 ∂2g(t) ∂t2

+bA

nπ L

2

sin

nπ L

x

2 ∂g(t) ∂t

(6.8)

+EA

nπ L

2

sin

nπ L

x

2 g(t)dx

=

F (t)

where F (t) is

L/2 ∂f (x, t) sin

nπ x

dx

−L/2 ∂t

L

Equation 6.8 can be simplified as

(6.9)

ρAL 2

∂2g(t) ∂t2

+

bAL 2

nπ L

2

∂g(t) ∂t

+

EAL 2

nπ

2
g(t) = F (t)

L

(6.10)

From equation 6.10, we can recognize the effective mass, damping ratio and ef-

fective spring constant of a length-extensional mode resonator with length L are

given by

ME f f

=

ρAL 2

ζ

=

bAL 2

nπ L

2

=

n2bAπ2 2L

KE f f

=

EAL 2

nπ L

2

=

n2EAπ2 2L

(6.11) (6.12) (6.13)

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6.2.2 Electromechanical Coupling Constant

The lateral stress, σ in PZT is governed by the constitutive equation

σ=E

−

e31

vAC t

(6.14)

where , e31, E and t are the strain, piezoelectric coefficient, Young’s Modulus and thickness of PZT respectively. If the PZT is free to deform, the total stress is zero,

and equation 6.14 becomes

0=E

−

e31

vAC t

and the strain is

= e31 vAC Et

The piezoelectric force, FP ZT due to PZT transduction is

(6.15) (6.16)

FP ZT =

EA

=

e31

A

vAC t

(6.17)

where the cross sectional area A = tP ZT x 2 x WP ZT (The width of the resonator bar

(W ) is approximately 2 x WP ZT ). By substituting e31 with d31 x E, equation 6.17

can be written as

FP ZT = 2 d31 E WP ZT vAC

(6.18)

The efficiency of electromechanical transduction by PZT is indicated by the electromechanical coupling constant η.

η = FP ZT vAC

= 2 d31 E WP ZT

(6.19)

108

Figure 6.4: Electrical equivalent circuit of a PZT transduced LEM resonator.

6.2.3 Electrical Equivalent Impedances of a PZT Transduced

LEM Resonator

The effective mass, damping ratio and effective spring constant can be related in

to

electrical

circuit

parameters.

By

substituting

∂g(t) ∂t

in

6.10

by

i(t) η

,

we

obtain

MEff ∂i(t) + ζ i(t) + KEff i(t)dt = F (t)

η ∂t η

η

(6.20)

or

ME f f η2

∂i(t) ∂t

+

ζ η2

i(t)

+

KE f f η2

i(t)dt = v(t)

(6.21)

From 6.21 we can define the motional resistance, capacitance and inductance of

the 2-port PZT-only transduced resonator in Figure 6.4. The feedthrough capaci-

tance in a two-port resonator originates from electric field coupling from the input

electrode to the output. The small signal electrical equivalent impedances a PZT

Transduced LEM resonator vibrating in fundamental mode (n = 1) are

RX_P ZT −only =

KEff MEff Qη2

=

π

ρ1 PZT 2

tP ZT

4Q

EP ZT

3 2

WP ZT

1 d312

CX_P ZT −only =

η2 KE f f

=

4 π2

WP ZT L tP ZT

EP

ZT

d312

(6.22) (6.23)

109

LX_P ZT −only =

ME f f η2

=

ρP ZT tP ZT L 1 EP ZT 2 WP ZT 4d312

(6.24)

Using the identical line of derivation, the motional resistance, capacitance and

inductance of the 2-port PZT-on-silicon transduced resonator are given by

RX_P ZT −on−silicon

=

π

ρE f f

1 2

EE f f

4Q EP ZT 2

1 2

(tSi + tP ZT ) 1 WP ZT d312

(6.25)

CX_P ZT −on−silicon

=

4 π2

WP ZT L (tSi + tP ZT

)

EP ZT 2 EE f f

d31

2

LX_P ZT −on−silicon

=

ρEff (tSi + tP ZT ) L 1

EP ZT 2

WP ZT

4d312

(6.26) (6.27)

where ρEff and EEff are the effective (PZT + silicon) density and Young’s mod-

ulus, WP ZT is the width of PZT transducer under the input electrode, d31 is the

transverse piezoelectric coefficient, and ρP ZT and EP ZT are the density and Young’s

modulus of the PZT thin-film.

6.3 Fabrication Process
The device fabrication is largely based on the fabrication sequence outlined by Polcawich et al [107]. This process flow is highlighted in Figure 6.5. We started with an SOI wafer with 10 μm thick silicon device layer. We deposited 50 nm SiO2 to mitigate lattice mismatch issues between the PZT-metal stack and the silicon. Then we successively deposited 100 nm platinum bottom metal, 0.5 μm PZT and another 100 nm platinum top metal. The PZT films were deposited using a chemical solution deposition method modified from reference [108] and using a crystallization temperature of 700◦C. We patterned the top metal electrodes and signal pads using lift-off followed by pattern and wet-etch of PZT to open ground pads. The resonator was then defined by anisotropic etching of the PZT, platinum, silicon dioxide, silicon device layer and the buried oxide [109]. A novel technique of dry releasing the devices using a gentle front-side XeF2 alleviated the need for
110

Figure 6.5: Fabrication process-flow for PZT-on-silicon and PZT-only resonators. 111

Figure 6.6: (a) SEM of a released PZT-only resonator. (b) SEM of a released PZT-on-silicon resonator. The isotropic pit due to the XeF2 etch can be seen in the background. backside DRIE used in [110]. An organic photodefinable layer was developed to provide protection of the resonator while allowing undercutting of the handle wafer silicon using a XeF2 etch. Finally, the PZT resonators were subjected to electric fields of 200 kV/cm for 10 minutes to align the ferroelectric domains. Figure 6.6 (a) and (b) show PZT-only and PZT-on-silicon bar resonators fabricated in this process.
112

Figure 6.7: Measured transmission response of PZT-only and PZT-on-silicon resonators with the exact same lateral dimensions in air at room temperature and pressure.
6.4 Measurement Results
6.4.1 Resonance Frequency, Motional Impedance, and Qual-
ity Factor
The resonators were characterized after performing SOLT calibration followed by SOT de-embedding. The DC bias is superimposed to the AC signal at both input and output ports using bias-T’s for all measurements. Measured transmission response of the PZT-only and PZT-on-silicon resonators with the exact same lateral dimensions in air at room temperature and pressure are shown in Figure 6.7. The PZT-on-silicon resonators exhibit higher Q, higher resonant frequency (fC) and lower motional impedance (RX ) compared to their PZT-only counterparts.
113

Table 6.1: The measured characteristics of PZT-on-silicon resonators

Parameter

Res 1 Res 2 Res 3

Dimensions (μm2) 240 x 40 280 x 60 260 x 60

Q 5, 040 3, 820 4, 224

fC (MHz)

15.94 13.65 14.72

RX (Ω)

167 319 290

Table 6.2: The measured characteristics of PZT-only resonators

Parameter

Res 1 Res 2 Res 3

Dimensions (μm2) 240 x 40 280 x 60 260 x 60

Q 202 91 241

fC (MHz)

6.88 5.47 5.78

RX (Ω)

4, 078 8, 812 3, 628

PZT-on-silicon resonators also have higher resonant frequency because the thick silicon device layer that dominates the composite structures causes an increase in the ratio of EEff to ρEff . These measurement results confirm that integrating PZT transduction with single-crystal silicon retains the mechanical energy within the high quality silicon device layer. The improvement in Q (35x) outweighs the increase in tSi (10 μm), resulting in a net decrease in RX . The performances of PZT-on-silicon and PZT-only resonators with the exact same lateral dimensions are summarized in Table 6.1 and 6.2.

114

Figure 6.8: (a) Measured transmission of a 190 μm x 40 μm PZT transduced resonator on 10 μm silicon with different bias voltages in air at room temperature and pressure. 0.2% frequency tuning capability is observed due to DC bias dependent Young’s modulus and density of PZT thin film. (b) Measured transmission of a 90 μm x 20 μm PZT-Only resonator with five different bias voltages in air at room temperature and pressure. 5.1% frequency tuning capability is observed due to DC bias dependent Young’s modulus and density of PZT thin film.
6.4.2 DC Voltage Tuning
Wang et al and Cho et al have demonstrated that PZT has a electric field dependent Young’s modulus, density and permittivity [102, 103]. As the DC bias increases, the transduction efficiency is improved. Therefore, by taking advantage of the electric field dependent k312, we can reduce RX and improve the insertion loss of the resonators. The measured transmission of a 190 μm x 40 μm PZT transduced resonator on 10 μm silicon with different bias voltages is shown in Figure 6.8 (a). A 0.2% frequency tuning capability is observed due to the DC bias dependent Young’s modulus of PZT thin film. Since the resonant frequency is dominated by the silicon device layer, there is very little resonant frequency tuning, whereas the improvement in electromechanical coupling leads to 11x improvement in motional impedance at 16 V DC bias. The measured characteristics of the resonator are summarized in Table 6.3.
In contrast, the measured transmission of a 90 μm x 20 μm PZT-only resonator
115

Table 6.3: The measured characteristics of PZT-on-silicon resonator with different bias voltages

Tuning Voltage (V) 0 4 8 12 16

Q 2, 020 2, 021 2, 021 2, 022 2, 023

fC (MHz) RX (Ω)

21.332 21.340 21.345 21.355 21.365

582 223 142 83

50

Table 6.4: The measured characteristics of PZT-only resonator with different bias voltages

Tuning Voltage (V) 0 4 8 12 16

Q 125 126 136 147 148

fC (MHz) RX (Ω)

20.025 20.250 20.440 20.610 20.730 1, 004 453 343 253 207

with different bias voltages in air at room temperature and pressure is shown in Figure 6.8 (b). The PZT-only resonators demonstrate 5.1% DC bias dependent frequency tuning capability, the highest tuning range reported by any piezoelectrically transduced contour mode resonators to date. The measured characteristics of the resonator are summarized in Table 6.4.

6.4.3 Linearity
The immunity of the resonators to the third-order intermodulation distortion IM3 was characterized similar to the procedure outlined in reference [80]. Two interferer signals f1 and f2 separated Δf away from each other are generated by the signal generators to excite the in-band IM3 at fC = 2f1 - f2. The PZT-only resonator exhibits the IIP3 value of +23.3 dBm at Δf = 100 kHz. By integrating PZT
116

Figure 6.9: Measured IIP3 of (a) a 90 x 20 μm2 PZT-only, and (b) a 190 x 40 μm2 PZT on 10 μm silicon resonator with 0 V DC bias in air at room temperature.
transduction with SCS, the nonlinear behavior of PZT can be strongly attenuated because the vibrating structure is dominated by silicon that has a superior acoustic linearity. This gives an improvement in IIP3 to a value of +35.3 dBm, as shown in Figure 6.9.
6.4.4 Hysteresis
The hysteresis of PZT causes undesirable resonance frequency shifts in the resonator. Figure 6.10 (a) shows the dynamically varying relative permittivity r of the PZT film caused by the influence of increasing and decreasing electric fields. This hysteresis effect is translated into a minor frequency shift, as shown in Figure 6.10 (b). This effect can be adjusted with the DC tuning.
6.5 High-overtone Width-extensional Mode Resonators
PZT transduced length-extensional mode resonators have been successfully demonstrated in the previous sections of this chapter. By varying the silicon thickness, tSi
117

Figure 6.10: (a) Measured hysteresis effect in the relative permittivity of a PZT thin film. (b) A PZT-on-silicon resonator shows imperceptible hysteresis, while a PZT-Only resonator shows a maximum of 0.17% center frequency (fC) shift.
118

(thereby the % mass of crystalline silicon in the resonator) and DC bias voltage we can define the desired Q and frequency tuning range of the resonators. However, various applications in wireless communication systems demand for higher frequency of operation. In order to reach fC above 100 MHz using length-extensional mode of vibration, the length of PZT-on-silicon resonator has to be scaled down to less than 40 μm. The length of PZT-only resonators has to be shrunk even more due to a lower acoustic velocity. Aggressive scaling in lateral dimensions of the resonator reduces the transduction area that leads into poor motional impedances.
In order to attain a high frequency of operation, alternative modes of vibrations will be explored. Thickness shear mode resonators in Chapter 2 have demonstrated a high resonance frequency and high Q. However, since the frequency of operation is mainly defined by the device thickness, they have a very limited frequency design space. Furthermore, the packaging process for these resonators is especially challenging. High-overtone square-extensional mode resonators presented in Chapter 3 were able to reach above 500 MHz frequency of operation. In Chapter 4 the design and packaging technology for a width-extensional mode (WEM) resonators were discussed. A high-overtone width-extensional mode of vibration can be excited to reach a high resonance frequency while acquiring a large transduction area. WEM resonators are excited by patterning IDT like electrodes on top of the resonators as shown in Figure 6.11 (a) and (b). By selectively patterning the interdigitated electrodes the higher-overtone of width extensional mode is excited as demonstrated in ANSYS modal analysis in Figure 6.11 (c).
6.6 Air-bridge Fabrication Process
The device fabrication is largely based on the fabrication sequence outlined in [109] with additional improvements in the process to eliminate the pad capacitances.
119

Figure 6.11: (a) Schematic of a PZT-only high-overtone width-extensional mode resonator. (b) Schematic of a PZT-on-silicon high-overtone width-extensional mode resonator. (c) ANSYS mode shape of a high-overtone width-extensional mode resonator.
120

Figure 6.12: Air-bridge process cross-section of PZT-only and PZT-on-silicon highovertone width-extensional mode resonators fabricated on the same wafer.
PZT is well known to have a large permittivity that can lead into large pad capacitances. Therefore, in this refined fabrication process, the air-bridge metal routings were implemented to carry electrical signals while avoiding large capacitances from the bond-pads. In addition, a novel fabrication technique was developed to fabricate the resonators with and without silicon layer using the same mask-set on the same wafer. A systematic study is essential to investigate the effect of silicon on quality factor (Q), resonant frequency (fC) and motional impedance (RX) of PZT transduced resonators at radio frequency. In this research effort, we fabricated PZT-only and PZT-on 3, 5 and 10 μm SCS high-overtone width-extensional mode resonators with identical lateral dimensions.
A thin elastic layer of SiO2 and a PZT actuator comprised of Ti/Pt/PZT/Pt were deposited on SOI wafers with 3 μm, 5 μm and 10 μm thick device layer and 250 nm of buried oxide. The input and output terminals of the resonators are lithographically defined by patterning the top Pt electrode on top of the PZT actuator. The current configuration of the resonator uses a common bottom Pt electrode underneath of the PZT for both the input and output ports. The process cross-section of released PZT-on-silicon and PZT-only resonators is shown in Figure 6.12. To ensure survival of the SCS component of the resonators, an organic
121

photo-definable layer was developed to provide protection of the resonator while allowing undercutting of the handle wafer silicon using a XeF2 etch. The PZT films were deposited using a chemical solution deposition method with a crystallization temperature of 700◦C to achieve full densification and high crystallinity. At the end of device fabrication, the PZT film already possesses some degree poling as a result of the plasma processing. In order to improve the degree of poling, the resonators were subjected to electric fields of 200 kV/cm for 10 minutes prior to testing. SEM images of released PZT-on-silicon and PZT-only filters are shown in Figure 6.13.
6.7 Measurement Results
The resonators were characterized in an RF probe station in a 2-port configuration using GSG probes. Parasitics up to the probe tips were first calibrated with SOLT measurements on a standard calibration substrate. All measurements were performed in air, at room temperature and pressure. The trade-offs in Q, fC and RX of resonators with different silicon thicknesses were recorded. Resonators with thicker silicon layer exhibit higher Q, higher fC and lower RX for frequency up to about 900 MHz as shown in Figure 6.14 (a). The loss-tangent of PZT starts to dominate the insertion loss and degrade the quality factor for frequency of operation above 1 GHz. The measured characteristics of the high-overtone width-extensional mode resonators with different silicon thicknesses are summarized in Table 6.5.
The measured resonance frequency of the resonators with different silicon thicknesses are in agreement with the theoretically analyzed and simulated data. Figure 6.14 (b) plotted the calculated, simulated and measured resonance frequency of PZT transduced high-overtone WEM resonators with different silicon thicknesses (tSi). By integrating PZT transduction with single-crystal silicon the figure of
122

Figure 6.13: SEM of the fabricated high-overtone width-extensional mode resonator. The zoom-in picture shows the air-bridge routing that isolates the resonator from the bonding-pads.
123

Figure 6.14: (a) Measured transmission response of PZT-only and PZT on 3 μm, 5 μm and 10 μm silicon resonators with the exact same lateral dimensions in air at room temperature and pressure. All measurements were performed using termination impedances (RL) of 50 Ω. (b) A plot of silicon thickness (tSi) vs the calculated, simulated and measured resonance frequency (fC).
merit, fC x Q is improved by one order of magnitude.
6.8 Conclusion
PZT transduced length-extensional mode resonators with and without silicon device layer have been theoretically modeled, designed, fabricated and characterized. By varying the silicon thickness (thereby the % mass of crystalline silicon in the resonator) and DC bias voltage we can define the desired Q and frequency tuning range of the resonators, and tradeoff between steep-walled narrow-bandwidth filters, low-Q wide-bandwidth filters, linearity and frequency agility. For the first time, electric field dependent properties of PZT are exploited to facilitate contour mode resonator design with a very large frequency tuning range.
The performances of PZT transduced high-overtone width-extensional mode resonators with various silicon thickness were systematically studied. A novel fabrication technique was developed to allow cancelation of large pad capacitances.
124

Table 6.5: The measured characteristics of high-overtone WEM resonators with different silicon thicknesses

tSi (μm)

0

3

5

10

Q

150 314

501

458

fC (MHz) 428

834

942 1, 018

RX (Ω) RL (Ω) fC x Q

390 296

435

700

50 50

50

50

6.4x1010 1.4x1011 4.71x1012 4.66x1011

The high-overtone excitation of the resonator is able to reach resonance frequency above 1 GHz. This technology will enable PZT transduced resonators and filters that covers up to low-band GSM frequencies.

125

CHAPTER 7 PZT TRANSDUCED MECHANICALLY-COUPLED
FREQUENCY-AGILE FILTERS
7.1 Introduction
The forthcoming software defined radios that have compact dimensions, miniscule weight, low power demands and robustness to process and temperature variations are greatly desirable. In addition to commercial applications, the U.S. military has been actively developing the Joint Tactical Radio System (JTRS) to work in harmony with existing military and civilian radios. This radio architecture demands the existence of high performance tunable filters and filter banks to discern signals with dynamic waveforms and bandwidths. A width-extensional mode (WEM) resonator discussed in Chapter 6 is an excellent constituent resonator to realize these filter-banks because it has a high quality factor (Q) and frequency of operation that can be defined lithographically. Furthermore, higher-overtone frequency response can be excited by selectively patterning the electrodes of the filter.
Dielectrically-transduced thickness shear mode filters with analog voltage tunable center frequency and bandwidth and digitally-tunable MEMS filter using mechanically-coupled resonator array have been demonstrated in Chapter 2 and 3. However, the barriers in frequency design space, bandwidths range and processing technology have motivated the investigations for a new transducer material that has a large electromechanical coupling coefficient and frequency tuning capability. PZT is an appealing transducer material because it has been previously shown to have up to 6% frequency tuning capabilities [102]. It also exhibits a large electromechanical coupling coefficient (kt2 = 35%) in thickness-extensional mode (TEM) [101]. The maximum % bandwidth (BW /fC) of the filter is determined
126

by the kt2 of the tranducer. The large kt2 of PZT facilitates a filter design with a large % bandwidth. In our previously reported research, we have fabricated and characterized PZT transduced contour-mode resonators that demonstrate 5.1% electric field dependent frequency tuning capability [109]. A bandpass filter with a small footprint, tunable bandwidth and center frequency agility can be realized by coupling PZT transduced contour-mode resonators mechanically.
An excellent stop-band rejection is a very desirable property in modern radio transceivers. A closely packed dense array of MEMS filters on the same chip introduces large feed-through capacitance between the drive and sense electrodes, leading to poor stop-band rejection of the filter. The fully-differential filter configuration cancels the feed-through capacitance and improves the stop-band floor of the filter [111].

7.2 PZT-only Mechanically-coupled Filters

7.2.1 Fully-differential High-overtone Width-extensional Fil-

ters

The resonant frequency of vibration for contour mode resonators and filters is defined by lithography. Therefore, contour-mode filters are preferred for realizing multi-band and multi-frequency filters on a single-chip [54]. The bulk-extensional mode resonance of a width-extensional mode resonator depends on W , with frequency of operation (fC) given by:

fC

=

n 2W

E ρ

(7.1)

where W is the width of the resonator, E and ρ are effective elastic modulus for 2 − D expansion and density of the resonator respectively, and n is the harmonic

127

Figure 7.1: (a) ANSYS modal analysis showing in-phase and out-of-phase mode of vibrations of a mechanically-coupled high-overtone width extensional filter. (b) SEM image of a PZT transduced high-overtone mechanically-coupled widthextensional filter with differential electrodes.

order. Higher frequency overtone modes of the width-extensional mode resonators

are selectively excited by patterning electrodes in differential interdigitated config-

uration on top of the resonator [111].

Mechanically-coupled devices demand smaller area since the coupling spring

is small. Furthermore, they do not require extra device area to implement a dif-

ferential configuration due to inherent mechanical inversion available through the

resonators [112]. To realize a two-pole mechanically-coupled filter, two resonators

are coupled using a suspension spring as shown in Figure 7.1. The length of the

coupling spring is designed to be a quarter acoustic-wavelength long to minimize

mass-loading of the resonators. The width of the coupling spring then defines the

stiffness of the coupling spring. The bandwidth (BW ) of such a mechanically-

coupled filter is given by:

BW = fC ks kij kr

(7.2)

where fC is the resonant frequency, ks and kr are the spring stiffness of the cou-

pling spring and resonator respectively and kij is the filter coefficient [27]. Figure 7.1(a) shows the in-phase and out-of-phase high-overtone modes of a width-

128

Figure 7.2: Testing configuration for a 2-pole mechanically-coupled high-overtone fully-differential filter.
extensional filter simulated in ANSYS. Device fabrication is the same as reported in reference [109]. The SEM image of a PZT transduced 2-pole fully-differential mechanically-coupled high-overtone width-extensional filter fabricated in this process is shown in Figure 7.1(b).
7.2.2 Measurement Results
Frequency Response
We characterized the 2-pole fully-differential mechanically-coupled filter using the measurement setup illustrated in Figure 7.2. The fully-differential configuration enables us to cancel feedthrough capacitances between drive and sense electrodes thereby improving the stop-band floor of the filter. The filter was characterized on a Cascade microwave probe station using GSGSG probes and a 2-port Agilent E8364B network analyzer. The DC bias is superimposed to the AC signal at both input and output ports using bias-Ts for all measurements. Figure 7.3 shows
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the differential filter response as the electric field tuning biases are applied to the electrodes. The wide frequency measurement was performed and all other harmonics modes of vibrations are strongly attenuated by at least 30 dB below the designed frequency of operation. The electric field not only improves the piezoelectric coupling coefficient (via poling of the ferroelectric domains), but also increases the Young’s modulus of the PZT film [109]. The increase in Young’s modulus of the PZT film, increases the effective acoustic velocity of the constituent resonators, thereby increasing the center frequency of the filter. The result is up to 3% increase in filter center frequency for a 32 V/μm applied electric field, the highest tuning range reported by any piezoelectrically transduced contour-mode filters to date. In addition, the applied electric field also increases the ratio of ks to kr, thereby providing up to 100% bandwidth tuning capability for a 32 V/μm applied electric field. The measured transmission response of a PZT transduced 2-pole high-overtone width extensional filter with electric field tuning of 8 to 32 V/μm in 8 V/μm increment step in air at room temperature are tabulated in Table 7.1. The center frequency and bandwidth tuning features demonstrated by this class of filter could eliminate the necessity of multiple-filter and switch networks in radio architecture [113].
Linearity
The immunity of the resonators to the third-order intermodulation distortion (IM3) was characterized by using a two-tones technique. Two interferer signals f1 and f2 separated Δf away from each other are generated by the signal generators to excite the in-band IM3 at fC = 2f1 - f2. Both interferer signals were excited in the bandpass region of the filter with Δf = 400 kHz. The filter demonstrated the third-order input intercept point (IIP3) of +21 dBm as shown in Figure 7.4.
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Figure 7.3: Measured transmission of a PZT transduced 2-pole high-overtone WEM filter with electric field tuning. Input and output terminals were terminated with 50 Ω termination impedances (RL) for all measurements.
Figure 7.4: Measured third-order input intercept point (Δf = 400 kHz) of the filter demonstrates IIP3 of +21 dBm.
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Table 7.1: The measured frequency response of a PZT transduced high-overtone WEM filter

Electric Field (V/μm)

8 16 24 32

IL (dB)

−22.4 −21.5 −21.3 −20.7

3dB BW (MHz)

3.03 3.9 5.5 6.3

fC (MHz)

259.1 260.5 262.3 264.2

Stop-band rejection (dB) 37.6 38.5 38.7 39.3

RL (Ω)

50 50 50 50

Hysteresis Effect
The hysteresis effect of PZT may cause the filter to experience undesirable center frequency shifts. The hysteresis effect was characterized on the filter by applying increasing and decreasing electric fields across the PZT thin film. A maximum frequency shift of 0.14% was recorded as shown in Figure 7.5.
Temperature Coefficient of Frequency (TCF)
All the measurement results demonstrated up to this point have shown the filter performances at room temperature and pressure. Several targeted applications of this filter, however, operate at environments with wide range of temperature fluctuations. Thus filters with high insensitivity to temperature variations are highly desirable. Temperature characterization was performed by placing the filter on the Cascade probe station with temperature control stage. Frequency responses were recorded while the device was cooled down to -20◦C and heated up to 100◦C. The filter with different DC bias voltages was characterized over the whole temperature range of operation and exhibits TCF between −22 to −25 ppm/◦C.

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Figure 7.5: Measured frequency shifts in PZT transduced high-overtone width extensional filter due hysteresis effect in PZT. A maximum frequency shift of 0.14% was recorded.
7.3 PZT-on-silicon Mechanically-coupled Filters
PZT-only mechanically-coupled filters with fully-differential electrodes configuration have been designed, fabricated and characterized in the previous section. The filter demonstrated a wide bandwidth, large frequency and bandwidth tuning range and excellent stop-band rejection. Narrow bandwidth tunable channel-select filters that exhibit smaller than 1 MHz nominal bandwidth have been presented in Chapter 2 and 3. The PZT-only mechanically-coupled filters have shown bandwidth coverage between 3 MHz to 6 MHz. A filter design that can give bandwidth coverage between 1 MHz to 3 MHz is highly desirable to enable the analog signal processor receiver architecture introduced in Chapter 1.
In order to overcome the low quality factor of PZT-only resonators, a novel fabrication technology has been developed and presented in Chapter 6 by integrating PZT transduction with single-crystal silicon. Since the mechanical energy in
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Figure 7.6: (a) Schematic of a mechanically-coupled PZT-on-silicon filter. (b) SEM image of a PZT-on-silicon high-overtone mechanically-coupled width-extensional filter with differential electrodes.
this class of resonators is retained in the single crystal silicon layer, the resonators have higher quality factors compared to PZT-only counterparts. By applying a DC bias across the PZT transducer, the transducer coupling coefficient and filter center frequency can be modestly tuned, enabling voltage-dependent dynamic voltage frequency tuning and trimming.
High-Q PZT-on-silicon high-overtone width-extensional-mode resonators can be mechanically-coupled to facilitate narrow-bandwidth filter design with a modest frequency tuning capability. The schematic of a mechanically-coupled PZT-onsilicon high-overtone width-extensional-mode filter is presented in Figure 7.6 (a).
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Integrating PZT transduction with silicon is also a potential solution to improve the filter linearity and reduce the hysteresis effect in filter response. PZT-onsilicon filters are fabricated using the same mask-set and on the same wafer as PZT-only filters according to the fabrication process outlined in Chapter 6. The fully-differential electrodes configuration is again implemented to cancel the feedthrough capacitance and improves the stop-band floor of the filter. The SEM image of the fabricated PZT-on-silicon mechanically-coupled fully-differential filter is shown in Figure 7.6 (b).
7.3.1 Measurement Results
Frequency Response
We characterized the 2-pole fully-differential mechanically-coupled PZT-on-silicon filter using the same measurement setup illustrated in Figure 7.2. The filter was characterized on a Cascade microwave probe station using GSGSG probes and a 2-port Agilent E8364B network analyzer. The DC bias is superimposed to the AC signal at both input and output ports using bias-Ts for all measurements. Figure 7.7 shows the differential filter response as the electric field tuning biases are applied to the electrodes. The wide frequency measurement was performed to make certain all other undesired harmonics modes of vibrations are significantly attenuated. The fully-differential configuration enables us to cancel feedthrough capacitances between drive and sense electrodes and demonstrated -62 dB stopband rejection floor.
The measured transmission response of a 2-pole PZT-on-silicon high-overtone width extensional filter with electric field tuning of 8 to 32 V/μm in 8 V/μm increment step in air at room temperature are tabulated in Table 7.2. The termination impedance (RL) of 50 Ω is used for all measurements. The filter demonstrated a
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Figure 7.7: Measured transmission of a PZT-on-silicon 2-pole high-overtone WEM filter with electric field tuning. Input and output terminals were terminated with 50 Ω termination impedances (RL) for all measurements.
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Table 7.2: The measured frequency response of a PZT-on-silicon high-overtone WEM filter

Electric Field (V/μm)

8 16 24 32

IL (dB)

−30.2 −28.4 −27.2 −26.7

3dB BW (MHz)

1.24 1.26 1.31 1.35

fC (MHz)

206.4 206.5 206.5 206.7

Stop-band rejection (dB) 29.8 31.6 32.8 33.3

RL (Ω)

50 50 50 50

narrower nominal filter bandwidth compared to PZT-only transduced filters. However, the 10 μm thick silicon layer that dominates the structure limits the frequency tuning capability of the filter. A 0.22% center frequency tuning was recorded due to a 32 V/μm applied electric field across the PZT thickness.
Linearity
The immunity of the resonators to the third-order intermodulation distortion (IM3) was characterized by using a two-tones technique. Two interferer signals f1 and f2 separated Δf away from each other are generated by the signal generators to excite the in-band IM3 at fC = 2f1 - f2. Both interferer signals were excited in the bandpass region of the filter with Δf = 400 kHz. By integrating PZT transduction with single-crystal silicon, the non-linear behavior of PZT can be suppressed because the vibrating structure is dominated by the thick silicon layer that has a superior acoustic linearity compared to PZT. The filter demonstrated the third-order input intercept point (IIP3) of +29 dBm as shown in Figure 7.8.

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Figure 7.8: Measured third-order input intercept point (Δf = 400 kHz) of the filter demonstrates IIP3 of +29 dBm. Hysteresis Effect Hysteresis of PZT can cause an undesirable resonance frequency shifts in the filter. By integrating PZT transduction with a 10 μm thick silicon layer, the frequency shifts due to hysteresis can be significantly minimized. The hysteresis effect in PZT-on-silicon is translated into very minor frequency shifts as shown in Figure 7.9.
Temperature Coefficient of Frequency (TCF) Temperature characterization was again performed by placing the filter on the Cascade probe station with temperature control stage. Frequency responses were recorded while the device was cooled down to -20◦C and heated up to 100◦C. The filter with different DC bias voltages was characterized over the whole temperature range of operation and exhibits TCF between −16 to −19 ppm/◦C. These values
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Figure 7.9: Measured frequency shifts in PZT-on-silicon high-overtone width extensional filter due hysteresis effect in PZT. An imperceptible frequency shift of 0.013% was recorded.
are comparable to AlN transduced resonators and filters and quartz crystals used in time-keeping applications for handsets [55].
7.4 Conclusion
The PZT transduced fully-differential mechanically-coupled filters have been designed, fabricated and characterized. The PZT-only filters have shown a large center frequency and bandwidth tuning range. These tuning features have never been demonstrated by any piezoelectrically transduced contour-mode filters reported to date. The fully-differential configuration eliminates the feedthrough capacitances between drive and sense electrodes, thereby improving the stop-band rejection floor of the transmission. The filter demonstrates excellent capability to overcome hysteresis effect by applying an electric field across the PZT transducer to adjust
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the center frequency. These features satisfy the filter specifications in JTRS to handle multiple waveforms, eliminate out-of-channel interferers, and substantially decrease the number of filters in next-generation radios.
PZT-on-silicon fully-differential mechanically-coupled filters have been designed, fabricated and characterized. The filters demonstrated a narrower nominal filter bandwidth compared to PZT-only filters. Integrating PZT transduction with silicon also improves the filter immunity to the third-order intermodulation distortion and hysteresis effect of PZT.
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CHAPTER 8 MONOLITHICALLY INTEGRATED PIEZO-MEMS SWITCHES
AND CONTOUR-MODE FILTERS
8.1 Introduction
RF MEMS has been a significant area of research for well over a decade due to the promise of improved performance and integration potential in commercial and military wireless communication and radar systems. RF MEMS switches have demonstrated superior performance in terms of insertion loss, isolation, power consumption, and linearity [114]. RF MEMS filter technologies can provide insertion loss, percent bandwidth, and rejection performance similar to off-chip crystal filters and surface acoustic wave (SAW) devices with the compact integration of multiple frequencies on the same chip [54,69,115]. The integration of these two technologies has long been a goal of researchers and will enable not only more compact and lower cost systems but previously unachievable signal processing functions [116].
A number of transduction approaches have been utilized for both MEMS switch and filter operation, including electrostatic, electromagnetic, electro-thermal, and piezoelectric. Piezoelectric and or ferroelectric transduction can provide superior electro-mechanical coupling and mechanical energy densities; metrics applicable to both switch and filter operation. Piezoelectric AIN is a popular filter material due to the high acoustic velocity, high mechanical quality factor, and the ease of post-CMOS integration [54]. AIN is generally the preferred material for direct piezoelectric effect transduction due to its favorable ratio of stress constant to dielectric constant.
Ferroelectric lead zirconate titanate (PZT) has an effective piezoelectric stress constant that is an order of magnitude larger than AIN and is generally the pre-
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ferred material for indirect piezoelectric effect transduction [117]. Thin films of ferroelectric PZT also permit tuning of the piezoelectric coefficients, some elastic constants, permittivity, and hence the electro-mechanical coupling factor of the material with a modest DC bias. Low-voltage (<10 V) ohmic contact series switches with high isolation and good insertion loss characteristics up through 65 GHz have been demonstrated with surface micro-machined PZT MEMS [107].
In Chapter 7, PZT-only and PZT-on-silicon contour-mode filters have been designed, fabricated and characterized. The integration of PZT thin films with high mechanical quality factor single crystal silicon features allows a tradeoff between steep-walled narrowbandwidth filters, low-Q wide-bandwidth filters, linearity and center frequency agility. Single pole dual throw (SP2T) PZT MEMS switches have also been previously demonstrated with better than 50 dB of isolation and less than 0.4 dB of insertion loss at 2 GHz [118]. These switches can be fabricated on the same wafer as PZT-only and PZT-on-silicon contour-mode filters presented in Chapter 7. The incorporation of these switches in the design facilitates the ability to cover all characteristics that have been demonstrated by both PZT-only and PZT-on-silicon contour-mode filters on a single chip. Unlike AIN, integration of high quality piezoelectric PZT films with CMOS remains a challenge for MEMS applications because of the high process temperatures. However, PZT thin films with high quality ferroelectric properties have been successfully integrated with CMOS for ferroelectric random access memory (FeRAM) [119].
Recently, Mahameed et al. successfully co-fabricated aluminum nitride (AIN) switches and resonators and reported cascaded S-parameter data illustrating how a switchable resonator should function [120]. In this Chapter, integration of a PZT RF MEMS single pole dual throw (SP2T) series switches with contour-mode mechanically coupled PZT-on-silicon high-Q filters and the first experimental demon-
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Figure 8.1: SEM image of an integrated single pole dual throw (SP2T) PZT-MEMS switch and two PZT transduced width-extensional contour-mode filters.
stration of monolithically integrated piezoelectric MEMS RF switches and filters will be presented.
8.2 Design of Integrated PZT transduced Switches and Fil-
ters
Using a single pole dual throw (SP2T) architecture similar to that reported previously [107], two normally-open, ohmic contact, series switches were used to select between two contour-mode mechanically coupled PZT-on-silicon high-Q filters as shown in Figure 8.1. As presented in Figure 8.1, a conductive pad and contacts are located on the dielectric structure mechanically coupling the two cantilevered PZT unimorph actuators. The switch resides in the gaps of the co-planar waveguide (CPW) transmission line. Unlike the cantilevered designs in [107,118], the RF gold air bridge contact structures above the switch contact pad were redesigned as clamped-clamped structures to mitigate deformation of these structures during and after fabrication. Two bias line air bridges located at the anchors of the actuators
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Figure 8.2: (a) SEM image of the air-bridge used for switch operation, and (b) reduced large pad capacitances in the filters.
electrically connect the top and bottom electrodes of the two actuators. To enable switch biasing with a single trace, the top electrode bias line air bridge anchors to one of the CPW ground planes and the bottom electrode bias line air bridge anchors to a single bias line. The typical switch actuator composite stress states, composition, and thicknesses are designed to provide static negative curvature in the switch to dictate the preferred initial contact gap. The application of voltage to the top and bottom electrodes provides d31 mode bending actuation to the switch and raises the contact pad into contact with the two clamped-clamped RF gold air bridges. These devices were designed with analytical models, ANSYS, ADS Momentum, and HFSS. The ohmic series switches and SP2T design are similar to the designs presented in [107, 118].
The filter designs in this work are based on the work presented in Chapter 7. The designs in this work feature significantly reduced parasitic shunt capacitances by reducing the top electrode contact area, not associated with the active transducer, through the use of air bridge structures available with the switch process steps as shown in Figure 8.2. The constituent resonators are fundamental width-extensional contour mode designs as shown in Figure 8.3 (a). Two of these
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Figure 8.3: (a) SEM image of the width-extensional contour-mode filter. (b) Anti-symmetric and symmetric ANSYS mode shapes of a fundamental widthextensional mode filter.
resonators are coupled via an acoustic quarter-wave coupling spring (not simulated) to create a two-pole mechanically coupled filter as shown in Figure 8.3 (b). The filters presented in this chapter were designed as 209 MHz and 313 MHz. The fundamental resonant frequency of the width extensional mode is given by Equation 7.1. To realize a two-pole mechanically-coupled filter, two resonators are coupled using a suspension spring as shown in Figure 8.3 (a). The length of the coupling spring is designed to be a quarter acoustic-wavelength long to minimize mass-loading of the resonators. The width of the coupling spring then defines the stiffness of the coupling spring. The bandwidth (BW ) of such a mechanicallycoupled filter is given by Equation 7.2.
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Relatively few modifications were required to integrate the two device types as most of the steps of the two individual processes were initially common. The substrate was chosen as SOI to accommodate the filters. The switch sacrificial layer features were altered to ensure proper release timing in the presence of the added passivation layer necessary to protect the device silicon features of the filter during the XeF2 release and the release sequence was reversed to accommodate the integration.
8.3 Fabrication Process
Device fabrication was done at the Specialty Electronic Materials and Sensors Cleanroom Facility, U.S. Army Research Laboratory, Adelphi, MD. The fabrication process for the monolithically integrated piezoelectric MEMS RF switches and filters utilized a silicon-on-insulator substrate with a 5 μm thick device layer with nominal resistivity of 30 Ω-cm. A 500 nm silicon dioxide thin-film was deposited by plasma-enhanced chemical vapor deposition (PECVD) and was followed by a sputtered Ti/Pt bottom electrode layer for the PZT deposition. The 518.5 nm PZT thin films were prepared via a chemical solution derived deposition process modified from that outline in [108]. After the final PZT anneal, a 105 nm platinum thin film was sputter-deposited directly onto the PZT surface at 300◦C.
The switch actuator and filter drive and sense electrode were patterned with the argon ion-milling of the top platinum layer and was followed by an additional ion-milling of the PZT and bottom electrode features. A wet-etch then opened up contact vias to the local bottom electrodes of the switches and filters. The switch structure was then further defined by patterning the silicon dioxide layer with a reactive ion etch to provide access to the silicon device layer for the eventual release etch. A titanium/gold bi-layer was then deposited with electron beam evaporation
146

and patterned via lift-off to define the CPW transmission line, contact structures for the switch, and anchor features required for gold air bridges. A lift-off process was then used to pattern the switch contact material. The filters were defined using a single photomask by an ion-milling of the PZT and bottom electrode, an RIE of the silicon dioxide layer, a DRIE of the device silicon layer, followed by an RIE of the buried oxide layer. A photo-resist sacrificial layer was then patterned and cured and was followed by the deposition and lift-off of 2 μm gold air-bridge features necessary for both the switches and filters. A thick photo-resist layer was then patterned to encase the silicon resonator features in resist and the buried oxide during release. The sidewalls of the switches and regions near the filters were not coated to permit a timed XeF2 etch of the silicon device layer directly beneath the switch and the silicon handle layer beneath the filter. The release process reversed the typical release sequence utilized in [117], with the XeF2 silicon etch preceding the oxygen plasma release of the gold air-bridge structures.
8.4 Measurement Results
8.4.1 Frequency Domain Measurement
All switch and filter measurements were completed with a network analyzer using a 50 Ω termination impedance (RL) in air at room temperature and pressure. Individual switches exhibited isolation better than -40 dB from DC through 500 MHz as shown in Figure 8.4 (a). Switch actuation was achieved with the application of 7 V resulting in an insertion loss (IL) less than -0.4 dB from DC to 500 MHz. Processing these devices on a relatively low-resistivity SOI wafer resulted in the insertion loss being higher than the individual switches processed on silicon substrates with a resistivity greater than 10 kΩ-cm in previously reported
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Figure 8.4: (a) S21 data at 0 V and 7 V for the PZT-MEMS switch co-fabricated with the PZT transduced width-extensional contour-mode filters. (b) S21 response of an integrated SP2T switch and filter with the switch in the Off-state (0 V), (c) S21 response for the left switch and filter with the switch On (7 V) and with 10 V VDC applied to the filter, and (d) S21 response for the right switch and filter.
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Figure 8.5: S21 response for a stand-alone PZT transduced contour-mode filter and an integrated PZT transduced switch + contour-mode filter with the DC bias at 10 V for both devices. The switch increases insertion loss (IL) by 0.4 dB.
research [117]. With both switches in the Off-state (i.e. 0 V applied), the output from both
the left or right filters exhibited a flat S21 response with a magnitude of -60 dB as shown in Figure 8.4 (b). This is somewhat surprising since a simple linear cascade of S-parameters of the switch and resonator should show the filter response shifted down by the individual switch isolation as in [107]. Although this curiosity is still under investigation, we believe it is most likely due to current shunting around the open switch effectively reducing its isolation. The exclusion of air bridges at the SP2T junctions is a likely source of this reduced isolation.
As each switch was actuated at 7 V, the associated filter response was detected
149

at the relevant output port for each filter as recorded in Figure 8.4 (c) and (d). For both filters, an improvement in the insertion loss was observed with the application of a DC voltage applied to the RF signal through the bias-Ts of the network analyzer. The impedance tuning agrees with the previous observation of Chandrahalim et al [109]. The filters exhibited out-of-band rejection of nearly -30 dB and a 50 Ω terminated IL of -17 dB and -24 dB (as measured from the minimum insertion loss) with the application of a 10 V DC bias as demonstrated in Figure 8.4 (c) and (d). Similar filter responses were observed in the integrated (add 0.4 dB insertion loss) as in the standalone filters fabricated on the same wafer. The similar performances between individual filters and filters integrated with SP2T switches as shown in Figure 8.5 suggest obtaining improved device performance is a matter of updating the filter design, which is currently in progress.
8.4.2 Time Domain Measurement
A series of time domain measurements were used to examine the switching and filter characteristics as a function of switch cycling. As shown in Figure 8.6, the output response from the integrated switch and filter is ringing up with each switching pulse. It is unclear whether this is due to ring up of the filter or is influenced by the electrical time constant due to the switch contact resistance. Similar to previous PZT switches, the switch cycle lifetime is expected to last in excess of tens of millions of switch cycles and improve with more suitable contact materials, switch optimization, and integrated packaging.
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Figure 8.6: Time domain measurements of the switch + filter highlighting the 7 V switching actuation pulses and the ring-up response of the filter with the switch in the On-state.
8.5 Conclusion
For the first time, piezoelectric MEMS RF switches and contour-mode filters have been monolithically integrated and demonstrated as a switchable filter array. Lead zirconate titanate (PZT) thin films were utilized to enable both low-voltage switch operation and filter tunability. By incorporating RF switches and contour-mode filters on the same chip, all the characteristics of PZT-only and PZT-on-silicon resonators and filters can be acquired and selectively excited. On-going research is focusing on improving the loss performance of the filters, suppressing spurious modes, addressing switch lifetime, and incorporating wafer-level packaging. The low-voltage switches and voltage tunable Piezo-MEMS filter array provides a dropin solution for frequency-agile channel selectivity.
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CHAPTER 9 FUTURE RESEARCH DIRECTIONS
Voltage tunable micromechanical resonators and filters have marvelous potential to reshape the contemporary wireless communication systems. The research efforts and results presented in this dissertation provide a foundation for future investigations and developments. However, additional refinements are essential to enhance the ultimate practicality of these devices.
9.1 Solid Dielectrically Transduced Devices
9.1.1 Transduction Efficiency
A vacuum-encapsulated, silicon nitride transduced resonators were successfully designed, fabricated and characterized in Chapter 4. The performance of the epitaxial-silicon packaging is also verified to sufficiently package VHF and UHF devices. Further research to investigate dielectric materials with higher dielectric constants (κ) to improve the transduction efficiency is necessary. Figure 9.1 predicted the values of motional resistance (RX ) versus DC bias voltage for different dielectric materials in the case of contour-mode disk resonators [121].
9.1.2 On-chip Fully-differential Configuration
In order to overcome the parasitic capacitances, the vacuum-encapsulated resonator presented in Chapter 4 was characterized using a pseudo-differential measurement technique as shown in Figure 9.2 (a). This measurement requires complex setup and extra off-chip wirings. Real wireless applications will require the inherent ability of the device to exhibit mechanical resonance at the desired res-
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Figure 9.1: Estimated values of motional resistance (RX) versus DC bias voltage for different dielectric materials.
onance frequency. The implementation of fully-differential devices on-chip will be greatly beneficial to reduce these parasitic capacitances. It also simplifies the characterization procedure enormously. Figure 9.2 (b) presents the design of the next generation on-chip fully-differential MEMS filter.
9.1.3 Long-term Stability
Open-loop measurement for long-term stability on a vacuum-encapsulated resonator has been performed by measuring the quality factor and resonance frequency of the resonator over four months period of time. The measured Q over time in Figure 9.3 (a) indicates that the quality factor of the resonator fluctuates between 8, 450 and 8, 650 during the measurement period. The resonance frequency of the resonator exhibits 1 MHz variation during the measurement period as shown in Figure 9.3 (b). The quality factor and frequency drifts could be due
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Figure 9.2: (a) Pseudo-differential measurement setup to characterize the vacuumencapsulated resonator. (b) On-chip fully-differential configuration to eliminate parasitic capacitances.
to the Network Analyzer, the probe-tips, RF cables etc. Further investigations are necessary to pinpoint the causes of these drifts. A closed-loop oscillator circuit can be designed to perform a proper study of phase noise and Allan deviation of the device.
9.1.4 Post-MEMS CMOS Integrated Systems
Traditionally RF MEMS devices are integrated with CMOS electronics using wirebonding technique as shown in Figure 9.4 (a) [122]. This kind of hybrid integration not only demands extra space but also introduces losses due to the wires. In Chapter 4 a successful packaging of MEMS resonators using CMOS compatible process has been demonstrated. The next step will be to develop a post-MEMS CMOS monolithically integrated system as shown in Figure 9.4 (b). The monolithically integrated system will provide low-loss interconnects between MEMS devices and CMOS integrated circuits. In addition, it facilitates devices with smaller size, lighter weight and cheaper cost.
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Figure 9.3: Open-loop long-term stability measurement of a silicon nitride transduced vacuum-encapsulated resonator. (a) Measured quality factor as a function of time, and (b) Measured frequency as a function of time.
Figure 9.4: (a) Hybrid-integration of a super-regenerative CMOS-MEMS transceiver. (b) Post-MEMS CMOS monolithically integrated system.
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9.2 Liquid Dielectrically Transduced Devices
Aqueous transduction is an excellent alternative to solid-dielectric transduction due to the high permittivity and low acoustic velocity of water. However, the operating frequency is limited up to 2 GHz as water has a significant loss tangent above that frequency [96]. Aqueous transduction also facilitates a large frequency tuning capability. The 3% limit of electrostatic tuning capability was mainly due to electrolysis of water and bubble formation, which suggests that using an alternate low loss-tangent liquid such as dielectric oil [99] will enable high resonant frequency operation and wide tuning range. In addition to RF applications, aqueous transduction can be used for thermal cooling and isolation, single-molecule mass detection in liquid media and frequency-domain dielectric spectroscopy.
Integration of contour-mode MEMS resonators and filters with micro-fluidic devices allows incorporation of fluid dielectric materials in the transducer gaps in a more controllable manner. Electrowetting method has been successfully demonstrated to create, transport, cut, and merge liquid droplets as shown in Figure 9.5 (a) [123]. Several research groups have been able to drive the motion of liquids on a flat solid surface using light as demonstrated in Figure 9.5 (b) [124]. The microheaters as shown in Figure 9.5 (c) have the capability to actuate liquid in a very controllable manner [125]. More recently, micro-structured surface ratchets have been fabricated to enhance the liquid droplet transport as presented in Figure 9.5 (d) [126]. These micro-fluidic devices and techniques to control liquids can be integrated with contour-mode MEMS resonators and filters to provide a more precise way to flow liquid dielectric materials into the transducer gaps.
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Figure 9.5: (a) Four fundamental fluidic operations considered essential to build digital microfluidic circuits, which can be used for lab-on-a-chip or micro total analysis system all by electrowetting. (b) Lateral photographs of light-driven motion of an olive oil droplet. (c) Top-view of a liquid droplet moving along a liquophilic microstripe. The array of Ti-resistors (shown in light gray) beneath the liquophilic stripes locally heat the droplet thereby modifying the surface tension and propelling the liquid toward the colder regions of the device surface. The dark gray stripes represent the leads and contacts (Au) for the heating resistors. (d) Time shots of droplets moving on ratchet-tracks.
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Figure 9.6: (a) ANSYS modal analysis of a high-overtone thickness-mode resonator. (b) Measured frequency response of a 50 Ω terminated PZT transduced high-overtone thickness-mode resonator in air at room temperature and pressure.
9.3 PZT Transduced Devices
9.3.1 High-Q SHF PZT Transduced Resonators
Using the latest deposited PZT film with a specifically engineered orientation we have been able to characterize the resonance of a high-overtone thickness-mode PZT-on-silicon resonator at 1.8 GHz. ANSYS mode shape and the measured frequency response of the resonator is presented in Figure 9.6. We can immediately see applications such as TV broadcast, amateur radio, mobile telephones, cordless telephones and wireless networking at this frequency range. The loss-tangent of PZT starts to dominate the loss at frequency above 2 GHz. A bulk-mode PZT transduced resonator with a particular texture design has been demonstrated at above 4 GHz resonance frequency [127]. However, the resonator exhibited Q of less than 200. Integration of textured PZT transduction with single-crystal silicon may be a potential solution to improve quality factor for super-high frequency operation.
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Figure 9.7: Applications within the radio frequency spectrum.
9.3.2 Monolithically-integrated PZT Based Microsystems
PZT transduction can cover a very wide range frequency of applications as shown in Figure 9.7. With our latest measured result PZT transduced resonators and filters can be used for numerous wireless applications at UHF band. We are hopeful that the high-Q textured PZT-on-silicon will be able to operate at SHF.
Our current fabrication technology has enabled us to monolithically integrate PZT transduced switches, resonators, filters, sensors and actuators on the same substrate. We can be optimistic to realize a PZT based 1 mm3 integrated microsystem that covers multi-function applications that operate from ultra-low frequency up to super-high frequency in the near future.
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APPENDIX A FABRICATION PROCESS OF THICKNESS SHEAR RESONATORS
AND FILTERS
------------------------------------------------------------------1. Start with 3 micron thick device layer heavily-doped SOI wafers n-type/Sb, <1 0 0> Resistivity: 0.01-0.02 Ohm-cm Run a standard MOS clean ------------------------------------------------------------------2. Deposit of 30 nm hafnia thin-film on the wafer by atomic layer deposition ------------------------------------------------------------------3. Dehydrate the wafer on the hot-plate at 115 degree Celsius for 2 minutes ------------------------------------------------------------------4. Spin SPR220-3 photoresist on the wafer at 3,000 rpm for 30 seconds to get a 3 micron thick photoresist mask ------------------------------------------------------------------5. Soft-bake the wafer on the hot-plate at 130 degree Celsius for 3 minutes ------------------------------------------------------------------6. Exposure of the alignment-mark mask (Mask 1) using GCA200 Auto Stepper for 0.6 seconds ------------------------------------------------------------------7. Post-exposure bake the wafer on the hot-plate at 130 degree Celsius for 3 minutes
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------------------------------------------------------------------8. Manually develop the mask using MIF300 developer for 2.5 minutes ------------------------------------------------------------------9. Bake the wafer inside convection oven at 90 degree Celsius for 2 hours ------------------------------------------------------------------10. Etch the wafer using Oxford 80 RIE etcher for 10 minutes to pattern the alignment mark on the dielectric layer Use standard CHF3/O2 oxide etch recipe ------------------------------------------------------------------11. Continue etching the wafer using Oxford 100 RIE etcher for 11 minutes to pattern the 1 micron thick alignment mark on the silicon device layer Use standard CF4 silicon etch recipe ------------------------------------------------------------------12. Run oxygen plasma recipe in Oxford 80 for 15 minutes to remove the photoresist on the wafer ------------------------------------------------------------------13. Dehydrate the wafer on the hot-plate at 115 degree Celsius for 2 minutes ------------------------------------------------------------------14. Spin S1813 photoresist on the wafer at 4,000 rpm for 30 seconds to get a 1.3 micron thick photoresist mask ------------------------------------------------------------------15. Soft-bake the wafer on the hot-plate at 115 degree Celsius
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for 2 minutes ------------------------------------------------------------------16. Exposure of the dielectric layer mask (Mask 2) using GCA200 Auto Stepper for 0.35 seconds ------------------------------------------------------------------17. Develop the mask using Hamatech automatic developer Use MIF300, spin at 2,500 rpm for 90 seconds ------------------------------------------------------------------18. Hard-bake the wafer on the hot plate at 115 degree Celsius for 2 minutes ------------------------------------------------------------------19. Etch the wafer using Oxford 80 RIE etcher for 10 minutes to pattern the dielectric layer Use standard CHF3/O2 oxide etch recipe ------------------------------------------------------------------20. Run oxygen plasma recipe in Oxford 80 for 15 minutes to remove the photoresist on the wafer ------------------------------------------------------------------21. Run a standard MOS clean process ------------------------------------------------------------------22. LPCVD of 50 nm n+ polysilicon layer at 620 degree Celsius for 20 minutes ------------------------------------------------------------------23. Deposit 38 nm undoped oxide mask to pattern polysilicon layer using GSI PECVD machine Use standard undoped oxide recipe for 10 seconds
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------------------------------------------------------------------24. Dehydrate the wafer on the hot-plate at 115 degree Celsius for 2 minutes ------------------------------------------------------------------25. Spin S1813 photoresist on the wafer at 4,000 rpm for 30 seconds to get a 1.3 micron thick photoresist mask ------------------------------------------------------------------26. Soft-bake the wafer on the hot-plate at 115 degree Celsius for 2 minutes ------------------------------------------------------------------27. Exposure of the polysilicon mask (Mask 3) using GCA200 Auto Stepper for 0.35 seconds ------------------------------------------------------------------28. Develop the mask using Hamatech automatic developer Use MIF300, spin at 2,500 rpm for 90 seconds ------------------------------------------------------------------29. Hard-bake the wafer on the hot plate at 115 degree Celsius for 2 minutes ------------------------------------------------------------------30. Use Oxford 80 RIE etcher to pattern the Oxide mask layer Use standard CHF3/O2 oxide etch recipe ------------------------------------------------------------------31. Run oxygen plasma recipe in Oxford 80 for 15 minutes to remove the photoresist on the wafer ------------------------------------------------------------------32. Etch the wafer using Plasma Thermal 770 etcher
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for 50 seconds to pattern the polysilicon layer Use the standard Chlorine gas etch recipe ------------------------------------------------------------------33. Dip the wafer in BOE (Buffered Oxide Etchant) 30:1 for 1 minute to remove the oxide hard-mask ------------------------------------------------------------------34. Spin SPR220-7 photoresist on the wafer at 3,000 rpm for 30 seconds to get a 7 micron thick photoresist mask ------------------------------------------------------------------35. Soft-bake the wafer on the hot-plate at 130 degree Celsius for 3 minutes ------------------------------------------------------------------36. Exposure of the silicon mask (Mask 4) using GCA200 Auto Stepper for 0.57 seconds ------------------------------------------------------------------37. Manually develop the mask using MIF300 developer for 3.5 minutes ------------------------------------------------------------------38. Bake the wafer inside convection oven at 90 degree Celsius for 2 hours ------------------------------------------------------------------39. Etch the wafer using Oxford 80 RIE etcher for 10 minutes to pattern the dielectric layer Use standard CHF3/O2 oxide etch recipe ------------------------------------------------------------------40. Continue etching the wafer using Unaxis 770 DRIE etcher
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for 10 cycles to pattern the the silicon device layer ------------------------------------------------------------------41. Use Branson Barrel asher for 40 minutes to remove the photoresist from the wafer ------------------------------------------------------------------42. Dice the wafer using KS7000 dicing saw ------------------------------------------------------------------43. Release the structures in 49% Hydrofluoric acid for 57 seconds ------------------------------------------------------------------44. Run a standard critical point dry process -------------------------------------------------------------------
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APPENDIX B CALIBRATION AND DE-EMBEDDING TECHNIQUES The resonators and filters are characterized in a Cascade RF probe station in a 2-port configuration using high-performance RF coaxial wires, GSG probes and bias-Ts. In order to characterize the 4-pole filters, additional in-phase and out-of-phase power-splitters are necessary. Parasitics up to the probe tips are first cancelled with Short-Open-Load-Thru (SOLT) RF measurements on a standard calibration substrate. De-embedding is then performed with Cascade WinCal software, using Short-Open-Thru (SOT) structures fabricated on-chip, but separate from the resonators [81]. All RF components such as bias-Ts and power-splitters are included in the de-embedding procedure. This de-embedding allows for the cancellation of the large pad capacitance and sheet resistance without canceling out any parasitics inherent to the resonators and filters, including the suspension beam routing and intrinsic capacitance between the transduction electrodes and the device body. Figure B.1 illustrates the SOT de-embedding procedure that is performed prior to every device characterization for all applied DC bias. The OP EN structure cancels parasitic capacitances in parallel to device under test (DUT). The SHORT structure removes parasitic elements in series to DUT. Finally, the T HRU structure is used to eliminate sheet resistances associated with bond pads of the device.
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Figure B.1: SOT de-embedding (a) schematic (b) equivalent circuit to cancel pad capacitance and sheet resistance without canceling out any parasitic elements inherent to the resonators and filters.
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