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Propagation Characteristics of Coplanar Waveguides at Subterahertz Frequencies

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Propagation Characteristics of Coplanar Waveguides at Subterahertz Frequencies Propagation Characteristics of Coplanar Waveguides at Subterahertz Frequencies by Jingjing Zhang Submitted in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy Supervised by Professor Thomas Y. Hsiang Department of Electrical and Computer Engineering The College School of Engineering and Applied Sciences University of Rochester Rochester, New York 2007 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. UMI Number: 3279168 INFORMATION TO USERS The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleed-through, substandard margins, and improper alignment can adversely affect reproduction. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion. ® UMI UMI Microform 3279168 Copyright 2007 by ProQuest Information and Learning Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. ProQuest Information and Learning Company 300 North Zeeb Road P.O. Box 1346 Ann Arbor, Ml 48106-1346 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. To Bo and Cathy Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Curriculum Vitae Bom in Hebei, China in 1973, the author attended the Beijing Institute o f Technology from 1991 to 1995 and graduated with a Bachelor o f Science degree. She came to the University o f Rochester in the Fall o f 2000 and began graduate studies in Electrical Engineering, acting as a teaching assistant in 2000 and 2001. She received a Frank Horton Fellowship from 2001 to 2006. Under the direction of Professor Thomas Y. Hsiang, she pursued her research in propagation characteristics of coplanar waveguides at subterahertz frequencies, receiving a Master of Science degree from the University of Rochester in 2002. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. iv Acknowledgments I would like to thank my thesis advisor, Professor Thomas Y. Hsiang, for his guidance and support throughout my study and research at the University of Rochester. I have greatly profited from his technical sharpness, intellectual creativity, and many writing lessons. I wish to express my thanks to Dr. William R. Donaldson for his invaluable suggestions and publication support, Professor Marc J. Feldman for his illuminating comments and advice on my research topic, and Professor Hui Wu for kindly allowing me to access his computing resources. I am grateful to Dr. Ross A. Speciale for his mentoring on my research and life in general. I also offer thanks to Dr. Xuemei Zheng, Dr. Jianliang Li, and Yunliang Zhu for countless helpful discussions. I thank the Laboratory o f Laser Energetics for awarding me a Frank Horton Fellowship. I dedicate this dissertation to my parents, my husband, my daughter, and my sister. Their support and encouragement are always my source o f power. I particularly thank my husband for his endless patience and constructive suggestions on my research and my daughter for her love. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. V Abstract In this thesis research, I have developed and used numerical techniques to study and model the propagation characteristics of coplanar waveguides (CPWs) over a broad frequency range, from about 10 GHz to nearly 1 THz. This research is important as CPWs gain broader applications in integrated circuits (ICs), both as interconnects and as passive circuit-elements. My research is also timely because experimentally measured waveguide properties have become available in recent years that allow comparison with theoretical studies. Two types of CPWs were investigated. The first type uses wide ground lines (WG) and closely approximates an ideal waveguide, which contains semi-infinite substrate thickness and ground-plane widths and has been analytically studied using conformal mapping. These WG CPWs are thus important as a testing venue where our numerically modeled waveguide characteristics are compared with both experiments and closed-form analysis. The second type o f CPWs uses narrow ground lines (NG) and is the practical choice in IC applications that have severe “real estate limitation,” i.e. where minimal chip area can be assigned to passive circuit components such as interconnects. These waveguides have, until this work, only been qualitatively studied. In this thesis, their properties will be thoroughly investigated and modeled. In one particular group o f waveguides, made on a GaAs substrate, my work is Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. vi compared with experiments for both the WG and NG waveguides. The close comparison lends strong support to the validity of my approach. The modeling is then extended to the practically important waveguides made on a silicon substrate. I will detail how parameters such as waveguide ground-plane widths and lateral line dimensions change the high-frequency characteristics and how they can be designed to improve circuit performance. Finally, some directions for future studies are discussed. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Table of Contents Curriculum V itae .........................................................................................................................iii Acknowledgments........................................................................................................................iv Abstract........................................................................................................................................... v Table of Contents ........................................................................................................................vii List of Tables ................................................................................................................................ix List of Figures................................................................................................................................x Glossary of Symbols .................................................................................................................. xv 1 Introduction ....................................................................................................................... 1 References...............................................................................................................................4 2 Coplanar Waveguide Theory ........................................................................................7 2.1 Introduction ....................................................................................................................7 2.2 Quasi-static Analysis .................................................................................................. 9 2.3 High-frequency Propagation ................................................................................... 13 2.4 Distributed Circuit Analysis................................................................................... 16 2.5 Dispersion ....................................................................................................................18 2.6 Attenuation .................................................................................................................. 20 References.............................................................................................................................26 3 Ultrafast Optoelectronic Characterization .............................................................. 30 3.1 The Electro-optic Sampling System .....................................................................30 3.2 Fabrication and Measurement .................................................................................32 3.3 T ime-domain Analysis ............................................................................................. 35 3.4 Frequency-domain Analysis ...................................................................................38 References.............................................................................................................................40 4 Full-Wave Analysis ......................................................................................................42 4.1 Galerkin’s Method in the Spectral Domain ........................................................ 42 4.2 Software Simulations ................................................................................................44 4.3 Microwave Network Analysis ............................................................................... 50 References.............................................................................................................................55 5 Propagation Characteristics ........................................................................................58 5.1 Attenuation .................................................................................................................. 59 5.1.1 The Effects of Ground-plane Width .............................................................59
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