Micromachined Circuits and Devices: Microwave to Sub-millimeter Applications (Lecture Notes in Electrical Engineering, 859) 9811694427, 9789811694424

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Lecture Notes in Electrical Engineering 859

Shiban Kishen Koul Sukomal Dey

Micromachined Circuits and Devices Microwave to Sub-millimeter Applications

Lecture Notes in Electrical Engineering Volume 859

Series Editors Leopoldo Angrisani, Department of Electrical and Information Technologies Engineering, University of Napoli Federico II, Naples, Italy Marco Arteaga, Departament de Control y Robótica, Universidad Nacional Autónoma de México, Coyoacán, Mexico Bijaya Ketan Panigrahi, Electrical Engineering, Indian Institute of Technology Delhi, New Delhi, Delhi, India Samarjit Chakraborty, Fakultät für Elektrotechnik und Informationstechnik, TU München, Munich, Germany Jiming Chen, Zhejiang University, Hangzhou, Zhejiang, China Shanben Chen, Materials Science and Engineering, Shanghai Jiao Tong University, Shanghai, China Tan Kay Chen, Department of Electrical and Computer Engineering, National University of Singapore, Singapore, Singapore Rüdiger Dillmann, Humanoids and Intelligent Systems Laboratory, Karlsruhe Institute for Technology, Karlsruhe, Germany Haibin Duan, Beijing University of Aeronautics and Astronautics, Beijing, China Gianluigi Ferrari, Università di Parma, Parma, Italy Manuel Ferre, Centre for Automation and Robotics CAR (UPM-CSIC), Universidad Politécnica de Madrid, Madrid, Spain Sandra Hirche, Department of Electrical Engineering and Information Science, Technische Universität München, Munich, Germany Faryar Jabbari, Department of Mechanical and Aerospace Engineering, University of California, Irvine, CA, USA Limin Jia, State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing, China Janusz Kacprzyk, Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland Alaa Khamis, German University in Egypt El Tagamoa El Khames, New Cairo City, Egypt Torsten Kroeger, Stanford University, Stanford, CA, USA Yong Li, Hunan University, Changsha, Hunan, China Qilian Liang, Department of Electrical Engineering, University of Texas at Arlington, Arlington, TX, USA Ferran Martín, Departament d’Enginyeria Electrònica, Universitat Autònoma de Barcelona, Bellaterra, Barcelona, Spain Tan Cher Ming, College of Engineering, Nanyang Technological University, Singapore, Singapore Wolfgang Minker, Institute of Information Technology, University of Ulm, Ulm, Germany Pradeep Misra, Department of Electrical Engineering, Wright State University, Dayton, OH, USA Sebastian Möller, Quality and Usability Laboratory, TU Berlin, Berlin, Germany Subhas Mukhopadhyay, School of Engineering & Advanced Technology, Massey University, Palmerston North, Manawatu-Wanganui, New Zealand Cun-Zheng Ning, Electrical Engineering, Arizona State University, Tempe, AZ, USA Toyoaki Nishida, Graduate School of Informatics, Kyoto University, Kyoto, Japan Federica Pascucci, Dipartimento di Ingegneria, Università degli Studi “Roma Tre”, Rome, Italy Yong Qin, State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing, China Gan Woon Seng, School of Electrical & Electronic Engineering, Nanyang Technological University, Singapore, Singapore Joachim Speidel, Institute of Telecommunications, Universität Stuttgart, Stuttgart, Germany Germano Veiga, Campus da FEUP, INESC Porto, Porto, Portugal Haitao Wu, Academy of Opto-electronics, Chinese Academy of Sciences, Beijing, China Walter Zamboni, DIEM - Università degli studi di Salerno, Fisciano, Salerno, Italy Junjie James Zhang, Charlotte, NC, USA

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Shiban Kishen Koul · Sukomal Dey

Micromachined Circuits and Devices Microwave to Sub-millimeter Applications

Shiban Kishen Koul Centre for Applied Research in Electronics Indian Institute of Technology Delhi East Delhi, India

Sukomal Dey Electrical Engineering Department Indian Institute of Technology Palakkad Palakkad, India

ISSN 1876-1100 ISSN 1876-1119 (electronic) Lecture Notes in Electrical Engineering ISBN 978-981-16-9442-4 ISBN 978-981-16-9443-1 (eBook) https://doi.org/10.1007/978-981-16-9443-1 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore

We would like to dedicate our efforts to our wonderful families who inspired and supported us through everything and to our students and colleagues for their support received during the preparation of this manuscript. We would also like to thank Astra Microwave Product Limited, Hyderabad, for helping us to perform some experiments under the leadership of Late Mr. V. S. R. Kirty.

Preface

Micromachining technology has been exhibiting in the last 25–30 years a paramount potential with respect to the manufacturing and fabrication of passive components for radio frequency (RF) applications, such as variable capacitors (varactors), inductors, switches, phase shifters, filters, antennas, and so on, commonly referred to as RF MEMS. The motivation for the fabrication of high frequency circuits using micromachining technology is due to high levels of functionality with low power consumption, precise dimensions and electrically activated moving parts. The most relevant advantages of passive components in MEMS technology compared to their standard counterparts (e.g., in semiconductor technologies or based on discrete components) reside in their high-performance and low fabrication cost, as well as in the possibility of integrating RF micromachined devices to yield circuits and functional blocks entirely based on such a technology. For example, varactors and inductors in MEMS technology present good linearity and large tuning ranges. One of the significant and successful exploitations of RF micromachining technology is in the manufacturing of reconfigurable functional blocks for RF circuits and telecommunication platforms. The smartphone market segment started to generate a factual need for highly reconfigurable and high-performance RF passive networks, and this increased the momentum of RF micromachining technology that was expected to take place more than one decade ago. On a broader landscape, the Internet of Things (IoT) and even the wider paradigm of the Internet of Everything (IoE) seem to be potential fields of exploitation for high-performance and highly reconfigurable passive components using RF micromachining technology. Over the past few years, micromachined-based on-chip resonators have shown significant potential for sensing and high frequency signal processing applications. This is due to their excellent features like small size, large frequency-quality factor product, low power consumption, low-cost batch fabrication, and integrability with CMOS IC technology. Radio frequency communication circuits like reference oscillators, filters, and mixers based on such MEMS resonators can be utilized for meeting the increasing count of RF components likely to be demanded by the next-generation multi-band/multi-mode wireless devices. Micromachined resonators can provide a feasible alternative to the present-day well-established quartz crystal technology vii

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that is riddled with major drawbacks like relatively large size, high cost, and low compatibility with IC chips. The book is divided into 11 Chapters covering wide varieties of RF micromachined devices starting from 1 GHz to 0.1 THz frequency range. The Chap. 1 serving as an introduction to radio frequency micro-electro-mechanical systems where an overview of different micromachined passive and active circuits are given followed by applications in modern transceiver architectures. Chapter 2 starts with the discussion on different micromachined passive circuits. The main emphasises is given on the understanding of micromachined Conductor Backed Coplanar Waveguide (CBCPW) lines with its discontinuities. Other different types of micromachined passive components are also discussed in this Chapter that includes varactor, inductor, power divider, and couplers. Chapter 3 discusses design, development, and complete characterization of micromachined single-pole-single-throw switches. The motivation is to observe the switch functionalities in-terms of mechanical behaviour, electrical behaviour, transient analysis, linearity, power handling, temperature behaviour, and S-parameters. Chapter 4 discusses design and implementation of different micromachined single-pole-multi-throw switching networks with respect to vertical and horizontal actuation movements. It includes single-pole-double-throw to single-polefourteen-throw configurations. Chapter 5 presents design and implementation of micromachined resonator and resonator-based circuits. Different types of micromachined resonance modes are discussed in this Chapter followed by discussion on three different transduction mechanisms. Finally, applications of micromachined resonator are presented for timing and oscillator circuits. Chapter 6 reports theory, design, and analysis of different types of micromachined phase shifters at microwave frequencies. It includes narrowband, wideband, and reconfigurable micromachined phase shifters. Chapter 7 describes two compact, high power, and reliable tunable bandpass filter for millimetre wave RF front end for 5G and radar applications at 28 GHz and 24 GHz, respectively. A comprehensive design guideline of tunable micromachined bandpass filters is given in this Chapter with special attention to bandwidth and center frequency reconfigurations. Chapter 8 discuses reliability analysis of RF micromachined devices with emphasis on multiport switching networks, 4 to 5-bit digital phase shifters and tunable filters. Chapter 9 presents different types of micromachined antennas at mmWave frequencies. Detail design guidelines are given on antenna designs at 60 GHz and 77 GHz. In addition, a comprehensive design analysis is given in this Chapter on one specific type of active antenna. Chapter 10 describes design and development of metamaterial inspired micromachined switches at submillimetre wave frequency. Design guidelines outlined here including design layout and Casimir repulsive force inspired resistive contact and capacitive micromachined switches. Finally, Chapter 11 describes future scope of RF micromachining in the design and development of different types of metamaterial-based frequency selective surfaces, absorbers, and other 3D-micromachined devices at THz regime. Delhi, India Palakkad, India

Shiban Kishen Koul Sukomal Dey

Contents

1

2

Introduction to Radio Frequency Micro Electromechanical Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Overview of Micromachined Radio Frequency Components . . . . 1.2 Micromachined Passive Circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.1 Transmission Line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.2 Varactor and Inductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.3 Switches and Other Passive Circuits . . . . . . . . . . . . . . . . . 1.2.4 Resonators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Fabrication of RF Micromachined Devices on Different Technology Platforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4 Applications of RF Micromachined Devices and Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5 Book Organisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Micromachined Microwave Passive Circuits . . . . . . . . . . . . . . . . . . . . . 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Micromachined Conductor Backed Coplanar Waveguide (CBCPW) Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1 Studies on Basic Micromachined Transmission Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.2 Design Data on Discontinuities in Membrane Microstrip . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.3 Design Data on Discontinuities in Membrane Coplanar Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.4 Tee-Junction Discontinuity . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Micromachined Varactors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1 Modelling and Design Optimization . . . . . . . . . . . . . . . . . 2.3.2 Quality Factor Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1 1 2 2 4 5 8 10 11 13 15 19 19 20 22 27 32 38 41 43 45

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2.3.3

Electro-Mechanical Modelling of the Varactor with Parametric Optimization . . . . . . . . . . . . . . . . . . . . . . . 2.3.4 Testing and Characterization of the Micromachined Varactor . . . . . . . . . . . . . . . . . . . . . 2.4 Micromachined Inductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5 Micromachined RF Power Divider and Coupler . . . . . . . . . . . . . . . 2.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

48 57 60 65 65

3

Micromachined Single-Pole-Single Throw Switches . . . . . . . . . . . . . . . 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Ohmic Contact Micromachined Switch . . . . . . . . . . . . . . . . . . . . . . 3.2.1 Switch Profile Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.2 Mechanical Resonance Frequency . . . . . . . . . . . . . . . . . . . 3.2.3 Electrical Responses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.4 Switching and Release Time Responses . . . . . . . . . . . . . . 3.2.5 Radio Frequency Performance . . . . . . . . . . . . . . . . . . . . . . 3.2.6 Temperature Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.7 Radio Frequency Power Handling Performance . . . . . . . 3.2.8 Intermodulation Distortion . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

69 69 70 71 73 74 77 80 83 84 89 92 92

4

Micromachined Single-Pole-Multi-throw Switching Networks . . . . . 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Vertical Actuation of Micromachined Switching Networks . . . . . 4.2.1 Single-Pole-Three-Throw (SP3T) Switch Design and Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.2 Single-Pole-Six-Throw (SP6T) Switch Design and Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.3 Single-Pole-Seven-Throw (SP7T) Switch Design and Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.4 Single-Pole-Eight-Throw (SP8T) Switch Design and Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.5 Single-Pole-Ten-Throw (SP10T) Switch Design and Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.6 Single-Pole-Eleven-Throw (SP11T) Switch Design and Measurements . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.7 Single-Pole-Twelve-Throw (SP12T) Switch Design and Measurements . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.8 Single-Pole-Fourteen-Throw (SP14T) Switch Design and Measurements . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.9 Design Guidelines of the MEMS SPMT Switches . . . . . 4.2.10 IIP3 Measurements of the Micromachined SPMT Switches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

95 95 96

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Contents

Design, Analysis and Measurements of Single-Pole-Sixteen-Throw Switch . . . . . . . . . . . . . . . . . . . . . . . 4.3.1 SP16T Switch Design and Analysis . . . . . . . . . . . . . . . . . 4.3.2 Measurements of the SP16T Switches . . . . . . . . . . . . . . . 4.4 Lateral Actuation of Switching Networks . . . . . . . . . . . . . . . . . . . . 4.4.1 Design and Measurements of Single Lateral MEMS Switch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.2 Design and Measurements of Different SPMT Lateral MEMS Switches . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5 Phase-Change Materials (PCMs) Based Micromachined RF Switches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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108 108 110 113 114 116 120 120 121

5

Micromachined Resonators and Circuits . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Basic Resonator Model and Properties . . . . . . . . . . . . . . . . . . . . . . . 5.3 Electromechanical Properties of MEMS Resonators . . . . . . . . . . . 5.4 Circuit Model Representation of MEMS Resonators . . . . . . . . . . . 5.4.1 Flexural Modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4.2 Bulk Modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4.3 Shear Modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4.4 Torsional Modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4.5 Coupled Resonators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5 Transduction Mechanism of Resonators . . . . . . . . . . . . . . . . . . . . . 5.5.1 Capacitive Transduction Mechanism . . . . . . . . . . . . . . . . . 5.5.2 Piezoelectric Transduction Mechanism . . . . . . . . . . . . . . . 5.5.3 Piezoresistive Transduction Mechanism . . . . . . . . . . . . . . 5.6 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.6.1 Applications in Timing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.6.2 MEMS Resonator-Based Oscillators . . . . . . . . . . . . . . . . . 5.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

123 123 124 126 127 127 129 130 132 132 133 133 135 136 139 139 140 150 150

6

Micromachined Phase Shifters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Classification of Phase Shifters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.1 Reflection Type Phase Shifter . . . . . . . . . . . . . . . . . . . . . . . 6.2.2 Switched-Line Phase Shifter . . . . . . . . . . . . . . . . . . . . . . . . 6.2.3 Loaded-Line Phase Shifters . . . . . . . . . . . . . . . . . . . . . . . . 6.2.4 Low-Pass/High-Pass Network Phase Shifter . . . . . . . . . . 6.2.5 Distributed MEMS Transmission Line (DMTL) Phase Shifter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

155 155 156 156 158 159 160 162

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6.3

Conventional Micromachined Switched Line Phase Shifters . . . . 6.3.1 Digital MEMS 5-Bit Switched Line Phase Shifter Using Two Back-To-Back SPDT Switches . . . . . . . . . . . . 6.3.2 4-Bit Switched Line Phase Shifters Using Two Back-To-Back SP16T Switches . . . . . . . . . . . . . . . . . . . . . 6.4 Different Types of DMTL Phase Shifters . . . . . . . . . . . . . . . . . . . . 6.4.1 Phase Shifters Using MAM Capacitors and MEMS Bridges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4.2 Push–Pull Type MEMS Digital DMTL Phase Shifters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5 Narrowband and Compact MEMS Phase Shifters . . . . . . . . . . . . . 6.6 Reconfigurable MEMS Digital Phase Shifters . . . . . . . . . . . . . . . . 6.7 Wide-Band MEMS Digital Phase Shifters . . . . . . . . . . . . . . . . . . . . 6.8 Other State-of-The-Art Micromachined Phase Shifters . . . . . . . . . 6.9 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

8

Micromachined Tunable Filters Using MEMS Switches . . . . . . . . . . . 7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2 Design Topology of the Tunable Bandpass Filter and Its Working Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3 Design and Testing of Individual Functional Blocks of the Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3.1 MEMS Switch Design and Measurements . . . . . . . . . . . . 7.3.2 MEMS Shunt Switch Array Design and Measurements: Block 2 . . . . . . . . . . . . . . . . . . . . . . . . 7.3.3 Design of Block 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.4 Testing of Tunable Bandpass Filter . . . . . . . . . . . . . . . . . . . . . . . . . . 7.5 Design Guidelines of the Proposed Filter and Future Scope for Improvements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.6 Frequency and Bandwidth Tunable Micromachined Bandpass Filter at 24 GHz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Reliability Analysis of RF MEMS Devices . . . . . . . . . . . . . . . . . . . . . . . 8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2 Testing the Reliability of RF MEMS Devices . . . . . . . . . . . . . . . . . 8.3 Reliability Analysis on MEMS Switching Networks . . . . . . . . . . . 8.4 Reliability Analysis on MEMS Digital Phase Shifter . . . . . . . . . . 8.5 Reliability Analysis on Tunable MEMS Filter . . . . . . . . . . . . . . . . 8.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

163 163 165 167 168 174 179 181 183 184 187 190 195 195 196 200 200 202 205 206 209 213 218 220 225 225 226 227 231 240 244 245

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9

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Micromachined Antennas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2 Micromachined Microstrip Patch Antennas . . . . . . . . . . . . . . . . . . 9.3 Micromachined Antennas for 60 GHz ISM Band . . . . . . . . . . . . . 9.3.1 Micromachined Antennas for 60 GHz ISM Band Using High Isolation SPDT Switch . . . . . . . . . . . . . . . . . . 9.3.2 Micromachined Antennas for ISM Band Sectoring Applications Using a SP9T Switch . . . . . . . . . . . . . . . . . . 9.4 Polarization Agile MEMS Antenna at 77 GHz . . . . . . . . . . . . . . . . 9.5 Millimeter Wave Micromachined Active Antenna . . . . . . . . . . . . . 9.5.1 Scaled Model (At K-band and on RT-duroid 10 Million Substrate) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.5.2 Scaled Model at Ka-band and on RT-duroid 5 Million Substrate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.6 Micromachined Two-Port Patch Antenna . . . . . . . . . . . . . . . . . . . . 9.7 Micromachined Active Antenna Element at Ka-band and on Silicon Substrate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.8 Design Guidelines for Micromachined Patch Antenna with Air Cavity at 35 GHz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.9 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

247 247 248 256

10 Micromachined Metamaterial Inspired Switches . . . . . . . . . . . . . . . . . 10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2 Micromachined Switch Using Capacitive Contacts . . . . . . . . . . . . 10.2.1 Basic Layout of Capacitive Shunt Switch . . . . . . . . . . . . . 10.2.2 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.3 DGS Inspired Micromachined Switch . . . . . . . . . . . . . . . . . . . . . . . 10.3.1 DGS Capacitive RF MEMS Switch . . . . . . . . . . . . . . . . . . 10.4 Metamaterial Inspired Micromachined Switch . . . . . . . . . . . . . . . . 10.4.1 Basic Switch Layout and Analysis . . . . . . . . . . . . . . . . . . 10.4.2 Shunt Switch with DGS Structures and Overlaid Secondary Switches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.5 Casimir Repulsive Force Inspired Micromachined Switch . . . . . . 10.5.1 Concept of Casimir Effect . . . . . . . . . . . . . . . . . . . . . . . . . . 10.5.2 Application of Casimir Effect in RF MEMS Switches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.6 Repulsive Casimir Force Inspired Resistive (Metal-to-Metal) Contact Micromachined Switch . . . . . . . . . . . . . 10.7 Casimir Repulsive Force Inspired Capacitive Contact Micromachined Switch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.8 Casimir Force Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.9 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

293 293 293 294 295 296 296 299 299

257 263 267 275 277 278 281 283 285 287 290

302 307 307 310 312 317 322 324 325

xiv

Contents

11 Future Scope of RF MEMS in THz Regime . . . . . . . . . . . . . . . . . . . . . . 11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Micromachined Metamaterial Based Devices in THz Regime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2.1 Micromachined Metamaterial Based Frequency Selective Surface at THz . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2.2 Micromachined Metamaterial Based Absorbers at THz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.3 2.5D-3D Micromachined Devices at Sub-Millimetre Wave . . . . . 11.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

327 327 328 328 332 338 342 343

Appendix A: Design Data on Micromachined Transmission Lines and Discontinuities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347 Appendix B: Details of Fabrication Process . . . . . . . . . . . . . . . . . . . . . . . . . . 373 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377

Abbreviations

D G c E H εr εreff λ fo μ0 εo S11 S21 ADS AR BAN CST FEM GPS GSM HFSS IEEE IOT ISM LCP LDV MEMS MOM PDA PSM RF

Directivity of Antenna Gain Velocity of Light Electric Plane Magnetic Plane Dielectric Constant of the Substrate Effective Dielectric Constant Free Space Wavelength Resonant Frequency Permeability of Free Space Permittivity of Free Space S-parameter indicating forward reflection Insertion loss/isolation Advanced Design System Axial Ratio Body Area Network Computer Simulation Technology Finite Element Method Global Positioning System Global System for Mobile Communication High Frequency Structure Simulator Institute of Electronics & Electrical Engineering Internet of Things Industrial Scientific Medical Liquid Crystal Polymer Laser Doppler Vibrometer Microelectromechanical System Methods of Moments Personal Digital Assistant Phase Change Material Radio Frequency xv

xvi

RFID SAR UWB VNA VSWR Wi-Fi WLAN

Abbreviations

Radio Frequency Identification Specific Absorption Rates Ultra-Wideband Vector Network Analyzer Voltage Standing Wave Ratio Wireless Fidelity Wireless Local Area Network

Chapter 1

Introduction to Radio Frequency Micro Electromechanical Systems

1.1 Overview of Micromachined Radio Frequency Components Micromachined Radio Frequency (RF) components that is commonly known as RF-MEMS, have been investigated by the research community starting from the late ‘90s. Microsystem (MEMS) technologies, at that time already exploited with a certain maturity in sensors and actuators applications [1–3], commenced to be ventured for prototyping RF passive components. The most relevant advantages of passive components in MEMS technology compared to their standard counterparts (e.g., in semiconductor technologies or based on discrete components) reside in their high-performance and low fabrication cost, as well as in the possibility of integrating RF MEMS devices to yield circuits and functional blocks entirely based on such a technology. Wireless communication technologies have witnessed major advances since the late 1980s. In the present wireless communication scenario, numerous standards such as CDMA (code-division multiple access), GSM (global system for mobile communication), the emerging 3G (3rd generation), 4G and 5G exist, which provide us with voice, data and broadband communication. But, in order to maintain the quality and reliability of these state-of-the-art technologies, the specifications given to a communication circuit design engineer are getting more and more stringent. The continual adoption of such stringent requirements as demanded by advanced wireless systems such as software defined radios and cognitive radio systems requires development of emerging technologies such as RF MEMS based devices [4]. RF MEMS switches, varactors, inductors, and resonators are ideal for reconfigurable systems at GHz range of operation. These components normally possess low insertion loss and very high-quality factor (Q) even up to tens of GHz frequency [5]. Moreover, RF MEMS devices generate very low intermodulation products. Thus, with the availability of high-performance passive components over wide frequency range of operation, and

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 S. K. Koul and S. Dey, Micromachined Circuits and Devices, Lecture Notes in Electrical Engineering 859, https://doi.org/10.1007/978-981-16-9443-1_1

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1 Introduction to Radio Frequency Micro Electromechanical Systems

the immense potential of integration with high volume industry mainstream complementary metal–oxide–semiconductor (CMOS) electronics; RF MEMS based circuits have become an important technology of interest to the wireless design fraternity [6].

1.2 Micromachined Passive Circuits A wide variety of micromachined devices and circuits have been reported in the literature and some of them are already commercialized. It includes micromachined transmission lines, switches, varactors, inductors, directional couplers, power divider, phase shifter, filter, antenna and resonator based active circuits. All these devices are discussed up to reasonable extent in this book.

1.2.1 Transmission Line A wide variety of micromachined devices and circuits have been reported in the literature in recent years. The microwave and millimetre wave communication systems have gained considerable interest and due to this, research activities are now directed towards microelectromechanical elements for the integration of off-chip components with the monolithic microwave integrated circuit (MMIC) technology. Using micromachining technology, it is possible to implement mmWave on-chip integrated circuits with high performance, low cost, and compact size. Most of the RF-MEMS devices are implemented using coplanar wave guide (CPW) because it is uniplanar in nature which leads to one of the best choices for any device due to fabrication simplicity, ease of integration with other components and chip level characterization. Microstrip transmission line also attracts attention in micromachining for high performance passive circuits. Figure 1.1a, b show 3D schematic views of a coplanar waveguide (CPW) and microstrip transmission lines, respectively. In the former, a

(a)

(b)

Fig. 1.1 Schematic 3D view of a Coplanar Waveguide (CPW) transmission line and b Microstrip transmission line

1.2 Micromachined Passive Circuits

3

central metallization acts as the RF signal line, while two wider metallized patches are meant to be reference ground planes for the travelling RF signal. The central line and ground planes are separated by a gap, and all the metal layers are printed on the same side of the substrate. As the RF signal propagates along the waveguide, the electromagnetic field is confined between the central line and the ground planes, partially through the dielectric material underneath the metal layers, and partially through the air above them. Very often, a thin insulating layer is deposited on the substrate prior to the electroplating/evaporation of the CPW itself. This helps to reduce dielectric losses due to the substrate. In the microstrip configuration, instead, the RF signal line is placed on top of the substrate, while a unique reference ground plane is metallized on the opposite face of the wafer. In this case, as the RF signal propagates along the waveguide, the electromagnetic field is mainly confined within the substrate, between the two metal layers (signal line and ground plane). A study on transmission lines with low loss and low dispersion is the first step in the implementation of millimetre-wave integrated circuits with low loss and high performance. The losses of the transmission line are mainly conductor ohmic loss and substrate dielectric loss. To reduce these losses, various transmission line structures are proposed. Most of the research is focused on the reduction of substrate dielectric loss and membrane technology was introduced to implement the low-loss microstrip line and CPW structures [7]. By fabricating the transmission line on thin dielectric membranes, such as silicon dioxide and silicon nitride, the line is separated from the substrate, resulting in low loss. However, the process of fabricating these structures is very complex and the process is not compatible with the conventional MMIC technology. Furthermore, lithography, electroplating, moulding (LIGA) or single crystal reactive etching and metallization (SCREAM) processes help in reducing the conductor loss [8]. All these processes are used in the fabrication of very thick structures and using a thick metal line, the conductor ohmic loss caused by the surface resistance can be reduced. However, these processes are also very complex and expensive. A new micromachined CPW transmission line with low loss and low dispersion is proposed in [9]. It can be easily fabricated with conventional MMIC technology. Two types of transmission lines with length of 1 cm are fabricated and the measured characteristics are compared with those of the conventional CPW transmission line in [9]. One is the elevated CPW (ECPW) transmission line and the other is the overlay CPW (OCPW) line. These transmission lines are composed of 3 µm-thick electroplated gold lines with overhanging parts. By elevating the metal lines from the substrate using micromachining technology, the conductor and substrate dielectric losses can be reduced and easily integrated with conventional monolithic microwave integrated circuits [9]. Compared with the conventional CPW line showing 2.65 dB/cm insertion loss at 50 GHz, the loss can be reduced to 1.9 and 1.25 dB/cm at 50 GHz in the case of the ECPW and OCPW transmission lines, respectively. Also, the OCPW transmission line shows that the insertion loss does not vary significantly with the change in the characteristic impedance. Micromachined cavity based CPW line has also gained considerable attention. The advantages of creating a small air gap beneath the signal conductor are: (a)

4

1 Introduction to Radio Frequency Micro Electromechanical Systems

a lower effective dielectric constant, hence wider circuit dimensions, (b) ease of fabrication and relaxed dimensional tolerances, (c) lower attenuation, (d) enhanced radiation efficiency in the case of antennas and (e) elimination of surface waves. Using the micromachined cavity-based lines, it is possible to design and develop high performance passive circuits and printed micromachined antennas at microwave and millimetre wave frequencies. This approach has been given considerable attention in this book.

1.2.2 Varactor and Inductors Micromachined passive circuits like varactors and inductors introduce good linearity and large tuning ranges. Maximum and minimum capacitance values (C max /C min ) better than 10:1 for capacitors, and a tuning range larger than 30–50% for inductors, respectively, with a quality factor (Q-factor) as good as 100–200, for both these reactive tunable elements are easily achievable. As an example, Fig. 1.2 shows the microphotograph of a typical varactor configuration realised in RF-MEMS technology in 1998 [9]. The varactor is framed in a CPW structure. A metal overpass (realising an air-gap) crosses the RF line, connecting the two RF ground planes. When no DC bias is applied between the suspended metal plate and the underlying fixed electrode (i.e., underpass), the shunt capacitance to ground is minimal. Differently, when the DC voltage drop between the two electrodes crosses the pull-in level, the suspended metal membrane collapses onto the underlying electrode, and the shunt capacitance to RF ground reaches its maximum value. In between the two ON/OFF configurations, the vertical position of the suspended membrane can be controlled in an analogue fashion, by driving the DC bias, thus enabling continuous tuning of the capacitance, in a range of vertical displacement equal to the 33% of the initial (OFF state) air-gap. Fig. 1.2 Microphotograph of an RF-MEMS varactor in CPW configuration [9]. Reproduced with permission from the IEEE

1.2 Micromachined Passive Circuits

5

1.2.3 Switches and Other Passive Circuits Micromachined switch is a miniature device that uses mechanical movements to achieve ON- or OFF-states in a transmission line. There are several ways to do these mechanical movements or actuations such as electrostatic, thermal, magnetostatic or piezoelectric. Electrostatic actuation is widely used due to its simplicity amongst all these actuation mechanisms. Although MEMS-based switches have the disadvantages like slow switching speed (1–100 µs) and lower power handling capability (3-bit) or switching networks. Switches are the key controlling elements, and they are being used later to make different micromachined microwave and millimetre-wave passive/active components. Switches with superior characteristics, their proper replication and (cross-) interconnection enabled the realisation of high-performance and widely reconfigurable micromachined passive networks like phase shifters, filters, antennas, and impedance matching networks. All these passive components can be made tunable or reconfigurable using micromachined switches and it gives substantial improvements in terms of power consumption. Another significant advantage of this technology abides in the typically low manufacturing costs. Micromachined passive components, indeed, have dimensions ranging from a few tens to a few hundred of micrometres, so their typical footprint and geometrical features are a few orders of magnitude larger than semiconductor-based devices. Integration of micromachined components within circuits and systems in standard technology, their encapsulation (i.e., packaging) and protection, as well as the mechanical reliability, power handling and stability of performance, are issues that add to the cost of RF micromachined components. More simply, RF micromachined devices are cheap to fabricate and test as standalone devices, but expensive to be qualified and made suitable for a specific application. Despite these aspects, significant effort and resources are being invested in the development of high-performance RF micromachined passive components for very critical applications, such as space applications, where the demand on the component specifications and characteristics overwhelm the investment effort for the realization of just a small batch of RF MEMS passive components with outstanding characteristics.

1.2.4 Resonators Micromachined based on-chip resonators have shown significant potential for sensing and high frequency signal processing applications. This is due to their excellent features like small size, large frequency-quality factor product, low power consumption, low-cost batch fabrication, and integrability with CMOS IC technology. Radio frequency communication circuits like reference oscillators, filters, and mixers based on such micromachined resonators can be utilized for meeting the increasing count of RF components likely to be demanded by the next-generation multi-band/multi-mode wireless devices. Micromachined resonators can provide a feasible alternative to the present-day well-established quartz crystal technology that is riddled with major drawbacks like relatively large size, high cost, and low compatibility with IC chips. Micromachined based resonators have emerged as an attractive alternative which can offer Q-values close to that for quartz in both vacuum as well as in air and operating frequencies up to the very-high frequency (VHF, 30–300 MHz) and ultra-high

1.2 Micromachined Passive Circuits

9

frequency (UHF, 300 MHz–3 GHz) ranges, consume less power, provide temperature stability better than 18 ppm over 27–107 °C and aging stability better than 2 ppm over one year, have shorter design and production cycle times, and can be monolithically integrated and fabricated using low-cost CMOS compatible processes [26]. In addition, MEMS resonators are very robust to shock and vibration, and provide an overwhelming size advantage. However, for replacement of the quartz crystal technology with MEMS, the latter must successfully overcome a few problems related to temperature stability, thermal hysteresis, long-term stability, and packaging. These issues are gradually being solved, and the timing and frequency control industry have started embracing the MEMS resonator-based devices. Both capacitive and piezoelectrically transduced versions of micromechanical resonators have been demonstrated [27, 28]. Capacitively transduced MEMS resonators are in general favoured than their piezoelectrically transduced counterparts. Also, among the former variety of micro-resonators, bulk acoustic mode of vibration is the preferred option for realizing high frequency of operation [29]. Piezoelectric based resonators are used for high frequency operation for making filters and oscillators. As an example, 1.05 GHz Pierce oscillator based on a piezoelectric MEMS resonator (Q of 2,200) wire-bonded to the CMOS IC chip has been demonstrated in [28]. It has shown a phase noise level of −81 dBc/Hz at 1 kHz offset frequency, and a phase noise floor of −146 dBc/Hz, with a dc power consumption of 3.5 mW. Circuit schematic of a Pierce oscillator circuit with micrograph of the devices are depicted in Fig. 1.5 [28]. Various applications encompassing such resonators, including RF filtering and mixing have also been reported in [26]. Some prior surveys on MEMS resonators are available in the literature. An excellent review by Nguyen in [26] focusses on various aspects of RF MEMS resonators, filters, and reference oscillators.

Fig. 1.5 Circuit schematic of a Pierce oscillator circuit. The micrograph shows a Pierce oscillator with the MEMS resonator wire-bonded to the amplifier IC [28]. Reproduced with permission from the IEEE

10

1 Introduction to Radio Frequency Micro Electromechanical Systems

1.3 Fabrication of RF Micromachined Devices on Different Technology Platforms RF micromachined devices are fabricated using Bulk micromachining and Surface micromachining processes. Bulk micromachining defines structures by selectively etching inside a substrate. Whereas surface micromachining creates structures on top of a substrate, bulk micromachining produces structures inside a substrate. Bulk micromachining starts with a silicon wafer or other substrates that are selectively etched, using photolithography to transfer a pattern from a mask to the surface. Surface micromachining builds microstructures by the deposition and etching of different structural layers on top of the substrate. Most of these process steps are common with those for standard semiconductor devices, such as diodes and transistors. Indeed, the fabrication of micro-devices is always based on the selective deposition and removal of stacked conductive and insulating layers, by means of pattern transfer (i.e. lithography), and the subsequent execution of steps such as the electro-deposition or sputtering of metal layers (gold, silver, copper, aluminium, and so on), the growth of insulating layers (e.g. silicon oxide, silicon nitride), and the selective removal of the same layers (wet or dry etching, plasma oxygen, and so on) [30]. A peculiar fabrication step of RF micromachined devices is the exploitation of the so-called sacrificial layer, which is a film of material (typically photoresist or oxide) needed for defining the movable membrane, and then removed in order to release the suspended structures. The stacked deposition and selective removal of multiple conductive and insulating layers onto a substrate (typically a silicon wafer) falls under the surface micromachining. This process is commonly used for the fabrication of RF passive components. In bulk micromachining process, the (silicon) substrate is selectively removed (from the bottom side), forming suspended and deformable membranes made of the same material of the substrate, rather than layers deposited above it [30]. In general, the bulk micromachining process cannot be completely used for the fabrication of RF micromachined devices, as movable structures made of silicon would excessively attenuate the RF signal (i.e., large resistive losses) with respect to a surface micromachined metal layer. It is mostly due to the fact that resistivity of the first material being significantly larger than that of gold, for instance. A solution to circumvent this problem resides in coating the MEMS constitutive silicon parts with highly conductive material (e.g., evaporated metal layers), along the path where the RF signal is expected to travel, reducing resistive losses. More interestingly, several examples of RF MEMS devices benefiting from a combination of surface and bulk micromachining processes are available in the literature. For instance, the work reported in [31] discusses a metal RF MEMS tunable inductor below which the silicon was removed (bulk micromachining) in order to have a suspended (in air) micro-device, consequently achieving reduction of resistive losses and capacitive coupling toward the substrate. The inductor reported in this work shows a Q-factor larger than 9 at 5 GHz, and a self-resonance frequency above 15 GHz [31]. There is considerable interest in developing reconfigurable and tunable

1.3 Fabrication of RF Micromachined Devices …

11

integrated micromachined RF-front ends using high dielectric constant substrates like Si, alumina and GaAs. In addition, due to the high dielectric constant of the substrate, there is a possibility of excitation of surface waves. These problems can be overcome by introducing a small air gap between the dielectric substrate and the ground plane.

1.4 Applications of RF Micromachined Devices and Components RF micromachining is a key enabling technology for next generations of radio platforms, spanning from handsets and mobile communications to radar systems due to its remarkable performance like low-loss, high-isolation, high quality factor (Q-factor), good linearity and, also importantly, ease in tunability/reconfigurability. Micromachined components are used in RF transceiver (transmitter/receiver) architecture. In terms of transceiver platforms for radio signals, one of the most widely diffused architectures is the super-heterodyne transmitter and receiver. Such an architecture operates a frequency up-conversion (transmitter) and down-conversion (receiver) of the baseband signal, to an intermediate frequency (IF) band lower than the RF band exploited for broadcasting the signal. The IF facilitates the manipulation and treatment of the signal to be transmitted/received (e.g., filtering, amplification, modulation/demodulation, and so on). Passive components in MEMS technology can replace traditional devices in several parts of a super-heterodyne transceiver, improving its performance and characteristics. A block diagram presented in Fig. 1.6 shows the typical configuration of a superheterodyne receiver, as reported, and discussed in [32]. All the blue coloured sub-blocks of the diagram can be replaced by implementations of passive components using RF micromachining technology. In particular, looking at the receiver from the antenna side to the output of the demodulated received signal (In-phase—I and Quadrature—Q) a MEMS switching unit can be used to select the

I RF Switch Filter

LNA

RF Filter

ADC

IF IF Filter Amplifier 900

Q LC tank

ADC

VCO

Resonator

PLL

IQ OSC

Resonator

Fig. 1.6 Block diagram of a super-heterodyne radio receiver, as reported by Nguyen in [32]. The blue coloured blocks can be realized with passive components based on RF micromachining technology, improving the performance and characteristics of the whole system

12

1 Introduction to Radio Frequency Micro Electromechanical Systems

proper antenna (i.e., hardware selection). Moreover, micromachined varactors (i.e., variable capacitors) and inductors are suitable to realize high Q-factor filters (both RF and IF) and reconfigurable LC-tanks to tune the oscillation frequency of the voltage-controlled oscillator (VCO). However, different MEMS switch-based filters are also reported in literature. Recently, a bandpass filter is reported in [33] where center frequency and bandwidth can be tunable simultaneously. This filter can work up to 1 billion cycles with 1 W of RF power. Finally, MEMS resonators can replace the typical quartz-based devices in the oscillators. Besides the realization of RF micromachined basic passive components, MEMS technology can be exploited for the fabrication of more complex blocks as well. Indeed, by merging several varactors, inductors and switches, it is possible to realize reconfigurable high-order switching matrices, phase shifters, couplers, delay lines, and so on, as will be discussed later in this Chapters. The availability of such networks leads to rethinking the architecture of a transceiver, rather than just replacing some of its base components with their micromachining counterparts. To this purpose, the architecture of the super-heterodyne receiver previously shown can be rearranged and simplified on the basis of micromachined based complex networks [32], as shown in Fig. 1.7. In this architecture, the availability of a multi-channel selector (i.e., MEMS switches) with several filtering functions would simplify the hardware complexity of the whole platform. For instance, the typical low loss of MEMS-based devices and networks compared to standard technologies would reduce the number of power amplifiers needed for regenerating the signal. Moreover, the high-reconfigurability of MEMS can be exploited to realize a widely tunable oscillator, extending the range of possible received signals that can be mixed and demodulated by the receiver, through the integration of a mixer-filter IF block based on RF MEMS technology as well. Recently, an on-wafer down conversion stage is implemented with mixer-filter performances in [34] with capacitive micromachined resonators. It is easy to envisage that MEMS passive components could be employed in several RF systems and applications apart from transceivers. In modern radar systems,

Channel selector ADC

Switch

LNA

Mixer-filter 900 ADC

Reconfigurable Oscillator IQ OSC

Resonator

Fig. 1.7 Block diagram of a super-heterodyne radio receiver, based on a modified architecture that features complex blocks entirely based on RF micromachining technology, namely, a multi-channel selector, a reconfigurable oscillator, and a mixer-filter, as reported in [32]

1.4 Applications of RF Micromachined Devices and Components

13

the electronic steering of the antenna beam has replaced the old rotary mechanical antennae, leading to a significant reduction in complexity and space occupation, as well as improved robustness of the system. However, phase shifters in standard technology needed for antenna beam orientation are typically rather lossy, and consequently require additional power amplifiers duplicated for each of the antenna array delay lines. A block diagram of the radar system, close to the transmitting antennae array and featuring standard phase shifters, is depicted in Fig. 1.8a and discussed in [35]. As visible in the scheme, a power amplifier is necessary before and after the phase shifter element in each branch, to regenerate the attenuated RF signal. For mid-power radar systems, traditional phase shifters can be replaced by highperformance and low-loss realizations of such networks using RF micromachining technology. In the latter case, the power consumption and hardware complexity of the system can be considerably reduced, as an amplifying stage can be omitted in each branch, as depicted in Fig. 1.8b. In addition, the most popular and useful method is to use phase shifters in combination with an antenna array [36, 37]. Many studies and experiments have been performed on the electronic beam steering principle utilizing micromachining technology.

1.5 Book Organisation The book contains total eleven Chapters with the first Chapter serving as an introduction to radio frequency micro-electro-mechanical systems where an overview of different micromachined passive and active circuits are given followed by applications in modern trans -receiver architectures. Chapter 2 starts with a discussion on different micromachined passive circuits. The main emphasises is given on the understanding of micromachined Conductor Backed Coplanar Waveguide (CBCPW) lines with their discontinuities. Other different types of micromachined passive components are also discussed in this Chapter that includes varactor, inductor, power divider and couplers. Chapter 3 discusses design, development, and complete characterization of micromachined single-pole-single-throw switches. The motivation is to observe the switch functionalities in-terms of mechanical behaviour, electrical behaviour, transient analysis, linearity, power handling, temperature behaviour, and S-parameters. Chapter 4 discusses design and implementation of different micromachined single-pole-multi-throw switching networks with respect to vertical and horizontal actuation movements. It includes single-pole-double-throw to single-polefourteen-throw configurations. Chapter 5 presents design and implementation of micromachined resonator and resonator-based circuits. Different types of micromachined resonance modes are discussed in this Chapter followed by the discussion on three different transduction mechanisms. Finally, applications of micromachined resonator are presented for timing circuits and oscillators. Chapter 6 reports theory, design, and analysis of different types of microwave micromachined phase shifters. It includes narrowband, wideband and reconfigurable micromachined phase shifters. Chapter 7 describes two compact, high power and reliable tunable bandpass

14

1 Introduction to Radio Frequency Micro Electromechanical Systems

RF out

RF feed line

(a)

RF out

RF feed line

(b) Fig. 1.8 Block diagram of a radar system employing electronically steerable beam antenna as reported in [35]. a Scheme employing phase shifters using standard technology, requiring power amplifiers in each branch to regenerate the signal attenuated by the lossy phase shifting elements, b scheme employing phase shifters in micromachining technology. Due to the very low loss of such elements the power consumption and hardware complexity of the system can be significantly reduced

1.5 Book Organisation

15

filter for millimetre wave RF front end for 5G and radar applications at 28 GHz and 24 GHz, respectively. A comprehensive design guideline of tunable micromachined bandpass filters is given in this Chapter with special attention on bandwidth and center frequency reconfiguration. Chapter 8 discuses reliability analysis on RF micromachined devices with emphasis on the multiport switching networks, 4–5bit digital phase shifters and tunable filters. Chapter 9 presents different types of micromachined antennas at mmWave frequencies. Detailed design guidelines are given on antenna designs at 60 and 77 GHz. In addition, a comprehensive design analysis is given in this Chapter on basic active antenna design. Chapter 10 attempts design and development of micromachined metamaterial inspired switches at submillimetre wave frequency. Design guidelines are outlined here including design layout and Casimir repulsive force inspired resistive contact and capacitive micromachined switch. Finally, Chap. 11 describes future scope of RF micromachining on the design and development of different types of metamaterial-based frequency selective surfaces, absorbers and other 3D-micromachined devices in the sub-THz regime.

References 1. Bernstein J, Cho S, King AT, Kourepenis A, Maciel P, Weinberg M (1993) A micromachined comb-drive tuning fork rate gyroscope micro electro mechanical systems. In: Proceedings of the IEEE international conference on micro electro mechanical systems MEMS, Fort Lauderdale, pp 143–148 2. Ziegler V, Siegel C, Schonlinner B, Prechtel U, Schumacher H (2005) RF-MEMS switches based on a low-complexity technology and related aspects of MMIC integration. In: Proceedings of the European gallium arsenide and other semiconductor application symposium EGAAS, Paris, pp 289–292 3. Aratani K, French PJ, Sarro PM, Wolffenbuttel RF, Middelhoek S (1993) Process and design considerations for surface micromachined beams for a tuneable interferometer array in silicon. In: Proceedings of the IEEE international conference on micro electro mechanical systems MEMS, Fort Lauderdale, pp 230–235 4. De Los Santos HJ, Fischer G, Tilmans HAC (2004) van Beek JTM RF MEMS for ubiquitous wireless connectivity: part II–Application. IEEE Mirowave Mag 5(4):50–65 5. Rebeiz GM (2003) RF MEMS theory, design and technique (book). Wiley 6. Tilmans HAC, Raedt WD, Beyne E (2003) MEMS for wireless communications: ‘from RFMEMS components to RF-MEMS-SiP.’ J Micromech Microeng 13:139–163 7. Weller TM, Katehi LPB, Rebeiz GM (1995) IEEE Trans Microw Theory Tech 43:534–541 8. Kudrle TD, Neves HP, Rodger DC, MacDonald NC (1999) Solid-state sensors and actuators workshop, pp 1276–1782 9. Goldsmith CL, Yao Z, Eshelman S, Denniston D (1998) Performance of low-loss RF MEMS capacitive switches. IEEE Microw Guid Wave Lett 8:269–271 10. Liu AQ (2010) RF MEMS switches and integrated switching circuits, Springer, New York 11. Sakata M, Komura Y, Seki T, Kobayashi K, Sano K, Horike S (1999) Micromachined relay which utilizes single crystal silicon electrostatic actuator. In: ieee international conference on microelectromechanical systems, Orlando, FL, pp. 21–24 12. Uno Y, Narise K, Masuda T, Inoue K, Adachi Y, Hosoya K, Seki T, Sato F (2009) Development of SPDT structured RF MEMS switch. In: International conference on transducers, solid-state sensors, actuators and microsystems, pp 541–544

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13. Majumder S, Lampen J, Morrison R, Maciel J (2003) A packaged, high-lifetime ohmic MEMS RF switch. In: IEEE MTT-S International microwave symposium digest, Philadelphia, PA, pp 1935–1938 14. Newman HS, Ebel JL, Judy D, Maciel J (2008) Lifetime measurements on a high-reliability RF-MEMS contact switch. IEEE Microw Wirel Compon Lett 18(2):100–102 15. Goins DA, Nelson RD, McKillop JS (2007) Design of a 20 GHz low loss ohmic contact RF MEMS switch. In: IEEE MTT-S international microwave symposium digest, Honolulu, HI, pp 371–374 16. Costa J, Ivanov T, Hammond J, Gering J, Glass E, Jorgenson J, Dening D, Kerr D, Reed J, Crist S, Mercier T, Kim S, Gorisse P (2008) Integrated MEMS switch technology on SOI-CMOS. In: IEEE Solid-state sensors, actuators, and microsystems workshop, Hilton Head, SC, pp 18–21 17. Nishijima N, Hung J-J, Rebeiz GM (2004) Parallel-contact metal-contact RF MEMS switches for high power applications. In: IEEE international conference on microelectromechanical systems, Maastricht, Netherlands, pp 781–784 18. Nishijima N, Hung J-J, Rebeiz GM (2004) A low-voltage, high contact force RF-MEMS switch. In: IEEE MTT-S international microwave symposium digest, Fort Worth, TX, pp 577–580 19. Yao J, Chang M (1995) A surface micromachined miniature switch for telecommunication applications with signal frequencies from dc up to 4 GHz. In: 8th international conference on solid-state sensors and actuators and Eurosensors IX. Transducers, vol 2, pp 384–387 20. Mihailovich RE, Kim M, Hacker JB, Sovero EA, Studer J, Higgins JA, DeNatale JF (2001) MEM relayfor reconfigurable RF circuits. IEEE Microw Wirel Compon Lett 11(2):53–55 21. De Silva A, Vaughan C, Frear D, Liu L, Kuo S, Foerstner J, Drye J, Abrokwah J, HugAmrine H, Butler C, Markgraf S, Denton H, Springer S (2001) Motorola MEMS switch technology for high frequency applications. In: Microelectromechanical systems conference, Berkeley, CA 22. Suzuki K, Chen S, Marumoto T, Ara Y, Iwata R (1999) A micromachined RF microswitch applicable to phased array antennas. In: IEEE MTT-S international microwave symposium digest, Anaheim, CA, pp 1923–1926 23. Sedaghat-Pisheh H, Kim J, Rebeiz GM (2009) A novel stress-gradient-robust metal-contact switch. In: IEEE international conference on microelectromechanical systems, Sorrento, Italy, pp 27–30 24. Sedaghat-Pisheh H, Rebeiz GM (2010) Variable spring constant, high contact force RF MEMS switch. In: IEEE MTT-S international microwave symposium digest, Anaheim, CA, pp 304–307 25. Singh T, Mansour RR (2019) Miniaturized DC–60 GHz RF PCM GeTe-based monolithically integrated redundancy switch matrix using T-type switching unit cells. IEEE Trans Microw Theory Tech 67(12):5181–5190 26. Nguyen CTC (2007) MEMS technology for timing and frequency control. IEEE Trans Ultrason Ferroelectr Freq Control 54:251–270 27. Hao Z, Pourkamali S, Ayazi F (2004) VHF single-crystal silicon elliptic bulk-mode capacitive disk resonators–part I: design and modeling. J Microelectromech Syst 13(6):1043–1053 28. Zuo C, Van der Spiegel J, Piazza G (2010) 1.05-GHz CMOS oscillator based on lateral-fieldexcited piezoelectric AlN contour-mode MEMS resonators. IEEE Trans Ultrason Ferroelectr Freq Control 57:82–87 29. Clark JR, Hsu WT, Abdelmoneum MA, Nguyen CTC (2005) High-Q UHF micromechanical radial-contour mode disk resonators. J Microelectromech Syst 14(6):1298–1310 30. Adams TM, Introductory MEMS (2009) Fabrication and applications. Springer, Berlin 31. Zine-El-Abidine I, Okoniewski M, McRory JG (2004) A tunable RF MEMS inductor. In: International conference on MEMS, NANO and smart systems, Alberta 32. Nguyen CTC (2001) Transceiver front-end architectures using vibrating micromechanical signal processors. In: Topical meeting on silicon monolithic integrated circuits in RF systems, Piscataway 33. Dey S, Koul SK (2021) Reliable, compact, and tunable mems bandpass filter using arrays of series and shunt bridges for 28-GHz 5G applications. IEEE Trans Microw Theory Tech 69(1):75–88

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34. Satija J, Dey S, Bhattachariya S, Pillai G, Li SS (2019) A chip-scale frequency down-conversion realized by MEMS-based filter and local oscillator, accepted in Elsevier sensors and actuators: a. Physical 35. Haridas N, Erdogan A T, Arslan T, Walton A J, Smith S, Stevenson T, Dunare C, Gundlach A, Terry J, Argyrakis P, Tierney K, Ross A, O’Hara T (2008) Reconfigurable MEMS antennas. In: NASA/ESA conference on adaptive hardware and systems, Noordwijk, ESA 36. Albani M, Cadili T, Di Maggio F, Gardelli R, Incorvaia A, Mollura C, Pomona I, Russo M, Sbarra E, Sorrentino R, Gatti RV (2007) A 2-D electronic beam steering phased array for pointmultipoint communication applications. In: European microwave conference, pp 1629–1632 37. Chia MY-W, Teck-Hwee L, Jee-Khoi Y, Piew-Yong C, Siew-Weng L, Chan-Kuen S (2006) Electronic beam-steering design for UWB phased array. IEEE Trans Microw Theory Tech 54(6):2431–2438

Chapter 2

Micromachined Microwave Passive Circuits

2.1 Introduction Micromachined microwave and millimeter wave components development has been identified as an area that has the potential to provide a major impact on existing systems in communications. The motivation behind fabrication of high frequency circuits on micromachined silicon substrates is due to precise dimensions, repeatability and reduced weight, cost, size, losses and power dissipation. Designing micromachined components at microwave and millimeter wave frequencies will require careful selection of a planar transmission structure that can be conveniently fabricated using conventional Si-micromachining technique. The most relevant advantages of passive components in MEMS technology compared to their standard counterparts (e.g., using semiconductor technologies or discrete components) reside in their high-performance and low fabrication cost, as well as in the possibility of integrating RF MEMS devices to yield circuits and functional blocks entirely based on such a technology. For example, varactors and inductors in MEMS technology present good linearity and large tuning ranges. For capacitors, ratio between the maximum and minimum capacitance values (C max /C min ) better than 10:1 and a tuning range larger than 30–50% for inductors, with a quality factor (Q-factor) as good as 100–200, for both these reactive tunable elements can be easily achieved. Micromachined passive components are always arranged as part of a suitable waveguide of certain length. The RF signal, indeed, is driven from the input of the waveguide to the intrinsic MEMS device, such as a variable capacitor or a microrelay, that is, the element that actually manipulates the signal, and then is driven to the output of the device. As is well known in microwave theory, several waveguide configurations are possible, depending on the number and placement of the conductive and ground planes, as well as of the insulating material/s. Since MEMS structures are typically planar devices with movable parts built above silicon (surface micromachining) or made of silicon (bulk micromachining), they can be easily framed within

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 S. K. Koul and S. Dey, Micromachined Circuits and Devices, Lecture Notes in Electrical Engineering 859, https://doi.org/10.1007/978-981-16-9443-1_2

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the planar waveguides, rather than coaxial or, in general, sandwiched configurations, where the metal conductive plane is embedded within multiple insulating layers. This Chapter gives more emphasis on the micromachined Conductor Backed Coplanar Waveguide (CBCPW) lines. It includes design data and closed form expressions on the characteristic parameters of CBCPW lines on Si-micromachined structures that are valid up to 40 GHz. Effect of various structural parameters are discussed in detail. Procedure for deriving lumped equivalent circuit models for discontinuities on Si-Micromachined substrate as a function of discontinuity physical parameters is also presented. Finally, this Chapter gives brief overview of other micromachined passive circuits like inductors, varactors, power divider, coupler, and impedance matching tuners.

2.2 Micromachined Conductor Backed Coplanar Waveguide (CBCPW) Lines The basic component for the realization of micromachined circuits is the printed transmission lines. The two most important planar transmission lines extensively used to build conventional microwave and millimeter circuits are the microstrip and the coplanar waveguide. The cross-sectional view of the microstrip along with electric and magnetic field lines is shown in Fig. 2.1. In this structure, a pure TEM mode cannot exist because it is not possible to satisfy the boundary conditions for this mode at the dielectric- air interface. However, at low frequencies, the mode of propagation closely resembles TEM mode, usually termed as quasi-TEM mode. As frequency increases, higher order modes can be supported by the structure. The coplanar waveguide consists of a strip conductor separated by a slot on either side from the two adjacent ground planes. The cross-sectional view of the coplanar waveguide along with electric and magnetic field lines is shown in Fig. 2.2. At low frequencies, this structure also supports quasi-TEM mode. At higher frequencies, the contribution from the longitudinal magnetic fields is sufficiently large, resulting in propagation of non-TEM higher order modes. Before attempting design of a component using MEMS technology, it is important to select a transmission medium that is suitable

Fig. 2.1 a Cross-section of microstrip, and b Electric and magnetic field lines

2.2 Micromachined Conductor Backed Coplanar Waveguide (CBCPW) Lines

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Fig. 2.2 a Cross-section of coplanar waveguide, and b field lines

at microwave and millimeter wave frequencies. It should also be possible to fabricate the structure using micro-machining technique. Extensive theoretical studies are carried out on the following transmission lines, in this Chapter. • • • • • •

Microstrip with air gap on Si substrate (Fig. 2.3a) Microstrip with air gap on SiO2 –Si substrate (Fig. 2.3b) Microstrip with air gap on SiO2 –Si-RT duroid substrate (Fig. 2.3c) Grounded Coplanar waveguide (GCPW) with air gap on Si (Fig. 2.4a) GCPW with air gap on SiO2 –Si substrate (Fig. 2.4b) GCPW with air gap on SiO2 –Si-RT duroid substrate (Fig. 2.4c).

Fig. 2.3 Cross-section of Microstrip with air gap on: a high resistivity Si (silicon), b SiO2 –Si substrate and c SiO2 –Si-RTduroid substrate. All dimensions are in μm

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Fig. 2.4 Cross-section of GCPW with a air gap on high resistivity Si, b air gap on SiO2 –Si substrate and c air gap on SiO2 –Si-RT duroid substrate. All dimensions are in μm

2.2.1 Studies on Basic Micromachined Transmission Structures Microstrip with air gap on Si substrate: The cross-section of this structure is shown in Fig. 2.3a. The structure was analyzed using HFSS. Figure 2.5 shows the attenuation characteristics of this structure as a function of d for three values of frequency. It is observed that in general attenuation increases as d or frequency is increased. Figure 2.6 shows the variations of characteristic impedance as a function of d for three values of frequency. It is observed that as d increases, characteristic impedance Fig. 2.5 Attenuation versus d for three values of frequencies

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Fig. 2.6 Characteristic impedance versus d for three values of frequency

decreases. As frequency increases, change in the value of characteristic impedance is rather small over the frequency range 20–40 GHz. Microstrip with air gap on SiO2 –Si-RT duroid substrate: The cross-section of this structure is shown in Fig. 2.3c. Figure 2.7 shows the attenuation characteristics of this structure as a function of frequency for various values of w. It is observed that in general attenuation increases as frequency is increased. Figure 2.8 shows the variations of characteristic impedance as a function of frequency for four values of w. It is observed that as w increases, characteristic impedance decreases. As frequency increases, change in the value of characteristic impedance is rather small over the frequency range 20–40 GHz. Grounded coplanar waveguide with air gap on SiO2 –Si substrate: The cross-section of this structure is shown in Fig. 2.4b. Figure 2.9 shows the attenuation characteristics of this structure as a function of frequency for various s. It is observed that, in general, attenuation increases as frequency is increased. The variations of effective dielectric constant as a function of frequency for various s are plotted in Fig. 2.10. For a fixed value of s, effective dielectric constant does not change significantly as frequency is Fig. 2.7 Attenuation versus frequency for different w values

24 Fig. 2.8 Characteristic impedance versus frequency for different w values

Fig. 2.9 Attenuation versus frequency for different s values

Fig. 2.10 Effective permittivity versus frequency for different s values

2 Micromachined Microwave Passive Circuits

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Fig. 2.11 Attenuation versus frequency for different s values

increased. It is observed from the simulated results that this structure also supports multiple modes. Grounded coplanar waveguide with air gap on SiO2 –Si-RT duroid substrate: The cross-section of this structure is shown in Fig. 2.4c. Figure 2.11 shows the attenuation characteristics of this structure as a function of frequency for various s. It is observed that in general attenuation increases as frequency is increased. The variations of effective dielectric constant as a function of frequency for various s are plotted in Fig. 2.12. For a fixed value of s, effective dielectric constant increases as frequency is increased. Figure 2.13 shows the variations of characteristic impedance as a function of frequency for various values of s. It is observed that as s increases, characteristic impedance decreases. As frequency increases, characteristic impedance is more or less constant over the entire frequency band 10–40 GHz. It was observed from the simulated results that single mode operation is possible over the entire 10–40 GHz band. Furthermore, the dominant mode is well identified from the field lots as shown in Fig. 2.14. In all the above computations, the resistivity of the silicon (Si) was assumed to be 5000  m and the value of d = 10 microns. The variations of attenuation constant Fig. 2.12 Effective Dielectric constant versus frequency for different s values

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Fig. 2.13 Characteristic Impedance versus frequency for different s values

Fig. 2.14 Simulated E-field distribution in the cross-sectional plane

and characteristic impedance versus frequency for various values of Si resistivity are plotted in Figs. 2.15 and 2.16, respectively. The structure considered is the same as shown in Fig. 2.4c. As observed from Fig. 2.15, attenuation constant reduces considerably as resistivity ρ of Si is increased from 100 to 5000  m.

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Fig. 2.15 Attenuation versus frequency for different ρ values

Fig. 2.16 Characteristic impedance frequency for different ρ values

2.2.2 Design Data on Discontinuities in Membrane Microstrip From the studies on the transmission lines, it was observed that to have single mode operation up to Ka-band, it is essential to use grounded coplanar waveguide on Si-substrate with air-cavity placed on low dielectric constant substrate as shown in Fig. 2.4c. In most of the practical situations, we need to integrate microstrip circuits with the coplanar waveguide transitions. It is therefore essential to consider the same-layered structure for the membrane microstrip line as well. The design data on discontinuities in membrane microstrip was therefore generated for the structure shown in Fig. 2.4c. Gap in the center conductor Symmetrical series gap in the center conductor of the membrane microstrip line can be modeled as a lumped pi-network of capacitors as shown in Fig. 2.17. This symmetrical series gap discontinuity in membrane microstrip shown in Fig. 2.17

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Fig. 2.17 Layout and equivalent lumped element model of series gap discontinuity in membrane microstrip

was analysed using full wave FEM simulator for series gap width g ranging from 10 to 150 μm. Tables A.1, A.2, A.3, A.4, A.5 and A.6 gives the data on S-parameters obtained for various gap widths in the Appendix A. To obtain values of series and shunt capacitors in the equivalent circuit, first, de-embedded port S-parameters with reference to the center of the series gap are obtained. Next, circuit simulator Agilent ADS is used to compute the capacitor values in the pi- equivalent model. Figure 2.18 shows typical variations of the gap equivalent circuit parameters of membrane microstrip as a function of gap width. As gap width is increased, the series

Fig. 2.18 Microstrip series gap equivalent circuit parameters as a function of series gap width (Z 0 = 50 )

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gap capacitance decreases whereas the shunt gap capacitance slightly increases. The value of shunt capacitor is small as compared with the series capacitor. Step in the center conductor The step junction discontinuity layout is shown in Fig. 2.19a. This discontinuity structure in membrane microstrip shown in Fig. 2.19b was analyzed using Full Wave FEM solver. The step ratio was taken around 146 (w1 = 1460 μm and w2 = 10 μm) and ports de-embedded to the junction pp’ as shown in Fig. 2.19a. The simulated S-parameters for this discontinuity are given in Table A.7 in the Appendix A. A possible equivalent circuit of the step discontinuity is shown in Fig. 2.20a, b. The model consists of a shunt capacitor with small transmission lines of characteristic

Fig. 2.19 a Step junction discontinuity layout and b microstrip structure on Si-substrate with air cavity placed on low dielectric constant substrate, all dimensions are in μm

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Fig. 2.20 a Step discontinuity layout, and b possible equivalent circuit

impedances as that of port impedances at both sides. The de-embedded S-parameter data was used to obtain the values of capacitor C1 and also line lengths l1 and l 2 . Table A.8 gives the values of the equivalent circuit parameters obtained for several step widths in the Appendix A. To validate the model, the S-parameters obtained using the 3D EM solver are compared with the values obtained from the lumped equivalent circuit model shown in Fig. 2.20b. Figure 2.21 shows the comparison for the scattering parameter magnitude. Excellent agreement is observed between the two results. Similar observations are seen for the phase plots. Tee-Junction Discontinuity The layout of the symmetric Tee-junction discontinuity is shown in Fig. 2.22. One of the three ports has conductor width ‘w1 ’ microns and the other two ports have conductor width ‘w2 ’ microns. Port ‘1’ (PP) is de-embedded at the edge of the junction and port ‘2’ (QQ) and port ‘3’ (RR) are de-embedded at the center of conductor, as shown in Fig. 2.22. S-parameters of this discontinuity in membrane microstrip structure shown in Fig. 2.19b are obtained using full wave simulator. The results after de-embedding are given in Tables A.9, A.10 and A.11 in the Appendix

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Fig. 2.21 Comparison of S-parameters obtained using the 3D finite element software (HFSS) with those obtained using the lumped equivalent circuit model Fig. 2.22 Tee-Junction discontinuity layout. All dimensions are in μm

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Fig. 2.23 Possible equivalent circuit of the T-junction discontinuity

A, for T-junction of 50–50–50  lines, 50–70–70  lines and 50–100–100  lines. The corresponding line widths for these three cases are as follows: For 050–050–050  line: w1 = 1300 μm; w2 = 1300 μm. For 050–070–070  line: w1 = 1300 μm; w2 = 840 μm. For 050–100–100  line: w1 = 1300 μm; w2 = 430 μm. A possible equivalent circuit of the T-junction discontinuity is shown in Fig. 2.23. The de-embedded S-parameter data was used to obtain the values of capacitor C 1 , inductance L 1 also line lengths at each port. The transformer ratio n turned out to be 1 in all cases. Table A.12 gives the values of the equivalent circuit parameters obtained for several T-junctions in the Appendix A. To validate the model, the S-parameters obtained using the 3D High Frequency Structure Simulator (HFSS) software are compared with the values obtained from the lumped equivalent circuit model shown in Fig. 2.23. Figures 2.24 and 2.25 show the comparison for the scattering parameter magnitudes and phase for a 50–70–70  T-Junction discontinuity. Excellent agreement is observed between the two results.

2.2.3 Design Data on Discontinuities in Membrane Coplanar Lines From the studies on the transmission lines, it was observed that in order to have single mode operation up to Ka-band, it is essential to use coplanar waveguide on Si-substrate with air-cavity placed on low dielectric constant substrate as shown in Fig. 2.26. The design data on discontinuities in membrane coplanar waveguide was

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Fig. 2.24 Comparison of magnitudes of S-parameters obtained using the 3D Finite element software (HFSS) with those obtained using the lumped equivalent circuit model

therefore generated for this structure. Gap in the center conductor Symmetrical series gap in the center conductor of the membrane coplanar waveguide can be modeled as a lumped pi-network of capacitors as shown in Fig. 2.27. Coupling capacitor C 1 seems to be a strong function of series gap and aspect ratio, while fringing capacitors follows a weak function of the same. Same procedure as reported earlier for the membrane microstrip was followed to obtain S-parameters and equivalent circuit parameters of the gap discontinuity in membrane coplanar waveguide. Tables A.13, A.14, A.15, A.16, A.17, A.18, A.19, A.20, A.21, A.22, A.23, A.24, A.25, A.26 and A.27 give the data on S-parameters obtained for various gap widths in the Appendix A. To obtain values of series and shunt capacitors in the equivalent circuit, first, de-embedded port S-parameters with reference to the center of the series gap are obtained. Next, circuit simulator Agilent Advanced Design System (ADS) is used to compute the capacitor values in the pi- equivalent model. Figures 2.28, 2.29 and 2.30 show typical variations of the gap equivalent circuit parameters of membrane coplanar waveguide as a function of gap width. As gap width is increased, the series

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Fig. 2.25 Comparison of phase of S-parameters obtained using the 3D Finite element software (HFSS) with those obtained using the lumped equivalent circuit model

Fig. 2.26 Grounded coplanar waveguide on Si-substrate with air cavity placed on low dielectric constant substrate

gap capacitance decreases whereas the shunt gap capacitance slightly increases. The value of shunt capacitor is small as compared with the series capacitor. Step in the center conductor The Step Junction discontinuity layout is shown in Fig. 2.31a. This discontinuity

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Fig. 2.27 Layout and equivalent lumped element model of series gap discontinuity in membrane coplanar waveguide

Fig. 2.28 Equivalent circuit parameters of series gap discontinuity in membrane CPW, s = 70 μm

structure in membrane coplanar waveguide shown in Fig. 2.26 was analyzed using Full Wave FEM solver. First the scattering parameters of the above structure are obtained with reference to the port locations. These are then de-embedded to the reference plane PP. The simulated S-parameters of the step discontinuity in membrane CPW are given in Tables A.28, A.29, A.30, A.31, A.32 and A.33 in the Appendix A. Figure 2.32 shows comparison of reflection coefficient of the step discontinuity computed using HFSS with the results obtained from the stepped impedance model shown in Fig. 2.31b using ADS. The results indicate that step junction in CPW has little effect over the frequency band under consideration. Figure 2.33 shows a better model for the CPW step-junction discontinuity. The model consists of a shunt capacitor with small transmission lines of characteristic impedances as that of port impedances at both sides. The de-embedded S-parameter data was used to obtain the values of capacitor C1 and also line lengths l 1 and

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Fig. 2.29 Equivalent circuit parameters of series gap discontinuity in membrane PW, s = 110 μm

Fig. 2.30 Equivalent circuit parameters of series gap discontinuity in membrane PW, s = 160 μm

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Fig. 2.31 Step junction discontinuity: a layout and b impedance model in membrane CPW

Fig. 2.32 Comparison of results from HFSS and ADS using simple model shown in Fig. 2.31b

Fig. 2.33 Accurate model of CPW step-junction discontinuity

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Fig. 2.34 Comparison of magnitudes of S-parameters obtained using the 3D finite element software (HFSS) with those obtained using the lumped equivalent circuit model

l 2 . Table A.34 in Appendix A gives the values of the equivalent circuit parameters obtained for several step widths. To validate the model, the S-parameters obtained using the 3D Finite element software (HFSS) are compared with the values obtained from the lumped equivalent circuit model shown in Fig. 2.33. Figures 2.34 and 2.35 show the comparison for the scattering parameter magnitude and the phase. Reasonably good agreement is obtained between the two results.

2.2.4 Tee-Junction Discontinuity The layout of the symmetric Tee-junction discontinuity in membrane CPW is shown in Fig. 2.36. To analyze CPW T-junction discontinuity shown in Fig. 2.36, first we need to analyze the CPW Line with a metal bridge, connecting the two grounds as shown in Fig. 2.37a, b. The dimensions of the bridge (specially the height g) are chosen such that the bridge provides a ground connection and does not affect transmission and reflection coefficients of the line significantly. Here the analysis is done for the variation of width of the bridge, keeping the height of the bridge to be 10 microns and the thickness of the bridge to be 1 micron. It was found that as the width of the bridge increases, transmission coefficient decreases, as shown in Table A.35 in the Appendix A. The effect is insignificant and for all practical purposes it can be neglected. Figure 2.38a, b shows the layout of the CPW T-junction showing de-embedded

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Fig. 2.35 Comparison of phase of S-parameters obtained using the 3D Finite element software (HFSS) with those obtained using the lumped equivalent circuit model

Fig. 2.36 Layout of symmetric T-junction in CPW

port location and the metal bridge location. For various T-junctions, S-parameters were obtained using High Frequency Structure Simulators and these S-parameters were de-embedded to the reference planes shown in Fig. 2.38a, b. Tables A.36, A.37, A.38, A.39 and A.40 in Appendix A give the de-embedded scattering parameters of various T-junctions in CPW.

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Fig. 2.37 a CPW line with metal bridge and b bridge dimensions

Fig. 2.38 a CPW T- junction showing de-embedded ports and b bridge dimensions

A possible equivalent circuit of the T-junction discontinuity in CPW is shown in Fig. 2.39. The de-embedded S-parameter data was used to obtain the values of capacitor C1 , inductance L1 also line lengths at each port. The transformer ratio n turned out to be 1 in all cases. Table A.41 gives the values of the equivalent circuit parameters obtained for several T-junctions, in the Appendix A. To validate the model, the S-parameters obtained using the 3D Finite element software are compared with the values obtained from the lumped equivalent circuit model shown in Fig. 2.39. Figure 2.40 shows the comparison for the scattering param-

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Fig. 2.39 Equivalent circuit of T-junction discontinuity in CPW structure shown in Fig. 2.26

eter magnitudes and phase for a 50–50–50  T-Junction discontinuity. Excellent agreement is observed between the two results.

2.3 Micromachined Varactors The Micro-electromechanical Systems (MEMS) technology is primarily used to develop miniaturized, and high-quality factor (Q) frequency selective circuits. HighQ devices are fundamental for different passive and active circuits and can substantially reduce the phase noise or power consumption of oscillators and amplifiers [1]. The Voltage Controlled Oscillator (VCO) at RF frequency is composed of the CMOS circuit and the LC tank in the conventional negative-gm topology. So, the capacitance changes in the MOS capacitor limit the tuning range and the operating frequency of the VCOs and the nonlinearity of the tuning devices degrade the phase noise of the RF VCOs [2]. The MEMS tuneable capacitors have been shown to give adequate quality factor when they are fabricated using either aluminium or silicon or gold surface micromachining technology. These devices are expected to offer an excellent linearity since they do not respond to high frequencies outside their mechanical resonance frequencies [3]. The tunability of the VCOs depends on the tuning range of the capacitors in the tank circuits. Lesson’s formula of phase noise of a VCO describes the inverse square relationship between phase noise and Q- factor of the tank circuit [4]. From that, it is evident that phase noise performance can be improved by increasing the Q-factor of the tank circuit. Since on-chip inductors do

42

2 Micromachined Microwave Passive Circuits

Fig. 2.40 Comparison of S-parameters obtained using the 3D Finite element software with those obtained using the lumped equivalent circuit model (50–50–50  CPW T-junction) where a magnitude and b phase

2.3 Micromachined Varactors

43

not give very high Q values, Q-factor of the varactor device needs to be increased. On-chip MOS varactors are very difficult to realize with low phase noise and highquality factor that can sustain wide process and temperature variation [5]. MEMS based varactor is therefore good replacement of the on-chip MOS varactors in this regard. Due to low loss, MEMS varactor possesses the property of very high Q values and is capable of withstanding wide process and temperature variation. In addition, conventional micro-machined tuneable capacitors [6] are not expected to respond to RF frequencies in the 1–2 GHz range especially since their mechanical resonant frequencies normally lie in the 10–100 kHz. Therefore, with RF frequencies 10,000 times the mechanical bandwidth, these devices are unlikely to produce a significant amount of harmonic content [7]. The main limitation of these devices, however, has been the fact that their tuning ranges thus far have been less than the theoretical calculations suggested [8]. In this paper, design optimization and simulation of two parallel plates variable capacitor for VCO application using the method of electrostatic actuation is presented. Suspension beams have been optimized for 3.3 V VCO power supply. The working principal is derived from changing the gap between two parallel plates using electrostatic actuation, one is fixed on the substrate and other one is suspended with four T-shaped suspension beams. This Section presents design and modelling of a micromachined varactor. Later, other different types of varactors are also outlined.

2.3.1 Modelling and Design Optimization The Micro-electromechanical Systems (MEMS) technology is primarily used to develop Electromechanically tunable capacitor consists of two parallel plates, four T-shaped suspension beams to suspend the top plate as shown in Fig. 2.41. The top plate is pulled down to bottom plate with electrostatic force. The dynamics of an electromechanical two plate varactor can be expressed by (2.1) [1] m

1 dcd (t) 2 d x(t) d 2 x(t) + kx(t) = V1 (t) +b dt 2 dt 2 dx

(2.1)

where m is the mass of the suspended plate, b is the mechanical resistance, k is the effective spring constant, C d is the desired capacitance and V 1 is the applied electrostatic potential between two parallel plates. The current flowing through the desired capacitance is given by (2.2) [1] i(t) = Cd (t)

dv1 (t) dCd (t) + V1 (t) 2 dt dt

(2.2)

The suspended plate moves towards the fixed plate until a point of instability occur where electrostatic force become exactly equal to the spring restoring force,

44

2 Micromachined Microwave Passive Circuits

Fig. 2.41 Schematic illustration of variable capacitor on substrate [9]. Reproduced with courtesy of the ISSS

corresponding to 50% capacitance increase. The equilibrium between the forces can be written mathematically as given by (2.3). kx =

1 εd AV12 1 dcd 2 V1 = − 2 dx 2 (d1 − x)2

(2.3)

where x is the displacement under dc condition, εd is the dielectric constant of air (εd = εair ε0 , where εair = 1.00054 and ε0 = 8.854 × 10–12 F/m), A is the overlapping area of two parallel plates, and d 1 is the separation of the capacitor plates when spring is in its relaxed state. In theory, the suspended plate can be pulled down at most by 1/3 of the original gap, so the maximum capacitance that can be tuned to is 3Cd /2, and maximum theoretical tuning range would be 1.5:1 as shown in (2.4). Tuning Ratio (TR) =

ε A/(2x/3) Cmax = 1.5 = Cmin ε A/x

(2.4)

Incorporating a worst-case-scenario fringing capacitance (C f ) of 40% of Cmax as indicated in [10], the value of capacitance tuning ratio is obtained as given by (2.5) TR=

Cmax + 0.4Cmax , since Cmax =1.5Cmin Cmin + 0.4Cmax

(2.5)

A semi-analytical model of the pull-in voltage can be obtained from [6] which calculate the total potential energy content of a fixed–fixed beam subject to electrostatic actuation without considering the fringing field effects, and then a correction factor is applied to account for the fringing field effects. The first-order fringing field effects have been approximately compensated by an effective beam width. Following [11], the pull-in voltage can be obtained as given in (2.6) [7],

2.3 Micromachined Varactors

 VPI =

45

 1  × 1 + 0.65 wx

c1 Eh 3 x 3 c2 (1 − ν)x 2 hσ0 + ε0 l 4 ε0 l 2

(2.6)

The constants c1 = 11.7 and c2 = 3.6, E is the Young’s modulus and υ is the Poisson’s ratio, x is the gap between the two parallel plate, l and h is the beam length and width respectively, w is the thickness of the beam and ε0 is the permittivity of free space. C 0 is the original capacitance without applying voltage or RF signal, K m the effective spring constant of the four T-shaped beams, which can be written as (2.7) K m = 4K eq , K eq =

k1 + 2k2 Ewi Ti , ki = k1 + 2k2 L i3

(2.7)

K eq is the equivalent spring constant of each T-shaped beams, L i , W i and T i are the length, width and thickness of the beams and E is the Young Modulus of the material.

2.3.2 Quality Factor Analysis In theory, Various sources of loss can affect the quality factor at high frequency. In our design two plates varactor is modelled with conductive and resistive plates. This is justified in our case where top plate is deposited with gold and bottom plate is made up with gold coated with silicon-dioxide. The expression of the quality factor of varactor obtained from the input admittance of the varactor, is given by (2.8) [4] √     ωτ  sin 2ωτ + 2 cos ωτ 2 2 Q+1 √  =   ωτ   ωτ Q−1 cos sinh 2ωτ + 2 sinh 2 2 sin

(2.8)

where τ is the time constant of the varactor that is expressed by (2.9) τ = RP CD

(2.9)

Here, RP is the resistance of the resistive plate (i.e., sheet resistance for a square plate capacitor) and C D is the total capacitance between the two parallel plates, Ñ is the operating frequency in radian. Since losses due to interconnect and the substrate parasitic are not considered in our design, the expression presented above represents the maximum theoretically achievable Q-factor. The above expression represents the maximum theoretically achievable Q-factor since losses due to the interconnect are not considered. At 1.9 GHz, and 2.4 GHz the calculated Q-factors are 460 and

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2 Micromachined Microwave Passive Circuits

381respectively, which suggests that a high-factor can be achieved in this process. The fabrication process details are given in Appendix B.

2.3.3 Electro-Mechanical Modelling of the Varactor with Parametric Optimization The varactor structure, as shown in Fig. 2.41 consists of a centrally placed rectangular gold proof-mass which is suspended with four symmetrically placed Tshaped suspension gold beams; two are on one side and two on other. All beams are rigidly clamped from two fixed walls on each side. Also, there is a gold electrode placed underneath the proof-mass along with dielectric layer; with an air gap of 2.5 μm. The behavioural analysis and electromechanical modelling are carried out in Coventorware platform. To realize the MEMS varactor model in Saber software, parallel conductor plates and clamped beams have been clubbed together and assigned with a particular point as knot in the 3- dimensional space as shown in Fig. 2.42.

Fig. 2.42 System model of the MEMS varactor in saber, [9]. Reproduced with courtesy of the ISSS

2.3 Micromachined Varactors

47

Fig. 2.43 SEM image of T-shaped suspension beam, [9]. Reproduced with courtesy of the ISSS

In this design, T-type suspension beam is modelled to operate the varactor with 3.3 V DC power supply. The varactor can be used in LC tank circuit in the VCO with this applied voltage at RF frequencies. A T-shaped suspension beam is used in the varactor as shown in Fig. 2.43. The lever length (l l ) and lever width (l w ) of the RF MEMS two plate varactor has been optimized with lumped parameter modelling. ll is varied from 60 to 120 μm and lw is varied from 20 to 50 μm in steps of 10 μm. Small signal ac analysis, pull-in voltage and capacitance variations are carried out through lumped parameter modelling in saber platform and verified with FEM based simulation as shown from Figs. 2.44, 2.45, 2.46, 2.47, 2.48, 2.49, 2.50 to 2.51. FEM-based simulation (Fig. 2.46) shows that point of instability occurs exactly 1/3 of gap (0.833 μm) from top (2.5/3) with a voltage of 3 V. Furthermore, analytical pull-in voltage of 3.8 V is obtained from (2.6), after parametric optimization. Fundamental mode of vibration of varactor is 3.24 kHz (Fig. 2.48) after parametric optimization. Pull-in voltage is set to 3.3 V after the parametric variation. Tuning Ratio (TR) of this varactor is set to 1.433 after optimization as shown in Fig. 2.51. So, 80 μm lever length and 20 μm lever width has been chosen for our design to actuate the varactor with 3.3 V. Final design parameter of the varactor is listed in Table 2.1. Material Properties of fabricated MEMS varactor is tabulated in Table 2.2. Fabrication details are stated in Appendix B.

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Fig. 2.44 Pullin voltage analysis with parametric variation of Lever length (l l ) where lever width (l w ) is 20 μm [9]. Reproduced with courtesy of the ISSS

2.3.4 Testing and Characterization of the Micromachined Varactor The scanning electron microscopic (SEM) image of the micromachined varactor is shown in Fig. 2.52. The mechanical and electrical tests have been performed on the varactor to examine the characteristics of the structure. Voltage actuation method has been used to detect the mechanical vibrations of the varactor. Small signal frequency sweep has been imposed over a dc actuation voltage to observe the frequency response of the structure. The out-of-plane vibration amplitude response is recorded for the frequencies of the signal. Polytec made Laser Doppler Vibrometer (LDV) is used to detect the displacement of the structure in the out of plane direction. The LDV uses Doppler frequency shift method to calculate displacement due to external excitation at the point where the laser pointer is focused. The first mode of vibration of the structure is captured at 1.475 kHz as depicted in Fig. 2.53. The variation of capacitance with actuation voltage of the structure has been performed using a DC probe station manufactured by Sus-Microtec, DC voltage source and a LCR meter manufactured by Agilent. To measure the C-V characteristics, the bottom fixed plate of the varactor is grounded and the required voltage sweep from 0 to 2.5 V is applied to the top suspended electrode using the probes. A small AC signal of 5 MHz has been imposed on the.

2.3 Micromachined Varactors

49

Fig. 2.45 Pullin voltage analysis with parametric variation of Lever width (l w ) where lever length (l l ) is 100 μm [9]. Reproduced with courtesy of the ISSS

DC actuation voltage to measure the capacitance. Open circuit offset measurement corrections are made before recording the capacitance values. The capacitance of the varactor with change in voltage was observed and plotted by the LCR meter as shown in Fig. 2.54. The steps in the measured capacitance value are due to asymmetry of the suspended electrode actuation over the fixed bottom electrode. The asymmetry is due to initial deformation of the top plate along with the bending motion of the T-shaped suspension beam. From the measured capacitances, the minimum and maximum capacitances available from the device are 0.86 pF and 0.896 pF respectively. The measured capacitances tuning ratio of the varactor is about 1.06:1 (6%). The measured tuning ratio of the experimental devices are lower than the designed values. Parasitic capacitance of the pads (Ground-Signal-Ground) along with the substrate capacitance effects the tuning range significantly which was not considered during simulation. Furthermore, residual stress in the suspended plate produces warping of the capacitor plates, which effectively results in a different plate separation and, thus, a different parallel-plate capacitance, which leads to effect on tuning ratio. Moreover, measurement is carried out in air ambient condition where air is used as a dielectric for the tunable capacitor, its properties as a function of pressure, temperature, and humidity must be examined. The tunable capacitor may be operated in vacuum, which resolves many issues that can arise when air is used as a dielectric. For example, the mechanical resistance

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2 Micromachined Microwave Passive Circuits

Fig. 2.46 Variation of gap with applied bias; lever length = 80 μm and lever width = 20 μm. a SABER based. b FEM based simulation [9]. Reproduced with courtesy of the ISSS

2.3 Micromachined Varactors

51

Fig. 2.47 Fundamental mode of vibration of RF MEMS varactor with 80 μm lever length and 20 μm lever width [9], with reproduced courtesy of the ISSS

Fig. 2.48 Capacitance variation with lever length (l l ) where lever width (l w ) is 20 μm [9]. Reproduced with courtesy of the ISSS

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2 Micromachined Microwave Passive Circuits

Fig. 2.49 Capacitance variation with lever width (l w ) where lever length (l l ) is 80 μm [9]. Reproduced with courtesy of the ISSS

Fig. 2.50 Variation of tuning ratio (TR) with the optimization of lever width (l w ) [9]. Reproduced with courtesy of the ISSS

2.3 Micromachined Varactors

53

Fig. 2.51 Capacitance variation with applied bias with 80 μm lever length and 20 μm lever width [9]. Reproduced with courtesy of the ISSS Table 2.1 Dimensions of two plate varactor

Table 2.2 Material properties of fabricated MEMS varactor

No

Two plate varactor Parameter

Dimensions (μm)

1

Substrate

700 × 700 × 625

2

Actuation electrode

350 × 250 × 1

3

Dielectric

370 × 270 × 0.5

4

Proof mass

350 × 250 × 1.25

5

Beam

80 × 20 × 1.25

6

Air gap

2.5

7

Number of beams

4

No 1

Young modulus of gold

45 GPa

2

Conductivity of gold

4.1 e7 S/m

3

Sheet resistance of bottom gold electrode 0.025 /square

4

Sheet resistance of top gold electrode

0.02 /square

5

Poisson ratio of gold

0.4

6

Density of gold

19300 kg/m3

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2 Micromachined Microwave Passive Circuits

Fig. 2.52 Micro-fabricated image of the micromachined varactor [9]. Reproduced with courtesy of the ISSS

Fig. 2.53 First mode of vibration of the micromachined varactor [9]. Reproduced with courtesy of the ISSS

can be dramatically reduced, and hence the mechanical Q-factor can be significantly improved when the tunable capacitor is placed in vacuum. In addition, the mechanical noise due to the thermal agitation of air molecules can be reduced as mechanical resistance is reduced. Note that, there is no dielectric breakdown in vacuum. Loss measurement of the varactor is carried out using Vector Network Analyser (VNA). The measured varactor is connected in series path of transmission line. Return

2.3 Micromachined Varactors

55

Fig. 2.54 Measured capacitance variation with applied voltage, Circle indicates pull-in point at 3.3 V. [9]. Reproduced with courtesy of the ISSS

loss better than 18.17 dB and 16.46 dB with insertion loss of 0.77 dB and 0.83 dB are obtained at 1.9 GHz and 2.4 GHz respectively, as shown in Fig. 2.55a, b. Return loss and insertion loss values are given at two different oscillation frequencies of the VCO; 1.9 and 2.4 GHz. Quality factor is obtained from measured S-parameter data (S 11 ) as given in (2.10). Q=

2|Im(S11 )| 1 − |S11 |2

(2.10)

Variation of Quality factor with frequency is shown in Fig. 2.56 which is obtained from (2.10) with measured return loss data. A comparison between RF-MEMS and semiconductor-based variable capacitors (varactors) is shown in Table 2.3. A few more similar types of varactors are shown in Fig. 2.57.

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2 Micromachined Microwave Passive Circuits

Fig. 2.55 a Return loss. b Insertion loss. Circles indicate return loss and insertion loss values at 1.9 and 2.4 GHz [9]. Reproduced with courtesy of the ISSS

2.4 Micromachined Inductors

57

Fig. 2.56 Variation of quality factor with frequency, circles indicate quality factor value at 1.9 GHz = 360 and at 2.4 GHz = 280 [9]. Reproduced with courtesy of the ISSS

Table 2.3 Performance and characteristics comparison between micromachined and solid state varactors No Varactor CMOS varactors

Micromachined varactors

1

Leakage currents

No significant leakages

2

Typical Q-factor of 30–40, in a few cases up Typical Q-factor of 200–300 to 50–60

3

Decreasing tuning range (Cmax /Cmin ) due to Tuning ranges typically spanning between 5 continuous downscaling. Maximum ratio of and 50 about 3 in the millimetre-wave range

4

Rather lossy in the millimetre-wave range

Always low-loss

2.4 Micromachined Inductors Micromachined inductor is one of the critical passive elements together with the varactors, in the realization of radio frequency filters, resonators, impedance matching networks, and so on. One of the most important features an inductor should present is a very high Q-factor, and MEMS technology enables improvement of this.

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2 Micromachined Microwave Passive Circuits

Fig. 2.57 SEM images of different meander line-based varactors [9]. Reproduced with courtesy of the ISSS

RF inductors are needed in wireless front-end circuitry; the performance of both transceivers and receivers depends heavily on this component. High-Q inductors reduce the phase noise and the power consumption of VCO’s, self-adjusting matching networks or power amplifiers and reduce the return loss of matching networks and filters. The quality factor of inductors can be increased by using a thick metal layer [12, 13] and by isolating the inductor from the substrate [10, 14, 15]. To isolate the inductor, bulk micromachining [10, 13–16] or self-assembly techniques [11, 17] can be used. Further, tunable inductors allow for performance optimization of RF front-end circuits. To date, there has not been a practical implementation of a highQ tunable inductor. Most of the reported micromachined inductors are static, fixed value inductors. One variable inductor using MEMS switches has been reported in [18]. In general, tunable capacitors have better tuning range and quality factor (Qfactor) than tunable inductors. However, the tunability of the tunable inductors provides additional functionality, design flexibility and robustness, which make the tunable inductors promising for applications in the field of portable communication systems. Tunable inductors can be divided into four categories: discrete-tuned (DT), metal shielding-tuned (MST), magnetic core-tuned (MCT) and coil-coupled-tuned (CCT). The discrete-tuned inductor often uses micro-switches [19–22] or microrelays reported in [22, 23] to increase or decrease the effective coil length of the inductor, but the combination of the micro-switches or micro-relays will reduce the

2.4 Micromachined Inductors

59

Fig. 2.58 3D schematic of the RF micromachined spiral inductor [9]. Reproduced with courtesy of the ISSS

Q-factor of the inductor. The metal shielded tuned inductor is realized using moveable metal structure with large range, resulting in the change in magnetic flux of the inductor [24]. The magnetic core-tuned inductor is realized using a solenoid inductor embedded with magnetic-core conductor, whose permeability can be changed by applying a magnetic field [25, 26]. The coil-coupled-tuned inductor mainly adjusts its mutual inductance between the primary coil and the secondary coil of the inductor [27–29]. A schematic view of the inductor is shown in Fig. 2.58. The centre of the spiral coil is connected to the output by means of an overpass, that is, a suspended metallization, which makes it possible to cross all the windings and bring the RF signal to the output. The Q-factor of MEMS inductors can be increased by choosing a low-loss substrate, such as alumina, as reported in [30], as well as by reducing the coupling of the inductor windings with the substrate by depositing a good insulating layer in between them [31]. Using such solutions, improvements of the Q-factor from 5–10 up to 40–70 have been experimentally demonstrated. However, MEMS technology also enables other solutions at manufacturing level that significantly reduce the losses of inductors and, in turn, enhance the Q-factor. Such solutions consist of having the metal inductor coil suspended above an air layer rather than lying on silicon [32]. The inductance of such a component can be approximated with the formula for a square loop inductor proposed in [33]; L  N2

 W 2W μ0 μair [ln − 0.77401] π r

(2.11)

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2 Micromachined Microwave Passive Circuits

Cs

Ls

C1 CP1

(a)

Rs

Rp1

CP2

C2 RP2

(b)

Fig. 2.59 a Micro-photograph of an micromachined suspended square loop inductor and b equivalent circuit model [9]. Reproduced with courtesy of the ISSS

where N is the number of turns, W the width of the coil external square, μ0 μair the magnetic permeability of air, and r the radius of the suspended coil metallization. Micro-photograph of an micromachined suspended square loop inductor is depicted in Fig. 2.59a. Equivalent circuit model of the inductor is shown in Fig. 2.59b where L s is the low-frequency inductance, Rs is the series resistance of the coil, C s is the capacitance between the different windings of the inductor and includes the fields in air and in the supporting dielectric layers, C 1 is the capacitance in the oxide (or polyamide) layer between the coil and the silicon (or GaAs) substrate, C p is the capacitance between the coil and the ground through the silicon substrate, and Rp is the eddy current losses in the substrate. This model has been used extensively by industry and academic labs, and it has been proven to fit very well with Y- and S-parameter measurements of planar inductors [1]. Micro-photograph of different micromachined inductor with the coil suspended in air realized with surface micromachining process is shown in Fig. 2.60. All these inductors were fabricated using the PolyMumps foundry process and related process details can be found in [34].

2.5 Micromachined RF Power Divider and Coupler Radio frequency (RF) power dividers/combiners and directional couplers are key elements in modern communication systems, including beam-forming networks [35], power control amplifiers [36], multiple-input/multiple-output (MIMO) systems, and adaptive antenna feedback mechanisms, which are getting more and more common to achieve high data throughput at limited power [37]. A directional coupler is a multi-purpose passive device used for sampling, splitting, combining, or isolating signals. Directional couplers are one of the most often used components in microwave circuits [38]. The directivity of a directional coupler, the ratio between the output

2.5 Micromachined RF Power Divider and Coupler

61

Fig. 2.60 Micro-photograph of different micromachined inductors fabricated using the PolyMumps foundry process [9]. Reproduced with courtesy of the ISSS

power on the coupled and the isolated port, is an important measure of its quality [38], besides its insertion loss. However, it is difficult to realize integrated directional couplers with high directivities [38] and typically directivity between 15 and 20 dB is obtained for tunable couplers operating between 1 and 10 GHz frequency [36, 39]. Directional couplers that are designed for high directivity unfortunately exhibit poor bandwidth characteristics [40]. With the recent advent of multi-standard frontends in modern telecommunication systems [41], directional couplers capable of operating with different frequency bands [40, 42] and with tunable coupling ratio [43, 44] are of particular interest for future reconfigurable architectures. The tuning range of the coupling ratio is usually limited to only a few decibels [45]. When tuned beyond this coupling ratio range, the input matching and directivity degrade drastically. The directional coupler in [46] tries to overcome these problems but falls short in terms of bandwidth. Thus, novel concepts are required where the input matching and directivity is maintained while the coupling ratio is tuned over a large, for instance, 10 dB, range. Previous attempts of tunable couplers consist of monolithic microwave integrated circuit (MMIC)-based active couplers [39, 47, 48] and varactor diode based passive couplers [45–47, 49, 50], and are predominantly designed for operation below 8 GHz.

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2 Micromachined Microwave Passive Circuits

Micromachining has gained considerable interest for reconfigurable/tunable circuits for frequency-agile front-end applications, due to their near-ideal signal handling behavior, ultra-low power consumption, low loss, large bandwidth, and the potential of low-cost production and easiness of integration since fabrication is compatible to integrated circuits. A micromechanically tunable parallel-plate capacitor with electrostatic actuation design is easily implemented with standard surface micromachining thin-film technology [1]. MEMS fabrication technology has also proven to be very suitable for creating on-wafer 3-D micromachined transmission lines, which offer reduced substrate and radiation losses as compared to conventional coplanar or microstrip lines [51, 52]. Despite MEMS being known for creating very low-loss tuning mechanisms, there have been very few attempts of implementing MEMS-based tunable couplers. A MEMS power divider concept based on two cascaded hybrid couplers is presented in [53]. This power divider is made on high resistivity silicon substrate with variable power ratio. The circuit is based on two cascaded hybrid couplers connected through a tunable phase shifter that produces the required power ratio. A prototype is fabricated on a 525 μm high resistivity silicon substrate employing two 3 dB branch line couplers and a reflection-line MEMS phase shifter. Later, it is reconfigured through two MEMS-switched open-ended lines, whose lengths can be varied through the actuation of eight ohmic contact MEMS switches. Measurements of the MEMS switch show an isolation and an insertion loss better than 15 dB and 0.2 dB, respectively, with a contact resistance lower than 1  in the entire power divider bandwidth. RF measurements of the power divider exhibit a return loss better than 16 dB and an isolation better than 17 dB over 11.8–12.2 GHz with nominal power ratios of 1:0, 6:1, 1:1, 1:6, and 0:1. A schematic and microscopic image of the fabricated circuit is shown in Fig. 2.61a, b, respectively.

Fig. 2.61 a Schematic of the power divider and b micro-photograph of micromachined reconfigurable power divider [53]. Reproduced with permission from the IEEE

2.5 Micromachined RF Power Divider and Coupler

63

Fig. 2.62 a Illustration of Concept 1, an ultra-wideband coupled line directional coupler based on geometrically tuning of the signal-to-ground coupling of the coupled lines and b Illustration of Concept 2, an ultra-wideband coupled line directional coupler based on geometrically tuning of the signal-to-ground coupling simultaneously with the signal-to-signal line coupling [54]. Reproduced with permission from the IEEE

This concept occupies a very large area. Coupled line directional couplers, on the other hand, can be designed much more space efficient, and to our knowledge, thus far only one research paper has reported on a MEMS-switched coupled line directional coupler concept [55]. Two novel concepts of area-efficient ultra-wideband micromachined reconfigurable coupled line directional couplers have been reported, whose coupling is tuned by mechanically changing the geometry of 3-D micromachined coupled transmission lines, utilizing integrated MEMS electrostatic actuators [54]. Two concepts were reported in [54] and illustration of these concepts are depicted in Fig. 2.62a, b. Concept 1 is based on symmetrically changing the geometry of the ground coupling of each signal line, while Concept 2 is simultaneously varying both the ground coupling and the coupling between the two signal lines. This enables uniform and well predictable performance over a very large frequency range, in particular a constant coupling ratio while maintaining an excellent impedance match, along with high isolation and a very high directivity. For an implemented micromachined prototype 3–6 dB coupler based on Concept 1, the measured isolation is better than 16 dB, and the return loss and directivity are better than 10 dB over the entire bandwidth from 10 to 18 GHz. Concept 2 presents an even more significant improvement. The directional coupler is fabricated using single mask silicon-on-insulator (SOI) process reported in [54]. Microfabricated image of the fabricated ultra-wideband coupled line directional coupler (concept 1 and concept 2) are shown in Fig. 2.63a, b. For an implemented 10–20 dB prototype based on Concept 2, the measured isolation is better than 40 dB and the return loss is better than 15 dB over the entire bandwidth from 10 to 18 GHz for both the states. The directivities for both states are better

64

2 Micromachined Microwave Passive Circuits

Fig. 2.63 SEM photographs of fabricated MEMS-tunable coupled line directional coupler of a concept 1 and b concept 2 [54]. Reproduced with permission from the IEEE

2.5 Micromachined RF Power Divider and Coupler

65

than 22 and 40 dB, respectively, over the whole frequency range. The measured data fits the simulation very well, except for higher through-port losses of the prototype devices and it can be found in more details in [54]. On the other hand, several examples of microwave and RF couplers entirely realized in RF MEMS technology are also available in literature. Two significant prototypes are discussed in [56–58], concerning the CPW and microstrip configurations, respectively.

2.6 Conclusions This Chapter presents different types of micromachined RF passive components. A detailed analysis on the conductor backed CPW on Si-micromachined substrate is presented. Extensive design data on effective dielectric constant and characteristic impedance for CBCPW line on Si-micromachined substrate, and lumped circuit models of discontinuity structures are discussed up to a reasonable extent. The data presented in this section should be useful in designing circuits using micromachined CBCPW lines at microwave and millimeter wave frequencies in the current era of Si-micromachining. Later, comprehensive design details of micromachined varactor are discussed. The main emphasis is to design a varactor with a fixed actuation voltage like 3.3 V for a specific application like VCO. Next, different varieties of micromachined inductors are discussed with special attention on spiral inductor. Finally, micromachined power divider and couplers are discussed with more focus on the reconfiguration which is one of the advantages in micromachining technology. A wide range of references are given against each section and readers may find it useful for better understandings.

References 1. Rebeiz GM (2003) RF MEMS theory, design and technique (book). Wiley 2. Dec A, Suyama K (2000) Microwave MEMS-based voltage-controlled oscillators. IEEE Trans Microw Theory Tech 48(11):1943–1949 3. Dec A, Suyama K (1998) Micromachined electro-mechanically tunable capacitors and their applications to RF IC’s. IEEE Trans Microw Theory Tech 46(12):2587–2596 4. Dec A, Suyama K (1998) RF micromachined varactor with wide tuning range. IEEE RFIC Symp Dig 1:309–312 5. Nieminen H, Ermolov V, Silanto S, Nybergh K, Ryhanen T (2004) Design of a temperaturestable RF MEM capacitor. IEEE J Microelectromech Syst 13(5):705–714 6. McCorquodale MS, Ding MK, Brown RB, A CMOS voltage-to-frequency linearizing preprocessor for paralie1 plate RF MEMS varactors. In: IEEE radio frequency integrated circuits symposium, pp 535–538 7. O’Mahony C, Hill M, Duane R, Mathewson A (2003) Analysis of electromechanical boundary effects on the pull-in of micro-machined fixed-fixed beams. J Micromech Microeng 13(4):75–80 8. Fedder G, Mukherjee T (2005) Tunable RF and analog circuits using on-chip MEMS passive components. In: Proceedings of the ISSCC, pp 390–391

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9. Dey S, Koul SK (2012) Design, fabrication and characterization of RF MEMS varactor for VCO application. Springer J Struct Syst 1:1–10 10. Ribas RP, Lescot J, Leclercq J-L, Karam JM, Ndagijimana F (2000) Micromachined microwave planar spiral inductors and transformers. IEEE Trans Microw Theory Tech 48(8):1326–1335 11. Lubecke VM, Barber B, Chan E, Lopez D, Gross ME, Gammel P (2001) Self-assembling MEMS variable and fixed RF inductors. IEEE Trans Microw Theory Tech 49(11):2093–2098 12. Pinel S, Cros F, Nuttinck S, Yoon S-W, Allen MG, Laskar J (2003) Very high-Q inductors using RFMEMS technology for system-on-package wireless communication integrated module. In: IEEE MTTS digest, pp 1497–1500 13. Chang JY-C, Abidi AA, Gaitan M (1993) Large suspended inductors and their use in a 2 μm CMOS RF amplifier. IEEE Electron Device Lett 14:246–248 14. Lakdawala H, Zhu X, Luo H, Santhanam S, Carley LR, Fedder GK (2002) Micromachined high-Q inductors in a 0.18 μm copper interconnect low-K dielectric CMOS process. IEEE J Solid-State Circ 37(3):394–403 15. Jiang H, Wang Y, Yeh J-LA, Tien NC (2000) On-chip spiral inductors suspended over deep copper lined cavities. IEEE Trans Microw Theory Tech 48(12):2415–2422 16. Yoon J-B, Kim B-I, Choi Y-S, Yoon E (2003) 3-D construction of monolithic passive components for RF and microwave ICs using thick-metal surface micromachining technology. IEEE Trans Microw Theory Tech 51(1):279–288 17. Dahlmann GW, Yeatman EM, Young PR, Robertson ID, Lucyszyn S (2001) MEMS high Q microwave inductors using solder surface tension self-assembly. In: IEEE MTT-S international microwave symposium digest, pp 394–403 18. Chu W-H, Mehregany M, Mullen RL (1993) Analysis of tip deflection and force of a bimetallic cantilever microactuator. J Micromech Microeng 3:4–7 19. Park P, Kim CS, Park MG, Kim SD, Yu HK (2004) Variable inductance multilayer inductor with MOSFET switch control. IEEE Electron Device Lett 25(3):144–146 20. Pham KD, Okada K, Masu K (2005) On-chip variable inductor using MOSFET switches. In: 2005 European microwave conference, vol 2, pp 1–4 21. Lin Y-S, Liang H-B, Chen J-L, Chen K-H, Lu S-S (2005) Variable inductance planar spiral inductors and CMOS wideband amplifiers with inductive peaking. Microw Opt Technol Lett 47(4): 305–309 22. Balachandran S, Lakshminarayanan B, Weller T, Smith M (2004) MEMS tunable planar inductors using DC contact switches. In: The 34th European microwave conference, vol 2, pp 713–716 23. Zhou S, Sun X-Q, Carr MN (1997) A micro variable inductor chip using MEMS relays. In: Proceedings of the IEEE international conference on solid-state Sensors Actuators. Chicago, IL, pp 1137–1140 24. Tassetti CM, Lissorgues G, Gilles JP, Tunable RF (2003) MEMS microinductors for future communication systems. In: Proceedings of the 2003 SBMO/IEEE MTT-S international microwave and optoelectronics conference, IMOC 2003, pp 541–545 25. Salvia J, Bain JA, Yue CP (2005) Tunable on-chip inductors up to 5 GHz using patterned permalloy laminations. In: IEEE international electron devices meeting, 2005. IEDM Technical Digest, pp 943–946 26. Shih WP, Li Z, McCormick DT, Tien NC, Hui CY (2004) Tunable solenoid microinductors utilizing permalloy electro-thermal vibromotors. In: 2004 17th IEEE international conference on micro electro mechanical systems (IEEE-MEMS 2004), pp 793–796 27. Tassetti C-M, Lissorgues G, Gilles J-P (2004) Reconfigurable RF systems based on tunable MEMS inductors. In: Proceedings of the 34th European microwave conference, Amsterdam, The Netherlands, pp 1165–1168 28. Zine-El-Abidine I, Okoniewski M, McRory JG (2005) Tunable radio frequency MEMS inductors with thermal bimorph actuators. J Micromech Microeng 15:2063–2068 29. Zine-El-Abidine I, Okoniewski M, McRory JG (2005) RF MEMs tunable inductor using bimorph microactuators. In: Proceedings of international conference on MEMS, NANO and smart systems, pp 436–437

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30. Blondy P, Palego C, Houssini M, Pothier A, Crunteanu A (2007) RF-MEMS Reconfigurable filters on low loss substrates for flexible front ends, Munich, EuMA 31. Van Beek J, Van Delden M, Van Dijken A, Van Eerd P, Van Grootel M, Jansman A, Kemmeren A, Rijks T, Steeneken P, den Toonder J, Ulenaers M, den Dekker A, Lok P, Pulsford N, van Straten F, van Teeffelen L, de Coster J, Puers R (2003) High-Q integrated RF passives and micromechanical capacitors on silicon, Toulouse, IEEE 32. Mizuochi Y, Amakawa S, Ishihara N, Masu K (2009) Study of air-suspended RF MEMS inductor configurations for realizing large inductance variations, Bariloche, IEEE 33. http://www.technick.net/public/code/cp_dpage.php?aiocp_dp=util_inductance_square 34. PolyMUMPs foundry handbook. http://www.ee.usm.maine.edu/courses/ele402/MEMS-Art icles/Polymumps-Reference.pdf 35. Yeung LK, Wang YE (2009) Mode-based beamforming arrays for miniaturized platforms. IEEE Trans Microw Theory Techn 57(1):45–52 36. Madic J, Bretchko P, Zhang S, Shumovich R, McMorrow R (2003) Accurate power control technique for handset PA modules with integrated directional couplers. In: IEEE MTT-S international microwave symposium digest, pp A201–A204 37. Godara LC (1997) Application of antenna arrays to mobile communications, part II: beamforming and direction-of-arrival considerations. Proc IEEE 85(8):1195–1245 38. Zelder T, Lluch EV, Geck B, Rolfes I, Eul H (2008) Tunable directional coupler. In: Proceedings of the German microwave conference, pp 1–4 39. Hur B, Eisenstadt WR (2013) Tunable broadband MMIC active directional coupler. IEEE Trans Microw Theory Techn 61(1):168–176 40. Kim C-S, Park J-S, Ahn D, Lim J-B (2000) Variable directional coupler with LC resonator. Electron Lett 36(18):1557–1559 41. Rebeiz GM, Entesari K, Reines I, Park S-J, El-Tanani MA, Grichener A, Brown AR (2009) Tuning in to RF MEMS. IEEE Microw Mag 10(5):55–72 42. Kim C-S, Yoon C-S, Park J-S, Ahn D, Lim J-B, Yang S-I (1999) A design of the novel varactor tuned directional coupler. In: IEEE MTT-S international microwave symposium on digest, pp 1725–1728 43. Toyoda S (1982) Variable coupling directional couplers using varactor diodes. In: IEEE MTT-S international microwave symposium on digest, pp 419–421 44. Wang S-M, Chang C-Y, Lin J (2007) A software configurable coupler with programmable coupling coefficient. In: IEEE MTT-S international microwave symposium on digest, pp 185–188 45. Yeung LK (2011) A compact directional coupler with tunable coupling ratio using coupled-line sections. In: Proceedings of the Asia–Pacific microwave conference, pp 1730–1733 46. Lehmann T, Mextorf H, Knoechel R (2008) Design of quadrature directional couplers with continuously variable coupling ratios. In: Proceedings of the European microwave conference, pp 199–202 47. Abdalla MAY, Phang K, Eleftheriades GV (2008) A compact highly reconfigurable CMOS MMIC directional coupler. IEEE Trans Microw Theory Techn 56(2):305–319 48. Scheeler R, Popovi´c Z (2012) GaAs MMIC tunable directional coupler. In: IEEE MTT-S international microwave symposium on digest, pp 1–3 49. Gatti RV, Ocera A, Bastioli S, Marcaccioli L, Sorrentino R (2007) A novel compact dual band reconfigurable power divider for smart antenna systems. In IEEE MTT-S international microwave symposium on digest, pp 423–426 50. Cheng KM, Yeung S (2013) A novel rat-race coupler with tunable power dividing ratio, ideal port isolation, and return loss performance. IEEE Trans Microw Theory Techn 61(1):55–60 51. Vo VT, Krishnamurthy L, Sun Q, Rezazadeh AA (2006) 3-D low-loss coplanar waveguide transmission lines in multilayer MMICs. IEEE Trans Microw Theory Techn 54(6):2864–2871 52. Farcich NJ, Asbeck P (2006) A three-dimensional transmission line with coplanar waveguide features. Microw Opt Technol Lett 48(11):2189–2192 53. Ocera A, Farinelli P, Cherubinil F, Mezzanottel P, Sorrentino R, Margesin B, Giacomozzi F (2007) A MEMS-reconfigurable power divider on high resistivity silicon substrate. In: IEEE MTT-S international microwave symposium on digest, pp 501–504

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54. Shah U, Sterner M, Oberhammer J (2013) High-directivity MEMS-tunable directional couplers for 10–18 GHz broadband applications. IEEE Trans Microw Theory Tech 61(9):3236–3246 55. Marcaccioli L, Farinelli P, Tentzeris MM, Papapolymerou J, Sorrentino R (2008) Design of a broadband MEMS-based reconfigurable coupler in band. In: Proceedings of the European microwave conference, pp 595–598 56. Nishino T, Kitsukawa Y, Hangai M, Lee S-S, Soda S-N, Miyazaki M, Naitoh I, Konishi Y (2009) Tunable MEMS hybrid coupler and L-band tunable filter. In: IEEE MTT-S international microwave symposium on digest, Boston, pp 1045–1048 57. Fang D-M, Yuan Q, Li X-H, Zhang H-X, Zhou Y, Zhao X-L (2010) High performance MEMS spiral inductors, Xiamen, IEEE 58. Ocera A, Farinelli P, Mezzanotte P, Sorrentino R, Margesin B, Giacomozzi F (2007) Novel RFMEMS widely-reconfigurable directional coupler. In: Proceedings of the European microwave conference, pp 122–125

Chapter 3

Micromachined Single-Pole-Single Throw Switches

3.1 Introduction Micromachined switches have demonstrated superior electrical performance (lower loss and higher isolation) compared to contemporary solid-state devices to implement reconfigurable microwave and millimeter (mmWave) circuits. Micromachined switch offers low power consumptions, low loss, high linearity, and high signal isolation compared to any other contemporary solid-state switches [1]. Furthermore, micromachined metal contact or ohmic contact switch is one of the best choices in modern telecommunication system for its broadband RF performance compared to micromachined shunt switches. In this book, prime focus will be given on the series switch. Micromachined series switch results in an open circuit in the transmission line (t-line) when no bias is applied (up-state position), and it results in a short circuit in the t-line when a bias voltage is applied (down state position). The switch is named a series switch because it is connected in series with the input/output port. Series switches are designed to operate from DC to higher frequencies, depending on the application. They use resistive or metal-to-metal contacts. Therefore, they permit operation down to DC. The first Rockwell Scientific series switch was developed by Yao and Chang and closely resembled the standard cantilever switch [2]. The switch is suspended 2–2.5 μm above the substrate and the pull-down voltage is 60 V. Motorola recently developed a compact DC-contact micromachined series switch on silicon substrates. The HRL (formerly Hughes Research Laboratories) series micromachined switch was developed by Hyman et al. during 1998–2000 on GaAs substrates [3]. It is mechanically very similar to the first-generation Rockwell switch developed by Yao and Chang. The measured insertion loss is 0.1–0.15 dB over 1–40 GHz, indicating a total switch resistance of 1–1.5 . The measured isolation is 45 dB at 4 GHz, and 25 dB at 40 GHz. McGruer and Zavracky at North-eastern University have teamed with Analog Devices to develop a very mature process for a DC-contact micromachined inline series switch on silicon substrates [4]. The cantilever is suspended 0.6–1.2 μm above the pull-down electrode, and it is fabricated using a thick layer of electroplated gold (7–9 μm). The inline switch has a © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 S. K. Koul and S. Dey, Micromachined Circuits and Devices, Lecture Notes in Electrical Engineering 859, https://doi.org/10.1007/978-981-16-9443-1_3

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pull-down voltage of 60–80 V, with a switching time of 1–2 μs (pull-down) and 2– 3 μs (release). Different types of ohmic contact switches are reported in the literature with few of them commercialized. This Chapter mainly concentrate on in-line ohmic contact switches and their behavioural analysis. These switches are fabricated using surface micromachining process on 635 μm Alumina substrate. Detailed fabrication process is discussed in Appendix B for better clarity. All switches are implemented on coplanar waveguide (CPW) transmission line and all metal layers are made with gold. This Chapter also includes different types of measurement methods.

3.2 Ohmic Contact Micromachined Switch Ohmic contact switch provides broadband performances and it can be used in series or shunt operation based on the need of circuit designers. Figure 3.1 shows two different metal contact switches. Both are fabricated using the same process discussed in Appendix B and operate with same physics. Figure 3.1a switch beam is made of with 2 μm gold whereas switch depicted in Fig. 3.1b is made up with 3.5 μm electroplated gold. Both switches are actuated using electrostatic actuation. Figure 3.1a switch consists of a rectangular cantilever beam that is anchored with two metal posts with two symmetrical springs (l1 ). The stiffness of the beam (k) is primarily dependent on the beam thickness (t b ) and length (L) as kα(t b /L)3 . The Young’s modulus (E) of the electroplated gold is 45 GPa. The total length of the beam was restricted to 200 μm for a robust mechanical design. To improve the stability of the structure, Fig. 3.1b switch is designed like a ‘push-up exercise’ with two hands (k 1 ) in front and legs (k 2 ) are in back which is supported by anchors. The schematic of these two switches is shown in Fig. 3.2. Bottom electrodes of both switches are covered

(a)

(b)

Fig. 3.1 Microscopic images of ohmic contact micromachined switch where movable beam thickness of a 2 μm [6] and b 3.5 μm [7]. Copyright/used with permission of/courtesy of Institute of Physics (IOP) publishing limited and IEEE

3.2 Ohmic Contact Micromachined Switch

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(a)

(b)

Fig. 3.2 Schematic of MEMS switches presented in a Fig. 3.1a [6] and b Fig. 3.1a [7]. Copyright/used with permission of/courtesy of Institute of Physics (IOP) publishing limited and IEEE

by silicon dioxide. Dimples (contacting points) are 5.5 μm in radius with 1 μm depth and they are used at the tip of the beam to overcome a direct contact with the DC-isolation dielectric, and this reduces the associated dielectric charging effect. Titanium tungsten is used as high resistive bias line that is covered by Si O2 A switch model including different model parameters is developed in Coventorware saber platform, as shown in Fig. 3.3. The series switch is designed using lumped Beam, Beam Electrode, Rigid plate, Mechanical bus connector and gap Generic squeeze damper modules [5] in Saber schematic. Later, measured damping coefficient (b) and mechanical resonance frequency are added to the module for the best mapping.

3.2.1 Switch Profile Analysis The out of plane deformation of the switch is required to be measured to observe the stress distribution on the cantilever beam. Taylor Hobson Optical Profilometer is one of the best choices for this kind to acquire surface topographies. Interferometric profilometry would be ideally suited in terms of height resolution. However, it cannot deal with the large local surface angles associated with the relatively high surface

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Fig. 3.3 Lumped representation of MEMS switch in saber architect [6]. Copyright/used with permission of/courtesy of Institute of Physics (IOP) publishing limited

roughness of the metallic MEMS. The tip deflection (z) of the cantilever beam can also be found analytically and is given by (3.1) [1], z =

σz L 2 2E eff

(3.1)

Here, E eff is the effective Young’s modulus and it is replaced by E/(1 − υ 2 ). σz is the residual stress gradient of the cantilever beam. The out of plane deformation of one of the switches and it top surface profiles are experimentally observed and shown in Fig. 3.4. Figure 3.4a shows deflection at the tip is more in the switch as shown in the 3D profile. Switch has an air gap of 3.4 μm which indicates that it has experienced 0.9 μm extra deformation than its initial gap height of 2.5 μm after release. The other switch shows negligible deformation due to higher spring coefficients. Note Fig. 3.4 3D view of micromachined switch (Fig. 3.1a) obtained from Optical Profilometer [6]. Copyright/used with permission of/courtesy of Institute of Physics (IOP) publishing limited

3.2 Ohmic Contact Micromachined Switch

73

that, due to non-uniform profile of the effective residual stress (σeff ), cantilever beam either deflects upward or downward. A positive stress gradient lifts the beam upward, whereas negative stress gradient bends the beam downward. The observed out-ofthe plane deformation is not uncommon in MEMS switches. Residual gradient stress causes undesirable out-of-plane deformation. When a thin film is deposited on a sacrificial layer at a temperature lower than its flow temperature, the intrinsic stresses develop in the film-sacrificial layer system. Detailed study has already been reported that theoretically explain the mechanisms of these stresses [8, 9]. Furthermore, inplane residual stress primarily increases the switch spring constant and is, therefore essential to control it within reasonable limit.

3.2.2 Mechanical Resonance Frequency The mechanical resonance frequency of the cantilever beam depends on the dimension of the beam and material properties, such as the Young’s modulus, residual stress, and material density. The fundamental resonance frequency can be found from (3.2), as given in [10]  tb f 0 = 0.16154 2 L

Ee ρ

(3.2)

where, ρ is the gold density and this value is 19300 kg m−3 . Voltage actuation method is used to detect the mechanical vibrations of the micromachined switch. Small signal frequency sweep is imposed over a dc actuation voltage to observe the frequency response of the structure. The out-of-plane vibration amplitude response is recorded for the frequencies of the signal. Polytec made Laser Doppler Vibrometer (LDV) is one of the best choices to detect the displacement of the structure in the out of plane direction. LDV is made up with MSA 400 Micro-motion analyzer, OFV 511 Laser Interferometer, an optical microscope with a CCD camera and OFV 3001 Vibrometer Controller, as reported in [11–15]. The LDV uses Doppler frequency shift method to calculate displacement due to external excitation at the point where the laser pointer is focused. Mechanical resonance frequency of the Fig. 3.1a switch is found using chirp voltage and seven modes of vibration are captured from LDV up to 0.5 MHz frequency as shown in Fig. 3.5. The vibration spectrum of the micromachined switch is plotted in Fig. 3.6a. Figure 3.1b switch gives mechanical resonance frequency of ~80 kHz with Q-factor of 6.8 in room air, as depicted in Fig. 3.6b. The quality factor and damping of switches can be extracted from the mechanical measurement.

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Mode 1

Mode 2

Mode 5

Mode 6

Mode 3

Mode 4

Mode 7

Fig. 3.5 Various modes of vibration of micromachined switch up to 0.5 MHz

(a)

(b)

Fig. 3.6 Measured vibration spectrums of micromachined switches presented in a Fig. 3.1a and b Fig. 3.1b [7], with permission from IEEE

3.2.3 Electrical Responses Voltage driving scheme of the cantilever-based contact switch is like the condition for parallel plate actuator under electrostatic actuation. The mass of the beam is the movable beam and that can be a cantilever type or fixed to fixed bridge. It is a movable electrode and maintains a gap from the fixed electrode. When a potential difference is created between two parallel plates, it pulls the beam towards the fixed electrode and reduces the plate separation. Elastic recovery force tends to pull the mass of the beam towards the initial position once voltage is removed. The balance position of the beam is simply obtained by the condition of force balance with electrostatic and restoring forces. When these two forces are equal then pull-in condition is reached.

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As the electrostatic force is inversely proportional to the square of the gap height, a non-linear behaviour is observed that cause the instability problem in the beam actuation. Note that, when mass of the beam is pulled-in, it would not be released until the electrostatic force is taken away completely. Moreover, pull-in effect takes place from 1/3 of the gap from beam top or 2/3 of the gap from the bottom fixed electrode. The pull-in voltage (V p ) of the beam is obtained by (3.3)  Vp =

8 kg 3 27Aε

(3.3)

where, k is the spring stiffness, g is the gap height, A is the overlap electrode area and ε is the permittivity. The actuation voltage of the switch shown in Fig. 3.1a can be found using (3.4)  Vp =

K g(g + z)2 2 Aε0 l 2

where, g = g0 +

td εr

(3.4)

Here, K is the spring constant, A is the electrode area, ε0 is the vacuum dielectric permittivity, g0 is the gap height or anchor height, t d is the dielectric thickness, εr dielectric permittivity, l is the beam length and Δz is the tip deflection. In this type of switch, cantilever beam snaps down and makes a physical contact with minimum contact force after the electrostatic unstable region (pull-in point) and its speed keeps on increasing to exceedingly high values. Contact force can be increased against damping with high actuation voltage (1.2–1.5 V pi ) which leads to low contact resistance. For a cantilever-based switch, the contact force (F c ) is equal to beam reaction force (Rb ) and electrostatic force (F e ) is equal to the applied load. The contact resistance for a micro-switch is a summation of the constriction (Rc ) and contamination film (Rcf ) resistances and it can be defined as (3.5). RC = Rc + Rcf

(3.5)

Maxwellian spreading resistance theory defines the constriction resistance from contacting surface topography [18], and is modelled analytically using (3.6) as follows Rc =

ρ 2reff

(3.6)

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where, ρ is the resistivity, and r eff is the effective radius of a circular contact area (3.6) assumes diffusive electron transport [16] as the main reason for the current flow. The effect of contamination film resistance [17] and ballistic electron transport [18] are not considered here (assuming clean testing environment). Abbott and Firestone’s material deformation model [19] revised the constriction resistance under plastic deformation condition using Holm’s contact resistance equation as follows in (3.7)  Rc = 0.866ρ

H Fc

(3.7)

where H is the contact material’s hardness. The hardness and resistivity values that are used for gold–gold contacts are 2–2.3 GPa and 2.5–2.8 μ cm, respectively. Electrical characterization of the switch is carried out using an Agilent 4284A LCR meter with a probe station. To measure the C–V characteristics of micromachined switches, the bottom fixed electrodes have been grounded and the required voltage sweep is applied to the top suspended cantilever beam using the probes. A small ac signal of 5 MHz has been imposed on the dc actuation voltage to measure the capacitance. Open circuit offset measurement corrections are made before recording the capacitance values. The measured actuation voltage of the switch in Fig. 3.1a is 26 V as depicted in Fig. 3.7a. To validate the experimental results, Saber schematic model of Fig. 3.3 is used where a voltage-pulse (0–40 V) is introduced. All structural and mechanical parameters like switch initial deformation (Z max ), damping (b), residual stresses and quality factor (Q) have been used in the model. The simulated pull-in voltage of the switch is 24 V which is much closer to the measured value, as shown in Fig. 3.7a. The point P1 in Fig. 3.7b indicates the point of instability after which beam suddenly snaps down to the bottom t-line. During the simulation, fringing field effect is ignored due to mathematical complexity. During the analysis

(a)

(b)

Fig. 3.7 a Measured and b simulated responses of switch (Fig. 3.1a) actuation voltage, [6]. Copyright/used with permission of/courtesy of Institute of Physics (IOP) publishing limited

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of this kind of switch model, non-homogeneous distribution of charges and fringing field effects are ignored. Moreover, switch initial deflection and residual stresses are considered. The spring-mass model of the switch shown in Fig. 3.1b contains three mechanical springs k 1 , k 2 and k 3 , respectively, where k 1 is the mechanical spring and k 2 , k 3 are shared tether in the cantilever. Total spring constant (k total ) of the switch can be calculated as; ktotal = 2k1 //(k2 + k3 ) where, 

3 t l1 + l2 + l3  3  3 t t k2 + k3 = Ew2 + Ew3 l4 l5 k1 = Ew1

(3.8)

(3.9)

where, w1 , w2 , w3 , l 1 , l 2 , l 3 , l 4 and l 5 are shown for completeness in Fig. 3.1b. E is Young’s modulus of the gold (45 GPa). Actuation area between cantilever beam and bottom electrode is le × w3 . Pull-in voltage (V p ) of the switch is defined as;  Vp =

8ktotal (g0 + td /εr )3 27ε0 le w3

(3.10)

where, g0 (2.5 μm) is the air gap between beam and electrode, t d and εr are thickness (0.7 μm) and relative permittivity (3.8) of the dielectric layer, respectively. Simulation results of the switch show pull-in voltage (V p ) at 108 V and mechanical resonance frequency (f 0 ) at 85.6 kHz, as shown in Fig. 3.8a, b. Measured actuation voltage is 109 V which is close to the simulated result.

3.2.4 Switching and Release Time Responses The switching time is a critical specification of a MEMS switch dynamics. The switches are based on mechanical movement between the open and closed states, and the actuation speed is limited by the mechanical response time. The actuation dynamics is nonlinear and numerical modelling has been used to characterize the switch dynamics. The motion of RF MEMS switch is governed by the classical second-order linear differential equation given by (3.11) as follows,

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Fig. 3.8 Simulated pull-in voltage response of the micromachined switch presented in Fig. 3.1b [7]. Reproduced with permission of IEEE

m

d 2 z max dz max +b + kz max = Fe + FLJ 2 dt dt

(3.11)

where F LJ is the Lennered-Jones force which contributes van-der walls attraction force and repulsive force in the numerical analysis of switch dynamics. The switch displacement is a function of time and majority of time is spent to reach the pull-in point, afterwards the gap is closed rapidly. In the switch shown in Fig. 3.1a, gap is relatively large (3.1–3.4 μm), hence the gap dependent damping has been taken as constant. Due to switch inertia, it moves initially slowly. Later, the damping limits the switch velocity. So, switching time or closing time (t s ) of micromachined switch is the summation of inertial and damping limited switching time. If the damping coefficient and the spring constant are zero, the inertia limited switching time (t m ) can be derived, as stated in [20, 21]. The damping limited switch actuation time can be obtained with zero effective mass and given in [20, 21]. Switch release time (t r ) can be obtained by the principal of energy conservation and the same is discussed in detail in [1]. Switch damping limited actuation time (t b ) and release time (t r ) both depends on the Qm . For lower quality factors, damping significantly increases the switching time. The switching time measurement is carried out using Agilent infiniium DSO-X 92,504 25 GHz high frequency digital storage oscilloscope. The measurement set up is shown in Fig. 3.9a. A square wave of 0–40 V with a frequency of 1 kHz is given to the actuation pad and the corresponding effects on switching (78 μs) and release time (123 μs) are recorded from Agilent Digital Storage Oscilloscope (DSO) as depicted in Fig. 3.9b. The release time is higher than the switching time due to the switch contact bouncing effect which takes a few more cycles to settle down at its initial position. The switch is lifted up at 86 μs and additional 37 μs takes to complete settle down the switch at its initial position. The pull-in and release voltage of the switch are 30 V and 16 V, respectively. Similar measurement method can be used to measure the actuation time of any MEMS switches. Figure 3.10 shows measured

3.2 Ohmic Contact Micromachined Switch

79

(a)

(b)

Fig. 3.9 a Measurement set up of switching and release time and b Measured switching and release time of DC contact MEMS switch (Fig. 3.1a) [6]. Copyright/used with permission of/courtesy of Institute of Physics (IOP) publishing limited Fig. 3.10 Measured mechanical switching time of the micromachined switch presented in Fig. 3.1b [7]. Reproduced with permission of IEEE

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3 Micromachined Single-Pole-Single Throw Switches

switching time (ON-time) of 12.6–9.5 μs with OFF-time of 6.8 μs at 108–120 V bias for the switch shown in Fig. 3.1b.

3.2.5 Radio Frequency Performance When the actuation voltage is applied between the membrane and the bottom electrode, the switch is activated in the ON-state (membrane pulled down and is in DC contact with the bottom t-line), it exhibits a contact resistance (RON ) which is extracted from the measurements. Note that, DC contact micromachined switches do not suffer from stiction and dielectric charging problems, when operated unpackaged. The dimple helps to minimize stiction problems and the dielectric charging problems, as well as create a better metal contact between the beam and the bottom t-line, when the micromachined switch is at the ON-state. When the membrane is at the up position, it exhibits a very small capacitance which will block the RF path. But when the actuation voltage is applied between the membrane and the bottom electrode, the membrane will be pulled down and it will be in DC contact with the bottom t- line which connects the output transmission line (RF out). The micromachined switch at the ON-state has a very small contact resistance and provides an RF through path. Let us check the S-parameter responses for the switch presented in Fig. 3.1a. The equivalent circuit model for an in-line DC-contact micromachined switch in the two states are shown in Fig. 3.11. As it is shown in Fig. 3.11a, when the switch is in the OFF-state (the membrane at the up position), it is modeled as a small inductance (L) of 115 pH in series with a small resistance (Rt ) of 0.6  and a small capacitance (C off ) of 11.13 fF. The parallel capacitance to ground (C p ) is 27 fF for the switch. The capacitance C off is from the parallel plate between the membrane and the bottom contact metal connecting to the output transmission line (t-line), while the parallel Fig. 3.11 Equivalent circuit model of DC-contact switch in a OFF and b ON states [6]. Copyright/used with permission of/courtesy of Institute of Physics (IOP) publishing limited

(a)

(b)

3.2 Ohmic Contact Micromachined Switch

81

capacitance C p is from the parallel plate between the membrane and the bottom fixed electrode. The 0.6  resistance (Rt ) is used to model the transmission line loss. The L s and C s are the t-line inductance and capacitance which contributes 50  to the RF input and output t-line. The contact resistance (RON ) which is extracted from the measurements is around 3.7 . The equivalent circuit model is shown in Fig. 3.11b. As seen, when the DC contact micromachined switch is in the ON-state, it is modeled as a small inductance (115 pH) in series with a resistance RON and is connected in parallel with a capacitance (C pon ) of around 37 fF. The inductance (L) of 115 pH is the same as when the micromachined switch is in the ON-state. The C g (≈6–8 fF) refers to the signal-line coupling capacitance due to the gap between each broken signal line. Since the membrane is in DC contact with the bottom output transmission line in the ON-state, the series capacitance (C off ) is removed, instead it shows a slightly higher resistance compared to the equivalent circuit model in the OFF-state (see Fig. 3.11a). This resistance is partially from the small transmission line loss (0.6  in Fig. 3.11a), and partially from the micromachined contact resistance (Rc ). Also noted in Fig. 3.11b, the capacitance (C pon ) in parallel is larger than the parallel capacitance (C p ) in Fig. 3.11b when it is in the OFF-state. This is because when the micromachined switch is in the ON-state, the membrane is pulled closer to the bottom electrode, thus, the capacitance produced by these two overlapped metal plates is larger. This can be found out from the fundamental capacitance formula given in (3.12). C p,pon =

ε0 Ae +Cf g0 + εtεr

(3.12)

where C f is the fringing field capacitance which is 20–60% of C p , depending on the switch dimensions and height (g0 ). The switch inductance (L) has been found from (3.13), √ Z h l εeff λg for l < L= c 12

(3.13)

where, c is the velocity of light velocity in free space, Z h is the high impedance line, λg is the guide wavelength and εeff is the effective permittivity. One can extract other switch functional lumped parameters from the measured S-parameter responses. The switch OFF-state capacitance (C off ) can be found from the isolation response (S 21 ), as given in (3.14) 2 |S21 |2 ≈ 4ω2 Coff Z 02

(3.14)

The ON-state resistance is the summation of transmission line resistance and contact resistance (Rc ). The contact resistance can be found from switch ON-state return loss (S 11 ), as given in (3.15)

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3 Micromachined Single-Pole-Single Throw Switches

 |S11 | = 2

RON 2Z 0

2 (3.15)

The inductance (L) can also be found from (3.16),  |S11 | = 2

ωL 2Z 0

2 (3.16)

where, ω is the operating frequency and Z 0 is the characteristic impedance (50 ). The switch ON-state and OFF-state performances can be checked using any 3D full wave electromagnetic simulation platform for better optimization purposes. The RF measurement of the fabricated switch is performed using Vector Network Analyzer with Ground-Signal-Ground (GSG) RF probes and DC probes. Then any one of the calibration standards should be used and one of the examples is short-open-loadthru (SOLT) standard. One of the switches (Fig. 3.1b) S-parameter responses are shown in Fig. 3.12a. All electrical parameters of the switch can be extracted from the measured results utilizing (3.14) to (3.16). The equivalent circuit model of the similar switch with all functional parameters is depicted in Fig. 3.12b. Figure 3.12a presents measured and fitted S-parameters of the switch with C off = ~16 fF, Rc = 1.14  and L b = 36 pH, respectively. The switch is well matched with return loss >28 dB up to 40 GHz. The measured insertion loss is 1.07 dB up to 40 GHz with 112 V. Isolation of the switch is 17.4 dB up to 40 GHz [7]. Fig. 3.12 a Measured versus fitted S-parameter responses, and b equivalent circuit model of the switch presented in Fig. 3.1b [7]. Reproduced with permission of IEEE

(a)

(b)

3.2 Ohmic Contact Micromachined Switch

83

3.2.6 Temperature Sensitivity When the actuation voltage is applied between the membrane and the bottom electrode, the temperature sensitivity and current density are primary sources of RF power handling capability of DC contact micromachined switch. The pull-in voltage of the switch is a function of the temperature. Temperature plays a crucial role on switch pull-in (V p ) and release (V r ) voltages. It is mostly due to the change in spring constant (k) of the switch at elevated temperatures. The spring constant of a cantilever structure do not have a stress dominating region whereas cantilever tip deflection is function of stress or stress gradient and it is represented by (3.17) z =

l 2 σ (1 − υ) l 2 σ (1 − υ) = 2E 2Et

(3.17)

where, σ = (σtop — σbottom )/t ≈ σ/t (for mathematical simplicity) is the linear stress gradient due to different deposition condition and υ is the Poisson ratio. The variation of inertial stress due to temperature or thermally induced stress is defined by (3.18), σ (T ) = α ET α = αbeam − αsubstrate T = Tbeam − Tsubstrate

(3.18)

where, α beam and α substrate are the coefficient of thermal expansion of the cantilever beam and substrate, respectively. As temperature is increased there is a relaxation of existed residual stress in the suspended cantilever structure. Here, combining (3.4), (3.17)–(3.18) yields fundamental relationship of the switch V p over temperature for a cantilever beam,  V p (T ) =

  σ (T )l(1 − υ) kg g + 2 Aε0 l 2Et

(3.19)

This equation reveals that the change in V p or V r voltage with temperature is solely due to different thermal expansion coefficient between alumina substrate and gold beam. For, E = 45 GPa (gold), α m = 14 μm/(m K), α s = 0 μm/(m K) (for worst case) and ΔT = 60 °C, the calculated variation of the inertial stress is ~−38 MPa which results in ~5 V reduction in the V p and V r voltages for one of the simple cantilever type switch shown in Fig. 3.13a. Measured change in V p and V r voltages with temperature variations are depicted in Fig. 3.13b for the same switch. The same process was repeated on 20 identical micromachined switches and their average response is also plotted in Fig. 3.13b. The primary reason of this deviation (~2.5 V) between all identical switch results is due to different electroplating thickness (1.9–2.4 μm) of gold cantilever beam that was found from the Scanning Electron Microscope (SEM) and validated under the Optical Profilometer. Non-uniform tip deflections (0.4–0.54 μm)

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3 Micromachined Single-Pole-Single Throw Switches

(a)

(b)

Fig. 3.13 a Microscopic image, and b Measured V p and V r voltages versus temperature responses of a simple cantilever type DC-contact MEMS switch [22]. Reproduced with permission of IEEE

were also observed over 20 identical switches under optical profilometer. It leads to the V p and V r variation with the same bias voltage (53 V).

3.2.7 Radio Frequency Power Handling Performance The beam temperature is a function of the incident power and temperature is higher at down- state compared to up-state in metal-contact switches. Figure 3.14 presents the power handling capability of the same cantilever switch (Fig. 3.13a) at three different temperatures. The results show that switch voltage decreases by 4 V after 1 W, 8 V after 2 W and 15 V after 3 W of the incident power at 25 °C. At incident

(a)

(b)

Fig. 3.14 Simulated heat dissipations on the DC-contact switch at 2 and 17 GHz frequencies [22]. Reproduced with permission of IEEE

3.2 Ohmic Contact Micromachined Switch

85

power of 3–4 W switch loses its control and enters the failure zone with 15–18 V change in the voltage. Result also shows that switch can withstand maximum up to 2 W of power with V r > 15 V from 25 to 70 °C. During this process, maximum V p changes from 43 to 27 V, but abrupt change in V r was observed. It is mostly due to the dielectric charging with incident power due to an increase in temperature and due to contact point degradation and contaminations with additional attractive force from the RF power. For clean metal contact, the incident RF power (Pinc ) and contact voltage (V c ) are represented by (3.20) and (3.21), respectively, as a function of temperature, where (Rc 2 W), sensitivity of loss and matching characteristics are affected more and probability of RF latching increases. Nevertheless, switch OFF-state performance is also affected due to reduction of switch effective spring contact as well as initial contact gap height at higher incident RF power level. It changes sensitivity of the switch isolation with higher C off . The RF power dissipation from the micromachined switch can be examined using full-wave simulation in any EM simulator. Symmetrical boundary condition should be used during the simulation and all S-parameter results can be obtained. Power dissipated (Pdiss ) by the MEMS switch can be calculated using (3.25), as given below: Pdiss = Pi (1 − |S11 |2 − |S21 |2 )

(3.25)

where, Pi is the incident power and Loss = 1 − |S11 |2 − |S21 |2 . Power dissipated in the entire switch is first determined from the S-parameter simulation after including the loss of the transmission line, dielectric, substrate, and micromachined beam. Fig. 3.15 Simulated variations of switch insertion losses with 0.1–2 W of RF power [22]. Reproduced with permission of IEEE

3.2 Ohmic Contact Micromachined Switch

(a)

87

(b)

Fig. 3.16 Simulated current distributions in a up-state and b down state positions at 20 GHz

To extract the loss of the switch alone, all other metal and dielectrics are taken as lossless in the simulations. The conductivity of the gold beam is taken as 4.7 × 107 S/m. These two processes were repeated in up- and down-states of the switch. The simulations show that Pdiss = 0.0633Pi (S 11 = 28 dB, S 21 = 0.15 dB) at down-state and Pdiss = 0.0083Pi (S 11 = 0.147 dB, S 21 = 16.2 dB) with up-state at 20 GHz frequency for the switch shown in Fig. 3.1a. Switch power dissipation is more in down-state compared to the up-state. It also attributes to the high current density in down- state compared to the up-state at 20 GHz, as depicted in Fig. 3.16. The figure also show that temperature rise in down-state is much higher than in the up-state over the frequency of interest. The temperature distribution on the beam follow the standard steady state heat equation and it is also equivalent to the power loss (Ploss ) per unit volume. Similar observation was made from the simple cantilever switch shown in Fig. 3.13a. Simulated current distribution of the switch is shown in Fig. 3.17 when it is connected in single-pole-multi-throw configuration. Figure 3.17 shows the change in surface current at 2 GHz and 17 GHz, respectively for SP4T Switch. The current spreads nearly evenly throughout the beam at 2 GHz with ideally contact current density. Whereas, current spreads mostly outside edges of the beam at 17 GHz with

Fig. 3.17 Simulated current distributions on the SP4T switch at 2 and 17 GHz with 0.1 W of incident RF power at 273 °K temperature [22]. Reproduced with permission of IEEE

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3 Micromachined Single-Pole-Single Throw Switches

(a)

(b)

Fig. 3.18 a Measured V p and V r voltage versus incident power at three different temperatures and b fabricated image with schematic side view of the switch [23]. Reprinted with permission of IEEE

no current on the beam interior due to skin effect. As a result, effective cross-sectional area of the beam decreases, and resistance increases more at 17 GHz compared to at 2 GHz. It leads to more heat dissipation on the beam at 17 GHz. RF power handling and temperature stability of a MEMS switch can be measured experimentally using the set up described in Chap. 8 in detail. Figure 3.18a shows power handling capability of a simple cantilever switch at three different temperatures (~25, 50 and 70 °C). Note that, this switch is also fabricated on 635 μm alumina substrate, it has air gap of 2.5 μm and beam metal (gold) thickness of ~3.5 μm. Microscopic image of the switch is shown in Fig. 3.18b [23]. The results show that switch voltage decreases by 2.2 V after 1 W, 6.4 V after 2 W, ~14 V after 3 W and ~23 V after 4 W of the incident RF power at 25 °C. Note that, switch was tested for ~5 min at each incident power level just to ensure the stability of the device. Switch performance started to degrade between 3 and 4 W after 50 °C with a ~20 V reduction in voltage due to self-actuation (V RFrms > V r ). Effect of dielectric charging with incident power and spring softening at higher temperature are also reasons for the failure [23]. Note that, Switch voltages V p and V r changes of 11 V is observed from the measurement from 25 to 85 °C, as depicted in Fig. 3.19. Average responses of 16 MEMS switches are also plotted. Result shows ~2.4–2.8 V deviation over all identical

3.2 Ohmic Contact Micromachined Switch

89

Fig. 3.19 Measured V p and V r voltage variation with temperature of the switch presented in Fig. 3.19b [23]. Reproduced with permission of IEEE

switches due to different electroplating deposition (3.45–3.65 μm) on the beam. Different thermal expansion coefficients between gold (α m ) and alumina substrate (α s ) causes the change in voltage. Beam in-plane stress changes into compressive at higher temperature and leads to downward deformation on the beam curvature. It decreases the V p and V r and proved analytically by (3.26)  V p (T ) =

  σ (T )l(1 − υ) kg g + 2 Aε0 l 2Et

(3.26)

where g = g0 +

td εr

where, k is the spring constant, A is the electrode area, ε0 is the vacuum dielectric permittivity, g0 is the gap height or anchor height, t d is the dielectric thickness, εr dielectric permittivity, l is the beam length, t is the beam thickness, E is the Young’s modulus, υ is the Poisson ratio and σ(T ) is the linear stress gradient and it is a function of temperature.

3.2.8 Intermodulation Distortion The Intermodulation Distortion (IMD) or linearity analysis is one of the very important parameters in any microwave devices and especially in RF switches. In contact type microswitches, the capacitance in the OFF-state (C off ) is very small and as an example, C off of the switch in Fig. 3.1a is ~12 fF. Capacitance is not only the major

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3 Micromachined Single-Pole-Single Throw Switches

source of IMD in DC-contact type switch. In the ON-state, the switch resistance is a weak function of contact force. The contact force typically changes only a few percent, even when the RF voltage is applied to the actuator as in the in-line series switch considered in this work. The switch resistance (RON ) is expected to change a little less because of the increased contact force caused by the applied RF voltage. Moreover, the modulation of switch resistance by ohmic heating of switch materials appears to dominate in the in-line series switch. The mechanical motion of the beam also takes part in IMD generation. Theoretical predictions of two sources of signal distortion are temperature dependent material properties and contact force variations. Theoretical modelling of IMD in micromachined switches can be found in [1, 6] to have better clarity. The third order intercept point (IIP3) is the fictitious input power for which the power of the sideband would be equivalent to the power of the input signal if all the input power is transmitted to the output. More detailed explanations and theoretical modelling of IIP3 in micromachined switches can be found in [1, 24, 6] for better clarity. IIP3 measurements can be experimentally carried out using two signal generators with carrier frequencies f 1 = 16.999998 GHz and f 2 = 17.0000013 GHz for the switch shown in Fig. 3.1a. The spacing between two carrier frequencies is kept as 3 kHz which is much lesser than the switch mechanical resonance frequency (typically 9 kHz). A power combiner is used in the measurement which has loss of -12dBm (including cable loss at 17 GHz). Two tone IMD has been performed on the above switches where 2f 2 − f 1 = 17.0000053 GHz and 2f 1 − f 2 = 16.9999947. Figure 3.20a shows the measurement setup where PT is the transmitted power, the power at the input port of DUT is PIN , the power at the output port of DUT is POUT and the received power at the spectrum analyser is PR . PIN is PT minus the loss incurred between the vector network analyser (VNA) and the input port of DUT (≈7 dB), and POUT is the sum of the loss incurred between the output port of DUT and spectrum analyser (≈5 dB) and PR . Figure 3.20b shows PR spectrum for PT = 0 dBm in initial state and actuated states of the switch. The IIP3 can also be expressed using (3.27) as: I I P3 =

P + PIN 2

(3.27)

IIP3 of the switch shown in Fig. 3.1b is 49 dBm and it is tested with two tones at f 1 = 1.94. GHz and f 2 = 1.98 GHz, respectively, at zero-bias condition, as shown in Fig. 3.21. The IIP3 of the switch was limited by the power divider loss, ground-signal-ground (GSG) probe contact resistance and transmission line loss (input, output) on the alumina substrate.

3.2 Ohmic Contact Micromachined Switch

91

(a)

(b)

Fig. 3.20 a IIP3 measurement setup and b measured intermodulation responses at up and down state of the switch presented in Fig. 3.1a [6]. Copyright/used with permission of/courtesy of Institute of Physics (IOP) publishing Fig. 3.21 Measured IIP3 response of the switch presented in Fig. 3.1b

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3 Micromachined Single-Pole-Single Throw Switches

3.3 Conclusions This Chapter presents micromachined DC contact switch design followed by different types of characterization. These include switch profile analysis, mechanical and electrical response, switching and release time, loss, power handling and linearity. All reported switches are implemented with Au/Au contact and electroplated with 2– 3.5 μm of gold layer. DC contact micromachined switch is chosen for this study due to its broadband microwave performances. The life cycle of these kind of switches can be taken care of by considering different failure issues like dielectric charging, contact contaminations and humidity. Dielectric charging can significantly affect the switch actuation after few cycles of operations. The bulk and surface charges are major sources of the dielectric charging in the micromachined switch. Bulk charge in the dielectric reduces the switch reliability regardless of the positive stress gradient. Furthermore, accumulation of surface charge at higher humidity level can also degrade the switch performance. During pitting and hardening process, contact area is significantly reduced and therefore contact temperature increases which also reduces contact resistance abruptly after few millions cycles of operations. To improve the contact point degradation; one possible solution is to use well suited contact materials for high temperature applications like rhenium, rhodium, or gold–palladium alloys. The softening temperature of rhodium is 700 °K which makes it more temperature stable during the conduction heat transfer process. It also increases the power handling capability. Interested readers may study [6, 25] for more information on all switches discussed in this Chapter.

References 1. Rebeiz GM (2003) RF MEMS theory, design, and technology. Wiley, Hoboken, NJ 2. Mihailovich RE, Kim M, Hacker JB (2001) MEM relay for reconfigurable RF circuits. IEEE Microw Wirel Compon Lett 11:53–55 3. Hyman D, Mehregany M (1999) Contact physics of gold microcontacts for MEMS switches. IEEE Trans Comp Packag Technol 22(3):357–364 4. Zavracky PM, McGruer NE, Morrison RH, Potter D (1999) Microswitches and microrelays with a view toward microwave applications. Int J RF Microw CAE 9(4):338–347 5. Coventorware ARCHITECT version 2008 Reference: MEMS and Microsystems System-level Design, Coventor, Inc, (2008). www.coventor.com. 6. Dey S, Koul SK (2014) Design and development of a CPW-based 5-bit switched-line phase shifter using inline metal contact MEMS series switches for 17.25 GHz transmit/receive module application. J Micromech Microeng 24:1–24 7. Dey S, Koul SK, Poddar A, Rodhe U (2018) Reliable and compact 3-bit and 4-bit phase shifters using MEMS SP4T and SP8T switches. IEEE J Microelectromech Syst 27(1):113–124 8. Thornton JA, Hoffman DW (1989) Stress related effects in thin films. Thin Solid Films 171:5–31 9. Hu SM (1991) Stress related problems in silicon technology. J Appl Phys 70:53–79 10. Tillman HAC, Legtenberg R (1994) Electrostatically driven vacuum-encapsulated polysilicon resonators. Part II. Theory Perform Sens Actuator A 45(1):67–84 11. Pandey AK, Pratap R (2007) Effect of flexural modes on squeeze film damping in MEMS cantilever resonators. J Micromech Microeng 2475–2484

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12. www.polytec.com 13. Dey S, Koul SK (2012) Design and development of a surface micro-machined push-pull-type true-time-delay phase shifter on an alumina substrate for Ka-band T/R module application. J Micromech Microeng 22(12):125006–125025 14. Chakraborty S, Bhattacharyya TK (2010) Development of a surface micro-machined binary logic inverter for ultra-low frequency MEMS sensor applications. J Micromech Microeng 20(10):105011–105026 15. Dey S, Koul SK (2012) Design, fabrication and characterization of RF MEMS varactor for VCO application. J ISSS 1(1):55–64 16. Holm R (1969) Electric contacts: theory and applications. Springer, Berlin 17. Hyman D, Mehregany M (1999) Contact physics of gold micro contacts for MEMS switches. IEEE Trans Comp Packag Technol 22:357–364 18. Majumder S et al (2001) Study of contacts in an electrostatically actuated micro switch. Sens Actuators A 93:19–26 19. Abbot E, Firestone F (1933) Specifying surface quantity—A method based on the accurate measurement and comparison. ASME Mech Eng 55:569 20. Koul SK, Dey S (2014) RF MEMS single-pole-multi-throw switching circuit. In: Vinoy KJ, Ananthasuresh GK, Pratap R, Krupanidhi AB (eds) An edited book Micro and smart devices and system. Springer, New Delhi 21. Koul SK, Dey S (2019) Radio-frequency micromachined switches, switching networks and phase shifters. CRC Press, Taylor and Francis Group 22. Dey S, Koul SK (2015) Reliability analysis of Ku-band 5-bit phase shifters using MEMS SP4Tand SPDT switches. IEEE Trans Microw Theory Tech 63(12):3997–4012 23. Koul SK, Dey S (2018) MEMS K-band 4-bit phase shifter using two back to back SP16T switching networks. IEEE J Microelectromech Syst 27(4):643–655 24. Johnson J, Adams GG, McGruer NE (2005) Determination of intermodulation distortion in a contact-type MEMS microswitch. IEEE Trans Microw Theory Tech 53(11):3615–3620 25. Dey S, Koul SK (2016) Systematic measurement of high isolation DC—20 GHz miniature MEMS SPDT switch. Wiley Microw Optic Technol Lett 58(5):1154–1159

Chapter 4

Micromachined Single-Pole-Multi-throw Switching Networks

4.1 Introduction Micromachined single-pole-multi-throw (SPMT) switches demonstrate superior performances in terms of isolation, loss, and linearity compared to contemporary solid-state switches [1]. Different types of SPMT switches have shown potential in RF communication systems especially in cellular networks like 3G/4G standard. Sion-insulator (SOI) or Si-on-sapphire (SOS) based switches demonstrate excellent characteristics up to 2.7 GHz frequency. Moreover, after 3 GHz their performance degrades due to their low-pass tuning networks and large off-state capacitance [2]. Note that, modern 5G standard recently introduced extend up in frequency range from 3 to 6 GHz [3]. Different technologies have been used globally for the development of SPnT switches using (a) PIN diodes, (b) CMOS and (c) micromachining technologies. Among all, RF micromachined based SPnT switches attracted attention due to their low power consumption, low loss, good linearity, and excellent isolation while operating with multiple ports at a time over a wide band It substantially increases the utility of these switches in modern cellular networks. Moreover, all these switching networks can be fabricated within a compact area using micromachining technology and that can also reduce the cost in large volume manufacturing processes. Thus, micromachined switches are very useful for satellite switching network and wide band radios. Various types of micromachined SPMT switches are reported by researchers using different switch design techniques [4–20]. Note that, ohmic contact switches are given prime attention in this Chapter for its inherent broadband performances. Any micromachined switch can be divided into two categories based on the electrostatic actuation: vertically actuated switch and laterally actuated switch. All these switches are used in different applications at microwave to millimetre wave frequencies. The main challenges in these RF micromachined SPMT switches are to get broadband performances with good reliability. The organization of this Chapter is as follows; first part addresses extensive list of vertically actuated SPMT switches with experimental validations. It discusses © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 S. K. Koul and S. Dey, Micromachined Circuits and Devices, Lecture Notes in Electrical Engineering 859, https://doi.org/10.1007/978-981-16-9443-1_4

95

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4 Micromachined Single-Pole-Multi-throw Switching Networks

compact and reliable SPMT switching network that operates up to the X-band. The second part discuss four variants of the laterally driven SPnT switches (where, n = 2, 3, and 6). A systematic performance evaluation is presented here to investigate the working functionalities for different SPMT switches. This work is greatly expanded from the single-pole-three-throw (SP3T) to single-pole-fourteen-throw (SP14T) networks. Finally, this Chapter concludes with different high isolation switching networks with measured results.

4.2 Vertical Actuation of Micromachined Switching Networks To develop any SPMT switching network, the first important thing is to develop a ‘good’ single switch. The ‘good’ signifies in terms of its electromagnetic and electromechanical performances. The schematic top and side views of the switch with dimensions are depicted in Fig. 4.1a, b, respectively. This switch is cantilever type in nature and placed on the CPW line (16/34/16 μm = 50 , εr = 9.8). The switch is made off with 3.5–3.7 μm thick electroplated gold with an active electrode area of 34 μm × 62 μm. Switch is actuated using isolated pull-down electrodes and that makes a dc-contact with the output transmission line using a 1 μm depth dimple. ktotal = 2k1 //(k2 + k3 ) where k1 = Ew1

 3 t l1

Fig. 4.1 Schematic diagram of the a top and b side views of the single switch [4]. Copyright/used with permission of/courtesy of Institute of Physics (IOP) publishing limited

4.2 Vertical Actuation of Micromachined Switching Networks Table 4.1 Designed dimensions of the micromachined switch

97

Parameter

Value (μm)

Length of the mechanical spring, l 1

44.5

Width of the mechanical spring, w1

15.5

Length of the sharred tether, l 2

34

Width of the sharred tether, w2

14

Length of the sharred tether, l 3

110

Width of the sharred tether, w3

34

Length of the fixed electrode, l e

62

Thickness of beam, t

3.5

Air gap, g0

2.5

Dimple area

10 × 10

Dimple depth

1

k2 + k3 = Ew2

 3  3 t t + Ew3 l2 l3

(4.1)

The spring-mass model of the proposed switch contains mechanical springs k 1 , k 2 and k 3 , respectively, where k 1 is the mechanical spring and k 2 , k 3 are shared tether in the cantilever. Total spring constant (k total ) of the switch can be calculated using (4.1), where, w1 , w2 , w3 , l 1 , l 2 and l 3 are shown in Fig. 4.1a and listed in Table 4.1 for completeness. The calculated k total is ~14 N/m. Overall area between single cantilever and bottom electrode is le × w3 . Pull-in voltage (V p ) of the switch is  Vp =

8ktotal g03 27ε0 le w3

(4.2)

where g0 is the gap between beam and pull-down electrode and this value is 2.5 μm. The theoretical pull-in voltage of the switch is ~59 V considering ε0 = 8.854 × 10–12 F/m. The microscopic image of the fabricated switch is shown in Fig. 4.2a. Note that, fabrication process details are discussed in the Appendix B. Optical profilometer shows initial tip deflection of ~ 144 nm (upward) with 2.18 MPa/μm of stress gradient along the length of the beam of a single switch, as shown in Fig. 4.2b. The capacitance–voltage (CV) profile of the switch shows measured pull-in (V p ) and release voltages (V r ) of 65 V and 47 V, respectively, as depicted in Fig. 4.3a. Contact resistances (Rc ) of the switch are measured using a four-point probe method. Measured ON-state resistances are varying from 3.84 to 3.4  with 65–75 Vbias voltage, as depicted in Fig. 4.3b. The same measurement is repeated on 10 identical micromachined switches to ensure the switch performances. Results are also validated using fitted measured S-parameters data and Rc is plotted accordingly at different actuation voltages. The difference in Rc is attributed to the increase of the contact force by

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4 Micromachined Single-Pole-Multi-throw Switching Networks

Fig. 4.2 a Microscopic image and b measured profile of the switch [4]. Copyright/used with permission of/courtesy of Institute of Physics (IOP) publishing limited

Fig. 4.3 Measured a pull-in and release voltages, b change in Rc with applied bias, c mechanical resonance frequency and d switching time [4]. Copyright/used with permission of/courtesy of Institute of Physics (IOP) publishing limited

4.2 Vertical Actuation of Micromachined Switching Networks

99

higher bias voltages. Mechanical resonance frequency of the switch is obtained using LDV and the value is 48 kHz with Qm = 8, as shown in Fig. 4.3c. An on-switching time (t on ) of 11.3–8.8 μs and off-switching time (t off ) of 5.2 μs are obtained with an actuation voltage of 65–85 V from the switch, as depicted in Fig. 4.3d. Finally, switch demonstrates measured return loss of >30 dB, worst case insertion loss of ~0.26 dB and isolation of >21 dB up to 12 GHz. Now, different SPMT switch configurations are developed using this SPST switch and discussed in detail in the subsequent Sections. Before moving into the next section, note that all SPMT switches are fabricated utilizing the same fabrication process and all RF measurements are carried out using Agilent PNA series E8361C Vector Network Analyzer using cascade dc probes. Calibration is done using the short-open-load-through (SOLT) method. The conditions are (a) ON-wafer and using a probe station, (b) room-air, (c) standard laboratory pressure, temperature, and humidity, (d) non-packaged, and (e) no nitrogen blowing in the device. Now, we will discuss on different SPMT switches where M varies from 3 to 14 using this switch. To give a compact size on the SPMT switches, all single switches are placed in-line and adjacent grounds planes are connected with air bridges. Air bridges equalize the ground potential for better matching. All switches are connected at the centre using a radial anchor. The radius of the centre anchor is optimized using full wave simulator. Each switch is actuated separately using isolated pull-down electrodes and that makes a dc-contact with the output line. Switch is made with symmetric configuration, and it achieves the same RF performance from the common port to any output port. The angle between two consecutive switches is controlled and it is a function of the number of outputs lines. All switches are closely connected with each other using three anchors without causing many problems in fabrication. It helps to develop compact SPMT switching networks. A schematic of an SP8T switching network is shown in Fig. 4.4 as an example for better clarity. To compensate for the effect of impedance mismatch from the input line to the output lines, a capacitance is introduced using a fixed-to-fixed beam with different beam width (w) as per the requirements. This capacitance is also placed at certain distance (l1 ) away from the centre circle. The effect of the matching was also critically observed in all SPMT switches using a full wave high frequency structure simulator (HFSS) platform. The radius of the central junction or central anchor (r) is also optimized, and it also depends on the number of output lines. The equivalent circuit model of the SPMT switch is shown in Fig. 4.5. In this circuit, L b represents inductance due to cantilever beam, C b is the parallel plate capacitance between beam and the fixed electrode. C off is the switch OFF-state capacitance at zero-bias state, Rc is the contact resistance of the beam, Rbias is the bias resistance, C p represents the parasitic capacitance, C j represents the junction capacitance, and l2 is the output transmission line length. Near-port and far-port behaviours of the SPMT switches are systematically observed with the additional effect from the coupling between all input and output lines along with bias lines (30 k bias resistance) and dc pads (80 × 80 μm2 ). SP8T switch configuration is chosen here as an example and the same analysis is applicable in all kinds of similar SPMT switching networks. Note that, in SP8T switches port 1

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Fig. 4.4 The schematic of one of the SPMT (SP8T) switching network [4]. Copyright/used with permission of/courtesy of Institute of Physics (IOP) publishing limited

Fig. 4.5 Equivalent circuit model of the SPMT switches where M varies from 3 to 14 [19]. Copyright/used with permission of/courtesy of Institute of Physics (IOP) publishing limitedCopyright/used with permission of/courtesy of Institute of Physics (IOP) publishing limited

and port 8 are near port and port 3 to port 7 are the far ports, [see Fig. 4.4]. Figure 4.6 shows simulated return loss and insertion loss performances between FEM (HFSS) and ADS circuit model responses. This performance is observed between port 1 (near-port) and port 4 (far-port). Figure 4.6a shows SP8T switch delivers excellent matching with a return loss of better than 18 dB and worst-case insertion loss of ~1.5 dB up to 40 GHz frequency. Matching between input to near port (port 1) is 2.89 dB better than the far port (port 4).

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Fig. 4.6 a Simulated return and insertion loss of SP8T switch using circuit model and HFSS simulation and b simulated input and output return loss of the SP8T switch with different C j [4]. Copyright/used with permission of/courtesy of Institute of Physics (IOP) publishing limited

It is observed that the far port exhibits narrower return loss bandwidth compared to the near port. This is mostly due to the strong coupling existing between input to port 1. Moreover, Fig. 4.6b shows 3.93 fF gives better matching compared to other junction capacitances (C j ) and it is formed with 22 μm of beam width (w). The isolation and matching responses of the SP8T switch is controlled by input and output lines, radius of the central junction, switch beam length, junction capacitance (C j ) and resistivity of the bias lines. Similar analysis is required to be carried out for all SPMT switching networks before going for the fabrication and measurement stages. Now electromagnetic performances of the different SPMT switches are discussed.

4.2.1 Single-Pole-Three-Throw (SP3T) Switch Design and Measurement The microscopic image of the single-pole-three-throw (SP3T) switching network is shown in Fig. 4.7a. All the three switches are placed at θ = 90° and they are in-line in nature. Measured isolation characteristics of the SP3T shows better than 26 dB of isolation up to 20 GHz with 18 fF of capacitance, as depicted in Fig. 4.7a. Switch demonstrates measured return loss of better than 22 dB and worst-case insertion loss of 0.35 dB up to 12 GHz with 62 V of bias voltage, as shown in Fig. 4.7a. Total area of the SP3T switch is 0.43 mm2 .

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Fig. 4.7 Microscopic images and S-parameter responses of the fabricated. a SP3T, b SP6T and c SP7T switches [19]. Copyright/used with permission of/courtesy of Institute of Physics and IOP publishing limited

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4.2.2 Single-Pole-Six-Throw (SP6T) Switch Design and Measurements The microscopic image of the fabricated single-pole-six-throw (SP6T) switch is shown in Fig. 4.7b. All switches are placed here with an angle of θ = 51.42°. All six switches are anchored at the center and center anchor radius is optimized to 18 μm for better matching without causing difficulties in fabrication. A junction capacitance (C j ) is introduced at the input line with a fixed-to-fixed beam structure. C j is optimized using an FEM solver to improve the matching performance of the switches. SP6T switch demonstrates measured return loss of >21 dB, worst case insertion loss of 18 dB up to 12 GHz, as depicted in Fig. 4.7b. Total area of the SP6T switch is 0.58 mm2 .

4.2.3 Single-Pole-Seven-Throw (SP7T) Switch Design and Measurements The microscopic image of the fabricated single-pole-seven-throw (SP7T) switch is shown in Fig. 4.7c. Central anchor radius is optimized to 29 μm. Total area of the SP7T switch is 0.64 mm2 . Switch shows measured return loss of better than 20 dB and insertion loss of ~14 dB up to 40 GHz, as depicted in Fig. 4.8d. Switch isolation result is obtained when all 8 switches are in the OFF-state that is 2–2.6 dB worse than the isolation with one switch in the ON-state condition, as depicted in Fig. 4.8d.

4.2.5 Single-Pole-Ten-Throw (SP10T) Switch Design and Measurements Microscopic image of the single-pole-ten-throw (SP10T) switch is shown in Fig. 4.8a.

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Fig. 4.8 a Microscopic image and b S-parameter responses of the fabricated SP10T switch [19]. Copyright/used with permission of/courtesy of Institute of Physics (IOP) publishing limited

Total area of the switch is 0.83 mm2 . Switch demonstrates return loss of >15 dB, worst case insertion loss of ~1.5 dB and isolation of 16.3 dB up to 12 GHz, as depicted in Fig. 4.8b.

4.2.6 Single-Pole-Eleven-Throw (SP11T) Switch Design and Measurements The fabricated image of the single-pole-eleven-throw (SP11T) switch is shown in Fig. 4.9a. The centre anchor radius is optimized to 120 μm and switches are placed at an angle of 30°. Switch demonstrates measured return loss of better than 15 dB,

Fig. 4.9 a Microscopic image and b S-parameter responses of the fabricated SP11T switch [19]. Copyright/used with permission of/courtesy of Institute of Physics (IOP) publishing limited

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Fig. 4.10 a Microscopic image and b S-parameter responses of the fabricated SP12T switch [19]. Copyright/used with permission of/courtesy of Institute of Physics (IOP) publishing limited

worst case insertion loss of 1.67 dB and isolation of >17 dB up to 12 GHz, as depicted in Fig. 4.9b. Total area of the SP11T switch is 0.92 mm2 .

4.2.7 Single-Pole-Twelve-Throw (SP12T) Switch Design and Measurements Microscopic image of the single-pole-double-throw (SP12T) switch is shown in Fig. 4.9a. Central anchor radius of the switch is 144 μm and total area of the SP12T switch is 1.03 mm2 . All 12 switches are placed at an angle of 27.7°. Switch demonstrates measured return loss of better than 15 dB, worst case loss of 1.67 dB and isolation of >17 dB up to 12 GHz, as depicted in Fig. 4.10b.

4.2.8 Single-Pole-Fourteen-Throw (SP14T) Switch Design and Measurements The microscopic image of the fabricated single-pole-fourteen-throw (SP14T) switch is shown in Fig. 4.11a. Total area of the switch is 1.2 mm2 . All 14 switches are anchored at the center and anchor radius is optimized to 178 μm. All SPST switches are placed at an angle of 24° to build the complete SP14T network. Switch shows return loss of >14 dB, insertion loss of 14.5 dB up to 12 GHz, as depicted in Fig. 4.11b.

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Fig. 4.11 a Microscopic image and b S-parameter responses of the fabricated SP14T switch [19]. Copyright/used with permission of/courtesy of Institute of Physics (IOP) publishing limited

4.2.9 Design Guidelines of the MEMS SPMT Switches After extensive measurements of the single micromachined switch, different SPMT switches are developed using identical switches. Each switch is actuated separately using an isolated pull-down electrode that makes dc-contact with the output line. To compensate for the effect of impedance mismatch from the input to the output line, a junction capacitance (C j ) is introduced on the input line and optimized for all switching configurations. SPMT switch parameters that vary with number of ports are mostly limited to (a) angle of switch separation, (b) central anchor radius, and (c) parasitic inductive effect from the central anchor and switches. In addition, non-uniform tip deflections may happen during batch production due to different electroplated thickness of the gold cantilever beam. It also affects the switch performances with different values of C off at non-actuated state and different values of Rc with the same bias voltage at ON-state. In these switches, 192–176 nm deformation was observed due to 3.4–3.72 μm variation from beam thickness. Note that, demonstrated isolations were measured when all switches were in the up-state that is 2.7–3.2 dB worse than the isolation with one switch in ON-state condition. The figure-of-merit (FOM) performance of the SPMT switch are obtained using (4.3) and the same are listed in Table 4.2 for completeness. FOM = f c =

1 2π Rc Coff

(4.3)

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Table 4.2 Circuit parameters of the SPMT micromachined switches (M = 3–14) [19] Parameter

SPST

SP3T

SP4T

SP6T

SP7T

SP10T

SP11T

SP12T

SP14T

l 1 (μm)

156

168

190

212

216

244

264

272

286

l 2 (μm)

156

172

196

218

228

250

278

293

302

C j (fF)

NA

NA

3.4

3.66

3.86

4.06

4.13

4.32

~4.4

L b (pH)

23

26

~27

27.8

28.6

32

37

41

46

Rc ()

0.42

0.68

0.87

1.02

1.18

1.48

1.6

1.77

1.82

C off (fF)

23

22.4

23.4

22

22.8

21.8

~23

22.7

24.12

Rbias (k)

9.8

9.4

9.7

~10

9.8

9.2

9.6

~10

10.2

C b (fF)

13.6

13.2

14.4

12.8

13.77

~14

13.96

14.12

14.08

V p (V)

63

63

64

64

64

67

65–68

67–70

67–70

FOM (THz)

16.48

14.45

7.82

7.09

5.91

4.93

4.32

3.96

3.62

4.2.10 IIP3 Measurements of the Micromachined SPMT Switches The third order intermodulation intercept point (IIP3) of the SPMT switches are measured using a two tone test up with f 1 = 1.94 GHz and f 2 = 1.98 GHz. The IIP3 measurement setup has already been shown in Fig. 3.21a. Single switch demonstrates measured IIP3 of 53 dBm at up-state, as shown in Fig. 4.12a. Later, IIP3 measurement is carried out on different SPMT switching networks using the same set up. Measured average IIP3 values of the SPMT switch are 50 dBm and 14 dBm at up- and downstates, respectively, as shown in Fig. 4.12b. A variation of IIP3 is found between 0.44 and 0.92 dBm from all SPMT switches, as depicted in Fig. 4.12b. IIP3 values plotted in Fig. 4.12b are the average values obtained from each port in up- and down-state conditions. Down state performance is entirely driven by Rc . Note that, one of the

Fig. 4.12 IIP3 measurements of the SPMT switches where, a SPST switch and b SPMT switch with different RF output ports [19]. Copyright/used with permission of/courtesy of Institute of Physics (IOP) publishing limited

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higher versions of the vertically actuated SPMT switch (SP16T) is discussed in the subsequent Sections.

4.3 Design, Analysis and Measurements of Single-Pole-Sixteen-Throw Switch 4.3.1 SP16T Switch Design and Analysis The Single-Pole-Sixteen-Thru (SP16T) switch is a standalone component in modern switched beam satellite antenna system. A SP16T switch has recently been reported with 5 SP4T switches in [21] where two switches need to be actuated to activate one arm. To improve the design complexity and performance further, a new topology of the SP16T switch is presented in this work. Here, in this topology only one switch needs to be actuated to get the output RF signal. SP16T switch is implemented on coplanar waveguide (CPW) line made off with 2 μm thick electroplated gold on the 635 μm alumina substrate. This CPW (16/34/16 μm = 50 ) line is routed in a circular configuration where it utilizes 16 cantilever type inline MEMS switches. The switch is made off with 3–3.5 μm thick electroplated gold with an active electrode area of 34 μm × 50 μm. Microscopic image and equivalent circuit model of the SPST switch is shown in Fig. 4.13. Figure 4.14 presents schematic diagram and equivalent circuit representation of the proposed symmetric and circular type MEMS SP16T switching network. To make compact size of the SP16T structure, CPW line is given a circular shape where all 16 MEMS switches are placed. The angle between two consecutive switches is 21.17° and all switches are closely packed without causing problems in fabrication. The effective radius of the dimple is 5.5 μm with a depth of 1 μm and it is placed on the CPW line.

Fig. 4.13 a Microscopic image and b equivalent circuit model of the SPST switch [22]. Reproduced with permission from IEEE

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109

Fig. 4.14 a Schematic diagram and b equivalent circuit model of the SP16T switch [22]. Reproduced with permission from IEEE

Moreover, all adjacent CPW ground planes are connected with air bridges to equalize the voltages on the two ground planes for better matching. Furthermore, to have desired performance bandwidth up to K-band, 8 air bridges were used to connect CPW center ground line to the adjacent ground plane, as shown in Fig. 4.14a. As shown in Fig. 4.14b, RON (3.08 ), C off (19.3 fF) and t-line elements are used to represent different sections. The distance between two consecutive switches was optimized to 138 μm. Near port and far port performances of the SP16T switch were investigated with the effect of coupling between lines in the switch with bias lines (24 k bias resistance) and dc pads, using full wave simulation. Here, in this configuration port 1 (P1) port 16 (P16), port 2 (P2) port 15 (P15) and port 3 (P3) port 14 (P14) are considered near ports. Rest all other ports are far port as they are apart 552 μm away from the centre point of the common port. Maximum far port distance is 1104 μm. In addition to this, bias line arrangement (in terms of length) between all odd to even or even to odd ports (like P1 and P16 or P4 and P13) was kept identical to achieve the same characteristic in S-parameters. To overcome the off-path resonance and to compensate for the impedance mismatch at the central junction, a metal-air-metal (MAM) capacitance (C j ) was introduced with 20 μm beam width and the effect of its input/output matching (S 11 and S 22 ) is also investigated up to 26 GHz using high frequency structure simulator (HFSS), as shown in. Figure 4.15a. Result shows 3.54 fF of capacitance gives optimum response in terms of matching. Also note that, placement of the C j is an important factor and it was optimized to be 60 μm from the central point of the T-junction. Moreover, C j also reduces the reflection coming back from the T-junction and equalize the ground potential between two CPW grounds up to a reasonable extent. To investigate the near-port (P1or P16) and far-port (P8 or P9) performances with the effect of coupling between lines in the SP16T switch, full wave FEM simulations were carried out in HFSS. As a matter of fact, ADS model is very useful to look inside through equivalent circuit model (see Fig. 4.14b) but it does not differentiate

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Fig. 4.15 a Simulated input and output return loss of the SP16T switch with different junction capacitances (C j ) and b Simulated return and insertion loss of SP16T switch using equivalent circuit model and HFSS simulation [22]. Reproduced with permission from IEEE

between near and far ports with the coupling between lines within the SP16T switch. Figure 4.15b reveals that the SP16T switch delivers good matching characteristics up to 26 GHz with return loss of better than 17.6 dB at 20 GHz and 15.4 dB at 26 GHz. Simulated worst case insertion loss is 1.63 dB at 20 GHz and 1.77 dB at 26 GHz, respectively. Impedance matching between central junction to near port (P1) is 3.3 dB better than the far port (P8) response. It is mostly due to the strong coupling effect between common port to near port. Far port exhibits narrower return loss bandwidth than the near port. In this SP16T switch configuration, matching and isolation responses are mostly limited by i/p and o/p transmission lines, length of the switch, junction capacitance and resistivity of the bias lines.

4.3.2 Measurements of the SP16T Switches Prior to start with the SP16T switch, single switch performances were critically evaluated. Initially, an optical profilometer shows initial tip deflection of ~130 nm (upward) with ~2.1 MPa/μm of stress gradient along the length of the cantilever. Switch gives measured mechanical resonance frequency of 52.3 kHz with a Q-factor of 7.9. Measured pull-in (V p ) and release voltages (V r ) of the switch are 72 V and 53 V, respectively. Measured on-switching (t on ) time of 11.2–8.03 μs and off-switching time of 4.78 μs were obtained with an actuation voltage of 72–85 V. RF measurement was done using Agilent PNA series E8361C Vector Network Analyzer using cascade dc probes. Measurements were calibrated using SOLT standard to the probe tips and the measurement include 740 μmCPW input and output transmission lines with an estimated loss of 0.16 dB up to 26 GHz. Figure 4.16a presents measured and modelled S-parameters of the single switch with C off = 18.7

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111

Fig. 4.16 a Measured versus simulated S-parameter performances of the SPST switch and b measured IIP3 of the SPST switch [22]. Reproduced with permission from IEEE

fF, Ron = 0.81–0.76  and L b = 390 pH, respectively. The switch is well matched with return loss >18 dB up to 26 GHz. The measured insertion loss is 0.46–0.39 dB up to 26 GHz with an applied bias of 72–80 V. Isolation of the switch is >18 dB till up to 26 GHz. No package was placed on top of the measured switch. Third-order intermodulation intercept point (IIP3) was measured for the SPST switch using a two-tone test at f 1 = 1940 MHz and f 2 = 1980 MHz, respectively. SPST switch shows IIP3 of 47 dBm, as shown in Fig. 4.16b. Here, switches passive intermodulation is weakly dependent on the metal contact non-linearity and it is mostly limited by the contact resistance of the ground-signal-ground (GSG) probe and input, output CPW transmission lines on the ceramic substrate. The microscopic image of the fabricated SP16T switch is shown in Fig. 4.17. SP16T switch demonstrates 1.47–1.89 dB of insertion loss from 18 to 26 GHz with Ron = 2.8–3.08 , as shown in Fig. 4.18a. The device is well matched with >14 dB of return loss up to 26 GHz with L b = 540 pH and C j = 3.54 fF, as shown in Fig. 4.18. These results are also verified by full wave simulation. The measured S-parameter responses for all odd ports (P1, P3, P5, P7, P9, P11, P13 and P15) are closely followed with even ports (P2, P4, P6, P8, P10, P12, P14 and P16) responses, as predicted from the simulation response (see Fig. 4.15b). Moreover, it is also observed that loss and matching are degraded from near port to far port. The maximum measured deviation of return loss between near port (P1 or P16) to far port (P7 or P9) is ~3 dB at 20 GHz and ~3.8 dB at 26 GHz which successfully validates simulated return loss deviation of ~3.3 dB. Moreover, insertion loss variation from near to far port is 1.5–1.72 dB at 20 GHz and 1.6–1.78 dB at 26 GHz with a bias voltage of 80 V. The isolation 14 dB at 26 GHz with C off of the SP16T switch is > 15.8 dB at 20 GHz and > ∼ = 19.3 fF, as depicted in Fig. 4.19a. C off change of 18.7–19.3 fF was observed between all 16 MEMS switches in SP16T due to 0.13–0.163 μm variation in beam tip deflection (upward). The demonstrated isolation was measured when all switches

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4 Micromachined Single-Pole-Multi-throw Switching Networks

Fig. 4.17 Microscopic images of the MEMS SP16T switching network [22]. Reproduced with permission from IEEE

were in the up-state that is 1.8–2.8 dB worse than the isolation with one switch ONstate condition. The device is unpackaged and has variation in the contact resistance for the different ports due to contact contamination. Measured IIP3 of the SP16T switch is 50 dBm as shown in Fig. 4.19b.

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Fig. 4.18 Measured return loss and insertion loss performances of the SP16T switch at all, a even ports and b odd ports over 18–26 GHz [22]. Reproduced with permission from IEEE

Fig. 4.19 a Measured and simulated isolation characteristics of the SP16T switch and b measured IIP3 of the SP16T switch [22]. Reproduced with permission from IEEE

4.4 Lateral Actuation of Switching Networks Lateral switches have attracted considerable attentions as the strongest alternatives to the conventional vertically driven micromachined switches owing to their high broadband isolation and no dielectric charging properties. The performance of the contact type lateral micromachined switches are investigated by different research groups and most variants are implemented in coplanar waveguide (CPW) transmission line. These switches demonstrate in-plane design flexibility, reliable mechanical stability, and high reliability [18–20]. The work reported in this Section greatly improves the overall performance of five variants of the SPMT community (where, n = 2, 3, 4, 6 and 7). All switches are fabricated using the same process as like before

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4 Micromachined Single-Pole-Multi-throw Switching Networks

and described in Appendix B. As before, single lateral switch performances will be discussed initially and this will be used as the functional building block in the SPMT networks.

4.4.1 Design and Measurements of Single Lateral MEMS Switch Microscopic images of the single lateral micromachined switch is depicted in Fig. 4.20a. The lateral switch includes 50  coplanar waveguide (CPW) line (G = 35 μm, W = 80 μm) and a movable beam between the input and output ports on alumina substrate (εr = 9.8). This movable beam is fixed at one port (input) which comes in contact with the output line based on electrostatic actuation. A spring is attached at the centre of the cantilever beam and is positioned between the cantilever beam and the ground of the CPW. The spring has a semi-triangular shape and optimized with different angle θ variations in electromechanical solvers. Finally, θ = 30° gives optimum response in terms mechanical stability with dedicated bias post and robust movable beam as shown in Fig. 4.20a. All optimized switch dimensions are marked in Fig. 4.20a. The mechanical force of the spring provides an additional force to move the beam back to its rest position when the switch is in the OFF-state.

Fig. 4.20 a SEM image of the fabricated lateral MEMS switch where all optimized structural parameters are marked and b its equivalent circuit model [23]. Reproduced with courtesy of The Electromagnetics Academy

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The electrostatic actuation (V a ) between the center line of the beam and ground causes it to move in a lateral direction towards the mechanical stopper of the output port (see Fig. 4.20a). Note that, when the beam moves, it is necessary to contact the second port of the center line without touching the ground line to avoid shortcircuited condition. Primary design criteria here is to keep a 14.5 dB have been obtained from the vertical SP14T switching configurations up to 12 GHz. Maximum area of the vertical SPMT switching network is 1.2 mm2 . Different lateral MEMS switching networks are presented. Matching and loss of MEMS lateral switching network can be further improved by reducing the parasitic

4.6 Conclusions

121

inductive effects caused by switches. These effects largely occur between the central junctions of adjacent switches. Parameters such as central junction length (as well as switch footprint, parasitic inductive effects) may be characterized using a full wave simulation. The results of the full wave simulation may then be utilized to modify the switch parameters, thereby improving, or optimizing overall performance. In addition, CPW discontinuities (e.g., between adjacent switches) may include inductive bends. The purpose of these bends is to eliminate higher order modes. The bias pads of the switches may also be routed in a manner that avoids signal leakage and other parasitic effects without affecting the switch performance. The bias pads and lines may themselves be made of a conductive material (e.g., titanium tungsten), and a film or layer of dielectric material (e.g., silicon dioxide) may be positioned between the bias lines and the CPW to prevent shorting. Another beneficial property of the configuration of above example switches is their symmetry (e.g., equal angle between each throw of a given switch). This configuration of the above example switches permits them to be placed closer together with one another (in designs that accommodate multiple switches). This means that a device with multiple MEMS RF lateral switches (e.g., a phase shifter) may be designed with greater compactness without any fabrication difficulties. The symmetry is especially beneficial for improving compactness of the design. All switch configurations may lead to reduction of overall area of a device including these switches on the order of square microns or even square millimetres, as compared to other conventional topologies. The maximum return loss of better than 12 dB, worst case insertion loss of ~5.89 dB and maximum isolation of >21 dB have been obtained from the SP7T lateral switching configurations up to 30 GHz. Switch performances could be improved further in hermetic condition to overcome the effect of surface charges trapped due to some residual humidity and stiction due to the non-clean environment. This Chapter concludes with a brief discussion on the current state-of-the-art phase-change materials based RF micromachined switches and switch matrix.

References 1. Lucyszyn S (2010) Advanced RF MEMS. Cambridge University Press 2. http://www.4gamericas.org/files/6514/3930/9262/4G_Americas_5G_Spectrum_Recommend ations_White_Paper.pdf 3. Botula A et al (2009) A thin-film SOI 180 nm CMOS RF switch technology. In: Proceedings of IEEE topical meeting silicon monolithic integrated circuits in RF systems, pp 1–4 4. Koul SK, Dey S, Poddar AK, Rodhe UL (2016) Ka-band reliable and compact 3-bit TTD phase shifter using MEMS single-pole-eight-throw switching networks. J Micromech Microeng 5. Dey S, Koul SK (2015) Reliability analysis of Ku-band 5-bit phase shifters using MEMS SP4T and SPDT switches. IEEE Trans Microw Theory Techn 63(12):3997–4012 6. Rebeiz GM, Theory RFMEMS (2003) Design, and technology. Wiley, Hoboken 7. Zareie H, Rebeiz GM (2014) Compact high-power SPST and SP4T RF MEMS metal-contact switches. IEEE Trans Microw Theory Tech 61(8):2397–2402 8. Liu AQ, Palei W, Tang M, Alphones A (2008) Single-pole-four-throw switch using high-aspectratio lateral switches. Electron Lett 40(18):1281–1282

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9. Patel CD, Rebeiz GM (2012) A high-reliability high-linearity high-power RF MEMS metalcontact switch for DC-40- GHz applications. IEEE Trans Microw Theory Tech 60(10):3096– 3112 10. Dey S, Koul SK (2016) Systematic measurement of high isolation DC—20 GHz miniature MEMS SPDT switch. Microw Opt Technol Lett 58(5):1154–1159 11. Lee J, Je CH, Kang S, Choi CA (2005) A low-loss single-pole six-throw switch based on compact RF MEMS switches. IEEE Trans Microw Theory Tech 53(11):3335–3344 12. Yang H-H, Yahiaoui A, Zareie H, Blondy P, Rebeiz GM (2013) Symmetric and compact singlepole multiple-throw (SP7T, SP11T XE “SP11T”) RF MEMS Switches. J Microelectromech Syst 24(3):685–695 13. https://www.rfmd.com/product-category/switches 14. Chaudhry Q, Bayruns R, Arnold B, Sheehy P (2012) A linear CMOS SOI SP14T antenna switch for cellular applications. In: IEEE radio frequency integrated circuits symposium, pp 155–158 15. Dey S, Koul SK (2013) Design and development of a CPW-based 5-bit switched-line phase shifter using inline metal contact MEMS series switches for 17.25 GHz transmit/receive module application. J Micromech Microeng 24(1):24 16. San HS, Chen XY, Xu P, Li G, Zhan LX (2008) Using metalinsulator-semiconductor capacitor to investigate the charge accumulation in capacitive RF MEMS switches. Appl Phys Lett 93(6):063506-1–063506-3 17. Li G, San HS, Chen XY (2009) Charging and discharging in ion implanted dielectric films used for capacitive radio frequency microelectromechanical systems switc. J Appl Phys 105(12):124503-1–124503-6 18. Yamane D, Sun W, Seita H, Kawasaki S, Fujita H, Toshiyoshi H (2011) A Ku-band dualSPDT RF-MEMS switch by double-side SOI bulk micromachining. J Microelectromech Syst 20(5):1211–1221 19. Dey S, Koul SK, Poddar AK, Rohde UL (2016) Extensive performance evaluations of RF MEMS single-pole-multi-throw (SP3T–SP14T) switches up to X-band frequency. J Micromech Microeng 27(1):1–9 20. Lee J, Je CH, Kang S, Choi CA (2005) A low-loss single-pole six-throw switch based on compact RF MEMS switches. IEEE Trans Microw Theory Tech 53(11):3335–3344 21. Kingsley N, Kirby P, Ponchak G,Papapolymerou J (2014) 14GHz MEMS 4-bit phase shifter on silicon. In: Topical meeting on silicon monolithic integrated circuits in RF systems, pp 326–328 22. Koul SK, Dey S (2018) MEMS K-band 4-bit phase shifter using two back-to-back SP16T switching networks. IEEE J Microelectromech Syst 27(4):643–655 23. Dey S, Koul SK, Poddar A, Roddhe U (2019) Compact, broadband and reliable lateral MEMS switching networks for 5G communications. In: Progress in electromagnetic research (PIERM), vol 86, pp 163–171 24. Singh T, Mansour RR (2018) Chalcogenide phase change material GeTe based inline RF SPST series and shunt switches. In: IEEE MTT-S international microwave workshop series on advanced materials and processes for RF and THz applications (IMWS-AMP 2018), Ann Arbor, MI, USA 25. Singh T, Mansour RR (2019) Miniaturized DC–60 GHz RF PCM GeTe-based monolithically integrated redundancy switch matrix using T-type switching unit cells. IEEE Trans Microw Theory Tech 67(12):5181–5190 26. Singh T, Mansour RR (2019) Characterization, optimization, and fabrication of phase change material germanium telluride based miniaturized DC–67 GHz RF switches. IEEE Trans Microw Theory Tech 67(8):3237–3250 27. El-hinnawy N, Borodulin P, Wagner BP et al (2013) A 7.3 THz cutoff frequency, inline, chalcogenide phase-change RF switch using an independent resistive heater for thermal actuation. In: IEEE compound semiconductor integrated circuit symposium (CSICS), Monterey, CA, pp 1–4

Chapter 5

Micromachined Resonators and Circuits

5.1 Introduction The concepts of MEMS resonators were introduced in their early form in the 1960s [1]. Today, MEMS resonators are generating considerable research interest and commercial applications. Significant improvements have already been made of the MEMS market because of their numerous large volume and high impact applications. These include sensing applications, where changes in a resonant element are used to monitor a given quantity [2], timing applications, where a resonant element is used within an electronic system to generate a high-quality clock signal [3], or in filtering applications, where resonant structures implement filters that can be of use in radiofrequency wireless transceivers [4]. MEMS resonator-based devices rely on resonant vibrations to accomplish one or more tasks effectively. MEMS resonators are expected to become prevalent in these applications because they are well-suited to low-cost batch fabrication, being manufactured with fabrication techniques similar to those widespread in integrated circuit manufacturing. Moreover, unlike other resonant elements such as quartz crystals, MEMS resonators have the potential for higher levels of integration with microelectronics at the die or package level [5]. These advantages can lead to reduced cost and form-factor systems that can have enhanced performance and more functionality. However, before MEMS resonators can completely replace other types of resonant elements, some challenges remain such as material limitations, temperature stability, packaging or batch integration with electronics. One needs to have a firm understanding of this highly interdisciplinary field and a firm understanding with the fundamental theory of mechanical vibrations.

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 S. K. Koul and S. Dey, Micromachined Circuits and Devices, Lecture Notes in Electrical Engineering 859, https://doi.org/10.1007/978-981-16-9443-1_5

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5.2 Basic Resonator Model and Properties In a vibrating mechanical system, the kinetic and potential energies are continuously converted to each other. Most systems exhibit a frequency-dependent response where this transfer of energy is optimum at certain frequencies (i.e., losses are minimum), known as the resonant frequencies of the system. For low enough damping, the system response shows peaks at these frequencies. Additionally, each resonant frequency corresponds to a particular pattern of motion for the components of the mechanical system, which is known as a mode shape. To exhibit resonance, a mechanical system must possess the capacity to store both kinetic and potential energies. Therefore, the basic resonator structure is a mass-spring system. In physical systems, additionally, there are always energy loss mechanisms. A simple model for mechanical losses is a damper. This combination of the mass-damper-spring system represents the simplest model for a resonator, as shown in Fig. 5.1. Using Newton’s laws of motion, the relationship between the displacements of the mass and input force is given by; Meff

∂2x ∂x + K eff x = Fin + ζeff ∂t 2 ∂t

(5.1)

where Fin is the input force, Meff is the effective mass of the system, K eff is the effective stiffness, and ζeff represents the effective total losses in the system. The system transfer function is given by 1 1 X (s) = = H (s) = 2 Fin (s) Meff s + ζeff s + K eff K eff



1 ω0 2 s + Q s + ω0 2

 (5.2)

where s is the complex frequency, ω0 is the undamped resonant frequency of the system (i.e., natural frequency) and Q is the quality factor. For a second-order system, the undamped resonant frequency is:  ω0 = 2π f o =

Fig. 5.1 Schematic of a mass-spring-damper system

K eff Meff

(5.3)

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The quality factor is defined as: Q = 2π

Average energy stored Energy lost per cycle

(5.4)

Parameters ω0 (or f 0 ) and Q are the two significant performance metrics in the microresonator domain. Due to their sizes, the resonant frequencies of micro devices are typically in kHz to MHz range but can be in the GHz range for properly designed devices [6–8]. For a device that is intended to be used as a micro-resonator, Q ranges from thousands to millions depending on the operating conditions and device design [9–11]. Many applications benefit from maximizing both the resonant frequency and quality factor of a resonator even though there is some trade-off between the two. Consequently, their product, f 0 .Q, is a common figure of merit stated for resonators [12, 13]. The relationship between resonant frequency, ωr , and the undamped natural frequency, ω0 , of a second-order system is [14]:  ωr = ω0

1 1− 2Q 2

 (5.5)

For large quality factors, as is the case for most micromachined resonators,ωr ≈ ωo. By running a single frequency response measurement, one can estimate the resonant frequency of a microresonator by locating the peak in the frequency response while the quality factor (for Q  1) can be estimated from: Q=

ω0 ∂H (ω)  f −3dB 2 ∂ω f0

(5.6)

where  f −3dB is the −3 dB bandwidth around the resonant frequency. In addition to a narrower bandwidth, high-Q systems exhibit a higher peak amplitude at resonance that is Q times the low-frequency response. While the basic second-order model of the resonator is quite useful to study a device response near its resonant frequency, it is often rather simplistic. Most mechanical systems, even those composed of discrete components, have numerous different mode shapes and corresponding resonant frequencies. If the resonant frequencies are far from each other, the device response can be analysed using the basic mass-springdamper method around each resonant frequency. Otherwise, a higher-order model needs to be constructed that can potentially include the coupling between different modes. Some continuous mechanical systems can be broken into simpler subsystems, allowing for the treatment of the system as a lumped one. This is particularly helpful when it is possible to estimate concentrated masses and the effective stiffnesses of bodies that connect them to each other within the structure. In many cases, however, the whole system needs to be treated as a distributed mass-spring system. Dynamics of such systems is studied using acoustic wave propagation models and theories [15].

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Distributed systems, in theory, have infinite mode frequencies and shapes. In practice, however, a limited number of these modes need to be studied in the frequency band of interest. The basic spring-mass-damper model can once again be used if one estimates the effective mass and stiffness of the system for the mode shape of interest. Rayleigh’s method is a fairly robust and yet simple technique to estimate the effective mass and stiffness of a system once good estimates for the mode shape of the device are available [16, 17]. If the losses can be ignored, the resonant frequency of the nth mode of the system can be found from: ωn2

− → − → [x] [K][x] =  − → − → ˙ [x] ˙ [M][x]

(5.7)

− → where [K] and [M] are the stiffness and mass matrices for the system and [x] and − → [x] ˙ are the displacement and velocity vectors for the nth mode shape of interest, respectively.

5.3 Electromechanical Properties of MEMS Resonators In a typical micro-resonator application, the micromechanical structure is forced into vibrations by converting an input electrical signal into a force and applying it to the device. Vibrations of the structure are then picked up and often converted back to the electrical domain through various transduction techniques. Consequently, from the point of view of interrogating instruments, the device is assumed electrical. On the other hand, it is common to use the analogy between electrical and mechanical resonators to build an equivalent electrical circuit for a micromachined resonator [15, 18–21]. Such a model is often built from a set of experimental measurements and then is used in electric circuit simulators. This approach is particularly useful if the resonator needs to be modelled with the drive or sense electronics, allowing for co-simulation of the entire system within the electrical domain. To represent a mechanical device with electrical elements, proper mapping of mechanical to electrical quantities is needed. A common set of mapping rules is summarized in Table 5.1 [17–19]. In most cases, a resonant device is modelled as a series Resistance-InductanceCapacitor (RLC) circuit. The transductions from the electrical to mechanical domain and vice versa are modelled with transformers with proper winding ratios or controlled voltage or current sources. Other elements, especially parasitic and feedthrough capacitors, may be added to the equivalent circuit so that the model produces results like experimental measurements. Figure 5.2 illustrates an equivalent electrical model for a micro-resonator with electrostatic input and output ports. The transformer at the input port converts an input voltage to a force and applies it to the mechanical system represented by the series RLC circuit. At the output,

5.3 Electromechanical Properties of MEMS Resonators Table 5.1 Correspondence between electrical and mechanical domains

Mechanical domain

127 Electrical domain

Force, F

Voltage, V

Velocity, x˙

Current, I

Displacement, x

Charge, q

Compliance, 1/K

Capacitance, C

Mass, M

Inductance, L

Damping, ζ

Resistance, R

Fig. 5.2 Equivalent electrical representation of an electrostatic resonator including the feedthrough capacitor C f and parasitic capacitors C pi and C po

another transformer converts velocities of the mechanical structure back to an electrical current. Similar models can be developed for other transduction mechanisms such as piezoelectric or thermal devices considering the mechanisms involved in converting the electrical signal to a mechanical one and vice versa. In all cases, the electromechanical coupling coefficients, ηin and ηout , need to be defined according to the employed transduction mechanism. It is common practice to simplify the model further by removing the transformers and scaling the equivalent circuit values accordingly. Note the inclusion of the feedthrough capacitance in the model. This parasitic capacitance, in many cases, poses a challenge in proper measurement of resonator response as the feedthrough current that travels through it can be significantly larger than the current produced by the resonator.

5.4 Circuit Model Representation of MEMS Resonators 5.4.1 Flexural Modes Flexural mode vibrations are characterized by bending of the structure along its length (l) such that the motion takes place in the transverse direction perpendicular

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Fig. 5.3 Common flexural mode beams classified according to the boundary conditions: a cantilever, b clamped–clamped beam, c free–free beam, [20]

to the length. Flexural modes can be excited in both the beam and plate structures. In the case of beams, the motion could be within the plane of fabrication (i.e., along its width w) or out of the plane (i.e., along its thickness t). For beam structures, the vibration mode shape is determined by the boundary conditions applied to the structure. Various examples of flexural mode shapes are illustrated in Fig. 5.3 along with the corresponding boundary conditions applied to the beam. The resonant frequency of a given mode for a beam resonator of length L and thickness t vibrating out of plane can be generalized according to the following formula: 



t f =β 2 L



E ρ

(5.8)

where β is a dimensionless coefficient that is determined by the shape of the vibration mode, which in turn depends on the respective boundary conditions applied to the structure (5.8) assumes that the beam is fabricated with one material whereby E denotes Young’s modulus and ρ is the density. As can be seen from (5.8), the resonant frequency is independent of the beam width when it is vibrating in the thickness direction. Figure 5.4 summarizes the most common flexural modes based on beam structures, classified according to the boundary conditions applied. The corresponding values of β have been referenced from [20]. Figure 5.4 illustrates the fundamental modes observed in membrane structures, most of which are square or circular. The edges of the membranes are clamped, and the maximum deflection occurs at the centre of the membrane. The resonant frequencies of plate structures

Fig. 5.4 Common flexural mode membrane resonators: a square membrane; b circular membrane

5.4 Circuit Model Representation of MEMS Resonators

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follow the form of the (5.8). Membrane resonators are commonly used to implement micromachined ultrasonic transducers (MUTs) [22].

5.4.2 Bulk Modes In contrast to flexural mode resonators, bulk mode resonators are characterized by deformation of the structure through planar expansions or contractions rather than bending. In terms of geometrical dependence, the resonant frequencies of bulk modes only depend on the lateral physical dimensions of the structure (e.g., width or length). In other words, the lateral features of the structure alone determine the acoustic wavelength (λ) of the vibration mode. As such, the resonant frequencies of bulk mode resonators can be generalized by the following form: 

f bulk

β = λ

 E bulk ρ

(5.9)

where E bulk is the effective modulus of the plate structure defined for a given axis of motion. Bulk modes resonators have been reported for beams [23], rectangular plates [24, 25], square plates [26], and circular disks [27]. In the case of bars/beams, E bulk simplifies to the Young’s modulus. In comparison to flexural mode resonators, bulk mode resonators are much stiffer for the same physical dimension scales. This in turn translates to higher frequencies for the same physical dimensions. As such, bulk mode resonators are favoured over flexural mode resonators for high frequency applications owing to their more efficient frequency-to-size scaling characteristic. The mode shapes of various examples of bulk mode resonators reported in the literature are illustrated in Fig. 5.5. In the case of bulk modes, the standing waves in the solid structures are longitudinal waves. It can also be seen that every part of the structure undergoes either compression or expansion apart from the center. The center of

Fig. 5.5 Bulk mode shapes based on a square-extensional (SE) mode in square plates, b radial breathing mode in circular disks and c length (top), width (bottom) extensional modes in rectangular plates

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Fig. 5.6 Displacement profile of the 5th order width-extensional (WE) mode of vibration

the structure is the most obvious choice to clamp the structure wherever possible from the viewpoint of the fabrication from the perspective of minimizing losses to the supports. It should be noted that the lateral bulk modes described in Fig. 5.3 can each be excited at higher order modes of vibration. This is rather commonly the case for the length-extensional (LE) and width-extensional (WE) modes. As an example, the 5th order mode of the WE mode of vibration is illustrated in Fig. 5.6, which can be described as having 5 nodal lines. Higher order modes are particularly common in the case of piezoelectric resonators [28]. Lateral bulk modes of resonance, particularly when applied to piezoelectric resonators, are referred to as contour modes [29] wherein the acoustic radiation patterns are viewed as contours in the plane of fabrication. This is in contrast to thickness vibration modes that are typically viewed by devices such as the film bulk acoustic resonator (FBAR) [30].

5.4.3 Shear Modes Shear mode resonators are like bulk mode resonators in that their acoustic wavelength is also determined only by the lateral features of the structure. However, in contrast to bulk modes, shear modes are defined by shear waves instead of longitudinal waves. As such, their stiffness constants are defined by the shear modulus of the structural material rather than the Young’s modulus. Therefore, the resonator frequency of lateral shear modes is given by the shear modulus G, instead of the Young’s modulus: 

f shear

β = λ

 G ρ

(5.10)

5.4 Circuit Model Representation of MEMS Resonators

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This feature of being defined by shear is evident when one considers the mode shapes. In square plates, shear modes that have been observed include the Lamé [31] and face shear (FS) [32] modes, which are depicted in Fig. 5.7a, b, respectively. In both cases, the direction of motion is always equal and opposite between two orthogonal axes within the plane of fabrication. In other words, while the structure is defined by expansion in one axis, it is simultaneously defined by contraction in the orthogonal axis. In every part of the plate, the in-plane strain components are equal and opposite, thereby cancelling each other out when summed up. As such, the volumetric change is theoretically zero everywhere across the square plate. This isochoric property leads to the interesting feature of lateral shear modes having theoretically no thermoelastic damping (TED). TED arises from irreversible heat flow between regions of expansion and contraction, and since there is no volume change during the operation of the resonator, TED is thus zero in principle. Low TED allows for resonators with high quality factors in the millions. Consequently, adding holes in the structure for the purpose of fabrication breaks the isochoric property and introduces TED, resulting in a substantial drop in quality factor [33]. The shear wave appears 45° to the primary axis of deformation. In either case of the Lamé and FS modes, nodes appear at specific points along the edges of the square plate, where the structure can be conveniently clamped to minimize support losses where the displacement is zero, but there is some rotation. For elastically anisotropic materials like single-crystal silicon, the relevant shear modulus is given by the axis of the shear wave. Shear modes have also been realized in circular disks, as shown in Fig. 5.7c, from which we can see once again that the motion in one axis is equal and opposite to the orthogonal axis. This is commonly referred to as the wine glass mode [34]. Given the symmetry of the structure, the same elliptical mode shape can occur in two axes 45° apart. In isotropic solids, the two modes share the same frequency, which is known as mode degeneracy. In anisotropic solids, the two modes occur at slightly different frequencies [35].

Fig. 5.7 Lateral shear modes based on a square plate resonator: a Lamé mode, b FS mode. c Wine glass mode observed in a circular disk resonator

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Fig. 5.8 A torsional mode paddle resonator

5.4.4 Torsional Modes Torsional mode resonators are most typically found in the form of paddle resonators, which comprise a plate that is supported on two opposite ends by beams. The paddle resonator oscillates by means of rotating about the axis along which the supporting beams lie as illustrated in Fig. 5.8. The supporting beams are clamped at the ends and experience a twisting motion as the plate oscillates about the axis of rotation. The beams undergoing torsion thus form the spring of the resonator and thereby define the spring constant while the rotating plate approximates to a rigid body that defines the proof mass of the resonator [36]. Torsional mode paddle resonators have been applied to sensing applications that include electrometers [37] and magnetometers [38].

5.4.5 Coupled Resonators Single resonators can in turn be mechanically coupled to realize an array of identical resonators. Assuming the same vibration mode for each resonator, the number of modes possible in an array increases with the size of the array. If the resonators are coupled to each other strongly, the frequency separation between the modes gets widened. This approach is particularly favourable for the purpose of increasing the output signal strength of MEMS resonators by creating arrays of the same resonator, synchronized to vibrate at the same frequency [39]. This is particularly useful in lowering the insertion loss of filters [40] as well as reducing the phase noise of MEMS oscillators [41]. Strong mechanical coupling has been demonstrated using coupling , structures with lengths that are multiples of the acoustic half-wavelength (i.e., nλ 2 where n = 1, 2, 3,…) [42]. An illustration of an array of square plate resonators mechanically coupled together for synchronized oscillation is provided in Fig. 5.9.

5.4 Circuit Model Representation of MEMS Resonators

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Fig. 5.9 Array of width extensional mode resonators realized through mechanical coupling

Note that all the resonators in the array are vibrating in the width extensional mode and the phase between the resonators are the same [42]. While strong coupling pushes the modes apart, weak coupling results in closely separate modes, such as in defining a narrow passband in filters [43]. Weak mechanical coupling is similarly achieved by using coupling structures with lengths that are odd multiples of a quarter λ, where n = 1, 2, 3,…) [40]. Alternatively, the of the acoustic wavelength (i.e., 2n−1 4 electrostatic spring tuning effect that arises from the nonlinearity in a capacitive gap transducer can be used to realize a weak spring that is a function of voltage across the transducer. This electrostatic spring is used as the mechanical coupling element between the resonators [44].

5.5 Transduction Mechanism of Resonators In this Section the most commonly used transduction mechanisms are briefly discussed, and their main properties are highlighted.

5.5.1 Capacitive Transduction Mechanism A voltage applied between two conducting plates separated by an insulating medium generates a force that could move the plates given one is free to move. Reversely, change of capacitance because of movement induces an electrical current given a

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constant voltage is applied to the conducting plates of the capacitor. This is the original mechanism exploited in capacitive resonators. Capacitive transducers are relatively easy to implement as there is no special requirement on the choice of material except for high electrical conductivity of the electrode plates. With this, it is no surprise that the first published micromachined mechanical resonators operated based on capacitive transduction was reported in [1] and it continues to be a very common choice for implementation of such resonators. As an example, disk resonator structure is presented in Fig. 5.10. A two-port disk resonator consists of a circular disk (made of say, polysilicon) suspended by a narrow cylindrical stem at its center. The centrally anchored disk resonator structure is favourable than a side-supported version where the disk is clamped to the anchors by using one or more thin support-beams attached to the lateral edge of the disk. This is because the central point is a nodal-point for the radial-contour bulk-mode vibrations. Hence, usage of anchors at the disk periphery leads to some energy loss of the vibration through the anchors. Nonetheless, side-supported structures are the desirable geometry for disks vibrating in the wine-glass mode where nodal-points appear at the disk boundary. The disk is surrounded by lateral capacitive-gap input and output electrodes along the perimeter, which act as electromechanical transducers. The schematic diagram of such a disk resonator is given in Fig. 5.10a. Cross-sectional view for the same is provided in Fig. 5.10b which illustrates the various material layers that can be utilized in fabricating the structure. Thus, the Poly1 layer of polysilicon can be used as the structural layer for making the disk, stem, and electrodes, while the Poly0 can be patterned for taking electrical connections. Also, a deposition of Nitride (or, silicon dioxide) is necessary for acting as an insulating layer above the substrate. The Metal film is generally used for realizing pads and interconnects. The material used for the resonant body is required to be highly conductive. In the past, doped silicon/polysilicon [6, 45] and doped polycrystalline diamond [46] have been the most common choices of material for a capacitive micro-resonator. Silicon and polysilicon are the most natural choices considering that the micro-fabrication industry is mainly developed around processing silicon-based material. Silicon is

Fig. 5.10 a Schematic diagram of the disk resonator, b The cross-sectional view illustrating the various material layers used in the fabrication of this polysilicon resonator by means of surface micromachining

5.5 Transduction Mechanism of Resonators

135

coincidentally an excellent choice of material for its excellent mechanical properties including, low loss and exceptional mechanical/chemical stability (i.e., negligible change of properties over time). Some of the highest f.Q products measured from MEMS resonators are reported for capacitive resonators as the resonant body could be fabricated from a single material which eliminates any interfacial loss existing in multi-layer resonators [47]. The electromechanical coupling factor for a capacitive resonator, defined as the ratio of the output mechanical force over the input electrical voltage, is derived from [48]: η = Vp

dC dx

(5.11)

where V p is the polarization voltage, C is the transducer capacitance, and x is the resonator displacement. From this equation one could conclude several basic properties of capacitive transduction. First, it is observed that the electromechanical coupling at microscale is a very small number. This implies that capacitive transduction is not inherently an efficient energy coupling mechanism. Secondly, it is observed that the electromechanical coupling could be improved by increasing the polarization voltage and increasing the rate of capacitance change with respect to displacement which is proportional to the capacitive area and inversely proportional to the second power of capacitive gap. Several approaches have been explored by designers to improve energy coupling. These range from simply increasing the capacitive area [24] or reducing the gap size to extremely small values [49]. Both approaches encounter limitations when the frequency of operation is pushed beyond 100s of MHz as the acoustic wavelength is excessively reduced and so should the resonator’s critical dimensions. The alternative solution for improving the coupling at higher frequency is by coupling a large number of resonators to each other [39]. This approach although very effective adds to the fabrication complexity and may lower the fabrication yield.

5.5.2 Piezoelectric Transduction Mechanism Piezoelectric resonators operate based on the direct conversion of electric polarization to mechanical stress (and vice versa) in a certain class of crystalline materials known as piezoelectric materials [31]. Piezoelectric resonators such as Quartz have been in use for many decades and is still the most prevalent technology in electronic applications. The main attractions of the piezoelectric transduction are the self-generating nature (there is no need for an electrical bias or power consumption) and the relatively large coupling coefficient indicative of efficient reciprocal conversion of electrical and mechanical energy. The main technical difficulty in working

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with piezoelectric material at micro-scale is their incorporation into mainstream microelectronics fabrication processes. Single crystalline piezoelectric material such as quartz and lithium niobate cannot be simply grown on a silicon surface in the form of thin functional film. Therefore, alternative deposition techniques for deposition of properly oriented polycrystalline piezoelectric material should have been developed before piezoelectric micromachined resonators could be considered relevant. Moreover, many piezoelectric materials contain metals with high diffusivity or toxicity (e.g., Zinc oxide (ZnO) and Lead Zirconate Titanate or (PZT)) which cannot be tolerated in microfabrication facilities. Some of the earliest instances of micromachined resonators were fabricated based on RF sputtered ZnO thin-film deposited on silicon substrate [50]. However, ZnO is a chemically-unstable material and resonators fabricated of ZnO have not been successfully commercialized. It was until the development of RF sputtered piezoelectric Aluminum nitride (AlN) [51] that the thin-film piezoelectric material slowly gained acceptance in microfabrication industry. In contrast to ZnO, AlN is a chemically stable material with excellent acoustic properties such as large stiffness and low loss. More importantly aluminum, the only metallic ingredient in AlN, is commonly used for metallization in microelectronics. Thin-film piezoelectric micro-resonators could be divided into two main categories. The first category is the devices that use the thin-film piezoelectric layer mainly as a transducer to generate/sense the acoustic waves in a second substrate material [50]. Such devices are sometimes referred to as thin-film piezoelectric-onsubstrate (TPoS) resonators and can significantly benefit from the proper choice of the substrate material to improve certain features of the resonator characteristic such as the quality factor and linearity [52]. In addition to common choices of substrate materials such as Silicon, polycrystalline Diamond has been demonstrated to be an excellent choice for high-frequency applications [53]. The combined high-Q and low motional resistance offered by TPoS devices enabled the demonstration of some of the best oscillator performances achieved from MEMS resonators [54]. The tradeoff in using a substrate under the piezoelectric layer in a TPoS resonator is the compromised coupling factor. A silicon bar resonator is excited in its 3rd and 9th longitudinal harmonic modes at 1.53 and 4.51 GHz, respectively [55]. The resonator demonstrates a 2 dB improvement in transduction efficiency in its 9th harmonic relative to its 3rd harmonic, normalized to the quality Q of the resonance. SEM of the dielectrically transduced silicon bar resonator and its 9th harmonic measured responses are depicted in Fig. 5.11a, b, respectively, [55].

5.5.3 Piezoresistive Transduction Mechanism Unlike capacitive and piezoelectric transducers, there are other transduction mechanisms that could only be used to either excite the vibration or sense the vibration (i.e., one-way transduction). For example, thermal actuators could only be used for excitation of vibration and piezoresistive elements could only be used to sense the

5.5 Transduction Mechanism of Resonators

137

Fig. 5.11 Scanning electron micrograph (SEM) of the a dielectrically transduced silicon bar resonator and b measured 9th harmonic responses [55]. Reproduced with permission from the IEEE

change in the resistance as the resonator vibrates. Despite such relative deficiency, both thermal and piezoresistive transducers are very attractive for their ease of implementation. All that is required in both cases is a conductive material through which an electrical current is passed to either generate heat (in the case of the thermal actuation) or to measure resistance (in the case of the piezoresistive sensing). In a thermally-actuated resonator, an alternating current is passed through the resistive heating elements to generate a dynamic heating power. This varying power will result in a dynamic temperature distribution (thermal wave) in the resonant structure which is the source of the desired actuation force. Once the frequency of the thermal wave matches the mechanical resonance frequency of the structure, the mechanical vibration is efficiently excited [48]. Thermal actuation is specially desired for applications in which a large force is required for excitation of the vibration in liquid medium [56]. The efficiency of the thermal transduction (force to heat ratio) is dependent on the thermal time constant associated with the structure. The equivalent model of a heat generator with a heat transfer path can be simplified to an RTH CTH circuit where RTH is the thermal resistance associated with the heat transfer and CTH is the thermal capacitance. In other words, the temperature (i.e., force) generated by an input alternating power reduces for higher frequencies. This fundamental behavior has led to the traditional belief that thermal actuators are “slow” and can only be used for low frequency applications. However, there is a growing body of evidence pointing to the contrary. Based on some recent and original work on this topic, the thermal actuation can be used for very high frequency applications [57]. It can be proved that the thermal time constant for a specific resonant structure scales much faster (it has second order dependency) than the resonant frequency (linear dependency) as the dimensions of the structure reduce [57]. In other words, the temperature of a structure follows the input power much faster (less lag) as the dimensions are scaled down. A fundamental limitation associated with the thermal actuation that continues to impede its spread is the required power consumption to

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generate considerable vibration amplitude especially at higher frequencies where the structure is stiffer, and the amplitude of the alternating temperature is lower for the same input power. In thermal resonators the mechanical vibration is commonly sensed through piezoresistivity which is the change of resistivity in response to stress. In the most general form, the piezo-resistivity in material is characterized by a 6 × 6 matrix of piezoresistive coefficients. Semiconductor materials such as doped single crystalline silicon possess exceptionally large piezoresistive coefficients [58] which enables an efficient sensing vehicle. Piezoresistive elements could be formed either by deposition and patterning of a thin film or selectively doping the surface of the silicon substrate [59] separate from the heating resistor, or alternatively be formed from the bulk of silicon [60]. Figure 5.12a shows a rotational disk resonator with boron-doped piezoresistive readout element and Fig. 5.12b depicts a solid single crystalline silicon disk resonator with combined heater/piezo-resistive silicon beams. The latter is an attractive approach as the same heating element could be used as the piezo-resistive sensing element simplifying the device interface (a two-terminal interface as opposed to four-terminal). Piezo-resistive sensing has been also coupled with other actuation mechanism such as capacitive to improve the effective electromechanical coupling [61] as piezo-resistive coupling can be enhanced through increasing the readout current. Piezo-resistivity is also the transduction of choice for extremely small scales [62] as other transducers loose efficiency while piezo-resistivity enhances it [63]. Piezoresistivity is also the most compatible transduction mechanism with mainstream CMOS fabrication as minimum alteration to the process required [64].

Fig. 5.12 a Schematic view of a thermally actuated disk resonator showing the qualitative distribution of AC temperature fluctuation amplitude in the resonator (red being the maximum and blue minimum). The electrical connections required for one-port operation of the resonator are also shown, b SEM of a fabricated 100 μm diameter disk resonator fabricated on an N-type low resistivity silicon substrate with device layer and BOX thickness of 20 μm and 2 μm respectively. The thermal actuators are along crystalline direction for optimized transduction [60]. Reproduced with permission from the IEEE

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5.6 Applications 5.6.1 Applications in Timing MEMS resonator-based oscillators have moved towards commercialization for timing applications [7, 65], mainly focusing on wired communications standards such as USB and on real-time clocks. The reason why MEMS oscillators are more slowly penetrating RF systems as frequency references is due to their stringent phase noise requirements. These requirements stem from the synthesized carrier spectral purity specified by most wireless standards. The close-in phase noise performance requirements are particularly challenging in wireless standards, as resonator nonlinear behavior and somewhat lower-Q-factor than quartz usually degrades performance at close-in offsets to be as competitive for such applications. However, in serial communications, where clock-data recovery circuits filter close-in phase noise due to their feedback nature, close-in phase noise performance is relaxed, allowing MEMS resonator-based oscillators to penetrate these applications regardless of their somewhat lower close-in phase noise performance [8]. In addition to phase noise performance, an important requirement of timing applications is the frequency stability of the oscillator. Recently, temperature compensation algorithms or resonator fabrication techniques have allowed MEMS resonators to match the performance of quartz temperature compensated oscillators (i.e., TCXOs) with regards to temperature stability [66]. Real-time clocks, requiring oscillators operating at 32.768 kHz are of particular interest such as demonstrated in [67], where the resonator-based oscillator is interfaced with a phased-locked loop to synthesize the desired frequency output and improve its temperature stability through the use of a temperature sensor and calibration data. In [68], a phase-locked loop is used for this purpose in order to reduce power consumption, but a state machine determines the fractional division ratio of the oscillator output based on the output of a temperature sensor and calibration data. This method achieves an output frequency stability of ±10 ppm over 0–50 °C. In [69], a resonator is placed in a Pierce oscillator loop shown in Fig. 5.13a [69]. Its 524 kHz output is fed to a dual-mode compensation circuit that can generate the 32 kHz required output, shown in Fig. 5.13b [69]. In compensated mode, a modified fractional-N phase-locked loop can be activated to provide precise temperature compensation by modulating its output frequency based on the output of a temperature sensor. This allows to maintain the output frequency steady regardless of frequency drift due to temperature in the MEMS oscillator. In low-power mode, the phase-locked loop can be bypassed to generate an uncompensated output for applications that do not require compensation, and which can benefit from the reduced power consumption. In low-power mode, the current consumption is of 0.6 μA (1.4 V supply), and when temperature compensated it is of 1.0 μA (1.4 V supply). The system achieves a ±100 ppm frequency stability over −40 to 85 °C in low power mode, and of ±3 ppm in temperature compensated mode. Note that the temperature compensation in this system requires calibration to allow for the

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Fig. 5.13 a A MEMS oscillator and b its compensation and frequency synthesis electronics [69]. Reproduced with permission from the IEEE

most effective compensation of the resonator’s temperature characteristic. Similar efforts have also been carried out and interested reader may check [70–74] for better understandings.

5.6.2 MEMS Resonator-Based Oscillators MEMS resonators are interfaced with sustaining amplifiers that allow for their use in electronic oscillators that generate an electrical signal at the resonant frequency of the resonator such as demonstrated in [75]. When used in sensors, resonators will usually operate through some functionalized MEMS resonator that varies its frequency in response to sensed element such as in [76]. When used in timing circuits as precision clocks or as RF carriers [9] MEMS resonators are used as the frequency reference element in timing circuits, [9]. Whether MEMS resonators are used in sensing or

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in timing applications, the sustaining amplifier needs to carefully be designed to consider the particularities of MEMS resonators in order to enable high quality oscillation [77–79]. The topology in Fig. 5.14a illustrates the configuration of a typical MEMS resonator-based oscillator, with a resonator’s typical amplitude and phase frequency responses shown in Fig. 5.14b. In a positive feedback loop, a sustaining amplifier with a frequency dependent gain, A(s), an input-referred noise and a non-linear characteristic has its frequency response filtered by a MEMS resonator having a frequency dependent motional resistance and thus frequency response, β(s) [80]. At power up, the noise present in the positive feedback loop gets amplified and filtered by the resonator after multiple passes around the loop until the sustaining amplifier or the mechanical resonator limit the signal growth because of non-linearity. This reduces the loop gain A(s)β(s) such that in steady-state, the gain around the loop (i.e., loop gain) has an effective value of unity, and a sustained constant oscillation can be observed. Important aspects of the loop gain are that for this constructive positive feedback to occur, and to allow for an oscillation be sustained, the linear gain around the loop must be larger than unity, usually with some safety margin to allow for fast start-up and design margins (e.g., 1.5 times the minimal gain required), and the phase shift around the loop must allow for the noise waveform propagating around the loop to constructively grow. These oscillation conditions, first defined by Heinrich Georg Barkhausen, can be expressed as (Fig. 5.15): |A(s)β(s)| > 1

(5.12)

∠(A(s)β(s)) = n360◦ , n = 0, 1, 2 . . .

(5.13)

Fig. 5.14 a Typical MEMS resonator-based oscillator loop; and b typical resonator transmission characteristic amplitude and phase [81]. Reproduced with permission from the IEEE

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Fig. 5.15 Typical phase noise power spectral density (single sided)

As can be seen in the phase condition above, the phase shift around the loop must either be zero or a multiple of 360°. Typically, oscillators will either operate around a 0° phase shift or a 360° phase shift. In the former, the resonator’s series-resonance, when the resonator’s impedance is lowest, is used with a sustaining amplifier having sufficient bandwidth to add negligible phase shift to the loop, while in the latter, its parallel-resonance, when the resonator’s impedance is largest, is used with an amplifier providing 180° phase-shift around the loop. In that case, the rest of the phase shift is provided by electrical passive components, usually capacitors, such that the phase shift at a frequency between the series and parallel resonances of the resonators is of 180°, yielding the total required 360°. Typically, series resonance provides more accurate oscillation frequency as it does not depend on electrical components that may be inaccurate in order to attain additional phase shift, however, designing an amplifier with negligible phase shift can be a challenge [82]. Provided that the amplifier has enough gain to offset the loss of the resonator at resonance, and that its bandwidth is wide enough to contribute negligible phase shift to the loop, the circuit will oscillate at the series-resonant frequency of the resonator [83], otherwise, an offset in frequency will occur and the amplifier will have to provide more gain to overcome the additional losses of the resonator at a frequency offset from the series resonance. For parallel resonant circuits, a negative gain (i.e., a 180° phase shift) amplifier can also be used with additional phase shift, such as in Pierce oscillators [84]. The Leeson phase noise model is a linear model that gives and expression for the phase noise in an oscillator. Leeson’s equation is given by [85]: 

 2    kT F fC f0 1+ 1+ dBc/Hz Lϕ ( f ) = 10log 2PS 2Q L  f f

(5.14)

where k is the Boltzmann constant, T is the operating temperature, F is the effective excess noise factor, mainly caused by the sustaining amplifier, PS is the signal power at the input of the amplifier, f 0 is the oscillation frequency of the oscillator,  f is

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the offset frequency at which the phase noise is measured, Q L is the loaded quality factor of the resonator, and f c is the corner offset frequency at which the phase noise starts to increase at a rate of 30 dB per decade. The conceptual power spectral density of the phase noise shown in Fig. 5.14 outlines that at far away offsets from the oscillation frequency, phase noise becomes white in spectrum, but within the half-power bandwidth of the resonator (i.e., f 0 /2Q L ), the phase noise increases by 20 dB per decade until it reaches a point where it increases by 30 dB per decade below f C . Leeson’s model is somewhat empirical as F and f c are often obtained by measurements since phase noise is often significantly affected by nonlinearities and time variance of the phase noise mechanisms in oscillators. More elaborate phase noise models exists such as that in [86], where a time-variant phase noise model is proposed. In a nutshell, higher the Q-factor of the resonator, the lower the phase noise in the MEMS oscillator because of the enhanced noise filtering. High Q-factor based resonator reduces close-to-carrier phase noise whereas high output power (Ps ) reduces far-from-carrier phase noise. For any MEMS based oscillator, first stage is to design and carry experimental study on the MEMS resonator. Once the resonator is ready, next thing is to package it. To make up an oscillator, the packaged resonator should be combined with a driver circuit that is typically realized in CMOS. Obviously, the highest level of integration that can be achieved is to integrate the resonator on the same die that also holds the CMOS circuitry. Several process flows have been described where the MEMS resonators are embedded in an existing CMOS flow [23–25]. Sustaining Amplifier design plays a crucial role in the MEMS based oscillator. MEMS resonators exhibit very high motional resistances compared to that of quartz crystals—typically in the order of several tens of kilo-ohms for electrostatically actuated resonators, and a few kilo-ohms for piezoelectrically actuated resonators. Accordingly, in order to operate at the series-resonance of the resonator, the motional current outputted by the resonator device needs to be amplified by a trans-impedance amplifier (TIA) having the following characteristics [79]: 1. 2. 3. 4.

high gain to offset the resonator losses. bandwidth which is an order of magnitude larger than the resonator’s frequency to ensure a small phase shift around the feedback loop. Low input and output impedances to avoid loading the resonator’s Q-factor. Automatic gain control capability to prevent large oscillations from exerting the resonator’s nonlinearities.

All these specifications are challenging to fulfil simultaneously and require carefully designed circuitry. The typical interconnection for a trans-impedance amplifier with automatic gain control used to bring a clamped–clamped beam resonator is shown in Fig. 5.16 [86]. In this configuration, an operational amplifier is put in shunt-shunt resistive feedback to provide a trans-impedance gain of −RAMP and a second stage provides an additional gain of −1 to provide a total positive gain with 0° phase shift and sufficient gain to offset the motional resistance of the resonator. Note that the resonator in this work has two transducer gaps, which reduces the feedthrough capacitance and thus mitigates the parallel resonance of the resonator.

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Fig. 5.16 The typical trans-impedance amplifier configuration providing 0° phase shift and sufficient gain around an electrostatic resonator [86]. Reproduced with permission from the IEEE

A level control circuit can modulate the gain by changing the feedback resistance, which is implemented with a triode transistor. Note that the use of a triode transistor can cause non-linear behavior of the circuit and detract from phase noise performance [87]. In addition, the input resistance of the shunt-shunt feedback amplifier is typically on the order of R F /A, where A is the gain of the operational amplifier in the shunt-shunt feedback. This implies that if very large gain is implemented with the amplifier or if it has insufficient gain, the input impedance may increase sufficiently to significantly load the quality factor of the resonator and deteriorate phase noise performance, as later discussed. As for resonator nonlinearity mitigation, many different amplitude limiting schemes exist, ranging from hard limiting using comparators or saturating circuits to soft limiting using variable gain amplifiers. In Fig. 5.17, a topology using a trans-impedance input stage with a second voltage gain stage to provide sufficient gain is shown [79]. The advantage of splitting the gain stages into two is that more gain bandwidth can be achieved per stage to allow for series-resonant oscillation up to 15 MHz in [74]. The shunt-shunt feedback is implemented in the variable gain amplifier. Again, an automatic gain control can regulate the gain to prevent resonator nonlinear limiting and enhance phase noise. This is implemented by varying the voltage stage gain in response to the amplitude detected at the output of the oscillator through the automatic gain control loop. At the transistor level, the trans-impedance structure has been used both for electrostatic resonators (e.g., [69]) or piezoelectric resonators (e.g., [88]). Many designs utilize a regulated cascode input stage to boost the current gain and reduce the input resistance of the trans-impedance at the input, to reduce the Q-loading on the resonator. This is important as Q-loading in series-resonant oscillators is given by: QL =

Q UL 1 + (Ri + Ro )/Rm

(5.15)

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Fig. 5.17 Typical trans-impedance amplifier (TIA) block diagram, showing a resonator connected in closed-loop [74]. Reproduced with permission from the IEEE

where Q UL is the unloaded Q-factor of the resonator, Rm its motional resistance, Ri the input resistance of the sustaining amplifier and Ro its output resistance. Moreover, in order to reduce the Q-loading of the resonator, all series-resonant circuits include an output stage which ensures a low output resistance, as shown in Fig. 5.17. This can be a common-source type buffer or a series-shunt feedback buffer circuit. Typically following the regulated cascode is a variable voltage gain amplifier in shunt-shunt feedback using a triode transistor to vary the gain such as in [89], and shown in Fig. 5.18 [89] following a regulated cascode input stage using two triode transistors M3 and M4 . The voltage gain amplifier in this case is composed of two inverters (M5 , M6 , and M7 , M8 ), with the second inverter in shunt-shunt feedback allowing for controllable gain through the biasing of transistor M f . Capacitor Cpk is included in this case to provide a peaking zero in the frequency response which extends the bandwidth of the amplifier and ensures a sufficient bandwidth to meet the 0° phase condition for series-resonant oscillation. Note that the first inverter in the voltage amplifier can be difficult to bias properly because of the sensitive nature of the inverter input node to DC bias. As such in [90], a less sensitive common source voltage gain stage is used before the shunt-shunt feedback tunable voltage stage. Another amplifier structure which has been used is the capacitive feedback transimpedance amplifier structure [91]. This structure is shown in Fig. 5.19 [83] and includes an operational amplifier which is configured with capacitive feedback, allowing for a very large gain and very low noise since the capacitor element does not contribute any noise to the circuit, unlike the feedback resistor used in shunt-shunt

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Fig. 5.18 Voltage gain stage used to increase the gain of the regulated cascade amplifier [89]. Reproduced with permission from the IEEE

Fig. 5.19 Capacitive sustaining amplifier circuit [92]. Reproduced with permission from the IEEE

configurations. This topology requires careful design of the frequency response of the circuit to ensure proper phase shift for oscillation. Figure 5.20a presents the SEM of a watch timing oscillator that combines a 16 kHz folded-beam micromechanical resonator with a Q of 50,000 together with sustaining CMOS transistor circuits using the process flow of Fig. 5.20b, but with tungsten as the metal interconnect to accommodate 625 °C structural polysilicon deposition temperatures [8]. Although the use of tungsten metallization instead of the more conventional copper and aluminium prevents the process of [8] from widespread use,

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Fig. 5.20 a SEM of a fully integrated 16 kHz watch timekeeper oscillator that combines CMOS and MEMS in a single fully planar process, b Cross sections immediately before (top) and after (bottom) release of a surface-micromachining process done directly over CMOS [7]. Reproduced with permission from the IEEE

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Fig. 5.21 Perspective schematic view of an oscillator driven at low-stiffness location for nonlinearity exploration [93]. Reproduced with permission from the Elsevier

other variants of this modular process have now been demonstrated that allow more conventional CMOS metals [9]. In addition, other non-modular merging processes [10] have been used in integrated MEMS products for many years now. Whichever process is used, the size and integration benefits are clear, as the complete timekeeper of Fig. 5.20a measures only 300 × 300 μm2 and could even be smaller if the transistors were placed underneath the micromechanical structure. A wide-width clamped–clamped beam (CC-beam) resonator was used to make a micromachined oscillator, as depicted in Fig. 5.21 [93]. The sustaining amplifier shown in the Fig. 5.21, can be any of the following: TIA (Transimpedance Amplifier), PLL (instrumentation, used here), off-chip commercially available amplifier or a tape-out IC. To maintain the oscillation across the closed loop, Barkhausen criterion needs to be followed which has two main conditions: (i) gain, A = (Ramp /Rtot ) > 1, where Ramp is the amplifier gain and Rtot = Rm + Ri + Ro is the total resistance, and (ii) phase around the positive feedback loop should be 0°. Here Ramp , Ri and Ro are the gain, input and output resistance of the amplifier, and Rm is the motional resistance of the CC-beam resonator. Once the criterion is met, a time-varying continuous sinusoidal output is observed in an oscilloscope and the oscillator should oscillate at just one frequency, providing delta function in the frequency domain. But practically, there are many losses or fluctuations resulting in sideband power other than the power at the fundamental frequency, treated as the phase noise. Figure 5.22 shows the perspective test setup for the oscillator measurement using the Zurich HF2LI lock-in amplifier and PLL [94]. The output of the device (sense signal) is fed into the input of the lock-in amplifier (I/P port), where it is compared with the internal reference signal. Over a certain range, the phase and frequency of the input signal are followed by the digital data generated by the PLL block. Then the digital to analog converter (DAC) uses this data and generates a signal with the

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Fig. 5.22 Measurement setup for an oscillator with the resonator driven under low-stiffness configuration for the verification of phase noise reduction [93]. Reproduced with permission from the Elsevier

same phase and frequency as the input signal. However, the power of this signal can be set independently. This generated signal at O/P port of the PLL is used to drive the resonator (drive signal) allowing it to operate as an oscillator at a lower power level. The sense electrode has been connected with the spectrum analyser (SA) to record the LO output [93]. The CC-beam resonator oscillator measurement is performed using the test setup depicted in Fig. 5.22 [93]. Figure 5.23a presents the frequency spectrum plot for the oscillator using a 50 μm wide CC-beam design under 8 V dc bias and −5 dBm input power (i.e., carrier power) for high-stiffness driving configuration which shows the output power of −36.12 dBm.

Fig. 5.23 a Fourier spectrum and b plot of phase noise (at 10 kHz offset) versus PLL drive power (from O/P port of Zurich HF2LI) for a 50 μm-wide CC-beam resonator oscillator driven at 8 V dc-bias [93], reproduced with permission from the Elsevier

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The performance of the superheterodyne receiver system is severely affected by the local oscillator’s performance, which is mainly characterized by its phase noise. Phase noise affects the signal integrity of overall frequency translation. Thus, it is very important to evaluate the phase noise performance of the local oscillator. Figure 5.23b plots the phase noise variation (at 10 kHz offset) with the carrier power (from HF2LI) for the same device under the same biasing conditions. The reduction of phase noise value is observed with an increase of carrier power.

5.7 Conclusions In this Chapter, different design aspects of micromachined resonators are studied. A description of the basic model and properties of a generic micromachined resonator are described. It includes mechanical and electrical properties of the micromachined resonators. Later, different resonances modes are discussed and that includes flexure mode, bulk modes, shear mode and tortional modes. Different varieties of transduction mechanisms are discussed. Capacitive transduction is the most common method in the early days of development. This variety of transduction mechanisms includes recent findings suggesting that thermal actuation has a place for actuation in high frequency resonators. Advancement in the field of micro-resonators has gone beyond the resonator itself to include interface electronics such as in the case of implementing oscillators. The key circuit topologies that have been employed to realize MEMS oscillators are studied systematically. MEMS resonator applications in timing and oscillations are discussed up to a reasonable extent. This Chapter concludes with different varieties of sustaining amplifier designs. Finally, a well set of extensive references are listed for further study on the micromachined resonators and related circuits.

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60. Rahafrooz A, Pourkamali S (2010) Rotational mode disk resonators for high-Q operation in liquid. In: Proceedings of IEEE sensors 61. Lin ATH, Lee JEY, Yan J, Seshia AA (2010) Methods for enhanced electrical transduction and characterization of micromechanical resonators. Sens Actuators A Phys 62. Ekinci KL (2005) Electromechanical transducers at the nanoscale: actuation and sensing of motion in nanoelectromechanical systems (NEMS). Small 63. He R, Yang P (2006) Giant piezoresistance effect in silicon nanowires. Nat Nanotechnol 64. Mile E et al (2010) In-plane nanoelectromechanical resonators based on silicon nanowire piezoresistive detection. Nanotechnology 65. Van Beek JTM, Puers R (2012) A review of MEMS oscillators for frequency reference and timing applications. J Micromech Microeng 66. Arumugam N et al (2015) 2-die wafer-level chip scale packaging enables the smallest TCXO for mobile and wearable applications. In: Proceedings—Electronic components and technology conference 67. Barrow HG et al (2012) A real-time 32.768 kHz clock oscillator using a 0.0154 mm2 micromechanical resonator frequency-setting element. In: 2012 IEEE international frequency control symposium, IFCS 2012, proceedings 68. Ruffieux D, Krummenacher F, Pezous A, Spinola-Durante G (2010) Silicon resonator based 3.2 μw real time clock with ±10 ppm frequency accuracy. IEEE J Solid-State Circ 69. Zaliasl S et al (2015) A 3 ppm 1.5 × 0.8 mm2 1.0 μa 32.768 kHz MEMS-based oscillator. IEEE J Solid-State Circ 70. Perrott MH et al (2010) A low area, switched-resistor based fractional-N synthesizer applied to a MEMS-based programmable oscillator. IEEE J Solid-State Circ 71. Perrott MH et al (2013) A temperature-to-digital converter for a MEMS-based programmable oscillator with 4-bit) phase shifters reported so far have experienced a challenge to achieve low loss, good matching simultaneously with good phase accuracy over large cycles of operations in-terms of power handling and life cycle.

6.3 Conventional Micromachined Switched Line Phase Shifters In this Section, one conventional type 5-bit switched line phase shifter is discussed where ten SPDT switches are used with different delay and reference line configurations. Later, a 4-bit switched line phase shifter is discussed where two back-to-back SP16T switch configurations are used.

6.3.1 Digital MEMS 5-Bit Switched Line Phase Shifter Using Two Back-To-Back SPDT Switches A conventional schematic of a switched line phase shifter is shown in Fig. 6.2. The working principal of the switched-line phase shifter is dependent only on two lengths of transmission lines (reference and delay lines) that are being switched. The differential path length between the two-line segments determines the amount of phase shift that can be achieved. Here, we will be discussing on a simple 5-bit phase shifter comprises of five primary bits: 11.25°, 22.5°, 45°, 90° and 180° phase bits. The footprint of the switch used in the phase shifter is like the one presented in Fig. 3.1a. It is always recommended to design, fabricate, and test all individual phase bits for optimum phase shifting performances. Hence, individual phase bits are fabricated using the fabrication process presented in Appendix B. All primary phase bits are designed using (6.1). The lengths of the reference and delay lines are optimized using FEM based solver HFSS. Reference line lengths used for 11.25°, 22.5°, 45°, 90° and 180° phase bits are 1675 μm, 1675 μm, 1675 μm, 570 μm and 570 μm, respectively. Similarly, the lengths of the delay lines for 11.25°, 22.5°, 45°, 90° and 180° phase bits are 1925 μm, 2150 μm, 2620 μm, 2480 μm and 4320 μm respectively. To achieve good matching, all corners of the individual phase shifter are realized using 90°CPW bends. The maximum measured return loss of better than 16.5 dB and worst-case insertion loss of 1.05 dB were obtained from individual phase bits over 13–18 GHz. Almost desired phase shift was achieved from individual phase bits with ~+0.79° of phase error which is also validated using full wave simulations. All dimensions of the bends are optimized using simulation tools to achieve little transmission distortion caused by intra-coupling in the line. For CPW ground discontinuities, it is well known that the ground plane must be connected by air-bridges at each discontinuity to sort out the parasitic slot line modes that are easily exited.

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Finally, all fabricated individual primary phase bits are cascaded together with a connecting CPW line to achieve a 5-bit phase shifter. The microscopic image of the complete phase shifter fabricated is shown in Fig. 6.6. The reference and delay paths are controlled by dedicated bias pads on either side of the phase shifter. The total area of the phase shifter is 9 × 4 mm2 . The length and width of the reference and delay arms and CPW pitch (G/W/G) are similar as they were taken for individual phase bits and switches. Note that, in this phase shifter two reference and delay arms are sharing one CPW ground plane which leads to the reduction of 25% of the chip area compared to any other conventional phase shifters where dedicated ground planes are used. All ground planes are connected together by air bridges at each CPW discontinuity to eliminate the propagation of parasitic slot line modes. For symmetric CPWs, quasiTEM modes are typically called the CPW or the even-mode and the coupled slotline or the odd-mode. Either of these two modes can propagate along the transmission line independently. They can couple to each other at discontinuities if they are excited. In general, coupled slotline mode is excited more in CPW circuits if there is any discontinuity or an asymmetry in the transmission line [23]. It is for this reason that air-bridges are used in the phase shifter circuit to equalize the voltages on the two ground planes of CPW lines. The connecting length (lc ) between two consecutive bit sections was chosen to be at 360 μm using FEM based simulation/optimization. The measured return loss of better than 14 dB and worst case insertion loss of 5.57 dB are obtained with 30–40 Vbias voltage over 17–17.5 GHz frequency, as shown in Fig. 6.7. In addition, maximum phase error (ΔΦ E ) of −1.12° to +1.45°

Fig. 6.6 SEM image of the 5-bit phase shifter [5]. Copyright/used with permission of/courtesy of Institute of Physics (IOP) publishing limited

6.3 Conventional Micromachined Switched Line Phase Shifters

165

Fig. 6.7 a Measured return loss and b measured and simulated average insertion loss from 32states of complete 5-bit phase shifter [5]. Copyright/used with permission of/courtesy of Institute of Physics (IOP) publishing limited

was obtained from this phase shifter. Note that, all measurements are carried out in standard laboratory environment and no package is placed on top of the device. Detailed analysis and information of this conventional type MEMS switched line phase shifter is available in [18]. It includes performance analysis of all primary phase shifts with extensive measurement results.

6.3.2 4-Bit Switched Line Phase Shifters Using Two Back-To-Back SP16T Switches K-band 4-bit phase shifter was designed using 16 delay lines and two SP16T switching networks, connected to the input and output transmission lines. The primary design aim is to achieve low insertion loss and compact size. The fabricated microscopic image of the device is shown in Fig. 6.8. All 16 CPW lines were placed between two back-to-back SP16T networks and phase shift was achieved by actuating MEMS switches. It substantially reduces the area of the device, thereby making the phase shifter more compact. The insertion loss of the phase shifter is mainly governed by the metal and switch losses. There are only two switches at each path, in contrast to any other conventional design based on 8 SPDT or 4 SP4T switches, which has 8 or 4 switches in each path. To obtain optimum device performance, reference line of the phase shifter was optimized to 481 μm (electrical length: 21° @ 20 GHz). All 15 delay lines of the phase shifter contain a section equal to the reference line plus additional delay line as per desired phase shift and optimized using full wave simulation in HFSS V.15. To achieve a compact design with minimum phase error without any unwanted resonance, all delay lines were routed with 90° CPW bends at each corner (see Fig. 6.8). Dimensions of the bends were also optimized using full wave simulation to

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Fig. 6.8 Microscopic images of the fabricated MEMS 4-bit phase shifter using two SP16T switches. Total area is 3.62 × 3.37 mm2 (including bias lines and dc pads) [31]. Reprinted with permission from the IEEE

obtain little transmission distortion caused by intra-coupling in the meandering lines and for better matching. Nevertheless, inductive bends were also used in all delay paths to overcome the excitation of coupled slotline modes at CPW discontinuities and any unwanted resonance. All delay lines were made as closely as possible to minimize the size. To check the effect of coupling between 16 lines, an extensive simulation process was adopted to observe any distortion in transmission phase of the lines. The S-parameters performance of the 4-bit phase shifter was measured systematically over the band of interest. Total area of the fabricated device is 15 mm2 including all bias lines and bias pads. Optical profilometer shows very negligible variation (133–165 nm) in tip deflection over all 32 MEMS switches used in the phase shifter. As a results, variation in C off and Ron were also very less throughout the different states on the phase shifters for actuation bias of 75–86 V. This variation in actuation voltage accross different states in the phase shifter is mostly due to the added capacitance between delay line and ground plane. In addition, this added capacitance is limited by the number of air bridges used on the delay line and length of the delay line. Finally, measured and average curve-fitted insertion loss and return loss performances of the reported phase shifter is shown in Fig. 6.9. The associated average return loss is better than 14 dB over 18–26 GHz, as shown in Fig. 6.9a. Althrough losses of the phase shifter were varrying from 3–4.62 dB from 18 to 26 GHz but device demonstrated an average loss of ~3.47 dB over 19.75–20.25 GHz (500 MHz), as shown in Fig. 6.9b. The measured loss was more (4.23 dB) at 337.5° phase state as line length was more here compared to the other phase state. Althrough, result shows multiple dips in the insertion loss response due to off-path resonance but

6.3 Conventional Micromachined Switched Line Phase Shifters

167

Fig. 6.9 Measured, a return loss and b insertion loss performances of the 4-bit phase shifter from 18 to 26 GHz, [31]. Used with permission from the IEEE

most of them occurs between 22 and 26 GHz which was out of band of interest. The variation in insertion losses are inherent in the design across the different phase states due to different delay line lengths. Proposed phase shifter can be readily adopted to a microstrip design to further reduce the line loss. The average phase error of the device was ~1.77° at 20 GHz. The Rc was maximum (4.1 ) in the 292.5° phase state and minimum (~3 ) at the 0°-phase state. The maximum measured differential time delays of ~169.47 ps with the delay step of ~9.06 ps was obtained over 19.75–20.25 GHz. Result also shows no unwanted resonance over the concern band of interest. Measured phase shift/length, phase shift/loss and maximum loss/length of the proposed phase shifter are 118°/mm, 78.9°/dB and 1.49 dB/mm, respectively. In addition, figure-of-merit (loss/bit) of this 4-bit phase shifter is 0.86 dB. Area/bit of the proposed circuit is 3.72 mm2 .

6.4 Different Types of DMTL Phase Shifters In this Section, two different version of 5-bit DMTL phase shifters are discussed. The first phase shifter is built with three fixed to fixed beams, one is switchable with electrostatic actuation and other two are fixed for metal air metal (MAM) capacitor. The second type of 5-bit phase shifter is designed and fabricated using a push–pull actuator. All individual primary phase bits (11.25°/22.5°/45°/90°/180°) which are fundamental building blocks of complete 5-bit phase shifter are fabricated separately and tested for both types of 5-bit phase shifters. The working methodologies of these are discussed in the subsequent sections.

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6.4.1 Phase Shifters Using MAM Capacitors and MEMS Bridges The DMTL phase shifter works on the principal of dispersion where an unloaded line is loaded with multiple distributed capacitances in a periodic manner. The changes in loaded capacitance on the line with applied bias contribute to a change in phase velocity which in turn produce differential phase shift. To achieve acceptable matching over a wide-band, it is always recommended not to model a DMTL structure with high down-state capacitances. A unit section of the DMTL phase shifter has been optimized with different structural parameters. Figure 6.10a shows the microscopic view of the unit cell phase shifter and Fig. 6.10b shows its equivalent circuit model. MEMS bridge is placed on the signal line which varies the loaded capacitance on the transmission line based on the actuation voltage. The aim of the design is to achieve desired phase shift with minimum insertion loss and good matching (>10 dB) over the X-band. In the proposed design, two MAM capacitors are in series with a MEMS bridge. MAM capacitor exhibits low capacitance per unit area and high-Quality factor compared to MIM capacitor. In the proposed scheme, bias can be applied to the MEMS bridge without affecting the MAM capacitor. The total loaded capacitance (C l ) seen by the line is the series combinations of MAM capacitances (C s ) and bridge capacitance (C b ) at zero-bias condition and it is given by (6.4) Cl =

Cs Cb Cs + Cb

(6.4)

Fig. 6.10 a SEM image and b equivalent circuit model of the unit cell DMTL phase shifter [4]. Used with permission from Institute of Physics (IOP) publishing limited

6.4 Different Types of DMTL Phase Shifters

169

At zero bias state, C b is much lower than C s and the effective loaded capacitance (C lu ) seen by the line is C b . When the MEMS bridge is in the down- state position, the bridge down state capacitance becomes much larger than C s , thereby the effective loaded capacitance (C ld ) is given by C s . The loaded transmission line (t-line) up-state (Z lu ) and down state (Z ld ) impedances are given by (6.5)  Z lu =

 s Lt , Z ld = sCt + Cb

s Lt  sCt + Cs

(6.5)

where, s is the unit section length, sL t and sC t are the per unit line inductance and capacitance. Furthermore, s can be calculated by (6.6), as given in [1] s=

Z ld c √ π f B Z 0 εr,eff

meter

(6.6)

√ Here, Z 0 and c/ εr,eff are the characteristic impedance and guided velocity of the unloaded high impedance CPW line. The Bragg frequency (f B ) is selected to be 3 times of the operating frequency (10 GHz). The f B decides the highest operating limit of a phase shifter after which no power will transfer, and impedance will become zero. Equations (6.7) and (6.8) are used to calculate C b and C s and are summarized here for the sake of completeness, as given in [1] C b = Cs Cs =

 2  2 2 Z ld Z 0 − Z ld   farads 2 2 Z 02 Z lu − Z ld 2 Z 02 − Z ld farads π f B Z 02 Z ld

(6.7)

(6.8)

The phase shift per unit section can be obtained with the change in phase velocity due to change in loaded characteristic impedance with applied bias and is calculated by (6.9), as [1]   √ sωZ 0 εr,eff 1 1 ϕ = rad/s − c Z lu Z ld

(6.9)

where, ω is the frequency in radians, c is the free space velocity and εr,eff is the relative effective dielectric constant of the unloaded transmission line, respectively. Two air bridges are placed at the input and output where 50  impedance changes to high impedance line for DMTL operation. These air bridges can equalize the ground potential and to overcome the effect of any unwanted modes for proper phase shifter operation. Two long air bridges are also placed at the unit section to improve the matching performance (~7 dB) of the phase shifter. The relevant design parameters of the unit cell phase shifter are optimized with S-parameter response

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Table 6.1 Dimensions of the unit cell phase shifter

Parameters

Value (μm) Parameters

Signal line width (W )

100

MAM capacitor width (wm )

CPW gap (G)

140

Air bridge length (l a )

MEMS bridge length (l b )

200

Air bridge width (wa )

15

MEMS bridge width (wb )

65

Fixed electrode width (we )

35

MEMS bridge thickness (t b )

2

Length of the unit cell (s)

300

92

Electrode thickness (t e )

2

MAM capacitor length (l m )

Value (μm) 20 370

using full wave simulation tool. Here, in this design all bias lines are covered with dielectric. It substantially improves the design simplicity where bias line can be routed anywhere without cutting the ground plane. So, the effect of added extra parasitic and RF leakages will be less on phase shifting operation. Table 6.1 summarizes the dimensions of all designed parts used to build a unit cell phase shifter. The total loaded capacitances seen by the line between normal state (C n ) to actuated state (C a ) can also be defined as: Cn = Ct +

Cs Cb Cs Cdb , Ca = Ct + Cs + Cb Cs + Cdb

(6.10)

where, C b and C db are MEMS bridge up-state and down-state capacitances, respectively. The C b and C s capacitances are optimized to be 8 and 24 fF for acceptable impedance matching over the band of interest. The total inductance (L b ) including of MEMS bridge and MAM capacitors is 90 pH. Although unit cell demonstrates a capacitance ratio (C a /C n ) of 13, but the effecting C s /C b of 3 plays a role to achieve the desired phase shift from the cell. The series resistance of the bridge (Rb ) and the Q factor of C s play a significant role in the phase shifter operation. The non-movable static capacitor (MAM capacitor) exhibits high Q factor (>2000 at 10 GHz). The loss of the structure also depends on MEMS bridge resistance in up-state (Rbu = 1.1 ) and down-state (Rbd = 0.6 ). The Q-factor of MAM capacitor and loss of the phase shifter are also affected by the bias resistances (Rb ). The Q-factor of MAM capacitor is found to be 2123 with a self-resistance (Rp ) of 25 k. Figure 6.10a shows TiW bias line that is placed inside the gap of the CPW and extended outside to connect with the bias pad. Internal TiW bias line is connected in shunt with Rp of MAM capacitor. Hence, overall Q factor is reduced to 473 from 2123 due to parallel combinations of Rp (25 k) and Rb (20 k) as shown in Fig. 6.10b. When two-unit cells are connected together with bias lines then the equivalent resistor of MAM capacitor reduces to Rp //(Rb /2)  and

6.4 Different Types of DMTL Phase Shifters

171

the Q factor again reduces to 367 from 473. The resistivity of the TiW bias line is optimized to be 380 /, which is an essential parameter to determine the overall loss of the phase shifter. The down-state characteristics change primarily with bias lines. The insertion loss of the unit cell is 0.045 dB without any bias line at 10 GHz which increases to 0.07 dB due to reduced Q factor of C s . The external bias resistor (Re ) that is routed underneath of the ground plane is only used to excite individual bit separately. The effective Re is very small (0.9 k) due to stronger coupling between the ground plane and external bias resistor underneath. So, the Q factor of MAM capacitor reduces accordingly to 58 from 367 for those five-unit cells which are connected externally with the bias pads for the 5-bit operation of the phase shifter. The insertion loss is also increased to 0.21 dB due the effect of Re . Return loss is not significantly affected by the bias lines. It depends on C b and C s along with unloaded t-line parameters and can be determined from the loaded line impedances Z ld and Z lu using (6.5). In this work, the ranges of the loaded characteristic impedances were designed to be 64  (Z lu ) and 49  (Z ld ), respectively for optimum phase shifter operation. The measured and simulated S-parameter response of the unit cell phase shifter is shown in Fig. 6.9. The cell is well matched with return loss (S 11 ) of 41 dB and insertion loss (S 21 ) of 0.07 dB at zero-bias state over 8–12 GHz, as shown in Fig. 6.11a. Later, unit cell gives a return loss of 31 dB and worst-case insertion loss of ~0.09–1.1 dB with 53–56 V bias voltage, respectively, as depicted in Fig. 6.11a. Measured differential phase shift of 5.92° is obtained between zero-bias to the actuated state at 10 GHz, as shown in Fig. 6.11b. Later, all phase bits are fabricated and tested separately to get the desired phase response. Individual phase bit gives maximum measured phase error of 2° at 10 GHz. Insertion loss of the phase shifter increases with high impedance CPW line, line loss of the high impedance bias lines and Q loss of the MAM capacitors. Loaded line loss is directly related to the unloaded line loss with a multiplicative factor of

Fig. 6.11 Measured versus simulated S-parameter response of the unit cell, a return and insertion loss and b phase versus frequency response [4]. Used with permission from Institute of Physics (IOP) publishing limited

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Fig. 6.12 Microscopic images of individual phase bits, a 11.25°, b 22.5°, c 45°, d 90° and e 180°, [4]. Used with permission from Institute of Physics (IOP) publishing limited

Z0 /Zld . Microscopic images of all fabricated individual phase bits are depicted in Fig. 6.12. After the design of a unit cell and primary phase bits, total 62 unit cells are placed with a periodic placement of 300 μm to build a complete 5-bit phase shifter. The schematic of the complete phase shifter including all bias lines and bias pads is shown in Fig. 6.13a. Figure 6.13b shows the SEM close image of part of the fabricated 5bit phase shifter. The complete phase shifter demonstrates average measured return loss of ~12 dB and average insertion loss of 4.72 dB over the 8–12 GHz from 32 phase states as shown in Fig. 6.14a–b. The maximum phase error of ±3.2° (average phase error ~1.84°) was obtained at 10 GHz from the 5-bit phase shifter, as depicted in Fig. 6.15. Total 32 air bridges are placed on the high impedance line after each 11.25° cell to improve the matching. The total area of the 5-bit phase shifter is 19.4 mm2 . The maximum initial deformation on the MEMS bridge is found to be 0.72 μm from the fabricated 62 bridges on the complete 5-bit phase shifter. The switching voltage is varied from 54 to 62 V for the 5-bit operation. Maximum MAM capacitance deformation of 0.17 μm (upward) is also captured from the surface profile data. The decrease in MAM capacitors (C s ) and MEMS bridge capacitors (C b ) deviates the Z lu and Z ld values which in turn change the desired phase shift obtained from the 5-bit phase shifter. The maximum variation in Z lu and Z ld was found to be ~±2  from the unit cell data (66.7 and 52.8 ). The increase of the attenuation constant of the unloaded line increases the loaded line loss. The measured MAM Q factor of 57 cells is 126 (simulated value ~ 157) and rest 5 cells which are connected to external bias

6.4 Different Types of DMTL Phase Shifters

173

Fig. 6.13 a Complete schematic of 5-bit DMTL phase shifter where bias lines are indicated with red lines, and b SEM image of fabricated phase shifter structure where all functional blocks are marked [4]. Used with permission from Institute of Physics (IOP) publishing limited

Fig. 6.14 Measured S-parameter response of the 5-bit phase shifter, a return loss, b insertion loss is verified with simulated average loss [4]. Used with permission from Institute of Physics (IOP) publishing limited

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6 Micromachined Phase Shifters

Fig. 6.15 Measured phase versus frequency characteristics of the complete cells [4]. Used with permission from Institute of Physics (IOP) publishing limited

resistors contribute a Q factor of 38 (simulated value ~ 57). It has been observed that the phase shifter is reliable with 1 W of RF power till up to 1.5 k cycles. Moreover, phase shifter reliability has been measured under 40–70 °C temperature variation and the results are discussed in [19]. The reliability of the 5-bit phase shifter could be improved with packaging and using lesser number of switching beams.

6.4.2 Push–Pull Type MEMS Digital DMTL Phase Shifters The micro-electromechanical push–pull actuator works on the principle of electrostatic actuation. The schematic image of the push–pull actuator is shown in Fig. 6.16. There are four fixed electrodes on the substrate, two are the push electrodes and the other two are the pull electrodes. When the pull voltage is zero and push voltage is applied, the central part is lifted upward. In other state, when voltage is applied to the pull electrode, central part of the beam moves down. Such a membrane is composed of different parts, central part acting as the mobile plate of the variable capacitor, two mobile electrodes implementing the toggling performance and two levers connected with the central parts and mobile electrodes. Bridge can be pushed up or down by applying a voltage on two couples of fixed electrodes, which are symmetric with respect to the central transmission line underneath the contact beam as shown in Fig. 6.16. The dynamic study of this electrostatic torsional push–pull bridge is discussed in detail in [32]. A CPW line is used as base transmission line with 100 μm wide centre conductor (W ) and 140 μm gaps (G) on the alumina substrate. This line is loaded with one MEMS bridge with a line length of 780 μm to make a unit cell which is the fundamental building block of complete distributed cell. Extra 200 μm length of 50  (W = 100 μm, G = 45 μm) line is kept in either side of the unit cell to start with the RF measurement. Microfabricated image of the unit cell is shown in Fig. 6.17. To maintain acceptable matching over a wide band, it is always recommendable not

6.4 Different Types of DMTL Phase Shifters

175

Fig. 6.16 Schematic of the top surface of the push–pull type MEMS bridge [4]. Used with permission from Institute of Physics (IOP) publishing limited

Fig. 6.17 SEM Images of Micro-fabricated unit cell phase shifter using MEMS push–pull bridge [4]. Used with permission from Institute of Physics (IOP) publishing limited

to overload the transmission line with an excessively large MEMS capacitance. In this circuit, saw-shaped centre conductor is used at the place where MEMS bridge is built to reduce the overlapping area and it leads to the reduction of the downstate impedance. It introduces an inductance of 4.02 nH on the line on either side

176

6 Micromachined Phase Shifters

Fig. 6.18 Measured versus simulated S-parameter response of a unit cell, a return loss and b insertion loss performance [4]. Used with permission from Institute of Physics (IOP) publishing limited

of the bridge. Finally, unit cell demonstrates measured return loss of better than 12 dB and worst-case insertion loss of 0.28 dB from 1 to 40 GHz, as shown in Fig. 6.18a–b. All measured responses are validated using a full wave simulator. The discrepancy between measured and simulation results in S-parameters is attributed to the overall height (g0 ) non-uniformities in the MEMS bridges that leads to the asymmetric distribution of loaded line capacitances. Measured phase shift of 32.12° is obtained from the unit cell. The measured figure-of-merit of the unit cell phase shifter is ~114.64°/dB at 40 GHz. The complete analog phase shifter is designed using 11 MEMS push–pull bridges. The spacing between each unit cell is 780 μm. The schematic image of the complete phase shifter is shown in Fig. 6.19a. A close SEM image of the distributed cell is shown in Fig. 6.17b. Measured return loss of better than 11.5 dB is achieved up to 40 GHz from the distributed cell, as shown in Fig. 6.20a. Maximum insertion loss of 3.75 dB is noticed up to 20 GHz. Later, it goes down to 5.7 dB at 40 GHz in pull states, as shown in Fig. 6.20b. The agreement between measured and simulated insertion loss is found to be within 15% tolerance limit due to asymmetric distribution of gap profile throughout the phase shifter. Typical height non-uniformities variations are 0.43–0.7 μm over the 11 MEMS bridges. Furthermore, the increase in insertion loss in the complete cell compared to the unit cell loss (0.28 dB) is likely due to the signal leakage via the Cr bias lines. The 36% reduction of bias resistance is found from 34.3 to 21.7 k from the distributed cell to the unit cell. The nature of normal and push state transmission losses is closely followed with each other, whereas push state loss degrades at high frequency (>25 GHz) which is closely validated with the nature of the unit cell performance. Measured variation of phase shift with applied bias for pull and push states with reference to the normal state are recorded from the measurements and these are shown in Fig. 6.19. The maximum differential phase shift of 317.15°/cm is obtained at 40 GHz with 4.1 V pull voltage, as shown in Fig. 6.21a. In the push state, maximum

6.4 Different Types of DMTL Phase Shifters

177

8.55 mm

1 mm

Saw-shaped CPW

(a)

(b) Fig. 6.19 a Layout of phase shifter, inset shows the saw-shaped CPW. Complete area of the phase shifter is 8.5 mm2 and b SEM images of the distributed MEMS phase shifter [4]. Used with permission from Institute of Physics (IOP) publishing limited

Fig. 6.20 Measured versus simulated S-parameter responses of the distributed cell, a return and b Insertion loss [4]. Used with permission from Institute of Physics (IOP) publishing limited

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6 Micromachined Phase Shifters

Fig. 6.21 Measured variation of phase shift with applied bias at a pull and b push states, respectively, at 40 GHz frequency [4]. Used with permission from Institute of Physics (IOP) publishing limited

44.1°/cm phase shift is obtained with reference to the normal state at 40 GHz with 8.1 V bias, as shown in Fig. 6.21b. A continuous phase shift of ~0–360° is obtained from fabricated device from push to pull state. Maximum phase shift per dB or FOM performance of 63.25°/dB is obtained from distributed cell at 40 GHz. The results suggest that the structure can be used as micromechanical varactor for phase shifter applications. However, there are few more aspects where extra care needs to be taken for obtaining better performance. The first is the asymmetric bridge actuation. The non-uniformity of different layers is an indeterminate parameter which determines the functionality of the device once they are pulled in. The stiffer torsional springs can reduce the probabilities of stiction induced failures with dielectric charging. The thickness or the length of the mobile plate can be modified to increase the stiffness. The width can also be a parameter to adjust for higher stiffness, but at the cost of increased damping. Therefore, the design must be an optimal one with respect to switching voltage, damping and chances of stiction. Another issue that may lead to degradation of the performance of the device is the effect of intrinsic residual stress on the mobile plate. Under this stress, structure experiences undesirable deformation at the free end over the push-electrode after removal of the sacrificial layer. Residual gradient stress causes undesirable deformation that tends to make suspended beam extremely warped. This results in structure actuating at higher voltage and higher up-state capacitances than anticipated. A tensile-compressive stress converter structure can be used for this purpose. An experimental low temperature release step must be performed at the end to guarantee minimal stress gradient and good planarity on the mobile plate.

6.4 Different Types of DMTL Phase Shifters

179

Later, similar push–pull actuation is being used to develop a band tunable reconfigurable phase shifter using DMTL topology. Detailed analysis behind the development of 5-bit TTD phase shifter using push–pull actuation with minimum insertion loss and good phase accuracy at different bands from 10 to 25 GHz is discussed in the last Section in this Chapter.

6.5 Narrowband and Compact MEMS Phase Shifters As of now, we have studied individual operation principle of switched line and DMTL phase shifters. In this Section, we will discuss a phase shifter that is made by combining both switched line and DMTL topologies. Figure 6.22 shows design schematic of a 4-bit phase shifter. Note that, in a conventional switched-line type 4-bit phase shifter, total 48 times of switch actuations over a complete cycle are needed. However, this design requires total 16 times of single switch actuation over one complete cycle for a 4-bit phase shifter operation. The salient features of the proposed phase shifter topology are as follows: 1.

2.

3. 4. 5.

It is a combination of switched-line and DMTL phase shifter topology. A 3-bit (4-bit) phase shifter uses two back-to-back SP4T (SP8T) switches and they are connected with four (eight) tunable delay lines. All four (for SP4T) and eight (for SP8T) delay lines are loaded with MEMS varactor for desired phase state. Note that, all varactors work within the pull-in limit, resulting in higher reliability. Each connecting line generates two phase states: one from the delay line length and other from the DMTL topology. Design drastically reduces the number of switch count per phase state and thus improves the overall reliability of the device. Switch and varactor are modelled and designed such that they operate at same bias voltages. It means, actuation voltage of the dc-contact switch is equal to the varactor control voltage.

Fig. 6.22 Schematic diagram of a MEMS phase shifter topology [26]. Reproduced with permission from IEEE

180

6.

6 Micromachined Phase Shifters

Proposed design results in substantial size reduction for a 4-bit MEMS phase shifter that operates at 35 GHz. Total area of the 4-bit phase shifter is ~7.5 mm2 .

Phase shift (φ) of this device is obtained using following two steps, as given in (6.11)–(6.12), √ ω εr,eff (ld − lr ) c   √ sωZ 0 εr,eff 1 1 Step 2 : ϕ = − c Z lu Z ld Step 1 : ϕ =

(6.11) (6.12)

Here, ld and l r are the lengths of delay lines and reference lines respectively, ω is the operating frequency, εr,eff is the effective dielectric constant, c is the free space velocity, Z lu and Z ld are loaded up and actuated state impedances. These two steps are followed at each connecting line between the two switches. Step 1 is used for odd numbers (0°, 90°, 180° and 270°) and step 2 is used for even numbers (45°, 135°, 225° and 315°) phase states for 3-bit. 4-bit phase shifter also follows the same logic. To ensure optimum device performance, all individual SPST, SP4T and SP8T switches are designed, fabricated, and tested extensively. The SPST switch details are discussed in Fig. 3.1b. All electromechanical and S-parameter performances of switches are checked systematically and can be found in [33]. The microscopic image of the SP4T and SP8T switches are shown in Fig. 6.23. RF performance of the SP4T switch demonstrates measured average return loss of >17 dB and insertion loss of 17 dB up to 40 GHz and it is measured at one port in the ON-condition [33]. Measured S-parameter performances of the SP8T switch results in maximum average return loss of >16 dB, average insertion loss of 13.6 dB up to 40 GHz [33]. The demonstrated isolation is measured when all switches are in the OFF-state that is 1.8–2.8 dB worse than the isolation with one switch in the ON-state condition. The actuation voltage of the switch is kept as 112 V for better contact.

Fig. 6.23 Microscopic images of a SP4T and b SP8T switching networks [26]. Reproduced with permission from IEEE

6.5 Narrowband and Compact MEMS Phase Shifters

181

Fig. 6.24 Microscopic images of the MEMS, a 3-bit and b 4-bit phase shifters at 35 GHz [26]. Reproduced with permission from IEEE

The device is unpackaged and had variation in contact resistance in other ports due to contact contamination. The 3-bit and 4-bit phase shifters are designed using two back-to-back SP4T and SP8T switches, respectively and connected with DMTL. Fabricated images of phase shifters are shown in Fig. 6.24a–b. Conventional switched line phase shifter uses two SP4T switches for 2-bit, but present topology provides 3-bit operation using same number of switches. It leads to substantial reduction of overall area of the device. Total areas of the 3-bit and 4-bit phase shifters are 4.3 mm2 and 7.5 mm2 , respectively. The insertion loss of the phase shifter is mainly governed by the metal and switch losses. Matching of the structure is mostly dominated by the design of the DMTL. The buckle type beam is used as a varactor for DMTL. The design of the beam is inspired from [34] and this beam design is less prone to temperature and stress. Finally, 3-bit phase shifter demonstrates measured average return loss of >14 dB, insertion loss of 12 dB, loss 30 GHz) with excellent phase setting resolution as compared to the switched-line true-time-delay (TTD) networks. DMTL phase shifter has been demonstrated by Pillans in 2012 [49], with 1.7 dB average insertion loss and 7° of average phase error in the 15–35 GHz band. All these phase shifters [12, 26, 32, 35–47] reported so far, operate at a single fixed frequency over the band of interest. DMTL type frequency reconfigurable phase shifter using triple-stub topology recently reported by Unlu in 2013 [50], can operate at any given frequency within a targeted band of 15–40 GHz with adjustable phase steps. However, this phase shifter [50] can work in wide band (8–26 GHz), but with different resolution. However, there are no reconfigurable digital phase shifters reported so far which can operate with constant resolution at each band over a wide frequency band of spectrum. Later, a phase shifter was proposed by Dey et al. [31, 48, 51–56] where a novel varactor topology was proposed, named it as push pull actuator and analog version of this phase shifter is discussed in Sect. 4.2. A systematic analytical design methodology of the push–pull actuator is comprehensively worked out and reported in detail in [51]. A band tunable reconfigurable 5-bit DMTL phase shifter was developed utilizing the push pull actuator over 10–25 GHz with thorough detailed analysis and experimental investigation. This work is primarily focused on development of a 5-bit TTD phase shifter using push–pull actuation with minimum insertion loss and good phase accuracy at different bands from 10–25 GHz [48]. In this work, the emphasis was given more on the reconfigurable 5-bit phase shifter that can provide 32 phase states with constant resolution (11.25°) at each band between 10 and 25 GHz. Top view of the unit cell phase shifter and its equivalent circuit model is shown in Fig. 6.25a, b, respectively. Later, individual phase bits were developed and finally fabricated 5-bit phase shifter demonstrates better than 13 dB of return loss with an insertion loss of 5.2 dB over 10–25 GHz band without having any

Fig. 6.25 a Top view of the unit cell phase shifter using push–pull actuator and b its equivalent circuit model [48]. Used with permission from Institute of Physics (IOP) publishing limited

6.6 Reconfigurable MEMS Digital Phase Shifters

183

unwanted resonance [48]. This phase shifter has the ability to perform as a multi-bit digital reconfigurable phase shifter with appropriate control of actuation voltage. In addition to this, the proposed phase shifter can also replace multiple phase shifters in wideband multi-frequency system and thereby permitting reduced overall system complexity. Total area of this phase shifter is 15.6 mm2 [48].

6.7 Wide-Band MEMS Digital Phase Shifters A wide-band phase shifter reported in [57] where four different DMTL phase shifters are connected between two back-to-back SP4T switches. The schematic of the proposed phase shifter model is shown in Fig. 6.26a [57]. The microscopic image of the phase shifter is shown in Fig. 6.26b [57]. This phase shifter works at 17 GHz (Ku-band), 25 GHz (K-band), 35 GHz (Ka-band) and 60 GHz (V-band) frequencies [57]. Finally, this 4-bit phase shifter demonstrates maximum loss of 10 dB and maximum phase error of ~5.9° at 60 GHz frequency over a 500 MHz bandwidth [57].

DMTL phase shifter (17 GHz) SP4T switch

DMTL phase shifter (60 GHz)

SP4T switch

DMTL phase shifter (35 GHz) DMTL phase shifter (25 GHz) (a)

(b) Fig. 6.26 a Schematic and b microscopic image of the proposed phase shifter bank using two MEMS SP4T switches and DMTL structures [57]. Used with permission from Institute of Physics (IOP) publishing limited

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Fig. 6.27 Schematic of the proposed single-ended reflective-type phase shifter (RTPS) consisting of a quadrature hybrid coupler terminated with two identical reflective loads. The desired phase shift in the output RF signal is added by the hybrid coupler and the reflective loads G is the reflection coefficient and X L is the tunable reactance of each reflective load [58]. Reproduced with permission from IEEE

6.8 Other State-of-The-Art Micromachined Phase Shifters The monolithically integrated reflective-type phase shifter (RTPS) utilizing micromachined silicon-on-insulator (SOI) was reported in [58]. The schematic of the proposed RF MEMS-based phase shifter is shown in Fig. 6.27. The proposed analog phase shifter employs a hybrid coupler and two identical reflective loads optimized to achieve a large phase shift range. The hybrid coupler is designed using two CPWbased couplers connected in a folded tandem configuration to achieve a compact size design. Various reflective load topologies are studied in [58] for optimum phase shift range and phase linearity over the bandwidth of interest. The device layout is shown in Fig. 6.28. The total device area is 4.0 mm × 2.6 mm. The output phase shift is controlled by the single control voltage provided to the pads of the MEMS Chevron actuator, which tunes the capacitance of each reflective load simultaneously providing change in phase shift between the input and output ports. This phase shifter gives a continuous measured 120° phase shift tunable range from 26 to 30 GHz. The mmWave phase shifter exhibits a low insertion loss of 5.35 dB ± 0.6 dB at 28 GHz. The fabricated phase shifter has an overall device footprint of 4 × 2.6 mm2 . All the components of the phase shifter module are co-fabricated in the 20 μm device layer of a SOI wafer, which provides the flexibility of monolithic integration with other RF modules in phased array antenna systems. Contactless thermally actuated MEMS varactors are used in the reflective loads which do not suffer from the conventional contact-based reliability issues. The microfabricated image of the phase shifter is depicted in Fig. 6.29. Once again, more details of this phase shifter can be found in [58].

6.8 Other State-of-The-Art Micromachined Phase Shifters

185

Fig. 6.28 Layout of the proposed RTPS showing the monolithic integration of a tandem quadrature coupler section with two identical reflective loads. Air bridges are used to connect the ground planes and the coupling signal lines. Thermally actuated Chevron actuators used to drive the varactors are highlighted along with the pads for providing the control voltage [58]. Reproduced with permission from IEEE

A 3-bit millimetre-wave switched true-time-delay (TTD) phase shifters was first implementation on phase-change material (PCM) germanium telluride (GeTe) in [59]. Two types of phase shifters were implemented using PCM GeTe. The first phase shifter is designed using four monolithically integrated PCM single-pole triple-throw (SP3T) switches to route the signal through delay lines. The insertion loss variation between various states is minimized by integrating two fixed PCM GeTe elements maintained in the crystalline state, along with the optimized width of the delay lines. The PCM switching cells are latching type, thus, consume no static dc power. The SP3T switches are connected back-to-back in two stages to provide a 3-bit phase shift with 20° precision. Schematic of a loss compensated 3-bit switched TTD phase shifter consisting of SP3T switches and delay lines is shown in Fig. 6.30. Optical micrograph of the monolithically integrated PCM-based 3-bit mmWave switched TTD phase shifter is shown in Fig. 6.31. This phase shifter exhibits a measured average loss of 4.3 dB with a variation of ±0.3 dB and a return loss better than

186

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Fig. 6.29 SEM micrograph of the monolithically integrated SOI RF MEMS-based 28 GHz RTPS fabricated at the University of Waterloo. The RF signal is provided at the input port and the phase shifted signal is measured at the output port, a zoomed-in view of the air bridge, b close-up of MEMS varactor [58]. Reproduced with permission from IEEE

20 dB. The second phase shifter is designed using two back-to-back connected PCM single-pole eight-throw (SP8T) switches. Both phase shifters are designed to operate over an 8 GHz wide frequency band with a center frequency of 30 GHz. The devices are fabricated in-house using an eight-layer microfabrication process. The second phase shifter demonstrates low average measured loss of 3.8 dB with only ±0.2 dB

6.8 Other State-of-The-Art Micromachined Phase Shifters

187

Fig. 6.30 Schematic of a loss compensated 3-bit switched TTD phase shifter consisting of SP3T switches and delay lines [59]. Reproduced with permission from IEEE

loss variation and return loss better than 17 dB at 30 GHz. Optical micrograph of the monolithically integrated PCM GeTe-based 3-bit latching switched TTD phase shifter using SP8T switches is shown in Fig. 6.32. Both phase shifters provide 180° linear phase shift with lower than 18 ps delay in the worst case. Once again, more details of this phase shifter can be found in [59–65].

6.9 Conclusions This Chapter presents a detailed design methodology of DMTL and switched line phase shifters. A push–pull type analog DMTL phase shifter gives 0°–360° phase shift variation with an 8 V actuation bias at 40 GHz. A conventional switched line phase shifter using 20 MEMS switches is presented and the measured response is validated with simulations up to a reasonable extent at 17 GHz operating frequency. A narrow-band phase shifter is discussed that is built with switched line and DMTL phase shifters. A detailed reference of these phase shifters is outlined with their performances. Finally, reconfigurable, and wideband MEMS phase shifters are discussed with large set of references reported till date.

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Fig. 6.31 Optical micrograph of the monolithically integrated PCM-based 3-bit mmWave switched TTD phase shifter: a optical micrograph of the zoomed-in view of a PCM-based SP3T switch, b SEM micrograph of a PCM SPST switch, and c optical micrograph of the fully integrated phase shifter PS-a [59]. Reproduced with permission from IEEE

6.9 Conclusions

189

Fig. 6.32 Optical micrograph of the monolithically integrated PCM GeTe-based 3-bit latching switched TTD phase shifter using SP8T switches: a optical micrograph of the SP8T switch, b zoomed-in view of a PCM GeTe SPST switch, and c optical micrograph of the fully integrated phase shifter [59]. Reproduced with permission from IEEE

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References 1. Koul SK, Bhat B (1991) Microwave and millimeter wave phase shifter, vol II. Artech House, Norwood, MA 2. Rebeiz GM (2003) RF MEMS theory, design, and technology. Wiley, Hoboken, NJ 3. Zhang WM, Hsia RP, Liang C, Song G, Domier CW, Luhmann NC Jr (1996) Novel low-loss delay line for broadband phased antenna array applications. IEEE Microw Guid Wave Lett 6:395–397 4. Dey S, Koul SK (2012) Design and development of a surface micro-machined push-pull-type true-time-delay phase shifter on an alumina substrate for Ka-band T/R module application. J Micromech Microeng 22:125006–125025 5. Dey S, Koul SK (2014) Design and development of a CPW-based 5-bit switched-line phase shifter using inline metal contact MEMS series switches for 17.25 GHz transmit/receive module application. J Micromech Microeng 24:1–24 6. Simons RN (2001) Coplanar waveguide circuits, components, and systems. Wiley, New York 7. Norvell BR, Hancock RJ, Smith JK, Pugh ML, Theis SW, Kviatkofsky J (1999) Micro electro mechanical switch (MEMS) technology applied to electronically scanned arrays for spaced based radar. In: Proceedings of the aerospace conference, pp 239–247 8. Koul SK, Bhat B (1991) Microwave and millimeter wave phase shifter, vol II. Artech House, Norwood, MA 9. Parker D, Zimmermann D (2002) Phased arrays—Part I: theory and architectures. IEEE Trans Microw Theory Tech 50(3):678–687 10. Kang DW, Lee HD, Kim CH, Hong S (2006) Ku-band MMIC phase shifter using a parallel resonator with 0.18 μm CMOS technology. IEEE Trans Microw Theory Tech 54(1):294–301 11. Kwang-Jin K, Rebeiz GM (2007) 0.13 μm CMOS phase shifters for X-, Ku-, and K-band phased arrays. IEEE J Solid-State Circ 42(11):2535–2546 12. Min B, Rebeiz GM (2008) Single-ended and differential–Band BiCMOS phased array frontends. IEEE J Solid-State Circ 43(10):2239–2250 13. Koh K-J, Rebeiz GM (2010) A 6–18 GHz 5-bit active phase shifter. In: IEEE MTT-S international microwave symposium on digest. Montreal, Anaheim, CA, pp 792–795 14. Choi JY, Cho M-K, Baek D, Kim J-G (2013) A 5–20 GHz 5-bit true time delay circuit in 0.18 μm CMOS technology. J Semicond Tech Sci 13(3):193–197 15. Liang C, Xinyu C, Youtao Z, Zhiqun L, Lei Y (2015) A high linearity X-band SOI CMOS digitally-controlled phase shifter. J. Semicond 36(6):1–8 16. Lucyszyn S (2010) Advanced RF MEMS. Cambridge University Press 17. Liu AQ (2010) RF MEMS switches and integrated switching circuits. Springer, New York 18. Tan G-L, Mihailovich R, Hacker J, DeNatale J, Rebeiz GM (2003) Low-loss 2- and 4-bit TTD MEMS phase shifters based on SP4T switches. IEEE Trans Microw Theory Tech 51(1):297– 304 19. Jian Z, Weil Y-Y, Chen C, Yong Z, Le L (2006) A Compact 5-bit switched-line digital MEMS phase shifter. In: IEEE international conference on nano/micro engineered and molecular systems, pp 623–626 20. Nordquist CD, Dyck CW, Kraus GM, Sullivan CT, Austin F, Finnegan PS, Balance MH (2008) Ku-band six-bit RF MEMS time delay network. In: Compound semiconductor integrated circuits symposium, 2008. CSIC ‘08. IEEE 21. Mortonand MA, Papapolymerou J (2008)A packaged MEMS-based 5-bit X-band highpass/low-pass phase shifter. In IEEE Trans Microw Theory Tech 56(9):2025–2031 22. Wallace J, Redd H, Furlow R (1999) Low cost MMIC DBS chip sets for phased array applications. In: IEEE MTT-S international microwave symposium digest, Anaheim, CA, pp 677–680 23. Pillans B, Coryell L, Malczewski A, Moody C, Morris F, Brown A (2012) Advances in RF MEMS phase shifters from 15 to 35 GHz. In: IEEE MTT-S international microwave symposium on digest. Montreal, QC, Canada, pp 1–3

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43. Hongjoon K, Kozyrev AB, Karbassi A, Van Der Weide DW (2005) Linear tunable phase shifter using a left-handed transmission line. IEEE Microw Wirel Compon Lett 15(5):366–368 44. Kang D-W, Lee HD, Kim C-H, Hong S (2006) Ku-band MMIC phase shifter using a parallel resonator with 0.18 μm CMOS technology. IEEE Trans Microw Theory Techn 54(1):294–301 45. Kwang-Jin K, Rebeiz GM (2007) 0.13 μm CMOS phase shifters for X-, Ku-, and K-band phased arrays. IEEE J Solid-State Circ 42(11):2535–2546 46. Koh K-J, Rebeiz GM (2010) A 6–18 GHz 5-bit active phase shifter. In: IEEE MTT-S international microwave symposium digest, Montreal, Anaheim, CA, pp 792–795 47. Lee S, Park J-H, Kim H-T, Kim J-M, Kim Y-K, Kwon Y (2004) Low-loss analog and digital reflection-type MEMS phase shifters with 1:3 bandwidth. IEEE Trans Microw Theory Tech 52(1):211–219 48. Pillans B, Coryell L, Malczewski A, Moody C, Morris F, Brown A (2012) Advances in RF MEMS phase shifters from 15 to 35 GHz. In: IEEE MTT-S international microwave symposium digest, Montreal, QC, Canada, pp 1–3 49. Vähä-Heikkilä T, Van Caekenberghe K, Varis J, Tuovinen J, Rebeiz GM (2007) RF MEMS impedance tuners for 6–24 GHz applications. Int J RF Microw Comput Aided Eng 17(3):265– 278 50. Hung J-J, Dussopt L, Rebeiz GM (2004) Distributed 2- and 3-bit W-band MEMS phase shifters on glass substrates. IEEE Trans Microw Theory Tech 52(2):600–606 51. Hayden JS, Rebeiz GM (2003) Very low loss distributed X-band and Ka-band MEMS phase shifters using metal–air–metal capacitors. IEEE Trans Microw Theory Tech 51(1):309–314 52. Barker NS, Rebeiz GM (2000) Optimization of distributed MEMS transmission line phase shifters—U-band and W-band design. IEEE Trans Microw Theory Tech 48(11):1957–1966 53. Goins DA, Nelson RD, McKillop JS (2007) Design of a 20 GHz low loss ohmic contact RF MEMS switch. In: IEEE MTT-S international microwave symposium digest, Honolulu, HI, pp 371–374 54. Majumder S, Lampen J, Morrison R, Maciel J (1938) A packaged, high-lifetime ohmic MEMS RF switch. In: IEEE MTT-S international microwave symposium digest, Philadelphia, PA, pp 1935–1938 55. Unlu M, Demir S, Akin T (2013) A 15–40 GHz frequency reconfigurable RF MEMS phase shifter. IEEE Trans Microw Theory Tech 61(8):2397–2402 56. Koul SK, Dey S (2013) Radio frequency micro electromechanical system—An overview. J Smart Struct Syst 2(2):27–75 57. Koul S, Dey S (2014) RF MEMS true-time-delay phase shifter. In: Vinoy KJ, Ananthasuresh GK, Pratap R, Krupanidhi AB (eds) Micro and smart devices and system. Springer. ISBN 0-978-81-322-1912-5 58. Singh T, Mansour RR (2020) Loss compensated PCM GeTe-based latching wideband 3-bit switched true-time-delay phase shifters for mmWave phased arrays. IEEE Trans Microw Theory Tech 68(9):3745–3755 59. Singh T, Khaira NK, Mansour RR (2021) Thermally actuated SOI RF MEMS-based fully integrated passive reflective-type analog phase shifter for mmWave applications. IEEE Trans Microw Theory Tech 69(1):119–131 60. Koul SK, Dey S (2019) Radio-frequency micromachined switches, switching networks and phase shifters. by CRC Press, Taylor and Francis Group, United Kingdom. ISBN: 978-0-81536143-5 61. Dey S, Koul SK (2015) 10–25 GHz frequency reconfigurable MEMS 5-bit phase shifter using push–pull actuator based toggle mechanism. J Micromech Microeng 25(6):19 62. Koul SK, Dey S (2014) RF MEMS single-pole-multi-throw switching circuit. In: Vinoy KJ, Ananthasuresh GK, Pratap R, Krupanidhi AB (eds) Micro and smart devices and system. Springer, New Delhi, ISBN:0-978-81-322-1912-5 63. Dey S, Koul SK (2014) 10–35 GHz frequency reconfigurable RF MEMS 5-Bit DMTL phase shifter using push-pull actuation based toggle mechanism. In: 2nd microwave and RF conference, 2014 IEEE MTT-S international (IMaRC 2014), Bangalore, India

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Chapter 7

Micromachined Tunable Filters Using MEMS Switches

7.1 Introduction Fifth generation (5G) cellular mobile networks will supply a solution to an everincreasing demand for higher data rates in mobile devices. All 5G RF front-end (RFFE) products used in zero intermediate frequency (IF) receiver or in a superheterodyne receiver will be driven by cost, power efficiency, and available space within the unit. In 5G communication, the RF main path simultaneously transmits and receives RF signals [1]. However, the introduction of carrier aggregation for both transmitting and receiving signals are making RF designs more complex. RF components must (a) handle high-power signals, (b) deliver best performance and (c) help to save valuable battery energy. The direct conversion radio architecture is widely used below 6 GHz for RFFE. The classic super-heterodyne radio architecture uses carrier aggregation, phased array antennas and massive MIMO (multiple input, multiple output) features at mm-wave frequencies. RFFE modules utilize the follow two different designs: (1) Discrete RFFE, and (2) Low-noise amplifier Multiplex Module (LMM) in RFFE, as shown in Fig. 7.1. The LMM components combine the advantages of discrete RFFE modules. One of the major differences between transceiver that operates for sub-6 GHz and the emerging mm-wave transceiver is that either sub-harmonic mixing or frequency multiplication technique is usually used for local oscillator generation. Unwanted harmonic associated with nonlinear active devices must be suppressed sufficiently to improve overall performance of the mmWave system. Hence, bandpass filtering plays a key role not only to suppress the harmonics but also used for impedance transformation and co-design with other active components. Unlike the power amplifier, where a single device can be used for multiple frequency bands and technologies, at the present time a single filter is required for each individual frequency band. Filters in the RF chain are a major contributor to loss, which is critical for total transmit efficiency, and the total noise figure in the receive path (SNR and data rate) [2]. The 5G communication system contains the millimeter-wave bands such as 27.5– 28.35, 37–38.6, and 38.6–40 GHz. The desired bandwidth is usually very narrow © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 S. K. Koul and S. Dey, Micromachined Circuits and Devices, Lecture Notes in Electrical Engineering 859, https://doi.org/10.1007/978-981-16-9443-1_7

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Fig. 7.1 Simplified block diagrams of Low-noise amplifier multiplex module [3]. Reproduced with permission from the IEEE

and should have high isolation for different mmWave bands. At present, innovations that enable 5G RFFEs will need to include reconfigurable and multi-band filters to optimize the complete system. High-performance filter designs have faced a lot of new challenges, such as low insertion loss, wide stopband suppression, and compact circuit size. Different types of filters have already been reported for mobile communication. The conventional RLC filter stores the energy in the charge on capacitors and current in inductors, waveguide and cavity filters store the signal in the electromagnetic resonance in the transmission lines or the cavity [4]. In addition, metamaterial based wide bandwidth bandpass filters have already attracted considerable attention [5, 6]. Several prior works can be found in the literature on bandpass filters utilizing silicon [7–20], GaAs [21–23], LTCC [24, 25], and MEMS [26–34, 35–41] technologies. MEMS offer attractive capability for RF systems, particularly in respect of switching, with variable capacitance and inductance tuning functionalities [26–28]. But one of the drawbacks of this is low reliability. This Chapter presents design and development of high reliable bandpass filter for 5G RFFE wireless system at 28 GHz (27–29 GHz). This design can substantially improve overall loss in RFFE and can also reduce system complexity up to a reasonable extent. A tunable 3rd order MEMS bandpass filters is discussed using arrays of MEMS ohmic contact switches and MEMS bridges. The designed bandpass filter is a combination of high-pass and low-pass filters tunable from 27 to 29 GHz. This filter has also an ability to increase the bandwidth.

7.2 Design Topology of the Tunable Bandpass Filter and Its Working Principle The tunable bandpass filter is designed utilizing a simple topology, as depicted in Fig. 7.2. The entire circuit consist of three blocks; block 1 represents the series switch array, block 2 represents bridge array and block 3 is the inductor implemented by a high impedance transmission line. The filter is designed using two high-pass and

7.2 Design Topology of the Tunable Bandpass Filter …

197

Fig. 7.2 Simplified circuit model of the proposed bandpass filter using series (Block 1) and shunt switch (Block 2) arrays [3]. Reproduced with permission from the IEEE

one low-pass section. High-pass section is implemented using tunable capacitors (C s ) placed in series to obtain 3rd order response. Series capacitor (C s ) is designed using in-line MEMS switch array. It provides a tuning range that control centre frequency (f c ) and bandwidth, respectively. The filter has a tuning range of ~40% of its centre frequency. Low-pass section is designed using high impedance line as a series inductor and tunable shunt varactors (C b ). Tunable varactor is made using fixed to fixed (parallel plate) MEMS bridges and it controls the centre frequency based on the electrostatic excitation. The primary aim is to achieve a compact bandpass filter with wide tuning range over 27–29 GHz for 28 GHz 5G applications. Target specifications of the device are tabulated in Table 7.1. Note that, any frequency can be tuned over the band (27–29 GHz) by precise tuning of C s and C b values. The band-pass filter is designed with third-order 3 dB ripple Chebyshev low-pass filter and series capacitor array to obtain a sharp roll-off above the cut-off frequency. The basic filter elements are extracted from the Chebyshev equal ripple low pass filter prototype. The normalized filter elements for a 3 dB ripple Chebyshev prototype are given as g1 = 3.3487, g2 = 0.7117, and g3 = 3.3487 with g4 = 1.00 as the load impedance [29]. The bandpass filter is fabricated on a 635 μm alumina substrate Table 7.1 Specifications of the MEMS bandpass filter at 28 GHz for 5G applications

Parameters

Targeted specification

Centre frequency (f c )

28 GHz

Bandwidth (BW)

850 MHz (~3%)

Max. in-band insertion loss

~3 dB (±0.5 dB)

In-band return loss

20 dB

Stop-band rejection

20–30 dB (f 0 ± 800 MHz)

Ripple or mismatch loss (dB) Depends on the VSWR, VSWR of 1.22 Power handling

1W

Reliability

>1 billion cycles

198

7 Micromachined Tunable Filters Using MEMS Switches

(εr = 9.8) to operate over the millimetre wave 5G band. The filter was designed and optimized initially on the Advanced Design System software from the Keysight technologies. All primary parameters like C s , and C b are modelled and tuned in such a way that any frequencies can be traced or passed between 27 and 29 GHz. The inductance is represented by a high impedance line of 94  and it is fixed for this proposed model. Figure 7.3a–g shows simulated matching (S 11 ) and loss (S 21 ) variations of the filter with different C b and C s values at three centre frequencies (f c ) over 27–29 GHz with 1 GHz steps. The salient features of the bandpass filter are as follows. (a)

(b) (c)

(d)

Figures 7.3a, c, e show fine tuning of f c with different C s values at fixed C b values. Results show f c tuning from 25.9 to 27 GHz, 26.8–28 GHz and 27.8– 29 GHz with C s values from 0.4 to 0.49 pF and C b values of 0.17 pF, 0.16 pF and 0.15 pF at 27 GHz, 28 GHz and 29 GHz, respectively. Noticeable bandwidth tuning is also observed at different f c values. All f c values are tuned back to a common f c of 27 GHz, 28 GHz and 29 GHz with fine tuning of C b and fixed C s , as shown in Fig. 7.3b, d, f, respectively. Bandwidth tuning is flexible with C s and it also decides selectivity of the filter. Lower C s values give sharp stop-band rejections with narrower bandwidth, but it shifts the f c at lower frequencies, as shown in Fig. 7.3a, c, e. The proposed topology demonstrates first order response and order of the filter can be increased with a greater number of similar stages. Lesser number of switches in switch array give better rejection but it increases the need for number of bridges to re-tune the frequency. It effects on the matching. Hence, here is a trade-off in selection of switches and bridges in arrays.

Table 7.2 presents final optimized functional parameters of the bandpass filter at 27, 28, and 29 GHz and related responses are depicted in Fig. 7.3g. This analysis sets a primary benchmark for the proposed bandpass filter with matching of better than 20 dB, passband insertion loss of 1.7 dB over 0.85 GHz, and stopband rejection of 25 dB over 1.6 GHz. Note that, bandwidth tuning is an additional feature in this filter. Figure 7.3h shows considerable matching of roll-off at high frequencies between bandpass and its lowpass section (Block 2, 3). Finally, the proposed topology has been duplicated using micromachining technology where all functional building blocks of the filters like single switch, switch array, and varactors are fabricated and tested individually for optimum filter performances. Later, all of them are cascaded together to build a tunable MEMS band-pass filter and discussed in the subsequent sections.

7.2 Design Topology of the Tunable Bandpass Filter …

199

Fig. 7.3 Simulated responses of the proposed tunable bandpass filter where a bandwidth and f c tuning with different C s and fixed C b values between 25.9 and 27 GHz, b bandwidth and f c tuning with optimized C s values from Fig. 7.3a and different C b values centered at 27 GHz, c bandwidth and f c tuning with different C s and fixed C b values between 26.8 and 28 GHz, d bandwidth and f c tuning with optimized C s values from Fig. 7.3c and different C b values centered at 28 GHz, e bandwidth and f c tuning with different C s and fixed C b values between 27.8 and 29 GHz, f bandwidth and f c tuning with optimized C s values from Fig. 7.3e and different C b values centered at 29 GHz, g f c tuning at 27, 28 and 29 GHz, and h insertion loss responses of the lowpass (block 2, 3) and bandpass sections [3]. Reproduced with permission from the IEEE

200

7 Micromachined Tunable Filters Using MEMS Switches

Table 7.2 Proposed bandpass filter functional parameters Frequency (GHz)

C b (pF)

C s (pF)

L b (nH)

FBW3dB (%)

27

0.17

0.42–0.45

0.322

6.6

28

0.16

0.42–0.45

0.322

6.2

29

0.15

0.41–0.45

0.322

7.3

7.3 Design and Testing of Individual Functional Blocks of the Filter MEMS arrays of switches and bridges are fabricated using a simple surface micromachining process presented in Appendix B. Detailed design descriptions and measurement results are discussed in next sections.

7.3.1 MEMS Switch Design and Measurements The single MEMS switch is fabricated and tested initially to ensure the optimum performances from the switch array. Microscopic image of the switch is presented in Fig. 3.1b and descriptions are given in Chap. 3. The analytical model of switch actuation voltage is presented in (3.33) Please Recheck this??. Measured mechanical resonance frequency of the switch was 80 kHz in room air and measured Vp, Vr voltages were in the range of 82–109 V. Switch voltage decreases by ~6 V after 0.5 W and 11 V after 1 W of RF power up to 85 °C due to RF latch. Measured ON-time of 12.6–9.5 μs with OFF-time of 6.8 μs was obtained at 108–120 V bias. RF measurement was done using Agilent Vector Network Analyzer (E8361C) using cascade dc probes and calibrated using short-open-load-thru (SOLT) standard to the probe tips. Although, switch performances were crucial over 26–29 GHz but its broadband performances are presented over 1–30 GHz, as depicted in Fig. 7.4a. The switch demonstrates measured return loss of better than 30 dB, worst case insertion loss of ~0.94 dB and isolation of better than 25 dB over 1–30 GHz with 112 V. Measured S-parameters were also validated with fitted circuit model with C off = 0.16 pF, Rc = 1.14  and L b = 36 pH. Figure 7.4b shows measured Rc variations of 1.2–1.03  with actuation voltage from 107 to 120 V at RF power of 0.1 W. Total four identical switches were tested and average responses are also plotted with fitted simulation response, as shown in Fig. 7.4b. Switch shows measured IIP3 of 49 dBm and it was limited by RF probe contact resistance and transmission lines. No package was placed on top of the switch during measurement.

7.3 Design and Testing of Individual Functional Blocks of the Filter

201

Fig. 7.4 a Measured versus fitted S-parameters responses of the switch and b Measured contact resistance versus applied voltage for the single switch and 4-element switch-array [3]. Reproduced with permission from the IEEE

7.3.1.1

Four-Element MEMS Series Switch Array Design and Measurements-Block 1

The first functional building block (Block 1) of the tunable bandpass filter is the switch array. In this work, four element arrays are chosen to achieve the adequate performance. The microscopic image of the fabricated switch array is depicted in Fig. 7.5a and equivalent circuit model is shown in Fig. 7.5b. One of the design challenges is to spread the current equally in each switch to result in reduction of ON-state resistance. In addition, with the bandwidth tuning, switch array also provides lower loss and that drastically improves overall pass-band loss of the filter. Figure 7.6a shows measured versus fitted S-parameter responses of 4-element switch array. It demonstrates measured return loss of better than 21 dB, worst case insertion

Fig. 7.5 a Microscopic image, and b equivalent circuit model of the 4-element MEMS switch array [3]. Reproduced with permission from the IEEE

202

7 Micromachined Tunable Filters Using MEMS Switches

Fig. 7.6 a Measured versus fitted S-parameters responses of 4-element MEMS switch array and b measured change in C s with V s at 28 GHz [3]. Reproduced with permission from the IEEE

loss of ~0.58 dB and isolation of better than 30.7 dB up to 30 GHz with 112 Vbias voltages. Note that, switch responses for filtering operation were closely checked from 27 to 29 GHz. Measured average return loss, insertion loss and isolation of the first block of the filter demonstrates 33, 0.48 and 23 dB over 27–29 GHz. All measured responses are validated using fitted model, as depicted in Fig. 7.6a. Note that, total Rc of 0.38  and C off of ~0.33 pF were obtained from the switch array. The variation of measured Rc of switch-array were found from 0.5 to 0.33  with 107–120 V and performances were verified by fitting measured 2-port S-parameter data, as depicted in Fig. 7.6a. The variation of switch C off (C s for the filter) with bias voltage is shown in Fig. 7.6(b) and it shows measured capacitance variation of 0.33–0.58 pF with V s of 88–105 V. The range of C s is within the desired operating range for the proposed filter as per Table 7.2. Note that, 4-element switch array was finalized for this work after extensive optimization with different elements using a finite element solver and the utility of using 4-element array is satisfied for the proposed filter. Performances of array are completely driven by contamination over unpackaged testing condition and all tests were done with 0.1 W RF power at room temperature.

7.3.2 MEMS Shunt Switch Array Design and Measurements: Block 2 The next block of the filter is the shunt switch array that primarily controls tuning of the centre frequency. The buckle type beam was used as a varactor for the filter. To get the desired values of C b (as per Table 7.1), different combinations were tried, and finally 4-element array bridge was chosen as varactor for the proposed filter configuration. The 4-element bridge array was fabricated individually, and

7.3 Design and Testing of Individual Functional Blocks of the Filter

203

Fig. 7.7 a Fabricated microscopic image, and b equivalent circuit model of the MEMS bridge array [3]. Reproduced with permission from the IEEE

microscopic image is shown in Fig. 7.7a. The design of the beam was inspired from [39] and this beam design is less prone to temperature and stress. The stiffness of the beam (k z ) is a combination of structural stiffness (k s ) and stiffness due to the biaxial residual stress (k b ). For this clamped–clamped structure, temperature change will effect on k b and thus on the pull-in voltage. The k z (k z = k s + k b ) is a function of the Young’s modulus of gold (45 GPa) and the structure geometry. The pull-in voltage of the beam (V pb ) is given by;  Vpb =

8(ks + kb )g 2   27 Cu + C f

(7.1)

where, C u is the up-state capacitance of the beam and it is defined by ε0 εr A/g where, A and g are the overlap area (l × w) and initial gap between the suspended beam and the bottom electrode. C f is the fringing capacitance between two plates. Note that, there may be some roughness associated with the dielectric layer underneath the bridge, the total capacitance (C b ) for this case is given by [28]; Cb =

  1 ε0 A εr + 2 tr + td /εr td

(7.2)

where, t r is the amplitude of the total roughness, t d is the thickness (0.5 μm) and εr is relative permittivity of the dielectric. The simple equivalent circuit model of the bridge-array is shown in Fig. 7.7b, where L n is the equivalent bridge inductance, Rn is the bridge resistance and suffix n denotes bridge element quantity. Note that, bridge will never reach in contact with bottom transmission line as they are working

204

7 Micromachined Tunable Filters Using MEMS Switches

Fig. 7.8 Simulated. a In-plane displacement versus in-plane stress and b vertical displacement with beam distance with σ = 100 MPa [3]. Reproduced with permission from the IEEE

as a varactor not as a switch. Hence, L n and Rn are not playing any major role in filtering action. In this design, thicker bottom electrode thickness (2 μm) was used that increases the vertical deflection of the beam due to bending moments associated at the step. It also creates non-planarized topography underneath the beam plane. The angle (ϕ) of the tilted spring was optimized to be 45° with 3.5 μm thickness and 10 μm of spring width. It substantially reduces this deflection due to in-plane displacement effects (δ σx ) from tensile stress in −x direction and this is irrelevant from an RF MEMS varactor perspective. COMSOL simulation shows tensile ϕ = 45° gives higher stiffness compared to other ϕ, as shown in Fig. 7.8a. Simulation also shows vertical deflection of 3

n/a

59

n/a

GaAs

NA

Feng et al. [23]

28

>2.5

n/a

11.1

n/a

GaAs

NA

Feng et al. [23]

28

>3

n/a

8.9

n/a

GaAs

NA

Tao et al. [46]

38.5

1.85

n/a

2

229

PCB

NA

Jiang et al. [24]

36

6.2

n/a

9.5

4.05

BST-on-sapphire

NA

Wang and cho [25]

30.3

4.8

n/a

6.7

21.9

LTCC

NA (continued)

7.6 Frequency and Bandwidth Tunable Micromachined Bandpass …

217

Table 7.6 (continued) EF* , Year

f c (GHz)

Loss (dB)

Filter order

FBW (%)

Area (mm2 )

Technology

Reliability

Wang and cho [25]

39.3

4.8

n/a

7.2

21.9

LTCC

NA

Martoglio et al. [35]

29

2.2

4

28

n/a

MEMS

NA

Stickel et al. [36]

29.7

1.5

3

2.2

n/a

MEMS

NA

Blondy et al. 37 [37]

2.3

2

3.5

n/a

MEMS

NA

Lucyszyn et al. [38]

2.95

3

9.8

4.97

MEMS

NA

Yang and 35.1 Peroulis [39]

1.5

2

4

NA

MEMS

140 million cycles

This work, [3]

1.92

1st

6.7

2.3

MEMS

1B cycles with 1 W

59.7

28

* Note The matching is better than 10 dB and all the results are extracted from the referred documents.

The loss mentioned in most of these documents and in this work is at the f c

= 61 fF), as expected from the design analysis (Fig. 7.14), as depicted by the blue line in Fig. 7.17. Measured loss of 1.64 dB and matching of ~21 dB are achieved at this stage [47]. Later, filter is retuned by changing C s from 0.5 to 0.3 pF (reducing V s from 102 to 92 V), as shown by the black lines in Figs. 7.16 and 7.17. Note that, reducing V s shifts f c at higher frequency and it is retuned further at 24 GHz with V b = 18 V. Matching is also affected during this process due to capacitively overloading the line and the same is noted in the circuit model simulation as depicted in Fig. 7.14e [47]. Note that, narrow band (NB) (over 250 MHz) and Ultra-Wide Band (UWB) (over 5 GHz) performances are marked in Fig. 7.17. Result shows, filter demonstrates average loss (matching) of ~1.87 dB (~18 dB) and 3.8 dB (11.3 dB) over 250 MHz and 5 GHz of bandwidth cantered at 24 GHz [47]. In this work, Filter responses are also validated using full wave simulation in Ansys HFSS and plotted in Fig. 7.17. All nonuniform deformations of bridges and switches are considered during simulation up to a reasonable extent but still deviations were noted between simulated and measured results. The related deviations are mostly attributed to nonuniform actuation between all twelve actuators under constant bias voltages (V s and V b ). It leads to nonuniform variation of loading capacitances (C s and C b ) and it is difficult to add these accurately as a function of gap height in the full wave simulations. Results indicate that the proposed MEMS based filter could be a good candidate for 24 GHz NB and UWB applications.

218

7 Micromachined Tunable Filters Using MEMS Switches

Fig. 7.14 Simulated responses of the proposed tunable bandpass filter where a f c tuning at 22, 23 and 24 GHz, bandwidth and f c tuning with different C s and fixed C b values between, b 22– 23.7 GHz starting from P1, c 23–24.5 GHz starting from P2, d 24–26.2 GHz starting from P3, and e bandwidth and f c tuning with optimized C s values from Fig. 3d and different C b values centered at 24 GHz for radar applications [47]. Reproduced with permission from the Wiley

7.7 Conclusions This Chapter presents design, development, and extensive characterization of a tunable MEMS bandpass filter for millimeter-wave applications. All functional blocks of the filter are fabricated and tested individually to ensure the optimum device performance. Finally, filter gives 1.9 dB, 2.1 dB and 3.7 dB of insertion loss at 27,

7.7 Conclusions

219

Fig. 7.15 Microscopic image of the fabricated MEMS tunable order bandpass filter. Total area of the filter is ~2.8 mm2 [47]. Reproduced with permission from the Wiley

Fig. 7.16 Measured, a insertion loss and b matching performances of the filter at center frequencies of 22–24 GHz with different V b and V s values [47]. Reproduced with permission from the Wiley

220

7 Micromachined Tunable Filters Using MEMS Switches

Fig. 7.17 Measured (solid line) versus full wave simulated (dashed line) maximum bandwidth tuning of the filter at 24 GHz with different V b and V s values [46]. Reproduced with permission from the Wiley

28 and 29 GHz, respectively with matching of better than 11.6 dB. Moreover, initial performance of the filter can cover total 8.71 GHz bandwidth (23.87–32.58 GHz) with 5 dB of insertion loss and matching of better than 10 dB. Total area of the filter is 2.3 mm2 including bias lines and pads. Finally, a complete set of design guidelines are given for readers. It also confirms that the proposed simple topology will be useful to design any tunable (both f c and FBW) filter at any frequency if one follows the guideline strictly. Note that, almost all kinds of measurement stages were adopted on the wafer except for the non-linearity measurements like 1 dB-compression points, and third-order intercept point (IIP3 ). Note that, in this Chapter prime focus is given on the tunable bandpass filter. However, tunable bandstop filter can also be designed using variable capacitive bridges and the RF MEMS switches.

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Chapter 8

Reliability Analysis of RF MEMS Devices

8.1 Introduction At the beginning of 2000, RF MEMS switch technologies were very promising but later they suffered from reliability problems. Reliability is generally defined as ‘the probability that a device will perform a required function under stated conditions for a stated period’. A survey undertaken on literature published on RF MEMS in 2005 showed that only 5% of the papers reported reliability data and most of the data was very limited from practical point of view. Early phases of MEMS development were typically dominated by considerations on design, functionality, and feasibility, but not reliability. Later, numerous research institutes started working on the reliability improvements on RF MEMS devices. In 2001, Rebeiz et al. wrote “RF MEMS technology is now at a turning point; important issues, such as long and short-term reliability, packaging technologies and their effect on reliability, and production costs, are currently being addressed” [1]. It is difficult to solve a reliability problem if the physical mechanisms behind the problem are not known. Therefore, knowing what can go wrong and understanding the physics of failure is certainly of interest if high reliability is to be achieved. In this Chapter, the improvement of reliability is discussed on few typical RF MEMS devices where multiple MEMS switches are operating simultaneously. In includes switching networks, multi-bit phase shifters and tunable filters. Two important question one can ask at this point are: How does one test the reliability of RF MEMS? What are the reliability test standards? The answer of the first question demands a dedicated reliability test set up that can be used to test any kinds of RF MEMS devices and we will discuss this in the first part of this Chapter. The answer to the second question depends on the operating principle of different RF MEMS devices under test. This aspect will be discussed in the subsequent Sections of this Chapter.

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 S. K. Koul and S. Dey, Micromachined Circuits and Devices, Lecture Notes in Electrical Engineering 859, https://doi.org/10.1007/978-981-16-9443-1_8

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8.2 Testing the Reliability of RF MEMS Devices A reliability test setup is shown in Fig. 8.1. Amplified RF signals of different power level (0.1–1 W) at 2.4 GHz is applied to the DUT. To monitor the power level of incoming RF signal, a power meter was connected with a 20 dB directional coupler. RF MEMS devices are controlled using a bias waveform. Waveform is maintained with a specific period and followed a ramp with a pre-defined rise time and fall time. The amplitude of the dc waveform was set to the required voltage level and that should be identical with the switch actuation voltage. Few time spans should be maintained during the switch contacting period if DC-contact switches are used.

Fig. 8.1 Measurement set up for switch temperature stability and power handing testing [10]. Reproduced with permission from IEEE

8.2 Testing the Reliability of RF MEMS Devices

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To monitor the contact resistance (Rc ) changes over lifetime, a four-point resistance measurement setup is connected with bias tee. The output RF signal was captured through a directional coupler to the RF detector. The proposed measurement can be performed at low frequency and a power amplifier (HD29702) is used here. All cable and bias-T losses must be calibrated and normalized out of the measurements. A back-to-back waveguide is used at the output port for coaxial-to- waveguide transition to decouple the DC and any step voltage leakages. Next, waveguide is connected to the power detector through an attenuator. Power detector output is connected with an Oscilloscope (HP54645A) channel 2 and channel 1 is connected to a function generator (HP3245A). A computer is connected between oscilloscope and function generator. Switch is actuated using a driver circuit using signal taken from the function generator and corresponding changes in pull-in (V p ) and release (V r ) voltages are recorded at different powers. Later temperature stability of the device can be measured by replacing Block 1 with Block 2 as shown in Fig. 8.1. Temperature stability of the RF MEMS devices is observed by measuring the change in switch V p and V r voltages as a function of temperature. The probe station chuck is connected to a temperature controller that set a stable operating temperature during measurement. Temperature is increased from 25 to 85 °C with 5 °C step from room temperature (~25 °C) and then again set to 25 °C. For any RF. MEMS devices where multiple MEMS switches are used, few guidelines need to be followed to obtain a good reliability. These are: (a)

(b)

Measure reliability of a single MEMS switch after successful fabrication; it includes (a) switch contact resistance variation with applied bias, (b) switch power handing over the cycle, (c) switch temperature stability at elevated temperatures and corresponding changes in switch contact resistance and Sparameters must be recorded. After successful measurement and satisfactory performance at least till 1 billion (B) cycles, the switch can be considered suitable for applications in RF MEMS devices like switching networks or multi-bit phase shifters. Repeat the power handing and temperature stability testing on the RF MEMS devices where multiple similar switches are being used. Note that, it is always recommended to use proper bias waveform during actuation of MEMS switches.

8.3 Reliability Analysis on MEMS Switching Networks In this Section, reliability performance on different single-pole-multi-throw (SPMT) vertically actuated switching networks are discussed. The S-parameter performance of these SPMT switches is presented in Chap. 4. As stated before, single switch reliability performance will be evaluated before one can proceed with the SPMT switches where same switch is being used in different output lines.

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8 Reliability Analysis of RF MEMS Devices

Fig. 8.2 Test waveform for cold switched reliability measurements of the MEMS SPMT switching networks [10]. Reproduced with permission from Institute of Physics (IOP) limited

Switch reliability measurement is performed using the set up shown in Fig. 8.1. During the reliability measurement, switch contact resistances were measured periodically using a 4-wire configuration between two bias-tees. Measurement is carried out at 2 GHz test frequency. The test is performed up to 1 billion cycles to check whether the device is operational or not within the point of stability in terms of self-actuation or contact point degradation. A square waveform is formed using a computer and followed through a function generator. Finally, all 9 SPMT switches are actuated using a waveform generator. Figure 8.2 shows the test waveform applied to the switches with 20 kHz cycle rate. The dc bias waveform is maintained with 50 μsec period and followed by a ramp with 15 μs rice time and 10 μs fall time. The amplitude of the dc waveform was set to be +70 V and 25 μs time span is maintained during the contacting period, as depicted in Fig. 8.2. Figure 8.3 presents measured switch reliability with 0.1–1 W of incident RF power in all fabricated SPMT switches. During this operation all switches were cycled up to 20 kHz with 0.1–1 W of RF power at 2 GHz. A power amplifier (PA) is used during the testing. Switches are measured till up to 1 B cycles at 25 °C and switch Rc is measured periodically using a four-point probe method. The measurement results were limited by the current density in closed state (Joule heating). Self-actuations (V RFrms > V p ) and latching (V RFrms > V r ) are observed over the reliability operations of the SPMT switches. Maximum power handling limitation (Pmax ) of the dc-contact type MEMS switches can be defined by (8.1)–(8.3), Vopen Iclosed 2  = 2 Z 0 Pmax

Pmax =

(8.1)

Vopen

(8.2)

 Iclosed =

Pmax Z0

(8.3)

8.3 Reliability Analysis on MEMS Switching Networks

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Fig. 8.3 Reliability performances of the SPMT switching networks with 0.1–1 W of incident RF power at room temperature [8]. Reproduced with permission from Institute of Physics (IOP) limited

where, V open is the OFF-state bias voltage of the dc contact switch, I closed is the ONstate current of the switch at the dimple and Z 0 is the characteristic impedance of the CPW transmission line. During the reliability operation, each arm of the SPMT switch is actuated individually. Failure is observed after ~500 million (M) cycles with 1 W of RF power in higher throw configurations (M > 10). Failure is mostly due to (a) dielectric charging effect and (b) effect of spring softening at higher incident RF power. To improve the reliability of the reported switching networks, one possible solution could be the reduction of the contact current density using higher values of Z 0 (>50 ), but the cost paid is in terms of higher loss and poor matching performance over the band of interest [2]. Thicker switch membrane can increase power handling capability of the switches, but price paid is in terms of higher actuation voltage. Note that, total 10 individual switches were tested, and primary reason of failure was mostly due to the electrostatic damage (ESD). Next, all switches are tested under the temperature range from 25 to 85 °C with 0.1–0.5 W of RF power. The chuck of the probe station is connected to a temperature controller (Temptronic Corporation, Mansfield, MA), as shown in Fig. 8.1 where Block 1 is replaced with Block 2. A stable operating temperature is maintained using this controller during the measurement. Probe chuck temperature is increased from 25 °C up to the 85 °C with 5 °C step and then again saturated to the room

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8 Reliability Analysis of RF MEMS Devices

temperature. Note that, all switches are actuated with the same actuation waveform voltage shown in Fig. 8.2. Switch contact resistance variations are tested using 4point wire at each operating temperature with 0.1, 0.3 and 0.5 W of incident RF powers. Figure 8.4 presents measured reliability results of the SPMT switches at 85 °C temperature for three different levels of RF power. The probability of failure is more at higher throw configurations. Result shows, SP14T switch sustained up to ~80 M cycles with 0.5 W of RF power at 85 °C. This measurement is limited to the thermal expansion coefficient difference between gold (α m ) and alumina substrate (α s ). Beam in-plane stress turns into compressive at higher temperature. As a result, it leads to the downward deformation of the gold cantilever beam. It drastically effects the switch spring constant due to change in switch pull-in voltage at the elevated temperature. The change in dc-contact switch pull-in voltage with temperature can be represented by (8.4) [3] as  V p (T ) =

  σ (T )l(1 − υ) kg g + 2 Aε0 l 2Et

Fig. 8.4 Reliability performances of the SPMT switching networks with 0.1–0.5 W of incident RF power at 85 °C temperature [8]. Reproduced with permission from Institute of Physics (IOP) limited

8.3 Reliability Analysis on MEMS Switching Networks

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where g = g0 +

td εr

(8.4)

where, K is the spring constant, A is the electrode area, ε0 is the vacuum dielectric permittivity, g0 is the gap height or anchor height, t d is the dielectric thickness, εr relative dielectric permittivity, l is the beam length, t is the beam thickness, E is the Young’s modulus, υ is the Poisson ratio and σ(T ) is the linear stress gradient and it is a function of temperature. During this reliability process, failure is mostly due to (a) contact point degradations due to additional attractive force from RF power at higher temperature, (b) different thermal expansion coefficients between alumina substrate and gold beam [2], and (c) charge injection problem after few cycles when beam curvature decreases with time. All these issues could be improved using (a) doping the dielectric materials [4] or no dielectric layer structures [5], (b) phase change material [6], and (c) well suited contact materials like ruthenium [7]. With precautionary anti-ESD handling can also improve the switching cycle up to a reasonable extent. Although all measurements are carried out at 2 GHz, but sensitivity of the S-parameters may get affected at higher frequency and even at higher incident power. It is mostly due to self-biasing and self-heating at higher RF power at high frequency due to the skin effect. In addition to this, switch OFF-state performance is also affected during this process due to the reduction in switch spring constant (k) and initial contact gap height at higher incident power level. It affects sensitivity of the switch isolation with higher C off . All performances could be improved in hermetic condition to overcome the effect of surface charges trapped due to some residual humidity and stiction due to the non-clean environment. More details of this work can be found in [8].

8.4 Reliability Analysis on MEMS Digital Phase Shifter In this Section, reliability performance on digital phase shifter is discussed. First thing to note here is that reliability performance of a digital phase shifter is function of number of switch count and in turn depends on number of bits. Higher bit phase shifter is prone to more failure than the lower bit. Let us first check with one of the higher bit phase shifters like 5-bit. One of the conventional switched line phase shifters discussed in Sect. 6.2.4 is used here. Out of total 20 switches in the phase shifter, 10 switches are required to be actuated to activate one phase state. It indicates these 10 switches need to operate 32 times to finish one complete cycle of operation. Hence, number of switch count plays very crucial role and in turn number of switch actuation per phase state plays a major role to improve overall reliability of a phase shifter. One of the 5-bit topology that can substantially reduce the total number of switches per phase state is shown in Fig. 8.5a. Compared with the conventional switched line phase shifter, in which a minimum of 10 switches are actuated at a time

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Fig. 8.5 a Schematic diagram of the 5-bit MEMS switched-line phase shifter based on SP4T and SPDT switches and b microscopic image of the fabricated 5-bit phase shifter [3]. Reproduced with permission from IEEE

[9], the present design requires only 6 switches to be actuated at a time to activate one phase state for 5-bit operation. The proposed topology contains a fine-bit (0°/11.25°/22.5°/33.75°), a coarse-bit (0°/45°/90°/135°) and a 1-bit (0°/180°) sections. Results of the SPST and SP4T switches used in the proposed topology are discussed in detail in [3]. To improve simplicity and reliability from the proposed topology, small footprint (130 × 40 μm2 ) of the cantilever beams is used for switching. It introduces the following salient features in the design: (1) (2)

Switch is less sensitive to stress due to its small size with a fast-switching time. A single-contact cantilever switch is less sensitive to planarity and stress which significantly improves the overall contact force and equal division of electrostatic force over all different paths in the phase shifter.

8.4 Reliability Analysis on MEMS Digital Phase Shifter

(3)

(4)

(5) (6)

233

A multi-contact cantilever switch is very prone to single contact failure (one contact permanently stuck down) or an actuator failure (permanent up). Single switch failure can completely damage the overall phase shifter performance for long range operations. Multi-contact, long and complex designs of cantilever switches are sensitive to stress gradient. The residual stress effects on uneven distribution of tip deflection between all identical structures. Hence, in most of the cases, different blocks need different voltages to actuate. It decreases overall yield of the device where at a time six switches are actuating. A simple cantilever beam can easily be placed on the CPW line which substantially improves the compactness in the SP4T and SPDT structures. Also, due to its small thickness (2 μm), it can be easily packaged using a thin-film package which is very compatible with CMOS process.

Individual primary fine-bit (2-bit), coarse-bit (2-bit) and 1-bit sections are fabricated and tested to ensure the complete phase shifter performance. Later, all of them are cascaded together to build the final 5-bit phase shifter. The fabricated image of the 5-bit phase shifter is shown in Fig. 8.5b. The total size of the phase shifter is 13 mm2 (including bias pads and bias lines). This phase shifter provides return loss of better than 22 dB up to 18 GHz and average insertion loss of less than 2.65 dB over all the states from 13 to 18 GHz with 70 V actuation voltage. The maximum average phase error is 0.68° at 17 GHz. Furthermore, the maximum measured group delay of ~159 ps with the delay step of ~4.06 ps is achieved at 17 GHz. Phase shifter also demonstrates 0.7 dB/bit figure-of-merit (FOM) at 17 GHz. To investigate the reliability of this phase shifter, initially switches responses are measured over cycles and it includes single MEMS switch and the SP4T switch. The single switch power handling capability is measured initially, and it is observed that switch can handle 0.1 W–3 W of RF power at four different temperatures with max. 15.8 V reductions in voltage. Switch Rc is measured periodically using four-point probes to ensure the switch performance at different RF powers. During this process, both SPST and SP4T switches are cycled up to 10 M cycles and corresponding changes in Rc are recorded at five different RF powers (0.5, 1, 2, 3 and 4 W) at 2 GHz. All measurements are carried out at room temperature with 70 V, as shown in Fig. 8.6a. Note that, Rc is recorded after each 100 cycles to ensure the stiction free condition. Result shows that SPST switch can handle >10 M cycles till up to 3 W with no contact failure or stiction. But reliability started degrading for 3–4 W of RF power with an abrupt change in Rc after ~105 cycles and failed after ~1 M cycles. Finally, the SPST switch can handle 2.5–3 W of RF power till up to 10 M cycles at 25 °C. SP4T switch is also characterized during this process. Each arm of the switch is actuated independently with 0.8–1.1 mN of contact force. During this cold switched reliability process, reported SP4T switch can withstand up to 1.5–2 W of incident power till up to 10 M cycles and 3 W for 105 cycles without failure of any of the contacts,

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8 Reliability Analysis of RF MEMS Devices

Fig. 8.6 Reliability results of a SPST and b SP4T switch with incident RF powers [3]. Reproduced with permission from IEEE

(see Fig. 8.6b). Again, to ensure the phase shifter performance, five identical SP4T switches are tested up to 100 M cycles with 0.5–1 W of power and test is stopped without failure. Phase shifter reliability is observed on a chip with 0.1 W of power at 25 °C. Initially, reliability performances are observed on individual sections (fine-bit, coarse-bit and higher bit), prior to start with the complete 5-bit phase shifter. All sections are measured up to 100 M cycles to ensure the optimum phase shifter performance. No failure is observed till up to 100 M cycles of operations in all fundamental blocks of the 5-bit phase shifter. Results show, maximum average loss and phase error of 1.64 dB and ~1.1°, respectively, at 17 GHz [3]. Finally, Fig. 8.7 shows phase shifter reliability results at four power levels (0.1 W, 0.5 W, 1 W and 2 W) at 25 °C. Result shows phase shifter works satisfactorily up to >30 M cycles with maximum average loss and phase error of 5.34 dB and ~2.8°, respectively, with 0.5 W–1 W of power levels. Furthermore, failure in the phase shifter is observed Fig. 8.7 Reliability results of 5-bit phase shifter with incident RF powers [3]. Reproduced with permission from IEEE

8.4 Reliability Analysis on MEMS Digital Phase Shifter

235

after 30 and 5 M cycles at 1 W and 2 W of power levels, respectively. In most of the cases failure occurs in higher bit section. At 1–2 W, the total rms current in the switch is 0.14–0.2 Arms and each contact is handling 35–50 mArms . Thus, reliability of the phase shifter at high power level is limited by the current density in closed state and due the effect of electro-migration like Joule heating [2]. Now, note that switch may stay at a particular position during phase shifting operation when one phase state needs to be active for longer time. Hence, a single switch performance is checked under a creep measurement. In this case, the same switch is actuated with 70 V and corresponding changes in V p are recorded after every 10 min where 1 cycle (pull-in and pull-out) takes ~15 s. The V p drifts ~6 V over the 8 h period of prolonged actuation. Primary reason of this voltage drift is due to initial height difference between anchor and cantilever tip, and it leads to the following formula (8.5); g0 + εtdr + z after V p×after = V p×before g0 + εtdr + z before

(8.5)

The calculation from (8.5) clearly justifies the variation of V p with ratio of 0.88 over the stress relaxation process. Almost ten identical switches are tested over the period and in few of the cases plastic and irreversible or permanent deformation is observed. Furthermore, this prolonged electrostatic actuation also changes the switch spring constant in terms of gold Young modulus [2]. In addition, shifting in voltage is also due to bulk and surface charges from the residual humidity when the switch was stressed in the air [3]. Now, to observe the 5-bit phase shifter performance under prolonged actuation condition, phase shifter is measured under ON-state condition at 25 and 50 °C temperatures with 0.1 W of RF power and with 70 V bias. The process is continued up to 6 h and corresponding changes in loss and phase error are recorded after every 10 min. During this stress relaxation process phase bits show ~1.36 dB (3.55–4.91 dB) of loss variation from the initial value and maximum ~1.24° (0.87°–2.11°) of phase error at 17 GHz and at 25 °C. This variation is more at higher temperature (50 °C) with extra 1.88 dB (3.57–5.44 dB) of loss and ~1.8° (0.87°–2.68°) of phase error [8]. These variations can be justified by (8.6)   Pin 1 − |S11 |2 − |S21 |2 × t = msT

(8.6)

where, s is the specific heat of the material (0.129 J/g °C at 25 °C for gold), m is the mass and T is the change in temperature (8.6) expresses that, the maximum power loss as heat in each time slot (t = 6 h is this case) is proportional to the heat dissipation from the DUT (m and s are constant here) over a prolonged ON-state condition. It leads to an increase in temperature by T and affect the sensitivity of the S-parameter. This measurement is entirely limited by the time where beam curvature decreases with time. Moreover, sensitivity of the S-parameter can change further with increase in power and with more time of operation (t). This effect can

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8 Reliability Analysis of RF MEMS Devices

00 = S2 + S6 + S9, 11.250 = S3 + S6 + S9, 22.50 = S1 + S6 + S9, 33.750 = S4 + S6 + S9, 450 = S2 + S7 + S9, 56.250 = S3 + S7 + S9, 67.50 = S1 + S7 + S9, 78.750 = S4 + S7 + S9, 900 = S2 + S5 + S9, 101.250 = S3 + S5 + S9, 112.50 = S1 + S5 + S9, 123.750 = S4 + S5 + S9, 1350 = S2 + S8 + S9, 146.250 = S3 + S8 + S9, 157.50 = S1 + S8 + S9, 168.750 = S4 + S8 + S9, 1800 = S2 + S6 + S10, 191.250 = S3 + S6 + S10, 202.50 = S1 + S6 + S10, 13.750 = S4 + S6 + S10, 2250 = S2 + S7 + S10, 236.250 = S3 + S7 + S10, 247.50 = S1 + S7 + S10, 258.750 = S4 + S7 + S10, 2700 = S2 + S5 + S10,281.250 = S3 + S5 + S10, 292.50 = S1 + S5 + S10, 303.750 = S4 + S5 + S10, 3150 = S2 + S8 + S10,326.250 = S3 + S8 + S10, 337.50 = S1 + S8 + S10, 337.50 = S1 + S8 + S10, 348.750 = S4 + S8 + S10

Fig. 8.8 Schematics of individual switch actuations from the 5-bit phase shifter over one complete cycle [3]. Reproduced with permission from IEEE

be improved further with appropriate choice of beam material like aluminium alloy and well-suited contact material like rhodium or gold–palladium alloys. The reliability operation of this phase shifter brings few interesting facts. Here, one switch cycle is defined by only one actuation state (ON and OFF) but in the case of phase shifter, one cycle counts 32 states of operation where fine and coarse bit switches are individually actuated 8 times whereas higher bit section actuated by 16 times. So, the probability of failure is always higher at higher bit section compared to other sections (fine and coarse bits) over the continuous reliability cycles. So, in this proposed 5-bit topology, a non-uniform switch actuation is found on the device throughout the reliability operation. Figure 8.8 clearly shows switches S9 and S10 (total four switches) are actuated 16 times compared to other switches on the phase shifter over one complete cycle. This non-uniform switch actuation is the primary reason for the device failure after tens of millions of cycles of operation and it will not be the common case for an even-bit phase shifter such as 4-bit (two SP4T) or 6-bit (two SP8T switches). The figure-of-merit for this kind of RF MEMS devices is defined by Mean Time to Failure (MTTF) or mean-time to the first failure. Here, in this 5-bit phase shifter lower limit of the reliability is defined by MTTF. The reason of MTTF of the proposed phase shifter is not the one, there are multiple reasons of failures encountered during the reliability test and primarily it is due to the effect from electro-migration for contact type switches and it is defined by (8.7), [2]; MTTF =

A − Ea e kT Jn

(8.7)

where, A is the cross-section area dependent constant, J is the conduction current density, k is the Bolzmann constant, E a is the effective activation energy and n is the

8.4 Reliability Analysis on MEMS Digital Phase Shifter

237

Fig. 8.9 Reliability results of 3-bit and 4-bit phase shifters with incident RF powers [10]. Reproduced with permission from IEEE

scaling factor (usually, n is set to 2). Primary reason of MTTR in the proposed 5-bit phase shifter is due to the effect of current crowding which gives rise to the contact heating with larger J at the operating frequency. Note that, mean-time to first failure of the device is limited by the factor of 1/J 2 over the operation. Reliability of this 5-bit phase shifter is primarily limited by the number of switch count per phase state. Moreover, non-uniform actuation of switch per cycle also leads to an early failure after few cycles. To improve the 5-bit phase shifter reliability one more topology shown in Fig. 8.9 can be tried. This topology contains two SP8T and two SP4T switches and connecting lines. This design requires only four switches to be actuated at a time to activate one phase state and it leads to a uniform actuation over the cycle. Few important points that need to be considered here. 1.

2.

3. 4.

5. 6.

The loss and matching of the phase shifter are entirely limited by the loss of the SP8T and SP4T switching network. Circular type configuration is very much useful for this kind with 40° and 72° angle between two in-line series switches for SP8T and SP4T switching network, respectively. This configuration also permits switches to be placed close together with more compactness without any fabrication difficulties. It leads to the reduction of overall area of the device up to few microns or millimeters square. Matching and loss of the overall phase shifter can be improved by reducing the parasitic inductive effect between the central junction and switches. Few more design parameters like junction capacitance, spoke length, and inductive bends are to be placed at each CPW discontinuity to eliminate the higher order modes. High resistive bias lines should be critically optimized and routed accordingly without effecting device performance with signal leakage and added parasitic. The connecting line length (lc ) between fine and coarse bit sections needs to be optimized using full wave simulation to nullify the effect of any off-path resonance over the band.

238

7.

8.

9.

8 Reliability Analysis of RF MEMS Devices

In-line MEMS switch is one of the most favorable options for better matching. In addition, thicker cantilever beam can significantly improve the reliability of the overall device. Power handling and temperature stability of the reported phase shifter can be drastically improved by proper selection of the contact material with higher softening temperature. Hermetic packaging of the device can significantly improve the reliability with lower contact contaminants.

Note that, this kind of topology is very much useful at lower microwave frequency (1 B cycles over 0.1–1 W of power at 25 °C. Maximum average loss and phase error variations are 5.28–9.12 dB and 1.67°–5.6°, respectively, at 35 GHz. Furthermore, reliability of the single MEMS bridges of the DMTL is checked under same power. Results show maximum C up variations of 62.1–64.88 fF up to 1 B cycle with 0.1–1 W power at 25 °C. Note that, the proposed device demonstrates maximum phase shift/length, phase shift/loss and loss/bit of 127°/mm, ~50°/dB, and 1.35 dB/bit, respectively. Primary design goal of this device is high reliability with long life cycle and compactness without compromising the RF performances. Readers should adopt following key points from this phase shifter (check microscopic images of phase shifters in Fig. 6.22); (a)

(b)

(c)

Switching network: Proposed phase shifters are designed combining DMTL with switched line techniques. DMTL is normally suitable for high frequency (>K-band) due to its distributed capacitive manner, while switched lines work much better at lower frequencies. Hence, designing of switching network (SP4T and SP8T) in terms of loss and matching at high frequency plays a very important role. Robust switch: To perform two steps systematically, two back-to-back switches are biased at ON-state for a longer time here in contrast to any other switchedline based topology. For this, switch must be robust and 3.5–4 μm thicker beam is used and two additional arms provide extra robustness to the structure (see Fig. 3.1b). Switch actuation voltage change over time shows ~9 V variations over 10 h and it is mostly due to stiction and mechanical contact deformation. Finally, phase shifters performance is tested under prolonged ON-state condition and loss and phase error variations are recorded up to 6 h. Loss variation of ~1.37 dB (4.23–5.6 dB) and phase error variations of ~1.26° (3.77°–5.03°) are observed at 35 GHz during the process. Varactor design: One of the design aims is to achieve same actuation voltage between switch and varactor. It means varactors will produce distributed capacitance per phase state with the same bias voltage as in the switch. It also improves the bias network simplicity. This process needs multiple iterations in terms of design and process yield.

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8 Reliability Analysis of RF MEMS Devices

(d)

DMTL and delay line design: In this technique, one line is used for two different phase states. Few important parameters here are spacing between two bridges (s), C up and inductive bends at each CPW discontinuity. Bias line: High resistive bias lines should be critically optimized and routed accordingly without affecting device performances with signal leakage and added parasitic. Fabrication process yield: It is one of the primary issues for any device to work with higher life cycle. In this work, yield is limited by the Critical Point Drying (CPD) process and optimized with multiple process steps. For this circuit, PI is cured at ~350 °C in the oven, and it was etched using EKC 265. Fabrication process is described in detail in Appendix B. Measurement setup: Reliability measurement setup is very crucial part here to improve the life cycle after successful fabrication (Fig. 8.1). A pulse wave and its duty cycle need to be carefully optimized and applied to the switch and varactor. More details on this phase shifter are available in [10].

(e)

(f)

(g)

8.5 Reliability Analysis on Tunable MEMS Filter In this Section, reliability performances on a tunable MEMS filter are discussed. The RF performances of this filter is discussed in detail in Chap. 7. The reliability of this filter is also checked using the same set up shown in Fig. 8.1. Note that, this filter is being made with switch and bridge array. Hence, flow will remain the same, that is, first check the switch reliability, then switch and bridge arrays will be checked. Finally, complete filter performance will be evaluated up to 1B cycle of operation. Please note, Fig. 3.1b switch is used in this filter. Readers are requested to refer to Chap. 7 before reading the reliability analysis. Single switch power handling capability is measured periodically at 20 kHz switching rate with 0.1–1 W of power using a bias waveform, as shown in Fig. 8.11a. The change in Rc is mostly due to contact contaminants with excessive temperature rise on contact at higher power in the non-hermetic conditions and due to dielectric

Fig. 8.11 Measured reliability performances of a single MEMS switch with 0.1–1 W of RF power, b MEMS switch-array with 0.1–1 W of RF power, c variation of C s as a function of cycle count at three different bias voltages with 0.1 W of RF power [11]. Reprinted with permission from IEEE

8.5 Reliability Analysis on Tunable MEMS Filter

241

charging. Next, reliability of the 4-element switch array is tested with four different power levels. The array demonstrates worst case average Rc variation from 0.4 to 2.23  with 1 W of RF power up to 1B cycles at 25 °C and with 112 V, as depicted in Fig. 8.11b. Note that, switch is operational even up to 10 B cycles at 1 W of power and large ohmic heat dissipation takes place during the contacting period in all the four switches and it controls the performance. Finally, the C s variations are measured with 0.1–1 W of RF powers at three V s values. Figure 8.11c shows measured C s variations of 350–357.3 fF, 410–423.6 fF and 450–463.3 fF with 91 V, 96 V and 100 V of V s , respectively, from 0.5 to 1 W change in RF power up to 1 billion cycles. These changes in C s are due to the spring softening over continuous actuation with RF powers. Switch and switch-array performance are measured here from 30 to 85 °C with 0.1 W of power and performances at three temperatures are shown in Fig. 8.12a up to 1B cycles. Initially, single switch is tested and maximum Rc variation of 1.8–5.19  is captured at 85 °C. Switch-array demonstrates maximum average Rc variation of 0.77–3.7  at 85 °C with 0.1 W power at 112 V. Results show an abrupt change in Rc from 5.8 to 6.3  after ~600 million cycles. It is mostly due to (a) contact point degradations due to additional attractive force from RF power at high temperature, (b) different thermal coefficients of expansion between substrate and gold beam [14], and (c) spring softening at higher temperature. All these issues could be improved with (a) doping the dielectric materials or having no dielectric layer structures, and (b) phase change material. Figure 8.12b shows negligible change in C s up to 1B cycles with 50 and 85 °C. Measured maximum variation is 7.7 fF at 85 °C with 100 V bias. It ensures good thermo-mechanical behaviour from 3.5 μm thicker gold cantilever beam. Note that, in this case switches will never come in contact with the transmission line, but its reliability operation was done with proper contacting criteria as a function of Rc . A good switch can only be judged with its proper contacting ability over many switching cycles.

Fig. 8.12 The change in switch Rc and C b up to 1 billion cycles at a 50–85 °C with 0.1 W of RF powers, b 50 and 85 °C with three different V s voltages [11]. Reproduced with permission from IEEE

242

8 Reliability Analysis of RF MEMS Devices

Bridge array reliability is tested with 0.1–1 W of RF power level at 27, 28 and 29 GHz, as shown in Fig. 8.13a–c, respectively. Results show maximum C b variations of 176.67–173.9 fF (2.77 fF) at 27 GHz up to 1 B cycle from 0.1 to 1 W RF power with 59 V at 25 °C. Figure 8.13d shows C b variation with 85 °C at 27, 28 and 29 GHz. Result shows maximum C d of ~2 fF with 0.1 W at 85 °C up to 1B cycles. The change in capacitance is mostly due to effect of spring softening at higher RF power and with elevated temperature. In this work, bridge is not coming in direct contact with bottom dielectric, hence the dielectric charging effect is minimum. Now, the time has come to check the reliability of the filter. The change or shift in the centre frequencies (27, 28, and 29 GHz) and BW of the fabricated filter are

Fig. 8.13 The change in bridge array capacitance C b up to 1 billion cycles at a 27 GHz center frequency with 0.1 and 1 W of RF powers and with V b = 59 V at 25 °C, b 28 GHz center frequency with 0.1 and 1 W of RF powers and with V b = 46.5 V at 25 °C, c 29 GHz center frequency with 0.1 and 1 W of RF powers and with V b = 39 V at 25 °C, d 27, 28 and 29 GHz at 85 °C with 0.1 W of RF power [11]. Reproduced with permission from IEEE

8.5 Reliability Analysis on Tunable MEMS Filter

243

measured with 0.5 and 1 W of RF powers up to 1B cycles and will be discussed now. The same test set up (Fig. 8.1) is used during this measurement. Reliability measurement is carried out at three centre frequencies with 0.5 W and 1 W of RF power levels. Reliability experiments on the tunable filter were done in two parts at four f c values (27.4 GHz, 27.98 GHz, 28.3 GHz, and 29 GHz). In the first part, insertion losses at f c were measured from 0.1–1 W of incident RF powers and corresponding changes were recorded at room temperature up to 1B cycles, as depicted in Fig. 8.14. Results show minimum deviation in loss at f c = 27.4 GHz and maximum deviation at f c = 29 GHz over 0.1–1 W of RF power variations at 1B cycle. In the second part, the shift in four f c values and average loss variations over the bandwidth (both, over 850 MHz and BW3dB ) were measured with 0.5 and 1 W of RF powers up to 1B cycles, as shown in Fig. 8.15. Maximum and minimum measured shift in f c were 1.2 GHz and 0.86 GHz at 27.4 GHz and 27.98 GHz, respectively, between 0.5 to 1 W powers at 1B cycle with V b voltages. All these changes in f c were mostly attributed to the change in C b with elevated power level. Measured maximum and minimum increase in average loss were 0.94 dB and 0.7 dB at f c = 27.4 GHz and f c = 29 GHz, respectively, over the 850 MHz BW between 0.5 and 1 W powers at 1B cycle. Furthermore, the average passband loss was maximum (0.83 dB) at

Fig. 8.14 Reliability measurements of the filter insertion loss at four f c with 0.1–1 W of RF powers up to 1B cycles [11]. Reproduced with permission from IEEE

244

8 Reliability Analysis of RF MEMS Devices

Fig. 8.15 Reliability responses of the filter show change in filter f c , insertion loss variations over BW850MHz and BW3dB with 0.5 W and 1 W of RF powers up to 1B cycles at four different f c values [11]. Reproduced with permission from IEEE

27.4 GHz and minimum at 28.3 GHz (0.7 dB) over BW3dB between 0.5 and 1 W of power at 1B cycle. In this experiment, special attention was given at 27.98 GHz for 5G applications. All results are within the acceptable limit and values are shown in Fig. 8.15 for better clarity. The loss reliability over the BW was checked with the same V s and V b voltages used in stage-1 to stage-4. Again, these changes were mostly due to the reduction of bridge restoring forces over the cycles with higher RF powers. BW changes were not affected much but their changes were abrupt over the cycle. Filter performances did not deviate much (~16 dB up to 65 GHz, as depicted in Fig. 9.25b. A schematic view of patch antenna is shown in Fig. 9.26. It is composed of CPW to microstrip transition feed line, a radiating element, and a ground plane. Air bridges with spacing of 45 μm between them, are also employed between the coplanar grounds to control the potential difference and avoid the existence of higher order modes such as slotline modes in the structure. Since, the antenna size at 60 GHz Fig. 9.24 Block diagram of sectored antenna configuration using MEMS SP9T switch [18]. Reproduced with permission from the IEEE

9.3 Micromachined Antennas for 60 GHz ISM Band

265

Fig. 9.25 a Fabricated microscopic image and b S-parameter responses of the MEMS SP9T switch [18]. Reproduced with permission from the IEEE

Fig. 9.26 Geometry of CBCPW to microstrip transition fed patch antenna. Dimensions are: L = 3, W = 1.4, pl = 0.503, pw = 0.8, mw = 0.61, ml = 0.81, t l = 0.75, α = 14.16°, g1 = 0.23, gl = 0.16, gw = 0.667, g = 0.016, s = 0.034, and h = 0.635. All the dimensions are in mm [18]. Reproduced with permission from the IEEE

is much smaller than commercially available V-connector, which causes ripples in radiation pattern and inaccurate results [14], probe-based designs (CPW feed line) are encouraged at higher frequencies and is employed in the present layout. The antenna is designed in exactly similar way as discussed in the last Section. The design is optimized using full wave simulator and all parameters are mentioned in Fig. 9.26. The microscopic image of SP9T switch integrated with antenna is illustrated in Fig. 9.27. It comprises of a CPW-to-CPW transition and a SP9T switch followed by an antenna. The transition is designed based on the probe pitch size available for the measurement. RF input signal is given from CPW transition trace. The CPW input

266

9 Micromachined Antennas

Fig. 9.27 Fabricated microscopic image of MEMS SP9T switch integrated with antenna on alumina substrate [18]. Reproduced with permission from the IEEE

feed trace of the antenna is connected with CPW output port of switch ‘s1 ’. The bottom electrode of switch ‘s1 ’ is connected with a bias pad and a line for biasing purpose. The antenna is excited and resonates at 60 GHz when the switch ‘s1 ’ is actuated in down state and turned ‘ON’ by DC bias voltage. Practical application of beam switching by utilizing sectored antenna configuration can be made possible by integrating output port of each switch to an antenna element. RF input signal can be provided from the CPW input feed trace and the same will be routed to the sectored path created by the actuated switch and antenna further. Only one switch can be turned ‘ON’ at a time and rest all will be in ‘OFF’ state. In this way, antenna beam can be switched from one angle to another according to desired direction and application. Figure 9.28a exhibits simulated return loss of

Fig. 9.28 Simulated, a return loss and b E and H plane radiation patterns at 60 GHz [18]. Reproduced with permission from the IEEE

9.3 Micromachined Antennas for 60 GHz ISM Band

267

antenna when switch ‘s1 ’ is in ‘ON’ state. It shows a return loss of −30 dB with a fractional bandwidth of 4.17% at 60 GHz. Simulated 2D E- and H -plane radiation patterns of antenna are displayed in Fig. 9.28b. A gain of 6.75 dB is realized at θ = 0° when the switch ‘s1 ’ is in the ‘ON’ state.

9.4 Polarization Agile MEMS Antenna at 77 GHz Significant attention has been paid to unlicensed band of 77 GHz ranging from 76 to 81 GHz for automotive radar applications such as adaptive cruise control, blind spot detection, and collision warning etc. [19]. A probe-based slot antenna [20] and a dipole antenna in package [21] is reported in the literature at 77 GHz. N. Shino reported a linearly polarized microstrip antenna array of 2 × 12 and 4 × 12 at 77 GHz for short range radar applications [22]. Cavity [23] and patch antenna array are reported in [24, 25] for medium and long-range radar applications at 77 GHz. In the following Section, 77 GHz MEMS SPST switch-based polarization reconfigurable antenna with capability of all the polarization states including LP, RHCP and LHCP is discussed. The antenna design consists of a compact tilted rectangle patch, perturbed parallelly along two opposite edges with triangular shaped conductors as parasitics. To switch the polarization state, the gap between each edge and parasitic is introduced with SPST switch. This work has potential for SRR (short range radar) and LRR (long range radar) automotive applications. Figure 9.29 shows the geometry of the proposed antenna where a rectangle patch of length ‘r l ’ and width ‘r w ’ is tilted from its corner and is connected to the feed line. The electric fields along the opposite pair of patch edges are perturbed by using a triangle shaped parasitic element kept in parallel to the patch edges with distance ‘d’ between them. The lengths of isometric triangle edges are ‘t l ’ and ‘t l1 ’. The gap between triangle and patch edge is incorporated with SPST switches named as s1 , s2 , s3 and s4 . The design details and extensive performances of SPST switch are illustrated in [26]. The polarization state of the antenna is regulated by providing bias voltage to individual SPST switches. The dimensions of triangle and distance ‘d’ are optimized to achieve best least value of axial ratio in circular polarization (CP) states with an acceptable return loss in all the states. The complete size of radiating element ‘radl × radw ’ is restraint to operate at 77 GHz whereas the size of ground plane is ‘W × L’. The dimensions of the proposed antenna are tabulated in Table 9.3. The antenna radiates linearly polarized waves, when all the SPST switches are biased either in ON (electrically short-case 1), or OFF (electrically open-case 2) states simultaneously, at a time. The radiating element must necessarily be physically and electrically symmetric in shape to excite the fundamental TM01 mode and achieve linear polarization state. In case-1, the shape of conventional rectangular patch is modified that leads to slight shift in resonance frequency, whereas in case 2, a compact rectangular shaped patch is formed and resonates at the desired frequency. Because

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9 Micromachined Antennas

Fig. 9.29 Geometry of CBCPW to microstrip transition fed patch antenna [27]. Reproduced with permission from the Wiley

Table 9.3 Geometric parameters of the proposed antenna

Parameters

Unit (mm)

Parameters

Unit (mm)

L

1.15

rw

0.155

W

0.69

tl

0.18

radl

0.5

R1

6.00

radw

0.54

t l1

0.255

rl

0.212

d

0.135

of larger physical size in case 1 than case-2, the operating frequency will be lower than that of case 2. To radiate circularly polarized waves, both pair of two opposite SPST switches must be in the ON state. Circular polarization is achieved by exciting two orthogonal near-degenerate resonance modes of same amplitude with 90◦ phase shift. When s2 and s4 switches, embedded in opposite edges at ϕ = 45° and 225° anticlockwise from feed point, are in the ON state (i.e., case 3), the current is disturbed along that direction. This tends to excite a near-degenerate resonance mode that is orthogonal to the dominant mode and hence CP is accomplished. The direction of circular polarization, right-handed or left-handed, can be determined from the direction of surface electric current distribution at operating frequency. From observing Fig. 9.30a, this case can be concluded as LHCP mode. Similarly, when s1 and s3 , located 90◦ opposite to case 3, are in the ON state (i.e., case 4),

9.4 Polarization Agile MEMS Antenna at 77 GHz

269

Fig. 9.30 Electric current distribution for a LHCP and b RHCP mode [27]. Reproduced with permission from the Wiley

RHCP is excited, as shown in Fig. 9.30b. The operating frequency in both the cases is not different as the symmetry in shape is maintained. Microscopic image of fabricated device is shown in Fig. 9.31 and the fabrication details are described in [26]. The S-parameters and radiation patterns are measured by properly actuating the switches according to the different polarization states of antenna. S-parameters are measured using on-wafer measurement system shown in Fig. 9.32a and closer views of probing the antenna can be seen in Fig. 9.32b. Figure 9.33a, b shows the simulated and measured return loss of the proposed antenna in all the polarization states, respectively. The measured reflection characteristics of the antenna in each polarization state are summarized in Table 9.4. As seen, good agreement is achieved between simulated and measured results. An acceptable return loss of >20 dB is achieved in all the configurations. Unlike case 2, the resonance frequency in case 1 falls out of the desired band and hence can be neglected. Both the cases of circular polarization (CP) and case 2 of linear polarization (LP) states resonate in the band of interest, i.e., 76–81 GHz. Since two orthogonal resonant modes radiate simultaneously in case of CP, the bandwidth obtained is much larger than that of LP. A band of 10% and 14.3% is achieved in case 2 and cases 3–4 at 77 GHz. The radiation patterns of antenna were measured in compact antenna test range (CATR) anechoic chamber (by MI technology) using the measurement set up shown in Fig. 9.34a. Here the horn antenna is used as reference transmitting antenna, located at the focal point of the reflector to generate a plane wave toward the antenna under test

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9 Micromachined Antennas

Fig. 9.31 Fabricated microscopic image of proposed polarization reconfigurable antenna [27]. Reproduced with permission from the Wiley

Fig. 9.32 a Return loss measurement set-up. b Closer view of measurement of the proposed device [27]. Reproduced with permission from the Wiley

(AUT) [28]. The radiation patterns of antennas are measured in the E- and H- Planes. A different set-up is designed to measure the pattern of probe-based feed antenna in chamber as shown in Fig. 9.34b. The complete tile is placed on thick aluminium sheet with probe and probe positioner. There are other designs also present on the tile apart from the proposed device. The probe is properly aligned on the feed line of the antenna and is verified under the microscope. The set-up is rotated by 90° for E- plane radiation pattern measurement, as in Fig. 9.34c and while doing the measurements, the set up interferes with the line of sight and however, degrades the pattern in range of theta from 30° to 90°. This phenomenon can be observed in

9.4 Polarization Agile MEMS Antenna at 77 GHz

271 0

0

Return loss (dB)

Return loss (dB)

-5 -10 -15 -20 -25 LP (ON) LP (OFF)

-30

LHCP RHCP

70

75

-10 -15 -20 LHCP RHCP

-25

-35 65

LP (ON) LP (OFF)

-5

80

65

85

Frequency (GHz)

70

75 80 Frequency (GHz)

(a)

85

(b)

Fig. 9.33 a Simulated and b measured return loss of the antenna in all the polarization states [27]. Reproduced with permission from the Wiley

Table 9.4 Antenna performance details for all polarization state Case

s1

s2

s3

s4

Polarization

Frequency (GHz)

Return loss (dB)

Bandwidth (%)

Case 1

ON

ON

ON

ON

LP

70.5

22

9.078

Case 2

OFF

OFF

OFF

OFF

LP

80

25

10

Case 3

OFF

ON

OFF

ON

LHCP

77

20

14.286

Case 4

ON

OFF

ON

OFF

RHCP

77

20

14.286

E-plane plots of the proposed antenna in all polarization states. Normalized E- and H-plane radiation pattern in LP state of antenna for case 1 and case 2 at 70 GHz and 80 GHz are shown in Figs. 9.35 and 9.36 respectively. As observed, 3 dB beam width of 90° and 59° are obtained in the E- and H-planes in case 1 at 70 GHz whereas 92° and 56° are obtained in case 2 at 80 GHz respectively. Normalized E- and H-plane radiation patterns in CP state of antenna for case 3 at 76 GHz and 77 GHz are shown in Figs. 9.37 and 9.38 respectively. Measured 3 dB beam width of 73° and 61° are obtained in the E- and H-planes in case 3 at 76 GHz whereas 94° and 64° are obtained at 77 GHz, respectively. Similar radiation patterns are obtained in case 4 also. Figure 9.39 depicts the simulated and measured axial ratio for CP state of the proposed antenna. A 3-dB axial ratio bandwidth of 7.14% is achieved cantered at 77 GHz. Least simulated and measured axial ratio of 0.61 and 1.10 dB are obtained at 77 GHz. The antenna gain is measured using the comparative method that involves measuring the signals received by the reference horn antenna and by AUT. The relative difference in the gain of both antennas is determined. The measured loss due to waveguide to coaxial adaptor is 1.3–1.6 dB over the frequency range of 70– 81 GHz. This loss was considered in the gain measurement. Simulated and measured gain of proposed antenna in cases 2–4 states are shown in Fig. 9.40. Gain of 1.9 dB and 2 dB is achieved at 76 GHz whereas 2.1 dB and 2.3 dB at 77 GHz is achieved, respectively in case 3 and case 4. 3.35 dB of gain is achieved in

272

9 Micromachined Antennas

Fig. 9.34 a Radiation pattern measurement set up where the AUT is in receiving mode, b set-up used for probe-based feed antenna measurement in the chamber and c its interfering region in E-Plane measurement [27]. Reproduced with permission from the Wiley

9.4 Polarization Agile MEMS Antenna at 77 GHz

273 0

0

-2 -2

-4 dB

dB

-4 -6 -8

-6 -8 -10

Simulated Measured

Simulated Measured

-12

-10

-14 -100-80 -60 -40 -20 0 20 40 60 80 100

-100-80 -60 -40 -20 0 20 40 60 80 100

Theta (deg)

Theta (deg)

(a)

(b)

Fig. 9.35 Normalized. a E-plane and b H-plane radiation pattern for case 1 [27]. Reproduced with permission from the Wiley 0

0

dB

dB

-5 -5

-10 -15

Simulated Measured

-10

Simulated Measured

-20 -25

-100-80 -60 -40 -20 0 20 40 60 80 100

-100-80 -60 -40 -20 0 20 40 60 80 100

Theta (deg)

Theta (deg)

(a)

(b)

Fig. 9.36 Normalized. a E-plane and b H-plane radiation pattern for case 2 [27]. Reproduced with permission from the Wiley 2

0

Simulated Measured

0

-5

-2 dB

dB

-10

-4

-15

-6

-20 -100 -80 -60 -40 -20 0 20 40 60 80 100 Theta (deg)

(a)

-25

Simulated Measured -100 -80 -60 -40 -20 0 20 40 60 80 100 Theta (deg)

(b)

Fig. 9.37 Normalized. a E-plane and b H-plane radiation pattern for case 3 at 76 GHz [27]. Reproduced with permission from the Wiley

274

9 Micromachined Antennas 0

0

-5

dB

dB

-2

-10

-4 -15

-6

Simulated Measured

Simulated Measured

-20

-100 -80 -60 -40 -20 0 20 40 60 80 100 Theta (deg)

-100 -80 -60 -40 -20 0 20 40 60 80 100 Theta (deg)

(a)

(b)

Fig. 9.38 Normalized. a E-plane and b H-plane radiation pattern for case 3 at 77 GHz [27]. Reproduced with permission from the Wiley

12

Simulated Measured

10

Axial ratio (dB)

Fig. 9.39 Simulated and measured axial ratio as a function of frequency [27]. Reproduced with permission from the Wiley

8 6 4 2 0

70

72

74

76

78

80

82

Frequency (GHz)

Fig. 9.40 Simulated and measured gain as a function of frequency [27]. Reproduced with permission from the Wiley

4.0

Gain (dBi)

3.5 3.0 2.5 Simulated all close LHCP RHCP

2.0 1.5 75

76

77

78

Frequency (GHz)

Measured all close LHCP RHCP

79

80

9.4 Polarization Agile MEMS Antenna at 77 GHz

275

case 2 at 80 GHz. A minimum of 2 dB of gain is achieved in all the states of proposed antenna across the band. Note that, array of similar structure can be used for short and long ranges radar applications at 77 GHz.

9.5 Millimeter Wave Micromachined Active Antenna Integrating active microwave devices with a passive antenna element in such a way that the antenna plays an important role of oscillator-cum radiating element yields an active antenna. The active antennas are valuable because of their lightweight, small size, low cost, lower loss, and multiple-functionality [29–33]. They may be oscillator type, amplifier type or frequency converter type depending on their functionality. Considerable interest has been developed in oscillator type active antennas in the last decade for localized power generation and reduced transition and transmission losses. Looking at advantages of silicon micromachined microwave and millimeter-wave systems, it is desirable to develop an active antenna element on silicon micromachined substrate for miniaturized integrated system. A reliable printed antenna on silicon is the rectangular patch on a micromachined membrane, in which silicon is removed underneath the patch area thereby reducing the effective dielectric constant. This results in improved antenna performance, suppression of surface waves and increased radiation efficiency of the antenna as compared to that on bulk silicon substrate. Micromachined active antenna employs one such micromachined patch antenna. A lot of design configurations for active antenna, employing active devices such as Gunn diode, FET etc. mounted on the patch itself, have been reported in the literature. When a micromachined patch antenna is to be employed, placing active device on thin membrane supported patch is not practical. Therefore, designs where the active device can be placed out of patch area, i.e., on bulk substrate instead of thin membrane need to be thought of. Some such designs have also been reported in the literature. One solution is to place the patch antenna working as both radiator and resonator in the positive feedback path of an amplifier. Two configurations employing this scheme are shown in Fig. 9.41. Result shows the patch antenna in the feedback path using quarter wave impedance transformer performs well. This is one of the simplest and robust design approaches. In other case, the patch resonator is electromagnetically coupled using microstrip T-junction feed (Fig. 9.41b). The principal advantage of this design is that it is compact, and its inherent dc isolation helps in eliminating dc blocking capacitors in the RF path. However, this is usually not the preferred option because of undesirable radiations from gap discontinuity nearby the patch antenna element. Therefore, the first approach (Fig. 9.41a) has been selected for further design and development. Designing of the active antenna, using the schematic shown in Fig. 9.14(a), needs the following design issues to be taken care of:

276

9 Micromachined Antennas

Fig. 9.41 Design layout of active antenna with active device outside patch area where, a with patch only and b with patch and T-junction coupled feed [27]. Reproduced with permission from the Wiley

• When the patch antenna is to be placed in the feedback loop as a resonator, it would be a two- port component instead of a usual single port antenna. Sufficient balance between radiated power and transmitted power must be maintained while designing the two-port patch. • An amplifier with sufficient gain to offset the loss due to antenna radiation needs to be designed. MMIC chip amplifier can also be employed. • Feedback loop length must be an integer multiple of effective wavelength. Prototyping a micromachined active antenna, using this approach as shown in Fig. 9.41a, involves several milestones. First, a scaled model at 18.5 GHz on 10 million RT-Duroid substrate, using HEMT as an active device, has been fabricated and tested. As a next step, another scaled model at Ka-band has been fabricated and tested. In this step a MMIC amplifier chip is used instead of assembled amplifier using discrete HEMT device. Before moving to the next step, repeatability of the design has been checked by fabricating 2 pieces of both the scaled models. Finally, a complete micromachined active antenna on silicon at Ka-band, using MMIC amplifier chip and micromachined two-port patch, has been fabricated and tested. All the active antenna designs require design, fabrication and testing of a two-port patch element as a separate component.

9.5 Millimeter Wave Micromachined Active Antenna

277

9.5.1 Scaled Model (At K-band and on RT-duroid 10 Million Substrate) Design layout of scaled model at K band (18.5 GHz) on 10 million RT-Duroid is shown in Fig. 9.42. The layout consists of a two-port patch, an amplifier, and a low pass filter as biasing network. For dc blocking, an Interdigital capacitor is printed to minimize the insertion loss instead of using a lumped capacitor. First, a two-port patch antenna has been designed using conventional textbook formulae. Physical parameters of the patch have been optimized using full wave FEM analysis; to bring the center frequency to 18.5 GHz. Measured result of the two-port patch (physical dimensions = 5.3 mm × 6.5 mm) is plotted in Fig. 9.43. Next, a broadband high gain amplifier has been designed using measured Sparameters of a discrete HEMT with Interdigital capacitor at both ends. Stub lengths and their positions have been optimized using circuit simulator to obtain maximum gain over maximum possible bandwidth. With V g = −0.3 V and V d = 3 V biasing,

Fig. 9.42 Design layout of scaled model at 18.5 GHz

278

9 Micromachined Antennas

Fig. 9.43 Measured response of two-port patch on 10 million RT-Duroid

measured result (Fig. 9.44) shows around 13 dB gain at the center frequency with gain more than 0-dB over 4 GHz bandwidth. When the two-port patch is placed in positive feedback path of the amplifier, with proper feed line lengths (ensuring 0° or 360° phase of the complete loop), an active antenna element is formed. Photograph and measured spectrum of the active antenna are shown in Fig. 9.45. All the four radiation patterns of the active antenna have been measured. Copolarization E- and Co-polarization H-patterns match well with standard microstrip patch antenna results. The 3-dB beam width of E-plane pattern is approximately 80° and that of H-plane pattern is approximately 70°. The cross-polarization power is almost 15 dB down from that of co-polarization fields (Fig. 9.46).

9.5.2 Scaled Model at Ka-band and on RT-duroid 5 Million Substrate Now moving a step ahead, active antenna element using MMIC amplifier chip from Alpha industries instead of discrete HEMT device-based amplifier, has been fabricated on 5 million RT-Duroid substrate, [34]. First, a two-port patch (physical dimension = 2.272 mm × 3.36 mm) at 35 GHz on the same substrate is designed and fabricated separately. Measured results of the same are as shown in Fig. 9.47. Then MMIC amplifier is placed in the circuit and wire bonded for RF input–output and bias network. The photograph of the complete Ka-band model is as shown in

9.5 Millimeter Wave Micromachined Active Antenna

279

Fig. 9.44 Measured response of amplifier on 10 million RT-Duroid

Fig. 9.45 Circuit photograph and measured spectrum of active antenna element at 18.5 GHz on 10 million RT-Duroid substrate

Fig. 9.48a. The oscillating frequency/spectrum obtained is very stable and radiated power measured from Ka-band horn shows −25 dBm on spectrum analyzer, as shown in Fig. 9.48b. The cross-polarization power is almost 15–20 dB down from that of co-polarization fields.

280

9 Micromachined Antennas

(a) 0

Relative Amplitude (dB)

-5 H plane (Co ó polarization)

-10

-15

-20 H plane (Cross ó polarization)

-25

-30

-35

-80

-60

-40

-20

0

20

40

60

80

Angle (degree)

(b) Fig. 9.46 Measured radiation pattern of active antenna using HEMT at 18.5 GHz, a E–plane pattern, b H–plane pattern

9.6 Micromachined Two-Port Patch Antenna

281

Fig. 9.47 Measured results of two-port patch at 35 GHz on 5 million RT-Duroid substrate

9.6 Micromachined Two-Port Patch Antenna As explained earlier, a two-port patch will be used in active antenna design, instead of a conventional single port patch. Designing by simple textbook formulae and then optimizing the dimensions for center frequency of 35 GHz, results in 3.625 mm × 3.625 mm patch size on 4 mm x 4 mm air cavity. 3D view of such a two-port patch is shown in Fig. 9.49a and its simulated S-parameters are shown in Fig. 9.49b. Scattering parameters from full wave FEM analysis of the two-port patch shows almost 50% of the input power is radiated out and transmission gain (S 21 ) of the antenna is 0.67. Figure 9.50 shows the photograph of the fabricated micromachined two-port patch antenna on silicon along with its measured response. The measured response, though shifted on frequency scale, illustrates expected power division between radiated and transmitted power.

282

9 Micromachined Antennas

Fig. 9.48 a Photograph and b measured spectrum of active antenna element at 35 GHz on 5 million RT-Duroid substrate

9.7 Micromachined Active Antenna Element at Ka-band …

283

Fig. 9.49 a 3D view of the micromachined two-port patch, and b Simulated results of micromachined two-port patch

Fig. 9.50 Measured response of the micromachined two-port patch

9.7 Micromachined Active Antenna Element at Ka-band and on Silicon Substrate In the earlier Sections, fabricating and testing scaled models of the active antenna at K-band and Ka-band on RT-Duroid substrate with repeatability have proved the design concept. However, fabricating a micromachined active antenna involves lot of fabrication issues. Stepwise development of the prototype of micromachined active antenna is explained as follows, along with addressing the key issues of probable fault.

284

9 Micromachined Antennas

(a)

Thickness of Silicon wafer is 270 μm, while that of MMIC amplifier chip (Alpha make) is around 130 μm. For proper wire bonding, top surface of the silicon wafer and the MMIC chip must be on same level. Therefore, the chip is first placed on a metallic bump of approximately 130 μm height. The metallic bump should have high accuracy in terms of flatness, size, and side edges. Then MMIC chip is stuck on the bump using silver epoxy for grounding and with proper alignment. Misalignment of chip with respect to metallic bump or improper flatness of metallic bump surface causes damaging of the chip by the head of wire-bonder during bonding. The mounting arrangement is as shown in Fig. 9.51. Gold plating of design layout on silicon wafer with properly aligned backside cavity is shown in Fig. 9.52. Thin membrane above cavity must be properly removed (see Fig. 9.53) for placing MMIC chip there. As a next step, the silicon wafer is glued to the housing with proper alignment with already glued MMIC chip. Care should be taken while aligning silicon wafer with the MMIC chip, so that epoxy at the back of silicon wafer does not spoil the MMIC chip. Making both biasing circuits common, proper external bias is applied. The photograph of the assembled micromachined active antenna on silicon substrate with MMIC chip and external biasing is shown in Fig. 9.54.

(b) (c) (d)

The oscillation from the fabricated micromachined active antenna shown in Fig. 9.55 is observed at 35.64 GHz with −47.17 dBm power output on spectrum analyzer. Measured spectrum is clean and stable. The cross-polarization power is almost 20 dB down from that of co-polarization fields as desired. Fig. 9.51 Micromachined active antenna Development: MMIC chip on metallic bump

9.8 Design Guidelines for Micromachined Patch Antenna …

285

Fig. 9.52 Micromachined active antenna development: a gold plating of design layout on silicon. b Backside aligned cavity

Fig. 9.53 Micromachined active antenna development: broken membrane for MMIC chip placement

9.8 Design Guidelines for Micromachined Patch Antenna with Air Cavity at 35 GHz Design guidelines for the development of micromachined patch antenna with air cavity at 35 GHz are stated below: (1) (2) (3) (4)

Select frequency = 35 GHz. Select height of the radiating patch from ground = 270 μm. Calculate the effective dielectric constant of multi-layer patch = 1.41 Calculate patch dimensions (assume square patch)

286

9 Micromachined Antennas

Fig. 9.54 Micromachined active antenna on silicon at Ka band

√ L p = w p = 0.98 × λ0 /2 εe f f = 3.5 mm (5)

Calculate input conductance at the antenna edge using (9.1)   1 wP 2 1 − (k0 h) G= 120λ0 24

(6)

Calculate input impedance at feed point using (9.2) Rin (y = y0 ) =

(7)

(9.1)

  π 1 cos2 y0 2G 1 LP

(9.2)

Calculate Quarter-wave Tx. impedance (= 84.73  in this case)

Note that, all parameters in (9.1) and (9.2) are shown in Fig. 9.56 for better clarity. The effect of placement and size of the cavity with respect to patch plays a crucial role in matching and it needs to be optimized using full wave simulations. As lateral dimensions of cavity are increased, the return loss gets reduced and operational frequency shifts to lower values, as depicted in Fig. 9.57. The reason for this is attributed to the impedance mismatch and change in electrical lengths due to change in effective dielectric constant. A 2 × 2 and 8 × 8 micromachined patch antenna arrays were also developed and tested on the same design platform, as depicted

9.8 Design Guidelines for Micromachined Patch Antenna …

287

Fig. 9.55 Measured spectrum of micromachined active antenna on silicon with oscillation frequency at 35.64 GHz

in Figs. 9.58 and 9.59, respectively. Measured matching performances ensure the optimum performances from the 2 × 2 and 8 × 8 micromachined patch antenna arrays, as shown in Figs. 9.58d and 9.59b, respectively.

9.9 Conclusions This Chapter presents different types of micromachined antennas mostly at millimeter-wave bands. The design and fabrication of a Ka-band microstrip centrally edge-fed equilateral triangular and rectangular patch antenna on a suspended 3 μm thick silicon–nitride membrane using silicon bulk-micromachining technique have been presented. Next, three different patch antennas integrated with MEMS SPDT and SP9T switches are presented at 60 GHz for different wireless applications at ISM band of 60 GHz. Finally, a 77 GHz linear/circular polarization reconfigurable antenna embedded with MEMS SPST switches is presented in this Chapter. Fabricated antenna illustrates a measured return loss of >20 dB, −10 dB bandwidth of 10% and 14.3% in LP and CP cases respectively, at 77 GHz. A minimum best value of 1.1 dB axial ratio is accomplished at 77 GHz in circularly polarized state of proposed antenna. Array of the proposed design would be designed in future for

288

9 Micromachined Antennas

Fig. 9.56 a Design schematic of micromachined patch antenna with air cavity, b top and c side views of the air cavity, d final optimized patch with design parameters

Fig. 9.57 Simulated matching performances of the antenna with different cavity area

9.9 Conclusions

289

(a)

(c)

(b)

(d)

Fig. 9.58 a Design schematic with all dimensions, b fabricated top view, c fabricated bottom view and d measured matching results of the 2 × 2 micromachined patch antenna array

Fig. 9.59 a Microfabricated image and b measured matching responses of the 8 × 8 micromachined patch antenna array

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9 Micromachined Antennas

short- and long-range radar applications at 77 GHz. Micromachined active antenna is discussed next. An active antenna with micro machined structures is an extremely versatile element for millimeter-wave systems. For example, a planar array of such antennas can deliver power levels not possible from single devices, and yet be relatively immune to failure of some elements. Features such as beam steering can be accommodated in such arrays. Another application is miniaturized transponders, which can be mounted in locations with severe space constraints. Finally, this Chapter concludes with the micromachned 2 × 2 and 8 × 8 micromachined patch antenna arrays with design guidelines. A large set of references have been added for further information on micromachined antennas.

References 1. Stotz M et al (1996) Planar single and dual polarized aperture coupled E-Band Antenna on GaAs using SiNx membranes. In: IEEE international antennas and propagation symposium and ursi national radio science meeting, Maryland, pp 1540–1543 2. Papapolymerou I, Drayton RF, Katehi LPB (1998) Micromachined patch antenna. IEEE Trans Antennas Propagat 46:275–283 3. Garg R, Bhartia P, Bahl I, Ittipiboon A (2001) Microstrip antenna design handbook. Artech House 4. Lee K-F, Luk K-M, Dahele JS (1988) Characteristics of the equilateral triangular patch antenna. IEEE Trans Antennas Propagation 36(11):1510–18 5. Guha D, Siddiqui JY (2004) Resonant frequency of equilateral triangular microstrip antenna with or without air gap. IEEE Trans Antennas Propag 52(8):2174–2177 6. Yong S-K, Xia P, Garcia AV (2011) 60 GHz Technology for Gbps WLAN and WPAN: from theory to practice. Wiley, Chichester 7. Christodoulou CG (2003) RF MEMS and its applications to microwave systems, antennas and wireless communications. In: Proceedings of the IEEE MTT-S international microwave symposium on digest, pp 525–531 8. Rebeiz GM (2003) RF MEMS: theory, design and technology. Wiley, New York 9. He J, Xiong YZ, Zhang YP (2012) Analysis and design of 60 GHz SPDT switch in 130 nm CMOS. IEEE Trans Microw Theory Tech 60(10):3113–3119 10. Thian M, Fusco V (2011)40–70 GHz 13 Gbps 1 dB loss SPST and SPDT differential switches in 0.35 μm SiGe technology. Act RF Devices Circ Syst Semin Belfast 11–15 11. Cheng S et al (2009)Switched beam antenna based on RF MEMS SPDT switch on quartz substrate. IEEE Antennas Wirel Propag Lett 8:383–386 12. Jaiswal A, Dey S, Abegaonkar M, Koul SK (2018) Design and development of 60 GHz antenna with integrated RF MEMS SPDT switch for transceiver modules. In: IEEE radio frequency integration technology (RFIT-2018). Melbourne, Australia 13. Jaiswal A, Dey S, Abegaonkar M, Koul SK (2016) High isolation RF MEMS SPDT switch for 60 GHz ISM band antenna routing applications. In: Proceedings of the IEEE Asia-Pacific microwave conference, New Delhi, India 14. Amadjikpè AL, Papapolymerou J (2010) Platform integrated 60 GHz antennas systems. In: School of electrical and computer engineering, georgia institute of technology, Atlanta, GA, p 30308 15. Zheng G, Papapolymerou J, Tentzeris MM (2003) Wideband coplanar waveguide RF probe pad to microstrip transitions without via holes. IEEE Microw Wirel Compon Lett 13(12):544–546 16. Rousstia MW, Herben MHAJ (2013) Design and multiphysics analysis of low-loss 60 GHz SPNT RF-MEMS switches. In: Proceedings of the 14th international symposium on RF-MEMS and RF-microsystems (MEMSWAVE 2013), vol 1

References

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17. Pranonsatit S, Holmes AS, Lucyszyn S (2010)Sectorised horn antenna array using an RF MEMS rotary switch. In: 2010 Asia-pacific microwave conference, Yokohama, pp 1909–1913 18. Jaiswal A, Dey S, Abegaonkar M, Koul SK (2017)Surface micromachined RF MEMS SP9T switch for 60 GHz ISM band antenna sectoring applications. In: IEEE CCECE, 2017. Windsor, Ontario 19. www.nxp.com/applications/adas-autonomousdriving/automotive-radar-systems:RADARSYSTEMS 20. Beer S, Adamiuk G, Zwick T (2009)Design and probe based measurement of 77 GHz antennas for antenna in package applications. In: Microwave conference, 2009. EuMC 2009. European, Rome, pp 524–527 21. Shino N, Uchimura H, Miyazato K (2005)77 GHz band antenna array substrate for short range car radar. In: IEEE MTT-S international microwave symposium digest, pp 4 22. Fischer A, Tong Z, Hamidipour A, Maurer L, Stelzer A (2011)A 77-GHz antenna in package. In: 2011 8th European radar conference, Manchester, pp 428–431 23. Vasanelli C, Ruess T, Waldschmidt C (2015)A 77-GHz cavity antenna array in PCB technology. In: 2015 IEEE 15th mediterranean microwave symposium (MMS), Lecce, pp 1–4 24. Wei W, Wang X (2018) A 77 GHz series fed weighted antenna arrays with suppressed sidelobes in E- and H-Plane. Progress In Electromag Res Lett 72:23–28 25. Xu J, Hong W, Zhang H, Wang G, Yu Y, Jiang ZH (2017) An array antenna for both longand medium-range 77 GHz automotive radar applications. IEEE Trans Antennas Propag 65(12):7207–7216 26. Jaiswal A, Dey S, Abegaonkar MP, Koul SK (2016)77 GHz polarization reconfigurable micromachined antenna for automotive radar applications. In: 2016 IEEE MTT-S Latin America microwave conference (LAMC), Puerto Vallarta, pp 1–3 27. Jaiswal A, Dey S, Abegaonkar MP, Koul SK (2020) 77 GHz polarization agile microelectromechanical system antenna.Wiley Microw Opt Technol Lett 62:2300–2306 28. Dadgarpour A, Zarghooni B, Virdee BS, Denidni TA (2015) Millimeter wave high-gain SIW end-fire bow-tie antenna. IEEE Trans Antennas Propag 63(5):2337–2342 29. Flynt RA, Fan L, Navarro JA, Chang K (1996) Low cost and compact active integrated antenna transceiver for system applications. IEEE Trans Microw Theory Tech MTT-44:1642–1649 30. Montiel CM, Fan L, Chang K (1998) An X-band self-mixing oscillator antenna for transceiver and spatial power-combining applications. IEEE Trans Microw Theory Tech MTT-46:1546– 1551 31. Chang K, Hummer KA, Gopalakrishnan GK (1988) Active radiating element using FET source integrated with microstrip patch antenna. Electron Lett 24(21):1347–1348 32. Fusco VF, Burns HO (1990) Synthesis procedure for active integrated radiating elements. Electron Lett 26(4):263–264 33. Kurup DG, Rydberg A (2003) Amplifying active reflect-antenna using a microstrip-T coupled patch-design and measurement. IEEE Trans Microw Theory Tech MTT-51:1960–1965 34. Koul SK, Basu A (2004) Design and development of MEMS based millimeter wave active antenna. In: C.A.R.E, IIT Delhi internal report for national programme on smart materialsNPSM

Chapter 10

Micromachined Metamaterial Inspired Switches

10.1 Introduction As discussed in Chaps. 3 and 4, RF MEMS switch technology provides reduced footprint and lower insertion loss as compared with semiconductor and electromechanical switches. Some important parameters that are desirable while designing the RF MEMS switch are: Low actuation voltage, higher isolation, less stiction and high reliability. The switches described earlier are narrow band and useful at microwave and lower millimetre wave frequencies. There is a need to carry out innovations in RF MEMS switches that offer broader bandwidths and enable use at higher millimetre wave frequencies (up to sub-Terahertz frequencies). The development effort presented in this Chapter discusses a modified serpentine membrane that helps in reducing the actuation voltage significantly. Next, the use of defective ground structure (DGS) along with secondary switches and metamaterial inspired capacitive contacts to improve RF MEMS switch performance into 100+ GHz range with lower insertion loss and higher isolation than the previous reported designs are presented. Further, the Casimir effect is discussed and new configurations that help in improving stiction and hence reliability in both resistive as well as capacitive RF MEMS switches are described [1–12].

10.2 Micromachined Switch Using Capacitive Contacts Capacitive switches use a thin layer of dielectric material to separate two conducting electrodes when actuated. The dielectric layer prevents direct metal-to-metal contact. Therefore, stiction of contacts due to thermal energy is less of a concern. However, the thin layer of dielectric material will only conduct signals with reasonable insertion loss when the coupling between conductor electrodes is above a certain frequency. Moreover, the isolation bandwidth of capacitive switches is limited by the ratio between the ON-and OFF- capacitances. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 S. K. Koul and S. Dey, Micromachined Circuits and Devices, Lecture Notes in Electrical Engineering 859, https://doi.org/10.1007/978-981-16-9443-1_10

293

294

10 Micromachined Metamaterial Inspired Switches

10.2.1 Basic Layout of Capacitive Shunt Switch The basic capacitive shunt switch uses a perforated membrane as shown in Fig. 10.1. The configuration is like that used in the paper by Vaha-Heikkila [1]. The switch is fabricated using coplanar geometry (not shown) with doubly supported perforated cantilever beam. An electrostatic actuator (not shown) is used for actuating the cantilever beam. The actuator is configured to apply a DC bias voltage between the doubly supported perforated cantilever and the ground line of the coplanar waveguide, thereby causing the cantilever beam to deflect down which results in change of capacitance. As the center conductor of the coplanar waveguide is covered with 325 um

65 um

60 um (a)

325 um c=1.2 um 2.5um 55um 60 um

0.2um Si₃N₄

h

SUBSTRATE

(b) Fig. 10.1 a Top view and b Side view of the RF MEMS switch using a doubly supported cantilever beam designed above a coplanar waveguide

10.2 Micromachined Switch Using Capacitive Contacts

295

thin dielectric layer of about 0.2 μm, a large shunt capacitance is obtained when the cantilever touches the dielectric layer. This large capacitance blocks the RF signal from propagating on the coplanar waveguide (ON-state). When the DC bias is removed, the doubly supported perforated cantilever returns to the original position and the RF signal propagates un-attenuated (OFF-state).

10.2.2 Simulation Results Mechanical analysis of the basic switch clearly shows the deflection in the doubly supported cantilever (Fig. 10.2) as DC bias is applied between the coplanar ground and the cantilever. For an air gap of 2.5 μm between the cantilever and the actuation pads, the pull in voltage observed is 37 V which is on the higher side. Another drawback of this shunt switch configuration is the isolation obtained between the input port and the output port in the ON-state. Figure 10.3 shows the isolation plot over 75–130 GHz band. Isolation in the range −12.4 to −19.7 dB is observed in this shunt switch. The typical insertion loss of the switch when closed is about 0.74 dB and return loss is about 10.04 dB. It is well known that the actuation voltage of the capacitive shunt switch can be reduced by using a serpentine structure in the cantilever beam shown in Fig. 10.4.

Fig. 10.2 Deflection in the doubly supported cantilever in μm

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10 Micromachined Metamaterial Inspired Switches

-11.25

Curve Info dB(S(2,1)) Setup1 : Sweep

-12.3816

-12.50

dB(S(2,1))

-15.00

-17.50

-19.7154

-20.00

-22.50

70.00

80.00 75.0000

90.00

100.00

110.00 Freq [GHz]

120.00

130.00

140.00

55.0000 130.0000

Fig. 10.3 Isolation versus frequency plot for RF MEMS switch shown in Fig. 10.1 in the open position

The serpentine structure is expected to decrease the spring constant of the cantilever beam, thereby reducing the actuation voltage. To the best of our knowledge such techniques are reported at lower RF frequencies and not at millimetre wave frequencies. Mechanical analysis of the modified switch clearly shows the deflection in the doubly supported cantilever shown in Fig. 10.5 as DC bias is applied between the coplanar ground and the cantilever. For an air gap of 2.5 μm between the cantilever and the actuation pads, the pull in voltage observed is 17 V which is much lower than the switch shown in Fig. 10.1. Figure 10.5 shows the isolation plot over 50–140 GHz band. Over the 75–130 GHz band isolation in the range −22.00 to −14.5 dB is observed in this modified shunt switch. The insertion loss of the switch when closed is about 0.6 dB and return loss is about 15.15 dB.

10.3 DGS Inspired Micromachined Switch 10.3.1 DGS Capacitive RF MEMS Switch The isolation characteristics of the above capacitive RF MEMS shunt switch can be further improved by incorporated DGS, particularly in the millimetre wave frequency band of 75–130 GHz. As ground plane defect resonates at a particular frequency (depending on the dimensions of the defect), a two-dimensional defected ground plane structure (DGS) can be incorporated in the ground plane of the switch as shown in Fig. 10.6. DGS structure essentially behaves as a band stop filter thereby

10.3 DGS Inspired Micromachined Switch

297

345 um

65 um

(a)

(b) Fig. 10.4 a Top view of the capacitive RF MEMS switch using a serpentine structure in the cantilever beam, b deflection in the doubly supported serpentine cantilever in μm

affecting the transmission characteristics of the switch. The return loss, insertion loss and isolation characteristics of the shunt switch of Fig. 10.4a with 2-dimensionsal DGS (Fig. 10.6) is shown in Fig. 10.7a, b. Although there is improvement in the isolation over a very narrow bandwidth, the switch with DGS in the ground plane offers much higher insertion loss.

298

10 Micromachined Metamaterial Inspired Switches

-12.50

Curve Info dB(S(2,1)) Setup1 : Sw eep

-14.5221

-15.00

dB(S(2,1))

-17.50

-20.00

-22.2325

-22.50

-25.00

50.00

60.00

70.00

80.00

90.00 100.00 Freq [GHz] 55.0000

110.00

120.00

130.00

140.00

130.0000

75.0000

Fig. 10.5 Isolation versus frequency plot for RF MEMS switch shown in Fig. 10.1 in the open position using a serpentine structure shown in Fig. 10.4 in the cantilever beam

DGS STRUCTURE

400 um

345 um

320 um Fig. 10.6 Top view of the defective ground structure (DGS) inspired RF MEMS switch

10.4 Metamaterial Inspired Micromachined Switch

299

0.00

Curve Info dB(S(1,1)) Setup1 : Sweep c='1.2um' h='4.5um'

S21

-2.1944

S11, S21 (dB)

-5.00

dB(S(2,1)) Setup1 : Sweep c='1.2um' h='4.5um'

-10.00

-10.3505

Y1

-11.2386

-15.00

S11

-20.00

-24.0312 -25.00 70.00

80.00

90.00

100.00

110.00

120.00

130.00

140.00

Freq [GHz] 75.0000

55.0000 130.0000

(a) -10.00

Curve Info

-11.5339

S21

-17.1412 -20.00 dB(S(2,1))

S21 (dB)

-15.00

dB(S(2,1)) Setup1 : Sweep c='1.2um' h='3.2um'

-25.00

-30.00

-35.00

70.00

80.00

90.00

100.00

110.00

120.00

130.00

140.00

Freq [GHz] 75.0000

55.0000

(b)

130.0000

Fig. 10.7 a Return loss and insertion loss and b isolation of RF MEMS Switch shown in Fig. 10.6, c = 1.2 μm, h = 4.5 μm

10.4 Metamaterial Inspired Micromachined Switch 10.4.1 Basic Switch Layout and Analysis To overcome higher insertion loss in the DGS inspired RF MEMS switch shown in Fig. 10.6, secondary MEMS switches are placed above the DGS as shown in Fig. 10.8 and the analysis of the metamaterial unit cell is carried out. Figure 10.9a, b show the top view and side view of the DGS structure. First a simple coplanar line without DGS is analysed for the transmission and reflection phase over a band of mmWave frequencies from 50 to 140 GHz, and the results are plotted in Fig. 10.10. No phase reversal is observed in this structure. Any shift in the transmission phase of the signal is met with a substantially equal (within about 20°) shift in the reflection phase.

300

10 Micromachined Metamaterial Inspired Switches

Fig. 10.8 Top view of the capacitive shunt micromachined switch showing secondary MEMS switches placed above the DGS

Fig. 10.9 a Top view and b side view of the DGS structure

Figure 10.11 shows transmission and reflection phases of the signal over the same band for the same coplanar waveguide with DGS structure incorporated at a height of 2.2 μm (distance from the top surface of the substrate) to the bottom surface of the secondary switch that is positioned above the DGS structure. As observed, the

10.4 Metamaterial Inspired Micromachined Switch

301

Fig. 10.10 Plot of the transmission and reflection phase of the coplanar line of the shunt switch shown in Fig. 10.8 without DGS

Fig. 10.11 Plot of the transmission and reflection phase of the coplanar line of the shunt switch shown in Fig. 10.8 with DGS for h1 = 2.2 μm

transmission and reflection phases donot shift equally across the frequency band, and even shift in opposite directions, eventually crossing one another at 85 GHz and again at 96 GHz. Figure 10.12 shows phases of transmission and reflection coefficients for the same coplanar waveguide but with DGS structure at a height of 2.8 μm. As observed, the transmission and reflection phases shift substantially equally until about 110 GHz and then begins shifting in opposite directions at frequencies above 115 GHz and even cross one another at about 128 GHz. The resonance frequency of the DGS structure thus varies depending on the height of the air gap between the ground plane and the beam. A plot of isolation characteristics for five secondary switches positioned over the DGS structures at varying heights is shown in Fig. 10.13. It is clearly observed that the resonant frequency of the structure shifts to higher frequencies as the air gap between the ground plane and the beam increases.

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10 Micromachined Metamaterial Inspired Switches

Fig. 10.12 Plot of the transmission and reflection phase of the coplanar line of the shunt switch shown in Fig. 10.8 with DGS for h1 = 2.8 μm

Fig. 10.13 Plot of the isolation characteristics of the shunt switch shown in Fig. 10.8 with DGS for various values of h1

10.4.2 Shunt Switch with DGS Structures and Overlaid Secondary Switches Figure 10.14 shows the top view of the final proposed metamaterial 3-dimentional unit cell structure with shunt switch of Fg. 10.4a. The side view of the same structure is shown in Fig. 10.15. Each DGS structure has a secondary MEMS switch over it to vary the resonance characteristics of the DGS. In the first instance, all the DGS structures are identical in nature. Subsequently, two different sets of DGS structures are used. Studies are also carried out for different actuations of the secondary switches to study effect on the insertion loss, return loss and isolation of the composite switch over the 75–130 GHz band. The working principle of the composite switch can be explained with the help of Fig. 10.16. The layout consists of switch 1 which is the

10.4 Metamaterial Inspired Micromachined Switch

303

Fig. 10.14 Top view of the metamaterial inspired RF MEMS shunt switch with DGS structure and overlaid secondary switches

Fig. 10.15 Side view of the metamaterial inspired RF MEMS shunt switch with DGS structure and overlaid secondary switches shown in Fig. 10.14

serpentine type of shunt switch, DGS structures with secondary switches (switch 2) on top and two actuation pads 1 and 2. Actuating Pad 1: In this condition serpentine type shunt switch remains in OFF-state (Up-position). As actuation voltage is applied to the secondary MEMS switch, they change to ON-state (Down position). This negates the effect of the DGS unit cells. The actuation of the switches in this state is shown in Fig. 10.17. The insertion and return loss characteristics of the switch over the entire 75–130 GHz band are plotted

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10 Micromachined Metamaterial Inspired Switches

Fig. 10.16 Layout of the metamaterial inspired RF MEMS shunt switch with DGS structure and overlaid secondary switches

Surface: Total displacement in (μm)

Fig. 10.17 Amount of downward deflection at several points of the secondary switches upon applying actuation voltage to pad #1

in Fig. 10.18. As observed, very good insertion loss and high return loss is achieved over the entire band. The negating effect of DGS unit cells is clearly seen in this Fig. 10.19. Actuating Pad 2: In this condition serpentine type shunt switch remains in ONstate (DOWN position). NO actuation voltage is applied to the secondary MEMS

10.4 Metamaterial Inspired Micromachined Switch

305

Fig. 10.18 Insertion loss (S 21 ) and return loss (S 11 ) versus frequency of the switch shown in Fig. 10.16 with secondary switch 2 actuated, a = 70 μm, a1 = 100 μm, b = 10 μm, h = 4.5 μm, h1 = 2.0 μm

Surface: Total displacement in (μm)

Fig. 10.19 Amount of downward deflection at several points of the Primary switches upon applying actuation to Pad#2

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10 Micromachined Metamaterial Inspired Switches

Fig. 10.20 Isolation versus frequency of the switch shown in Fig. 10.16 with secondary switch 2 actuated, a = 80 μm, a1 = 80 μm, b = 15 μm, h1 = 2.3 μm

switches, they change to OFF-state (Up position) and the effect of DGS unit cells is now incorporated. The actuation of the switches in this state is shown in Fig. 10.19. Figure 10.20 shows the isolation characteristics of the switch shown in Fig. 10.16 when the primary switch is ON, and the secondary switches are OFF. In this figure the same DGS structure is used. This leads to a significant improvement in isolation at a relatively narrow band. As observed, at 75 GHz isolation is about −23.1 dB and at 130 GHz, isolation is about −23.9 dB. But at about 95 GHz, isolation is improved to about −52 dB. Figure 10.21 shows plots of isolation and insertion loss characteristics of MEMS switch utilizing different structures. The metamaterial construction leads to an overall improvement of isolation over a wider band of frequencies. The structure yields improved isolation at about 84 GHz (−51 dB) and at about 112 GHz (about − 59 dB) and is not worse than about −24 dB between 75 and 130 GHz. The insertion loss characteristics of the DGS switch is poor compared to the regular switch with metamaterial versions. The structure of the switch shown in Fig. 10.16 gives considerable flexibility when the serpentine type of shunt switch remains in the ON-state (DOWN position) and the secondary switches are also actuated. In this case, high isolation characteristics are obtained over reconfigurable narrow bands as shown in Fig. 10.22. In the entire band 75–130 GHz, reasonable isolation of the order of better than 22 dB can also be achieved. Table 10.1 shows comparison of performance of different geometries tried [2]

10.5 Casimir Repulsive Force Inspired Micromachined Switch

307

Fig. 10.21 a Isolation and b insertion loss versus frequency of the switch shown in Fig. 10.16 with different topologies

10.5 Casimir Repulsive Force Inspired Micromachined Switch 10.5.1 Concept of Casimir Effect The Casimir force is due to the interaction of the surfaces with the surrounding electromagnetic spectrum, and it exhibits a dependence on the dielectric properties of the surfaces and the medium between the surfaces. Casimir forces between macroscopic surfaces have the same physical origin as atom-surface interactions and those between two atoms or molecules (also known as van de Waals forces), because they originate from quantum fluctuations. In the case of two uncharged metal plates positioned closely to one another and in parallel, a force causing the two plates to move towards one another has been reported [1]. Figure 10.23 shows the practical evidence

308

10 Micromachined Metamaterial Inspired Switches

Fig. 10.22 Isolation versus frequency characteristics of the switch shown in Fig. 10.16 for various values of h1 (Refer to Fig. 10.15)

Table 10.1 Comparison of different MEMS switch performance Parameters

Shunt switch (Fig. 10.1)

Shunt switch (Fig. 10.4)

Shunt switch with DGS and without secondary switches actuated (Fig. 10.16)

Shunt switch with DGS and with secondary switches actuated (Fig. 10.16)

Pull in voltage (V)

37

17

17

17

Isolation(75–130 GHz) (dB)

−12 to −19

−15 to −24

−11 to −32

−24 to −59

Insertion loss

0.74

0.6

2–11

0.6

Material

Molybdenum

Gold

Gold

Gold

Cantilever height (μm)

2.5

2.5

2.5

2.5

of Casimir force ‘F’ on parallel plates kept in vacuum. It is shown that the effective force F ∝ A/d 4 , where A is the area of plate and d is the distance between the plates [7]. The Casimir force is known to be proportional to the effective permittivity of metal plates [7, 8]. Therefore, by decreasing the effective permittivity on the metal plates, the Casimir force can be decreased. This can result in reduced forces preventing the plates from separating from one another, thus at least partially mitigating the stiction problem observed in MEMS switches [1]. Figure 10.24 depicts the polaritonic char-

10.5 Casimir Repulsive Force Inspired Micromachined Switch

309

Fig. 10.23 Practical evidence of Casimir force ‘F’ on parallel plates kept in vacuum, [7]

Fig. 10.24 Plots show the region of Casimir force of attraction and repulsion [8]

acteristics of the Casimir force of interaction that includes repulsion and attraction [7]. There are several ways to reduce stiction in the RF MEMS switches. One way to reduce the likelihood of stiction is by increasing the bias voltage applied to the switch as discussed earlier. Alternatively, instead of increasing bias voltage, the electric field of the switch can be increased by distancing the top electrode from ground [3–6]. This can be accomplished, for example, by sandwiching the conductive layer (e.g., gold) between two dielectric layers (e.g., silicon oxynitride). One can also modify the beam to maximize its restoring force without having to increase the bias voltage. Improved restoring force is influenced by such parameters as increased plate size,

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shortened beam length, or increased dielectric thickness. In addition to controlling the distance between the electrode and ground and controlling the structural parameters of the switch contacts, one can contemplate to weaken or reverse the forces applied to the switch contacts due to their proximity.

10.5.2 Application of Casimir Effect in RF MEMS Switches By reducing permittivity between plates, a repulsive force can be produced if the effective permittivity is sufficiently decreased, such as by engineered materials known as metamaterials [6]. Thus, generating a repulsive Casimir force can result in even less of a liability for the contacts to effectively become “welded” together due to stiction. Figures 10.25 and 10.26 illustrate the repulsive force, described as Casimir effect [7–13]. Figure 10.25 is a force diagram illustration of an experimental setup, in which a plane of metal is positioned in parallel to a metamaterial. The metal and metamaterial are positioned apart from one another at a distance “d.” The forces illustrated in the setup in Fig. 10.25 are shown using arrows. A first force applied to the metal and metamaterial bring the two planes closer to one another. However, application of this first force has been observed under the specific conditions of the experimental setup illustrated in Fig. 10.26 to result in a second and opposite force “F” that causes the two planes to separate from one another. Figure 10.26a shows a first metal plate ‘1’separated from a second metal plate ‘2’ by a distance ‘d’. The two metal plates may be thought of as opposing contacts in a MEMS switch and may be liable to become permanently stuck to one another at distances ‘d’ that are sufficiently small. By contrast, Fig. 10.26b shows a thin layer of metamaterial ‘2’ affixed to a surface of the first metal plate ‘1’ and positioned in between the metal plates ‘1’, ‘4’. A Casimir force ‘3’ is produced at the boundary between the metamaterial ‘2’ and the second metal plate’4’, thereby causing the

Fig. 10.25 Demonstration of the Casimir force in metamaterial structure, [3, 7–9]

10.5 Casimir Repulsive Force Inspired Micromachined Switch

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Fig. 10.26 Demonstration of the Casimir force in a metal plates and b metamaterial structure [3, 7–9]

second metal plate to further separate from the first metal plate’1’ by a distance d’. This additional separation may even counteract gravitational forces, and thus cause the second metal plate ‘4’ to levitate. In some cases, the metamaterial may be made by split ring structure using gold foil [7–10]. In the application of a MEMS switch structure, the switch may include a deflectable beam having a shorting bar positioned on a surface of the beam and aligned with the contact of the signal line. The shorting bar may be made of metal, such as a thin layer of gold foil. When the shorting bar touches the signal line, the metal-to-metal contact surfaces may stick to one another in the form of strong adhesion. This adhesion causes undesirable stiction problems, which in turn may cause the switch to be electrically shorted, and it may take a considerable amount of force to separate the shorting bar from the signal line. The MEMS switch generally relies on stresses accumulating in the beam because of the beam’s deflection to counteract the adhesive forces and to return the beam back to its at-rest or equilibrium position. This counteractive force, which is the sum of the stresses in the beam, is referred to as the restoring force that “restores” the beam to its at-rest position. However, this force is not always sufficient to counteract adhesive forces between the metal contacts. By providing a metamaterial structure between the metal contacts, the restoring force

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Fig. 10.27 Three-layer composite structure with layer 1 or layer 3 incorporating a metamaterial unit cell such that ε1 < ε2 < ε3 or ε1 > ε2 > ε3

of the beam can be supplemented using the repulsive Casimir force generated when the shortening bar touches or comes within proximity to the signal line. The Casimir force can be controlled by providing a permittivity gradient in the contact of the deflectable beam. The permittivity gradient can be provided by interfacing three layers of media in either decreasing or increasing order of permittivity. In Fig. 10.27, three layers of media are provided: a first layer having permittivity ε1 , a second layer having permittivity ε2 , and a third layer having permittivity ε3 . The first and third layers may be metal layers, and the second layer may be a dielectric layer. The layers may be interfaced such that either ε1 < ε2 < ε3 or ε1 > ε2 > ε3 . This may be possible by providing one metal layer with positive permittivity, and another metal layer with negative permittivity. For instance, the first layer may be made of gold and have an infinite permittivity, the second layer may be made of a dielectric (e.g., silicon mononitrate (SiN)) and have a small but positive permittivity (e.g., 7) and the third layer may include a metamaterial unit cell and may have a zero or even negative permittivity. In other examples, the first layer can also include a metamaterial unit cell to acquire the desired permittivity gradient [2].

10.6 Repulsive Casimir Force Inspired Resistive (Metal-to-Metal) Contact Micromachined Switch Figures 10.28a–d are illustrations of an example MEMS switch incorporating metamaterial cells to provide a repulsive Casimir force between contacts of the switch. Figure 10.28a is the 3D view of the switch in the OFF-State, Fig. 10.28b is a bisected cross-sectional perspective view of the switch in the open position, Fig. 10.28c is the 3D view of the switch in the ON-state, and Fig. 10.28d is a bisected cross-sectional perspective view of the switch in the closed position. As shown in Fig. 10.28, Metamaterial inspired MEMS switch is formed in a coplanar waveguide positioned having two ground planes and formed above a substrate. The ground planes are separated by a channel and a signal line is formed lengthwise in the channel. The signal line includes each of an input port through which a signal is received (arrow in) and an output port through which the signal is transmitted (arrow out). It can be noticed that MEMS switch in Fig. 10.28 includes a cantilevered beam that moves in and out of the plane of the coplanar waveguide to move in and out of

10.6 Repulsive Casimir Force Inspired Resistive …

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Fig. 10.28 Illustrations of an example resistive MEMS switch incorporating metamaterial cells to provide a repulsive Casimir force between contacts of switch: a 3D view of the switch in the OFF-state, b bisected cross-sectional perspective view of the switch in the open position, c 3D view of the switch in the ON-state, and d bisected cross-sectional perspective view of the switch in the closed position

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Fig. 10.28 (continued)

contact with the signal line. The beam includes multiple layers. In the example of Fig. 10.28, from top to bottom, the layers include: a top layer of dielectric material, a first metal layer, a dielectric layer, and a second metal layer. Each of the first and second metal layers, may include a metamaterial device encased within, as shown in the cross-sectional view of Fig. 10.28c. In the above structure, metamaterial unit cells are made of split rings as shown in Fig. 10.29. These are included in second metal layer and optionally in the first metal

Fig. 10.29 Layout of split ring metamaterial unit cell

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315

layer. Figure 10.29 illustrates an example metal layer ‘2’ having each of a first split ring ‘3’ having width L, and a second split ring ‘1’, formed in the layer, whereby forming the rings may involve cutting out the rings from the layer. Each of the rings may be concentric and may be aligned so that the splits ‘5’ in the respective rings are positioned on opposing sides of the layer ‘2’. Each of the rings may have a uniform width W, and the splits ‘5’ may have a uniform width G. The rings may further be separated from one another by a uniform separation’4’ having width S. Different engineered structures may provide different metamaterial unit cells that can exhibit characteristics at the relevant band of frequencies for MEMS switch [3–5]. The parameters of the metamaterial unit cell can be varied to produce different transmission and reflection characteristics. Several metamaterial unit cells were analysed, and their performance optimized. Using the transmission and reflection data, permeability and permittivity of the metamaterial cells has been extracted using parameter extraction procedure reported in the literature [13]. The parameter extraction for the composite structure shown in Fig. 10.28 is shown in Fig. 10.30. As can be seen from Fig. 10.30, the composite structure exhibits near zero permittivity as well as permeability at a band of frequencies cantered around 80 GHz. Therefore, it is clear from Fig. 10.30 that these structures would produce a repulsive Casimir force around the band of frequencies ranging from about 60 GHz to about 130 GHz. Figures 10.31 and 10.32 further demonstrate the overall response of the Resistive Metal to Metal MEMS switch in the ON- and OFF- states, respectively. In Fig. 10.31, when the switch is OFF, and thus not passing the transmitted signal between input and output ports, the reflection characteristics are shown to be just slightly less than

Fig. 10.30 Plot of permittivity and permeability extracted from the S-parameters of the composite structure in Fig. 10.28 for a particular split ring metamaterial unit cell

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Fig. 10.31 Response of the resistive metal contact MEMS switch in the OFF-state

Fig. 10.32 Response of the resistive metal contact MEMS switch in the ON-state

0 dB even at frequencies up to 130 GHz, and the transmission characteristics are between about −20 and −15 dB between operating frequencies of about 60 GHz to about 130 GHz. In Fig. 10.32, when the switch is ON, and thus passing the transmitted signal between input and output ports, the reflection characteristics are as low as about − 73.5 dB at 80 GHz with the transmission characteristics as high as −0.33 dB while the reflection and transmission characteristics at 163 GHz are both about −6.75 dB. The examples of Fig. 10.28 through Fig. 10.32 demonstrate the possibility of incorporating metamaterial structures into a high frequency resistive MEMS switch to reduce the effects of stiction.

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10.7 Casimir Repulsive Force Inspired Capacitive Contact Micromachined Switch The theory of repulsive Casimir force and application in resistive contact MEMS switch is discussed in detail in the earlier Section. In this Section, method to reduce stiction effects in the capacitive (metal-insulator-metal) contact MEMS switch is discussed for applications in modern electronic circuits and 5G communications. Metamaterial unit cells realized by composite engineered structure, provide promising characteristics at the relevant band of frequencies for the capacitive MEMS switch. Test results for transmission and reflection characteristics of several perspective unit cell structures have been studied in detail and the same are documented in the literature [3–6]. An example capacitive MEMS switch is shown in Fig. 10.33. Figure 10.33a is a top-down view of the switch, Fig. 10.33b is a side view of the switch, and Fig. 10.33c is a perspective view of the switch. As illustrated in Fig. 10.33, the switch includes a structure formed over a signal line having an input side ‘3’ and an output side’6’. A metamaterial structure having an outer split ring ‘7’ and inner split ring’8’ is formed in the signal line contact between the input side ‘3’ and output side ‘6’, through which a signal is received (arrow in) and an output port through which the signal is transmitted (arrow out). Each of the ground planes ‘5’, ‘9’ and the signal line are formed from a conductive material such as gold, and are formed on top of a dielectric material ‘10’ such as silicon nitride (Si3N4), which itself is formed on top of a substrate ‘12’. One of the ground planes ‘5’ includes a post ‘1’ extending downward from the ground plane ‘5’ into the dielectric material ‘10’, and a beam “2’ extending from the post ‘1’ in the direction of the signal line’6’. The edge of the beam ‘2’ is aligned with the opposing edge of the signal line ‘3’, ‘6’, such that the end of beam ‘2’ is positioned underneath the metamaterial structures ‘7’, ‘8’, of the signal line ‘3’, ‘6’. In Fig. 10.33a, c, the post ‘1’ can be seen through an opening ‘4’ in the ground plane ‘5’. In the example of Fig. 10.33 the ground planes and the signal line have a width (in the direction of the beam ‘2’ length) of about 73 μm and the beam has a length of about 168 μm. The metamaterial structure formed on the signal line contact has a ring width W of about 15 μm, a split width G of about 8 μm, and spacing between rings S of about 5 μm. Transmission and reflection characteristics of the switch over a range of frequencies are shown in Fig. 10.34. As can be seen from this Fig. 10.34, the metamaterial is most reflective at about 175 GHz and most transmissive at about 80 GHz. Based on these results, a material parameter extraction was performed to determine the permittivity and permeability of the metamaterial structure. The extraction of the permeability and permittivity are shown over a range of frequencies in Fig. 10.35. As seen from Fig. 10.35, the metamaterial structure exhibits near zero permittivity and permeability between about 50 and 150 GHz. This indicates that the structure of Fig. 10.33 is suitable for reducing the stiction using Casimir force of interactions (repulsive) in the desired frequency band.

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Fig. 10.33 Illustrations of capacitive MEMS switch incorporating metamaterial cells to provide a repulsive Casimir force between contacts of switch: a top-down view of the switch, b side view of the switch, and c perspective view of the switch

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Fig. 10.34 Transmission and reflection characteristics of capacitive MEMS switch shown in Fig. 10.33

Fig. 10.35 Plot of permittivity and permeability extracted from the S-parameters of the capacitive MEMS switch shown in Fig. 10.33

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Fig. 10.36 Perspective view of a capacitive shunt MEMS switch utilizing a metamaterial signal line contact to reduce stiction in the switch

Figure 10.36 shows a perspective view of a capacitive shunt MEMS switch utilizing a metamaterial signal line contact to reduce stiction in the switch. Many of the features of switch illustrated in Fig. 10.36 are compared to those of switch described in Fig. 10.33a–c: ground planes ‘1’ and ‘4’ and substrate ‘12’ compares to planes ‘5’ and ‘9’ and substrate ‘12’; signal line input and outputs’3’ and ‘9’ compares to ‘3’ and ‘6’; split ring metamaterial structure ‘10’ and ‘11’ compares to structure ‘7’ and ‘8’; dielectric layers ‘10’ and ‘2’ are comparable; openings ‘6’ and’6’ are comparable; posts ‘1’ and ‘7’ are comparable; and beams ‘2’ and ‘8’ are comparable. The switch shown in Fig. 10.36 includes a deflectable serpentine beam ‘5’. The deflectable serpentine beam ‘5’ is supported by a pair of posts formed on top of the ground planes ‘1’ and ‘4’, respectively, and is configured to deflect downward towards the signal line when actuated by a bias voltage. In operation, the bias voltage causes a midpoint of the beam ‘5’ to deflect downward until it meets the signal line contact, thereby causing the signal line to turn OFF (or in other case to turn ON). When the bias voltage is removed, the midpoint of the beam ‘5’ deflects back upward. Because the midpoint of the beam is aligned with the metamaterial structure ‘10’, ‘11’ of the signal line contact, the Casimir effect at the interface between the beam and the signal line contact is diminished or even repulsive, thereby reducing the liability of stiction between the beam ‘5’ and the signal line. Although not shown in Fig. 10.36, the signal line contact may further include a layer of dielectric material above the metal layer including the metamaterial structure. The dielectric layer may be made of SiN and may function as an isolation layer to achieve the desired permittivity gradient, as discussed above in connection with Fig. 10.27. Stated another way, the beam ‘5’ may have infinite permittivity, the isolation layer may have a positive but smaller permittivity, and the metal layer including the metamaterial structure in the signal line contact may have a near zero, zero or

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even negative permittivity, thereby satisfying ε1 < ε2 < ε3 condition or vice-versa. Performance of the capacitive MEMS switch (Fig. 10.36) is shown in Figs. 10.37 and 10.38, which are plots of both reflection and transmission characteristics of the switch across a range of high RF frequencies. Figure 10.37 demonstrates operation of the switch in the ON-state (transmitting signals) and Fig. 10.38 demonstrates operation of the switch in the OFF-state (cutting off transmission of signals). As observed from Fig. 10.37, at 10.3 GHz, return loss is as high as −29.8 dB while insertion loss is as low as about −0.07 dB. Even at 100.2 GHz, return loss is as high as −8.9 dB while insertion loss is only about −1.23 dB. This demonstrates good operation of the switch in the ON-state across a wide range of high frequencies, from 10 to 100 GHz. In Fig. 10.38, the switch is OFF, thus changing to being reflective instead of transmissive. At 29.3 GHz, insertion loss is as high as about −22.2 dB while return loss is as low as about −0.26 dB. Even at 100.2 GHz, insertion loss is as high as − 14.9 dB while return loss is only about −0.82 dB. This demonstrates good operation of the switch in its OFF-state across nearly the same wide range of high frequencies, from about 20 to 100 GHz. Altogether, good insertion loss and return loss characteristics of the MEMS Switch in the ON- and OFF-states are achieved over 30–100 GHz frequency band. This makes the presently described switch a good candidate for high frequency switching operations over a wide bandwidth of frequencies. Accordingly, the switches described in this section can improve operation and performance in applications requiring high frequencies (e.g., 10 GHz or greater) over a wide bandwidth. Such technologies may include, but are not limited to, 5G/6G communications, switching networks, phase shifters (e.g., in electronically scanned phase array antennas) and Internet of Things (IoT) applications.

Fig. 10.37 Transmission and reflection characteristics of capacitive MEMS switch shown in Fig. 10.36 in the ON-state

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Fig. 10.38 Transmission and reflection characteristics of capacitive MEMS switch shown in Fig. 10.36 in the OFF-State

10.8 Casimir Force Study In Sects. 10.3 and 10.4, it was shown that a combination of a primary shunt switch, DGS structures and secondary shunt switches behave like a metamaterial. In Sect. 10.5, concept of Casimir effect and its application in MEMS switch was described. In Sect. 10.6, improvement of resistance to stiction of the MEMS switches using metamaterial layers within the design of resistive switch contact was covered. Finally in Sect. 10.7, the metamaterial layers are used as part of the signal line contacts to realize shunt capacitance switch to improve stiction and hence reliability. To get more insight into the repulsive Casimir forces generated in these structures, a detailed study of a shunt switch with serpentine signal line with and without metamaterial underneath was carried out using COMSOL software. Figures 10.39, 10.40 and 10.41 show electric field distribution, surface charge distribution and electric surface stress tensor of a shunt switch with serpentine signal line with and without metamaterial underneath. From these results one can approximately estimate Casimir forces. The estimated Casimir force of a shunt switch serpentine signal line with and without metamaterial underneath is shown in Fig. 10.42 and Table 10.2 shows key parameters for the serpentine structure with and without the metamaterial. As observed the structure with metamaterial underneath exhibits Casimir repulsive force.

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Fig. 10.39 Electric field distribution of a shunt switch with serpentine signal line and a with and b without metamaterial underneath

Fig. 10.40 Surface charge density of a shunt switch with serpentine signal line and a with and b without metamaterial underneath

Fig. 10.41 Electric surface stress tensor of a shunt switch with serpentine signal line and a with and b without metamaterial underneath

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Fig. 10.42 Estimated Casimir force of a shunt switch with serpentine signal line and a with and b without metamaterial underneath

Table 10.2 Key parameters for serpentine structure with and without metamaterial underneath No.

Parameter

Serpentine structure with metamaterial underneath

Serpentine structure without metamaterial underneath

1.

Electric field (V/m)

1.32×107

1.1×107

2.

Electric charge (C)

−9.65×10−5

−9.98×10−5

3.

Electric surface tensor (Pa)

−766

−771

4.

Calculated force (10−5 N)

−18.5

1,980

10.9 Conclusions In this Chapter, it is shown that both DGS structures and secondary switches can achieve improvements in insertion loss and isolation of Micromachined switches at microwave and millimetre wave frequencies. These improvements contrast with the trade-offs conventionally seen when using either only a shunt switch (good insertion loss, poor isolation) or only DGS structure (improved isolation but poor insertion loss). It is shown that the proposed combination of a primary shunt switch, DGS structures and secondary switches behave like a metamaterial. Next, the principle of repulsive Casimir force is applied to improve stiction of the resistive contact MEMS switch. A sandwich of metal dielectric layers are used to achieve the desired permittivity interface, such as having a gold layer with infinite permittivity, a dielectric layer with positive but low permittivity and a metamaterial layer with a permittivity in the range nearly zero or negative. Finally, Casimir effects are explored to design metamaterial inspired shunt micromachined switches. The noteworthy improvements in switch characteristics should be useful for applications in 5G/6G communication, switching networks, phase shifters and IOT applications. The metamaterial structures described in the Chapter are mostly based on split ring configurations. However, one can explore other metamaterial structures that can provide similar permittivity and permeability characteristics within the desired range of frequencies.

References

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References 1. Vaha-Heikkila T, Ylonen M (2006) CMOS compatible switched MEMS capacitors Up to 220 GHz applications. In: 2006 European microwave conference, Manchester, pp 1060–1063 2. Mahajan C (2018) Design and analysis of RF MEMS switches (70–130 GHz), M.Tech dissertation, CARE, IIT Delhi 3. Koul S, Poddar A, Rohde U (2020) Microelectromechanical switch with metamaterial contacts. US patent 10,784,066 granted 4. Koul S, Mahajan C, Poddar A, Rohde U (2020) A micro-electromechanical switch with metamaterial contacts, part I: concepts and technology. Microw J 82–108 5. Koul S, Mahajan C, Poddar A, Rohde U (2020) A micro-electromechanical switch with metamaterial contacts, concepts and technology, part II. Microw J 64–78 6. Shiban Koul, Pranav Srivastava, Ajay Poddar and Ulrich Rohde, “A Micro-electromechanical Switch with Metamaterial Contacts, Part III, Reducing Stiction” Microwave Journal, pp. 52–68, July 2020. 7. Lambrecht A (2002) The Casimir effect: a force from nothing. Phys World 8. Intravaia F, Henkel C (2009) New frontiers of Casimir force, Santa Fe, New Mexico 9. Leonhardt U, Philbin TG (2007) Quantum levitation by left-handed metamaterials. New J Phys 10. Mercado et al (2003) A mechanical approach to overcome RF MEMS switch stiction problem. ECTC 11. Sun J, Hua XK, Gao L (2012) Repulsive and attractive casimir forces between magnetodielectric slabs. Solid State Commun 152(17):1666–1669 12. Yannopapas V, Vitanov NV (2009) First-principles study of Casimir repulsion in metamaterials. Phys Rev Lett 103(12):120401 13. Chen X et al (2004) Robust method to retrieve the constitutive effective parameters of metamaterials. Phys Rev E70:016608

Chapter 11

Future Scope of RF MEMS in THz Regime

11.1 Introduction In recent years, RF-MEMS have been identified as the most significant enabling technology in developing the reconfigurable wireless systems. New wireless standards are coming up which require replacement of bulky, expensive, and off-chip passive RF components with RF-MEMS technology-based devices having small size, high linearity, low power consumption and multi-band tunability. In general, the outstanding performance of the RF-MEMS is due to the air gap between the active elements and lossy substrate, use of high conductivity metals and integration compatibility with existing IC fabrication technologies. The availability of radio frequency systems working at sub-THz frequencies (from 100 GHz up to 1 THz) has been increasing in the past few years due to technological advances improving the performance of both passive waveguide components and active circuits in this frequency range [1, 2]. Due to rapid development of terahertz (THz) technology in recent years, many new applications have emerged [1]. THz frequency selective surfaces (FSSs) are widely used as important components in these applications [3–9]. In most of the THz research, metamaterial concept is adopted to develop frequency selective surface (FSS), absorbers, polarization converters etc. Three-dimensional (3D) micromachined switches have gained attention in recent years to develop waveguide-based switches, filters, phase shifters etc. 3D Micromachining offers a number of advantages for the fabrication of waveguide components, which become particularly beneficial when approaching terahertz frequencies. The ability to implement small feature sizes with accurate tolerances allows for the integration of components of complex geometries [10]. The accurate tolerances, when combined with volume batch processing, result in high product uniformity and low fabrication costs. Micromachining also makes it possible to achieve low surface roughness and near-ideal metallic bonding, reducing the insertion loss of a waveguide and allowing for the use of H-plane split designs. H-plane split waveguides are less sensitive to misalignment than E-plane split waveguides, simplifying waveguide assembly. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 S. K. Koul and S. Dey, Micromachined Circuits and Devices, Lecture Notes in Electrical Engineering 859, https://doi.org/10.1007/978-981-16-9443-1_11

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This Chapter presents a quick tour on micromachined devices and circuits in the THz regime.

11.2 Micromachined Metamaterial Based Devices in THz Regime Metamaterial is a material engineered to offer properties that are not found in natural materials. They are made from assemblies of multiple elements realized using composite materials such as metals and plastics. The materials are usually arranged in repeating patterns, at scales that are smaller than the wavelengths of the phenomena they influence. Metamaterials derive their properties not from the properties of the base materials, but from their newly designed structures. Their precise shape, geometry, size, orientation, and arrangement gives them their smart properties capable of manipulating electromagnetic waves: by blocking, absorbing, enhancing, or bending waves, to achieve benefits that go beyond what is possible with conventional materials. Potential applications of metamaterials are diverse and include optical filters, medical devices, remote aerospace applications, sensor detection and infrastructure monitoring, smart solar power management, crowd control, radome, highfrequency battlefield communication, lenses for high-gain antennas, improved ultrasonic sensors, and even shielding structures from earthquakes. Metamaterials offer the potential to create super lenses. Such a lens could allow imaging below the diffraction limit that is the minimum resolution that can be achieved by conventional glass lenses. A form of ‘invisibility’ was demonstrated using gradient-index materials. Acoustic and seismic metamaterials are also potential research areas. Terahertz (THz) radiation (also known as sub-millimetre wave radiation, THz waves, tremendously high frequency (THF), T-rays, T-waves, T-light, T-lux or THz (consists of electromagnetic waves within the ITU-designated band of frequencies from 0.3 to 3 THz), although the upper boundary is somewhat arbitrary and is considered by some sources as 30 THz. One terahertz is 1012 Hz or 1000 GHz. Wavelengths of radiation in the THz band ranges from 1 to 0.1 mm. Note that, terahertz radiation begins at a wavelength of around one millimetre and proceeds into shorter wavelengths, it is sometimes known as the sub-millimetre band, especially in astronomy.

11.2.1 Micromachined Metamaterial Based Frequency Selective Surface at THz Frequency selective surface (FSS) is typically a 2D layered surface, composed of multiple layers of metal and dielectric substrate. As the name suggests, a FSS selects

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specific frequency regions in the EM spectra of the incident wave, for transmission, or rejection, depending on the function for which the FSS is deployed. The metal surface is typically a periodic surface, repeating in two directions, creating the required 2D structure. The unit cell of an FSS, the basic unit that repeats to generate the surface, is designed according to the requirements on the transmission or rejection spectra. A frequency selective surface (FSS) based on hexagon substrate integrated waveguide (HSIW) technology is proposed in [11] and designed at the center frequency of 140 GHz. The periodic element comprises a HSIW cavity, and two circular slots etched on the top and bottom conductor claddings of the cavity. Based on the hexagon cavity, this type of FSS has a better polarization stability and a closer element arrangement compared with square cavity FSS and circular cavity FSS, respectively. Besides, circular slots are better than polygonal slots which have round corners at their corners when fabricated using normal printed circuit board process. Thus, the HSIW FSS can achieve a good and stable performance at terahertz band. The proposed structure is fabricated, and the measured result has a good agreement with the simulated one. The device photographs and its experimental responses can be found in [11]. A multiband frequency-selective surface (FSS) device is proposed in [12] with an irregular electromagnetic structure that has five resonance peaks in the THz regime. This compact asymmetric structure utilizes all components efficiently. Different modes, including LC and quasi-quadrupole resonances, are also induced in each unit cell. Simulation studies indicate that each of the five resonance peaks has independent characteristics with different electric field and surface current distributions. This multiband FSS provides an alternative way to design THz multiband filters, modulators, absorbers, and sensors at small planar dimensions. The Schematics of the proposed FSS structure is shown in Fig. 11.1. The performance of the FSS is checked up to 1.2 THz, [12]. Fabrication of the FSS begins with patterning of a negative photoresist AZ5214 by photo-etching on a Si substrate. A 300 nm Al film was then deposited on the photoresist, followed by a lift-off process. Fig. 11.1 The Schematics of the FSS structure [12]. Reproduced with permission from the IEEE

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A new class of FSS for THz applications is proposed in [13] and investigated both numerically and experimentally. A periodic FSS array of cross shaped apertures is patterned on aluminium, deposited on thin foils of the low-loss cyclo-olefin polymer Zeonor. Apart from the fundamental filtering response of the FSS elements, authors also observe very narrow-linewidth peaks with high transmittance, associated with guided-mode resonances in the dielectric substrate. The effect of the filter’s geometrical parameters on its performance is systematically studied via finite element method simulation and confirmed by time domain spectroscopy characterization of the fabricated samples [13]. A THz bandpass FSS with high selectivity is proposed in [14]. The proposed three-layered FSS filter consists of identical tri-pole resonators located on the top and bottom layers and rectangular coupling apertures etched on a conducting plane in between. Multiple signal paths exist between the top and bottom resonators through the coupling apertures. Therefore, this aperture-coupled resonator (ACR) structure exhibits a narrow bandpass response, and two transmission zeros appear near the skirts of the passband. These zero points considerably improve the frequency selectivity and suppress the sidebands of the FSS. For demonstration, a microfabrication process was used to realize an ACR FSS at 850 GHz. The frequency performance of the ACR FSS in terms of insertion loss is investigated numerically and experimentally. The measured transmission responses at normal incidence based on time-domain as well as frequency domain measurements agree well with the simulated one, thus verifying the proposed design. Furthermore, the frequency-domain measurement reveals that the FSS response remains stable at various incident angles for both TE and TM polarizations. The design schematic of the proposed THz ACR FSS is shown in Fig. 11.2 for better clarity. A novel frequency-selective surface (FSS) with polarization selection and dual band polarization conversion characteristics is proposed in [15] for THz applications. The FSS is composed of two layers of metallic periodic arrays separated by a polymer dielectric spacer. Perspective view of the proposed FSS schematic is depicted in Fig. 11.3. The top and bottom arrays provide bandpass and bandstop characteristics for TE- and TM-polarized incidences, respectively. Geometrical parameters of the top and bottom arrays are tuned such that the phase differences of the TE and TM transmissions at the lower (f 1 ) and upper (f 2 ) crossover frequency points are −90° and +90°, respectively. Therefore, for normal incidence, a 45° linearly polarized incident wave is converted into a right-handed circularly polarized and left-handed circularly polarized transmitted wave at f 1 and f 2 , respectively. Equivalent circuit models are established to explain the operation principle of the proposed FSS [15]. A prototype is fabricated using micromachining with its transmission characteristics, namely, polarization selectivity and dual-band polarization conversion, validated by time-domain and frequency-domain measurements [15]. The recent development of some high-power THz vacuum electronic devices calls for the application of space filters such as FSSs and polarization dividers. The work reported in [16] presents the comparative study of two types of FSSs for a THz gyro multiplier output system, one with high-pass characteristic while the other one with low-pass functionality. Both FSSs are designed, fabricated, and experimentally tested

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Fig. 11.2 Proposed THz ACR FSS, a The 3-D view of the FSS, b Side view of the FSS, c The 3-D view of the FSS unit cell [14]. Reproduced with permission from the IEEE

between 200 and 1600 GHz to verify their capability of separating the dual-frequency output from the gyro multiplier. The high-power operation capability of the FSSs is also characterized by taking both the corona discharge and volumetric breakdown into consideration at the frequencies of interest. Based on the comparative study of the performance, the fabrication challenge, and the high-power capability between the two FSSs, a generalized conclusion is given in [16] regarding the choice of the FSSs for high-power THz applications. More details can be found in [16]. The 3-D FSS is proposed for THz applications, [17]. The simplest form of 3-D FSS is considered in this work. It consists of a two-dimensional periodic array of non-resonant apertures, which are etched out of two conducting surfaces of a printed circuit board (PCB). Quality factor of this FSS can be easily controlled by the size of non-resonant coupling apertures. Unlike other reported THz FSS designs, the proposed structure does not require a silicon substrate and microfabrication chamber. Instead, it can be fabricated on a commonly available double-sided copper PCB, through a low-cost fabrication method. Prospective view of the proposed FSS is depicted in Fig. 11.4. A tunable multiband THz frequency selective surface (FSS) is developed based on hybrid metal–graphene structures in [18]. The tunability characteristics are realized by inserting graphene strips between metal patches. The proposed FSS is studied based on the equivalent circuit model, which is validated against the simulation results using numerical methods. It is shown that the proposed hybrid structure has

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Fig. 11.3 Topology of the proposed FSS, a perspective view of the proposed FSS (2 × 2-unit cells), Unit cells on b top and c bottom metallic layers [15]. Reproduced with permission from the IEEE

good performance in terms of bandwidth, gain, and tunability, and it is easy to be built as a potential competitor for THz applications, [18]. In addition, a nanofabricated FSS was reported in [19] and it shows performances in the near infrared region (150–300 THz) with a typical unit-cell electrical size of one fifth of the free-space wavelength and a remarkable resonance-anti-resonance contrast of up to 35 dB.

11.2.2 Micromachined Metamaterial Based Absorbers at THz Electromagnetic absorbers have aroused outstanding interest due to their range of application which spans from the microwave to optical frequency regime passing through THz spectrum. At microwaves they are employed as electrically thin layers

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Fig. 11.4 Prospective view and unit-cell details of our proposed FSS, [17]. Reproduced with permission from the IEEE

to reduce the radar signature of targets, for power imaging purposes, to improve the electromagnetic compatibility of electronic devices or even as chip less Radio Frequency Identification (RFID) tags. In the THz range they are used in photodetectors or microbolometers and phase modulators. Several modifications of the designs for absorbers have been proposed over the years because of the disadvantage of thickness. Recent introduction of metamaterials has provided a new perspective on the electromagnetic absorbers and led to the development of novel design techniques for radar absorbing materials. Metamaterial absorbers are so popular mainly due to their ultra-thin profile. A broadband THz absorber with an array of graphene dielectric multi-layered frustum pyramids on a metal sheet is proposed in [20]. The multi-layered graphenedielectric structure can be considered an effectively homogenous metamaterial with a hyperbolic dispersion and anisotropic permittivity. High absorption with an extremely wide bandwidth, from 8 to 100 THz, is observed. The schematic diagram of the suggested graphene-based metamaterial absorber (GMA) is shown in Fig. 11.5a, which consists of an array of graphene-dielectric multi-layered frustum pyramids with a homogeneous metal film as the substrate to block the transmission. A unit cell of the GMA is shown in Fig. 11.5b. The composite metamaterial is made by alternately stacking graphene sheets and dielectric layers. The pyramid form is then tapered linearly (through some etching process) from the top to the bottom. A four-band and polarization-insensitive terahertz metamaterial absorber formed by four square metallic rings and a metallic ground plane separated by a dielectric layer is proposed in [21]. It is found that the structure has four distinctive absorption bands whose peaks are over 97% on average. The mechanism of the four-band absorber is attributed to the overlapping of four resonance frequencies, and the mechanism of the absorption is investigated by the distributions of the electric field. In particular, the frequency of each absorption peak can be flexibly controlled by varying the size of the corresponding metallic ring. The proposed concept is applicable to

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Fig. 11.5 a Schematic diagram for a line array of graphene-dielectric multi-layered frustum pyramids backed with a homogeneous metal film, b a unit cell of the GMA, with P = 10 µm, wb = 8 µm, wt = 1 µm, t d = 400 nm and T = 6 µm. Light of TM polarization is incident along -z direction [20]. Reproduced with permission from the IEEE

other types of absorber structures and can be readily scaled up to the structures that are working in the microwave frequency range. Moreover, the characteristic of the design can be used to design a five-band metamaterial absorber by adding one more metallic ring. The proposed absorber has potential applications in detection, imaging, and stealth technology. The design schematic and more details can be found in [21]. A broadband terahertz (THz) metamaterial absorber (MMA) using asymmetric split ring resonator (ASR) was designed, fabricated, characterized, and reported in [22]. The design schematic of the proposed absorber is depicted in Fig. 11.6. By breaking the symmetry of a split ring resonator, two asymmetric resonances are excited from a dipole resonance, which enhance both the absorption and Q-factor. With the integration of four different ASRs into one unit cell, a broadband absorber experimentally obtained a 0.82 THz bandwidth with absorptivity of more than 0.9, which is 3.4 times as wide as the 0.24 THz bandwidth of the symmetric dipole

Fig. 11.6 Schematic diagram of a perspective view and b top view of the unit cell of the MMA [22]. Reproduced with permission from the IEEE

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peak. The broadband ASR MAAs were fabricated with microfabrication techniques. First, a 20/80 nm thick Cr/Au film was sputtered on the 525 µm single polished Si substrate as the ground plane. Then, a dielectric spacer of SiO layer was deposited by plasma-enhanced chemical vapor deposition (PECVD). Finally, Cr/Au resonator arrays were sputtered with layer thickness of 20/80 nm and patterned by a standard lift-off process. The fabricated MAs were characterized by a Fourier transform infrared (FTIR) spectrometer (Bruker IFS125HR) extended to THz range by a mercury vapor source. Radiation from 1.0 to 7.0 THz is sampled with a resolution of 7.6 GHz. The proposed broadband absorber has great application potential in the THz spectroscopy, imaging, and sensing. The quest of novel materials and structures to design an efficient absorber for realizing wave trapping and absorption at terahertz (THz) frequencies is an open topic. But the design of a thin, wideband, and tunable THz absorber is still an arduous job. A hybrid THz metamaterial absorber integrated with a cascaded graphene FSS, with ultra-high absorbance over a wide frequency range is designed using an analytical equivalent circuit model in [23]. Such an approach provides a feasible way to optimize the device by interrelating the effective electromagnetic and circuit parameters with the unit cell dimensions of FSS. Systematic study and critical analysis over a wide range of device parameters including graphene chemical potential and FSS design variables is demonstrated. A five-layer hybrid THz-MMA structure has been proposed here in [23], as shown in Fig. 11.7a along with a corresponding transmission line model (TLM) as depicted in Fig. 11.7b. Here, graphene monolayer based FSSs, separated by a thin layer of polyimide, were embedded into the dielectric substrate (relative permittivity εrl of 5) backed with a ground plane. Two types of graphene monolayer FSS, i.e., graphene square patch array, and graphene square aperture array, have been considered for the design of a tunable THz-MMA. The schematic diagrams of proposed FSSs with corresponding equivalent circuit (EC) diagrams are presented in Fig. 11.8a–d, respectively. The design variables for square patch FSS (SP-FSS) are g, and P. Here, g is the gap between the square patches, and P is the periodicity of the SP-FSS unit cell. A peak dip in reflection coefficient of −30.27 dB is observed at 2.94 THz for an optimal device with a chemical potential (μc ) of 0.38 eV (μc1 ), and 0.25 eV (μc2 ) in the

Fig. 11.7 Proposed five layered THz-MMA. a Schematic device structure, and b TLM [23], licensed under CC BY-ND 2.0

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Fig. 11.8 Proposed FSS geometries and corresponding ECs. a SP-FSS. b EC of SP-FSS. c SA-FSS, and d EC of SA-FSS, by [23], licensed under CC BY-ND 2.0

range of 0.1–4.0 THz. The cascaded FSS configuration results in the unique antireflection-based absorption phenomena, which is responsible for the achievement of −10 dB absorption bandwidth of 2.34 THz (0.85–3.19 THz). In addition, the frequency dependent effective permittivity, permeability, and impedance is extracted using reflection data, to understand the device physics. Such ultra-thin and broadband absorbing device architecture may confer potential application perspectives in THz sensing, imaging, and detection. A THz metasurface, with the unit cells consisting of double metal loops and a metallic backed film on both sides of the dielectric layer, is investigated to find the connection between reflectivity and pattern geometry in [24]. An equivalent circuit of the unit cell is also given to ease the analysis and prediction of the reflection coefficient and to provide a guideline for tuning the impedance of the metasurface. An absorber and a reflect array, as two typical applications of the metasurface that need low and high reflection efficiency, respectively, are demonstrated at ∼0.9 THz by varying dimensional parameters of the metal loops. The absorber can reach 0.102THz bandwidth for reflectivity below −10 dB under normal incidence and shows independence on polarization and incident angle, while the reflect array antenna gain can reach 22 dBi at 0.875 THz. Finally, an absorber and a reflective surface prototype were fabricated and measured [24]. A broadband switchable metamaterial absorber is investigated in [25]. The switchable response is achieved by utilizing the phase transition property of vanadium dioxide (VO2 ) that is thermally controlled. A novel band extension scheme is presented in this work by introducing capacitive coupling effects among the resonators. By exploiting the coupling effect, near octave bandwidth is achieved when referred to an absorptivity of 90%. The proposed switchable broadband absorber is composed of a composite resonant structure made of Tantalum Nitride (TN) on a multi-layer dielectric plate backed with a gold ground plane. The composite resonant structure consists of a crisscross structure and four-square patches with the thickness of 0.021 mm, while the dielectric plate is made of three layers: (i) foam layer, (ii) VO2 layer, (iii) SiO2 layer with the thickness of 0.12 mm, 0.008 mm and 0.024 mm, respectively. The foam film is an important layer here that serves as the effective dielectric layer. The VO2 film is responsible for switching the two operational states.

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Fig. 11.9 Schematic of unit cell of the reported broadband absorber in [25], licensed under CC BY-ND 2.0

A switchable broadband absorber is developed by employing the phase change material, VO2 . At the room temperature (25 °C), the achieved frequency band referring to an absorptivity over 90% is from 0.32 to 0.56 THz. But when temperature rises to the phase-transition point (68 °C) of VO2 , an absorption frequency band from 0.356 to 0.682 THz is observed. Moreover, the studied absorber is insensitive to the polarization direction of incident wave and exhibits good absorption under a large incident angle up to 50°. The design schematic is shown in Fig. 11.9. With optimal designs, the geometric dimensions of each unit cell are found to be: a = 0.5 mm, b = 0.048 mm, c = 0.274 mm, d = 0.24 mm, w1 = 0.012 mm, w2 = 0.024 mm. The broadband and switchable properties are discussed in detail based on the resonant structure, surface current distributions, electric field distributions and impedance matching. It is noted the presented method can be scaled to another adjacent THz frequency band. The frequency of reported absorbers is usually fixed and operates over a limited bandwidth, which greatly hampers their practical applications. Active or dynamic control over their resonance frequency is very often desirable. A novel approach for efficient tuning of the frequency of the absorber by shifting the movable part of the composite structure composed of the fixed and movable parts is proposed in [26]. Other different types of metamaterial-based structures are also reported in the literature. It includes polarization converters (linear to linear and linear to circular) [27, 28], different types of THz filters, etc., [29, 30].

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11.3 2.5D-3D Micromachined Devices at Sub-Millimetre Wave Micromachining offers several advantages for the fabrication of waveguide components, which become particularly beneficial when approaching terahertz frequencies. The ability to implement small feature sizes with accurate tolerances allows for the integration of components of complex geometries. Accurate tolerances, when combined with volume batch processing, result in high product uniformity and low fabrication costs. Micromachining also makes it possible to achieve low surface roughness and near-ideal metallic bonding, reducing the insertion loss of a waveguide and allowing for the use of H-plane split designs. H-plane split waveguides are less sensitive to misalignment than E-plane split waveguides, simplifying waveguide assembly. Three different WR-3 band (220–325 GHz) circuits, namely a WR-3 band straight through waveguide, a bandpass filter and a dual-band filter are demonstrated in [31]. For the measurements, a conventionally precision machined metal block is used for the WR-3 band waveguide and the bandpass filter to achieve good calibration and accurate interconnection with standard waveguide flanges, whereas, for the dualband filter, two back-to-back right-angle bends are added to achieve accurate, reliable waveguide interconnection without using the metal block. A measured average insertion loss of 0.03 dB/mm has been achieved for the 14.97 mm long straight through waveguide. This is comparable to the loss of around 0.02 dB/mm for a standard metal waveguide at this frequency. The fifth-order waveguide filter exhibits an 8% 3 dB bandwidth at the centre frequency of around 300 GHz. The minimum passband insertion loss measured was around 1 dB and the return loss was better than 10 dB throughout the passband. The filter results showed a notable improvement over those obtained from the separate SU8 layer technique that was also used to make the same devices for comparison. To further demonstrate the advantages of the new two-layer SU8 micromachining technique, the dual-band filter included isolated regions in the waveguide channels that would have not been possible for micromachining using the previous separate single layer technique. The performance of the micromachined dual band filter is excellent in terms of very low insertion losses on both passbands. Interested reader can find more related information in [31]. A sub-millimetre wave 500–750 GHz micromachined waveguide switch based on a reconfigurable surface to block/unblock the wave propagation through the waveguide is reported in [32]. The waveguide switch reported in this work [32], comprises a single-pole single-throw design utilizing a micromachined reconfigurable surface inserted in the cross-sectional plane of the rectangular waveguide, as shown in Fig. 11.10. The use of the MEMS-reconfigurable surface for blocking/unblocking the wave propagation into a waveguide has been reported by Baghchehsaraei et al. [33] and Baghchehsaraei and Oberhammer [34] for V-band. Figure 11.10b shows the two states of the micromachined waveguide switch. In the non-blocking state, the gap between the contact cantilevers allows for the electromagnetic wave to propagate freely through the MEMS-reconfigurable surface

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Fig. 11.10 Sub-millimetre-wave MEMS waveguide switch design using a MEMS-reconfigurable surface: a 3-D illustration of the cross section and b nonblocking and blocking state of the MEMS waveguide switch [32]. Reproduced with permission from the IEEE

and in the blocking state, the movable contact cantilevers are moved to contact the fixed contact cantilevers to form a series of vertical columns which short circuit the electric field lines of the TE10 mode blocking the electromagnetic wave propagation. The overall switch performance is influenced by the number of horizontal bars (rows), the number of vertical contact cantilevers (columns), and the overlap of the contact cantilevers. A detailed design parametric study is carried out in this work to determine the best combination of the number of horizontal bars and vertical columns of the MEMS-reconfigurable surface for achieving a low insertion loss in the non-blocking state and a high isolation in the blocking state for the 500–750 GHz band [32]. The performance variation based on these model parameters are simulated using fullwave simulations. The simulation results show that the isolation in the blocking state improves, while the insertion loss in the non-blocking state degrades with increasing number of vertical columns [32]. The number of horizontal bars has a minimal impact on the isolation performance in the blocking state since the horizontal bars are perpendicular to the short-circuited electric field lines. In the nonblocking state of the switch, the insertion loss is significantly higher when three horizontal bars are

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used instead of four or five horizontal bars. This is an indirect effect resulting from the larger contact cantilever length used for a switch design with lower number of horizontal bars to maintain the same contact overlap. The longer contact cantilevers adversely affect the waveguide electric field lines in the non-blocking sate since the contact cantilevers are parallel to the field lines. The degradation of the insertion loss with increasing length of the contact cantilevers is also observed when the contact overlap is increased from 2 to 8 µm. In a nutshell, the electromagnetic wave can pass freely through the MEMS reconfigurable surface in the non-blocking state, while in the blocking state, the electric field lines of the TE10 mode are short-circuited that blocks the wave propagation through a WM-380 (WR-1.5) waveguide [32]. This design parametric study makes it clear that for the optimal switch design, the selection of the number of horizontal bars and vertical columns requires a compromise between insertion loss, isolation, and the return loss. Figure 11.11 illustrates a SEM image of a single MEMS waveguide switch chip showing the MEMS-reconfigurable surface, the comb-drive actuators, and the mechanical springs. The total dimensions of the MEMS waveguide switch elements are 1.6 mm × 1.5 mm. Measurements of the switch prototypes show a superior RF performance of the capacitive-contact switch. The measured isolation of the capacitive contact switch designed with an 8 µm contact overlap is 19–24 dB and the

Fig. 11.11 Close-up SEM image of the fabricated MEMS waveguide switch chip with MEMSreconfigurable surface and the comb-drive actuators [32]. Reprinted with permission from the IEEE

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measured insertion loss in the non-blocking state is 2.5–3 dB from 500 to 750 GHz including a 400 µm long micromachined waveguide section [32]. Finally, reliability measurements in an uncontrolled laboratory environment on a comb-drive actuator with an actuation voltage of 28 V showed no degradation in the functioning of the actuator over one hundred million cycles. More details can be found in [32]. In addition, almost similar concept was adopted in [35] to develop a 3.3-bit micromachined phase shifter integrated in micromachined waveguide at submillimetrewave frequencies. The phase shifter uses MEMS-reconfigurable surfaces to individually block/unblock the E-plane stubs from the micromachined waveguide. Each MEMS-reconfigurable surface is designed so that in the nonblocking state, it allows the electromagnetic wave to pass freely through it into the stub, while in the blocking state, it serves as the roof of the main waveguide and blocks the wave propagation into the stub. The phase-shifter design comprises three micromachined chips that are mounted in the H-plane cuts of the rectangular waveguide [35]. Experimental results of the first device prototypes show that the MEMS- reconfigurable phase shifter has a linear phase shift of 20° in ten discrete steps (3.3 bits). The measured insertion loss is better than 3 dB, of which only 0.5–1.5 dB is attributed to the MEMS surfaces and switched stubs, and the measured return loss is better than 15 dB in the design frequency band of 500–550 GHz. It is also stated that a major part of the insertion loss is attributed to misalignment and assembly uncertainties of the micromachined chips and the waveguide flanges, shown by simulations and reproducibility measurements in [35]. The proposed micromachined reconfigurable phase shifter is also operated in an analog tuning mode for high phase resolution. More details can be found in [35] for better understandings. However, it is difficult to apply SU-8 uniformly and stabilize it. Therefore, deep reactive-ion etching (DRIE) of trenches in silicon with subsequent metallization is the most common fabrication technique for micromachined waveguides. In [36], an additional oxidation and etch-back step was added to decrease the surface roughness, reducing the insertion loss for an E-plane split waveguide to 0.05–0.07 dB/mm. A novel cavity-backed coplanar waveguide (CBCPW) to rectangular waveguide transition having a 2.5D geometry compatible with micromachining fabrication technique is presented in [37]. This transition makes use of a short-circuited pin (as opposed to a suspended probe) in conjunction with resonant sections of CPW line over the broad wall of a reduced height waveguide segment to facilitate impedance matching. Although the bandwidth of this transition is smaller than the standard suspended probe transitions, its fabrication at sub-millimetre-wave and terahertz bands is rather straightforward and does not require assembly of many small parts with very high precision. The design procedure starts with an equivalent circuit model which is then fine-tuned using a full-wave approach. A silicon micromachining process for the fabrication of the proposed transition is also presented in [37]. To validate the design and demonstrate the feasibility of the fabrication process, a prototype transition operating at 240 GHz is fabricated and tested. S-parameter measurement of the transition is performed using a dual source PNA-X with OML frequency extenders, as shown in Fig. 11.12.

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Fig. 11.12 WR-3 (220–325 GHz) measurement setup. It consists of a dual source PNA-X with OML frequency extenders connected to GSG probes to excite the CPW [37]. Reproduced with permission from the IEEE

It is shown that a back-to-back transition prototype at 240 GHz provides less than 1 dB of insertion loss over more that 17% fractional bandwidth [37]. It is also shown that the measured S-parameters of the back-to-back transition are in good agreement with the simulation results. The microfabrication process and associated tolerances allows for scaling the dimensions and frequency of operation to THz frequencies. Interested reader can also refer to references [38–40] for more up-to-date survey on the THz micromachined devices.

11.4 Conclusions This Chapter presents a brief survey on most recent state-of-the-art micromachined devices at THz regime. THz micromachined metamaterial-based devices are discussed in the initial phase. There is a growing interest in developing metamaterialbased designs in the THz regime. The interest is due to the possibility of metamaterials being able to exhibit properties not found in natural materials (e.g., negative refractive index). This Chapter explores various designs using metamaterials to realize conventional devices such as absorbers, frequency selective surfaces, polarization

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converters and filters. To understand the full variety of applications that are enabled by metamaterials, one needs to explore the literature further and invent ways to apply it to improve designs and find applications in areas such as imaging. The later part of this Chapter describes micromachined devices like waveguide-based switches, phase shifters, etc. using 2.D–3D micromachining process. A submillimetre-wave 500–750 GHz MEMS waveguide switch comprising a MEMS-reconfigurable surface is discussed. In addition, a 3.3-bit phase shifter operating over the frequency band of 500–550 GHz is also discussed. Other different types of micromachined structures like 2.5D CBCPW to rectangular waveguide transition at 240 GHz is reported in this Chapter. Readers may go through the references for more information on this exciting field of micromachining at THz regime.

References 1. Kemp MC, Taday PF, Cole BE, Cluff JA, Fitzgerald AJ, Tribe WR (2003) Security applications of terahertz technology. Proc SPIE 5070:44–52 2. Stanec JR, Smith CH, Barker NS (2010) Integrating micromachined circuits into submillimetre systems. In: European Microwave Conference 2010, pp 53–56 3. Biber S, Bozzi M, Gunther O, Perregrini L, Schmidt LP (2006) Design and testing of frequency-selective surfaces on silicon substrates for submillimeter-wave applications. IEEE Trans Antennas Propag 54(9):2638–2645 4. Lin XQ, Cui TJ, Fan Y, Liu X (2009) Frequency selective surface designed using electric resonant structures in terahertz frequency bands. J Electromagn Waves Appl 23:21–29 5. Sanphuang V, Yeo WG, Volakis JL, Nahar NK (2015) THz transparent metamaterials for enhanced spectroscopic and imaging measurements. IEEE Trans THz Sci Technol 5(1):117– 123 6. Dickie R, Cahill R, Fusco V, Gamble HS, Mitchell N (2011) THz frequency selective surface filters for earth observation remote sensing instruments. IEEE Trans THz Sci Technol 1(2):450– 461 7. Poojali J, Ray S, Pesala B, Venkata KC, Arunachalam K (2017) Quadband polarizationinsensitive millimeter-wave frequency selective surface for remote sensing. IEEE Antennas Wirel Propag Lett 16:1796–1799 8. Sushko O, Pigeon M, Donnan RS, Kreouzis T, Parini CG, Dubrovka R (2017) Comparative study of sub-THz FSS filters fabricated by inkjet printing, microprecision material printing, and photolithography. IEEE Trans THz Sci Technol 7(2):184–190 9. Munk BA (2000) Frequency selective surfaces. Wiley, New York, NY, USA 10. Kerr AR, Litton C, Petencin G, Koller D, Shannon M (2009) Loss of gold plated waveguides at 210–280 GHz. ALMA, ALMA Memo 585 11. Wang HB, Cheng YJ (2018) 140 GHz frequency selective surface based on hexagon substrate integrated waveguide cavity using normal PCB process. IEEE Antennas Wirel Propag Lett 17(3):489–492 12. Qiao S, Zhang Y, Zhao Y, Zhou Y, Liang S, Yang Z (2016) multiband frequency-selective surface with five resonance peaks in terahertz band. IEEE Trans THz Sci Technol 6(2) 13. Ferraro A, Zografopoulos DC, Caputo R, Beccherelli R (2017) Broad- and narrow-line terahertz filtering in frequency-selective surfaces patterned on thin low-loss polymer substrates. IEEE J Selec Top Quantum Electron 23(4) 14. Wang DS, Chen BJ, Chan CH (2016) High-selectivity bandpass frequency-selective surface in terahertz band. IEEE Trans THz Sci Technol 6(2)

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Appendix A

Design Data on Micromachined Transmission Lines and Discontinuities

See Tables A.1, A.2, A.3, A.4, A.5, A.6, A.7, A.8, A.9, A.10, A.11, A.12, A.13, A.14, A.15, A.16, A.17, A.18, A.19, A.20, A.21, A.22, A.23, A.24, A.25, A.26, A.27, A.28, A.29, A.30, A.31, A.32, A.33, A.34, A.35, A.36, A.37, A.38, A.39, A.40 and A.41. Table A.1 S-parameters of membrane microstrip series gap; w = 1300 µm S. Freq Gap = 10 µm No (GHz) S 11 Mag

Angle

Gap = 20 µm S 21 Mag

S 11 Angle

Mag

S 21 Angle

Mag

Angle

1

26

0.5072 −60.1495 0.8611 29.7458 0.6111 −53.4099 0.7908 36.4900

2

27

0.4930 −61.1190 0.8694 28.7765 0.5966 −54.4991 0.8018 35.4018

3

28

0.4793 −62.0382 0.8770 27.8573 0.5825 −55.5406 0.8121 34.3610

4

29

0.4663 −62.9109 0.8841 26.9845 0.5689 −56.5377 0.8218 33.3647

5

30

0.4538 −63.7403 0.8905 26.1548 0.5557 −57.4927 0.8308 32.4103

6

31

0.4419 −64.5297 0.8965 25.3651 0.5429 −58.4084 0.8392 31.4952

7

32

0.4304 −65.2819 0.9021 24.6125 0.5306 −59.2868 0.8470 30.6173

8

33

0.4195 −65.9994 0.9073 23.8943 0.5187 −60.1305 0.8544 29.7741

9

34

0.4090 −66.6849 0.9121 23.2083 0.5071 −60.9412 0.8613 28.9637

10

35

0.3989 −67.3404 0.9166 22.5521 0.4959 −61.7211 0.8678 28.1841

11

36

0.3891 −67.9680 0.9207 21.9237 0.4851 −62.4720 0.8739 27.4334

12

37

0.3798 −68.5695 0.9246 21.3213 0.4746 −63.1955 0.8797 26.7101

13

38

0.3708 −69.1467 0.9283 20.7430 0.4645 −63.8933 0.8851 26.0123

14

39

0.3622 −69.7013 0.9317 20.1873 0.4546 −64.5671 0.8902 25.3387

15

40

0.3538 −70.2349 0.9349 19.6528 0.4451 −65.2181 0.8951 24.6878

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 S. K. Koul and S. Dey, Micromachined Circuits and Devices, Lecture Notes in Electrical Engineering 859, https://doi.org/10.1007/978-981-16-9443-1

347

348

Appendix A: Design Data on Micromachined Transmission Lines and Discontinuities

Table A.2 S-parameters of membrane microstrip series gap; w = 1300 µm S. Freq Gap = 30 µm No (GHz) S 11 Mag

Angle

Gap = 40 µm S 21 Mag

S 11 Angle

Mag

S 21 Angle

Mag

Angle

1

26

0.6864 −48.1381 0.7264 41.7884 0.7446 −43.6931 0.6666 46.2112

2

27

0.6725 −49.2817 0.7393 40.6465 0.7318 −44.8495 0.6806 45.0558

3

28

0.6589 −50.3839 0.7515 39.5461 0.7192 −45.9711 0.6940 43.9351

4

29

0.6456 −51.4464 0.7630 38.4852 0.7067 −47.0590 0.7067 42.8480

5

30

0.6326 −52.4711 0.7738 37.4620 0.6945 −48.1145 0.7187 41.7931

6

31

0.6199 −53.4600 0.7840 36.4746 0.6824 −49.1388 0.7302 40.7695

7

32

0.6075 −54.4148 0.7936 35.5212 0.6705 −50.1332 0.7412 39.7756

8

33

0.5954 −55.3370 0.8028 34.6002 0.6588 −51.0988 0.7516 38.8105

9

34

0.5836 −56.2284 0.8114 33.7101 0.6473 −52.0369 0.7615 37.8728

10

35

0.5721 −57.0905 0.8196 32.8491 0.6360 −52.9486 0.7710 36.9614

11

36

0.5609 −57.9248 0.8273 32.0159 0.6249 −53.8351 0.7800 36.0753

12

37

0.5500 −58.7329 0.8346 31.2090 0.6141 −54.6975 0.7887 35.2131

13

38

0.5393 −59.5160 0.8416 30.4269 0.6034 −55.5369 0.7969 34.3740

14

39

0.5289 −60.2754 0.8482 29.6686 0.5929 −56.3543 0.8047 33.5567

15

40

0.5187 −61.0124 0.8544 28.9326 0.5826 −57.1507 0.8122 32.7604

Table A.3 S-parameters of membrane microstrip series gap; w = 1300 µm S. No

Freq Gap = 50 µm (GHz) S 11

S 21

Mag

Mag

Angle

Gap = 60 µm S 11 Angle

Mag

S 21 Angle

Mag

Angle

1.

26

0.7814 −40.8545 0.6230 49.0353 0.8164 −37.8864 0.5764 52.0527

2.

27

0.7697 −42.0071 0.6375 47.8833 0.8059 −39.0220 0.5911 50.9192

3.

28

0.7580 −43.1299 0.6513 46.7611 0.7953 −40.1330 0.6052 49.8101

4.

29

0.7465 −44.2237 0.6646 45.6678 0.7848 −41.2200 0.6189 48.7250

5.

30

0.7350 −45.2892 0.6773 44.6027 0.7743 −42.2835 0.6320 47.6634

6.

31

0.7236 −46.3276 0.6894 43.5649 0.7638 −43.3240 0.6446 46.6246

7.

32

0.7124 −47.3395 0.7011 42.5534 0.7533 −44.3423 0.6568 45.6079

8.

33

0.7012 −48.3261 0.7122 41.5673 0.7430 −45.3389 0.6686 44.6130

9.

34

0.6902 −49.2881 0.7229 40.6057 0.7326 −46.3144 0.6799 43.6389

10. 35

0.6794 −50.2266 0.7331 39.6677 0.7224 −47.2696 0.6908 42.6851

11. 36

0.6686 −51.1425 0.7429 38.7524 0.7122 −48.2052 0.7013 41.7509

12. 37

0.6580 −52.0366 0.7523 37.8588 0.7021 −49.1217 0.7114 40.8357

13. 38

0.6476 −52.9098 0.7614 36.9861 0.6921 −50.0200 0.7212 39.9387

14. 39

0.6373 −53.7631 0.7700 36.1335 0.6821 −50.9006 0.7306 39.0593

15. 40

0.6271 −54.5972 0.7783 35.3001 0.6723 −51.7642 0.7397 38.1969

Appendix A: Design Data on Micromachined Transmission Lines and Discontinuities

349

Table A.4 S-parameters of membrane microstrip series gap; w = 1300 µm S. No

Freq Gap = 70 µm (GHz) S 11

S 21

Mag

Mag

Angle

Gap = 80 µm S 11 Angle

Mag

S 21 Angle

Mag

Angle

1.

26

0.8433 −35.5118 0.5364 54.4331 0.8631 −33.6874 0.5040 56.2119

2.

27

0.8339 −36.6249 0.5510 53.3229 0.8545 −34.7761 0.5185 55.1235

3.

28

0.8243 −37.7178 0.5651 52.2330 0.8458 −35.8477 0.5325 54.0520

4.

29

0.8148 −38.7908 0.5788 51.1628 0.8371 −36.9024 0.5461 52.9973

5.

30

0.8052 −39.8442 0.5921 50.1122 0.8283 −37.9406 0.5594 51.9590

6.

31

0.7956 −40.8785 0.6050 49.0807 0.8195 −38.9624 0.5722 50.9370

7.

32

0.7860 −41.8941 0.6174 48.0679 0.8106 −39.9682 0.5848 49.9308

8.

33

0.7764 −42.8913 0.6295 47.0734 0.8017 −40.9584 0.5969 48.9402

9.

34

0.7668 −43.8709 0.6411 46.0966 0.7927 −41.9332 0.6087 47.9649

10. 35

0.7572 −44.8330 0.6524 45.1372 0.7838 −42.8932 0.6202 47.0044

11. 36

0.7476 −45.7784 0.6634 44.1945 0.7748 −43.8386 0.6314 46.0583

12. 37

0.7381 −46.7076 0.6740 43.2680 0.7659 −44.7699 0.6423 45.1262

13. 38

0.7286 −47.6209 0.6842 42.3574 0.7569 −45.6876 0.6528 44.2077

14. 39

0.7192 −48.5191 0.6942 41.4619 0.7479 −46.5921 0.6631 43.3023

15. 40

0.7098 −49.4026 0.7038 40.5810 0.7390 −47.4838 0.6730 42.4096

Table A.5 S-parameters of membrane microstrip series gap; w = 1300 µm S. Freq Gap = 90 µm No (GHz) S 11 Mag

Angle

Gap = 100 µm S 21 Mag

S 11 Angle

Mag

S 21 Angle

Mag

Angle

1

26

0.8777 −32.3080 0.4781 57.6044 0.8911 −30.9911 0.4527 58.9435

2

27

0.8698 −33.3780 0.4923 56.5357 0.8839 −32.0409 0.4666 57.8960

3

28

0.8618 −34.4334 0.5061 55.4814 0.8766 −33.0787 0.4801 56.8605

4

29

0.8538 −35.4745 0.5196 54.4413 0.8692 −34.1044 0.4934 55.8371

5

30

0.8456 −36.5013 0.5328 53.4155 0.8617 −35.1183 0.5064 54.8254

6

31

0.8374 −37.5143 0.5456 52.4035 0.8541 −36.1205 0.5192 53.8255

7

32

0.8291 −38.5135 0.5581 51.4053 0.8464 −37.1111 0.5316 52.8371

8

33

0.8208 −39.4992 0.5703 50.4204 0.8387 −38.0904 0.5437 51.8601

9

34

0.8124 −40.4718 0.5822 49.4487 0.8309 −39.0586 0.5556 50.8941

10

35

0.8040 −41.4316 0.5938 48.4898 0.8230 −40.0160 0.5673 49.9390

11

36

0.7955 −42.3789 0.6051 47.5434 0.8150 −40.9629 0.5786 48.9945

12

37

0.7870 −43.3140 0.6161 46.6092 0.8070 −41.8996 0.5897 48.0601

13

38

0.7785 −44.2374 0.6269 45.6866 0.7990 −42.8263 0.6006 47.1357

14

39

0.7700 −45.1493 0.6374 44.7755 0.7909 −43.7435 0.6112 46.2210

15

40

0.7614 −46.0504 0.6476 43.8754 0.7828 −44.6514 0.6216 45.3155

350

Appendix A: Design Data on Micromachined Transmission Lines and Discontinuities

Table A.6 S-parameters of membrane microstrip series gap; w = 1300 µm S. No

Freq Gap = 110 µm (GHz) S 11 Mag

Angle

Gap = 120 µm S 21 Mag

S 11 Angle

Mag

S 21 Angle

Mag

Angle

1.

26

0.9033 −29.6494 0.4279 60.2596 0.9133 −28.6778 0.4062 61.2659

2.

27

0.8968 −30.6735 0.4414 59.2365 0.9073 −29.6833 0.4194 60.2623

3.

28

0.8901 −31.6875 0.4547 58.2232 0.9012 −30.6805 0.4323 59.2669

4.

29

0.8833 −32.6916 0.4677 57.2199 0.8950 −31.6692 0.4450 58.2799

5.

30

0.8765 −33.6858 0.4805 56.2265 0.8887 −32.6497 0.4575 57.3011

6.

31

0.8695 −34.6703 0.4930 55.2426 0.8822 −33.6221 0.4698 56.3302

7.

32

0.8624 −35.6452 0.5053 54.2682 0.8757 −34.5864 0.4819 55.3672

8.

33

0.8552 −36.6108 0.5174 53.3032 0.8691 −35.5429 0.4938 54.4120

9.

34

0.8480 −37.5672 0.5292 52.3474 0.8623 −36.4917 0.5055 53.4645

10. 35

0.8406 −38.5146 0.5408 51.4004 0.8555 −37.4331 0.5169 52.5244

11. 36

0.8332 −39.4533 0.5522 50.4622 0.8486 −38.3671 0.5282 51.5914

12. 37

0.8257 −40.3835 0.5633 49.5324 0.8416 −39.2942 0.5393 50.6654

13. 38

0.8182 −41.3055 0.5742 48.6107 0.8345 −40.2145 0.5502 49.7461

14. 39

0.8105 −42.2196 0.5850 47.6970 0.8273 −41.1283 0.5609 48.8333

15. 40

0.8028 −43.1261 0.5955 46.7909 0.8201 −42.0358 0.5715 47.9266

Table A.7 S-parameters of membrane microstrip step discontinuity S. Freq S 11 No (GHz) Mag

S 21 Angle

Mag

S 12 Angle

Mag

S 22 Angle

Mag

Angle

1.

26

0.743465 −13.365

0.6677 −6.61511 0.667792 −6.61511 0.741242 −0.57695

2.

27

0.744556 −13.8554 0.6665 −6.90216 0.666541 −6.90216 0.74229

3.

28

0.745693 −14.3448 0.6652 −7.19213 0.665232 −7.19213 0.743389 −0.75103

4.

29

0.746877 −14.8336 0.6638 −7.4852

5.

30

0.748107 −15.3217 0.6624 −7.78148 0.662445 −7.78148 0.745736 −0.95498

6.

31

0.749383 −15.8094 0.6609 −8.08113 0.660963 −8.08113 0.746983 −1.06846

7.

32

0.750705 −16.297

8.

33

0.752075 −16.7844 0.6578 −8.69122 0.657822 −8.69122 0.749627 −1.3185

9.

0.663867 −7.4852

−0.66028

0.744538 −0.84923

0.6594 −8.38433 0.659423 −8.38433 0.74828

−1.1896

34

0.753491 −17.2722 0.6561 −9.00193 0.656161 −9.00193 0.751024 −1.45516

10. 35

0.754953 −17.7604 0.6544 −9.31672 0.654437 −9.31672 0.752472 −1.59968

11. 36

0.756462 −18.2496 0.6526 −9.63554 0.652651 −9.63554 0.753969 −1.75189

12. 37

0.758018 −18.7398 0.6508 −9.95874 0.650802 −9.95874 0.755517 −1.91189

13. 38

0.75962

14. 39

0.761269 −19.7253 0.6469 −10.6188 0.646909 −10.6188 0.758761 −2.25493

15. 40

0.762964 −20.2214 0.6448 −10.956

−19.2316 0.6488 −10.2865 0.648887 −10.2865 0.757114 −2.0796 0.644865 −10.956

0.760457 −2.43788

Appendix A: Design Data on Micromachined Transmission Lines and Discontinuities

351

Table A.8 Equivalent circuit parameters of microstrip step discontinuity S. No

Microstrip step junction (µm)

C1 (pF)

Len1 (°)

Len2 (°)

1

1460–10

0.0408

−11.81

3.312

2

1460–50

0.0392

−11.967

5.133

3

1460–200

0.0351

−11.979

5.897

4

1300–10

0.0307

−10.884

3.478

Table A.9 S-parameters of membrane microstrip tee-junction discontinuity [50−50−50  lines] S. No

Freq (GHz)

S 11 Mag

Angle

Mag

S 21

1.

26

0.4223

174.252

0.6405

2.

27

0.4305

173.556

0.6378

3.

28

0.4392

172.806

4.

29

0.4484

171.998

5.

30

0.4582

6.

31

7.

32

8.

33

9.

34

10.

35

11.

36

12. 13.

S 12 Angle

S 22

Mag

Angle

Mag

Angle

4.9030

0.2923

−178.963

0.7100

9.6018

4.8326

0.2887

−179.236

0.7139

9.9351

0.6348

4.7260

0.2848

−179.544

0.7181

10.262

0.6315

4.5802

0.2808

−179.889

0.7225

10.583

171.131

0.6280

4.3919

0.2764

179.7285

0.7273

10.897

0.4686

170.200

0.6241

4.1576

0.2718

179.3068

0.7323

11.201

0.4797

169.201

0.6198

3.8732

0.2669

178.8446

0.7377

11.496

0.4915

168.130

0.6152

3.5346

0.2617

178.3408

0.7435

11.780

0.5041

166.983

0.6101

3.1368

0.2561

177.7946

0.7496

12.051

0.5174

165.754

0.6044

2.6744

0.2501

177.2043

0.7561

12.306

0.5316

164.437

0.5982

2.1414

0.2437

176.5703

0.7631

12.543

37

0.5467

163.024

0.5913

1.5312

0.2369

175.892

0.7706

12.760

38

0.5628

161.509

0.5837

0.8361

0.2295

175.1702

0.778

12.953

14.

39

0.5799

159.881

0.5752

0.0477

0.2216

174.4074

0.7871

13.118

15.

40

0.5980

158.129

0.5658

−0.8436

0.2131

173.6076

0.7963

13.250

Table A.10 S-parameters of membrane microstrip tee-junction discontinuity [50−70−70  lines] S. Freq S 11 No (GHz) Mag

Angle

S 21

1.

26

0.2463

−166.954 0.6860 10.6408 0.3745

2.

27

0.2521

−167.118 0.6850 10.8860 0.37144 −168.733 0.6265 10.0770

3.

28

0.2581

−167.334 0.6840 11.1103 0.3682

4.

29

0.2646

−167.6

0.6828 11.3122 0.3647

−168.495 0.6328 10.7338

5.

30

0.2713

−167.917 0.6815 11.4905 0.3612

−168.419 0.6362 11.0541

6.

31

0.2784

−168.284 0.6801 11.6435 0.3574

−168.372 0.6398 11.3683

7.

32

0.2860

−168.699 0.6786 11.7699 0.3535

−168.356 0.6436 11.676

8.

33

0.2939

−169.164 0.6769 11.8678 0.3493

−168.37

9.

34

0.3023

−169.676 0.6751 11.9354 0.3450

−168.416 0.6517 12.2695

Mag

S 12 Angle

Mag

S 22 Angle

Mag

−168.895 0.6235 −168.6

Angle 9.7412

0.6295 10.4080

0.6476 11.9766 (continued)

352

Appendix A: Design Data on Micromachined Transmission Lines and Discontinuities

Table A.10 (continued) S. Freq S 11 No (GHz) Mag

S 21 Angle

S 12

Mag

Angle

Mag

S 22 Angle

Mag

Angle

10. 35

0.31113 −170.237 0.6732 11.9708 0.3405

−168.494 0.6562 12.5538

11. 36

0.3204

−170.846 0.6710 11.9718 0.3357

−168.603 0.6608 12.8288

12. 37

0.3302

−171.503 0.6687 11.9360 0.3307

−168.745 0.6657 13.0934

13. 38

0.3406

−172.21

−168.92

14. 39

0.3515

−172.968 0.6633 11.7440 0.3199

−169.128 0.6763 13.5870

15. 40

0.3630

−173.778 0.6602 11.5816 0.3141

−169.368 0.6820 13.8133

0.6661 11.8610 0.3254

0.6709 13.3466

Table A.11 S-parameters of membrane microstrip tee-junction discontinuity [50−100−100  lines] S. No

Freq (GHz)

S 11 Mag

Angle

Mag

S 21 Angle

Mag

S 12 Angle

Mag

S 22 Angle

1.

26

0.0848

−112.403

0.7040

16.185

0.4742

−162.573

0.5290

10.5557

2.

27

0.0888

−113.743

0.7037

16.693

0.4719

−162.128

0.5315

10.9091

3.

28

0.0929

−115.09

0.7033

17.187

0.4695

−161.702

0.5341

11.2565

4.

29

0.0972

−116.441

0.7030

17.666

0.4670

−161.297

0.5368

11.5976

5.

30

0.1017

−117.792

0.7026

18.130

0.4643

−160.912

0.5396

11.9323

6.

31

0.1065

−119.138

0.7022

18.577

0.4615

−160.547

0.5426

12.2601

7.

32

0.1115

−120.477

0.7017

19.006

0.4586

−160.202

0.5457

12.5807

8.

33

0.1168

−121.802

0.7012

19.417

0.4555

−159.876

0.5489

12.8934

9.

34

0.1224

−123.111

0.7006

19.808

0.4523

−159.57

0.5523

13.1981

10.

35

0.1283

−124.402

0.7

20.179

0.4489

−159.282

0.5558

13.4941

11.

36

0.1346

−125.671

0.6993

20.527

0.4453

−159.012

0.5595

13.7808

12.

37

0.1412

−126.917

0.6986

20.852

0.4416

−158.759

0.5634

14.0575

13.

38

0.1483

−128.137

0.6977

21.153

0.4377

−158.524

0.5674

14.3234

14.

39

0.1557

−129.333

0.6968

21.427

0.4336

−158.306

0.5717

14.5777

15.

40

0.1637

−130.502

0.6958

21.673

0.4294

−158.103

0.5761

14.8193

Table A.12 Equivalent circuit parameters of microstrip T-junction discontinuity S. No

Microstrip T-junction

L1 (pH)

C1 (pF)

Len1 (°)

Len2 (°)

1

50–50–50

171.16

0.0284

−31.5

−4.5

2

50–70–70

124.99

0.0373

−34

−6.1

3

50–100–100

115.02

0.0463

−42.6

−8.2

Appendix A: Design Data on Micromachined Transmission Lines and Discontinuities

353

Table A.13 S-parameters of membrane coplanar waveguide series gap [(s + 2w) = 240 µm and s = 160 µm] S. No

Freq Gap = 10 µm (GHz) S 11

S 21

Mag

Mag

1.

26

0.9706 −17.1933 0.2335 72.5645 0.9840 −14.5337 0.1697 75.1905

2.

27

0.9686 −17.7354 0.2413 72.0280 0.9829 −14.9782 0.1755 74.7513

3.

28

0.9666 −18.2676 0.2491 71.5010 0.9819 −15.4129 0.1812 74.3213

4.

29

0.9646 −18.7902 0.2568 70.9835 0.9808 −15.8382 0.1869 73.9006

5.

30

0.9625 −19.3032 0.2644 70.4749 0.9797 −16.2541 0.1925 73.4891

6.

31

0.9604 −19.8070 0.2719 69.9755 0.9785 −16.6608 0.1981 73.0865

7.

32

0.9582 −20.3019 0.2794 69.4846 0.9773 −17.0587 0.2036 72.6922

8.

33

0.9560 −20.7880 0.2867 69.0021 0.9761 −17.4480 0.2091 72.3063

9.

34

0.9537 −21.2659 0.2940 68.5280 0.9749 −17.8288 0.2146 71.9289

10. 35

0.9514 −21.7357 0.3013 68.0614 0.9737 −18.2017 0.2200 71.5590

11. 36

0.9490 −22.1980 0.3084 67.6024 0.9724 −18.5670 0.2254 71.1963

12. 37

0.9467 −22.6531 0.3156 67.1502 0.9711 −18.9250 0.2307 70.8409

13. 38

0.9442 −23.1015 0.3226 66.7044 0.9698 −19.2762 0.2360 70.4919

14. 39

0.9418 −23.5439 0.3297 66.2647 0.9685 −19.6212 0.2413 70.1491

15. 40

0.9392 −23.9807 0.3366 65.8304 0.9671 −19.9603 0.2466 69.8117

Angle

Gap = 20 µm S 11 Angle

Mag

S 21 Angle

Mag

Angle

Table A.14 S-parameters of membrane coplanar waveguide series gap [(s + 2w) = 240 µm and s = 160 µm] S. No

Freq Gap = 30 µm (GHz) S 11

S 21

Mag

Mag

Angle

Gap = 40 µm S 11 Angle

Mag

S 21 Angle

Mag

Angle

1.

26

0.9906 −12.6060 0.1267 77.2605 0.9936 −11.7807 0.1034 78.0198

2.

27

0.9900 −12.9897 0.1311 76.8895 0.9932 −12.1308 0.1069 77.6768

3.

28

0.9894 −13.3646 0.1354 76.5268 0.9928 −12.4720 0.1104 77.3429

4.

29

0.9888 −13.7309 0.1397 76.1730 0.9924 −12.8043 0.1139 77.0173

5.

30

0.9881 −14.0887 0.1440 75.8272 0.9920 −13.1279 0.1174 76.6998

6.

31

0.9875 −14.4381 0.1482 75.4897 0.9915 −13.4428 0.1208 76.3909

7.

32

0.9868 −14.7794 0.1524 75.1603 0.9911 −13.7494 0.1242 76.0899

8.

33

0.9861 −15.1127 0.1565 74.8388 0.9907 −14.0476 0.1276 75.7972

9.

34

0.9854 −15.4383 0.1607 74.5247 0.9902 −14.3378 0.1310 75.5114

10. 35

0.9847 −15.7564 0.1648 74.2180 0.9897 −14.6202 0.1343 75.2334

11. 36

0.9840 −16.0675 0.1688 73.9184 0.9893 −14.8952 0.1376 74.9629

12. 37

0.9833 −16.3716 0.1729 73.6253 0.9888 −15.1630 0.1409 74.6990 (continued)

354

Appendix A: Design Data on Micromachined Transmission Lines and Discontinuities

Table A.14 (continued) S. No

Freq Gap = 30 µm (GHz) S 11

S 21

Mag

Mag

Angle

Gap = 40 µm S 11 Angle

Mag

S 21 Angle

Mag

Angle

13. 38

0.9825 −16.6692 0.1769 73.3387 0.9883 −15.4239 0.1442 74.4416

14. 39

0.9817 −16.9608 0.1810 73.0576 0.9878 −15.6784 0.1475 74.1899

15. 40

0.9810 −17.2468 0.1850 72.7824 0.9873 −15.9268 0.1507 73.9445

Table A.15 S-parameters of membrane coplanar waveguide series gap [(s + 2w) = 240 µm and s = 160 µm] S. No

Freq Gap = 50 µm (GHz) S 11

S 21

Mag

Mag

1.

26

0.9950 −11.4684 0.0873 78.4035 0.9961 −10.9769 0.0736 78.9834

2.

27

0.9947 −11.8097 0.0903 78.0748 0.9959 −11.2995 0.0761 78.6737

3.

28

0.9944 −12.1423 0.0933 77.7537 0.9957 −11.6132 0.0786 78.3717

4.

29

0.9941 −12.4661 0.0962 77.4418 0.9955 −11.9182 0.0811 78.0772

5.

30

0.9938 −12.7814 0.0991 77.1381 0.9952 −12.2145 0.0835 77.7921

6.

31

0.9935 −13.0882 0.1020 76.8428 0.9950 −12.5022 0.0860 77.5144

7.

32

0.9931 −13.3866 0.1049 76.5552 0.9947 −12.7814 0.0884 77.2443

8.

33

0.9928 −13.6769 0.1077 76.2759 0.9945 −13.0523 0.0908 76.9828

9.

34

0.9925 −13.9593 0.1106 76.0044 0.9943 −13.3151 0.0931 76.7288

10. 35

0.9921 −14.2339 0.1134 75.7404 0.9940 −13.5700 0.0955 76.4821

11. 36

0.9918 −14.5010 0.1162 75.4834 0.9937 −13.8173 0.0978 76.2425

12. 37

0.9914 −14.7610 0.1189 75.2339 0.9935 −14.0571 0.1001 76.0098

13. 38

0.9910 −15.0141 0.1217 74.9906 0.9932 −14.2898 0.1024 75.7841

14. 39

0.9907 −15.2606 0.1244 74.7538 0.9929 −14.5158 0.1047 75.5640

15. 40

0.9903 −15.5010 0.1271 74.5228 0.9927 −14.7352 0.1070 75.3504

Angle

Gap = 60 µm S 11 Angle

Mag

S 21 Angle

Mag

Angle

Table A.16 S-parameters of membrane coplanar waveguide series gap [(s + 2w) = 240 µm and s = 160 µm] S. No

Freq Gap = 70 µm (GHz) S 11

S 21

Mag

Mag

Angle

Gap = 80 µm S 11 Angle

Mag

S 21 Angle

Mag

Angle

1.

26

0.9970 −9.4527

0.0631 80.2911 0.9975 −9.5923

0.0549 80.2344

2.

27

0.9968 −9.7427

0.0653 80.0079 0.9974 −9.8878

0.0568 79.9485

3.

28

0.9967 −10.0261 0.0675 79.7296 0.9972 −10.1766 0.0587 79.6689

4.

29

0.9965 −10.3029 0.0696 79.4581 0.9971 −10.4589 0.0606 79.3945 (continued)

Appendix A: Design Data on Micromachined Transmission Lines and Discontinuities

355

Table A.16 (continued) S. No

Freq Gap = 70 µm (GHz) S 11

S 21

Mag

Mag

Angle

Gap = 80 µm S 11 Angle

Mag

S 21 Angle

Mag

Angle

5.

30

0.9963 −10.5730 0.0718 79.1933 0.9970 −10.7345 0.0624 79.1274

6.

31

0.9961 −10.8367 0.0739 78.9339 0.9968 −11.0036 0.0643 78.8661

7.

32

0.9960 −11.0940 0.0760 78.6806 0.9967 −11.2663 0.0661 78.6107

8.

33

0.9958 −11.3449 0.0781 78.4336 0.9965 −11.5227 0.0679 78.3615

9.

34

0.9956 −11.5897 0.0802 78.1923 0.9964 −11.7728 0.0697 78.1185

10. 35

0.9954 −11.8283 0.0822 77.9570 0.9962 −12.0167 0.0714 77.8813

11. 36

0.9952 −12.0611 0.0843 77.7264 0.9961 −12.2548 0.0732 77.6495

12. 37

0.9950 −12.2881 0.0863 77.5016 0.9959 −12.4870 0.0749 77.4223

13. 38

0.9948 −12.5096 0.0883 77.2821 0.9958 −12.7137 0.0766 77.2013

14. 39

0.9946 −12.7258 0.0903 77.0670 0.9956 −12.9350 0.0783 76.9852

15. 40

0.9944 −12.9369 0.0923 76.8568 0.9954 −13.1512 0.0800 76.7738

Table A.17 S-parameters of membrane coplanar waveguide series gap [(s + 2w) = 240 µm and s = 160 µm] S. No

Freq Gap = 90 µm (GHz) S 11

S 21

Mag

Mag

Angle

Gap = 100 µm S 11 Angle

Mag

S 21 Angle

Mag

Angle

1.

26

0.9979 −9.1640

0.0474 80.6214 0.9982 −8.8835

0.0415 80.8288

2.

27

0.9978 −9.4484

0.0490 80.3447 0.9981 −9.1586

0.0429 80.5592

3.

28

0.9977 −9.7267

0.0506 80.0743 0.9980 −9.4278

0.0443 80.2967

4.

29

0.9976 −9.9989

0.0522 79.8106 0.9980 −9.6908

0.0457 80.0393

5.

30

0.9975 −10.2649 0.0538 79.5515 0.9979 −9.9477

0.0471 79.7872

6.

31

0.9974 −10.5248 0.0554 79.2988 0.9978 −10.1986 0.0484 79.5409

7.

32

0.9973 −10.7786 0.0569 79.0522 0.9977 −10.4435 0.0498 79.3011

8.

33

0.9972 −11.0265 0.0585 78.8108 0.9976 −10.6826 0.0511 79.0670

9.

34

0.9970 −11.2685 0.0600 78.5752 0.9975 −10.9157 0.0524 78.8389

10. 35

0.9969 −11.5048 0.0615 78.3453 0.9974 −11.1432 0.0537 78.6152

11. 36

0.9968 −11.7354 0.0630 78.1204 0.9973 −11.3650 0.0550 78.3974

12. 37

0.9967 −11.9606 0.0645 77.9009 0.9972 −11.5813 0.0563 78.1851

13. 38

0.9965 −12.1806 0.0659 77.6865 0.9971 −11.7923 0.0575 77.9768

14. 39

0.9964 −12.3954 0.0674 77.4768 0.9970 −11.9982 0.0587 77.7742

15. 40

0.9963 −12.6053 0.0688 77.2714 0.9969 −12.1990 0.0600 77.5766

356

Appendix A: Design Data on Micromachined Transmission Lines and Discontinuities

Table A.18 S-parameters of membrane coplanar waveguide series gap[(s + 2w) = 240 µm and s = 190 µm] S. No

Freq Gap = 010 µm (GHz) S 11

1.

26

0.9735 −19.4345 0.2177 70.1439 0.9863 −15.3387 0.1530 74.3355

2.

27

0.9719 −19.9427 0.2246 69.6425 0.9855 −15.7602 0.1581 73.9177

3.

28

0.9703 −20.4330 0.2313 69.1588 0.9846 −16.1685 0.1631 73.5127

4.

29

0.9686 −20.9062 0.2380 68.6924 0.9837 −16.5637 0.1681 73.1199

5.

30

0.9669 −21.3629 0.2446 68.2424 0.9828 −16.9464 0.1730 72.7393

6.

31

0.9652 −21.8038 0.2511 67.8082 0.9819 −17.3170 0.1779 72.3699

7.

32

0.9634 −22.2299 0.2576 67.3890 0.9810 −17.6760 0.1827 72.0119

8.

33

0.9616 −22.6421 0.2641 66.9837 0.9800 −18.0240 0.1876 71.6641

9.

34

0.9598 −23.0414 0.2705 66.5911 0.9790 −18.3619 0.1924 71.3256

10. 35

0.9579 −23.4290 0.2769 66.2103 0.9780 −18.6903 0.1972 70.9965

11. 36

0.9559 −23.8061 0.2832 65.8401 0.9770 −19.0102 0.2020 70.6748

12. 37

0.9539 −24.1741 0.2896 65.4789 0.9759 −19.3226 0.2068 70.3601

13. 38

0.9519 −24.5346 0.2960 65.1249 0.9748 −19.6289 0.2117 70.0509

14. 39

0.9498 −24.8897 0.3025 64.7764 0.9737 −19.9308 0.2166 69.7452

15. 40

0.9476 −25.2418 0.3090 64.4304 0.9725 −20.2304 0.2215 69.4409

Mag

Angle

Gap = 020 µm S 21 Mag

S 11 Angle

Mag

S 21 Angle

Mag

Angle

Table A.19 S-parameters of membrane coplanar waveguide series gap[(s + 2w) = 240 µm and s = 190 µm] S. No

Freq Gap = 30 µm (GHz) S 11

S 21

Mag

Mag

Angle

Gap = 40 µm S 11 Angle

Mag

S 21 Angle

Mag

Angle

1.

26

0.9915 −11.9079 0.1184 77.8878 0.9941 −10.9814 0.0956 78.7994

2.

27

0.9910 −12.2687 0.1226 77.5373 0.9937 −11.3124 0.0989 78.4792

3.

28

0.9904 −12.6214 0.1267 77.1943 0.9933 −11.6359 0.1022 78.1658

4.

29

0.9899 −12.9662 0.1307 76.8590 0.9930 −11.9519 0.1055 77.8598

5.

30

0.9893 −13.3035 0.1347 76.5307 0.9926 −12.2607 0.1087 77.5607

6.

31

0.9887 −13.6335 0.1388 76.2095 0.9922 −12.5626 0.1120 77.2684

7.

32

0.9881 −13.9564 0.1428 75.8947 0.9918 −12.8577 0.1152 76.9826

8.

33

0.9875 −14.2727 0.1467 75.5865 0.9913 −13.1465 0.1184 76.7026

9.

34

0.9868 −14.5829 0.1507 75.2839 0.9909 −13.4294 0.1217 76.4284

10. 35

0.9862 −14.8873 0.1547 74.9865 0.9905 −13.7069 0.1249 76.1591

11. 36

0.9855 −15.1868 0.1587 74.6937 0.9900 −13.9796 0.1281 75.8939

12. 37

0.9848 −15.4821 0.1627 74.4046 0.9895 −14.2484 0.1314 75.6325 (continued)

Appendix A: Design Data on Micromachined Transmission Lines and Discontinuities

357

Table A.19 (continued) S. No

Freq Gap = 30 µm (GHz) S 11

S 21

Mag

Mag

Angle

Gap = 40 µm S 11 Angle

Mag

S 21 Angle

Mag

Angle

13. 38

0.9841 −15.7742 0.1667 74.1182 0.9890 −14.5140 0.1346 75.3737

14. 39

0.9833 −16.0645 0.1707 73.8330 0.9885 −14.7781 0.1380 75.1154

15. 40

0.9825 −16.3552 0.1749 73.5465 0.9880 −15.0426 0.1414 74.8561

Table A.20 S-parameters of membrane coplanar waveguide series gap [(s + 2w) = 240 µm and s = 190 µm] S. No

Freq Gap = 50 µm (GHz) S 11

S 21

Mag

Mag

1.

26

0.9954 −11.3467 0.0794 78.5060 0.9964 −11.6405 0.0657 78.0630

2.

27

0.9952 −11.6688 0.0821 78.1950 0.9963 −11.9539 0.0679 77.7586

3.

28

0.9949 −11.9815 0.0848 77.8933 0.9961 −12.2560 0.0701 77.4649

4.

29

0.9946 −12.2847 0.0875 77.5995 0.9959 −12.5471 0.0723 77.1826

5.

30

0.9944 −12.5789 0.0901 77.3152 0.9957 −12.8276 0.0744 76.9102

6.

31

0.9941 −12.8640 0.0928 77.0388 0.9955 −13.0976 0.0765 76.6484

7.

32

0.9938 −13.1408 0.0954 76.7707 0.9953 −13.3576 0.0786 76.3961

8.

33

0.9935 −13.4093 0.0980 76.5100 0.9951 −13.6080 0.0807 76.1525

9.

34

0.9932 −13.6702 0.1006 76.2568 0.9949 −13.8493 0.0828 75.9181

10. 35

0.9929 −13.9239 0.1032 76.0094 0.9947 −14.0821 0.0849 75.6917

11. 36

0.9926 −14.1712 0.1059 75.7684 0.9945 −14.3072 0.0870 75.4721

12. 37

0.9922 −14.4128 0.1085 75.5320 0.9943 −14.5254 0.0891 75.2596

13. 38

0.9919 −14.6499 0.1112 75.2993 0.9940 −14.7379 0.0913 75.0513

14. 39

0.9915 −14.8837 0.1139 75.0691 0.9938 −14.9461 0.0935 74.8468

15. 40

0.9911 −15.1165 0.1167 74.8382 0.9935 −15.1522 0.0957 74.6432

Angle

Gap = 60 µm S 11 Angle

Mag

S 21 Angle

Mag

Angle

Table A.21 S-parameters of membrane coplanar waveguide series gap [(s + 2w) = 240 µm and s = 190 µm] S. No

Freq Gap = 70 µm (GHz) S 11

S 21

Mag

Mag

Angle

Gap = 80 µm S 11 Angle

Mag

S 21 Angle

Mag

Angle

1.

26

0.9971 −9.7747

0.0582 79.9419 0.9976 −8.9595

0.0506 80.7553

2.

27

0.9970 −10.0647 0.0602 79.6603 0.9975 −9.2342

0.0524 80.4866

3.

28

0.9968 −10.3474 0.0621 79.3857 0.9974 −9.5029

0.0541 80.2243

4.

29

0.9966 −10.6230 0.0641 79.1173 0.9973 −9.7657

0.0558 79.9669 (continued)

358

Appendix A: Design Data on Micromachined Transmission Lines and Discontinuities

Table A.21 (continued) S. No

Freq Gap = 70 µm (GHz) S 11

S 21

Mag

Mag

Angle

Gap = 80 µm S 11 Angle

Mag

S 21 Angle

Mag

Angle

5.

30

0.9965 −10.8916 0.0661 78.8555 0.9971 −10.0228 0.0576 79.7137

6.

31

0.9963 −11.1535 0.0680 78.6009 0.9970 −10.2743 0.0593 79.4668

7.

32

0.9961 −11.4089 0.0700 78.3521 0.9969 −10.5204 0.0610 79.2239

8.

33

0.9960 −11.6580 0.0719 78.1086 0.9967 −10.7614 0.0627 78.9861

9.

34

0.9958 −11.9014 0.0739 77.8709 0.9966 −10.9976 0.0644 78.7516

10. 35

0.9956 −12.1394 0.0758 77.6381 0.9964 −11.2294 0.0661 78.5212

11. 36

0.9954 −12.3726 0.0778 77.4094 0.9963 −11.4573 0.0679 78.2944

12. 37

0.9952 −12.6018 0.0797 77.1843 0.9961 −11.6820 0.0696 78.0688

13. 38

0.9950 −12.8278 0.0817 76.9612 0.9959 −11.9045 0.0714 77.8452

14. 39

0.9948 −13.0521 0.0838 76.7388 0.9958 −12.1257 0.0732 77.6207

15. 40

0.9946 −13.2767 0.0859 76.5151 0.9956 −12.3479 0.0751 77.3938

Table A.22 S-parameters of membrane coplanar waveguide series gap [(s + 2w) = 240 µm and s = 190 µm] S. No

Freq Gap = 090 µm (GHz) S 11 Mag

Angle

Gap = 100 µm S 21 Mag

S 11 Angle

Mag

S 21 Angle

Mag

Angle

1.

26

0.9979 −9.2736

0.0427 80.4938 0.9980 −9.9599

2.

27

0.9978 −9.5477

0.0441 80.2284 0.9979 −10.2384 0.0385 79.6171

3.

28

0.9977 −9.8147

0.0456 79.9686 0.9978 −10.5080 0.0397 79.3573

4.

29

0.9976 −10.0747 0.0470 79.7156 0.9978 −10.7686 0.0409 79.1057

5.

30

0.9975 −10.3277 0.0484 79.4681 0.9977 −11.0206 0.0421 78.8626

6.

31

0.9974 −10.5740 0.0499 79.2267 0.9976 −11.2641 0.0433 78.6265

7.

32

0.9973 −10.8139 0.0513 78.9915 0.9975 −11.4994 0.0445 78.3985

8.

33

0.9972 −11.0476 0.0527 78.7622 0.9974 −11.7268 0.0457 78.1786

9.

0.0372 79.8852

34

0.9971 −11.2753 0.0541 78.5373 0.9973 −11.9467 0.0469 77.9631

10. 35

0.9970 −11.4976 0.0555 78.3170 0.9972 −12.1596 0.0481 77.7555

11. 36

0.9968 −11.7150 0.0569 78.1014 0.9971 −12.3661 0.0493 77.5528

12. 37

0.9967 −11.9282 0.0583 77.8880 0.9970 −12.5669 0.0505 77.3535

13. 38

0.9966 −12.1380 0.0598 77.6771 0.9968 −12.7629 0.0517 77.1581

14. 39

0.9965 −12.3457 0.0613 77.4659 0.9967 −12.9555 0.0530 76.9641

15. 40

0.9963 −12.5533 0.0629 77.2525 0.9966 −13.1468 0.0544 76.7691

Appendix A: Design Data on Micromachined Transmission Lines and Discontinuities

359

Table A.23 S-parameters of membrane coplanar waveguide series gap [(s + 2w) = 240 µm and s = 220 µm] S. No

Freq Gap = 10 µm (GHz) S 11

S 21

Mag

Mag

1.

26

0.9807 −16.3057 0.1774 73.0516 0.9891 −13.5165 0.1248 75.9084

2.

27

0.9795 −16.7213 0.1831 72.6390 0.9884 −13.8505 0.1289 75.5781

3.

28

0.9784 −17.1212 0.1888 72.2415 0.9878 −14.1702 0.1330 75.2606

4.

29

0.9772 −17.5061 0.1944 71.8577 0.9872 −14.4761 0.1370 74.9564

5.

30

0.9760 −17.8764 0.2000 71.4880 0.9865 −14.7685 0.1410 74.6647

6.

31

0.9748 −18.2330 0.2055 71.1311 0.9858 −15.0481 0.1450 74.3841

7.

32

0.9735 −18.5766 0.2110 70.7866 0.9851 −15.3155 0.1489 74.1152

8.

33

0.9722 −18.9079 0.2165 70.4536 0.9844 −15.5712 0.1528 73.8566

9.

34

0.9709 −19.2279 0.2219 70.1312 0.9837 −15.8161 0.1567 73.6081

10. 35

0.9695 −19.5375 0.2273 69.8187 0.9830 −16.0509 0.1606 73.3689

11. 36

0.9682 −19.8376 0.2328 69.5151 0.9822 −16.2764 0.1645 73.1376

12. 37

0.9667 −20.1292 0.2382 69.2194 0.9814 −16.4934 0.1685 72.9142

13. 38

0.9653 −20.4134 0.2436 68.9304 0.9806 −16.7029 0.1724 72.6975

14. 39

0.9638 −20.6913 0.2490 68.6472 0.9798 −16.9058 0.1763 72.4862

15. 40

0.9622 −20.9641 0.2545 68.3688 0.9790 −17.1030 0.1802 72.2796

Angle

Gap = 20 µm S 11 Angle

Mag

S 21 Angle

Mag

Angle

Table A.24 S-parameters of membrane coplanar waveguide series gap [(s + 2w) = 240 µm and s = 220 µm] S. No

Freq Gap = 30 µm (GHz) S 11

S 21

Mag

Mag

Angle

Gap = 40 µm S 11 Angle

Mag

S 21 Angle

Mag

Angle

1.

26

0.9929 −10.5340 0.0978 78.7457 0.9947 −10.6627 0.0755 78.5104

2.

27

0.9925 −10.8339 0.1012 78.4509 0.9945 −10.9393 0.0780 78.2370

3.

28

0.9920 −11.1254 0.1045 78.1644 0.9942 −11.2052 0.0805 77.9730

4.

29

0.9916 −11.4087 0.1078 77.8855 0.9939 −11.4606 0.0830 77.7191

5.

30

0.9912 −11.6840 0.1111 77.6139 0.9936 −11.7058 0.0854 77.4752

6.

31

0.9907 −11.9516 0.1143 77.3497 0.9933 −11.9412 0.0878 77.2398

7.

32

0.9903 −12.2118 0.1176 77.0925 0.9931 −12.1672 0.0902 77.0139

8.

33

0.9898 −12.4650 0.1208 76.8416 0.9927 −12.3841 0.0926 76.7969

9.

34

0.9893 −12.7116 0.1240 76.5970 0.9924 −12.5926 0.0950 76.5872

10. 35

0.9888 −12.9520 0.1272 76.3578 0.9921 −12.7929 0.0974 76.3858

11. 36

0.9883 −13.1866 0.1304 76.1246 0.9918 −12.9858 0.0998 76.1906

12. 37

0.9878 −13.4160 0.1336 75.8956 0.9915 −13.1718 0.1021 76.0024 (continued)

360

Appendix A: Design Data on Micromachined Transmission Lines and Discontinuities

Table A.24 (continued) S. No

Freq Gap = 30 µm (GHz) S 11

S 21

Mag

Mag

Angle

Gap = 40 µm S 11 Angle

Mag

S 21 Angle

Mag

Angle

13. 38

0.9873 −13.6406 0.1368 75.6711 0.9911 −13.3515 0.1045 75.8200

14. 39

0.9867 −13.8611 0.1400 75.4504 0.9908 −13.5256 0.1069 75.6420

15. 40

0.9862 −14.0781 0.1432 75.2326 0.9904 −13.6949 0.1093 75.4691

Table A.25 S-parameters of membrane coplanar waveguide series gap [(s + 2w) = 240 µm and s = 220 µm] S. No

Freq Gap = 50 µm (GHz) S 11

1.

26

0.9960 −9.2382

0.0622 80.0328 0.9966 −8.8895

0.0528 80.5239

2.

27

0.9958 −9.4930

0.0643 79.7829 0.9964 −9.1341

0.0546 80.2900

3.

28

0.9956 −9.7396

0.0664 79.5404 0.9963 −9.3707

0.0564 80.0642

4.

29

0.9954 −9.9780

0.0685 79.3060 0.9961 −9.5994

0.0581 79.8443

5.

30

0.9952 −10.2086 0.0705 79.0785 0.9959 −9.8204

0.0598 79.6322

6.

31

0.9950 −10.4314 0.0726 78.8579 0.9958 −10.0341 0.0615 79.4267

7.

32

0.9947 −10.6469 0.0746 78.6440 0.9956 −10.2406 0.0632 79.2280

8.

33

0.9945 −10.8551 0.0766 78.4362 0.9954 −10.4402 0.0649 79.0350

9.

34

0.9943 −11.0567 0.0786 78.2350 0.9952 −10.6333 0.0666 78.8482

10. 35

0.9941 −11.2517 0.0806 78.0397 0.9950 −10.8201 0.0683 78.6667

11. 36

0.9938 −11.4408 0.0825 77.8497 0.9948 −11.0012 0.0699 78.4902

12. 37

0.9936 −11.6242 0.0845 77.6641 0.9946 −11.1769 0.0716 78.3187

13. 38

0.9933 −11.8025 0.0865 77.4832 0.9944 −11.3478 0.0733 78.1509

14. 39

0.9930 −11.9761 0.0885 77.3061 0.9942 −11.5142 0.0749 77.9875

15. 40

0.9928 −12.1457 0.0905 77.1317 0.9940 −11.6767 0.0766 77.8258

Mag

Angle

Gap = 60 µm S 21 Mag

S 11 Angle

Mag

S 21 Angle

Mag

Angle

Table A.26 S-parameters of membrane coplanar waveguide series gap [(s + 2w) = 240 µm and s = 220 µm] S. No

Freq Gap = 70 µm (GHz) S 11

S 21

Mag

Mag

Angle

Gap = 80 µm S 11 Angle

Mag

S 21 Angle

Mag

Angle

1.

26

0.9969 −9.0327

0.0449 80.6346 0.9973 −8.7676

0.0390 80.7897

2.

27

0.9968 −9.2798

0.0464 80.4027 0.9972 −9.0070

0.0403 80.5611

3.

28

0.9967 −9.5186

0.0479 80.1792 0.9971 −9.2382

0.0415 80.3385

4.

29

0.9965 −9.7492

0.0493 79.9621 0.9969 −9.4614

0.0428 80.1227 (continued)

Appendix A: Design Data on Micromachined Transmission Lines and Discontinuities

361

Table A.26 (continued) S. No

Freq Gap = 70 µm (GHz) S 11

S 21

Mag

Mag

Angle

Gap = 80 µm S 11 Angle

Mag

S 21 Angle

Mag

Angle

5.

30

0.9964 −9.9719

0.0508 79.7524 0.9968 −9.6766

0.0440 79.9146

6.

31

0.9963 −10.1868 0.0522 79.5502 0.9967 −9.8843

0.0452 79.7123

7.

32

0.9961 −10.3941 0.0536 79.3528 0.9966 −10.0845 0.0465 79.5153

8.

33

0.9960 −10.5942 0.0550 79.1625 0.9965 −10.2775 0.0477 79.3244

9.

34

0.9958 −10.7874 0.0564 78.9774 0.9963 −10.4637 0.0489 79.1406

10. 35

0.9957 −10.9741 0.0578 78.7987 0.9962 −10.6433 0.0500 78.9602

11. 36

0.9955 −11.1545 0.0592 78.6240 0.9961 −10.8167 0.0512 78.7855

12. 37

0.9953 −11.3293 0.0606 78.4547 0.9959 −10.9844 0.0524 78.6152

13. 38

0.9951 −11.4987 0.0620 78.2886 0.9958 −11.1467 0.0536 78.4484

14. 39

0.9950 −11.6633 0.0634 78.1271 0.9956 −11.3041 0.0547 78.2855

15. 40

0.9948 −11.8236 0.0647 77.9676 0.9955 −11.4572 0.0559 78.1255

Table A.27 S-parameters of membrane coplanar waveguide series gap [(s + 2w) = 240 µm and s = 220 µm] S. No

Freq Gap = 90 µm (GHz) S 11

S 21

Mag

Mag

Angle

Gap = 100 µm S 11 Angle

Mag

S 21 Angle

Mag

Angle

1.

26

0.9977 −7.8820

0.0340 81.6555 0.9976 −8.7971

0.0298 80.7950

2.

27

0.9976 −8.1127

0.0351 81.4399 0.9975 −9.0415

0.0308 80.5680

3.

28

0.9975 −8.3372

0.0363 81.2311 0.9974 −9.2780

0.0317 80.3486

4.

29

0.9974 −8.5557

0.0374 81.0264 0.9974 −9.5068

0.0327 80.1356

5.

30

0.9973 −8.7683

0.0384 80.8261 0.9973 −9.7279

0.0336 79.9305

6.

31

0.9971 −8.9751

0.0395 80.6321 0.9972 −9.9416

0.0345 79.7305

7.

32

0.9970 −9.1763

0.0406 80.4413 0.9971 −10.1481 0.0354 79.5391

8.

33

0.9969 −9.3721

0.0416 80.2564 0.9970 −10.3476 0.0362 79.3520

9.

34

0.9968 −9.5626

0.0427 80.0742 0.9969 −10.5404 0.0371 79.1709

10. 35

0.9967 −9.7482

0.0437 79.8975 0.9968 −10.7269 0.0380 78.9939

11. 36

0.9966 −9.9290

0.0447 79.7232 0.9967 −10.9073 0.0388 78.8243

12. 37

0.9965 −10.1055 0.0457 79.5530 0.9966 −11.0821 0.0397 78.6572

13. 38

0.9963 −10.2779 0.0468 79.3855 0.9965 −11.2515 0.0405 78.4949

14. 39

0.9962 −10.4465 0.0478 79.2199 0.9964 −11.4162 0.0414 78.3367

15. 40

0.9961 −10.6119 0.0488 79.0576 0.9962 −11.5765 0.0422 78.1798

362

Appendix A: Design Data on Micromachined Transmission Lines and Discontinuities

Table A.28 S-parameters of membrane coplanar waveguide step junction [(s + 2w) = 240 µm] S. Freq Step 190–10 µm No (GHz) S 11 Mag

Angle

Step 190–20 µm S 21 Mag

S 11 Angle

Mag

S 21 Angle

Mag

Angle

1

26

0.5300 −10.8843 0.8458 −2.5056 0.4858 −9.0689 0.8724 −2.4389

2

27

0.5301 −11.0104 0.8456 −2.5957 0.4863 −9.1717 0.8721 −2.5200

3

28

0.5303 −11.1125 0.8454 −2.6858 0.4868 −9.2540 0.8718 −2.6005

4

29

0.5304 −11.1909 0.8453 −2.7759 0.4872 −9.3159 0.8715 −2.6803

5

30

0.5305 −11.2459 0.8452 −2.8665 0.4877 −9.3579 0.8712 −2.7597

6

31

0.5306 −11.2784 0.8450 −2.9573 0.4881 −9.3806 0.8709 −2.8387

7

32

0.5307 −11.2886 0.8449 −3.0486 0.4885 −9.3843 0.8706 −2.9173

8

33

0.5308 −11.2774 0.8448 −3.1405 0.4889 −9.3696 0.8703 −2.9958

9

34

0.5309 −11.2455 0.8446 −3.2331 0.4893 −9.3373 0.8701 −3.0742

10

35

0.5310 −11.1940 0.8445 −3.3266 0.4896 −9.2882 0.8698 −3.1526

11

36

0.5310 −11.1238 0.8444 −3.4211 0.4900 −9.2228 0.8696 −3.2311

12

37

0.5311 −11.0359 0.8443 −3.5168 0.4903 −9.1424 0.8693 −3.3102

13

38

0.5312 −10.9316 0.8442 −3.6141 0.4906 −9.0477 0.8691 −3.3901

14

39

0.5313 −10.8122 0.8440 −3.7137 0.4909 −8.9397 0.8689 −3.4715

15

40

0.5313 −10.6791 0.8439 −3.8168 0.4912 −8.8193 0.8687 −3.5557

Table A.29 S-parameters of membrane coplanar waveguide step junction [(s + 2w) = 240 µm] S. Freq Step 190–30 µm No (GHz) S 11 Mag

Angle

Step 190–40 µm S 21 Mag

S 11 Angle

Mag

S 21 Angle

Mag

Angle

1.

26

0.4547 −10.3792 0.8892 −2.5893 0.4257 −9.7692

0.9036 −2.3535

2.

27

0.4554 −10.4978 0.8888 −2.6714 0.4265 −9.8711

0.9032 −2.4271

3.

28

0.4560 −10.5929 0.8885 −2.7525 0.4272 −9.9501

0.9029 −2.4997

4.

29

0.4567 −10.6650 0.8881 −2.8329 0.4278 −10.0063 0.9025 −2.5714

5.

30

0.4573 −10.7146 0.8878 −2.9125 0.4285 −10.0403 0.9022 −2.6424

6.

31

0.4578 −10.7421 0.8875 −2.9914 0.4291 −10.0524 0.9018 −2.7127

7.

32

0.4584 −10.7481 0.8871 −3.0699 0.4297 −10.0434 0.9015 −2.7825

8.

33

0.4589 −10.7334 0.8868 −3.1481 0.4303 −10.0138 0.9012 −2.8518

9.

34

0.4594 −10.6986 0.8866 −3.2259 0.4308 −9.9643

0.9009 −2.9209

10. 35

0.4598 −10.6446 0.8863 −3.3038 0.4314 −9.8959

0.9007 −2.9897

11. 36

0.4603 −10.5724 0.8860 −3.3817 0.4318 −9.8091

0.9004 −3.0586

12. 37

0.4607 −10.4829 0.8858 −3.4602 0.4323 −9.7049

0.9001 −3.1277

13. 38

0.4611 −10.3769 0.8856 −3.5394 0.4327 −9.5844

0.8999 −3.1976

14. 39

0.4614 −10.2555 0.8853 −3.6201 0.4331 −9.4480

0.8997 −3.2687

15. 40

0.4617 −10.1195 0.8851 −3.7038 0.4335 −9.2964

0.8995 −3.3426

Appendix A: Design Data on Micromachined Transmission Lines and Discontinuities

363

Table A.30 S-parameters of membrane coplanar waveguide step junction [(s + 2w) = 240 µm] S. Freq Step 190–70 µm No (GHz) S 11 Mag

Angle

Step 190–80 µm S 21 Mag

S 11 Angle

Mag

S 21 Angle

Mag

Angle

1.

26

0.3510 −10.9783 0.9352 −2.2391 0.3270 −11.2801 0.9439 −2.2218

2.

27

0.3518 −11.0857 0.9348 −2.3088 0.3278 −11.3780 0.9436 −2.2918

3.

28

0.3526 −11.1666 0.9345 −2.3776 0.3285 −11.4480 0.9433 −2.3610

4.

29

0.3534 −11.2216 0.9342 −2.4456 0.3293 −11.4905 0.9430 −2.4295

5.

30

0.3541 −11.2510 0.9339 −2.5128 0.3300 −11.5059 0.9427 −2.4974

6.

31

0.3547 −11.2554 0.9336 −2.5795 0.3306 −11.4950 0.9425 −2.5647

7.

32

0.3554 −11.2355 0.9334 −2.6456 0.3312 −11.4583 0.9422 −2.6316

8.

33

0.3560 −11.1921 0.9331 −2.7114 0.3318 −11.3969 0.9420 −2.6982

9.

34

0.3565 −11.1261 0.9329 −2.7769 0.3323 −11.3112 0.9418 −2.7645

10. 35

0.3571 −11.0381 0.9326 −2.8423 0.3327 −11.2024 0.9416 −2.8308

11. 36

0.3575 −10.9289 0.9324 −2.9077 0.3332 −11.0714 0.9414 −2.8972

12. 37

0.3580 −10.7996 0.9322 −2.9734 0.3336 −10.9190 0.9413 −2.9640

13. 38

0.3584 −10.6510 0.9321 −3.0398 0.3339 −10.7462 0.9411 −3.0314

14. 39

0.3587 −10.4837 0.9319 −3.1074 0.3342 −10.5535 0.9410 −3.1001

15. 40

0.3590 −10.2974 0.9317 −3.1777 0.3344 −10.3409 0.9409 −3.1712

Table A.31 S-parameters of membrane coplanar waveguide step junction [(s + 2w) = 240 µm] S. Freq Step 190–90 µm No (GHz) S 11 Mag

Angle

Step 190–100 µm S 21 Mag

S 11 Angle

Mag

S 21 Angle

Mag

Angle

1.

26

0.3037 −12.0715 0.9516 −2.1781 0.2795 −12.0626 0.9590 −2.1111

2.

27

0.3044 −12.1738 0.9513 −2.2473 0.2802 −12.1276 0.9588 −2.1790

3.

28

0.3052 −12.2461 0.9511 −2.3158 0.2809 −12.1594 0.9585 −2.2464

4.

29

0.3059 −12.2887 0.9508 −2.3836 0.2816 −12.1586 0.9583 −2.3133

5.

30

0.3066 −12.3024 0.9506 −2.4508 0.2822 −12.1258 0.9581 −2.3797

6.

31

0.3072 −12.2878 0.9503 −2.5176 0.2828 −12.0620 0.9579 −2.4457

7.

32

0.3078 −12.2457 0.9501 −2.5841 0.2833 −11.9678 0.9577 −2.5115

8.

33

0.3084 −12.1768 0.9499 −2.6503 0.2838 −11.8442 0.9575 −2.5772

9.

34

0.3089 −12.0822 0.9497 −2.7163 0.2842 −11.6919 0.9574 −2.6428

10. 35

0.3094 −11.9628 0.9496 −2.7823 0.2846 −11.5121 0.9572 −2.7085

11. 36

0.3098 −11.8193 0.9494 −2.8485 0.2850 −11.3058 0.9571 −2.7744

12. 37

0.3101 −11.6529 0.9493 −2.9150 0.2853 −11.0739 0.9570 −2.8407

13. 38

0.3105 −11.4642 0.9491 −2.9823 0.2855 −10.8176 0.9569 −2.9078

14. 39

0.3107 −11.2542 0.9490 −3.0507 0.2857 −10.5374 0.9568 −2.9760

15. 40

0.3110 −11.0226 0.9489 −3.1215 0.2859 −10.2333 0.9567 −3.0465

364

Appendix A: Design Data on Micromachined Transmission Lines and Discontinuities

Table A.32 S-parameters of membrane coplanar waveguide step junction [(s + 2w) = 240 µm] S. Freq Step 190–130 µm No (GHz) S 11

S 21

Mag

Mag

Angle

Step 190–140 µm S 11 Angle

Mag

S 21 Angle

Mag

Angle

1.

26

0.2061 −16.2318 0.9773 −1.9981 0.1794 −17.4430 0.9825 −1.8465

2.

27

0.2067 −16.2731 0.9771 −2.0647 0.1800 −17.4620 0.9824 −1.9083

3.

28

0.2073 −16.2677 0.9770 −2.1309 0.1806 −17.4292 0.9822 −1.9699

4.

29

0.2079 −16.2164 0.9768 −2.1970 0.1811 −17.3460 0.9821 −2.0313

5.

30

0.2084 −16.1198 0.9767 −2.2628 0.1815 −17.2127 0.9820 −2.0926

6.

31

0.2089 −15.9793 0.9766 −2.3286 0.1819 −17.0310 0.9819 −2.1538

7.

32

0.2093 −15.7956 0.9765 −2.3943 0.1822 −16.8014 0.9818 −2.2151

8.

33

0.2096 −15.5702 0.9764 −2.4602 0.1824 −16.5254 0.9818 −2.2764

9.

34

0.2099 −15.3038 0.9763 −2.5262 0.1827 −16.2041 0.9817 −2.3380

10. 35

0.2101 −14.9981 0.9762 −2.5925 0.1828 −15.8387 0.9816 −2.3998

11. 36

0.2103 −14.6546 0.9761 −2.6592 0.1829 −15.4309 0.9816 −2.4619

12. 37

0.2105 −14.2739 0.9761 −2.7264 0.1829 −14.9815 0.9816 −2.5246

13. 38

0.2106 −13.8581 0.9760 −2.7942 0.1829 −14.4921 0.9815 −2.5879

14. 39

0.2106 −13.4076 0.9760 −2.8631 0.1829 −13.9640 0.9815 −2.6521

15. 40

0.2107 −12.9233 0.9760 −2.9338 0.1828 −13.3971 0.9815 −2.7177

Table A.33 S-parameters of membrane coplanar waveguide step junction [(s + 2w) = 240 µm] S. Freq Step 190–150 µm No (GHz) S 11

S 21

Mag

Mag

Angle

Step 190–160 µm S 11 Angle

Mag

S 21 Angle

Mag

Angle

1.

26

0.1516 −20.8065 0.9871 −1.7645 0.1180 −20.8477 0.9919 −1.4907

2.

27

0.1521 −20.8083 0.9870 −1.8243 0.1184 −20.8404 0.9919 −1.5431

3.

28

0.1525 −20.7482 0.9870 −1.8840 0.1187 −20.7696 0.9918 −1.5955

4.

29

0.1528 −20.6275 0.9869 −1.9436 0.1189 −20.6369 0.9918 −1.6479

5.

30

0.1531 −20.4468 0.9868 −2.0032 0.1191 −20.4424 0.9917 −1.7004

6.

31

0.1534 −20.2074 0.9867 −2.0629 0.1192 −20.1879 0.9917 −1.7530

7.

32

0.1535 −19.9099 0.9867 −2.1227 0.1193 −19.8739 0.9916 −1.8057

8.

33

0.1536 −19.5557 0.9866 −2.1828 0.1193 −19.5012 0.9916 −1.8585

9.

34

0.1537 −19.1462 0.9866 −2.2431 0.1193 −19.0719 0.9916 −1.9117

10. 35

0.1536 −18.6825 0.9866 −2.3038 0.1193 −18.5862 0.9916 −1.9651

11. 36

0.1536 −18.1656 0.9866 −2.3649 0.1192 −18.0462 0.9916 −2.0188

12. 37

0.1534 −17.5972 0.9866 −2.4265 0.1190 −17.4522 0.9916 −2.0729

13. 38

0.1533 −16.9789 0.9866 −2.4888 0.1189 −16.8069 0.9916 −2.1275

14. 39

0.1531 −16.3113 0.9866 −2.5520 0.1186 −16.1107 0.9916 −2.1826

15. 40

0.1529 −15.5955 0.9866 −2.6164 0.1184 −15.3644 0.9916 −2.2386

Appendix A: Design Data on Micromachined Transmission Lines and Discontinuities Table A.34 Equivalent circuit parameters of CPW step discontinuity S. No

CPW step junction (µm)

C1 (pF)

Len1 (°)

Len2 (°)

1.

190 − 10

0.0157

−6.11

1.37

2.

190 − 40

0.0117

−8.96

3.63

3.

190 − 70

0.0177

−9.8

4.47

4.

190 − 100

0.0151

−8.98

5.11

5.

190 − 130

0.0134

−8.40

5.53

6.

190 − 160

0.0091

−7.71

6.25

Table A.35 Effect of bridge width on propagation characteristics of CPW line

S. No

Freq = 35 GHz, g = 10 µm ; t = 1 µm W (µm)

Mag. S 11

Mag. S 21

1.

0

0.0179

0.9993

2.

10

0.0386

0.9988

3.

15

0.0443

0.9985

4.

20

0.0744

0.9967

5.

30

0.0530

0.9981

6.

40

0.0734

0.9968

7.

50

0.0550

0.9980

8.

60

0.0935

0.9951

9.

70

0.0841

0.9960

10.

80

0.1158

0.9928

11.

90

0.2220

0.9746

12.

100

0.1373

0.9901

365

|S11 |

0.386949

0.386785

0.386416

0.385875

0.385202

0.384440

0.383640

0.382854

0.382140

0.381557

0.381164

0.381019

0.381179

0.381691

0.382597

Freq (GHz)

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

0.649949 0.650113 0.650376 0.650734 0.651177 0.651698 0.652286 0.652931 0.653620 0.654340 0.655078

−162.7907

−163.8112

−164.9644

−166.2499

−167.6668

−169.2129

−170.8847

−172.6771

−174.5830

−176.5931

−178.6953

174.608220

176.885523 0.657258

0.656551

0.655820

0.649889

−161.9023

179.124828

|S12 |

∠S11

0.323056 0.316990 0.310971 0.305126

−22.723375 −23.345459 −23.970274

0.329060

0.334909

0.340523

0.345834

0.350788

0.355339

0.359452

0.363099

0.366261

0.368924

0.371081

|S22 |

−22.105754

−21.493865

−20.888593

−20.290489

−19.699808

−19.116558

−18.540518

−17.971273

−17.408238

−16.850684

−16.297758

−15.748507

∠S12

154.223033

157.969331

161.453854

164.685807

167.676846

170.439802

172.987820

175.333791

177.489989

179.467859

−178.7220

−177.0703

−175.5684

−174.2087

−172.9847

∠S22

Table A.36 De-embedded S-parameters of membrane CPW tee-junction discontinuity [50−50−50  lines]

0.689034

0.687095

0.685043

0.682920

0.680762

0.678603

0.676474

0.674403

0.672415

0.670532

0.668773

0.667153

0.665684

0.664377

0.663238

|S23 |

−37.6079

−36.3312

−35.0978

−33.9056

−32.75268

−31.6367

−30.5556

−29.5071

−28.4890

−27.4989

−26.5345

−25.5933

−24.6729

−23.7708

−22.8847

∠S23

366 Appendix A: Design Data on Micromachined Transmission Lines and Discontinuities

|S11 |

0.162404

0.161907

0.161329

0.160679

0.159970

0.159216

0.158434

0.157642

0.156861

0.156113

0.155423

0.154813

0.154304

0.153914

0.153653

Freq (GHz)

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

|S12 | 0.698455 0.698490 0.698534 0.698585 0.698642 0.698704 0.698769 0.698836 0.698901 0.698964 0.699022 0.699074 0.699119 0.699155 0.699183

∠S11

−160.49452

−160.93287

−161.48398

−162.14964

−162.93112

−163.82914

−164.84344

−165.97261

−167.21351

−168.56080

−170.00625

−171.53785

−173.13868

−174.78545

−176.44639

−18.196907

−17.74128

−17.27488

−16.80124

−16.32304

−15.84226

−15.36045

−14.87871

−14.39789

−13.91864

−13.44137

−12.96644

−12.49403

−12.02426

−11.55718

∠S12

0.426689

0.427432

0.428142

0.428804

0.429409

0.429949

0.430419

0.430816

0.431137

0.431380

0.431544

0.431631

0.431641

0.431576

0.431438

|S22 |

161.226103

162.475568

163.674581

164.823630

165.923331

166.974373

167.977367

168.933123

169.842322

170.705685

171.523938

172.297812

173.028053

173.715419

174.360683

∠S22

Table A.37 De-embedded S-parameters of membrane CPW tee-junction discontinuity [50−70−70  lines]

0.573556

0.573039

0.572555

0.572115

0.571727

0.571394

0.571119

0.570902

0.570743

0.570641

0.570595

0.570601

0.570658

0.570763

0.570912

|S23 |

−23.45228

−22.76486

−22.1033

−21.46282

−20.83963

−20.23064

−19.63338

−19.04569

−18.46580

−17.89220

−17.32359

−16.75881

−16.19689

−15.63694

−15.07822

∠S23

Appendix A: Design Data on Micromachined Transmission Lines and Discontinuities 367

|S11 |

0.343254

0.342870

0.342432

0.341943

0.341411

0.340843

0.340247

0.339633

0.339011

0.338392

0.337787

0.337205

0.336656

0.336143

0.335666

Freq (GHz)

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

|S12 | 0.667280 0.667789 0.668308 0.668833 0.669361 0.669888 0.670410 0.670921 0.671419 0.671898 0.672354 0.672784 0.673186 0.673559 0.673906

∠S11

−168.75027

−168.96981

−169.25266

−169.5993

−170.00989

−170.48423

−171.02168

−171.62104

−172.28043

−172.9971

−173.76724

−174.58563

−175.44525

−176.33671

−177.24739

−15.79202

−15.34221

−14.88669

−14.42857

−13.97017

−13.51323

−13.05904

−12.60858

−12.16254

−11.72142

−11.28551

−10.85511

−10.43021

−10.0108

−9.596910

∠S12

0.322831

0.324209

0.325609

0.327010

0.328396

0.329751

0.331063

0.332320

0.333511

0.334629

0.335665

0.336615

0.337473

0.338238

0.338906

|S22 |

165.347649

166.988100

168.540607

170.006252

171.386462

172.682848

173.897130

175.031090

176.086547

177.065338

177.969308

178.800300

179.560156

−179.74923

−179.12620

∠S22

Table A.38 De-embedded S-parameters of membrane CPW tee-junction discontinuity [70−70−70  lines]

0.664472

0.664155

0.663851

0.663571

0.663325

0.663116

0.662950

0.662826

0.662748

0.662714

0.662724

0.662777

0.662873

0.663008

0.663180

|S23 |

−24.26467

−23.56924

−22.89275

−22.23216

−21.585

−20.94926

−20.32321

−19.7054

−19.09458

−18.48966

−17.88966

−17.29373

−16.7011

−16.11106

−15.52306

∠S23

368 Appendix A: Design Data on Micromachined Transmission Lines and Discontinuities

|S11 |

0.499525

0.500454

0.501351

0.502214

0.503043

0.503835

0.504589

0.505306

0.505985

0.506625

0.507227

0.507788

0.508307

0.508779

0.509194

Freq (GHz)

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

|S12 | 0.612910 0.612485 0.612058 0.611626 0.611191 0.610750 0.610304 0.609852 0.609392 0.608925 0.608450 0.607968 0.607477 0.606982 0.606488

∠S11

−174.53746

−174.70222

−174.90081

−175.13309

−175.39875

−175.69733

−176.02817

−176.39036

−176.78269

−177.20363

−177.65114

−178.12269

−178.61465

−179.12279

−179.64111

−12.18027

−11.90185

−11.61474

−11.32126

−11.02342

−10.72236

−10.41917

−10.11463

−9.809315

−9.503632

−9.197893

−8.892306

−8.587003

−8.282059

−7.977487

∠S12

0.252122

0.252341

0.252732

0.253260

0.253901

0.254623

0.255403

0.256220

0.257052

0.257883

0.258696

0.259477

0.260216

0.260902

0.261527

|S22 |

164.694681

166.745908

168.684055

170.509926

172.224973

173.830442

175.328126

176.719933

178.007949

179.194402

−179.71836

−178.72790

−177.83172

−177.02727

−176.31197

∠S22

Table A.39 De-embedded S-parameters of membrane CPW tee-junction discontinuity [100−70−70  lines]

0.754000

0.753530

0.753003

0.752431

0.751827

0.751199

0.750557

0.749907

0.749256

0.748608

0.747970

0.747344

0.746736

0.746147

0.745582

|S23 |

−20.65324

−19.98164

−19.32864

−18.69213

−18.071

−17.46344

−16.86848

−16.28515

−15.71257

−15.14998

−14.59667

−14.05196

−13.51524

−12.98592

−12.46344

∠S23

Appendix A: Design Data on Micromachined Transmission Lines and Discontinuities 369

|S11 |

0.337946

0.338119

0.338251

0.338344

0.338403

0.338431

0.338434

0.338419

0.338392

0.338358

0.338326

0.338302

0.338290

0.338344

0.338307

Freq (GHz)

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

0.667852 0.667803 0.667757 0.667714 0.667671 0.667625 0.667577 0.667523 0.667461 0.667389

−168.29475

−168.58371

−168.92686

−169.32338

−169.77201

−170.27105

−170.81811

−171.4101

−172.04292

−172.71114 0.667213

0.667906

−168.06047

−174.12274

0.667966

−167.88111

0.667357

0.668034

−167.75663

164.078505

|S12 |

∠S11

0.332504

0.333269

−9.341505

0.334046

−20.37393

0.334816

0.335563

0.336274

0.336938

0.337548

0.338096

0.338577

0.338985

0.339317

0.339573

0.339749

0.339847

|S22 |

−8.884409

−8.646472

−8.405158

−8.161912

−7.917754

−7.673584

−7.429832

−7.186937

−6.945161

−6.704670

−6.465551

−6.227830

−5.991484

∠S12

173.189710

174.403701

175.546945

176.621557

177.629324

178.571792

179.450231

−179.73382

−178.97951

−178.28565

−177.6512

−177.07513

−176.55644

−176.09413

−175.6872

∠S22

Table A.40 De-embedded S-parameters of membrane CPW tee-junction discontinuity [100−100−100  lines]

0.666485

0.666010

0.665540

0.665083

0.664646

0.664233

0.663850

0.663496

0.663175

0.662888

0.662635

0.662417

0.662233

0.662083

0.661966

|S23 |

−15.38464

−14.90706

−14.44705

−14.00175

−13.56893

−13.14678

−12.73379

−12.32885

−11.93077

−11.53868

−11.15177

−10.76934

−10.39072

−10.01534

−9.642670

∠S23

370 Appendix A: Design Data on Micromachined Transmission Lines and Discontinuities

Appendix A: Design Data on Micromachined Transmission Lines and Discontinuities Table A.41 Equivalent circuit parameters of CPW T-junction discontinuity S. No 1.

CPW T-junction 50–50–50

L 1 (pH)

C 1 (pF)

Len1 (°)

Len2 (°)

58.86

0.0557

−11.3

12

2.

70–70–70

33.99

0.0211

−5.4

8.2

3.

100–100–100

20.79

0.0114

−3.3

4.6

4.

50–70–70

1.99

0.0107

−0.4

9

5.

100–70–70

111.25

0.0194

−13.6

7.1

371

Appendix B

Details of Fabrication Process

The process starts with a 0.025 thick Alumina substrate polished on both sides. The relative permittivity of the substrate is 9.8 with loss tangent of 0.0001 at 1 MHz. The masks that are used for the process are E-beam-write chrome masks. Alumina substrate is used in this work because of its following properties. 1. 2. 3. 4. 5. 6.

Good mechanical strength. Good heat conductivity and fire resistance. Good corrosion and wear resistance. Very good electric insulation. Good surface with high smoothness and less porosity. Stable in very high temperature and corrosive chemical. Characteristic of Substrate materials (Al2 O3 ) is given in Table B.1. The fabrication process requires six masks and steps as shown in Fig. B.1.

Step 1:

After the RCA cleaning of the wafer, the first layer of chromium (Cr) or Titanium Tungsten (TiW) is deposited and patterned using the lift-off technique. This layer is used to make electrical biasing in the circuit by mask 1. (Except Chap. 6, all other devices fabricated and reported in this book use TiW as a bias line).

Table B.1 Characteristic of substrate material Properties

Values

Substrate, Al2 O3

99.6%

Appearance

White

Bulk density (g/c.c.)

3.85

Grain size average (µm)

1014

Flexure strength (MPa)

500

(Step 1)

(Step 2)

(Step 3)

(Step 4)

(Step 5)

(Step 6)

.

(Step 7) Fig. B.1 Schematic view of micro-fabrication process steps. Note The fabrication process steps are used in most of the devices reported in this book

Step 2:

Step 3:

A 0.3–0.7 µm of Silicon Oxide (SiO2 ) is deposited using plasma enhanced chemical vapour deposition (PECVD) and patterned. RIE is employed to pattern the oxide and remove the patterning photo resist. This is a passivation layer and deposited on the last layer (Cr/TiW) by mask 2. The sheet resistance of this layer is 0.025 /square An evaporated 400Å chromium/100nm gold bilayer is deposited as a seed layer. A photo-resist mould is formed in the third lithographic step and 1–2µm gold is electroplated (based on the design requirement) inside the mould. The mould and seed layers will be removed afterwards. Chromium

Appendix B: Details of Fabrication Process

Step 4:

Step 5:

Step 6:

Step 7:

375

is applied as an adhesion layer for the gold. This layer is used to pattern the CPW line, fixed electrodes, and bias pad by mask 3. A 300Å of Titanium Tungsten (TiW) film is sputtered followed by the deposition of 0.5–0.7 µm silicon oxide using PECVD at 250 °C. The dielectric and TiW layers are dry etched. The TiW layer serves as an adhesion layer for the silicon oxide to the gold. This layer is patterned by mask 4 to make an insulation layer on CPW line and on actuation electrodes. Spin coated Polyimide (PI) is used as the sacrificial layer for this process. Initially, it is coated to a thickness of 2.5 µm. Next, it is patterned by mask 5 (anchor mask) in an RIE step to etch the PI and fully clear the anchor holes. The top gold layer consists of a sputtered gold seed layer and an electroplated gold. The total thickness of this layer varying from 1.25 to 3.5 µm (based on the design requirement), and it is used as the structural layer for the devices. Moulding Method is used to define this layer. This layer is patterned to make mobile electrode by mask 6. The sheet resistance of this layer is 0.02 /square Last most step is the release process. In this process sacrificial layer is removed in an oxygen plasma dry etch process. In some of the devices, sacrificial layer is released using CO2 Critical Point Drying process at 350 °C in the oven and etched using EKC 265.

Index

A ADS, 33, 35, 37, 100, 109, 208. See also Advanced design system Agilent, 28, 33, 48, 76, 78, 99, 110, 115, 200, 248 Anechoic chamber, 269 Antenna(s), 2, 4, 8, 11, 13–15, 60, 108, 184, 195, 247–272, 275–290, 321, 328, 336 Attenuation constant, 25, 26, 172

B Bias voltage, 69, 84, 97, 99, 101, 106, 111, 115, 164, 171, 179–181, 202, 205, 208, 217, 229, 239, 240, 261, 264, 266, 267, 294, 309, 320 Biaxial residual stress, 203 Bragg frequency, 156, 169 Bulk Micromachining, 10, 19, 58, 254

C Cantilever beam, 70–73, 75–77, 83, 99, 106, 114–117, 230, 232, 233, 238, 241, 294–298 Capacitive coupling, 10, 336 Casimir force, 307–313, 315, 317, 318, 322, 324 Characteristic impedance, 3, 22–27, 30, 35, 65, 82, 115, 169, 171, 205, 229 CMOS circuits, 41 COMSOL, 204, 322

Contact force, 75, 85, 90, 97, 232, 233 Contact materials, 76, 92, 231, 236, 238 Contact resistance, 62, 75, 76, 80, 81, 90, 92, 97, 99, 111, 112, 181, 200, 201, 227, 228, 230 CPW, 2, 3, 4, 35, 37–42, 65, 70, 96, 108–111, 113–115, 117, 121, 162–166, 169–171, 174, 177, 184, 204, 206, 211, 229, 233, 237, 240, 257, 258, 264–266, 341, 342, 365–371, 375. See also Coplanar waveguide (CPW) Critical point drying, 211, 240, 375

D Damping coefficient, 71, 78 DC contact, 79–81, 83, 86, 92, 229 Deflection, 72, 75, 77, 83, 97, 106, 110, 111, 115, 128, 166, 204, 233, 295–297, 304, 305, 311 Dielectric charging, 71, 80, 85, 88, 92, 113, 178, 229, 241, 242 Dielectric constant, 4, 11, 23, 25, 27, 29, 32, 34, 44, 65, 169, 180, 247, 248, 251, 275, 285, 286 Dielectric loss, 3 Dielectric material, 3, 121, 231, 241, 293, 314, 317, 320 DMTL, 155, 156, 162, 167–169, 173, 174, 179, 181–183, 187, 239, 240. See also Distributed MEMS transmission line

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 S. K. Koul and S. Dey, Micromachined Circuits and Devices, Lecture Notes in Electrical Engineering 859, https://doi.org/10.1007/978-981-16-9443-1

377

378 Down-state capacitance, 157, 168, 170 DRIE. See also Deep reactive ion etching Dynamic analysis, 115

E Electromechanical modelling, 46, 115 Electrostatic actuation, 5, 43, 44, 62, 70, 74, 95, 114, 115, 167, 174, 235 Electrostatic actuator, 63, 294 Electrostatic force, 43, 75, 115, 232 Etchant, 254

F Fabrication process, 46, 70, 97, 99, 136, 163, 211, 240, 247, 252, 256, 258, 341, 373, 374 FEM, 29, 35, 47, 50, 100, 103, 109, 163, 164, 209, 248, 251, 277, 281. See also Finite element method Filter(s), 2, 8, 9, 12, 15, 57, 58, 123, 132, 133, 139, 160, 161, 195–202, 205–220, 225, 240, 242–245, 277, 296, 327–330, 337, 338, 343 FOM, 161, 167, 176, 178, 233, 236. See also Figure-of-merit Fringing field effect, 44, 76, 77 Full wave simulator, 30, 99, 117, 176, 265

G Ground planes, 3, 4, 11, 19, 20, 109, 117, 118, 163, 164, 166, 170, 171, 185, 257, 264, 267, 296, 297, 301, 312, 317, 320, 333, 335, 336

H Hermetic packaging, 238 HFSS, 31–35, 37–39, 99–101, 109, 110, 163, 165, 208, 217, 258. See also High frequency structure simulator High power level, 235

I Inductor(s), 1, 2, 4, 10, 12, 13, 19, 20, 41, 57–61, 65, 115, 160, 161, 196, 197 Insertion loss, 1, 3, 5, 7, 55, 56, 61, 62, 69, 82, 86, 99–101, 103–105, 110, 111, 113, 116, 118, 120, 121, 132, 155, 156, 159, 161–168, 171–173, 176, 177, 179–182, 184, 185, 196–200,

Index 202, 204, 207–209, 215, 218–220, 233, 243, 244, 257, 258, 262, 264, 277, 293, 295–297, 299, 302, 304–308, 321, 324, 327, 330, 338–342 Isolation, 5, 7, 11, 62, 63, 69, 71, 81, 82, 86, 95, 96, 99, 101, 103–106, 110–113, 116–121, 180, 196, 200, 202, 231, 247, 256, 257, 261, 264, 275, 293, 295–299, 301, 302, 306–308, 320, 324, 339, 340

J Junction capacitance, 99, 101, 103, 106, 110, 159, 237

L Lateral switch(es), 113–115, 117, 121 LDV, 48, 73, 99. See also Laser doppler vibrometer Lithography, 3, 10 LTCC, 213, 216, 217. See also Low temperature cofired ceramic Lumped element, 28, 35 Lumped model, 20, 27, 28, 30–35, 38, 39, 40, 42, 65 Lumped parameters, 47, 81

M Matching network, 8, 57, 58, 159 Mechanical resonance frequency, 41, 71, 73, 77, 90, 98, 99, 110, 115, 116, 137, 200 MEMS bridge, 162, 168–170, 172, 174–176, 196, 197, 203, 205, 206, 239 Metamaterials, 15, 196, 293, 299, 302–304, 306, 310–318, 320, 322–324, 327, 328, 332–337, 342, 343 Microfabrication, 5, 6, 136, 186, 330, 331, 335, 342 Microstrip transmission line, 2 MIM, 168, 317. See also Metal-insulator-metal MTTR, 237. See also Mean time to failure

N Noise, 9, 41, 43, 54, 58, 132, 139, 141–145, 148–150, 195, 196

Index O On-wafer calibration technique, 99 Oxygen plasma, 375

P Packaging, 8, 9, 123, 174, 212, 213, 225, 238 Parasitic capacitance, 49, 99, 127, 159 coupling effect, 110, 336 inductive effect, 106, 121, 237 slotline modes, 164, 166, 264 PECVD, 374, 375. See also Plasma-enhanced chemical vapour deposition Phased arrays, 184, 195, 257 Phase error-, 155, 158, 159, 162–165, 167, 171, 172, 181–183, 233–235, 239 Phase shifter(s) loaded line, 156, 159, 160, 162 low-pass / high-pass, 155, 160–162 reflection, 156, 157, 181 switched-line, 155, 156, 158, 159, 162, 163, 232, 257 TTD, 156, 179, 182, 185, 187–189. See also True-time-delay Photoresist Poisson’s ratio, 45 PSD, 142, 143. See also Power spectral density Pull-in voltage, 44, 47, 75–78, 83, 97, 203, 210, 230, 235 Pull-out voltage, 235 Push-pull actuator, 167, 174, 182

Q Quality factor, 1, 4, 8, 11, 19, 41, 43, 45, 55, 57, 58, 73, 76, 78, 124, 125, 131, 136, 143, 144, 168, 204, 331

R Reconfigurable phase shifter, 179, 181–183, 341 Reliability, 1, 5, 7, 8, 15, 92, 95, 113, 115, 174, 179, 184, 196, 197, 209–211, 213, 215–217, 225–245, 293, 322, 341 Residual stress, 49, 72, 73, 76, 77, 83, 178, 203, 233 Resonators, 1, 2, 8, 9, 12, 13, 57, 123–146, 148–150, 204, 275, 276, 330, 334, 335

379 RIE, 375. See also Reactive ion etching

S Scattering parameters, 35, 39, 281 Shunt switch, 5, 69, 157, 159, 197, 202, 294–297, 301–304, 306, 308, 322–324 SOI, 63, 95, 184, 186. See also Silicon-on-insulator SOLT, 82, 110, 115, 200, 206, 215. See also Short-open-load-through SP3T, 101, 102, 118, 185, 187, 188. See also Single-pole-three throw SP4T, 87, 108, 118, 155, 165, 179–181, 183, 232–234, 236–239. See also Single-pole-four-throw SP6T, 102, 103, 118, 119. See also Single-pole-six-throw SP8T, 99–101, 103, 179–181, 186, 187, 189, 236–239, 264. See also Single-pole-eight-throw SP10T, 103, 104. See also Single-pole-ten-throw SP11T, 104, 105. See also Single-pole-eleven-throw SP12T, 105. See also Single-pole-twelve-throw SP14T, 96, 105, 106, 120, 230. See also Single-pole-fourteen-throw SP16T, 108, 109–113, 163, 165, 166. See also Single-pole-sixteen-throw SPDT, 116–118, 158, 159, 161, 163, 165, 232, 233, 257–259, 261, 262, 264, 287. See also Single-pole-double throw SPST, 6, 99, 105, 107, 108, 111, 180, 188, 189, 232–234, 261, 264, 267, 268, 287. See also Single-pole-single-throw Surface roughness, 72, 206, 327, 338, 341

T Thermal expansion coefficient, 83, 89, 230, 231 T-junction, 32, 38–42, 109, 275, 276, 352, 371

V Varactor(s), 1, 2, 4, 5, 12, 13, 19, 20, 41, 43, 45–49, 51, 53–55, 57, 58, 61, 65,

380

Index 162, 178, 179, 181, 182, 184–186, 197, 198, 202, 204, 239, 240

VNA, 90, 249, 254, 260. See also Vector network analyzer

W Wire bonding, 117, 284

Y Young’s modulus, 45, 73, 128–130