Ferroelectrics in microwave devices, circuits and systems: physics, modelling, fabrication and measurements

Engineering Materials and Processes

Series Editor Professor Brian Derby, Professor of Materials Science Manchester Materials Science Centre, Grosvenor Street, Manchester, M1 7HS, UK

Other titles published in this series Fusion Bonding of Polymer Composites C. Ageorges and L. Ye

Fuel Cell Technology N. Sammes

Composite Materials D.D.L. Chung

Casting: An Analytical Approach A. Reikher and M.R. Barkhudarov

Titanium G. Lütjering and J.C. Williams

Computational Quantum Mechanics for Materials Engineers L. Vitos

Corrosion of Metals H. Kaesche Corrosion and Protection E. Bardal Intelligent Macromolecules for Smart Devices L. Dai Microstructure of Steels and Cast Irons M. Durand-Charre Phase Diagrams and Heterogeneous Equilibria B. Predel, M. Hoch and M. Pool Computational Mechanics of Composite Materials M. Kamiński Gallium Nitride Processing for Electronics, Sensors and Spintronics S.J. Pearton, C.R. Abernathy and F. Ren Materials for Information Technology E. Zschech, C. Whelan and T. Mikolajick

Modelling of Powder Die Compaction P.R. Brewin, O. Coube, P. Doremus and J.H. Tweed Silver Metallization D. Adams, T.L. Alford and J.W. Mayer Microbiologically Influenced Corrosion R. Javaherdashti Modeling of Metal Forming and Machining Processes P.M. Dixit and U.S. Dixit Electromechanical Properties in Composites Based on Ferroelectrics V.Yu. Topolov and C.R. Bowen Charged Semiconductor Defects Edmund G. Seebauer and Meredith C. Kratzer Modelling Stochastic Fibrous Materials with Mathematica® William W. Sampson

Spartak Gevorgian

Ferroelectrics in Microwave Devices, Circuits and Systems Physics, Modelling, Fabrication and Measurements

123

Spartak Gevorgian, Prof. Chalmers University of Technology Department of Microtechnology and Nanoscience Gothenburg Sweden and Ericsson AB Moelndal Sweden [email protected]

ISSN 1619-0181 ISBN 978-1-84882-506-2 DOI 10.1007/978-1-84882-507-9

e-ISBN 978-1-84882-507-9

British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Library of Congress Control Number: 2009926143 © Springer-Verlag London Limited 2009 Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms of licences issued by the Copyright Licensing Agency. Enquiries concerning reproduction outside those terms should be sent to the publishers. The use of registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant laws and regulations and therefore free for general use. The publisher makes no representation, express or implied, with regard to the accuracy of the information contained in this book and cannot accept any legal responsibility or liability for any errors or omissions that may be made. Cover design: eStudioCalamar, Figueres/Berlin Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)

It is not the strongest species that survive, nor the most intelligent, but the ones most responsive to change Charles Darwin

Preface

Today’s wireless communications and information systems are heavily based on microwave technology. Current trends indicate that in the future along with microwaves, the millimeter wave and Terahertz technologies will be used to meet the growing bandwidth and overall performance requirements. Moreover, motivated by the needs of the society, new industry sectors are gaining ground; such as wireless sensor networks, safety and security systems, automotive, medical, environmental/food monitoring, radio tags etc. Furthermore, the progress and the problems in the modern society indicate that in the future these systems have to be more user/consumer friendly, i.e. adaptable, reconfigurable and cost effective. The mobile phone is a typical example which today is much more than just a phone; it includes a range of new functionalities such as Internet, GPS, TV, etc. To handle, in a cost effective way, all available and new future standards, the growing number of the channels and bandwidth both the mobile handsets and the associated systems have to be agile (adaptable/reconfigurable). The complex societal needs have initiated considerable activities in the field of cognitive and software defined radios and triggered extensive research in adequate components and technology platforms. To meet the stringent requirements of these systems, especially in agility and cost, new components with enhanced performances and new functionalities are needed. In this sense the components based on ferroelectrics have greater potential and already are gaining ground. After years of research efforts in materials science, device physics and demonstration of large number laboratory demonstrators, the ferroelectric technology for microwave applications is making its way to the industry and commercial applications. Ferroelectrics are a class materials characterized by spontaneous polarization (in ferroelectric phase). In this phase they are widely used in memory cells. The piezoelectric properties are used in sensors, actuators etc. Components based on ferroelectric phase have a wide range of commercial applications. Ferroelectrics in paraelectric (non polar) phase have even greater potential for microwave applications. A large class of ferroelectrics, especially perovskites, are very good dielectrics characterized by extremely high dielectric permittivity which depend on the vii

viii

Preface

applied electric field, mechanical stress and temperature. Good dielectric properties (low microwave loss and leakage currents) and electric field dependent permittivity makes the parametric phase ferroelectrics attractive for the development of a wide range of tunable microwave devices for applications in agile microwave systems. The materials properties from engineer’s perspective, device, circuit and system applications of the paralectric phase ferroelectrics are the main subjects of the book. The book consists of an introduction, several chapters covering the physics of ferroelectrics (engineer’s perspective), methods of fabrication and microscopic analysis, modeling and microwave measurements of the materials and devices. The basic ferroelectric components – varactors and their microwave applications in devices (phase shifters, delay lines, filters etc.), circuits (oscillators, amplifiers etc.) and systems (i.e. phased arrays) are in the focus of the book. The Introduction gives a general overview of the main material properties. It reviews the main competing tunable technologies and gives a historical overview on the ferroelectric materials and their microwave applications, current status, potential and trends. Chapter 2 gives a brief introduction to the physics of the ferroelectrics. The temperature, DC field, and frequency dependences of the dielectric permittivity and microwave losses are considered and simple engineering formulas useful for device modeling are included. This chapter includes acoustic properties of the ferroelectrics where the emphasis is put on induced piezoelectric effect in paraelectric phase – a new phenomena useful for the development of tunable acousto-electric devices. The fabrication processes of bulk (single crystal and ceramic), and film (thick, thin) are considered in Chap. 3. The fabrication process of the thin films, suitable for the industrial scale mass production (RF magnetron sputtering, sol-gel etc.), are described in more details. This chapter includes also methods and the results of the microstructure analysis of the ferroelectric films and correlation of the dielectric properties with the microstructure – allowing optimization of the fabrication processes and film properties. The laser ablation process is considered as a flexible and express method for the experiments with the new ferroelectric compositions. The ferroelectric varactors, as the basic components used in tunable lumped and distributed devices and passive components (i.e. high density capacitors), are considered in Chap. 4. A comparison between the two main varactor designs – coplanar plate and parallel plate varactors is given. The equivalent circuit models and the design formulas for these varactors are provided. The power handling capability and tuning speed are considered in this chapter. The effects of the electrodes/interfaces, the substrates and the integration possibilities are considered and a detailed analysis of high resistivity silicon as the most promising substrate for integrated microwave modules incorporating ferroelectric (and other emerging components) is given. The passive components, such as high density decoupling capacitors based on ferroelectric films, dielectric spacers in MEMs and gates in field effect transistors are also included in this chapter.

Preface

ix

Chapter 5 looks at the ferroelectric devices. It includes delay lines and delay line type phase shifters with frequency independent tunable delay time and phase shifters with frequency independent tunable phase shift. These devices along with tunable resonators, filters, matching networks, tunable power splitters and antennas are the most representative components considered for applications in microwave systems. Applications of the ferroelectric varactors in nonlinear devices like harmonic generators, frequency converters, power limiters, pulse shapers and parametric amplifiers are briefly reviewed. A new type of device – a tunable thin film bulk acoustic resonator using induced piezoelectric effect in paraelectric films concludes the chapter. Chapter 6 is devoted to the circuit and system applications of the ferroelectric materials and components. Voltage Controlled Oscillators (VCO), power amplifiers, beam steering networks for the phased arrays and reconfigurable antennas are the typical applications considered. The nontraditional and lens type steerable beamformers based on ferroelectrics allow size and cost reduction. Modeling of the microwave components and devices based on ferroelectrics and methods of the measurements and are considered in Chaps. 7 and 8. The simple analytic formulas are mainly based on the conformal mapping technique and assume uniform dielectric permittivity distribution in ferroelectrics layers. They are useful for device optimization and measurements of the dielectric properties of the ferroelectric layers. Chapter 8 discusses resonant and broad band measurements of the dielectric properties of bulk, thick and thin films ferroelectrics. It includes also methods for the measurement of the nonlinearities and tuning speeds. Chapter 9 considers the further potential and perspectives of agile materials. New promising agile materials, like multiferroics, ferroelectric and ferromagnetic nanotubes, pyrochlores, oxides with resistive switching, and liquid crystals are reviewed in this chapter. Potentials for applications in metamaterials and THz technology are considered. New effects in ferroelectrics, like resistivity switching in doped SrTiO3, nanoscale effects, integration with semiconductors and High Temperature Superconductors (HTS), are reviewed. The concluding Chap. 10 summarizes the main performance features of the ferroelectric devices including temperature stabilization, nonlinearity and power handling capability, hysteresis, long term stability etc. It is shown that these and other “traditional” concerns pose no limitations on commercialization and wide scale applications of ferroelectrics in agile microwave devices and systems. The book is an introduction into the field intended to give practical knowledge in physics, fabrication technology, methods of design, modeling and measurements of tunable components and circuits based on ferroelectrics. It is intended for students (undergraduate and graduate), microwave device, circuit and system designers both in academia and industry. Gothenburg, Sweden September 2008

Spartak Gevorgian

Contents

1

Introduction: Overview of Agile Microwave Technologies ................ 1.1 Introduction................................................................................... 1.2 Ferroelectrics: The Main Material Properties ............................... 1.2.1 Ferroelectric Properties .................................................... 1.2.2 Dielectric Properties......................................................... 1.2.3 Acoustic Properties .......................................................... 1.2.4 Typical Microwave Paraelectrics ..................................... 1.3 Microwave Applications ............................................................... 1.3.1 Historical Overview ......................................................... 1.3.2 Current Status................................................................... 1.3.3 Potential and Trends......................................................... 1.4 Other Agile Microwave Technologies .......................................... 1.5 Conclusions................................................................................... References ................................................................................................

1 1 2 3 4 5 6 7 7 8 11 15 18 18

2

Physics of the Tunable Ferroelectric Devices....................................... 2.1 Introduction................................................................................... 2.2 Crystal Structure, Non-Polar (Paraelectric) and Polar (Ferroelectric) Phases.................................................... 2.3 Dielectric Models of the Ferroelectric and Paraelectric Phases .... 2.3.1 Phenomenological (Thermodynamic) Theory.................. 2.3.2 Microscopic Theory ......................................................... 2.4 Engineering Models of the Dielectric Permittivity ....................... 2.4.1 Barrett’s Formula. Bulk Single Crystals .......................... 2.4.2 Rupprecht–Bell–Silverman Model. Bulk Single Crystals......................................................... 2.4.3 Vendik’s Model. Bulk Single Crystals............................. 2.4.4 Granular Ceramics and Composites ................................. 2.4.5 Columnar Thin Film Ceramics and Composites ..............

21 21 22 24 24 27 29 29 30 31 32 34

xi

xii

Contents

2.5

Models of the Loss Tangent.......................................................... 2.5.1 Loss Mechanisms and Early Models of the Loss Tangent.......................................................... 2.5.2 Models of the Main Loss Mechanisms............................. 2.6 Dielectric Nonlinearities ............................................................... 2.6.1 Nonlinear Performance of Paraelectrics........................... 2.6.2 Nonlinearity and Power Handling Capability .................. 2.7 Thin Films vs. Bulk....................................................................... 2.7.1 Thin Film vs. Bulk Single Crystal.................................... 2.7.2 Strain ................................................................................ 2.7.3 The Effects of the Strain on Dielectric Properties of the Thin Films.............................................................. 2.8 Electro-Acoustic Properties .......................................................... 2.8.1 Electrostriction ................................................................. 2.8.2 Piezoelectricity and Electrostriction................................. 2.8.3 Electric Field Induced Piezoelectricity in Paraelectric Films......................................................... 2.9 Bulk Conductivity ......................................................................... 2.10 Conclusions................................................................................... References ................................................................................................ 3

Fabrication of Ferroelectric Components and Devices ....................... 3.1 Introduction................................................................................... 3.2 Fabrication of Devices Using Single Crystals............................... 3.2.1 Growth Techniques of Single Crystals............................. 3.2.2 Structural Characterization............................................... 3.2.3 Bulk Single Crystal Devices ............................................ 3.2.4 Thin Film Single Crystal Capacitors ................................ 3.3 Fabrication of Devices Using Bulk Ceramics ............................... 3.3.1 Ceramic Processes............................................................ 3.3.2 Bulk Ceramic Device Fabrication .................................... 3.3.3 Structure of the Bulk Ferroelectric Ceramics................... 3.4 Thick Film, HTCC and LTCC Technologies................................ 3.4.1 Fabrication of Devices Using Thick Film Technology .... 3.4.2 Fabrication of HTCC and LTCC Devices ........................ 3.4.3 Structure of Thick and HTCC/LTCC Films..................... 3.5 Fabrication of Thin Ferroelectric Films ........................................ 3.5.1 Chemical Deposition Methods ......................................... 3.5.2 Physical Deposition Methods........................................... 3.6 Thin Film Device Processing ........................................................ 3.6.1 Coplanar-Plate Configuration .......................................... 3.6.2 Parallel-Plate Configuration............................................. 3.7 Substrate Micromachining and Passivation .................................. 3.7.1 Substrate Micromachining ............................................... 3.7.2 Substrate Passivation........................................................

37 37 39 44 44 45 46 46 48 50 52 52 52 54 56 57 57 61 61 63 63 64 65 66 68 68 68 73 74 74 76 78 80 81 87 98 99 101 106 106 107

Contents

xiii

3.8 Conclusions................................................................................... 108 References ................................................................................................ 109 4

5

Substrates, Varactors and Passive Components.................................. 4.1 Introduction................................................................................... 4.2 Substrates ...................................................................................... 4.2.1 Common Substrates ......................................................... 4.2.2 Silicon as a Microwave Substrate .................................... 4.2.3 High Resistivity Silicon ................................................... 4.3 Varactors. Basic Designs and Figure of Merit .............................. 4.3.1 Basic Designs of Ferroelectric Varactors ......................... 4.3.2 Figure of Merit, Structure and Performance of Ferroelectric Films ....................................................... 4.3.3 Correlation of the Design with the Film Structure ........... 4.3.4 Varactor Design Issues..................................................... 4.4 Equivalent Circuit Model of the Varactors ................................... 4.4.1 Equivalent Circuit ............................................................ 4.4.2 Impedance of Parallel-Plate Varactors ............................. 4.5 Low Frequency and Tuning Performances ................................... 4.5.1 C-V and P-V Performances.............................................. 4.5.2 I-V Performance............................................................... 4.5.3 Tuneability and Response Time ....................................... 4.6 Microwave Performance ............................................................... 4.6.1 Parallel-Plate Varactors.................................................... 4.6.2 Coplanar-Plate Varactors ................................................. 4.6.3 Distributed Varactors ....................................................... 4.7 Power Handling Capability and High Power Varactors................ 4.7.1 Parallel-Plate Varactors.................................................... 4.7.2 Coplanar-Plate Varactors ................................................. 4.8 Ferroelectrics in Passive Devices as High Permittivity Dielectric...................................................... 4.8.1 High Density Capacitors .................................................. 4.8.2 MEMs with Ferroelectric Spacers.................................... 4.8.3 MOS Transistors with Ferroelectrics as Gate Dielectric ............................................................. 4.9 Conclusions................................................................................... References ................................................................................................ Ferroelectric Devices.............................................................................. 5.1 Introduction................................................................................... 5.2 Tunable Delay Lines and Delay Line Type Phase Shifters ........... 5.2.1 Figure of Merit ................................................................. 5.2.2 Periodically Loaded Lines................................................ 5.2.3 Uniformly Loaded Delay Lines........................................ 5.2.4 Other Delay Lines ............................................................

115 115 116 116 118 119 125 125 128 129 134 139 139 143 144 144 146 149 151 151 156 161 162 163 164 165 165 167 168 169 170 175 175 176 176 177 182 186

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Contents

5.3

Phase Shifters................................................................................ 5.3.1 Figure of Merit of an Analog Phase Shifter ..................... 5.3.2 Periodically Loaded Line Phase Shifters.......................... 5.3.3 Reflection Type Phase Shifters ........................................ 5.3.4 Phase Shifters Based on All Pass Filter Topology ........... 5.3.5 Other Phase Shifters......................................................... 5.4 Tunable Filters .............................................................................. 5.4.1 Tunable Resonators.......................................................... 5.4.2 Bandpass Filters ............................................................... 5.4.3 Notch Filters..................................................................... 5.5 Matching Networks (Impedance Tuners)...................................... 5.6 Power Splitters .............................................................................. 5.7 Antennas ....................................................................................... 5.8 Nonlinear Devices......................................................................... 5.8.1 Harmonic Generators ....................................................... 5.8.2 Frequency Up-Converters ................................................ 5.8.3 Power Limiters ................................................................. 5.8.4 Pulse Shapers ................................................................... 5.8.5 Parametric Amplifiers ...................................................... 5.9 TFBARs ........................................................................................ 5.9.1 Basic Designs and Resonant Frequencies ........................ 5.9.2 Tunable TFBARs ............................................................. 5.10 Conclusions................................................................................... References ................................................................................................

187 187 188 192 192 194 196 196 199 203 204 206 207 208 208 208 209 210 211 212 212 213 217 217

6

Circuit and System Applications of Tunable Ferroelectric Devices .. 6.1 Introduction................................................................................... 6.2 Voltage Controlled Oscillators...................................................... 6.3 Amplifiers ..................................................................................... 6.4 Steerable Phased Array and Beam Antennas ................................ 6.4.1 Phased Arrays .................................................................. 6.4.2 Steerable Beamformers and Phased Arrays ..................... 6.4.3 Nontraditional and Lens Type Steerable Beamformers ... 6.5 Conclusions................................................................................... References ................................................................................................

225 225 226 229 231 231 232 236 241 242

7

Modeling.................................................................................................. 7.1 Introduction................................................................................... 7.2 Coplanar-Plate Transmission Lines .............................................. 7.2.1 The Equivalent Circuit of the Lines ................................. 7.2.2 Coplanar-Strip Waveguides ............................................. 7.2.3 Coplanar Waveguides ...................................................... 7.3 Multilayer Substrate Coplanar-Plate Capacitors ........................... 7.3.1 Coplanar Plate Capacitors with the Straight Gap (Slot) ... 7.3.2 Interdigital (IDC) Coplanar-Plate Capacitors...................

245 245 246 246 249 259 260 260 265

Contents

8

9

xv

7.4 Parallel-Plate Capacitor................................................................. 7.5 Conclusions................................................................................... Appendix A .............................................................................................. Appendix B .............................................................................................. Appendix C .............................................................................................. Appendix D .............................................................................................. References ................................................................................................

267 271 273 276 280 285 285

Measurements of the Dielectric Properties .......................................... 8.1 Introduction................................................................................... 8.2 Resonant Techniques .................................................................... 8.2.1 Disk Resonator Technique ............................................... 8.2.2 Courtney Resonator.......................................................... 8.2.3 Composite Resonator Method.......................................... 8.2.4 Split-Post Dielectric Resonator Method for Thick and Thin Films ................................................................. 8.2.5 Open Resonator Technique .............................................. 8.2.6 Resonant Technique for on Wafer Characterization of the Ferroelectric Varactors and Films .......................... 8.2.7 Transmission Line Resonator Method ............................. 8.2.8 Near Field Scanning Microscope ..................................... 8.2.9 Uncertainty of Resonant Measurements........................... 8.3 Broadband Techniques.................................................................. 8.3.1 Transmission/Reflection Method. Bulk Samples in Waveguides.................................................................. 8.3.2 Film Measurements Using Coplanar Waveguide (CPW) .............................................................................. 8.3.3 Film Measurements Using Coupled Microstrip Lines ..... 8.3.4 Measurements Using Test Varactors................................ 8.4 Nonlinear Measurements of Ferroelectrics ................................... 8.5 Switching Time of Ferroelectric Films ......................................... 8.6 Conclusions................................................................................... Appendix E............................................................................................... Appendix F............................................................................................... Appendix G .............................................................................................. References ................................................................................................

287 287 289 289 291 295

Potentials and Perspectives.................................................................... 9.1 Introduction................................................................................... 9.2 Multiferroics.................................................................................. 9.3 Ferroelectric Nanotubes. Ferromagnetic Nanowires ..................... 9.4 Metamaterials................................................................................ 9.5 Bridging the “THz Gap” ............................................................... 9.6 Other Tunable Materials ............................................................... 9.6.1 Pyrochlores.......................................................................

351 351 352 354 357 360 361 362

297 299 302 306 308 311 317 317 321 325 326 330 332 334 336 343 346 347

xvi

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Contents

9.6.2 Resistive Switching in Oxides.......................................... 9.6.3 High Temperature Superconductors (HTS)...................... 9.6.4 Liquid Crystals ................................................................. 9.7 Other/New Effects......................................................................... 9.7.1 Resistivity Switching in Doped SrTiO3............................ 9.7.2 Nanoscale Effects............................................................. 9.7.3 Integration with Semiconductors ..................................... 9.8 Conclusions................................................................................... References ................................................................................................

364 367 367 370 370 372 372 373 374

Concluding Remarks.............................................................................. 10.1 Introduction................................................................................... 10.2 Stabilization of the Temperature Dependences............................. 10.2.1 Intrinsic Temperature Dependences of Permittivity and Tuneability................................................................. 10.2.2 Materials and Device Design Based Methods of Stabilization ................................................................. 10.3 Nonlinearity and Power Handling Capability ............................... 10.4 Hysteresis, Retention, Long Term Stability and Noise ................. 10.5 Reliability...................................................................................... 10.6 Integration Trends ......................................................................... References ................................................................................................

379 379 379 380 381 384 384 387 388 389

Index ................................................................................................................ 391

Abbreviations

1D, 2D AC ACRT AFM BJT BST, BSTO BZN CCVD CIS CMOS CPS CPW CRLH CSD CVD DC DFT DRAM EDS FDTD FRAM FWHM GGG HBV HEMT HFET HR

One dimensional, two dimensional Alternating current Accelerated crucible rotation technique Atomic force microscopy Bipolar junction transistor Barium strontium titanate Bismuth zinc niobate Combustion chemical vapor-phase deposition Crystal ion slicing Complementary metal-oxide-semiconductor Coplanar strip waveguide Coplanar Waveguide Composite right/left hand Chemical solution deposition Chemical vapor deposition Direct current Density function theory Dynamic random memory Energy dispersive spectroscopy Finite difference time domain Ferroelectric dynamic random memory Full width at half maximum Gadolinium-gallium garnet Heterojunction barrier varactor High electron-mobility transistor Heterojunction field effect transistor High resistivity

xviii

HTCC HTS, HTSC IDC IDL IL IMD ITRS JCPDS LC LD LED LH LTCC MCM MEM MFOS MIM MMIC MN MOCVD MOD MOS MUT NDR NEM OR PVD QCL RF RFIC RH RTA SCLC SEM SHS SI SiP SoC SPDR SRR TE TEM

Abbreviations

High temperature co-fired ceramics High temperature superconductor Interdigital capacitor Interlayer dielectric Insertion loss Intermodulation distortion International technology roadmap for semiconductors Joint committee on powder diffraction standards Liquid crystal Laser diode Light emitting diodes Left hand Low temperature co-fired ceramics Multichip module Microelectromechanical Metal-ferroelectric-oxide-semiconductor Metal-insulator-metal Microwave monolithicintegrated circuit Matching network Metal organic chemical vapor deposition Metal organic decomposition Metal oxide-semiconductor Material under test Negative differential resistance Nanoelectromechanical Open resonator Physical vapor deposition Quantum cascade lasers Radio frequency RRadio frequency integrated circuit Right hand Rapid thermal annealing Space charge limited current Scanning electron microscopy Self propagation high temperature synthesis Semi-insulating System-in-package System-on-chip Split-post dielectric Resonator Split ring resonator Transverse electric Transverse electro magnetic

Abbreviations

TFBAR TM TSSG VCO VNA VRH XRD YIG

xix

Thin film bulk acoustic wave resonator Transverse magnetic Top seeded solution growth Voltage controlled oscillator Vector network analyzer Variable range hopping X-ray diffraction Vttrium iron garnet

Chapter 1

Introduction: Overview of Agile Microwave Technologies

Abstract This chapter gives an overview of the agile microwave technologies and a general introduction into the microwave applications of ferroelectrics starting with a brief qualitative description of the ferroelectric, dielectric and acoustic properties of ferroelectrics. A short historical overview, the current status and the perspectives are considered in the last sections of this chapter. The chapter intended for a general reader who has very little, or no knowledge at all, on the applications of ferroelectrics in microwave devices. Those who are familiar with the technology may skip this chapter.

1.1 Introduction Since the late 80s and early 90s of the last century (almost a century after the discovery of radio) the wireless communication became a commercial technology involving cellular, terrestrial and space systems. Figure 1.1.1 (a) shows a telephone pole in early 1920s New York. For comparison Fig. 1.1.1 (b) depicts a tower of radio link antennas (modern “telephone pole”) in central Gothenburg, Sweden. Each of the antennas on the tower shown in Fig. 1.1.1 (b) may handle almost as many communications channels as the telephone pole shown in Fig. 1.1.1 (a). Despite today’s achievements in the hardware technology and information density, the truly large scale, commercial microwave-wireless communication seems to be in its first stages of development. The progress shown in Fig. 1.1.1 became possible due to the advances in microwave, and particularly in semiconductor technology. At present, and more importantly in the nearest future, microwave communication systems are going to be more flexible-reconfigurable and adaptable, handling higher information densities and speeds. Further developments of these systems depend entirely upon the availability of new components with enhanced performances and functionalities. In this respect the semiconductor technology, e.g. microwave monolithic integrated circuits (MMIC) is going to play a major 1

2

1 Introduction: Overview of Agile Microwave Technologies

role. However, new materials, new physical phenomena and components based on them are under extensive consideration. Microwave photonics is gaining ground (IEEE MTT 1999). RF micromachined components still seem to be quite promising (Rebeiz 2003). 1D, 2D and 3D periodical dielectric/dielectric or metal dielectric structures, revisited recently as microwave bandgap or photonic bandgap structures (Eleftheriades and Balmain 2005, Caloz and Itoh 2006), offer complex performance improvement and new functional devices for millimeter wave systems. Despite the original anticipations and a large number of excellent demonstrators the attitude of the industry towards the HTS technology is quite “cool”, mainly due to the cryocooling problems. However, given the potential, this technology may be more extensively considered in future microwave systems. Yet another new “old” technology, ferroelectric microwave devices, is making its way from-the-labs-to-the-fabs (Bao et al. 2008, York 2008).

(a)

(b)

Fig. 1.1.1 From wired to wireless communications: from New York 1921 (a) to Gothenburg Sweden 2001 (b)

1.2 Ferroelectrics: The Main Material Properties Ferroelectrics, especially complex oxides with perovskite structure, are truly multifunctional materials. The sensitivity of the physical properties (permittivity,

1.2 Ferroelectrics: The Main Material Properties

3

polarization, refractive index, magnetic permeability etc.) of these materials to temperature, external electrical, magnetic, and mechanical fields (stresses), especially near the temperatures of phase transitions, make them attractive for applications in electronic and optical devices. Ferroelectrics are inherently multifunctional materials. The dielectric, electric, acoustic/mechanical, temperature, magnetic and optical properties of these materials are used in a wide number of electronic applications. In this section a short description of the basic properties, useful for applications in microwave devices, is given. The multifunctional properties of the ferroelectric may be summarized as follows: • Ferroelectric (polar phase) materials possess a stable spontaneous polarization which may be switched by an applied electric field (Böttger et al. 2005); • Antiferroelectric materials possess antiparallel dipole moments that completely cancel each other; • Ferroelastic materials possess a stable and switchable spontaneous deformation; • Piezoelectrics possess a change in strain as a linear function of applied electric field. They also posses a change in polarization as a linear function of applied stress; • Electrostriction describes a change in strain as a function of applied electric field. In contrast to piezoelectricity the electric field dependence is a quadratic function; • Multiferroics are another class of materials that have both ferroelectric and ferromagnetic properties. They are considered in Chap. 9. Two main types of ferroelectrics are distinguished-order-disorder and displaceive. In order-disorder type ferroelectrics the ferroelectricity, i.e. the spontaneous polarization is associated with the ordering of the ions below phase transition temperature. Crystals with the hydrogen bounding, like KH2PO4, belongs to this type of ferroelectrics. In displaceive ferroelectrics one sublattice of the crystal is displaced relative to the other resulting in spontaneous polarization below phase transition temperature. Complex metal oxides with perovskite structure belong to this group. In this book mainly perovskite ferroelectrics (e.g. solid solution BaxSr1–xTiO3) are considered for tunable microwave applications.

1.2.1 Ferroelectric Properties Ferroelectrics may be in polar (ferroelectric, antiferroelectric) or paraelectric, i.e. non-polar, phases. In ferroelectric phase the polarization vs. electric field dependence is characterized by a hysteresis loop, Fig. 1.2.1, similar to that observed in ferrites.

4

1 Introduction: Overview of Agile Microwave Technologies

ε(T)

P

P

+Pr

E

E -Pr

Nonvolotile

Paraelectric: tunable

TC

T

microwave devices

mempry

Fig. 1.2.1 Hysteresis loop used in nonvolatile memory cells

In spite of prefix “ferro” these materials may not have iron ions at all. The prefix appeared in the early stages of study of this class of materials, where they exhibited properties (i.e. hysteresis loop) similar to ferrites. In fact, some of the ferroelectrics do have iron ions, but the presence of the iron is not a necessary condition for having ferroelectricity. The magnetic properties of the ferrites are associated with the spin of the magnetic elements (i.e. Fe), while the ferroelectric/dielectric properties of the ferroelectrics are associated with the electric dipoles, i.e. pairs of negative and positive ions (not necessarily magnetic) in the crystal. Memory cells are one of the main applications of ferroelectrics in polar (ferroelectric) phase, where the hysteresis loop with two equilibrium states of the spontaneous polarization (+Pr and –P r, Fig. 1.2.1) is used to store binary information in nonvolatile memory cells.

1.2.2 Dielectric Properties In the paraelectric (non-polar) phase the ferroelectric is characterized by a high dielectric permittivity which depends strongly on temperature, applied external electric field and mechanical stress. The high dielectric permittivity is utilized in high capacitance capacitors. These type of capacitors are industry standard (i.e. XR7) and are considered currently for integrated circuit (IC) applications. The temperature dependence is used in pyrometers and considered for applications in infra red (IR) detectors. In paraelectric phase, the dependence of the permittivity on the applied electric field, which is the main subject of this book, is considered for applications in phase, frequency and amplitude agile microwave systems. At given temperature the electric, E, field dependence of the permittivity, ε(E), may be approximated as:

ε (E) =

ε (0) ⎛ E 1 + ⎜⎜ ⎝ Eo

⎞ ⎟ ⎟ ⎠

2

(1.2.1)

1.2 Ferroelectrics: The Main Material Properties

5

where ε(0) is the permittivity at zero bias, and Eo is a material parameter. More advanced formulas are given in Chap. 2. A capacitor (varactor) using a paraelectric phase ferroelectric as a dielectric, is the basic building component of these systems. Components like tunable phase shifters, delay lines, filters etc. based on ferroelectric varactors may have advantages over competing technologies in electrical/microwave performance, reduced control power consumption, sizes and cost.

1.2.3 Acoustic Properties In principle all crystals, including non-ferroelectric ones, are electrostrictive, i.e. they change their sizes under applied electric field. In one dimensional case the electric field induced relative change in the crystal length (strain) is related to the electric field quadratically: S=

l ( E ) − l (0) = gE 2 l (0)

(1.2.2)

where g is the electrostrictive coefficient, l(0) is the length at zero, and l(E) under electric field E. Strain is not sensitive to the change in the sign of the applied field. This is one of the features used for distinguishing the electrostriction from the converse piezoelectric effect. Piezoelectric and converse piezoelectric effects are observed only in special class of materials-piezoelectrics. Ferroelectrics in polar phase, and some of them in paraelectric phase, are also piezoelectric. The strain induced in a piezoelectric crystal via converse piezoelectric effect is given as: S=

l ( E ) − l ( 0) = dE l ( 0)

(1.2.3)

where d is the piezoelectric coefficient. The piezoelectric strain changes the sign upon changing the direction (sign) of the electric field. The piezoelectric crystals are also characterized by generation of electric charges (field) on the opposite surfaces of the crystal upon application of a mechanical pressure. Electrostriction and converse piezoelectric effects are used in electromechanical transducers, and particularly thin film bulk acoustic wave resonators (TFBAR). Ferroelectrics are characterized by a rather high electrostrictive effect. All properties of the ferroelectrics considered above, polarization, permittivity, acoustic/elastic constants g, d etc., depend on temperature, external electric field and mechanical strain. In fact there is a rather strong coupling between these parame-

6

1 Introduction: Overview of Agile Microwave Technologies

ters. The electrical and acoustic parameters of the ferroelectrics are related by the equations: S = sT + (d + gE ) E

(1.2.4)

D = ε oε r E + dT

(1.2.5)

where S is the strain (Δl/lo), T (N/m2) is the stress, D (C/m2) is the electrical displacement, E is the electric field (V/m), s (m2/N), g(m2/V2) and d (m/V) are correspondingly the elastic compliance, electrostrictive and piezoelectric constants at constant electric field, ε is the relative dielectric permittivity (at constant T), εo =8.85 10–12 (F/m) is the dielectric constant of vacuum.

1.2.4 Typical Microwave Paraelectrics From the large number ferroelectric materials known today, only a limited number of them are considered for microwave applications. Both polar (ferroelectric) and paraelectric phases may be useful in tunable microwave devices, provided they have low losses and reasonable tuneability. However, the paraelectric phase is preferred since in this phase there is no hysteresis associated with the domains, Fig. 1.2.1. In this respect the quantum paraelectrics, SrTiO3, KTaO3, and CaTiO3 should be given the priority since they do not possess transition into polar (ferroelectric) phase at any temperature. However they need to be cooled down to cryogenic temperatures in order to get reasonable tuneabilities at relatively low DC fields. For the majority of commercial applications the room temperature operation is preferable. Fortunately some of the solid solution of the quantum paraelectrics (BaxSr1–xTiO3, KxLi1–xTaO3, CaxSr1–xTiO3 etc.) are in paraelectric phase at near room temperatures with reasonable high tenability. Currently the solid solutions BaxSr1–xTiO3 are the material of choice for different reasons. This is the most studied at microwave frequencies composition, which allows microwave engineers to use the available data without getting too much involved in materials study. In addition, it allows controlling the Curie temperature by a simple change of the Ba content. At room temperature paraelectric phases of BaxSr1–xTiO3 have low microwave losses, tanδ, and substantial tuneability, Tε(E)=[ε(0)–ε(E)]/ε(0), at relatively week DC fields. Nevertheless, some ferroelectric phase compositions, such as KxNa1–xNbO3, PbxZr1–xTiO3, are also considered for tunable microwave applications. Ferroelectrics have rather high permittivity (for thin films >100), allowing a substantial reduction in the sizes of microwave components. The main advantages of ferroelectric films for microwave applications include frequency independent tuneability (up to 50% or more), high tuning speed (<1.0 ns), extremely small leakage currents and DC control power, high breakdown field, and radiation hardness. In microwave devices they are used in the form of single crystals (bulk thin film) and ceramics (bulk, film).

1.3 Microwave Applications

7

1.3 Microwave Applications 1.3.1 Historical Overview Since late 1960s and early 1970s ferroelectrics have been regarded as attractive for applications in electrically tunable microwave devices, and a number of practical devices have been demonstrated in the past several decades (Bete 1970), (Vendik 1979), (Babbitt et al. 1992, Varadan 1992, Das 1991). In those early days, and up to late 1980s, microwave technology as a whole, and partly ferroelectrically tunable devices, have been considered almost exclusively for military applications. A pioneering and most comprehensive research has been set up at the Electrotechnical Institute named after V.I. Ulyanov (Lenin), S.-Petersburg (Leningrad). These research activities resulted in a considerable number of publications covering fundamental aspects of physics, devices design and experiment. In spite quite promising demonstrators, the tunable microwave devices did not found applications in practical microwave systems, predominantly due to the high dielectric losses. It is generally assumed (even if not stressed specifically in some publications) that for applications in electrically tunable microwave devices ferroelectrics should be in a paraelectric phase. Ferroelectrics in polar phase have not been considered for applications in tunable microwave devices. The reason is that most of the ferroelectrics in polar phase are also piezoelectric and piezoelectric transformations cause large losses at relatively low microwave frequencies (typically less than 10 GHz). Additional losses in polar phase and at low frequencies are associated with the domain wall movements. Hysteresis, which appears in permittivityDC field dependence, was another reason hindering the applications of a ferroelectric in a polar phase. Hence, limited attempts have been undertaken in the past to make electrically tunable microwave devices utilizing the ferroelectric phase. In these respect piezoelectric devices, both surface acoustic wave, and bulk acoustic wave (including bulk and thin film) are exceptions. On the other hand, some recent experiments indicate that such “discrimination” is not valid. For example, rather low microwave losses along with substantial tuneability, Tε(V)=[ε(0)– ε(V)]/ε(0)], of the dielectric permittivity is observed in ferroelectric (piezoelectric) Na0.5K0.5NbO3 (NKN) films at frequencies up to 50 GHz (Abadei et al. 2001). This indicates that at millimeter wave frequencies, the domain wall movements and piezoelectric transformations do not contribute to the microwave losses, and polar phase ferroelectric may be used in tunable microwave devices if they have substantial tuneability and the hysteresis may be compensated electronically. Current developments in communication, information and industrial systems in general, and particularly in microwave communication systems put extreme requirements on the cost/performances of the new devices and components used in them. To meet these requirements a number of new materials, devices and system architectures have been demonstrated recently. Particularly:

8

1 Introduction: Overview of Agile Microwave Technologies

• Silicon industry made impressive progress in developing high-speed (microwave) transistors and ICs (MMICs, RFICs). Improvement in transistor performance (CMOS, bipolar) has been pushing the gate-lengths and feature sizes well below 100 nm, considerably increasing the cost ($/mm2) of the chips. In this respect integration of the lengthy (large size, comparable with the wavelengths) passive microwave components with silicon MMIC chips became even less cost effective. Additionally, the losses associated with on-chip passive microwave components are high due to the decreased conductor cross section and low resistivity of silicon substrate; • Quite promising new microwave device technologies have been demonstrated, including MEMs, micromachined devices, TFBARs, tunable ferroelectric devices, metamaterials and electromagnetic bandgap (EBG) structure etc. These new technologies offer performance/cost improvement, and enhanced functionality, opening up possibilities for the development of reconfigurable and adaptable microwave systems. For the current state of standard silicon technology, these new components with enhanced performances (MEM, TFBAR, micromachined cavities, ferroelectrics etc.) are not compatible with the standard processes used in the silicon industry. At present these components are not considered, by silicon foundries, for integration with (silicon) MMICs. It seems that at present, and in the nearest future, the System-On-Chip concept, including new components with enhanced performances is not feasible, (at least commercially) when it comes to microwave circuits, especially front ends.

1.3.2 Current Status The III-V based semiconductor industry made considerable progress in developing transistors with transit time and maximum oscillation frequencies well above 100 GHz. The traditional digital silicon industry also, driven by increasing market demands and cost constrains, put substantial efforts in developing analog/microwave circuits. Silicon based bipolar and CMOS transistors with transit times and maximum oscillation frequencies above 100 GHz are now available, making it possible to develop Monolithic Microwave ICs (MMICs) for frequencies up to 100 GHz. Along with the transistors, varactors are the other widely used components used in microwave technology for analog (non-digital) tuning purposes. In spite of the progress achieved in the transistor technology, no semiconductor varactors with high enough Q-factor and tuneability are available for frequencies above 10–20 GHz. Typically, the Q-factor of semiconductor varactors decrease with the increased frequency as Q~f–1, and at 50 GHz it is of the order 10 or less. There is a lack of varactors with adequate (compatible with the transistors) performance in this frequency range.

1.3 Microwave Applications

9

The current progress indicates that, to a certain degree, the “varactor gap”, may be filled in by ferroelectric varactors. After several decades of research considerable progress has been achieved in tunable permittivity ferroelectrics, making it possible to develop ferroelectric varactors with performances better than semiconductor analogs in the frequency range above 10–20 GHz (Vorobiev etc. 2003). Thin film ferroelectric varactors have substantially higher Q-factor at microwave and millimeter wave frequencies, higher tuning speed and lower power consumption. Additionally, due to the high dielectric permittivity, the sizes of tunable components based on ferroelectrics may be smaller in comparison with other technologies. Extra flexibility in terms of tuning, enhanced functionalities and performances of tunable devices may be achieved by combination of ferroelectrics with ferrites, ferroelectrics with semiconductors or ferrites with semiconductors. Devices based on such multifunctional materials offer dual, i.e. electric, magnetic tuning possibility and extra flexibility in designing and shaping the device performances. For example, in delay lines and phase shifters it is possible to tune the delay time while maintaining the input/output impedances on a desired level. Present microwave applications of ferroelectrics may be summarized as follows. In piezoelectric devices (Fig. 1.3.1): • Surface acoustic wave components; • Thin film bulk acoustic wave devices (resonators, filters). In passive components (Fig. 1.3.2) • High density capacitors in integrated circuits; • Low impedance transmission lines; • Dielectric spacer in Microelectromechanical (MEM) switches. In tunable microwave devices, circuits and systems (Fig. 1.3.3): • • • • • • •

Lumped element and distributed varactors; Tunable delay lines, phase shifters; Tunable resonators, filters and matching networks; Tunable impedance and frequency selective surfaces; Microwave beam scanning antennas; VCOs and power amplifiers; etc.

Surface acoustic wave (SAW) devices (Fig. 1.3.1 (a)) already perform filtering and other functions in commercial systems at frequencies up to 5.0 GHz, while thin film bulk acoustic resonators (Fig. 1.3.1 (b) and Fig. 1.3.1 (c)) and filers are partly commercialized and partly under extensive research stage. They seems to be promising at frequencies up to 10 GHz. Application examples of ferroelectrics as passive high dielectric constant films in high density (F/m2) MMIC capacitors and in low impedance transmission lines are shown in Fig. 1.3.2. In these applications

10

1 Introduction: Overview of Agile Microwave Technologies

the tuneability is not required while good temperature stability is desirable. Low impedance lines are used, for example, in matching networks of high speed (microwave) photodetectors and laser diodes, high power amplifiers etc. Attempts are made also to use high dielectric constant ferroelectric films as passive isolators in MEM devices (Fig. 1.3.2 (b)). In this case higher Con/Coff ratio is achieved due to increased dielectric constant in “on” state capacitor. Transducers (interdigital electrodes)

Piezofilm

(a) Top and bottom electrodes Piezofilm Micromachined (etched) silicon

(b)

Acoustic (Bragg) reflector Piezofilm

(c) Fig. 1.3.1 Surface (a) and bulk (b), (c) acoustic wave devices

More efforts and a large number of publications in recent years are devoted to electrically tunable ferroelectric microwave devices in the form of lumped element varactors and sections of transmission lines incorporating ferroelectrics (Fig. 1.3.3 (a) and Fig. 1.3.3 (b)). Tuneability and loss tangent are the basic parameters characterizing ferroelectrics for applications in tunable microwave devices. A considerable progress is achieved in improving the dielectric properties (high tuning, low loss tangent) of thin film ferroelectrics and their applications in agile microwave comports. A number of companies (Agile RF, Paratek, Gennum, nGimat, Kyosera, Murata, Fujitsu, NXP etc.) either market agile microwave components based on ferroelectrics or run development projects.

1.3 Microwave Applications

11

Top and bottom electrodes

Substrate

Top and bottom electrodes

(a)

Paraelectric film

Substrate

(b)

Paraelectric film

CPS

SiO2 Substrate

(c)

Fig. 1.3.2 Paraelectric films in a high-density capacitor (a), MEM (b), and low impedance low loss transmission line (c)

Applications in microwave are reviewed in recent publications, see for example (Bao et al. 2008, York 2008), while the other modern applications of ferroelectrics are reviewed in (Scott 2007).

1.3.3 Potential and Trends Today double and triple band handsets use ceramics and SAW filters, TFBAR based filters are considered for these applications. However, using a large number of filters increases the complexity and is not cost effective. Similar problems occur in wireless radio links (i.e. Ericsson’s MINILINK), where the filters make the major part of the cost. A possible solution is replacing the large number of passive filters by one or two filters with tunable passband.

12

1 Introduction: Overview of Agile Microwave Technologies

Metal

Ferroelectric

(a)

Metal

Ferroelectric

(b)

Ferroelectric

Metal D

G

S

(c) p+

p+

Fig. 1.3.3 Ferroelectrics in parallel-plate (a) and coplanar-plate (b) varactors, and MIS (MFS) transistor (b)

The growing number of communication standards and the overcrowded frequency spectrum urged to create new radio systems for more efficient and intensive use of the available frequency spectrum. The cognitive radio (CR) technology is considered as an attractive solution for exploiting the limited spectral resources. In a simplified way of saying, cognitive radio means sensing-cognition-adoption. It is based on software defined radio (SDR) platform (http://www.sdrforum.org/) with agile front ends being the core of the hardware performing adoption on hardware level. On the other hand it allows “peaceful” coexistence of the existing and merging heterogeneous wireless networks, such as wireless Personal Area (PAN) and Local Area (WAN), Metro Area (MAN)Networks, TV broad casting etc. (Laskar et al. 2006). The lack in adequate agile front ends, including reconfigurable analog-digital interfaces, is the main bottleneck hindering the implementation of the potential of the cognitive radio. In general, the functional aspects of an agile terminal include: • • • • •

Better intelligence to adaptively re-tune to less crowded frequency spectrum; Better dynamic range to reduce IMD; Better IF filters to remove signals on adjacent channels; Better intelligence to change modulation and power; Better directional antennas to isolate desired signal.

1.3 Microwave Applications

13

Depending on the agile front end architecture, the main devices needed are: • • • • • • • •

Tunable filters; VCOs (frequency synthesizers); Tunable matching networks; Tunable/reconfigurable amplifiers; Tunable antennas; Tunable ADC (DAC); Frequency selective (tunable) switches; Phase shifters and delay lines, etc.

MN

~

MN

Fig. 1.3.4 Possible architecture of a multi-standard agile front end

A possible generic example of such an agile front end is shown in Fig. 1.3.4. On a component level these devices may be implemented by using transistors/ICs and tunable passive components such as varactors, inductors and resistors. Today several competing technologies are considered for the utilization of these components: semiconductor devices (i.e. transistors, varactors, pin diodes, transistor switches), MEMs, ferroelectrics, liquid crystals etc. All components, except for LNA, shown in this generic front end are already implemented in agile ferroelectric technology and prove to have advantages over the competing technologies. The next few paragraphs consider some of the modern trends in microwave ferroelectric technology. Shift to Millimeter Wave Frequencies: A comparison between ferroelectric and semiconductor varactors shows that the frequency range, where the ferroelectric varactors may successfully compete with semiconductor analogs, lays above 10– 20 GHz, where the quality factor of the semiconductor varactors decrease drastically (Q~ 1/f), while the Q-factor of ferroelectric varactors my remain rather high. However, at low frequencies (f<10 GHz) where the Q-factor of semiconductor varactors is rather high, typically above 50, applications of ferroelectric varactors may be limited, since the semiconductor counterparts have the advantage of better integration with MMICs.

14

1 Introduction: Overview of Agile Microwave Technologies

Back to Cost Effective Ceramics: In early experiments mainly ceramics (bulk, thick film) in paraelectric phase have been used in tunable microwave devices. Later predominantly epitaxial films (SrTiO3, BaxSr1–xTiO3) and also single crystals (SrTiO3, KTaO3) have been considered due to the lower losses. The cost is a critical issue where the commercialization of the ferroelectric devices is concerned, and in many cases ceramics offer cost effective solutions. Somehow poor performance (loss, tuneability) is the penalty one has to pay. Integration with Semiconductors, Especially Silicon and GaAs: Ferroelectrics (both in polar and paraelectric phase) are extensively investigated as field dielectrics in non-volatile memory cells in metal-insulator-semiconductor transistors, Fig. 1.3.3 (c). Such a combination in microwave transistors may be used to realize a new class of microwave devices with enhanced functionalities. Higher Q-factor, tuneability and tuning speed at millimeter wave frequencies (in comparison with semiconductor and MEM analogs) are the other advantages making the integration of ferroelectric varactors with MMICs desirable. Integration with HTS: New HTS materials with performances (nonlinearity, surface impedance, Tc) better than YBCO, and more importantly, the problem of more efficient use of the available frequency (microwave) spectrum, may force the industry to reconsider application of HTS technology in the future microwave communications systems. This may accelerate the already started attempts to develop new ferroelectric materials with lower losses, and tunable devices integrated with HTS electrodes. New Agile Materials: Multiferroics, pyrochlores, oxides and non-oxides with dielectric (semiconductor)/metal phase transition etc. are new materials systems constituting hot research topic for physicists, researchers in memory, optical and microwave communities. Some of these materials have promising agile microwave properties considered in Chap. 9. Heterogeneous Integration: The Moore’s low (More Moore concept) is pushing the feature sizes (i.e. gate-length in CMOS) of the transistors below 10–20 nm limit enabling system-on-chip (SoC) integration of digital and mixed digital/analog electronics systems. With the reduction of the feature sizes and increased integration density the cost of the chip area (Euro/mm2) drastically increases. When it comes to RF and microwave electronics the fundamental relationships between the wavelengths of the microwave signals and physical lengths of the passive components put extra limitations on the SoC integration. The cost of a simple inductor coil or quarter wavelength transformer integrated on a chip with nanometer gate-length transistors may be too high. Moreover, the typical microwave circuits and systems use only a very limited number of transistors, in contrast to digital systems. Additionally, the market demand for the microwave ICs and systems is not as high as it is for the digital ICs and systems. These arguments make the application of the SoC concept to most of the microwave ICs seems economically unreasonable. Furthermore, there are a number of new and advanced microwave components based on materials and fabrication processes presently not compatible with the standard semiconductor IC fabrication process. Ferroelectric, ferromagnetic/ferrite, MEM, micro-machined etc. components are

1.4 Other Agile Microwave Technologies

15

only some of them to mention. The on chip integration of these and similar components require substantial investments, which the semiconductor IC companies my find not justified economically, given the limited size of the market (compared with the digital ICs). Hence, in the foreseeable future, the heterogeneous integration of the advanced microwave components seems possible only in the form of Multichip modules where the system-in-package (SiP) concept of integration may lead to substantial cost reduction, performance improvement, and development of the systems with new functionalities. In other words, the More-than-Moore concept seems to be of particular interest in applications to microwave systems, allowing utilization of not only today’s proved technologies, but also present and future non-semiconductor materials and components. The advanced and future microwaves systems will definitely benefit enormously from the More-thanMoore concept. The integration of heterogeneous technologies is expected to trigger system level (SiP) integration of mixed digital, analog and microwave circuits.

1.4 Other Agile Microwave Technologies Mechanical The mechanical tuning is the first tuning technique used in microwave technology. Early mechanically tunable devices make use of coaxial lines or hollow metal waveguides and trimming screws/motors/stepper motors. These devices are simple to implement, offer low loss solutions; however, they are bulky, slow, not cost effective, sensitive to vibrations, require high control powers (with motors/stepper motors), or laborious (automated and manual) trimming. Bulk or thin film piezotransducers are used as actuators to develop relatively small size and relatively fast tunable devices. Bulk piezotransducer based devices are also simple to implement and offer low loss, low control power solutions. Nevertheless, the bulk piezotransducers are still rather slow, sensitive to vibrations, and not suitable for cost effective integration. In contrast, the thin film bulk acoustic piezotransducers offer better performances in terms of speed and cost effective integration possibilities. These types of transducers are used as actuators in microelectromechanical (MEM) devices. Recently MEMs and NEMs switches and varactors attracted considerable attention. These devices offer low loss and low control power solutions, better integration possibility, and higher speeds than bulk mechanical devices. Although the idea behind MEMs devices is very simple, the large scale commercial applications of MEMs based tunable (reconfigurable) devices turned out to be not that simple. They require vacuum packaging; still suffer from sticking/reliability problems. For analog tuning (MEM varactor) the design and fabrication processes are rather complex. MEMs varactors have rather complex design in comparison with MEM switches, small Q-factor, and small range of tuneability (also in comparison with the semiconductor and ferroelectric) varactors. Nanoelectromechanical devices are

16

1 Introduction: Overview of Agile Microwave Technologies

gaining ground and most probably in the future they may become a major technology offering new tunable devices with high integration possibilities and operation speeds comparable with semiconductor devices. No tunable nanomechanical microwave devices are reported so far. However, it seems that acoustic oscillations of micro/nano sized bars (cantilever, fixed ends) activated by electrostatic forces offer a possibility to develop tunable resonators with extremely high Q-factors. Magnetic Tunable devices using magnetic properties of materials have a rather long history of applications in microwave technology. Magnetic properties of ferrites, magnetostatic (spin) waves, and magnetostriction is considered for tunable microwave applications. Devices based on ferromagnetic resonance make use of the external magnetic field induced (magnetic field dependent) resonances with rather high Q-factor (narrow bandwidth). In general, tunable filters based on ferromagnetic resonance offer high selectivity and larger tuning ranges compared with other technologies. However the magnetically tuned devices require coils/currents and are rather slow. In spite of these disadvantages it seems that the tunable devices making use of magnetic properties of the materials are given the second chancespintronics is a new and rapidly developing field opening up new possibilities in terms of new functionalities, integration possibilities, size, control power and cost reduction. Optical Microwave photonics makes use of optical fibers and optically controlled semiconductors for transmission, reception and processing/control of microwave signals. Optically controlled devices have the advantage of remote control, inherent decoupling of control and microwave circuits. No decoupling networks for DC bias are required, and they are potentially wide and ultra wide band. The main disadvantage of the optically controlled/tuned devices is that they consume relatively large power for tuning. Liquid Crystal Liquid crystals are also considered for microwave applications in the past. The tuneability of permittivity is associated with the anisotropy of the molecules, which was not large enough to get substantial tunings in microwave devices. Recent reports shows that microwave devices with quite acceptable performances may be developed using specially synthesized liquid crystals with very large anisotropy. Besides integration and cost issues the main disadvantage of the liquid crystals is the low speed of tuning. The delay lines based on liquid crystals have rather high figure of merit, especially at millimeter wave frequencies. However, the applications may be limited due to the issues like high cost, low speed, and narrow temperature range.

1.4 Other Agile Microwave Technologies

17

Semiconductor Semiconductor varactors (junction, heterojunction, Schottky, MOS etc.) and transistors are widely used in tunable microwave devices. They allow high density integration. Today the tunable/switchable semiconductor microwave devices are by far the most cost effective components used in both commercial and defense systems. While the transistors based on Si, SiGe, and GaAs meet most of the strict requirements of modern microwave systems, there is a lack of adequate high Q-factor and high speed varactors, especially for frequencies above 10–20 GHz. Additionally, for large arrays, such as phased arrays with up to 10000 and more radiating elements, the power consumption and heat sink are major problems hindering applications of semiconductor devices. The desirable features of varactors for these systems include low power consumption, high tuning speeds and high tuneability at millimeter sub-millimeter wave frequencies. A comparison between ferroelectric and other competing technologies is given in Table 1.4.1. Table 1.4.1 Technology comparisons Technology

Semiconductor Schottky (GaAs) HBV (GaAs)

Magnetic

Ferroelectric

Mechanical

Speed

Q-factor at 10 GHz

<1 mW

<5 V

< 1 ns

200

< 1 mW

<20 V

< 5 ns

40

Abrupt p-n junction (Si)

<5 mW

<30 V

< 10 ns

30

P-I-N diode

<0.1 mW

<10 V

High

Current (coil)

<1 μs 1 ns <5 ms

>3000

FET YIG (variable permeability, ferromagnetic resonance) Remnant magnetization

Low

Current (coil)

Magneto-static (spin) wave

Low

–

<5 ms <5 ms

– Low

Thin film

Negligible

<30 V

< 1 ns

>100

Thick film

Negligible

<1000 V

< 10 ns

<100

Bulk

Negligible

<15 kV

>500

< 40 V

< 10 ms

< 1μs <20

Photoconductivity

<10 mW

Current (LD, LED)

10 fs –10 ms

< 10

Fiber-optical

<10 mW

Current (LD, LED)

10 fs –10 ms

–

Bulk

High

Current (motor/coil)

> 1 ms

>1000

MEM varactor

Negligible

<50 V

> 10 μs

>200

Piezotransducer

Negligible

>100 V

>100 μs

>500

Liquid crystal Negligible Optical

Power con- Bias sumption

18

1 Introduction: Overview of Agile Microwave Technologies

1.5 Conclusions Agile microwave technologies available today have the potential to facilitate industrial scale development of the components, circuits and systems for the reconfigurable and adaptable microwave systems. Perhaps none of these technologies may be recommended as a universal panacea to “heal” the agility problems of all microwave systems. Each of these technologies will have their own niche of applications. A careful analysis of all available technologies is needed before one makes a decision for using any of these technologies. Nevertheless, the ferroelectrics have a number of advantages making them preferable for most of the applications. The exceptional tuning speed, extremely low powers required for tuning, low losses in combination with the high tuning ranges, radiation hardiness etc. are some of them to mention. The other chapters in this book are aiming at unwrapping the full potential of the ferroelectrics for advanced agile microwave systems. Thin film (epitaxial, ceramic/textured), thick (HTCC, LTCC) film, and bulk (single crystal, ceramics) ferroelectrics are considered for tunable microwave applications. Ferroelectric varactors and tunable devices based on them have the potential of future integration with standard Si and GaAs processes. Extra flexibility in terms of tuning, enhanced functionalities and performances of tunable devices may be achieved by combination of ferroelectrics with ferrites, ferroelectrics with semiconductors or ferrites with semiconductors. Devices based on such multifunctional materials offer dual (electric, magnetic) tuning possibility and extra flexibility in designing and shaping the device performances. For example, in the case of delay lines it is possible to tune the delay time while maintaining the input/output impedances on a desired level.

References Abadei S, Gevorgian S, Cho C-R et al. (2001) DC Field Dependent Properties of Na0.5K0.5NbO3/Si Structures at Millimeter-Wave Frequencies. Appl Phys Lett 78:1900–1902 Babbitt R W, Koscica T E, Drach W C (1992) Planar Microwave Electrooptic Phase Shifters. Microwave Journal, June:63–79 Bao P, Jackson T J, Wang X et al. (2008) Barium strontium titanate thin film varactors for roomtemperature microwave device applications. J Phys D: Appl Phys 41:1–21 Bete K (1970) Uber Das Mikrowellenverhalten Nichtlinearer Dielektrika. Philips Reserach Reports Suppliments, vol 2 Böttger U (2005) Dielectric Properties of Polar Oxides. In: Waser R, Böttger U, Tiedke S (Ed) Polar Oxides: Properties, Characterization, and Imaging. Wiley, New York Caloz C, Itoh T (2006), Electromagnetic Metamaterials, Wiley, New York Das S (1991) High Power Tunable Filters Use HTS Ferroelectrics. Microwaves&RF, September:93–102 Eleftheriades G V, Balmain K G (2005) Negative-Refraction Metamaterials: Fundamental Principles and Applications. John Wiley & Sons, IEEE Press IEEE MTT (1999) Special Issue on Microwave and Millimeterwave Photonics. IEEE Trans Microwave Theory Techn vol 47, No 7

References

19

Laskar J, Mukhopadhyay R, Hur Y et al. (2006) Reconfigurable RFICs and Modules for Cognitive Radio. Dig SiRF:283–286 Rebeiz G M (2003) RF MEMS Theory, Design, and Technology. Wiley-Interscience Scott J F (2007) Applications of Modern Ferroelectrics. Science 315:954–959 Varadan V K, Ghodgoankar D K, Varadan V V et al. (1992) Ceramic Phase Shifters for Electronically Steerable Antenna Systems. Microwave Journal, January:118–127 Vendik O G (1979) Ferroelectrics in Microwave Technology (in Russian). Sov Radio, Moscow Vorobiev A, Rundqvist P, Khamchane K et al. (2003) Silicon substrate integrated high Q-factor parallel-plate ferroelectric varactors for microwave/millimeterwave applications. Appl Phys Letters 83:3144–3146 York B (2008) Tunable Dielectrics for RF Circuits. In: Steer M (Ed) Multifunctional Adaptive Microwave Circuits and Systems. Scitech, Raleigh

Chapter 2

Physics of the Tunable Ferroelectric Devices

Abstract This chapter gives an introduction to those aspects of the theory of ferroelectricity that a microwave engineer needs for understanding the physics behind tunable microwave devices. In spite of the simplicity the provided theory is quite useful for designing microwave devices and the interpretation of the experimental results. The crystalline structure of the displacive perovskite ferroelectrics, the DC field dependent dielectric permittivity and loss tangent are in the focus. The dynamic nonlinearity and acoustic properties are also considered.

2.1 Introduction Crystalline, dielectric and electroacoustic properties of ferroelectrics are briefly reviewed in this chapter. The main focus is on crystalline/polycrystalline ferroelectrics with perovskite structure. Perovskite ferroelectrics are extensively studied in the past. They are rather well understood and commonly used in tunable microwave devices. Ferroelectrics used in tunable microwave devices may have one of the following forms: • Single crystal (SrTiO3, KTaO3 etc.): – –

Bulk Thin film

• Single phase (i.e. BaxSr1–xTiO3) and composite (i.e. MgO+SrTiO3) ceramics: – – –

Bulk-granular Thick film (HTCC, LTCC)-granular Thin film-granular, columnar

i.e. they have either single crystal, granular or columnar structure. The amorphous ferroelectrics, typically thin films deposited at low/room temperatures, are used in passive none tunable MIM capacitors. They are not considered in this chapter. The 21

22

2 Physics of the Tunable Ferroelectric Devices

same ferroelectric composition (i.e. SrTiO3) may have different dielectric properties depending not only on the structure (single crystal, granular or columnar), but also on the mechanical strains. In the past relatively simple dielectric models based on thermodynamic and microscopic theories for the uniform single crystal (bulk, epitaxial film) ferroelectrics have been developed (Barrett 1952), (Rupprecht et al. 1961, Vendik and Zubko 1997). These models have been extended and applied to ceramics (granular, columnar, composite) ferroelectrics (Tagantsev et al. 2005). Quite recently the models based on the density function theory (DFT) are considered extensively. The DFT seems to be especially useful when it comes to nanostructured ferroelectric films and devices. The interested reader is refereed to adequate publications in this field (Chosez and Junquera 2006).

2.2 Crystal Structure, Non-Polar (Paraelectric) and Polar (Ferroelectric) Phases The complex metal oxide ferroelectrics, i.e. perovskites such as Titanates (CaTiO3, BaTiO3 etc.), Tantalites (KTaO3 etc.), Niobates (KNbO3 etc.) etc. are characterized by a common chemical formulae, ABO3, and have the same crystal structure (Fig. 2.2.1). Above polar-to-non-polar phase transition temperature their crystal lattice has cubic structure (Fig. 2.2.1 (a)). In this phase the crystal has no spontaneous polarization. Its permittivity is rather high, DC field, temperature and strain dependent. Below the phase transition temperature the crystal lattice becomes non cubic, non center-symmetric, the centers of the positive and negative charges per unit cell shift as shown Fig. 2.2.1 (b) and the crystal is characterized by spontaneous polarization. One for the surfaces of a macroscopic crystal is charged positively, while the opposite surface is charged negatively.

(a)

(b)

Fig. 2.2.1 3D unit cell of ABO3 (e.g. BaTiO3) perovskites in paraelectric (a) and polarferroelectric (b) phases

2.2 Crystal Structure, Non-Polar (Paraelectric) and Polar (Ferroelectric) Phases

23

Figure 2.2.2 illustrates the 1D model of a perovskite crystal in paraelectric and ferroelectric phases. It is customary to represent the electrostatic interaction faces by mechanical springs. In these simplified models, in paraelectric-centersymmetric phase (Fig. 2.2.2 (a) and Fig. 2.2.2 (b)) the central ion oscillates about the equilibrium (x=0) and its free energy is characterized by a parabolic dependence (=kx2, where k is the spring constant) as shown in Fig. 2.2.2 (a). An applied external electric field (along x axis) shifts the central ion from its equilibrium position inducing an electrical dipole. The ion continuous its oscillations about this new position with somehow less intensity (reduced permittivity). The ion comes back to its equilibrium position (x=0) as soon as the external field is switched off. This is the basic electric field tuning mechanism of the permittivity used, for example, in tunable microwave devices. In polar, i.e. ferroelectric phase the positive ion is slightly shifted from the lattice center to the left (Fig. 2.2.2 (d)), or to the right (Fig. 2.2.2 (e)). In these two new positions the free energy of the crystal is minimum (Fig. 2.2.2 (c)). The ion remains in one of these two off-center poisons as far as no external forces (electrical, mechanical, temperature) are applied. It is characterized by an internal dipole, i.e. spontaneous polarization. Under external DC field the center ion may be switched from its left to its right position-changing the direction of the polarization vector (direction). Changing the direction of the external field brings the ion back to its left position-restoring the direction of the previous polarization. This is the main polarization switching/reversing mechanism used, for example, in memory cells. Free energy Free energy

Distance, x

(a) Distance, x

-

+

(c)

(b)

-

+

-

(d)

-

(e)

Lattice constant, ao Lattice constant, a

-

+ Lattice constant, a

Fig. 2.2.2 Free energy destitution in 1D unit cells of ABO3 (e.g. BaTiO3) perovskites in paraelectric (a, b) and polar-ferroelectric (c, d, e) phases

24

2 Physics of the Tunable Ferroelectric Devices

2.3 Dielectric Models of the Ferroelectric and Paraelectric Phases 2.3.1 Phenomenological (Thermodynamic) Theory This theory is based on the expansion of the free energy of a ferroelectric crystal as a function of polarization P (Tagantsev et al. 2005): 1 1 F ( P, T ) = αP 2 + βP 4 ... 2 4

(2.3.1)

At this instance the higher order terms in this expansion are ignored. It contains only even terms to reflect the fact the free energy of the crystal dose not depended on the polarization reversal. The physical meanings of the dielectric permittivity and nonlinearity coefficients α and β are disclosed below. Notice that this relationship holds true both for paraelectric and ferroelectric (polar) phases. The first derivative of this function is: ∂F ( P, T ) = E = αP + βP 3 ... ∂P

(2.3.2)

From the simple relationship between the electric field and polarization it becomes clear that the coefficient α should have a meaning of the inverse permittivity: α=1/(εεo), where ε is the relative dielectric permittivity and εo is the dielectric constant of vacuum. Furthermore, taking into account the experimentally observed temperature dependence of the permittivity, i.e. the Curie-Weiss low, ε=C/(T–Tph), the coefficient α takes the form:

α=

T − T ph

ε oC

(2.3.3)

C is the Curie constant and the temperature Tph is equal or lower than the Curie temperature Tc. Its meaning will be clear a couple of lines below. In polar (ferroelectric) phase the spontaneous polarization, Ps, is found when the externally applied electric field E=0, i.e. from (2.3.2) αPs+βPs3= Ps(α+βPs2)=0. The last equation has two solutions: Ps=0 and (α+βPs2)=0. From the second solution, taking into account (2.3.3), one arrives at: Ps = (T ph − T ) /( βε oC )

(2.3.4)

which is valid below temperature T=Tph. At T=Tph the spontaneous polarization Ps=0, i.e. Tph is the phase transition temperature. Below this temperature the ferro-

2.3 Dielectric Models of the Ferroelectric and Paraelectric Phases

25

electric is in polar (ferroelectric) phase with P=Ps. Above the ferroelectric is in paraelectric phase with Ps=0. In this case the paraelectric-to-ferroelectric phase transition is of the second order and the phase transition temperature is identical with the Curie-Weis temperature Tc=Tph. For the first order phase transition (Vendik and Zubko 2000) the phase transition temperature is less than the CurieWeiss temperature, Tph
ε=

1 ∂E 1 = ε o ∂P ε o (α + 3β P 2 )

(2.3.5)

In paraelectric (T>TC=Tph) phase, and without external electric field, i.e. P=0, from (2.3.5) and (2.3.3) one gets Curie-Weiss low:

ε=

C T − Tc

(2.3.6)

For ferroelectric, polar phase (T
ε=

(2.3.7)

T>Tc

Paraelectric Free energy

Ps; 1/ε

Ferroelectric 2(Tc-T)/C

C 2(Tc − T )

T=Tc T
1/ε=(T-Tc)/C

Ps

Tc

Temperature

P +Ps

-Ps

(a)

(b)

Fig. 2.3.1 2nd order paraelectric to ferroelectric phase transition. Temperature dependences of the polarization and inverse permittivity (a), and polarization dependent free energy (b)

The temperature dependences of the spontaneous polarization and inverse permittivity for a ferroelectric crystal with 2nd order phase transition, defined by (2.3.4), (2.3.6) and (2.3.7) are depicted in Fig. 2.3.1 (a). Figure 2.3.1 (b) depicts the dependences of the free energy on the polarization (2.3.1) for ferroelectric

26

2 Physics of the Tunable Ferroelectric Devices

(TTc) and phase transition (T=Tc) temperatures. The two minima in ferroelectric phase correspond to two equilibrium states of the spontaneous polarization, shown previously in Fig. 2.2.2 (c), while the dependence with a single minimum (T>Tc) corresponds to the case shown in Fig. 2.2.2 (a). The hysteresis (Fig. 2.3.2 (a)) with the two equilibrium polarization states is used to utilize nonvolatile memory cells. The corresponding permittivity-field dependence (computed using the derivative in (2.3.5)) is shown in Fig. 2.3.2 (b), where the maximums in permittivity appear at coercive field ±Ec. In principle, this type of “butterfly” permittivity-field dependence may be used in analog tunable microwave varactors provided that the associated losses are small and the required tuning speeds are not high. In this case the bias field has to be increased from zero or decreased from Emax in order to establish the required permittivity on the given branch of the ε(E) dependence. The polar phase with ε(E) hysteresis may be used also as a microwave switch if the ratio εm/εn of the permittivity at the points m and n (Fig. 2.3.2 (b)) is sufficient for the targeted application. Additionally, in polar phase all ferroelectrics also are piezoelectric and, as such, some of them are used in acoustoelectronic devices. +Ps

P

P

+Pr -Ec +Ec

E

(a)

-Pr -Ps

m

ε(E)

(c) ε(E)

n -Ec

+Ec

E

(b)

E

(d)

Fig. 2.3.2 Polarization (a and c) and permittivity (c and d) dependences on the applied electric field for ferroelectric (a and c) and paraelectric (b and d) phases

In paraelectric, T>Tc, phase the spontaneous polarization is zero and the inverse permittivity is a nonlinear function of the applied electric field (Fig. 2.3.1 (a)). At small bias fields the free energy is a parabolic function of the polarization (Fig. 2.3.1 (b)) as it appears in (2.3.5). The P(E) dependence in this phase is again nonlinear but without hysteresis loop (Fig. 2.3.2 (c)). The ε(E) performance is also essentially nonlinear (Fig. 2.3.2 (d)) and for small bias fields is characterized with a parabolic dependence, as shown below. In this phase, using

2.3 Dielectric Models of the Ferroelectric and Paraelectric Phases

27

the relationship between polarization and applied field, P=εoε(0)E, one gets from (2.3.5): ε(0)=1/(αεo). By using this results in (2.3.5) one arrives at

ε (E,T ) =

ε (0, T ) 1 + 3βε o3ε 3 (0, T ) E 2

(2.3.8)

where the temperature dependence of the permittivity at zero bias field, ε(0,T), is given by (2.3.6).

2.3.2 Microscopic Theory In general, the thermodynamic theory considered in the previous section does not care about the microscopic, ionic structure and chemical composition of the ferroelectric crystal. The change in crystal symmetry at phase transition is the only concept which the thermodynamic theory considers. The microscopic theories consider the chemical/ionic structure of a ferroelectric crystal and thermal oscillations (vibrations) of the ions about their equilibrium positions, and their interactions. The microscopic, dynamic theory of ferroelectrics is based on the vibrations of the ions in the crystal considered by (Cochran 1969, Vendik and Zubko 1997). It was rather successfully used in the past for interpretation of dielectric and ferroelectric properties of ferroelectrics. At present there are a number of different approaches (Dawber et al. 2005), and among them the density function theory is the most powerful (Chosez and Junquera 2006), which, with the advances of computers, will enable to solve such a complex problem as synthesis of ferroelectrics with the desired properties. Here the main features of the dynamic theory will be considered. It does not result completely correct temperature and frequency dependences of the dielectric properties. However, it helps to understand the essence of the dynamic theory and introduce the “soft” mode frequency, often used in the dynamic theory of the ferroelectrics.

-

+ ξ

-

-

ξ

+

-

+

(a)

+

(b)

Fig. 2.3.3 Longitudinal (a) and transversal (b) oscillations in a chain of ions

28

2 Physics of the Tunable Ferroelectric Devices

In a simple one dimensional model of an ionic crystal shown in Fig. 2.3.3 the interactions between the ions is represented by mechanical springs allowing propagation of the oscillations along the ionic chain. The ions may oscillate along the chain (longitudinal phonons) and perpendicular to the chain (transverse phonons). In terms of quantum mechanics the thermal oscillations are regarded as phonons characterized by energy hv, where h is the Plank’s constant and v is the frequency of the oscillations. The ferroelectric properties of the crystal are explained by instability of thermal oscillations (vibrations) of the ions, i.e. phonons. The motion of the ions is controlled by long range Coulomb interaction forces and inertial (Newton) forces. In contrast to non ferroelectric crystals, to characterize the ferroelectric phase transformation, in a ferroelectric crystal the non-Coulomb (short range) inharmonic interaction forces are also taken into account. ε’(ω)

(a)

γ1 γ2>γ1

ω ωΤΟ

(b) γ1

ε’’(ω)

γ2>γ1

ω ωΤΟ

Fig. 2.3.4 Frequency dependencies of the real and imaginary parts of the permittivity following from (2.3.9) for two damping coefficients γ

The complex permittivity may be written as:

ε = ε opt +

ε DC − ε opt ⎛ ω 1 − ⎜⎜ ⎝ ωTO

2

⎞ ⎛ ω ⎟⎟ + jγ ⎜⎜ ⎠ ⎝ ωTO

⎞ ⎟⎟ ⎠

(2.3.9)

where εDC and εopt are permittivity at low, ω<<ωTO, and optical, ω>>ωTO, frequency limits. Typically εopt<< εDC and εopt may be ignored at microwave fre-

2.4 Engineering Models of the Dielectric Permittivity

29

quencies. It is shown that the frequency of the transverse optical mode, ωTO~(T– Tc), i.e. it goes to zero at phase transition (Curie) temperature. The frequency dispersion of the permittivity given in (2.3.9) is known as dumped resonance dispersion, where γ is the damping coefficient. The frequency dependences of the real and imaginary parts of the permittivity corresponding to (2.3.9) are shown in Fig. 2.3.4. With no damping, i.e. γ=0, the real part of the permittivity ε'→0 at ω=ωTO. At very low frequencies (for SrTiO3 f< 0.5–1.0 THz) the real part of the permittivity is constant. At frequency ω=ωTO, known as the “soft” mode frequency, the real part of the permittivity is zero (Fig. 2.3.4 (a)). With increasing damping, γ2>γ1, the resonant feature (increase in real part of permittivity, Fig. 2.3.4 (a)) disappears and the dispersion of the permittivity, below ωTO, similar to Debye relaxation. When the forces (destabilizing the symmetric phase) in the unit cell of a dielectric crystal tend to displace a ferroelectrically active ion (i.e. Ti in BaTiO3) from its position of symmetry it is said the crystal becomes instable. In other words the forces lead to appearance of a dipole moment in the unit cell. At the same time the crystal tends to stabilize its symmetric phase, which causes fluctuations of the ferroelectrically active ions about their equilibrium positions. In the case these fluctuations result in dynamic stabilization of the symmetric phase the crystal is said to be virtual (incipient) or quantum paraelectric. They do not stabilize in ferroelectric-polar phase at any temperature. There are only a few quantum paraelectrics (Lemanov et al. 1999): SrTiO3, CaTiO3, KTaO3, TiO3 etc. On the other hand the polar ferroelectric phase in these (incipient ferroelectric) crystals may be induced/stabilized by extra external forces like strain (Haeni et al. 2004) and electric field (Hemberger et al. 1995). In some crystals the destabilizing (the symmetric phase) are so strong that they do not undergo paraelectric phase transitions up to the melting point. These crystals are said to be pyroelectrics.

2.4 Engineering Models of the Dielectric Permittivity 2.4.1 Barrett’s Formula. Bulk Single Crystals The first useful formula for temperature dependence of the permittivity was proposed by Barrett (Barrett 1952):

ε = A+

C (T1 / 2) coth [(T1 / 2T ) − To ]

(2.4.1)

For perovskites, known as quantum paraelectrics or incipient ferroelectrics, the parameters involved in the above formula are given in Table 2.4.1 (Lemanov et al. 1999).

30

2 Physics of the Tunable Ferroelectric Devices

Table 2.4.1 Parameters of Barett’s model for incipient ferroelectrics ε(300K)

ε(0K)

A

C, 104K

To, K

43.9

4.77

–111

110

8

35.5

80

5.45

13.1

56.9

CaTiO3

168

331

SrTiO3

305

20 000

KTaO3

239

3840

TiO2

170

257

47.7

T1,K

2.4.2 Rupprecht–Bell–Silverman Model. Bulk Single Crystals Later, based on the experimental results, Rupprecht et al. (1961) proposed an empirical formula for the temperature and DC electric field dependent permittivity for STO:

ε (E , T ) =

ε (0, T ) , 1 + ( Ahkl / C )ε 3 (0, T ) E 2

(2.4.2)

where the temperature dependent permittivity at zero bias field is given by (2.3.6):

ε (0, T ) =

C T − Tc

(2.4.3)

(2.4.2) is valid for temperature range 90–230 K and is essentially the same as (2.3.8) where the experimentally defined coefficients A characterize the anisotropic static nonlinearity: A100 = 1.15 ⋅10 −18 ,

Km 2 / V 2

A110 = 0.96 ⋅10 −18 ,

Km 2 / V 2

A111 = 0.69 ⋅10 −18 ,

Km 2 / V 2

These anisotropic nonlinearity constants are frequency and temperature independent, but have noticeable dependences upon the orientation of the applied external electric field E with respect to crystallographic axes. These formulae predict some anisotropy above structural phase transition temperature 110 K, indicating the slight deviation from ideal cubic structure, observed at room temperature becomes enhanced with the reducing temperature and leads to cubic-totetragonal structural phase transition. Similar anisotropy in single crystal STO above phase transition temperature 110 K is observed in other experiments (Eriksson et al. 2003). As it is shown below, this anisotropy has a stronger impact on the loss tangent.

2.4 Engineering Models of the Dielectric Permittivity

31

2.4.3 Vendik’s Model. Bulk Single Crystals A phenomenological model for the DC filed and temperature dependent permittivity, for paraelectric phase BxSr1–xTiO3, proposed by Vendik and Zubko (2000); takes into account also the defects in the crystal: ε (E , T ) =

[

ε oo

]

⎧ ξ ( E ) 2 + η (T )3 0.5 + ξ ( E ) ⎫ ⎨ ⎬ ⎩ ⎭

2/3

[

]

0.5 + ⎧⎨ ξ ( E ) 2 + η (T )3 − ξ ( E ) ⎫⎬ ⎩ ⎭

2/3

, (2.4.4) − η (T )

where

ξ ( E ) = ( E / E N ) 2 + ξ s2 η (T ) = (Θ / 4Tc ) 2 + (T / Tc ) 2 − 1

[

E N = 2 DN / ε o (3ε oo )3 / 2

]

DN=4.2 C/m2. The involved in the above expressions parameters for BxSr1–xTiO3, SrTiO3 and KTaO3 are given in Table 2.4.2 (Vendik et al. 2002). Table 2.4.2 Modal parameters for BxSr1–xTiO3 (x<0.5) SrTiO3

BxSr1–xTiO3

KTaO3 2

Tc , K

42

Tc(x)= 42+439.37x–95.95x

32.5

C

0.86

C(x)= (0.86+1.1x2)105

0.45·105

Θ, K εoo(x)

175

175

170

2080

= C(x)/Tc(x)

1390

EN(x), kV/cm

19

EN(x)=8.4/{εo[3εoo(x)]3/2}

15.6

ξs

0.18

0.3

0.02

The defects induce local fields and cause statistical dispersion of the external DC bias field. The local fields may be associated with the residual polar phases and/or charged defects. In oxides, including the perovskites, the oxygen vacancies are the most common positively charged defects. They induce local mechanical strain and electric field around them. Not only charged, but also neutral defects may cause local polar phases and associated local fields in single crystal paraelectrics. The parameter ξ(E) in the above formulas takes into account these effects via statistical averaging of the applied DC and local electric fields. Notice once more, that the above formulae are valid for paraelectric phase, where ξ(E)2+η(T)3>0. It is shown in (Vendik and Zubko 2000) that in a ferroelectric (excluding incipient ferroelectrics) the ferroelectric phase transition Tph, the

32

2 Physics of the Tunable Ferroelectric Devices

Curie temperature Tc, and the temperature of the permittivity maximum, Tm, are related as: Tph
SrTiO3

800 Permittivity

5V/μm 600

0V/μm B Sr TiO 0.5

0.5

3

5V/μm 10V/μm

400

10V/μm

200 0

0

100 200 300 400 500 600 Temperature, K

Fig. 2.4.1 Permittivity vs. temperature for at DC bias fields 0, 5 V/μm/ and 10 V/μm

2.4.4 Granular Ceramics and Composites Ceramic ferroelectrics consist of nanometer-micrometer sized and tightly packed grains. Typically the surfaces/interface layers of the grains have different than the cores of the grains dielectric properties. For the modeling purposes the structure of the ceramics (bulk, thick or thin film) used in tunable microwave devices is represented by simplified models (Fig. 2.4.2). The simple single phase ceramics consist of tightly packed nano or micro sized ferroelectric grains (Fig. 2.4.2 (a)) and columns (Fig. 2.4.2 (d)), perhaps with some ferroelectrically active or passive (“dead layer”) grain boundaries. The ceramic composites may consist of the grains of more than one ferroelectric composition (or/and phase) and may contain nonferroelectric grains (Fig. 2.4.2). The thin films may have composite layered structure (Fig. 2.4.2 (c)), columnar ceramic (Fig. 2.4.2 (d)), and composite columnar (Fig. 2.4.2 (e)) structure. Figure 2.4.3 shows an experimental example of how adding a non-ferroelectric MgO transforms Ba0.8Sr0.2TiO3 from simple ceramics to doped and finally to composite ceramic structure (Su and Button 2004). The models of simple granular ceramics (with grain boundaries) and composite ceramics have been considered in the past (Tagantsev et al. 2005). The analysis of the reported performances show that the microwave performances (loss tangent, tuneability) of the granular ceramics (thin, thick film, bulk) are not as good as the performances of the single crystals and columnar epitaxial films.

2.4 Engineering Models of the Dielectric Permittivity

(a)

(b)

33

(c)

(d)

(e)

Fig. 2.4.2 Models of ceramics: (a) granular single phase, (b) granular composite, (c) layered composite, (d) columnar single phase, and (e) columnar composite

Composite

Permittivity

8000

6000 4% 4000

2%

0%

Doping 0.5%

1%

1.5%

10%

2000

0 -80

-60

-40

-20

0

20

40

60

80

Temperature, °C

Fig. 2.4.3 The effect of MgO on permittivity of Ba0.8Sr0.2TiO3 (Courtesy of T. Button, University of Birmingham, UK)

The apparent permittivity of two-phase composite layered, Fig. 2.4.2 (c), and columnar, Fig. 2.4.2 (e), are given by:

ε ap =

ε1ε 2

pε 2 + (1 − p)ε1

ε ap = qε1 + (1 − q)ε 2

(2.4.5)

(2.4.6)

In these expressions p=t1/(t1+ t2) and q=A1/(A1+ A2) are the relative content (concentrations) of the phases, where t1 and t2 are the thicknesses of the phases 1 and 2 (Fig. 2.4.2 (c)), while A1 and A2 are the areas of the two phases (Fig. 2.4.2 (e)). In general one of the phases may be passive, i.e. non-ferroelectric. In the case of single phase ceramics the interfacial/inter-columnar non-ferroelectric (“dead”) layers may be considered as one of the phases appearing in (2.4.5) and (2.4.6).

34

2 Physics of the Tunable Ferroelectric Devices

2.4.5 Columnar Thin Film Ceramics and Composites

Void

In contrast to granular ceramics, the performance of the columnar films (losses, tuneability etc.), especially in parallel-plate varactors, is close to the single crystals.

BSTO

Electrode

(a)

(b)

(c)

Fig. 2.4.4 Cross-sectional SEM (a) and in-plane TEM (b, c) images of a laser ablated Ba0.25Sr0.75TiO3 film

The cross-sectional scanning electron microscope (SEM) photo (Fig. 2.4.4 (a)), and in-plane transmission electron microscope (TEM, Fig. 2.4.4 (b) and (c)), images of a columnar BSTO film are shown in Fig. 2.4.4. The column boundaries are amorphous, and in some cases contain voids (Fig. 2.4.4 (c)). A distorted region near the electrode/ferroelectric interface at the bottom electrode and amorphous regions at the grain/column boundaries are clearly seen. The analysis of the microstructure and the C-V performance shows that the interfacial distorted layer is about 50–100 nm thick and it is strained. Figure 2.4.5 represents a simplified model of the columnar film. Each nanocolumn consists of single crystal core, column boundaries, and an electrode/ferroelectric interface layer. Typically the interfacial layer has lower permittivity due to the dislocations, strain, etc. The grain boundaries play a substantial role both in dielectric properties and reliability of the devices based on ferroelectric varactors. The lower permittivity and tuneability in paraelectric films, in comparison with the bulk single crystal and ceramics of the same composition, have been attributed to the stresses, “dead” layers at the interfaces with the electrodes, non-stoichiometry, voids in the granular/columnar structure, etc. Besides, there are also fundamental effects associated with the surfaces/interfaces. For example, the near surface layer of pure bulk single crystal STO, (which has no ferroelectric phase at any temperature), undergoes a structural phase transition (ferroelectric phase) at about 45 K above the structural phase transition (at about 110K) of bulk single crystal STO (Mishina et al. 2000). With decreasing the film thickness, the contribution of the interface properties increases, relative to the bulk properties and, in nano-size limits, may dominate over the bulk properties.

2.4 Engineering Models of the Dielectric Permittivity

35

Cint Cgb Cgc

(a)

(d)

Agb Agb Agc tgb

D

Core

Agc

(b)

(c)

Fig. 2.4.5 Simplified out-of plane (a) and in-plane (b, c) cross sections of a ferroelectric column in a parallel-plate varactor, and its equivalent circuit (d). Reprinted with permission from Wiley©2008 100

εgc q fraction, %

80

D= 30 μm 50 μm

60 40

70 μm

20

Ei (a)

E

0 0

2

4 6 t , μm gb

8

10

(b)

Fig. 2.4.6 C-V of the core with the inflection point (a) and fraction q vs. thickness of the grain boundary for circular shaped cylindrical column. Reprinted with permission from Wiley©2008

36

2 Physics of the Tunable Ferroelectric Devices

The in-plane cross section of the predominantly cylindrical nano-columns (Fig. 2.4.4 (a)) may be modeled by circular (Fig. 2.4.5 (b)), or triangular (Fig. 2.4.5 (c)) shapes. In general, all three regions of the nanograin (Fig. 2.4.5 (a)) may have different properties (due to stress, compositions etc.), and they experience different changes under the applied to the plates voltage. The integral change in the capacitance under the applied electric field is a result of changes taking place in all three parts of the nano-column. These parts of the nano-column may be represented by equivalent capacitances, as shown in Fig. 2.4.5 (d). Then the capacitance of the grain is C (E , T ) = ε apε 0 Ag t g , with εap being the apparent (measured) permittivity defined as:

ε ap = qε gb + (1 − q )

ε intε gc pε gc + (1 − p)ε int

(2.4.7)

q=Agb/Ag, p=tint/g, where Ag=(Agc+ Agb) and tg=tgc+tint, Agc, and Agb are correspondingly the areas of the grain core and boundary, tgc and tint are correspondingly the thickness of the grain core and interfacial layer (Fig. 2.4.5). The first term in (2.4.7) is due to the grain boundary, while the second term is due to grain core and interface. In this simplified model the grain boundaries and the interface layer of the films are assumed to have DC field independent permittivity, εgb and εint. The apparent permittivity (2.4.7) may be rewritten in a simpler form:

ε ap = qε gb + (1 − q )ε eff

(2.4.8)

where εeff is the effective permittivity of the layered column (“composite”) consisting of a grain core (εgc) and interface (εint):

ε eff =

ε intε gc pε gc + (1 − p )ε int

(2.4.9)

An analytic expression for εeff may be found in (Tagantsev et al. 2005). An alternative approach, given here, is based on (2.3.8) and modified Curie-Weiss low (Rupprecht and Bell 1964) representing the zero bias temperature dependence of the permittivity in bulk single crystals as:

ε gc (0, T ) = ε L +

Ck T − Tc

(2.4.10)

where the temperature independent term ε L is the background permittivity, i.e. the permittivity at very high (“infinite”) temperature where there is no soft mode contribution. The extrapolation, using (2.4.10), gives εL in the range 39–58 for typical perovskites like BaTiO3, SrTiO3, CaTiO3, KTaO3 (Rupprecht and Bell

2.5 Models of the Loss Tangent

37

1964). However this extrapolation seems questionable sine it is based on the soft mode permittivity whereas the permittivity of the crystal at extremely high temperatures may be associated with other phonons. Typically εL is assumed to be about 7–8 (Noeth et al. 2007). For applied DC voltage V the electric field developed in ferroelectrically active core of the column is: Egc =

ε int (1 − p ) V ε gc p + ε int (1 − p ) t gc

(2.4.11)

where εgb and εint are DC bias and temperature independent. The temperature and the DC bias dependences of εgc are given by (2.4.10) and (2.3.8). Finally, the apparent permittivity of the film is:

ε ap ( E , T ) = qε gb + (1 − q )

ε gc (0, T ) 1 ⎛ E gc ⎞⎟ 1 + ⎜⎜ 3 ⎝ Ei (T ) ⎟⎠

2

,

(2.4.12)

where Ei(T) is the field corresponding to the inflection point in the C-V dependence of the bulk single crystal (Fig. 2.4.6 (a)): Ei =

[

1

]

3 β ε oε gc (0, T ) 3

(2.4.13)

(2.4.13) is easy to deduce by taking the second derivative of (2.3.8) vs. field. The nonlinearity coefficient β itself is temperature dependent. For SrTiO3 β ≈8⋅109 JC−4 m−5 at room temperature. (2.4.12) may be used to develop scalable field and temperature dependent capacitance of parallel-plate varactors. Required for modeling parameters: p, q, εgb and εint, Ck, Tc, ε L , β, T and V, where p, q, εgb and εint, are ferroelectric film (fabrication method) specific-available from experiments, while Ck, Tc, ε L , β are fundamental parameters for the given ferroelectric.

2.5 Models of the Loss Tangent 2.5.1 Loss Mechanisms and Early Models of the Loss Tangent In the past, loss has been a major problem hindering the commercialization of tunable microwave devices based on ferroelectrics. Although recently a considerable progress has been achieved, especially in thin film ferroelectrics, the problem of loss is still an issue for some demanding applications, and needs further theoretical

38

2 Physics of the Tunable Ferroelectric Devices

and experimental treatments. In this section the main loss mechanisms are considered briefly. Ferroelectrics in only paraelectric phase are considered. A rather comprehensive overview of the losses in microwave ferroelectrics is given by Tagantsev etc. (Tagantsev et al. 2005). There are two major groups of microwave losses in paraelectric phase ferroelectric; intrinsic and extrinsic (Fig. 2.5.1). In a perfect, single crystal paraelectric, the dissipation (losses) of the microwave power is associated with the absorption of the (microwave) electromagnetic waves by the thermal oscillations of the ions, and by the free charge carriers. In ideal single crystals ferroelectric (e.g. SrTiO3, KaTaO3, BaxSr1–xTiO3 etc.) without defects, used in tunable microwave devices, these fundamental-intrinsic losses are typically very small and may not be eliminated or reduced. These losses define the minimum value of the loss tangent which a given paraelectric may have. In real crystals, and especially in thin films, the dissipation of the microwave energy is associated with the defects and may be much higher. These are externally imposed losses and may be reduced or, in an ideal case, eliminate by synthesis of crystals with the reduced defect density. They are especially high in ceramics and thin ferroelectric films. The reduction of the defect density, especially in thin epitaxial films used in integrated tunable microwave devices, was and remains a challenging problem. Microwave losses in paraelectric phase

Extrinsic losses (Crystals with defects)

Intrinsic losses (Ideal/perfect crystals)

Interfacial

Local polar regions

Charged defects

Universal relaxartion law (Curie-von Scweidler)

Acoustic

Field induced

Quasi Debye

Four-quantum

Three-quantum

Free carrier absorption

Fundamental

Fig. 2.5.1 Brief classification of the loss mechanisms in paraelectrics

Both the theoretical and experimental study of the loss in ferroelectrics is a more complex problem that that of the permittivity. In the past, a systematic experimental study of the dielectric properties, and particularly the losses has been carried out by (Bete 1970), (Rupprecht and Bell 1962) etc.

2.5 Models of the Loss Tangent

39

Rupprecht–Bell–Silverman model of the nonlinear loss tangent, which is based on experiments using single bulk crystal STO, reads: tan δ = tan δ o + tan δ F

(2.5.1)

The field dependent part of it: tan δ F = ω ( Bkkl / C )ε 5 (T ,0) E 2

(2.5.2)

The anisotropic nonlinearity constants are field, frequency and temperature independent. For (100)STO B100 = 4.8 ⋅ 10 −7 , Km 2 s / V 2 . The empirical formula for the temperature dependent term

[

]

tan δ o = α + β T + γT 2 /(T − TC )

(2.5.3)

For a single crystal STO α=0, β=6.53·10–4, γ=2.54·10–6K–1. Vendik’s (1998) model is theoretical, based on four quantum mechanism, and predicts qualitatively correct frequency, temperature and permittivity dependence for the loss tangent discussed below. However, the electric field dependence predicted by this model does not explain the experimentally observed increase in the loss tangent in single crystal paraelectrics STO and KTO. This field dependent loss tangent explained by quasi-Debye mechanism considered in the next section.

2.5.2 Models of the Main Loss Mechanisms Regardless the mechanisms, the losses, in general, are additive, i.e. the total loss tangent of a paraelectric crystal is a sum of the loss tangents of all involved mechanisms: tan δ = ∑ tan δ i , where i denote the loss of a specific loss mechai

nism, partly discussed below and indicated in Fig. 2.5.1.

Intrinsic Losses The ferroelectrics used as tunable dielectrics are typically good dielectrics with extremely small density of the free electrons and holes. The mobility of these carriers is also small. Hence the losses associated with the absorption of the electromagnetic energy by the free charge carriers may be ignored in most of the cases (Gevorgian et al. 1997). The fundamental losses are associated with the interactions of the electromagnetic (microwave) energy with the thermal oscillations (phonons hv, h is the Plank’s constant, v is the oscillation frequency) of the ions. Most of the following discussions are based on (Tagantsev et al. 2005). In homogeneous perfect bulk single crystal paraelectrics, such as displacive ferroelectrics with a center-symmetric cubic crystal structure (e.g. SrTiO3, KaTaO3, BaxSr1–xTiO3 etc.) the fundamental losses are associated with the interac-

40

2 Physics of the Tunable Ferroelectric Devices

tions of the microwave field with the phonons. The loss tangent deduced from simple damped resonance (dispersion) model gives the following temperature and frequency dependences: tanδ~ωεT, which, due to used simplifications and assumptions, does not reflect the experimentally observed slopes of the temperature ε(T) and frequency ε(ω) dependences. Microwave energy is absorbed by thermal phonons of the crystal and the dissipated energy heats the crystal. In fact, the energy of phonons, hv, in the crystal is much higher then the quantum hf of the microwave field, hv> hf. Here f is the frequency of microwave field. In terms of quantum mechanics the absorption takes place via three and four quantum mechanism. In the first case the absorption process involves one microwave quantum hf and two phonons. In microwave and millimeter wave and near room temperature regions this theory predicts the following frequency and temperature dependence: tan δ ph ∝ ωε 3 / 2T 2

(2.5.4)

ε is the relative permittivity of the ferroelectric.

In the case of four-quantum process one microwave quantum hf interacts (dissipated) with three phonons of the crystal. In the same temperature and frequency regions this theory predicts frequency and temperature dependences of loss tangent similar to three-quantum one (2.5.4). However, for the typical paraelectrics (BTO, STO), KTO) the three quantum dissipation is dominant. The four phonon mechanism is applicable to crystals with non-center symmetric structure, e.g. ferroelectrics in polar phase. In perfect crystals, besides the fundamental phonon losses discussed above, extra microwave losses appear due to free charge carries and under the external electric field. The external fields, both DC, and even high power microwave fields break the symmetry of the crystal structure of the paraelectric phase by virtue of electrostrictive effect. In a crystal with a symmetric lattice structure (i.e. cubic as in SrTiO3, KaTaO3, and in paraelectric phase BaxSr1–xTiO3) the external field shifts the centers of the positive and negative charges. The induced non-center symmetric unit cell of the crystal lattice becomes polarized with an external field dependent dipole moment. The microwave field experiences microwave losses typical to actual non-center symmetric crystals, although the crystal is still in paraelectric phase. In an extreme case the external DC field may cause paraelectric to ferroelectric phase transformation (Hamburger et al. 1996), resulting in a rapid increase of microwave losses. The induced electric dipole initiates two extra mechanisms of the microwave losses: i) DC filed induced Quasi-Debye, and ii) Microwave to acoustic transformations. The field induced Quasi-Debye mechanism is proposed by Tagantsev (Tagantsev et al. 2005) and for small tuneability (T(E)=((ε(0)–ε(E))/ε(E))<<1) the losses associated with this mechanism are characterized by the following functional dependences of the loss tangent on the frequency and electric field: tan δ QD = AI ( E )ωT ( E )

(2.5.5)

2.5 Models of the Loss Tangent

41

where T(E) is the tuneability of the dielectric permittivity: T (E) =

ε ( 0) − ε ( E ) ε (0)

(2.5.6)

A is a material related constant. Experimental values of A for single crystal STO and KTO are accordingly 23·10–3/GHz and 17·10–3/GHz, I(E)≈1 for small tuneability, T(E)<<1. For small tuneability, using (2.3.8), (2.5.4) may be reduced to: tan δ QD = 3 Aβ [ε oε ( E )]3ωE 2

(2.5.7)

i.e. the functional dependence on E and ω coincide with (2.5.2). The parabolic dependence of tanδQD measured at about 0.8 GHz at 40 K, for a bulk single crystal [100] STO (Eriksson et al. 2003), is shown in Fig. 2.5.2. The maximum applied DC field is 1.0 V/μm. At fields below about 0.2 V/μm [T(0.2V/μm)<0.1] the dependence is to larger degree parabolic. However, at about 0.5 V/μm the losses reach maximum and start reducing slightly, as predicted by Quasi-Debye mechanism at high electric field (and larger tuneability, Astafiev et al. 2005). In thin SrTiO3 films devices the applied fields are typically much higher, up to 100 V/μm and above. Hence this loss mechanism should result in slight reduction of the losses, at least above 10.0 V/μm. For Ba reach compositions the field dependence of the Quasi-Debye losses is weaker. 0,0045

Bulk single crytal [100]SrTiO

0,004

3

T=52K, 0.8 GHz

Loss tangent

0,0035 0,003 0,0025 0,002 0,0015 0,001 0,0005

0

0,2

0,4

0,6

0,8

1

DC bias, V/μm

Fig. 2.5.2 DC field dependence of the loss tangent of [100] STO at 52 K and about 0.8 GHz

The electric field induced microwave to acoustic transformations in a homogeneous bulk single crystal paraelectric is associated with the electrostriction and inverse piezoelectric effects. Due to these two effects the electromagnetic field

42

2 Physics of the Tunable Ferroelectric Devices

generates acoustic waves with the same frequency as the microwave signal itself. In a non-ferroelectric piezoelectric (i.e. Quartz) the amplitude of the acoustic waves generated by electrostriction is proportional to E2, while the converse piezoeffect generates acoustic waves with amplitudes proportional to E. However, in a paraelectric with induced dipole moment this dependence is more complex, since the dipole moment itself depends on the applied DC field. In homogeneous paraelectric crystals the losses of the microwave energy are associated with the attenuation of the acoustic waves. In a crystal with a limited sizes (e.g. by electrodes) the acoustic waves may additionally attenuated in the interfacing materials. On the other hand, the limited sizes of the crystal may cause reflections resulting in acoustic waves resonances and resonant absorption (peaks in loss tangent) of the microwave energy. Typically, the resonant peaks in loss tangent associated with the acoustic resonances are visible in experiments where the density of the defects is very low and the extrinsic losses are smaller. In crystals much larger than the acoustic wavelength (i.e. in STO disk resonator (Eriksson et al. 2003) these resonances may form a quasi-continuous spectrum. In thin films a clear discrete spectrum is observed (Gevorgian et al. 2006). The losses in resonant absorption should increase linearly or quadratic with the increasing external DC field depredating on the relative contributions of the induced piezoelectric and/or electrostriction effects. In general, the field induced transformations of microwaves into acoustic waves are negative for analog tunable microwave devices. On the other hand this effect may be utilized in DC field tunable TFBARs (Berge et al. 2008). Typically, especially in thin films, all intrinsic losses are “screened” by higher contributions from extrinsic losses discussed below. However, in high quality bulk, and recently in epitaxial films, the intrinsic and extrinsic losses appear to be comparable. With decreasing the density of the defects the intrinsic losses start dominating. In an ideal paraelectrics crystal without defects, where all extrinsic losses are removed, the electric field induced quasi-Debye losses and the losses associated with the microwave to acoustic transformations will limit the achievable minimum losses.

Extrinsic Losses In crystals with defects there are extra losses associated with the defects in the crystal structure. The extrinsic losses are the main trouble makers, and they are much higher then the intrinsic losses. However, in contrast to the intrinsic losses, these losses may be reduced by reducing the density of the defects. Given below is a brief overview of the main loss mechanisms, caused by defects. Universal (Curie-von-Schweidler) relaxation mechanism is the most common defect related mechanism for all dielectrics in general, including paraelectrics. tan δ ur = Rω n

n=0–1 depredating on the material nature of the defects in it.

(2.5.8)

2.5 Models of the Loss Tangent

43

Charged defects are one of the most common defects. Both in chemically pure bulk single crystals, ceramics and thin films ferroelectrics any charged point defects and charged dislocations create local static electric field. Even the neutral defects may locally distort the crystal symmetry and create local dipoles and static fields around them. The oxygen vacancies seem to be the most common positively charged point defects in chemically pure crystals. In such local felid both electrostrictive (Vendik and Platonova 1971) and converse piezoelectric effects are active and the electromagnetic (microwave) waves generate acoustic waves. From these point sources (in contrast with the defectless case discussed above) the acoustic waves travel in the crystal taking with them some energy from the electromagnetic waves, i.e. causing loss of the microwave signal. Some local increase in the loss tangent also may be expected by virtue of the quasi-Debye mechanism. The loss tangent associated with the charged defects is approximated by: tan δ ch = Fεω

1 Z 2 n ⎧⎪ 1− 3 ⎨ 4πρν t ⎪ 1 + (ω /ω ) 2 c ⎩

[

⎫⎪ , 2⎬ ⎪⎭

]

(2.5.9)

where F≈1 is a material specific constant, Z the effective charge (C) of the defect, n is the density (m–3)of the defects, ρ is the density of the crystal (kg/m3), vt is the acoustic velocity, ωc=vt/rc, rc is the correlation length of the charge distribution, i.e. the distance at which the electro-neutrality in the crystal is restored. As it follows from (2.5.8) the loss tangent in this case is proportional to the permittivity, indicating that it follows the same temperature and field dependences. For a paraelectric this means a reduction of the losses with increased field and temperature. The charged defects may be uniformly distributed in the bulk of the crystal and/or concentrated at the interfaces with the grains and electrodes. Recent publications indicate that oxygen vacancies are the main charged defects and, in some cases, the main contributors to the losses in thin ferroelectric films. Notice that in contrast to external DC field induced microwave and acoustic transformations considered above as a part of the intrinsic losses, the losses in this case associated solely with the defects, i.e. they have extrinsic nature, and may be reduced by eliminating the defects. On the other hand the losses associated with the external filed induced acoustic transformation in perfect, defectless crystal are more of intrinsic nature. They are “hidden” in the perfect crystal, and appear as soon as an external field is applied. Under an applied DC bias both these intrinsic and extrinsic losses contribute in the total losses of a tunable ferroelectric device. After removing the external field, only the extrinsic part associated with the charged defects contribute. Other Sources of Extrinsic Losses: Local polar regions occur in normally paraelectrics (Hubert et al. 1997) at the interfaces between the phases, grains/ columns, electrodes and other layers (i.e. dielectric and metallic buffer layers). No reports are available on the losses associated with these defects.

44

2 Physics of the Tunable Ferroelectric Devices

In paraelectric phase single crystals (e.g. SrTiO3, KTaO3 etc.) the quasi-Debye mechanism (2.5.7) dominates, as it is seen from the experimental result shown in Fig. 2.5.2. It is characterized by linear frequency dependence and a field dependence which at low field strengths may be approximated by a quadratics function (2.5.2). The temperature dependence is similar to the temperature dependence of the permittivity as in (2.5.7). One expects to have similar frequency, field and temperature dependences in high quality defect free thin films. However, the experiments reported until now indicate that the losses in the thin films increase linearly with the frequency and decrease with the electric field as it is predicted by (2.5.9), i.e. it seems the losses associated with the charged defects dominate. At the same time the losses in the reported paraelectric phase decrease with the increasing temperature, as one also expects from the temperature dependent permittivity in (2.5.9).

2.6 Dielectric Nonlinearities 2.6.1 Nonlinear Performance of Paraelectrics Ferroelectrics are essentially nonlinear materials. In some applications (i.e. harmonic generators, pulse compressors, limiters) the nonlinearity is a desired effect, however, in most of the applications nonlinearities cause serious problems such as harmonic generation and intermodulation distortion (known as IP3). When considering nonlinearities one has to distinguish between the static and dynamic nonlinearities. The static nonlinearity appears in DC dependent permittivity and microwave losses tangent. In this case the level of the microwave probe signal is low and does not cause any measurable nonlinearity. The dynamic nonlinearity is characterized by substantial dependence of the permittivity and loss tangent on the level of the RF/microwave power, even without any applied DC field. Theoretically, for paraelectric phase for BaxSr1–xTiO3 and similar ferroelectrics, the dynamic nonlinearity is four times smaller then the static nonlinearity (Tagantsev and Glazunov 1998). The field and temperature dependence of a ferroelectric in paraelectric phase, based on the thermodynamic theory of Landau, may be represented as (2.3.8):

ε ( E,T ) =

ε (0, T ) 1 + 3βε o3ε 3 (0, T ) E 2

where β is the coefficient of the dielectric nonlinearity, and the temperature dependence of the permittivity is given by Curie-Weiss low (2.3.6):

ε (0, T ) =

C T − Tc

2.6 Dielectric Nonlinearities

45

Under a small electric field, the static (i.e. under DC bias) and the dynamic (Tagantsev and Glazunov 1998) nonlinear coefficients are given by:

β DC = β AC =

3ε o3 3ε o3

Δε DC

(2.6.1)

4Δε AC

(2.6.2)

2 [ε (0, T )]4 EDC

2 [ε (0,T )]4 E AC

where ΔεDC=ε(0)–ε(EDC) and ΔεAC=ε(0)–ε(EAC) EAC is the amplitude of the microwave signal (E=EACCos(ωt)). The relative changes in permittivity may be given as:

[

]

3 2 Δε DC = 3β DC ε o ε (0, T ) E DC ε (0, T )

[

]

3 2 1 Δε DC Δε AC = 3β AC ε o ε (0, T ) E AC ≈ ε (0, T ) 4 ε (0, T )

(2.6.3) (2.6.4)

It follows from the above expressions that at EDC=EAC the microwave signal causes four time smaller changes in the permittivity. In other words the widely speculated concern (which is based on the DC dependent permittivity) about negative effects associated with the nonlinearities seems to not be justified. Moreover, in tunable microwave devices the DC field is much higher then the AC field: EDC>EAC, i.e. while designing a ferroelectric varactor/device one may reduce the nonlinear effects by trading the low nonlinearity against the higher tuning voltages. Apart from appearance of undesirable harmonics in microwave systems, in some passive device applications the transformation of a part of microwave power into the higher order harmonics may be seen as extra loss, i.e. some useful microwave power ”lost” in generated harmonics. Fortunately the dynamic nonlinearity of ferroelectrics is much lower in comparison with the semiconductors and its impact may be effectively reduced by scaling the sizes of the devices and using smart device designs. Some ways of decreasing the nonlinearities and increasing the power handling capabilities are discussed in Sect. 4.7.

2.6.2 Nonlinearity and Power Handling Capability In general, the power handling capability may be defined as the maximum power level at which the performance parameters of the devices are still in the specified limits. The performance indicators are device/application specific. As a universal criterion one may compare the amplitude of the microwave signal and the applied DC voltage, i.e. The system/device application limit/specify the maximum amplitude of the microwave field, EAC, with respect to the maximum DC field, EDC, i.e. the EAC/EDC ratio the system may tolerate. The EAC/EDC ratio may be limited by tolerated maximum i) heating, ii) power of higher order harmonics and/or

46

2 Physics of the Tunable Ferroelectric Devices

iii) losses. In general, the ferroelectric varactors are characterized with higher than semiconductor analogs power handling capability. In contrast to semiconductor competitors, the ferroelectric devices may be easily scaled to support higher microwave powers by i.e. increasing the thickness of the ferroelectric film in parallel-plate varactors and the gap in coplanar plate varactors. Moreover, the varactors may be cascaded allowing low DC control voltages and at the same time supporting higher microwave powers (see Sect. 4.7).

2.7 Thin Films vs. Bulk 2.7.1 Thin Film vs. Bulk Single Crystal The simple models considered in previous sections (e.g. (2.3.8)), in general, are valid for the bulk single crystals. They are useful for understanding the physics of the tunable ferroelectric devices, and in many cases, for modeling of the microwave devices with a reasonable accuracy. In single crystal paraelectric phase perovskites, the deviations from ideal cubic structure cause anisotropy in dielectric properties. For example, the bulk single crystal STO has only very slight tetragonality at room temperature and remains in paraelectric phase at all temperatures up to near 0 K (Muller and Burkard 1979). With the decreased temperature the permittivity increases, and below the phase transition temperature 110 K it becomes tetragonal, with clear anisotropy in the dielectric permittivity. The microwave losses undergo similar changes with the reduction of the temperature, and below phase transition temperature become essentially anisotropic. Figure 2.7.1 shows the measured at microwave frequencies anisotropy in the dielectric losses in bulk single crystal STO (Eriksson et al. 2003). Although chemically the same, the dielectric properties of the thin ferroelectric (epitaxial, textured) films are substantially, sometimes even drastically, different from their bulk counterparts. The experiments with a 75 nm thick free standing single crystal BaTiO3 film, cut from a bulk single crystal, reveal (Saad et al. 2004) that with the ideally symmetric electrodes and with no substrate the dielectric properties of the film are identical with the single crystal. Typically, in the thinner films the lower permittivity and tuneability, in comparison with the bulk single crystal, are attributed to the low permittivity dead layers at the interfaces with the electrodes. The thickness of the dead layer assumed to be of the order of several nanometers (Stengel and Spaldin 2006). Naturally, its effect will be more pronounced for the films that have thicknesses comparable with the thickness of the dead layer. In thin films grown on host substrates and ceramics the misfit strain (mismatch in lattice parameters and thermal expansion), non-stoichiometry, voids in the granular/columnar structure etc., may have drastic effects on the dielectric and acoustic properties of the films. These factors appear in different degrees in the films produced by different laboratories and methods. Besides, there are also fundamental effects associated with the surfaces/interfaces. With decreasing the film thickness, the contribution of the surface properties, relative to the bulk properties increases

2.7 Thin Films vs. Bulk

47

Fig. 2.7.1 Orientation dependent dielectric losses in bulk single crystal STO. Reprinted with permission from AIP©2003

and, in nanostructure limits, may dominate over the bulk properties. The surface of the ferroelectric may have drastically different properties in comparison with the bulk of the crystal. For example, pure bulk single crystal SrTiO3 has no ferroelectric phase at any temperature. On the other hand, a structural/ferroelectric phase transition, at about 155 K is observed in a near surface layer in bulk single crystal STO, (Mishina et al. 2000). Polar gain boundaries in undoped SrTiO3 ceramics are detected by Raman scattering (Petzelt et al. 2001). It is shown, in this work that the polarization is perpendicular to the tetragonal c-axis, and it is temperature independent. This polarization may be associated with the fundamental effects at the interfaces/surface considered above (Mishina et al. 2000), tilted grain boundaries (McGibsson et al. 1996), ad/or charged defects (i.e. oxygen vacancies) at the grain boundaries. Donor type space charge is reported at the grain boundaries (Hagenbeck and Waser 1999). These observations indicate that similar polar phases may be in thin films with granular and columnar structure. The in-plane anisotropy is even more pronounced in thin the STO and paraelectric phase BSTO films. Under interfacial/misfit strain the lattice of STO and BSTO films are strongly distorted and, in most cases, have tetragonal structure, although being in paraelectric phase. In these films one should expect a substantial anisotropy in the permittivity and microwave losses similar to bulk STO shown in Fig. 2.7.1. Attempts to measure the orientation dependent in-plane anisotropy in the permittivity and losses tangent in strained ferroelectric films have been reported recently. For example, in a parallel plate varactor the films with [110] and [111] orientations are preferable. BSTO films with surface normal orientations (001), (011) and (111) epitaxially grown (001), (011) and (111) oriented MgO substrates (Moon et al. 2003) had slight in-plane anisotropy in permittivity. The in-plane Q-factor (=1/tanδ) measured at 9.0 GHz is substantially higher for (111) film. In another experiment (Chang et al. 2005), STO films epitaxially grown on (110)

48

2 Physics of the Tunable Ferroelectric Devices

DyScO3 substrate, measured in plane [100], [010], [110] and [–110] orientations had substantially different permittivity and tuneability in these orientations, largest in in-plane [010] orientation. The effect of the misfit strain becomes dominant with decreasing the film thickness (grain sizes). In relatively thicker films the strain is released and it has no substantial effect in the bulk of the film, thicker than strain released transition layer. The strain may cause ferroelectric to paraelectric (and vice versa) phase transitions (Pertsev et al. 1998). An extreme case of induced ferroelectric phase transition in strained epitaxial STO film has been demonstrated experimentally (Haeni et al. 2004). Hence, the size associated ferroelectric to paraelectric phase transition is associated with the shift in Curie temperature due to misfit strains. For a given film (composition) the shift depends on the film composition, the difference in the lattice and thermal expansion coefficients between the film and interfacial layers/substrate, the temperature, and the film thickness. The strong anisotropy in the dielectric losses has to be taken in practical applications of STO, especially in thin film. For example, the gap between the electrodes in coplanar-plate varactors has to be normal to the in plane orientation with the largest tuneability and smallest losses (for example [010], as in (Chang et al. 2005). The films in parallel plate varactors should have [110] and [111] orientation normal to the plates to ensure highest tuneability and smallest losses.

2.7.2 Strain The strain is defined as a fractional change of the crystal sizes. In terms of the lattice constant, for 1D model, Fig. 2.7.2, it is given as u=Δa/ao. The strain in crystals may be caused by changes in:

• Temperature – this corresponds to thermal expansion; • Mechanical stress – known as elastic deformation; • External DC field. In this case one has to distinguish between the converse piezoelectric and electrostrictive effects. Thin films deposited on substrates experience a 2D misfit strain due to the lattice parameter and thermal expansion coefficient differences between the film and substrate. Both of them cause elastic deformations according to i) and ii) above. An extra strain in ferroelectric films used in microwave devices is associated with the applied electric field. The converse piezoelectric effect may be explained by considering the simple 1D model shown in Fig. 2.7.2, where the interaction forces between the ions are represented by springs. The soft and hard springs represent the different interaction forces between the neighboring ions. In polar phase the external DC field applied to the crystal causes more changes in the length of the soft spring in comparison with the hard spring. As a result the size of the whole unit cell changes, and the change, i.e. the strain is proportional to the external DC field: u = dE

(2.7.1)

2.7 Thin Films vs. Bulk

49

where d is the piezoelectric coefficient, and the strain is an odd function of the applied field E, i.e. the sign of the strain depends on the direction of the external field. In paraelectric (cubic, center-symmetric) phase, the positive ion is located in the center where its free energy is minimum. In this equilibrium state the springs connecting to the neighboring ions are similar, and the external DC field should not cause strain. In reality, the forces developed between the ions are not linearly related to the external DC field. They are characterized by quadratic dependences with the different spring constants for the left and right springs: k1(Δa)2 and k2(Δa)2. In fact the spring constant is slightly larger when one tries to push the ions closer. This means the crystal is easier to expand than contract (press). The force trying to return the ion into the center equilibrium position is then proportional to the difference (k1–k2) (Δa)2. This small difference produces a strain which is independent of the direction of the external field: u = gE 2 ,

(2.7.2)

where g is the electrostriction coefficient. Notice that the strain in the case of electrostriction is an even function of the applied field, i.e. it does not depend on the direction of the field. This is another feature that may be used to distinguish between the converse piezoelectric and electrostrictive effects. In thin films the thermal, acoustic and electric and electrical properties have mutual coupling. This coupling is discussed in the next section. No external field

Lattice constant, ao

(a)

External field, E

Δa~E2 ao+Δa

(b)

Fig. 2.7.2 1D model of a paraelectric crystal without (a) and with (b) external field

In tunable microwave devices, based on thin film ferroelectrics, the consideration of the electroacoustic properties is of great importance. In tunable devices the films are clamped by substrate, hence they are subject to lattice mismatch and thermal expansion mismatch strains. In contrast to free standing bulk counterparts, these strains generate stresses, which affect dielectric properties of the films, and

50

2 Physics of the Tunable Ferroelectric Devices

may cause large shifts in the Curie temperature and Curie constant, and even result in paraelectric-to-ferroelectric phase transitions (Haeni et al. 2004). Additionally, via electrostriction and inverse piezoelectric effects, induced strains and stresses are generated in the films. The electric filed induced strains are limited in the plane of the film. However, in out of plane orientation, films have freedom for strains. Besides the dielectric properties the acoustic parameters of the film also undergo changes under complex action of misfit and field induced strains. The films, otherwise in paraelectric phase, may take field induced piezoelectric properties. In short, one has to expect substantial differences in both dielectric and acoustic (piezoelectric) properties of the ferroelectric films and their bulk single crystal counterparts. Due to substrate clamping these properties turn to be more interdependent, and while analyzing the film performances and designing devices one has to take these complex interdependences into account.

2.7.3 The Effects of the Strain on Dielectric Properties of the Thin Films As it was indicated, the properties of the ferroelectrics are sensitive function not only of the electric field and temperature, but also the strain. A thin ferroelectric film clamped by the substrate and other interfacing films experience in plane misfit strain, um, associated with the differences in lattice parameters and thermal expansion coefficients of the interfacing layers. The films are free along out of plane direction and are not strained. Under the in-plane strain the lattice of the films undergo certain deformations. For example, normally cubic lattice of a paraelectric film may become tetragonal or orthorhombic, i.e. its symmetricity is reduced. Then the film, though the same chemically, becomes different physically, with the different dielectric and acoustic properties. Particularly the film, otherwise in paraelectric phase, may undergo paraelectric to ferroelectric phase transformation indicated in the previous section. Figure 2.7.3 shows the conventional axis notations used in the following analysis. Thickness +3 –2

+1

–1

–3

Fig. 2.7.3 Axis notations

+2 Width

Length

2.7 Thin Films vs. Bulk

51

The analysis (Tagantsev et al. 2005) shows that, for a film in paraelectric phase (cubic lattice), the in-plane misfit strain caused by an isotropic substrates result in the following in-plane (εin=ε11=ε22) and out-of-plane (εout=ε33) permittivities: ⎧1 ⎡ ⎤⎫ 2η ε in = ⎨ − 2ε oum ⎢q11 + q12 − q12 ⎥ ⎬ 1 −η ⎣ ⎦⎭ ⎩ε

ε out

⎧1 ⎡ ⎤⎫ 2η = ⎨ − 2ε o u m ⎢2q12 − q11 ⎥ ⎬ 1 −η ⎣ ⎦⎭ ⎩ε

−1

(2.7.3)

−1

(2.7.4)

where ε is the unstrained permittivity of the film which practically is the same as the permittivity of the bulk single crystal at the same temperature without an applied electric field, q11 and q12 are elements of the electrostriction tensor. For an isotropically strained film the in-plane misfit strain um= u11 = u22:

(

)

u m = u mR + α s − α f (T − TR )

(2.7.5)

Here αs and αf are the thermal expansion coefficients of the substrate and the film correspondingly, and umR is the misfit strain at a given temperature (typically at room TR). The misfit strain at a given temperature may be measured using a grazing angle X-ray analysis: umR =

aR − ao , ao

(2.7.6)

where aR is the measured in-plane lattice constant of the film, ao is the lattice constant of the unstrained film, which is the same as the lattice constant of the bulk single crystal at temperature TR. Alternatively, if the out-of-plane lattice constant c is available from the XRD analysis one may use the Poisson’s ratio η to compute the in-plane strain:

u mR = u33

1 −η

η

,

(2.7.7)

cR − co co

(2.7.8)

where u33 is the out-of plane strain: u33 =

The numerical values of the parameters for SrTiO3 are given Table 2.7.1 (Tagantsev et al. 2005).

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2 Physics of the Tunable Ferroelectric Devices

Table 2.7.1 Modal parameters for SrTiO3 Ferroelectric parameters

η

q11, m/F

q12, m/F

Thermal expansion coefficient α, K–1 SrTiO3

SrTiO3

0.24 2.2⋅1010

0.2⋅1010 11⋅10–6

MgO

Al2O3

Si

13⋅10–6

6⋅10–6

4⋅10–6

2.8 Electro-Acoustic Properties 2.8.1 Electrostriction The term electrostriction is used describe electric field induced strain, i.e. fractional change of the sizes of a solid under applied electric field (2.7.2). In one dimensional case the strain is simply the ratio u=Δa/ao= Δl/lo, where lo the original length of the sample, Δl is its change under the electric field. Electrostriction is general phenomena for all solids, however in ferroelectrics, especially near phase transition temperature, the effect is considerably larger. Electrostriction appears both in crystals with centrosymmetric lattice and in crystals without inversion symmetry, like ferroelectrics (e.g. BaxSr1–xTiO3) in paraelectric (cubic) and ferroelectric (tetragonal) phases. If the material is also piezoelectric the acoustic and electric properties are coupled via constitutive equations considered in the next section.

2.8.2 Piezoelectricity and Electrostriction Ferroelectrics in polar (ferroelectric) phase, including complex oxides with perovskite structure, are piezoelectric. The indices used below correspond to axis notations shown in Fig. 2.7.3. The out-of plane (i.e. along axis 33) electric field displacement D3 (C/m2) and strain S3 developed under the applied electric, E3 (V/m), field, and stress, T3 (N/m2) are related via constitutive equations (Gonnard 2002): T D3 = ε 33 E3 + d 33T3

(2.8.1)

E S 3 = d 33 E 3 + s 33 T3

(2.8.2)

where P3 is the polarization, the superscripts T and E stand for constant temperature and electric field (shorted electrodes), ε33 is the dielectric permittivity, s33 (m2/N) is the elastic compliance, d33 (m/V=C/N) is the piezoelectric coefficient along 33 axes.

2.8 Electro-Acoustic Properties

53

The electric field and strain developed under stress and displacement: D S 3 = s33 E3 + g 33 D3

(2.8.3)

T E3 = − g 33T3 + β 33 D3

(2.8.4)

with g33 = d33/ε33 (C/N=m/V). β33 = 1/ ε33 is the stiffness (inverse dielectric permittivity). The longitudinal coupling coefficient is defined as: 2 2 T E D E k33 = d 33 /( s33 ε 33 ) = 1 − s33 / s33

(2.8.5)

It shows the fraction of the electrical energy that covert into mechanical energy (and vice versa). In most of the practical cases the films deposited on a substrate are under interfacial (in-plane) strain T1. In this case the associated relationships are: E S1 = s11 T1 + d31E3

(2.8.6)

D S1 = s11 T1 + g 31 D3

(2.8.7)

T D3 = ε 33 E3 + d13T1

(2.8.8)

T E3 = − g 31T13 + β 33 D3

(2.8.9)

In the above relationships g31=d31/sT33, 2 2 T E D E k31 = d 31 /( s33 ε 11 ) = 1 − s11 / s11

(2.8.10)

The small signal losses are taken into account by assuming the dielectric permittivity, elastic compliance, and piezoelectric coefficient are complex quantities: ' '' ' ε 33 = ε 33 − jε 33 = ε 33 (1 − j tan δ d )

(2.8.11)

' '' ' (1 − j tan δ m ) s33 = s33 − js33 = s33

(2.8.12)

(

' '' ' d 33 = d 33 − jd 33 = d 33 1 − j tan δ p

)

(2.8.13)

where the real and imaginary parts of the parameters have standard meanings and the tanδd, tanδm, and tanδp are dielectric, mechanical (elastic) and piezoelectric loss tangents. For a paraelectric film with no piezoelectric effect the piezoelectric coefficients d33 = d31 = 0. On the other hand it follows from (2.8.8) that in a polar, piezoelectric phase an in-plane strain T1 will induce electric field via piezoelectric coefficient

54

2 Physics of the Tunable Ferroelectric Devices

d13 even with no applied electric field, E3 = 0. One may expect a similar effect in films with paraelectric composition if a biaxial misfit strain induces piezoelectricity. Then a strain induced electric field may appear across the film normal to the substrate which may cause imprint in a parallel-plate capacitor even if the electrode/ferroelectric interfaces (potential barriers) are symmetric.

2.8.3 Electric Field Induced Piezoelectricity in Paraelectric Films In general, one should not expect piezoelectric effect in crystals with centersymmetric crystal structure. However, the electromechanical study of single crystal STO (Rupprecht and Winner 1967) shows that the slight deviation from the ideal centrosymmetric-cubic structure, bulk single crystal STO exhibits a week piezoelectric effect with temperature, T, and electric field, E, dependences characterized by ~E/(T-Ta). Moreover, as it is indicated above the crystalline structure of the thin films having paraelectric composition (i.e. BaxSr1–xTiO3, x<0.6) is often far from being centrosymmetric due to the lattice mismatch and the mismatch in thermal expansion coefficients. A clamped by substrate and other interfacing layers film may experience additional lattice deformation due to electrostriction induced strains. Hence one may expect a substantial induced piezoelectric effect in thin films in comparison with the bulk single crystalline cubic counterparts. In (Tappe et al. 2004, Gevorgian et al. 2004) the piezoelectric effect in thin paraelectric films manifested itself as resonant absorption of microwave power, i.e. sharp increase in loss tangent at certain frequencies under increasing applied DC field. In summary, in paraelectric BaxSr1–xTiO3 films, the induced piezoelectric effect is associated with the strong electrostrictive effect. In paraelectric films there are no acoustic resonances without applied DC field. Under applied DC field the symmetry of the crystal is broken and for the superimposed RF signal the crystal pretends to be piezoelectric. In fact a thin film paraelectric capacitor with induced piezoelectricity acts as a Thin Film Bulk Acoustic Wave resonator (TFBAR). The simple theory of induced piezoelectricity in thin STO film given in (Gevorgian et al. 2006) explains the DC induced absorption peaks in parallel-plate BaxSr1–xTiO3 varactors. More advanced theories are proposed in (North et al. 2007, Vendik et al. 2008). For an idealized TFBAR, assuming the thicknesses of the electrodes zero (no acoustic loading), the series resonance and parallel-resonance (anti-resonance) given in (Noeth et al. 2007) may be represented in simplified form: fp =

1 2t

D c33

(2.8.14)

ρ

fs = f p 1 − 8

kt2

π2

(2.8.15)

2.8 Electro-Acoustic Properties

55

where kt2 =

4q 233 ε oε 33f (0) PDC 2 cD

2 c D = c o − (m333 + 4q 33ε oε b )PDC

(2.8.16) (2.8.17)

PDC is the polarization under applied DC field EDC, i.e. PDC=ε33(E)εoEDC, co, q33, and m333 are corresponding components of the tensors of elastic constants εb is the background permittivity associated with the non-ferroelectric (non-soft mode) contribution in the dielectric permittivity, ρ is the density of the ferroelectric. The DC bias dependent real part of the permittivity, ε33(E)=ε(E, 300) may be calculated by (2.3.8) and any of appropriate formula given in Sects. 2.3 and 2.4. The numerical values of the acoustic parameters depend on the composition of the ferroelectric film quality, crystal orientation temperature etc. Currently they are being investigated and corrected. One has to keep in mind that the model described above is valid for small DC bias and RF fields. A similar model of induced piezoeffect is reported in (Vendik et al. 2008) where the second term in the brackets in (2.8.18) is missing.

Freauency, GHz

5.42 f

5.4

p

5.38 5.36 f

s

5.34 5.32 0

5 10 DC bias, V

15

Fig. 2.8.1 Resonant frequencies for 0.5 μm thick SrTiO3 assuming C=8⋅104 K–1, T=300 K, Tc=35.5 K, β=8⋅109 JC–4m–5, m333=–0.25⋅1012, co=3.16⋅1011 N/m2, q33=2.53⋅1010 m/F, εb=7, ρ=5130 kg/m3

The current temperature and composition dependent measurements on BaxSr1–xTiO3 (Berge et al. 2008) show that depending on temperature and composition the coefficient m333 may be positive or negative. The DC field dependent resonant frequencies calculated using (2.8.14), (2.8.15), (2.3.6) and (2.3.8) for a membrane based TFBAR are shown in Fig. 2.8.1. As it is expected from (2.8.15) the series resonant frequency is always smaller than the parallel one and its tuning is higher since it depends not only on the bias dependent cD, but also on bias dependent k2t.

56

2 Physics of the Tunable Ferroelectric Devices

The impedance of the idealized (membrane based and infinite thin electrodes) TFBAR is: Z=

1 ⎡ tan (φ ) ⎤ 1 − kt2 jωC ⎢⎣ φ ⎥⎦

(2.8.18)

Where φ =kt/2, C is the DC dependent parallel-plate capacitance and t is the thickness of the ferroelectric film, and the k is the acoustic wave number: k =ω

ρ cD

(2.8.19)

2.9 Bulk Conductivity In all ferroelectric devices the electrodes play a major role in their I-V performance. Additionally, the conductivity in ceramics is heavily affected by the grain boundaries. In this section only the basic conduction mechanisms in bulk single crystals are briefly outlined. The conductivity of the ferroelectric films and the leakage currents in ferroelectric varactors is discussed in Chap. 4, while the associated reliability and lifetime are addressed in Chap. 10. Chemically (no impurities) and physically (no defects) clean ferroelectrics, i.e. BaxSt1–xTiO3, especially the quantum paraelectrics SrTiO3, TiO2, KTaO3, CaTiO3, have rather high resistibility, typically more than 108 Ohm cm. To achieve high tuneabilities, in microwave devices based on ferroelectrics, the applied DC and often superimposed RF electric fields are very high. This is a typical situation in most thin film parallel-plate varactors. In the past the conductivity of the single crystal ferroelectrics studied mainly at relatively low electric fields. Recent experiments using very thin (77 nm) single crystal BaTiO2 plates (Morrison et al. 2005) allowed to distinguish a number of conduction mechanisms characterized by different slops in I-V dependence. Typically, below about 10 V/μm the conduction is negligible and the currents are dominated by injection of charge carriers over the electrode/ferroelectric barrier characterized by exp(V/2KT) dependence followed by a region with linear (not Ohmic) I-V dependence (Morrison et al. 2005). Pool-Frenkel Effect: At relatively high temperature and electric field the conductivity may be associated with the Pool-Frenkel effect. The trapped electrons and holes are excited into shallow traps or conduction levels, due to the complex action of temperature and electric fields. In ferroelectric thin films the PoolFrenkel emission becomes dominant above about 10V/μm, both in the surface layers and in the core of the ferroelectric film (Grossmann et al. 2002). Thus traps for electrons are assumed to be neutral when occupied and positive charged when empty (i.e., they are donors). Traps for holes are assumed to be neutral when emptied of an electron. Thus besides providing free charge carries the trapping/

References

57

detrapping results in changes in the charged states of the defects and hence contribute in the local polarization. Hopping: This mechanism in SrTiO3 (Fuchs et al. 2001) consider I(E)=Aexp [(–(E/E*)0.25] current dependence where A is a temperature independent constant and E* is a critical field. It is assumed that this conduction mechanism is active above 100–200 V/μm. Space Charge Limited Currents (SCLC): It is shown in (Morrison et al. 2005) that in single crystal BaTiO3 above 200 V/μm the currents are predominantly space charge limited.

2.10 Conclusions Physics of the ferroelectrics, particularly for microwave applications, is rather well understood. The available models for the temperature, electric field and stress dependent permittivity, loss tangent and leakage currents are simple, rather correct and useful for development of scalable circuit models for ferroelectric varactors and complex microwave devices and systems based on them. At the same time the physical models are indispensable for the optimization of the synthesis process of the ferroelectric films, composites and fabrication devices.

References Astafiev K F et al. (2005) Quasi-Debye microwave loss as an intrinsic limitation of microwave performance of tunable components based on SrTiO3 and BaxSr1− xTiO3 ferroelectrics. J Appl Phys 97:014106-1- 014106-8 Barrett J H (1952) Dielectric Constant in Perovskite Type Crystals. Phys Rev 86:118 Berge J et al. (2008) Field and temperature dependent parameters of the dc field induced resonances in BaxSr1–xTiO3-based tunable thin film bulk acoustic resonators. J Appl Phys103:064508 Bete K (1970) Uber Das Mikrowellenverhalten Nichtlinearer Dielektrika. Philips Research Reports Supplements, vol 2 Chang W et al. (2005) In-plane anisotropy in the microwave dielectric properties of SrTiO3 films. J Appl Phys 98:024107 Chosez P, Junquera J (2006) First-Principles Modeling of Ferroelectric Oxides Nanostructures. In: Rieth M, Schommers W (Ed) Handbook of Theoretical and Computational Nanotechnology. American Scientific Publisher, Stevenson Ranch California Cochran W (1960) Crystal stability and theory of ferroelectricity. Adv Phys 9:387–423 Dawber M et al. (2005) Physics of thin film ferroelectric oxides. Rev Modern Phys 77:1083–1130 Eriksson A et al. (2003) Orientation and direct current field dependent dielectric properties of bulk single crystal SrTiO3 at microwave frequencies. J Appl Phys 93:2848–2854 Fuchs D, Adam M, Schneider R (2001) Dielectric properties of Ti-deficient SrTiO3–δ thin films. J. Physics IV France 11:71–76 Gevorgian S et al. (1997) HTS/Ferroelectric Devices for Microwave Applications. IEEE Appl Supercond 7(2):2458–2461

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Gevorgian S et al. (2004) A Tuneable resonator. International Application No.: PCT/ SE2004/001099, International Filing Date: 06.07.2004, Publication Date:12.01.2006 (WO 2006/004470 A1) Gevorgian S et al. (2006) DC field and temperature dependent acoustic resonances in parallelplate capacitors based on SrTiO3 and Ba0.25Sr0.75TiO3 films. Experiment and modeling. J Appl Phys 99:124112 (1–11) Gonnard P (2002) Piezoelectric materials for high power applications: Electromechanical characterization and models. In: Setter N (Ed) Piezoelectric Materials and Devices, Ceramics Laboratory, EPFL, Lausanne Grossmann M et al. (2002) The interface screening model as origin of imprint in PbZrxTi1–xO3 thin films. Numerical simulation and verification. J Appl Phys 92(5):2688–2696 Haeni J H et al. (2004) Room temperature ferroelectricity in strained SrTiO3. Nature 430:758– 761 Hagenbeck R, Waser R (1999) Detailed temperature dependence of the space charge layer width at grain boundaries in acceptor doped SrTiO3-ceramics. J Eur Ceramic Society, 19(6):683–686 Hemberger J et al. (1995) Electric field dependent dielectric constant and susceptibility in SrTiO3. Phys Rev 52:1359–1362 Hemberger J et al. (1996) Quantum paraelectric and induced ferroelectric state in SrTiO3. J Phys: Condens Matter 8:4673–4690 Hubert C et al. (1997) Confocal scanning optical microscopy of BaxSr1–xTiO3 thin films. Appl Phys Lett 71: 3353–3355 Lemanov V V et al. (1999) Perovskite CaTiO3 as an incipient ferroelectric. Solid State Communications 110:611–614 McGibsson M M et al. (1996) The atomic structure of asymmetric tilt boundaries in SrTiO3. Phyl Magazine A.73:625–641 Mishina E D et al. (2000) Observation of a Near-Surface Structural Phase Transition in SrTiO3 by Optical Second Order Harmonic Generation. Phys Rev Lett 85 (17):3664–3667 Moon S E et al. (2003) Orientation dependent microwave dielectric properties of ferroelectric Ba1–xSrxTiO3 thin films. Appl Phys Lett 83:2166–2168 Morrison F D et al. (2005) High field conduction in barium titanate. Appl Phys Lett 86:152903 Muller K A, Burkard H (1979) SrTiO3: An intrinsic quantum paraelectric below 4 K. Phys Rev B 19:3593–3602 Noeth A et al. (2007) DC bias—dependent shift of the resonant frequencies in BST film membranes. IEEE Utrasonics, Ferroelectrics and Frequency Control 54:2487–2492 North A et al. (2007) Tuning of direct current bias-induced resonances in Ba0.3Sr0.7TiO3 micromachined thin film capacitors. J Appl Phys102:114110 Pertsev N A et al. (1998) Effect of mechanical boundary conditions on phase diagram of epitaxial ferroelectric thin films. Phys Rev Lett 80:1988–1991 Pertsev N A et al. (2000) Phase transitions and strain induced ferroelectricity in SrTiO3 epitaxial films. Phys Rev B 61:R825–R829 Petzelt J et al. (2001) Polar grain boundaries in undoped SrTiO3 ceramics. J Eur Cer Soci 21:2681–2686 Rupprecht G et al. (1961) Nonlinearity and Microwave Losses in Cubic Strontium-Titanate. Phys. Rev. 123 (1):97–98 Rupprecht G, Bell O (1962) Microwave Losses in Strontium Titanate Above Phase Transition. Phys Rev 125 (6):1915–1920 Rupprecht G, Bell O (1964) Dielectric Constant in Paraelectric Perovskites. Phys Rev135 (3A):A708–A752 Rupprecht G, Winner W H (1967) Electromechanical Behavior of Single-Crystal Strontium Titanate. Phys Rev155:1019–1028 Saad M (2004) Intrinsic dielectric response in ferroelectric nanocapacitors. J Phys Cond Matt 16:L451–L456 Stenge M, Spaldin N A (2006) Origin of the dielectric dead layer in nanoscale capacitors. Nature 443: 679–682

References

59

Su B, Button T (2004) Microstructure and Dielectric Properties of Mg doped barium strontium titanate ceramics. J Appl Phys 95 (3):1382–1385 Tagantsev A K (2005) Permittivity, tuneability and losses in ferroelectrics for reconfigurable high freauency electronics. In: Setter N (Ed) Electroceramic Based MEMs, Springer Tagantsev A K and Glazunov A E (1998) Dielectric Nonlinearity and the nature of polarization response of PbMg1/3Nb2/3O3 reloaxor ferroelectric. J of the Korean Phys Soci 32:S951– S954 Tappe S et al. (2004) Electrostrictive resonances in BaxSr1–xTiO3 thin films at microwave frequencies. Appl Phys Lett 85:624–626 Vendik I B et al. (2008) Modeling tunable bulk acoustic wave resonators based on induced piezoelectric effect in and films. J Appl Phys103:014107 Vendik O G, Platonova L M (1971) Effect of charged lattice imperfections on the dielectric properties of materials. Sov Phys Solid State 13:1353–1359 Vendik O G, Ter-Martirosyan L T and Zubko S P (1998) Microwave losses in incipient ferroelectrics as functions of the temperature and the biasing field. J Appl Phys 84:993 Vendik O G, Zubko S P (1997) Modeling the dielectric response of incipient ferroelectrics. J Appl Phys 82:4475–4483 Vendik O G, Zubko S P (2000) Ferroelectric phase transition and maximum dielectric permittivity of displacement type ferroelectrics (BxSr1–xTiO3). J Appl Phys 88:5343–5350 Vendik O G, Zubko S P, Nikol’ski M A (2002) Microwave loss-factor of BaxSr1–xTiO3 as a function of temperature, biasing field, barium concentration, and frequency. J Appl Phys 92:7448 Vendik O, Mironenko I, and Ter-Martirosyan L (1994) Superconductors Spur Applications of Ferroelectric Films. Microwaves & RF, July:67–70

Chapter 3 Fabrication of Ferroelectric Components and Devices Andrei Vorobiev and Spartak Gevorgian

Abstract The subject of this chapter is fabrication of ferroelectric components and microwave tunable devices based on them. The main methods of fabrication of ferroelectric components are considered including the single crystal growth and slicing techniques; bulk ceramic sintering; thick film, HTCC and LTCC technologies; chemical and physical deposition methods. The methods of fabrication of ferroelectric components are considered in association with structural characterizations which allows one to establish correlations between processing parameters and device performance. The basic principles and details of processing of devices utilizing ferroelectric components are given by examples of devices described in the Chap. 5. Special sections describe the general technology platforms of fabrication of microwave tunable devices based on thin films grown by chemical and physical deposition methods.

3.1 Introduction In tunable microwave devices ferroelectrics are used in bulk (single crystal, ceramic) and film (thin, thick) forms. Different fabrication technologies are proposed in the past for bulk and film components. The single crystal ferroelectrics used in tunable microwave devices are grown by different methods. Due to the large sizes, relatively low defect density and lower cost the crystals grown by Verneuil method (MTI Corporation 2008, Semiconductor Wafer Inc. 2008, MaTecK GmbH 2008) are the most used in tunable microwave devices. The early tunable devices (Domenico et al. 1962, Johnson et al. 1962, Das 1964) use bulk ceramic processes.

61

62

3 Fabrication of Ferroelectric Components and Devices

HTCC, and especially LTCC processes are considered as the most cost effective processes. In some cases the HTCC process might appear preferable since it result in better crystalline structure in the grains. However, the selection of the metals for the electrodes (to withstand high temperature) is very limited. In this sense the LTCC is preferable and cost effective, although it requires careful selection of the additives lowering the sintering temperature (Jantunen et al. 2004). The surface roughness of the films is a common problem for thick film, HTCC and LTCC processes. Most of them use screen printing to pattern the films (ferroelectric, metal, and dielectric) which have resolution limitations. In the best case the minimum line width and slotwidth may be about 50 μm. In high volume production the line/spacing resolution, using screen printing methods, typically is about 100 µm. Narrower line/spacing (down to 20 μm) is achieved by using special thick film processes, e.g. photoimageable inks or etching. These processes need additional processing steps in production and suffer some limitations. A fine-line and high volume printing techniques for electronics applications, known as gravure printing, is developed by Microelectronics Laboratory, University of Oulu. The process allows 20 µm wide conductor lines with 50 µm pitch on LTCC and alumina with fired thickness up to 10–18 µm (Yeo et al. 2004, Hagberg et al. 2003). However, for smaller sizes the granular structure of the films and surface/interface roughness result in non-uniformity and sometimes even interruptions in ferroelectric films and metal strips and causes microwave loss and reliability problems. Thin film processes based on the growth of ferroelectric films (PLD, RF magnetron sputtering, sol-gel etc.) combined with standard photo lithography processes of patterning, extensively considered recently, allow high spatial resolution and heterogeneous integration of agile ferroelectric components with other advanced technologies (like MEMs, micromachined cavities etc.), i.e. in line with the “More-than-Moore” concept promoted by ITRS. The PLD deposition of the ferroelectric films is a versatile/flexible process allowing experiments with different materials and compositions. However it is not cost effective when it comes to industrial processes used for large scale productions. RF magnetron sputtering and sol-gel processes are more useful for large scale commercial production. Recently combustion chemical vapor deposition (CCVD) is proposed (http://www.ngimat.com/technology/ccvd.html) as an alternative process for large scale production of tunable ferroelectric devices. Analysis of the published result shows that the best ferroelectric films in terms of density and low losses are produced by RF magnetron sputtering. Typically standard photolithographic processes are used for fabrication of microwave derives. In some cases the ferroelectric films are not patterned, in some cases wet or dray (ion milling) etching is used to remove the ferroelectric films where they are not needed. Defects in crystal structure, like dislocations, point defects in the form of oxygen vacancies and background impurities may have significant effects on electric (conductivity) and dielectric (loss tangent) properties. For example, in high resistivity single crystal STO the stepwise changes (“switching”) in dielectric permit-

3.2 Fabrication of Devices Using Single Crystals

63

tivity is explained by charged point defects (Gevorgian et al. 2002), while high density of the oxygen vacancies drastically increase the microwave losses. Nb doped STO has metallic conductivity (Guo et al. 2003) and Ni doped STO is considered for applications in resistive switching memory cells. The structure of the ferroelectric, the nature, density and distribution of the defects, to a larger extent, are fabrication process specific. Optimization of the device fabrication processes and correct interpretation of the experimentally observed performances require detailed crystallographic and structural analysis of the ferroelectrics used in microwave devices.

3.2 Fabrication of Devices Using Single Crystals 3.2.1 Growth Techniques of Single Crystals A wide variety of crystal growth techniques, including Verneuil (Bednorz and Scheel 1977), floating zone (Bednorz and Arend 1984), Czochralski pulling from skull (Buse 1993), top seeded solution growth (Rytz et al. 1990) and flux methods (Varatharajan et al. 2001), are used and intensively studied for growing Ba1–xSrxTiO3 single crystals with large dimensions and high structural perfection (Nabokin et al. 2003, Scheel 2000). The most perfect single crystals are obtained by solution growth and flux methods. However, for commercial production the required structural perfection has to be compromised for timely crystal delivery and economics. Figure 3.2.1 compares the growth conditions, growth times and structural perfection of SrTiO3 crystals grown by three different techniques. The dislocation densities of Verneuil grown crystals are 106/cm2, of TSSG-grown 102/cm2, and of flux/ACRT-grown zero in large fractions of crystal. Strontium titanate grown in a day by the Verneuil method with a large temperature gradient has more than 106 dislocations per cm2. Low-dislocation crystals can be achieved by growth from high-temperature solutions with small temperature gradients at the cost of long duration of growth, one week for top-seeded solution growth (TSSG), and two months for flux growth with accelerated rotation crucible technique (ACRT) to grow a 3 cm long crystal with large dislocation free sections (Scheel 2000). Apart from the long duration of crystal growth the solution and flux growth methods currently produce crystals with small lateral dimensions which do not exceed 3–5 mm (Nabokin et al. 2003). For this reason the commonly employed technique for commercial production of the Ba1–xSrxTiO3 single crystals with large diameters up to 30 mm is the Verneuil method (MTI Corporation 2008, Semiconductor Wafer Inc. 2008, MaTecK GmbH 2008).

64

3 Fabrication of Ferroelectric Components and Devices

Fig. 3.2.1 Comparison of growth conditions, growth times and structural perfection of SrTiO3 crystals grown by three different techniques. Arrows indicate heat flux. Reprinted with permission from Elsevier©2000 (Scheel 2000)

3.2.2 Structural Characterization There are only a few studies of structural perfection of the SrTiO3 crystals grown by the Verneuil method. The dislocations, sub-grain textures and other long-range strains are studied by reflection and transmission X-ray topography (Yoshimura et al. 1998). It is found that dislocations are nearly aligned along the 〈100〉 directions and most of them are of pure edge type, presumably as a property of annealed crystals with simple cubic lattice. This entire dislocation alignment causes a strong long-range distortion about the [001] axis in anisotropic (110) oriented

3.2 Fabrication of Devices Using Single Crystals

65

crystal plates. Burgers vectors both of 〈100〉 and 〈110〉 types are observed. It is also found that the surfaces of some samples are finished highly strain free as well as optically flat by the mechanochemical polishing. For the as-grown and annealed STO single crystal grown by the Verneuil method the optical density, photoluminescence spectra, complex impedance spectra, and crystal structure are studied in (Mochizuki et al. 2007). The as-grown crystal is dark blue and reveals high electrical conductivity (>10–3 Ω–1 cm–1), and a colossal static dielectric constant (>106). With the annealing at 973 K in air, the as-grown single crystal becomes colorless transparent insulator and the static dielectric constant decreases down to approximately 300. The X-ray crystallographic studies indicate that the crystallinity (lattice parameter 0.390498 nm and rocking curve 0.0501°) is almost independent of the annealing. The X-ray fluorescence spectroscopic analysis has shown that the oxygen content of as grown crystal is smaller by 0.2% than that of fully annealed crystal. The annealing decreases oxygen defect in number and reduces microscopic semiconducting domains in both number and size. Thus the Maxwell-Wagner relaxation at the interfaces between an insulating stoichiometric domain and a semiconducting nonstoichiometric one is suppressed by annealing, which extinguishes the colossal dielectric constant. In (Eriksson et al. 2003) the dielectric properties of STO single crystal with different crystal orientations have been studied using circular disk shaped parallel plate resonators. The results of experiments indicate clearly that the microwave losses have a minimum about 45–50 K for all orientations. STO crystals in [111] direction have substantially lower loss tangent (10–4 at about 1.0 GHz) in comparison with [110] and [111] orientations.

3.2.3 Bulk Single Crystal Devices Bulk single crystals quantum paraelectrics (SrTiO3 and KTaO3) and other ferroelectrics in paraelectric phase (i.e. BaxSr1–xTiO3, x<0.5 at room temperature) may be used for fabrication of high power tunable microwave devices. Crystals in polar phase are less preferable due to the higher losses and dielectric hysteresis. Fabrication of microwave devices using bulk single crystal ferroelectrics starts with cutting plates from a crystal and polishing. The plates may have circular and square shape. Since the permittivity of the crystals is very high (300 for STO at room and even more at cryogenic temperatures) the sizes of the crystals need to be controlled with high accuracy, especially where they are used as resonators with specified frequencies. Moreover, a carefully polishing may be required; otherwise the large roughness of the surface may lead to scattering of the electromagnetic waves and degradation of the device performance. In the case of HTSC (for example YBa2Cu3O7) electrodes (Jackson et al. 1992, Eriksson et al. 2004) the surfaces have to be epitaxial grade polished allowing epitaxial growth of high quality HTSC films with low surface impedance and losses. In the case of normal electrodes, e.g. Au, Ag and

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Cu (Deleniv et al. 2002) the plates may be optical grade polished and adhesion/thermal expansion matching layers applied to ensure low microwave losses in the electrodes. Typically Ti may wok rather well as an adhesion layer. In contrast to thin film devices the thickness of the bulk single crystals used in the devices is much larger than the thickness of the Schottkey barrier and the leakage currents are limited by the high resistance of the bulk material. The bulk single crystal devices, i.e. resonators, operate at relatively low microwave frequencies, typically below 1–3 GHz and the normal metal electrodes have to be rather thick, typically 3 skin depth, to ensure low losses. Sometimes this may require extra buffer layers for thermal expansion matching between the ferroelectric crystal and thick electrodes. To keep the tuning DC voltages low (up to 500 V) the thickness of the single crystal plates typically should be less than 0.5 mm. At the same time for this thickness and low operation frequencies no higher order thickness modes are excited. For example, the resonators are electrically thin, i.e. its thickness h is much smaller then the wavelength of the microwave signal and the lowest order modes in parallel-plate resonators are essentially of TM type (Deleniv et al. 2002). Electrode stack

SrTiO3 or KTaO3

Fig. 3.2.2 The schematic cross section of a parallel-plate disk resonator. Reprinted with permission from IEEE©2004

Cross section of a disk resonator is shown in Fig. 3.2.2. In (Eriksson et al. 2004) 300 nm YBaxCu1–xO7 films (electrodes) are deposited by co-evaporation technique (Prusseit et al. 1993). A 0.5 μm thick Au layer is deposited on top of YBCO to protect it from degradation and provide ohmic contact for the DC bias. In this experiment the diameter of the STO resonator disk is of the order of 10 mm and it is epitaxial grade polished. In YBCO electrodes on a single crystal (001)STO substrate are grown by pulsed laser ablation and patterned by ion milling. In (Deleniv et al. 2002) the 4.0 µm thick Cu layers are used. Thin (30 nm) Ti serves as adhesion layer. The Cu/Ti electrode stack is deposited in-situ by e-beam evaporation.

3.2.4 Thin Film Single Crystal Capacitors A relatively recently developed approach allows fabrication of thin films of single crystal ferroelectrics by exfoliation from a bulk crystal using deeply implanted ions, so called crystal ion slicing (CIS). According to (Kub et al. 1999) the flexibility of this approach promises electronic and physical properties that are more

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compatible with present microwave technologies than bulk ferroelectric materials and lower microwave losses than approaches that utilize the growth of thin films.

Fig. 3.2.3 Implanted STO anodically bonded to a patterned Pyrex glass layer on Si (a) and exfoliation of patterned STO thin films via thermal treatment (b). Reprinted from with permission from AIP©2006.

Figure 3.2.3 shows the main stages of the CIS process including patterning of STO film on Pyrex 7740 glass or on Si using a glass interlayer (Lee et al. 2006). The fabrication process of patterned thin films consists of H+ ion implantation of a bulk single crystal STO followed by anodic bonding of the implanted STO to a patterned Pyrex bonding film or substrate. After separation of these two samples a bonded patterned STO film remains on the Pyrex. The pattern of the STO films duplicates the initial Pyrex patterning. The separation occurs during thermal treatment consisting of heating and cooling the sample rapidly (>10°C/s). This thermal treatment is needed to coalesce the interstitial H2 into nanobubbles, thus generating delamination stress in the implanted region. The 1 µm STO single crystal films have been fabricated using this technology (Lee et al. 2006). The measured XRD full width at half maximum (FWHM) of STO film (100) diffraction peak is 0.172° which is slightly large than that of the single crystal counterpart (0.114°), probably, due to residual sample strain. An interdigital capacitor have been fabricated using lithography for patterning of electrodes consisting of 200 nm thick gold layer with 20 nm Cr adhesion layer. The resulting capacitor has 26 finger pairs with 7.5 µm finger gaps and a 500 µm overall length. The evaluated loss tangent is 0.0152 at 100 kHz and permittivity is 268.5 at frequencies up to 2 GHz which is close to that of the bulk crystal (300). No measured tunability has been reported. In (Kub et al. 1999) the planar interdigital capacitors on 500 nm thick single crystal STO layer are fabricated by CIS process. The metal electrodes of the interdigitated fingers consist of a 20 nm thick Cr adhesion layer, 1.5 µm thick Ag layer, and a 50 nm Au cap layer to ensure a good probe contact and to prevent tarnishing. A typical capacitor consist six finger pairs with l0 µm finger width, 6 µm finger gaps, and 80 µm overlap length. The capacitors revealed high measured Q-factor of nearly 100 at 10 GHz. However, the measured tuneability is low (0.3% at 40 V dc bias), probably due to relatively large finger gaps.

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A different method of exfoliation for fabrication of 10 µm thick single crystal KTaO3 films by CIS technology is reported in (Izuhara et al. 2002). To prepare the samples for crystal ion slicing, singly charged 3.8 MeV helium ions are implanted at 5° from the surface normal on (001) KTaO3 surfaces. The localization of stress in the implantation region allows for selective lateral etching which is based upon stress induced etch rate enhancement. Etching is accomplished with dilute 5% hydrofluoric acid such that a deep undercut develops in the KTaO3 after several hours, centered 10 µm below the top surface. The stand alone films are mounted on a MgO substrate without bonding agents which allows avoiding unnecessary contamination of the surface. The films annealed at 300°C for 3 hours in Ar+O2 atmosphere reveal dielectric permittivity 200 and loss tangent 0.0040 at 1.7 GHz. The slight degradation, in comparison with those of implanted bulk (245 and 0.0009, respectively), is explained by surface degradation and/or sample stress.

3.3 Fabrication of Devices Using Bulk Ceramics 3.3.1 Ceramic Processes Fabrication of the tunable microwave devices using ceramics follows the basic electroceramic fabrication routes. It consists of the following main processes: • Powder preparation; mixing and grinding include the following main routs: mixed oxide or solid state, oxalate, alkoxide, hydrothermal synthesis, Self Propagation high temperature synthesis (SHS), sol-gel etc. • Calcination; • Shaping may include one of the following processes: dry-pressing, isostaticpressing, jolleying, extrusion, colloidal processing: slip-casting, tape-casting, calendering and viscous polymer processing, injection-moulding, films and layers etc. • High-temperature processing (densification, hot-pressing, isostatic hot-pressing, Glass-ceramics); • Finishing. For details an interested reader is recommended to read (Setter 2005, Moulson and Herbert 2003).

3.3.2 Bulk Ceramic Device Fabrication Varadan’s group developed bulk ceramics based phase shifters (Varadan et al. 1992), filters and antennas using sol-gel powder based BSTO ceramics. For example for a tunable antenna (Teo et al. 2000) two alternative routs for the preparation

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of the sol-gel BST powder are considered: i) an aqueous based process that starts from a solution of a metal salt, and ii) an alcohol based route that starts from a solution of a metal alkoxide. The sol-gel method enables uniform distribution of the dopants in the BST ceramic, as compared to the conventional methods. In this experiment the graphite, added to the powder, is burned off after firing of the mixture results in a highly porous BST substrate. Inorganic filler is added to the fired substrate to enhance its physical rigidity. Low loss Ba1–xSrxTiO3 ceramic is achieved by doping with Mn, Ca or Fe. The BSTO substrate of the tunable antenna reported in (Vinoy et al. 1999) is processed using a procedure described in (Herner et al. 1993). The BaCO3, SrCO3, TiO2, and powders of high purity are mixed in the appropriate amounts for each composition. Each batch is wet ball milled in absolute ethanol with zirconia media for 6 h to thoroughly mix the powders and then dried in a ventilated oven at 80 °C. The mixed powder is calcined at 800°C for 5 h and at 1150°C for 10 h. The calcined powder is wet ball milled in absolute ethanol with zirconia media for 24 h. The powder is dried and weighed. Polyvinyl alcohol (PVA) is then added as a binding agent in the amount of 2 wt% and mixed in distilled water with the powder for 2 h in the ball mill with zirconia media. The powder with binder is then dried and seive through a 230 mesh seive (63 µm opening), pressed under 600 MPa of pressure into disks 12.70 mm in diameter and ≈3 mm in thickness. The disks are sintered in air at 1450°C for 1 h, after holding at 500°C for 1 h to allow for binder burnout. A heating rate of 180°C/h is used. Figure 3.3.1 shows the geometry of the rectangular microstrip patch antenna printed on the sintered BSTO substrate with thickness 2.35 mm. The dimensions of the patch are: length 46 mm and width 33.5 mm. This antenna resonates at 850 MHz under normal operating conditions. A high permittivity superstrate is placed on top of this antenna, and the air gap is carefully adjusted to get the best performance with regard to the received power.

Fig. 3.3.1 Antenna configuration based on a BSTO substrate. Reprinted with permission from Wiley©1999

A steerable bean antenna (see Sect. 6.4.2), consisting of a large size (100x 100x1 mm3) core plate (Tageman et al. 2003) made of 0.46Ba0.63Sr0.37TiO3+ 0.54MgO, is fabricated using a standard ceramic process. The plate is formed by pressing and sintered at 1425°C for 8 hours. The composition of the BaxSr1–xTiO3 and the content of the MgO are optimized to achieve high tuning of the permittivity and low microwave losses. From a 10 kHz LCR measurement its permittivity is determined to be 1057 at 22°C and zero bias. The thickness of the ferroelectric

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plate, 1.0 mm, is selected by trading between the low control voltages and large phase shift. To ensure large phase shift the thickness of the plate has to accommodate as many wavelengths as possible, i.e. the plate needs to be electrically thick. On the other hand, to completely utilize the available from the used ferroelectric composition tuneability, electric fields up to 15 kV/mm are required. Thus the plate thickness is selected by trading between the phase shift (tuneability) and required DC bias voltage. A special high resistivity composition, based on LaMnO3:SrTiO3, is developed to facilitate application of the DC bias. The resistivity (~100 MOhm/sq) and the thickness (~ 10 μm) of the resistive film are selected from low microwave loss and low DC current considerations. To ensure low microwave losses the sheet resistance and the thickness are selected so that the skin depth in K-band is much larger than the thickness of the resistive film. In addition, the high resistance ensures small currents at very large DC bias voltages used for tuning of the permittivity. An area of 83x83 mm2 of the back and front surface of the core ferroelectric plate was covered with 100 MOhm/square resistivity films, by means of screen-printing. Solderable silver electrodes are screen printed, such that they slightly overlapped with the resistive films on two opposing sides, and used for connecting high voltage cables. To avoid the reflection losses associated with the large difference between the high permittivity ferroelectric core and free space, two quarter wave transformer plates (permittivity 34) are used. They are milled to thickness 0.32 mm and are attached to the frond and back surfaces of the ferroelectric plate using 75 μm thick epoxy films (glue). The experiments show that this complex multilayer quarter wave structure provides a rather good matching along with negligible losses at about 30 GHz.

Fig. 3.3.2 Mounting schematic of the planar phase shifter on a conventional microstrip transmission line. Reprinted with permission from IEEE©1997

Bulk ferroelectric ceramic is used in phase shifter operating at 2.4 GHz (De Flaviis 1997). In this work the ceramic is prepared using Ba0.8Sr0.2TiO3 powder synthesized using sol-gel process (De Flaviis et al. 1995). Subsequently, it is pressed into pellets at a pressure of 2000 kg/cm prior to sintering at 1300°C for 1 h. After firing, the sample is thinned down to 0.1 mm (to reduce the required control voltages), the faces are polished using diamond wheels and the plate is

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used as a substrate for a microstrip line. The ground plane and the microstrip line are fabricated, evaporating three layers of metal such as Cr/Cu/Au under vacuum to prevent oxidation. Chromium is used to ensure a good cohesion to the ceramic, copper serves as a buffer layer and makes cohesion between the nichrome and gold. The gold layer provides low microwave losses. The two extremes of the microstrip line have patches which facilitate the connection of the device with the circuit. These patches also allow multiple wire bonds in order to reduce the parasitic inductance associated with the connection. The sample is mounted using wire bonds on the two ends of the 50-Ω microstrip line printed on alumina substrate. The ground contact is established using multiple vias. Epoxy glue is used to hold the sample on the circuit, Fig. 3.3.2 (De Flaviis 1997). Development of processes for fabrication of BSTO ceramics components with rather complex shapes is reported in (Kanareykin et al. 2006, Nenasheva et al. 2003). The large diameter Ba1–xSrxTiO3 ceramic ring, Fig. 3.3.3, is a key component used as a high-power ferroelectric switch. BSTO with its fast switching (< 10 ns) and low loss offers significant advantages for RF adjustment and tuning in accelerators (linear colliders) including X band and Ka band high power ferroelectric switches. The solid solutions (Bax Sr1−x)TiO3 (x = 0.4–0.6) are synthesized by ceramic processing from titanium dioxide (TiO2) and strontium and barium carbonates (SrCO3, BaCO3) or prefabricated barium and or strontium titanates (BaTiO3, SrTiO3). The initial powders of the solid solutions and magnesium oxide of the required proportions are developed by mixing them in a vibration mill for three hours to result in particles with sizes of 1 μm. Samples of required geometrical shape and size are prepared by hydraulic pressing. A 10% solution of polyvinyl alcohol is taken as a binder. The prepared samples are sintered in air within the temperature range of 1380–1540°C (3 h) in a chamber electric furnace until zero water absorbance. A specially developed technology of double layer magnetron metal deposition is used to apply the gold contacts for the bias voltage (Kanareykin et al. 2006). This technology allows deposition of a 1–2 μm thick gold layer on adhesion layers and meeting the mechanical requirements of the device, Fig. 3.3.3. The rings with 108 mm in diameter, 20 mm in length and 2.8 mm in thickness are fabricated for the active ferroelectric RF switches.

(a)

(b)

Fig. 3.3.3 Prototype BST(M) ferroelectric ring (a) and field distribution in cavity operating mode TE031 (b). Reprinted with permission from AIP©2006

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Ferroelectric ceramics (slabs) may be integrated with ferrite ceramics to produce composite ceramics that provide dual tuning possibilities, i.e. tuning of the dielectric permittivity and magnetic permeability. In (Kim et al. 2004) ferromagnetic/ferroelectric composite ceramics are successfully fabricated. Garnet ferrite powder and commercial Pb(Zr0.52Ti0.48)O3 powder (PZT) are mixed and the composition ratio is changed. After sintering, the samples are polished up to 0.1–0.2 mm thickness. Silver paste is applied to both sides of specimen to form electrodes. No cracking or shrinkage is observed and both ferroelectric (P-E) and ferromagnetic (B-H) hysteresis loops are clearly measured. In another experiment the bulk BSTO ceramic slabs are used to develop tunable ferrite-ferroelectric hybrid wave microwave resonators which combine the advantages of ferrite and ferroelectric devices such as high Q-factor, wide tuning range, fast resonant frequency adjustment and low power consumption (Ustinov et al. 2006, Semenov et al. 2006). The combination also provides the possibility of simultaneous magnetic and electric tuning. The schematic view of the ferrite-ferroelectric hybrid wave resonator is shown in Fig. 3.3.4 (Ustinov et al. 2006). The 500 µm thick ferroelectric part of the resonator is fabricated using Ba0.6Sr0.4TiO3. A rectangular resonator of length 1.15 mm and width 1 mm is cut from the ceramic slab. For a permittivity 2500–3000, the lowest mode of the dielectric resonance for the BST slab is in the range of 5 GHz. 50 nm thick Cr electrodes are deposited on the both surfaces of the BSTO plate by vacuum evaporation and 3 µm thick microstrip transducer is fabricated by conventional photolithography on a grounded alumina substrate of thickness 500 µm. The structure consists of a 50 µm wide, 2 mm long short circuited microstrip antenna for the resonator excitation and the 50 Ω microstrip transmission line for feeding the antenna.

Fig. 3.3.4 Schematics of a ferrite-ferroelectric resonator consisting of a barium strontium titanate (BST) slab and YIG film on a GGG substrate. Reprinted with permission from AIP©2006

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3.3.3 Structure of the Bulk Ferroelectric Ceramics In (De Flaviis 1997) the sintering process of the bulk Ba1–xSrxTiO3 ceramic is optimized for low loss ferroelectric ceramics used in the phase shifters. A correlation is established between the loss tangent, grain size of the ceramics with different compositions, sintering temperature and duration. It is shown that the grain size of SrTiO3 ceramic increases from 1 µm up to 30 µm with sintering temperature (from 900°C to 1500°C) and duration (up to 27 hours in total). Simultaneously the loss tangent decreases from 0.003604 down to 0.00208. The microstructure of the BSTO ceramics with and without dopants (Mn, Fe, Bi, Ga, Y, and Nb), used for fabrication of the tunable microstrip patch antenna (Vinoy et al. 1999), is studied in (Herner et al. 1993) and a correlation is established with the dielectric response (dielectric constant and loss tangent). Doping with1.0 mol% Fe produced the smallest loss tangent (0.005 at 1 MHz and room temperature) of all dopants studied while dielectric permittivity (3000 at room temperature) is not substantially changed with respect to the undoped material. Figure 3.3.5 shows SEM micrographs of undoped and Fe doped samples. The grains of the undoped material are square shaped with sharp edges. Doping with Fe shows more rounded grains (typical for liquid phase sintered materials) but with grain sizes virtually unchanged as compared with the undoped material (see Fig. 3.3.5). No substantial amounts of phases are seen at the grain boundaries in any of these materials in the SEM micrographs. (a)

(b)

Fig. 3.3.5 SEM micrographs of undoped (a) and Fe-doped (b) BSTO. Reprinted with permission from Elsevier©1993

The microstructure of bulk (Bax Sr1−x)TiO3 ceramics used in high power ferroelectric switches (Kanareykin et al. 2006) is studied by means of XRD in the range of composition x = 0.4–0.6 in (Nenasheva et al. 2003). The unit cell parameters evaluated from XRD spectra are presented in Table 3.3.1. One can see that the increase in barium content causes increased the unit cell parameter and the dielectric permittivity, especially for x >0.45.

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Table 3.3.1 X-ray data and dielectric permittivity of (Bax Sr1−x)TiO3 solid solution (Tsin = 1540°C) Composition (x) 0.40 0.45 0.50 0.55 0.60

Unit cell parameter (a, Å) 3.9366 (8) 3.9456 (10) 3.9475 (7) 3.9498 (11) 3.9568 (5)

ε (20°C) 490 540 1350 1480 1620

tan δ (1 MHz) 0.0028 0.0042 0.0065 0.0136 0.0174

3.4 Thick Film, HTCC and LTCC Technologies The thick film, high temperature co-fired ceramic (HTCC) and low temperature co-fired ceramics (LTCC) are three main types of technologies for fabrication of multilayer ceramic integrated circuits using additive principle of layer patterning. These technologies are based on three common key processes: • Screen-printing (or similar/alternative technique); • Drying; • Firing. The standard thick film process starts with a pre-fired ceramic substrate which is used for sequential screen printing and firing the conductor and dielectric pastes. The paste consists of powder of a ferroelectric, thinners and binders. This process has an upper practical limit of about seven layers, above which yields begin to drop. Generally it is not used for producing of complex packages. The HTCC/LTCC processes differ from the sequential thick film process. In this case the base substrate and all the dielectric layers are initially in the unfired condition. The unfired tape is called green tape. The green tapes/layers of a HTCC/ LTCC module are processed separately, then aligned and co-fired as a single unit. This is the key advantage of the HTCC/LTCC processes, in comparison with thick film technology. They allow fabrication of very high density multilayer interconnects of up to 60 layers (Licari and Enlow 1988). The manufacturing processes for both HTCC and LTCC are very similar. The difference is that the LTCC uses pastes based on glass composition similar to those used in thick film technology. The HTCC process typically uses 96% of alumina which results in difference in sintering temperature: 850°C for LTCC and 1350°C for HTCC processes.

3.4.1 Fabrication of Devices Using Thick Film Technology The first stage of the thick film technology is screen-printing. The basic concept in screen-printing is to force a viscous paste through apertures of a stencil screen in order to deposit a pattern onto a substrate. The screen is a stainless steel wire mesh

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that is adhesively attached to a cast aluminum frame. A negative mask is generated on the mesh so that the pastes can be squeegeed producing a positive pattern on the substrate. The mask is patterned by a standard photolithography process. A rubber blade called a squeegee is used to force the paste through the screen, Fig. 3.4.1 (Hobby 1997). The printed dielectric layers may be of any thickness, often 40 μm. The screen-printed layers are dried and fired in air atmosphere, typically at 850°C. It is followed by printing, drying and firing of the upper layers. The thick film is a long established technology for fabrication of multilayer ceramic integrated circuits. A number of BSTO thick film microwave tunable devices have been fabricated, such as varactors (Ditum and Button 2003, Su et al. 2003, Zimmermann et al. 2004), phase shifters (Yeo et al. 2004, Hu et al. 2005, Kozyrev et al. 2000), filters (Keis et al. 1998, Scheele et al. 2004), matching networks (Scheele et al. 2005) etc.

Fig. 3.4.1 Thick film screen-printing process

Fig. 3.4.2 Reflection type phase shifter based on thick BSTO film. Reprinted with permission from IEEE©2005

As an example Fig. 3.4.2 shows a reflection type phase shifter based on BSTO thick film fabricated by standard thick film technology (Hu et al. 2005). The details of the technology are given in (Su et al. 2003). The ink is prepared by com-

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bining BSTO powders produced via a solid state route together with a commercial vehicle (Blythe 6321 Medium) at a solids loading of 40 vol.%. The BSTO films are sintered at temperatures 1200–1300°C for 2 h with a ramp of 2°C/min. The electrodes on the top surface of the BSTO film are also screen printed using silver pastes. They are sintered at 850°C for 10 min. The BSTO film is located in the gaps of the transmission lines (Fig. 3.4.2). Silver paste with thickness of 8±2 μm is used to form the main transmission line. The left end of the termination circuit is cut into the desired length then it is edge grounded via a piece of silver conducting film to the metal package.

Fig. 3.4.3 Production process for HTCC/LTCC

3.4.2 Fabrication of HTCC and LTCC Devices The manufacturing process of both LTCC and HTCC are very similar. Figure 3.4.3 shows the main stages of the process (Al-Taei et al. 2001). The ceramic powder, organic binders and solvents are spread to the desired thickness and cut into correct size sheets (green tape). Via holes and component cavities are then punched into the tape using an automated punching tool, this is followed by the metallization of via holes and conductors which is accomplished using screen printing of the metal paste. For HTCC it is usually tungsten or molybdenum. For LTCC low resistivity conductors such as silver or copper may be used. The layers are then assembled in order and laminated together. It is followed by a burn off process to remove the solvents and organic binder. The burn off process requires 350°C in the case of LTCC technique. The HTCC process requires 500–600°C and hydrostatic pressure. In the next step the LTCC and HTCC structures are sintered at 850°C for 15 min in air, and at 1350°C for 40 min in a gaseous atmosphere. The LTCC uses paste compositions similar to those used in thick film technology. HTSS, typically, uses 96% alumina pastes.

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First attempts of using an LTCC compatible technology for fabrication of tunable ferroelectric components (e.g. phase shifters) is considered in (Jantunen et al. 2004). The specifics of the ferroelectric LTCC technology, i.e. relatively thin films (about 40 μm) with rather high permittivity (>100) imposes specific design and device fabrication requirements. Figures 3.4.4 and 3.4.5 show two novel designs of the phase shifters proposed in (Deleniv et al. 2005). A phase shifter with bias independent matching (Fig. 3.4.4) is realized as a distributed periodic microstrip structure consisting of patterned ground plane/bottom electrode M1 and metal layer M2 on top of the ferroelectric film.

Fig. 3.4.4 Cross-section (a) and layout (b) of the phase shifter with bias independent matching. Reprinted with permission from IEEE©2005

(a)

(b)

(c)

Fig. 3.4.5 Cross section (a), photos of the top microstrip with a via (b), and coplanar-plate varactor embedded in the ground plane (c) of the phase shifter fabricated using an LTCC compatible process

The second design of the phase shifter (Fig. 3.4.5) is aimed for reduction of the overall loss by using the lumped ferroelectric varactors. The 200 μm wide 60 Ohm microstrip line is loaded with a number of varactors. The coplanar-plate varactors are integrated in the ground plane. The vias connect the top microstrip with the square plate of the varactor formed in the opening in the ground plane (Fig. 3.4.5 (c)). Photographs of the microstrip in M2 with a via, and the varactor in the ground plane M1 are shown in Figs. 3.4.5 (b) and 3.4.5 (c). The details of LTCC technology used for fabrication of both phase shifters are given in (Deleniv et al. 2003). The commonly used ferroelectric compositions (BSTO) and their low loss version (BSTO with MgO addition) have sintering temperatures less than 1350°C. The ferroelectric composition used in these works has sintering temperature in the range of 900–950°C. This improvement is achieved by using a mixture

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of B2O3 and Li2CO3 as a sintering aid for B0.5Sr0.45TiO3 + 0.6 MgO (prepared by Filtronic Comtek (UK) Ltd.). The total amount of this addition is 4.5 wt-%. The novel composition is labeled as BSTM-BL. The ferroelectric green tape for the test structures is fabricated by tape casting process using B98 (polyvinyl butyral) based slurry system and the casting is done by a single doctor blade with 250 µm wide gap. The multilayer structures are prepared by using Al2O3 (96%) as a basic substrate on which a uniform ground electrode layer is screen printed by using Pt paste (Heraeus 5545). After drying, a ferroelectric layer is formed on it by laminating the cast BSTM-BL green tape at 70°C using 20 MPa pressure and 20 min dwell time. The whole multilayer is then co-fired at 950°C. Finally, the designed pattering on the top surface is screen printed with silver paste (Heraeus C 1075) and post fired at 850°C. The screen printing provides approximately 200 µm resolution. The possibility to fabricate the BSTO ferroelectric components for the microwave devices using HTCC technology is demonstrated in (Kim et al. 2006). The ceramic (Ba0.6Sr0.4)TiO3 powder is sintered by a solid state reaction using ball milled BaTiO3 and SrTiO3 powders. The sintered BSTO powder is ball milled for 24 h with a solvent (60 Methyl Ethyl Ketone-40 Ethyl Alcohol) and a dispersant (Texaphor 60). The mixture is ball milled again for 24 h with a binder (PolyVinyl Butyrate) and a plasticizer (Dibutyl Phthalate) to make slurry for tape casting. The green sheets are made by passing the slurry below a doctor blade and drying. Organic materials in the dried green sheets are burned out at 500°C for 24 h followed by sintering at 1350°C for 2 h. The thicknesses of the final films are measured to be about 300 μm. In order to change dielectric properties, one side of as casted BST thick film is annealed by a line focused beam radiated from a halogen lamp. While the line focused beam was stationary, the samples are moved constantly at speed of 0.4 and 0.1 mm/min by the motorized sample transfer stage. Since the width of the line focused beam was about 1 mm, the samples are annealed by the beam for 150 and 600 s. To form capacitors the gold electrodes are deposited on the BSTO films by an ion sputtering system using a shadow mask. The dielectric constants of BSTO films are 5700 and 7000 before and after focused beam annealing, respectively. This demonstrates the possibility of using HTCC technology for integration of BSTO ferroelectrics into low cost microwave tunable devices.

3.4.3 Structure of Thick and HTCC/LTCC Films The dielectric properties of thick Ba0.5Sr0.5TiO3 films depend on microstructure, grain size and density. These parameters may be controlled by proper selection of the fabrication routes (Ditum et al. 2003). In this work the powders used in inks for screen printing of thick films are prepared by two different routes: i) calcination of BaCO3, SrCO3 and ii) TiO2 by a conventional solid state reaction, and through mixing of uncalcined nano-sized BaTiO3 and SrTiO3. In both sets of films the grain sizes rapidly increase above a certain sintering (grain growth) temperature (Tgg). For nano-scale films Tgg is between 1300 and 1350°C, and the grain

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Fig. 3.4.6 SEM micrographs of surfaces of carbon-derived (a) and nano-size derived (b) Ba0.5Sr0.5TiO3 films. Reprinted with permission from Elsevier©2003

size increases to 20–30 µm. For carbonate films Tgg is between 1400 and 1450°C, and the grain size increases to 20–50 µm. The microstructures after grain growth for carbonate-derived and nano-size derived films are illustrated in Fig. 3.4.6 (a) and Fig. 3.4.6 (b) respectively. For carbonate films the grain growth is accompanied by considerable densification. However, nano-scale films are still very porous. Previous studies on bulk samples made from nano-size powders have shown that the majority of densification occurs by 1300°C. Therefore in the case of films, although grain growth removes small scale porosity, there is still large scale porosity remaining. Above Tgg the permittivity increases dramatically as a result of the densification and grain growth. The permittivities of nano-size-derived films sintered above 1250°C (approximately 200 at room temperature) are lower than those for carbonatederived films (approximately 1000 at room temperature), which is due to their lower overall density and the increased influence of any interfacial (grain boundary effects). In the paraelectric region (above –50°C), the dielectric losses appears to be dependent on density. Both the nano-size-derived films and the carbonatederived film sintered at 1250°C have large peaks in losses at high temperatures. These are due to the low density of the samples allowing moisture to be introduced during the measurement procedure which increases the dielectric loss. The measured loss tangent is as high as 0.02 in carbonate-derived films, and 0.33 in nano-size derived films (measured at 1 kHz). For the higher density carbonatederived films (i.e. those sintered at ≥1300°C), the loss tangent generally decreases with increasing sintering temperature and is generally <0.004. The microstructure characterization of BSTO films fabricated by HTCC, and improved by additional focused beam annealing, are presented in (Kim et al. 2006). Analysis of X-ray diffraction pattern indicates that the BSTO films have a cubic perovskite lattice structure with lattice constant of 0.396 nm. With increased annealing time the reflection peaks become shaper and more intense indicating the improvement of crystallinity which is associated with increased grain size. However, the particle size visible on SEM images, Fig. 3.4.7, decreases with annealing time. The discrepancy between XRD and SEM observations is explained by ambiguous definition of grain and/or particle. Careful observation of the as-cast film,

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Fig. 3.4.7 Surface morphologies of BSTO films fabricated by HTCC before (a) and after focused beam annealing during 600 s (b). Reprinted with permission from Springer©2006

Fig. 3.4.7 (a), reveals that there is contrast fluctuation in the particle ‘A’, which may suggest smaller domain or coherent area. The particles are group of small grains, and the grain boundaries are filled with non-crystallized materials. It is believed that the apparent boundary observed in SEM image is not the same with the grain boundary. After annealing, however, each grain has a chance to grow while consuming the materials around grain boundaries. Therefore, grain boundaries have been developed clearly in Fig. 3.4.7 (b). The composition of BSTO films are investigated by EDS. In general, Ti deficiency is observed in all of the samples. Furthermore, Ti concentration at the film surface is lower than that at the center. After annealing, Ba/(Sr+Ba) ratio is changed slightly, which may suggest that Ba diffused into the center of the film, while Sr diffused out to the surface of the film. The observed results could be explained by the temperature gradient introduced during the focused beam annealing. The temperature gradient along the depth of the thick film may produce a driving force of Sr and Ba atom diffusions. Chemical changes including oxygen as well as thermal history change the formation of the grain in the film. The changed grain size and chemical composition affects the dielectric properties of the BSTO films resulting in changes in the dielectric permittivity after annealing.

3.5 Fabrication of Thin Ferroelectric Films Synthesis of the ferroelectric film is the central process in the fabrication of tunable thin film ferroelectric devices. Considered in this section are the widely used processes that produce best quality films. Apart from the quality of the thin ferroelectric films, the performance of the devices strongly depend on the electrode/ferroelectric interface and misfit strains-requiring careful selection of the materials and structure of the electrodes, especially when it comes to growth of ferroelectric films on base metal/electrode used in parallel-plate varactors. The processes commonly used for patterning of the electrodes and dielectric (ferroelectric) films are also considered in this section. The considered device examples attempt to disclose the specifics of different processes and their effects on the overall device performances.

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3.5.1 Chemical Deposition Methods In general the chemical deposition includes chemical vapor deposition (CVD) and chemical solution deposition (CSD). Both cases employ chemical precursors that undergo chemical reactions for formation of thin films (Waser et al. 2005). For the processing of metal composites and ferroelectrics specials precursors in the form of organometallic compounds are developed. Metal-organic-CVD (MOCVD) is a special subgroup of CVD technique. CSD includes sol-gel techniques and Metalorganic decomposition (MOD). It typically uses spin-on techniques for the distribution of a solute film which is subsequently processed and crystallized (Waser et al. 2005). 3.5.1.1 Metal-Organic Chemical Vapor Deposition (MOCVD) The MOCVD is one of the most promising methods for integration of ferroelectric films into microwave systems (York et al. 2000). It provides excellent composition control, large area coverage, and the potential for area homogeneity and conformal coating of complicated topography (Tombak et al. 2003). Figure 3.5.1 illustrates schematically configuration of one of the MOCVD systems designed for growth of ferroelectric films (Foster 1997).

Fig. 3.5.1 MOCVD setup for growth of PZT films

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The quartz reactor is a cold wall, horizontal flow design. Film growth occurs on a substrate located on resistively heated inconel susceptor. The system is equipped with three pressure-regulated, temperature-controlled liquid-source bubblers containing the organometallic precursors. These bubblers are equipped with temperature and pressure regulation. Since the vapor pressure of most organometallic sources are nonlinear functions of both temperature and pressure, a stable precursor vapor pressure is maintained using constant source temperature and source pressure. In this case, the precursor mass transport is directly proportional to the flow rate of the inert carrier gas through the source bubbler. This type of system design is typical for an MOCVD apparatus using liquid sources. For low-vaporpressure, solid-source precursors, the traditional delivery technique of using direct sublimation of the solid or evaporation of the melt into the carrier gas flowing through a bubbler may also be used (Foster 1997). The voltage controlled bandpass filters described in (Tombak et al. 2003) employs varactors based on BSTO thin films fabricated by MOCVD technique (Stauf et al. 1999). The (BaSr)TiO3 films (300 nm thick) are deposited in a modified Watkins-Johnson Select CVD reactor. Addition of a temperature controlled chamber, including a showerhead type gas distributor, helps to grow uniform films over 6” wafers. The reactor is operated at low pressure, typically 750 mTorr, with 500 sccm each of oxygen and nitrous oxide as oxidizers. Attached to this reactor is a liquid delivery system, which injects MOCVD precursors, dissolved in an organic solvent, into an Ar carrier gas stream which transports them into the reactor. Precursors for BSTO growth are: Ba(thd)2-tetraglyme, Sr(thd)2-tetraglyme and Ti(i-OPr)2(thd)2. Delivery rates of the precursor to the reactor averaged around 60 µmol/min. The details of the CVD reactor and the range of deposition conditions investigated are described in (Kirlin et al. 1995). The BSTO films are uniformly deposited on 150 mm Si wafers, thus indicating the suitability for commercial mass production (Tombak et al. 2003).

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Fig. 3.5.2 Schematic illustration of the parallel-plate BSTO capacitor (a) and description of the multilayer ground-plane (b). Reprinted with permission from IEEE©2003

Figure 3.5.2 (a) shows the schematics of a parallel-plate BSTO capacitors fabricated and utilized in the bandpass filter. The cross section (Fig. 3.5.2 (b)) shows the multilayer structure of the ground plane consisting of alternating layers of 25 nm IrO2 and 200 nm Pt. The stack has a total thickness of 1.3 µm. This type of developed hybrid composite bottom electrodes allows combination of good adhesion and mechanical stability with low microwave loss. Sputtering or electron-

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beam evaporation techniques are used to deposit the 300 nm thick Pt top electrodes completing the parallel-plate varactor structures. The top platinum electrode is patterned using standard photolithographic methods and reactive ion etching. 3.5.1.2 Chemical Solution Deposition (CSD) The main advantage of CSD for fabrication of ferroelectric films is low capital investment costs. It is suitable for continuous manufacturing of tapes and Si integrated circuits (Schwartz et al. 1999). A generalized flow chart of the CSD of oxide thin films is shown in Fig. 3.5.3 (Waser et al. 2001) where the bars describe the states during the CSD procedure, while the arrows indicate the treatment and the internal processes. The process starts with the preparation of a suitable coating solution from precursors according to the designated film composition and the chemical route. Besides mixing, preparation may include addition of stabilizers, partial hydrolyzes, refluxing etc. The solution is then deposited onto substrates by spin-coating, dip coating, or spray coating. The wet film may undergo drying, hydrolysis and condensation reactions depending on the chemical route.

Fig. 3.5.3 Flow chart of the CSD technique

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The as-deposited films reveal a chemical or physical network. Upon subsequent heat treatment, a further hydrolyzes and condensations/pyrolysis of organic ligands may take place, depending on the chemical route. The resulting film consist of amorphous or nanocrystalline oxides and/or carbonates. Upon further heat treatment the carbonates decompose and the film crystallizes through a homogeneous or a heterogeneous nucleation. Typically, the desired film thickness is build up by multiple coating and annealing. Depending on the type and reactivity of the precursors, the chemistry shows a wide spectrum of reaction types. There are the pure sol-gel reactions i.e. alkoxide precursor systems, which undergo hydrolysis and condensation reactions. On the other hand, there is metal organic decomposition (MOD) that typically starts from carboxylates of the cations. Upon the further heating they pyrolytically decompose into amorphous or nanocrystalline oxides (Waser et al. 2005).

Fig. 3.5.4 Reflection-type BSTO phase shifter fabricated using CSD technique. Reprinted with permission from IEEE©2001

The digital reflection type phase shifter described in (Sherman et al. 2001) is based on the planar capacitor with BSTO film fabricated using CSD technique. The BSTO film used in the phase shifter is 0.5 µm thick and deposited by CSD on the sapphire substrate. The details of a standard MOD route are given in (Sigman et al. 2008). BSTO solutions are made by chelating titanium (IV) isopropoxide (99.999%) with propionic acid, then mixing in a solution of barium acetate and strontium acetate which is predissolved in glacial acetic acid and electronic grade methanol. The resulting 0.05–0.4M solutions are spun on substrates at 3000– 5000 rpm for 30 s. Films are then pyrolyzed on a 200–400°C hotplate for 1–5 min. This process is repeated until the desired number of film depositions is reached and the film is ready to be crystallized. Multiple spinning and crystallization sequences are used to achieve preferred microstructures and thicknesses. The BSTO films are crystallized in air for 30 min by direct insertion into a furnace preheated to 700– 800°C. A copper layer of 4 µm thickness is patterned by wet photolithography. The layout of the phase shifter is presented in Fig. 3.5.4. The tunable capacitor is realized as a short section of a coplanar line of 100 µm width with 20 µm gaps.

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3.5.1.3 Structure of MOCVD and CSD Films The results of comprehensive studies of microstructure of Ba0.65Sr0.35TiO3 films grown by MOCVD on platinized Si substrates are given in (Kotecky et al. 1999). The BSTO films typically reveal columnar grain structure with lateral average grains size of about 15 nm in a 30 nm thick film. X-ray diffraction studies indicate that the films may have either (110) or (100) strong fiber texture depending on the growth conditions. Plan view TEM image indicates that many of the grain boundaries of (110) texture (Fig. 3.5.5 (a)) are inclined in the film and thus have an appreciable twist component to their grain boundary structure. The grains also contain many (111) twin boundaries. In the films with strong (100) fiber texture (Fig. 3.5.5 (b)) the grain boundaries lie almost normal to the substrate, i.e. the grain boundaries are predominantly tilt boundaries. In several instances the dislocation arrays that make up the tilt boundaries are visible in the image.

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Fig. 3.5.5 Plan-view TEM images of (110) (a) and (100) (b) textured 30-nm BSTO films

Studies of microstructure development during early stages of deposition show that strong texture is present in the films even before BSTO grains have coalesced to form a continuous film. X-ray diffraction studies indicate that both (110) and (100) textures are present in the film at this growth stage. The dominant texture develops only in the later stages of film growth. The faceting of the BSTO on (100) planes could result in sideways spreading of the (110)-oriented grains, occluding the (100) grains. This would result in inclined grain boundaries in the film, as observed in the (110)-textured films. The underlying bottom Pt electrode has a strong (111) texture and a grain size of about 80 nm. Thus, many BSTO grains nucleate and grow on each Pt grain. The diffraction from individual grains shows that there is no preferred orientation relationship between the Pt and BSTO grains. No intermediate phase at the electrode interfaces is found. The grain boundaries may act as low-dielectric-constant capacitive elements in series with the capacitance of the grains. However, in the columnar grain structure produced by the MOCVD process, most grain boundaries lie perpendicular to the parallel-plate electrodes and do not act in series with the BSTO grains. Measurements of the

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parallel-plate capacitors based on different MOCVD grown films indicate that texture and microstructural differences have only a secondary effect on the permittivity of the films. The other factors such as composition, electrode heat treatment, and stress tend to dominate in the performance of the capacitor.

(a)

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Fig. 3.5.6 Scanning electron microscopy cross sections of 8 layer BaTiO3 films deposited in a layer by layer manner (a) and with all layers deposited before film crystallization

Correlation of the dielectric response with the microstructure (columnar versus granular) of BaTiO3 films fabricated by CSD is given in (Sigman et al. 2008). Figure 3.5.6 (a) shows an 8 layer BaTiO3 film with all layers deposited before film crystallization. As it is seen, the film reveals granular structure. An alternative approach is used to shift the driving force of film growth toward heterogeneous nucleation at the substrate interface, which enables columnar grain microstructures. The film nucleation kinetics is altered to favor of heterogeneous nucleation at the substrate interface by using single heat treatment for each individual layer. The resulting films, shown in Fig. 3.5.6 (b), display both a columnar grain structure and higher density (due to easy film densification in these thinner layers crystallized in a stepwise manner). This approach of growth of columnar BaTiO3 films by CSD was successfully demonstrated also in (Schwartz et al. 1999). Solution concentration and spin rate during deposition are important as heterogeneous nucleation appears to dominate (and columnar grains result) only when individual deposited layers are thinner than 15 nm. For the film shown in Fig. 3.5.6 (b) a solution of 0.1M concentration is deposited at 5000 rpm. A fivefold increase in the apparent permittivity is detected when a columnar grain structure is achieved. Brick wall dielectric models of grain cores and boundary layers in BaTiO3 support this experimental data. The columnar grains may be modeled as a group of capacitors in parallel with only a small volume fraction of low permittivity grain boundaries, while randomlyoriented films with granular microstructures are better represented by capacitors in series, with a higher volume fraction of grain boundaries between electrodes (Frey et al. 1998, also see Chaps. 2 and 4). Through this effect, the grain boundaries and pores in fine-grained, polycrystalline materials cause greater series dilution of film capacitance and therefore decreased apparent permittivity. While this effect is generally undesirable because it results in reduced tuneability, these films display higher capacitance temperature stability that can meet specifications required for many electronic applications. Loss tangent of the granular films measured in MHz range (approximately 0.03) is higher than that of the columnar films (approximately 0.01) indicating contribution of grain boundaries in the total loss balance.

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3.5.2 Physical Deposition Methods The physical vapor deposition (PVD) includes a variety of methods where the thin films of the material are deposited on a substrates according to the following sequence of steps: i) the material to be deposited is converted into vapor by physical means; ii) the vapor is transported from its source to the substrate across a region of low pressure; and iii) the vapor undergo condensation on the substrate to form the thin film (Waser ed. 2005). The majority of publications considering thin ferroelectric film tunable microwave devices use PVD methods. The overwhelming use of PVD methods is due to, first of all, their compatibility with standard semiconductor technology and high quality of the ferroelectric films. The most frequently cited PVD methods of fabrication of ferroelectric films for microwave devices are pulsed laser deposition (PLD) (Kim et al. 2006, Wang et al. 2007, Miranda et al. 2008, Kuylenstierna et al. 2006, Kuylenstierna et al. 2005, Berge et al. 2008, Moeckly and Zhang 2001) and sputtering (Zinck et al. 2004, Schreiter et al. 2004, Samoilova et al. 2005, Mahmud et al. 2006, Kozyrev et al. 2002, Kozyrev et al. 2001). The co-evaporation (Moeckly and Zhang 2001) is not used that often. 3.5.2.1 Pulse Laser Deposition (PLD) PLD allows easy reproduction of the target’s stoichiometry in the deposited film. The desired stoichiometry of the film is achieved by using targets with the same stoichiometry. This becomes possible due to the short laser pulses (in the fs-ps range) provide condition of non-equilibrium heating, when the heated thickness is less or comparable with the ablated thickness. This is the main advantage of the PLD. In early days of development of the PLD systems the high density of the point defects, bouldering of surface morphology by droplets transferred from the target (splashing) and small areas (< 10x10 mm2) have been regarded as the main disadvantages. However, the scanning of laser beam, substrate rotation/translations and off-axis positioning (Chrisey and Hubler 1994) allows fabrication of thin films with high thickness and composition uniformity (±4%) over 8-inch area (Eason 2007). Optimization of process parameters (Chrisey and Hubler 1994) and deposition system configuration allows significant reduction of splashing (Irissou et al. 2006). Large area PLD technique is used to grow 6 different compositions using three targets (BaTiO3, SrTiO3 and Ba0.6Sr0.4TiO3) suitable for high-k MOSFETS, memory cells, and microwave components and arrays (Navuduri et al. 2006). Sakai et al. (2007) have developed a large-area pulsed-laser deposition system, suited in particular for depositing high-k dielectric and ferroelectric thin films of high quality on Si wafers of 8” in diameter. The PLD concept is simple (Fig. 3.5.7). A pulsed laser beam (typically 30 ns pulses with energy in the range 0.01–0.1 J and at a repetition frequency of 10 Hz) is focused onto the target. Both the focusing lens and the laser are external to the

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Fig. 3.5.7 Laser ablation system for deposition of oxide thin films

vacuum chamber. For high efficiency of radiation absorption by target material lasers with radiation in UV spectrum, typically excimer (ArF, KrF, etc.), are used. Above threshold laser fluence, a luminous plume of material is ejected normal to the target surface. The ejected material is deposited on a substrate that is suitably positioned and heated. The deposition process is controlled by rotating the target, varying the target-substrate distance and varying the lens-target distance. Typically turbopumps are used to evacuate the chamber to the high-vacuum (10-5 to 10-7 mbar). The turbopumps allow a rapid turn around time and avoids hydrocarbon contamination in the chamber. A rotary pump is used in the second pumping port for pumping the deposition gas (oxygen for growth of ferroelectric films) through the chamber. The pressure in the chamber is controlled by a needle valve. The removable shutter is positioned across the substrate prior to deposition to allow the target to be cleaned by ablating the surface with the laser beam without contamination of the substrate. The fact that PLD can operate at high ambient pressure is an advantage for the in situ deposition of multicomponent oxides. The PLD method is one of the cheapest deposition methods, especially where the laser is shared between several deposition systems. For BSTO thin films, the typical growth conditions are: growth temperature –650°C, laser fluence at the target –1.5 J cm–2 and oxygen ambient pressure –0.1 mbar. The basic PLD setup is simple relative to other deposition techniques. However, the physical phenomena of laser-target interaction and film growth are quite complex (Chrisey and Hubler 1994). First the energy of the absorbed by the target laser pulse is converted to electronic excitation and then into thermal, chemical and mechanical energy. All these complex processes result in evaporation, ablation, plasma formation and exfoliation. The ejected from the target plume contains neutral (molecules, atoms, clusters, particulates and molten globules) and charged (electrons, ions) particles. During the PLD process, material is removed from the BSTO target by an intense UV laser pulse within a very short time interval (typically 30 ns, as mentioned above); therefore, the composition of the BSTO films is maintained to be the same as that of the target (Bao et al. 2008).

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Fig. 3.5.8 A cross-section (a) and schematic (b) vies of the phase shifter. Reprinted with permission from IEEE©2006

A microwave phase shifter based on BSTO varactors fabricated using PLD is described in (Kim et al. 2007) where TiO2 buffer layer is used between BSTO film and high resistive Si substrate. It is demonstrated that the TiO2 buffer layer allows significant increase of tuneability and decrease of power loss via the high resistive Si substrate (Kim et al. 2006). It is assumed that the TiO2 buffer layer controls the orientation and, hence, improves the quality of the BSTO film. Besides it increases the overall average dielectric constant and thereby minimizes electric field attenuation in coplanar designs (Kim et al. 2007). Figure 3.5.8 shows schematic and cross-section views of the phase shifter. The TiO2 buffer layer with thickness of 50 nm is deposited onto n-type Si (100) substrates using titanium ethoxide [Ti(OCH2CH3)4] and water at the low temperature of 220°C by atomic layer deposition. n-type Si (100) substrates are etched in 10% HF solution for 1 min to remove the native oxide and treated by ozone to increase nucleation sites. Titanium ethoxide is held at 90°C to achieve desired vapor pressures. The water is maintained at 20°C. One cycle consists of injection of titanium ethoxide, purging with nitrogen, injection of water, and then purging with nitrogen. The TiO2 buffer layer is formed by repeating the above cycles until the desired thickness is achieved. To improve the crystalline structure and dielectric properties of the TiO2/HRSi structure, the TiO2 buffer layer is annealed at 700°C in an oxygen atmosphere for 30 min. After annealing the buffer layer, a 500 nm thick Ba0.6Sr0.4TiO3 thin film is deposited onto the TiO2/Si substrate by PLD. The substrate temperature and oxygen ambient pressure are 750°C and 50 mTorr, respectively. Laser ablation is carried out at a laser power density of 1.5 J/cm2 and a repetition rate of 5 Hz using a KrF excimer source (λ=248 nm). For fabrication of the top electrode the photoresist is first deposited and patterned. The 1.5 µm thick Au/Cu/Ti electrodes are deposited using DC magnetron sputtering. The Ti adhesion layer is 25 nm thick. A 25 nm thick gold layer is deposited on top of Cu to protect its surface and for electrical contact. To define the CPW structure, samples are placed in acetone for 10 min. After that, they are agitated and sonicated to remove photoresist residue. The measured phase shift is 142° and the FoM is 107.3 degree/dB at 16 GHz and 50 V dc bias.

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Fig. 3.5.9 Layer structure of the varactors (a) and photograph of a segment of the CPS line loaded with three varactors (b). Reprinted with permission from IOP©2007

The details of fabrication of another phase shifter using PLD of BSTO films integrated with HTCS YBCO electrodes is reported in (Wang et al. 2007). Figure 3.5.9 shows the layer structure and photograph of a segment of the coplanar strip (CPS) transmission line loaded with three BSTO varactors. The 500 nm thick YBCO and 500 nm thick Ba0.1Sr0.9TiO3 are deposited on the 10 × 10 × 0.5 mm3 LaAlO3 (LAO) substrate using a PLD system with a KrF excimer laser (Lambda Physik, 248 nm, 30 ns) at 3 Hz repetition frequency, with an energy density of 250 mJ/pulse. The deposition is conducted for 45 minutes, at a substrate temperature of 720°C and a chamber oxygen pressure of 0.1 mbar. The substrate-target distance is 50 mm (Yan et al. 2004). The 150 × 70 μm2 BSTO patches are fabricated by a liftoff method presented in (Ong and Tan 2005), where YBCO film is used as a refractory masking layer. The negative image of the required BSTO thin film is pre-patterned in YBCO using a conventional UV photolithography and wet etching in diluted weak acid such as H3PO4. The subsequently deposited BSTO thin film grows directly on the LAO substrate in the required regions or on the YBCO mask in other regions. The YBCO masking layer, with the BSTO thin film upon it, is etched away with diluted nitric acid in an ultrasonic bath. The substrate with the patterned BSTO thin film is used to grow a 500 nm thick YBCO thin film as a conductor layer. The same patterning process (used for making the masking layer) is used for the circuit fabrication. The circuit is packaged hermetically (Tan and Ong 2006) and demonstrated an average phase shift of 20° at 200 V dc bias. The PLD is used for fabrication of parallel plate BSTO varactors utilized in ultrawide-band tunable true-time delay lines described in (Kuylenstierna et al. 2005). Figure 3.5.10 shows the schematic cross section view and microphoto of a segment of the device with a load varactor (see also Fig. 5.2.6). The processing of the device started with commercially available oxidized n-type high-resistive (ρ> 5 kΩcm) Si (100) covered with TiO2 (15 nm) and Pt (100 nm). The TiO2 is used as an adhesion layer. For reduction of metal losses in the bottom electrode, a 0.5-µm-thick Au film is deposited on top of the thin Pt film. A 50-nm thick Pt is used on top of Au to facilitate lattice matched heteroepitaxial growth of the Ba0.25Sr0.75TiO3 film. Au and Pt are deposited in situ by electron-beam evaporation

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Fig. 3.5.10 Schematic cross section view (a) and microphoto of a segment of the delay line including the load varactors (b). Reprinted with permission from IEEE©2005

at room temperature. Before deposition of the ferroelectric film, the bottom electrode stack is prepatterned by ion etching to form the required in the layout shapes. After prepatterning of the bottom electrode, the ferroelectric film is grown over the wafers entire surface by laser ablation using a KrF excimer laser operating at 10 Hz and 1.5 J/cm2. During the film deposition, the substrate temperature is maintained at 650°C and oxygen pressure at 0.4 mbar. After deposition, the pressure of oxygen is increased to 950 mbar and the samples are cooled down to room temperature. When the film deposition is finished, the top electrode stack, consisting of 50 nm Pt and 0.5 m Au, is deposited by e-beam evaporation. Finally, the top electrode and the entire layout are patterned by a liftoff process, using AZ1514E photoresist. At room temperature the device reveal an absolute group delay of 70 ps with tuneability of 20% under 20 V dc bias. The insertion loss is less than 3.5 dB. The SEM cross section of a tunable thin film bulk acoustic resonator (TFBAR) based on PLD BSTO thin film (Berge et al. 2008) is depicted in Fig. 3.5.11. In this device the Au and SiO2 layers of the Bragg reflector and bottom electrode stack are deposited in situ onto an oxidized high resistivity silicon substrate using DC magnetron sputtering and reactive RF magnetron sputtering, respectively.

Fig. 3.5.11 SEM cross section of the TFBAR. Reprinted with permission from AIP©2008

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Thin Ti (10 nm) layers are sputtered in between each layer to improve adhesion. No intentional heating or cooling of the substrate is provided. The Bragg reflector and bottom electrode are patterned using Ar ion milling at 45° incident angle, followed by pulsed laser deposition of the ferroelectric film at a substrate temperature of 650°C and 20 Pa O2 pressure. Laser pulses with an energy density of 1.5 J cm–2 and a repetition rate of 10 Hz, supplied by a KrF excimer laser (λ=248 nm, τ =30 ns) are used to ablate the ceramic target. The Al/Au top electrodes are deposited by dc magnetron sputtering and electron beam evaporation, respectively, and patterned using lift-off processes. The thin layer of Au on top of the Al prevents Al from being exposed to the corrosive alkaline developer used during photolithography for the thick Au interconnects. The tuneability of the series and parallel resonances for the Ba0.25Sr0.75TiO3 TFBAR are 1.7% and 0.3%, respectively at 15 V DC bias (see also Fig. 5.9.3). The TFBAR quality factor is more than100. 3.5.2.2 Magnetron Sputtering The sputtering is regarded as one of the most promising methods of fabrication of ferroelectric films for integration into microwave tunable devices (York et al. 2000). It offers high uniformity over the large area wafers, scalability, compatibility with standard IC processing, and low investment cost. In most cases reactive RF magnetron sputtering is used for deposition of the ferroelectric films. For deposition of the oxide films, such as perovskite ferroelectrics, oxygen is routinely added to an inert gas, normally Ar. A typical reactive sputter deposition system is shown in Fig. 3.5.12.

Fig. 3.5.12 Reactive sputter deposition system

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The system contains a sputtering source/cathode (i.e. magnetron), inlets for inert (i.e. Ar) and reactive (i.e. oxygen) gases, a sample/substrate on which the films are deposited and pumps. Several hundred watts of power applied to the target/cathode leads to the ignition of a plasma discharge where the pressure in the chamber is in the range of 102–10–3 mbar. It results in an acceleration of the positively charged Ar ions towards the target. These accelerated particles sputter off the deposits, which arrive at the substrate mostly as neutral atoms. The discharge is maintained as accelerated secondary electrons continuously ionize new ions by collisions with the sputter gas (Waser ed. 2005). The ionization probability is close to 100% in the magnetron systems where additional magnetic field is configured radially and parallel to a planar cathode surface. This additional magnetic filed results in a closed-loop drift path for the secondary electrons. The secondary electrons are trapped in the ring close to the cathode and can lead to very high levels of ionization of the background gas (Powell 1999). For sputtering of insulating targets of oxide ferroelectrics a high frequency plasma discharge must be applied in order to avoid the accumulation of electric load. The RF power, typically at frequency of 13.6 MHz, is capacitively coupled to the target and there is only a small voltage decay across the electrode. As the electrons are much faster than the ions a negative potential at the electrodes as compared to the plasma potential evolves during each voltage cycle. A non-symmetric arrangement, i.e. the generally applied grounding of the substrate and the deposition chamber, results in some negative bias voltage applied to the substrate which allows maintaining the gas discharge (Waser ed. 2005). Magnetron sputtering is extensively used by Kozyrev’s group for fabrication of BSTO films utilized in filters and phase shifters (Kozyrev et al. 2001), Kozyrev et al. 2002). For example, the phase shifter depicted in Fig. 5.3.2 is prepared in a Leybold Z-400 setup by ionplasma RF magnetron on-axis sputtering of a Ba0.3Sr0.7TiO3 ceramic target with a diameter of 76 mm. This target composition is considered to be optimum for the synthesis of the ferroelectric films with the best FoM. In this example the films are deposited onto ceramic alumina (Al2O3) substrates in a pure oxygen atmosphere at a pressure of ~10 Pa and a substrate temperature of 905°C. The film thickness varied from 0.5 to 1 µm. After deposition, the films are cooled in pure oxygen at a rate of 2–3 K/min. The Ba0.3Sr0.7TiO3 film is covered with a 1 µm thick layer of copper deposited by thermal evaporation in vacuum. The phase shifter topology is patterned by chemical etching. The same magnetron sputtering technology is used for fabrication of microwave up-converters based on BaxSr1–xTiO3 varactor (Samoilova et al. 2004). The BaxSr1–xTiO3 films with compositions in the range of x=0.3–0.6 are deposited on 0.5 mm alumina-based ceramic substrate and used in both co-planar and parallelplate varactors. In parallel-plate varactors Pt is used as a bottom plate. Compared with the coplanar-plate design, the parallel-plate capacitors allow reduced voltages for controlling the capacitance. This fact is of crucial importance for selecting the pump power. Experimental up-conversion from 0.8 to 4.4 GHz is reported. An RF magnetron sputtering process developed for elaboration of tunable TFBARs based on PZT thin films is reported in (Zink et al. 2004). The films are

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sputtered in a MRC 903 tool, using a ceramic 37 × 12 0.6 cm3 PZT target in the morphotropic phase, Pb(Zr0.25Ti0.48)O3. The deposited films are amorphous since the substrate is not heated during deposition. Argon is used as a sputtering gas and the used RF power density was 3 W⋅cm–2. During the sputtering the wafer is scanned in order to obtain the better homogeneity on a 4 inch wafer. After deposition, a 20 minutes thermal annealing crystallization is performed at 675°C in N2 + O2 atmosphere. Figure 3.5.13 presents the complete process flow used to realize the TFBARs. Starting from a double side polished silicon wafer, 1 μm of SiO2 is thermally growth on both sides of the wafer. A 500 nm SiN thin film is deposited on silicon oxide to act as a support for the device. Then, Ti(50 nm)/Pt(100 nm) bottom electrode is deposited by DC sputtering and patterned by ion beam etching, Fig. 3.5.13 (a).

Fig. 3.5.13 PZT based TFBAR process flow. Reprinted with permission from IEEE©2004

The PZT thin film (370 nm) is deposited by RF magnetron sputtering, patterned by a wet etch and then crystallized by annealing (Fig. 3.5.13 (b)). Electrical isolation of the top electrode is achieved by deposition of 400 nm of SiO2 by plasma enhanced chemical vapor deposition. Then SiO2 film is opened above the PZT capacitors in order to realize the TFBAR active zone (Fig. 3.5.13 (c)). The Pt/Ti/Pt (20/30/100 nm) top electrode is deposited and patterned (Fig. 3.5.13 (d)). The Ti/Pt top electrode is not desirable since, it is assumed, that the Ti reduces the ferroelectric properties of the PZT. The first platinum layer is patterned with the same mask as the PZT layer to recover the PZT. Then, the titanium layer is used in order to have a good seed layer for Pt on SiO2. The Ti/Pt films are then patterned using a separate mask. Finally, square apertures are opened from the backside of the silicon wafer by the deep reactive ion etching of silicon (Fig. 3.5.13 (e)). The front side SiO2 layer is wet etch by the back side (Fig. 3.5.13 (f)).

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Schreiter et al. (2004) reported a different approach for deposition of ferroelectric films by magnetron sputtering. The PZT films are used in TFBARs. The PZT thin films are reactively deposited in a multitarget sputtering system using three separate metallic targets (Pb, Zr and Ti) in a 50/50 Ar/O2 mixture. The substrate temperature and sputtering pressure are fixed at 525°C and 0.4 Pa, respectively. The film thickness ranging between 350 and 425 nm produce resonance frequencies about 2 GHz. Figure 3.5.14 depicts the plain view of the TFBAR structure. Four inch silicon wafers covered with acoustic λ/4-mirrors (to decouple resonators from the substrate) and Pt bottom electrodes are used as the substrate. The Pt ground (bottom electrode) is connected to the ground by wire bonding.

Fig. 3.5.14 Schematic plot of the PZT TFBAR.(Reprinted with permission from Elsevier©2004

This mirror is realized as a 3-fold stack of alternating Pt and ZnO layers having high and low acoustic impedances. During PZT deposition the substrates rotate over the targets, thus the film grows sequentially layer by layer in the ferroelectric perovskite phase, i.e. no thermal treatment after deposition is needed. The Zr content x in Pb(ZrxTi(1–x))O3 is varied between 0.25 (PZT25/75) and 0.6 (PZT60/40) simply by changing the power delivered to the individual targets. Thus both thin films of the tetragonal and rhombohedral phase were realized. The films of these compositions show significant differences concerning self polarization, permittivity and hysteresis, making them interesting for electroacoustic hysteresis studies. A top layer of Au with a thickness of 100 nm is deposited onto the PZT film and patterned to give test resonators with different sizes (30 × 30 µm2 up to 500 × 500 µm2). For frequencies of 2 GHz the ground signal is capacitively coupled to the bottom electrode. To enable a bias voltage to be supplied, the bottom electrode is uncovered at one spot on the wafer and connected to the ground by wire bonding. 3.5.2.3 Structure of Films Grown by PVD The structure of ferroelectric films grown by PVD methods are defined by growth conditions (substrate temperature, gas composition and pressure, substrate-totarget distance etc.) and physical properties of the substrate/template (crystallinity, thermal expansion coefficient, surface conditions etc.). In this section the micro-

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structure of films grown by PLD and magnetron sputtering on crystalline matched substrates and metallized substrates/templates (bottom electrodes) are considered. Crystalline Substrates The growth on crystalline matched substrates (see Chap. 4) at optimized growth conditions, normally, results in high quality epitaxial ferroelectric films (Cukauskas et al. 2000, Carlsson et al. 2000). Figure 3.5.15 (a) shows XRD scan of a Ba0.5Sr0.5TO3 film grown by inverted cylindrical magnetron sputtering on (100) MgO substrate (Cukauskas et al. 2000) at optimized growth temperature 750°C, oxygen partial amount 85% and substrate-to-target distance 8.6 mm. The BSTO films (Fig. 3.5.15 (a)) are strongly (h00) oriented. It is found out that the substrates positioned closer to the gun resulted in films having many of the BSTO powder peaks. Films deposited with small amounts of oxygen (<5%) did not have the BSTO structure. Films deposited in 100% oxygen are predominantly (110) oriented. Diffraction peak height increases with increasing deposition temperature. The surface roughness also increases with deposition temperature from specular (rms ∼20 nm) at 550°C to rough (rms ∼70 nm) at 750°C. The increase of surface roughness is associated with formation of large protruding (h00) grains with lateral grain size ∼250 nm. The BSTO films grown at optimal conditions reveal optimal dielectric properties. The Q-factor of this coplanar-plate structure is 200 at 10 GHz and 0 V dc bias.

(a)

(1)

(2)

MgO

MgO

(1)

(2)

LAO

LAO

(b)

Fig. 3.5.15. XRD scan of a BSTO film deposited by magnetron sputtering on MgO substrate (a), rocking curves and φ scans of BSTO films deposited by PLD on MgO and LAO substrates (b). Reprinted with permission from AIP©2000

In (Carlsson et al. 2000) the microstructure of as-deposited and annealed (in oxygen flow at 1100°C for 5 hours) Ba0.4Sr0.6TO3 films grown by PLD is studied. The as-deposited and annealed BSTO films are epitaxial on both MgO and LAO substrates in the cube-on-cube orientation. 2-2θ XRD scans have only (00l) peaks and remain unchanged after annealing for films on both substrates. For as-deposited BSTO films, the FWHM of the rocking curve ω and φ scans are larger on MgO substrates (Δω(200)∼0.7°, Δφ(110)∼1.1°) than on LAO (Δω(200)∼0.2°, Δφ(110)∼0.9°) as shown in Fig. 3.5.15 (b). The anneal decreases the widths (dashed

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lines in Fig. 3.5.15 (b) for BSTO/MgO (Δω(200)∼0.3°, Δφ(110)∼0.9°) to values comparable to films on LAO whose XRD characteristics remained essentially unchanged. The lower degree of crystal perfection for the as-deposited films on MgO is likely due to the larger lattice mismatch of BST with MgO (–6.8%) than with LAO (+4.0%). The annealing also affects the surface morphology of the BSTO films. The surface is extremely smooth (rms ~8 Å before, and 3 Å after annealing) with no grains discernable on the annealed surface by AFM. Cross-sectional transmission electron microscopy confirms columnar grain morphology with typical dimensions of 100 nm wide by 300 nm tall for both as-deposited and annealed films. The figures of merit of 30 GHz phase shifters made of these films is ~45°/dB with a phase shift of ~400° under 500 V (~13 V/µm) DC bias. Metallized Templates The BSTO films grown by PVD methods on Pt/Au templates, usually, reveal columnar grain texture with preferred (111) and/or (110) orientations. The effect of Pt and Pt/Au templates on microstructure and dielectric response of BSTO films are analyzed in details in many papers (see, for instance, (Rundqvist et al. 2006, Baumert et al. 1997) and references therein).

(a)

(b)

Fig. 3.5.16 XRD scans of BSTO/Pt/Au/Pt/TiO2/SiO2/Si structure (dashed line) and Pt/Au/Pt/TiO2/SiO2/Si template (solid line): (a) in the range 2θ =30–50°, and (b) in the range 2θ=37°–42°. Reprinted with permission from AIP©2006 (Rundqvist et al. 2006)

Masking of the BSTO{111} peak by strong Pt{111} peak is an issue when it comes to XRD analysis of the BSTO films on Pt/Au template. Rundqvist et al. (2006) and Baumert et al. (1997) analysed the XRD scans of the Ba0.25Sr0.75TO3 films grown by PLD on Pt/Au/Pt/TiO2/SiO2/Si templates (Fig. 3.5.16). For the sake of comparison, the template is annealed at 650°C. In Fig. 3.5.16 (a) the peak at 32.27° is identified as BSTO (110). The (111) BSTO peak is identified by overlapping XRD plots with and without BSTO films as shown in Fig. 3.5.16 (b) and

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normalizing the Au (111) peaks to the same intensity. The extracted intensity of BSTO (111) allows texture analysis (suggested in (Padmini et al. 1999)) by comparing the ratios of the intensities of the BSTO (111) and the (110) peaks to that of a JCPDS file. It is shown that the BSTO (111) and BSTO (110) are the preferred orientations with BSTO (111) dominating. This is in agreement with TEM analysis of Ba0.5Sr0.5TO3 films deposited by magnetron sputtering on Pt bottom electrode (Baumert et al. 1997). The TEM analysis shows that the BSTO films are strongly [111] oriented in the growth direction, i.e. aligned with the [111] growth direction of the underlying Pt film. Figure 3.5.17 (a) shows TEM cross-section image of a Ba0.25Sr0.75TiO3 film grown by PLD (Vorobiev et al. 2007). The image reveals columnar grain structure which is typical for BSTO films grown by both methods (PLD and magnetron sputtering). The lateral grain size of the films grown at optimal conditions is distributed in the range 30–50 nm (Berge et al. 2007). The in-plain sections as shown in Fig. 3.5.17 (a) are prepared for investigation of the inter-grain area. The corresponding plain views for PLD and magnetron sputtered films are shown in Fig. 3.5.17 (b) and Fig. 3.5.17 (c), respectively. It is found out that, typically, the inter-grain area in PLD films consist of voids and/or amorphous material. The voids are potential regions for formation of pinholes. This is, probably, the reason for high probability of premature short-circuiting of the capacitors with electrode area large than 1000 µm2. In contrast, as it can be seen in Fig. 3.5.17 (c), the density of BSTO films deposited by magnetron sputtering is higher. This allows fabrication of varactors/capacitors with large area electrodes and high values of capacitance. For example, the BSTO capacitance with total area 2 mm2 and total capacitance up to 10 nF is reported in (Vorobiev et al. 2007). (a)

(b)

(c)

Fig. 3.5.17 TEM cross section view (a), plan section view (b) of a BSTO film grown by PLD, and plan section view (c) of a BSTO film grown by magnetron sputtering on Pt/Au bottom electrodes

3.6 Thin Film Device Processing In general, there are two approaches for manufacturing of hybrid IC utilizing patterning via either additive or subtractive techniques. Additive patterning is typically realized through thick film, HTCC and LTCC, technologies (see Sect. 3.4).

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Subtractive patterning is typically realized through thin film fabrication technology. With this method, substrate is covered by layers of IC component materials using chemical and/or physical deposition methods. After deposition the layers are subsequently patterned using photolithography and processes involving dryetching, wet-etching and lift-off techniques. In this section the basic fabrication process flows of thin film ferroelectric devices are considered including some aspects of processing of the electrodes, substrate passivation and micromachining. The basic processes of manufacturing of ferroelectric devices are similar to most standard IC capacitor technologies. The ferroelectric capacitor structure, depending on device application, may be designed, fabricated and utilized as varactor, decoupling capacitor, TFBAR etc. The other passives, such as CPW lines, inductors etc, are fabricated together with bottom and/or top electrode metallization. Ferroelectric capacitors/varactors used in tunable microwave devices have two basic configurations: parallel-plate and coplanar-plate (see Chap. 4). The configuration of the given capacitor defines a certain set of processing steps for device manufacturing.

3.6.1 Coplanar-Plate Configuration The coplanar-plate capacitors are simpler to fabricate and integrate into circuits in comparison with parallel-plate designs. Another potential advantage of the coplanar-plate configuration is the possibility of epitaxial growth of ferroelectric films directly on matched crystalline substrates. Figure 3.6.1 depicts a general process flow diagram of fabrication of thin the film device utilizing coplanar-plate capacitors. The first processing step (Fig. 3.6.1 (a)) is growth of the ferroelectric film directly on the substrate or on the previously deposited appropriate buffer layer. The crystalline substrates (LaAlO3, MgO, SrTiO3 etc.) suitable for epitaxial growth of perovskite ferroelectric films are described in Chap. 4. They are extensively used for fabrication of high quality coplanar-plate ferroelectric capacitors (Carlsson 2000, Petrov 1998, Kim 2000, Chang 1999). Buffer layers (YSZ, CeO2, TiO2 etc.) are used in the case of misfit substrates (mainly SiO2/Si) to support the crystalline growth of the ferroelectric films (Vorobiev et al. 2003, Kim et al. 2006). The next processing steps are deposition and patterning of the top electrode. The patterning may be realized via either lift-off process or wet/dry etching of top electrode using masks of photoresist. Figure 3.6.1 (b) shows the lift-off route where the top electrode is deposited on the mask of photoresist. The main condition for the proper lift-off process is the separation between the parts of the layer deposited on top of substrate and top of the photoresist. This requires (firs of all) formation of the undercuts at photoresist edges, as shown in Fig. 3.6.1 (b). The undercuts allows reproducible lift-off of the films with thickness even exceeding the resist thickness where the films are deposited by evaporation. The maximum thickness of the deposited layer is limited by the condition of separation which, to some extent, is an issue when it comes to patterning the top electrode using a lift-off process. The condition of low microwave

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BSTO film Buffer layer

Substrate (a)

Photoresist

Electrode

Substrate

Substrate (b) Photoresist

(c) Electrode

Substrate

(d)

Fig. 3.6.1 The process flow diagram for the fabrication of the co-planar BSTO capacitor

loss in metal requires thickness of 2–3 skin depth which for Au, for example, is approximately, 0.5 µm at 20 GHz. The standard image reversal (negative) photoresists (AZ5214E etc.) allows reliable lift-off of the films with thickness up to 1 µm. However, the relatively recently developed photoresist TI 35ES (MicroChemicals®) specially designed for the image reversal technology enables lift-off of the evaporated solid films up to a thickness of 5 µm. The evaporation is most suitable technique for deposition of the layers intended for lift-off patterning. Due to long free mean path of the evaporants and point-like source configuration the deposition on the side walls of the photoresist is excluded leading to easy separation. The lift-off route is, normally, accomplished by soaking in the photoresist remover and results in patterning of the top electrode (Fig. 3.6.1 (c)). Figure 3.6.1 (d) shows an alternative wet/dry etching route. In this case the top electrode stack is deposited first on the ferroelectric film and, subsequently, patterned by wet/dry etch through a mask of photoresist (normally, positive). The refractory based electrodes (Pt/Au) have proved difficult to etch chemically. Normally, wet etching is used for patterning of Cu/Ti based electrode stacks. Besides, the chemical etchant should be selective and not dissolve the ferroelectric film or cause its degradation. The dry etching techniques (ion milling, reactive plasma etc.) may be used for patterning of, practically, any materials. However, careful etching rate calibration or use of stop end techniques are required to prevent damage of the ferroelectric’s active area. There is no principle layer thickness limitation for patterning by etching. However, wet etching and reactive plasma etching produce underetch which increases with layer thickness and should be taking into account. The etching by ion milling results in either sloped sidewalls, or ear shaped edges from re-deposition of material on the mask which is difficult to remove. After removing of photoresist mask, the wet/dry etching rout results in the formation of the same top electrode pattern as the lift-off process (Fig. 3.6.1 (c)). An example of the process flow involving lift-off patterning of the electrode (Fig. 3.6.1 (a, b and c)) used for manufacturing of a microwave phase shifter is

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described in (Kim et al. 2007). A phase shifter fabricated by wet etching of a 4 µm thick Cu film is reported by Sherman et al. (2001) while Tombak et al. (2003) utilised a reactive ion etching to pattern the 300 nm thick Pt electrode for fabrication of a tunable filter. In general, the lift-off technique is considered to be gentler and non-destructive, in comparison with wet/dry etching, because it does not assume exposing of the ferroelectric (active area) to aggressive chemicals, reactive plasma or ion radiation. For this reason the lift-off routs are more frequently used for patterning of the electrode stacks in coplanar-plate and the top electrodes in parallel-plate devices. In the process flows considered above the substrates are covered by nonpatterned ferroelectric films. However, sometimes patterning of ferroelectric film is required. Usually, the ferroelectric film is patterned by wet etching (see next section). An original lift-off method for patterning of the BSTO film is reported by Wang et al. (2007) where YBCO film is used as a refractory masking layer. The patterning of the BSTO film in this process is motivated by necessity to provide truly epitaxial growth conditions of YBCO film on LaAlO3 substrate.

3.6.2 Parallel-Plate Configuration In spite of the more complex processing, in comparison with the coplanar-plate design, the parallel-plate design is considered as most attractive for microwave applications due to higher tuneability at lower controlled voltages which are easily manipulated through control of the ferroelectric film thickness (see Chap. 4). The main difference of manufacturing of the ferroelectric parallel-plate devices, in comparison with the standard IC capacitor technologies, is that the high temperature and oxygen environment (used for the ferroelectric film growth) requires special bottom electrodes. Typically the bottom electrodes consist of refractory metals (Pt and/or Au) and contain additional adhesive and buffer layers. More detailed analysis of the bottom electrode and processing is given in the next section. The main differences in fabrication processes of the parallel-plate ferroelectric devices are associated with the differences in the (thick) bottom electrode stacks. Different bottom electrode stacks involving different numbers processing flows are reported. The most advanced process flows used for fabrication of successful device demonstrators are considered below. In an early process flow reported by Acikel (2002) the ferroelectric film is sandwiched between the bottom and top electrodes (Fig. 3.6.2). In the case where prepatterning of the bottom plate is needed, the thickness of the bottom electrode is limited by the thickness of the ferroelectric film. Additionally the higher electric field at the steep edges of the bottom electrode causes premature breakdown when high bias voltage or large amplitude ac signals are applied. Using crossover dielectrics (to some extent) helps to solve this problem (Fig. 6.3.2). In the process proposed by York et al. (2006) the Ti/Au/Pt (3.5/200/100 nm) bottom electrode stack is deposited on sapphire substrate by e-beam evaporation and prepatterned by lift-

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off process (Fig. 3.6.3 (a)). RF magnetron sputtering is used to grow a 300 nm BSTO film (Fig. 3.6.3 (b)). The Pt/Au (100/300 nm) top electrode is deposited by e-beam evaporation and patterned by lift-off process (Fig. 3.6.3 (c)). To facilitate ohmic contacts the BSTO film is etched down to the bottom electrode using buffered HF as shown in Fig. 3.6.3 (d). In the next step a 300 nm thick SiO2 dielectric crossover is deposited by e-beam evaporation and patterned by lift-off process, (Fig. 3.6.3 (e)). Top electrode

Breakdown region

Substrate

Fig. 3.6.2 A parallel-plate varactor with a simplest structure

Bottom electrode

Substrate

(b)

(c)

Contact metal, passives

(f)

Substrate

Substrate

(a)

Substrate

Top electrode

BSTO film

Dielectric crossover

Substrate

(e)

Substrate

(d)

Fig. 3.6.3 The process flow diagram for fabrication of the BSTO capacitor with crossover dielectric and patterning of the BSTO film

The dielectric crossover serves i) as a cross-over layer, isolating the top contact from the edge of the bottom electrode (a problem region for premature breakdown) and ii) as an environmental encapsulation to protect the BST film from exposure to subsequent contamination in processing or operation. Several materials, such as SiO2, SiN and Al2O3, are proven adequate for encapsulation (York 2009). Additionally, the opening in the dielectric crossover defines the varactor/capacitor area. The last steps of the process flow include deposition of a thick interconnect stack Ti/Au (30 nm/3 µm) by e-beam evaporation and lift-off patterning (Fig. 3.6.3 (f)). Figure 3.6.4 shows the layout and photo of a varactor fabricated using process shown on Fig. 3.6.3. The “U”-shaped connection to the thick

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metal interconnect layer is designed to minimize the series resistance associated with the bottom electrode layer (York 2009). Notice that in spite of the cross over dielectric this design, similar to the simple design shown in Fig. 6.3.2, may suffer lower breakdown voltages due to vertical side walls in the bottom electrode produced by the lift-off process. (a)

(b)

Fig. 3.6.4 The layout (a) and photo (b) of a varactor fabricated using process shown on Fig. 3.6.3

Figure 3.6.5 shows the diagram of process flow developed for fabrication of parallel-plate structures based on two back-to-back connected varactors (York 2000). In this process the bottom electrode is patterned after patterning of the ferroelectric film. This allows better interface between ferroelectric film and bottom electrode which is not exposed to any processing before deposition of the ferroelectric. Potentially, in-situ deposition of the bottom electrode and ferroelectric film is possible. Another advantage of the two series varactor configuration is the symmetric C-V and I-V dependences due to symmetry of the electrode structure.

BSTO film Bottom electrode

Substrate

Substrate

Substrate

(a)

(b)

(c)

Top electrode

(e)

Substrate

Dielectric crossover

Substrate

(d)

Fig. 3.6.5 Fabrication process flow for the back-to-back connected varactors with crossover dielectric and patterning of the BSTO film

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The process flow shown in Fig. 3.6.5 is used for fabrication of ferroelectric phase shifters (York et al. 2001). The Pt/TiO2 (100/100 nm) bottom electrode is deposited on SiO2/Si substrate followed by deposition of 100 nm BSTO film by magnetron sputtering (Fig. 3.6.5 (a)). The next steps are photolithography and wet etching of BSTO film down to the bottom electrode using buffered HF (Fig. 3.6.5 (b)) which is followed by an ion-milling of the Pt base electrode (Fig. 3.6.5 (c)). The BSTO/Pt island is then encapsulated by SiN. Holes are dry etched (reactive ion etching) in SiN to define the top contact area as shown in Fig. 3.6.5 (d). The Pt top electrode is deposited by e-beam evaporation and patterned by lift-off (Fig. 3.6.5 (d)). Use of the dielectric crossover in the processes described above is motivated mainly by need to isolate the top contact from the vertical edge of the bottom electrode and increase the breakdown voltage. An alternative way to increase the breakdown voltage is reported in (Vorobiev et al. 2008) where the bottom electrode stack has sloped sidewalls. It allows conformal coverage the slope by the layers deposited subsequently. In this case the properties of BSTO film in the area of sloped sidewall are identical to that on the flat area. The details of fabrication and characterization of the sloped sidewall structure are given is the next paragraph. Bottom electrode sloped sidewall

Substrate

(a)

BSTO film

Substrate

(b)

Top electrode, passives

Substrate

(c)

Fig. 3.6.6 The process flow diagram for the fabrication of the BSTO varactors using sloped sidewalls in the bottom electrode

The process flow shown in Fig. 3.6.6 is used for fabrication of the tunable delay lines based on BSTO varactors (Kuylenstierna et al. 2005). The Pt/Au (50/500 nm) bottom electrode stack is deposited on platinazed Si substrate. The bottom electrode is patterned using Ar ion milling under certain angle of incidence combined with the sample rotation. This results in formation of the sloped side walls (Fig. 3.6.6 (a)). In the next step a 550 nm thick BSTO film is deposited by PLD (Fig. 3.6.6 (b)). Then the Au/Pt (500/50 nm) top electrode is deposited by e-beam evaporation and patterned by lift-off process (Fig. 3.6.6 (c)). The varactors are formed in the overlap area between the patterned bottom and top electrodes, as shown on Fig. 3.6.6 (c). The additional capacitance associated with sloped side walls contributes in total varactor capacitance and should be taken into account in the case of small area (several μm2) varactors. Another feature of this process flow is the non-patterned BSTO film. The large area capacitance between the bottom metal layer and the top metal interconnect (Fig. 3.6.6 (c)) provides effective DC and RF connections to the bottom plate. Avoiding patterning of the BSTO makes

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the process simpler and more reproducible and more reliable devices. Nevertheless, in circuit applications one may need ohmic contacts (via) to the bottom plates to avoid the floating charge (in floating bottom plate) problem and to increase the tuning speed. (b)

(a)

(c)

2.0 µm

Fig. 3.6.7 Photo of the alignment sensitive (a) and SEM image of the alignment insensitive (b) varactors and SEM image of the sloped side wall in the bottom plate (c)

Figure 3.6.7 (a) shows photo of a simplest varactor design fabricated using process flow shown in Fig. 3.6.6 (a). The overlap area between the plates and hence the capacitance are quite sensitive to mask alignments during fabrication of the varactor. The modified design shown in Fig. 3.6.7 (b) is insensitive to the misalignment. Indeed, any shift of top electrode within the mask alignment tolerances (typically several microns) results in no changes of varactor area/capacitance. Unfortunately there is a price to pay for this: the parasitic resistance of the narrow strips, typical for this design, reduces the overall Q-factor of the varactor (Vorobiev et al. 2008). This design is used in the tunable delay lines based on BSTO varactors (Kuylenstierna et al. 2005). Figure 3.6.7 (c) shows SEM image of a parallel-plate varactor with a sloped side wall bottom plate where the transparent ferroelectric film is sandwiched between the top and bottom plates. In contrast to Fig. 3.6.2 the step coverage is much better and the breakdown voltages are higher. However, the ferroelectric film, and as it may be seen the top electrode, still have some defects on the sloped wall. These defects are “weak links” (especially for thin ferroelectric films on thicker bottom plate) responsible for the relatively low breakdown voltages and reliability issues. The negative impact of these defects and the parasitic contribution of the narrow interconnect strips (Fig. 3.6.7 (b)) may be reduced by using dielectric crossovers. In this case the varactor area/capacitor is defined mainly by opening in the dielectric crossover. Figure 3.6.8 shows the fabrication process flow of the parallel-plate BSTO varactors with sloped sidewall bottom electrode and crossover dielectric (Vorobiev et al. 2008). The process flow is identical with that shown in Fig. 3.6.6 until the step of formation of the dielectric crossover. The 150 nm SiOx dielectric crossover is deposited by e-beam evaporation and patterned by lift-off process (Fig. 3.6.8 (b)). The Au/Ti (500/50 nm) top electrode is deposited by e-beam evaporation and patterned by lift-off process (Fig. 3.6.8 (b)). The Ti adhesion layer is used to ensure adhesion to the SiO2 patches. The top electrode fabrication process is similar to that used in the process flows shown in Fig. 3.6.4. How-

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ever, using the sloped side wall (Fig. 3.6.8) eliminates the troublemaking region at the edge of the bottom electrode and increases further the breakdown voltage. Photos of single and back-to-back varactors fabricated using this process flow are shown in Figs. 3.6.9 (a) and (b) respectively (Vorobiev 2008). The sloped sidewalls are visible as double lines at the perimeters of the bottom electrodes. BSTO film

Substrate

Dielectric crossover

Top electrode, passives

Substrate

(a)

(b)

Substrate

(c)

Fig. 3.6.8 The process flow for the fabrication of the BSTO varactors with sloped sidewall bottom electrode and crossover dielectric

(a)

(b)

Fig. 3.6.9 The photos of varactor structures fabricated using process flow shown on Fig. 3.6.8

3.7 Substrate Micromachining and Passivation High resistivity Si is currently used as a substrate for development of microwave devices because of its low cost, low microwave losses and integration capabilities. The main issue in using Si as a substrate is the high surface conductivity induced by the positive charges (most probably oxygen vacancies) in the native and deposited SiO2 layers. This conductive surface layers cause extra microwave losses and parasitic couplings/field dependences (see Chap. 4). At present micromachining and/or additional passivation layers are used to overcome these problems.

3.7.1 Substrate Micromachining Making trenches between the components (strips) by surface micromachining of the Si somehow helps to reduce microwave losses in coplanar microwave devices.

3.7 Substrate Micromachining and Passivation

107

Figure 3.6.10 shows a process flow used for micromachining of a Si substrate used for fabrication of the ferroelectric phase shifters (York et al. 2001). The process of micromachining starts after the last step of fabrication of parallel-plate varactor (Fig. 3.6.5 (e)). Pt bottom layers that are preserved outside varactor area (not shown in Fig. 3.6.5 (e)), act as mask layer for etching of Si (Fig. 3.6.10 (a)). For etching potassium hydroxide is used. In this case the etching procedure is anisotropic and only SiO2/Si material is etched away in the gaps of the CPW resulting in structure shown in Fig. 3.6.10 (b). The trenches reduce the microwave losses but they do not eliminate the parasitic substrate couplings. Using additional passivation layers is a more efficient way to reduce or eliminate the negative effects associated with the surface conductivity of the high resistivity silicon. CPW line

SiO2

(a)

(b)

Si substrate

Fig. 3.6.10 Micromachining of Si substrate

3.7.2 Substrate Passivation Passivation is achieved by introducing high density recombination centers in deposited silicon layers or damaged surface layers that cause high recombination rate. This prevents formation of accumulation, depletion, and inversion layers, and, hence, reduces the associated negative effects, i.e. extra microwave losses and parasitic couplings. High trap density may be achieved by a high-dose implantation using a neutral impurity, such as argon (Spirito et al. 2005). It is also shown that the re-crystallization, by rapid thermal annealing (RTA), of the deposited amorphous silicon layers results in passivation layers smoother and higher stability of the resistivity (Lederer and Raskin 2005). Figure 3.6.11 shows the process flow used for passivation of Si substrate where the polysilicon layer is crystallized by rapid thermal annealing (Lederer and Raskin 2005). The passivation process starts with deposition of 300 nm thick amorphous Si layers by low pressure chemical vapor deposition at 525°C, Fig. 3.6.11 (a). In the next step a 500 nm thick covering oxide is deposited by plasma enhanced CVD at low temperature (350°C) to avoid oxidation of the amorphous Si (Fig. 3.6.11 (b)). The amorphous Si is then crystallized by rapid thermal anneal during 120 s at 900°C (Fig. 3.6.11 (c)). A 1 µm thick aluminum layer is deposited and patterned to form CPW shown in Fig. 3.6.11 (d).

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3 Fabrication of Ferroelectric Components and Devices SiO2

Amorphous Si

Poysilicon

Si substrate

Si substrate

(a)

(b)

Si substrate CPW line

(d)

(c)

Si substrate

Fig. 3.6.11 The process flow used for passivation of Si substrate

3.8 Conclusions For applications in tunable microwave devices requiring exclusively low losses the single crystals of incipient ferroelectrics (SrTiO3, KTaO3) grown by TSSG and especially by ACRT are the most appropriate. They offer lowest density of dislocations and hence lowest microwave losses and instabilities. However, for less demanding applications where the cost is a critical issue the larger crystals grown by Verneuil method may be used. The fabrication process of the devices using bulk crystals is relatively simple. However their integration in complex microwave IC (i.e. MCM) is costly, even though the crystal ion slicing (CIS) and wafer bonding technique considered in (Lee et al. 2006) is intended to overcome this problem and utilize excellent properties of the bulk single crystal in ICs. The bulk ceramic and screen printed thick film devices are fabricated using standard ceramic processing routs. The HTCC, and especially LTCC process and devices based on them are characterized by lowest cost. In comparison with the single crystal counterparts the ceramic devices have lower tuneability and lower Q-factor. The high voltages required for tuning is the main common disadvantage of the bulk (single crystal, ceramic) and thick film ferroelectric devices. Growth of high quality ferroelectric films on large area wafers is the key process in the fabrication of tunable thin film microwave devices. MOCVD, CSD, PLD, RF magnetron sputtering and other methods qualified for industrial scale growth of ferroelectrics on large wafers (6”–8”) are considered. Perhaps the magnetron sputtering is one of the most preferable methods allowing growth of dense and high quality conformal films. The fabrication process of tunable thin film microwave devices using thin ferroelectric films is based on standard thin film process including photolithographic processes. Different modifications of the two main tracks are considered:

References

109

• Pre-patterning of the films before the next layers are deposited; • Patterning of the stacked films after their deposition. The choice of the method depends on the available fabrication tools. In contrast to the bulk and thick film devices the devices based on thin film processes offer higher degree of integration, lower cost and better performance.

References Acikel B (2002) High performance barium strontium titanate varactor technology for low cost circuit applications, PhD thesis, University of California, Santa Barbara. Al-Taei S et al. (2001) Multilayer ceramic integrated circuits (MCICs) technology and passive circuit design, Proceedings of the London Communication Symposium, 10–11 September 2001, 6th Annual London Conference on Communications:139–142. Bao R et al. (2008) Barium strontium titanate thin film varactors for room-temperature microwave device applications. J Phys D: Appl Phys 41:063001 Baumert B A et al. (1997) Characterization of sputtered barium strontium titanate and strontium titanate-thin films. J Appl Phys 82:2558 Bednorz J G, Arend H ( 1984) A 1 kW mirror furnace for growth of refractory oxide single crystals by a floating zone technique. J Cryst Growth 67:660–662. Bednorz J G, Scheel H (1977) Flame-fusion growth of SrTiO3. J Cryst Growth 41:5–12 Berge J et al. (2008) Field and temperature dependent parameters of the DC field induced resonances in Ba0.25Sr0.75TiO3-based tunable thin film bulk acoustic resonators. J Appl Phys 103:064508-064508-8 Berge J, Vorobiev A, Gevorgian S (2007) The effect of growth temperature on the nanostructure and dielectric response of BaTiO3 ferroelectric films. Thin Solid Films 515: 6302 Buse K, Baller F, Pankrath R et al. (1993) Photorefractive and related properties of Ba0.984Sr0.016TiO3 Crystals. Solid State Commun 88:587–591 Carlson C M, Rivkin T V, Parilla P A et al. (2000) Large dielectric constant (ε/ε0>6000) Ba0.4Sr0.6TiO3 thin films for high performance microwave phase shifters. Appl Phys Lett 76:1920 Chang W, Horwitz J S, Carter A C et al. (1999) The effect of annealing on the microwave properties of Ba0.5Sr0.5TiO3 thin films. Appl Phys Lett 74:1033 Chrisey D B, Hubler G K (1994) Pulsed Laser Deposition of Thin Films. John Wiley & Sons Cukauskas E J, Kirchoefer S W Pond J M (2000) Low-loss Ba0.5Sr0.5TiO3 thin films by inverted cylindrical magnetron sputtering. J Appl Phys 88:2830 Das S N (1964) Quality of a ferroelectric material. IEEE Trans MTT 12(7):440 De Flaviis F (1997) Planar Microwave Integrated Phase Shifter Design with High Purity Ferroelectric Material. IEEE Trans MTT 45:963–969 De Flaviis F et al. (1995) Ferroelectric materials for wireless communications. COMCON 5th Int Conf Advances in Commun and Control, Rithymnon, Crete, Greece, June 26–30 Deleniv A et al. (2003) Tunable ferroelectric components in LTCC technology. Digest IEEE Int Microwave Symposium 2:1997–2000 Deleniv A et al. (2005) LTCC Compatible Ferroelectric Phase Shifters. IEEE IMS’2005 Deleniv A, Eriksson A, Gevorgian S (2002) Design of Narrow-Band Tunable Band-Pass Filters Based on Dual Mode SrTiO3 Disk Resonators. IEEE MTT-S International Microwave Symposium Digest 2:1197–1200 Ditum C M, Button T W (2003) Screen printed barium strontium titanate films for microwave applications. J European Ceramic Society 23:2693–2697

110

3 Fabrication of Ferroelectric Components and Devices

Domenico M D, Johnson D A, Pantell R H (1962) Ferroelectric harmonic generator and the large-signal microwave characteristics of a ferroelectric ceramic. J Appl Phys 33:1697 Eason R (2007) Pulsed laser deposition of thin films: applications-led growth of functional materials. Wiley, New York Eriksson A, Deleniv A, Gevorgian S (2003) Orientation and direct current field dependent dielectric properties of bulk single crystal SrTiO3 at microwave frequencies. J Appl Phys 93:2848–2854 Eriksson A, Deleniv A, Gevorgian S (2004) Two-Pole Tunable Bandpass Filter Based on YBCO Plated Single Crystal KTO Disk Resonators. IEEE Trans Appl. Supercond 14:1–6 Foster C M (1997) In: Ramesh R (Ed) Thin Film Ferroelectric Materials and Devices. Kluwer Acad Publ, Boston Frey M H et al. (1998) The Role of Interfaces on an Apparent Grain Size Effect on the Dielectric Properties for Ferroelectric Barium Titanate Ceramics. Ferroelectrics 206–207(1–4):337–53 Gevorgian S, Eriksson A, Deleniv A et al. (2002) The double loop hysteresis in DC dependent dielectric permittivity of SrTiO3. J Appl Phys 92:61656171 Guo X G, Chen X S, Sun Y L et al. (2003) Electronic band structure of Nb doped SrTiO3 from first principles calculation. Physics Letters A 317:501–506 Hagberg J et al. (2003) Printing with gravure methods in electronics. 14th European Microelectronics and Packaging Conference & Exhibition, Friedrichshafen, Germany, 23–25 June 2003 Herner S B et al. (1993) The effect of various dopants on the dielectric properties of barium strontium titanate. Mater Lett 15:317–324 Hobby A (1997) Printing Thick Film Hybrids. DEK Printing Machines Ltd Hu W et al. (2005) Cost Effective Ferroelectric Thick Film Phase Shifter Based on ScreenPrinting Technology. IEEE MTT-S: 591–594 International Technology Roadmap for Semiconductors (ITRS). 2005 Edition, Executive Summary Irissou E et al. (2006) Influence of an inert background gas bimetallic cross-beam pulsed laser deposition. J Appl Phys 99:034904 Izuhara T, Osgood R M Jr, Levy M et al. (2002) Low-loss crystal-ion-sliced single-crystal potassium tantalate films. Appl Phys Lett 80:1046–1048 Jackson C M et al. (1992) Novel monolithic phase shifter combiing ferroelectric and high temperature superconductors. Micr Optic Technol Letters 5:722–726 Jackson T J and Palmer S B (1994) Oxide superconductor and magnetic metal thin film deposition by pulsed laser ablation: a review. J Phys D: Appl Phys 27:1581–1594 Jantunen et al. (2004) Ferroelectric LTCC for multilayer devices. J Ceram Soc Jap 1305 [1129]:S1552–S1556 Johnson, K M (1962) Variation of dielectric constant with voltage in ferroelectrics and its application to parametric devices. J Appl Phys 33:2826 Kanareykin A et al. (2006) Fast Switching Ferroelectric Materials for Accelerator Applications. In: Conde M, Eyberger C (Ed) 12th Advanced Accelerator Concepts Workshop AIP Conference Proceedings 877:311–319 Keis V N et al. (1998) 20 GHz tunable filter based on ferroelectric (Ba,Sr)TiO, film varactors. Electronics Letters 34:1107–1109 Kim J-Y et al. (2004) Magnetically and electrically tunable devices using ferromagnetic/ferroelectric ceramics. Phys Stat Sol (b) 241:1714–1717 Kim KB, Yun TS, Lee JC et al. (2007) Integration of microwave phase shifter with BSTO varactor onto TiO2/Si wafer. Electronics Letters. doi:10.1049/el:2007 0448 Kim K-B et al. (2006) Integration of Coplanar (Ba,Sr)TiO3 Microwave Phase Shifters onto Si Wafers Using TiO2 Buffer Layers. IEEE Transactions Ultrasonics, Ferroelectrics, and Frequency Control 53:518–524 Kim S S et al. (2006) Dielectric properties of ferroelectric (Ba0.6Sr0.4)TiO3 thick films prepared by tape-casting, J Electroceram 17:451–454 Kim W J, Chang W, Qadri S B et al. (2000) Microwave properties of tetragonally distorted (Ba0.5Sr0.5)TiO3 thin films. Appl Phys Lett 76:1185

References

111

Kirlin P et al. (1995) MOCVD of BaSrTiO3 for ULSI DRAMS. Integrated Ferroelectrics 7:307 Kotecky D E et al. (1999) (Ba,Sr)TiO3 dielectrics for future stacked-capacitor DRAM. IBM J Res Develop 43:367–382 Kozyrev A B et al. (2001) Ferroelectric (Ba,Sr)TiO3 Thin-Film 60-GHz Phase Shifter. Technical Physics Letters 27: 1032–1034 Kozyrev A B et al. (2002) A Finline 60-GHz Phase Shifter Based on a (Ba,Sr)TiO3 Ferroelectric Thin Film. Technical Physics Letters 28:239–241 Kozyrev A et al. (2000) Application of ferroelectrics in phase shifter design. IEEE MTT-S 3:1355–1358 Kub F J, Hobart K D, Pond J M et al. (1999) Single-crystal ferroelectric microwave capacitor fabricated by separation by hydrogen implantation. Electron Lett 35:477–478 Kuylenstierna D et al. (2005) Ultrawideband tunable true-time delay lines using ferroelectric varactors. IEEE Trans. Microwave Theory Tech 53:2164–2170 Kuylenstierna D et al. (2006) Composite Right/Left Handed Transmission Line Phase Shifter using Ferroelectric Varactors. IEEE Microwave and Wireless Components Letters 16:16–169 Lederer D, Raskin J-P (2005) New Substrate assivation Method Dedicated to SOI Wafer Fabrication with Increased Stability of Resisitivity. IEEE Electron Device Lett 26:805–807 Lee Y S, Djukic, D, Roth R M et al. (2006) Fabrication of patterned single-crystal SrTiO3 thin films by ion slicing and anodic bonding. Appl Phys Lett 89:122902-1-122902-3 Licari J, Enlow L (1988) Hybrid Microcircuit Technology Handbook. Noyes Publications, New Jersey Mahmud A et al. (2006) A 1-GHz Active Phase Shifter with a Ferroelectric Varactor. IEEE Micr Wireless Comp Lett 16:261–263 MaTecK GmbH. http://mateck.de/index.asp.html. Accessed 13 August 2008 Miranda F A et al. (2008) BaxSr1–xTiO3 Thin Film Ferroelectric-Coupled Microstripline Phase Shifters with Reduced Device Hysteresis. J Am Ceram Soc 91:1864–1868 Mochizuki S, Fujishiro F, Shibata K et al. (2007) Optical, electrical, and X-ray-structural studies on Verneuil-grown SrTiO3 single crystal: Annealing study. Physica B 401–402:433–436 Moeckly B H and Zhang Y (2001) Strontium Titanate Thin Films for Tunable YBa2Cu3O7 Filters. IEEE Trans Appl Supercond 11:450–453 Moulson A J, Herbert J M (2003) Electroceramics Materials Properties Applications. John Wiley & Sons MTI Corporation. http://mtixtl.com/index.asp. Accessed 13 August 2008 Nabokin P I, Souptel D, Balbashov A M (2003) Floating zone growth of high-quality SrTiO3 single crystals. J Cryst Growth 250:397–404 Navuduri P, Abdel-Motaleb I M, Yoo Y-Z et al. (2006) Characterization of Large Area PLD Grown Combinatorial Compositions of Barium Strontium Titanium Oxides. International Conference on Solid-State and Integrated Circuit Technology, ICSICT 2006:1004–1006 Nenasheva N et al. (2003) Ceramics Materials Based on (Ba,Sr)TiO3 Solid Solutions for Tunable Microwave Devices. J Electrocer 13:235–238 Ong C K and Tan C Y (2005) Electrically tunable microwave devices with patterned ferroelectric thin film. US Patent Application 11/074, 417 Padmini P, et al. (1999) Realization of high tunability barium strontium titanate thin films by rf magnetron sputtering. Appl Phys Lett 75:3186 Petrov P, Carlsson E F, Larsson P et al. (1998) Improved SrTiO3 multilayers for microwave application: Growth and properties. J Appl Phys 84:3134 Powell R A, Rossnagel S M (1999) PVD for Microelectronics-Sputter Deposition Applied to Semiconductor Manufacturing. Academic Press Prusseit W, Boatner L A, Rytz D (1993) Epitaxial YBaxCu1–xO7 growth on KTaO3 (001) single crystals. Appl Phys Lett 63:3376–3378 Rundqvist P, Liljenfors T, Vorobiev A et al. (2006) The effect of SiO2, Pt and Pt/Au templates on microstructure and permittivity of Ba0:25Sr0:75TiO3 films. J Appl Phys 100:114116 Rytz D, Wechsler B A, Nelson C C et al. (1990) Top-seeded solution growth of BaTiO3, KNbO3, SrTiO3, Bi12TiO20 and La2-xBaxCuO4. J Cryst Growth 99:864–868

112

3 Fabrication of Ferroelectric Components and Devices

Sakai S, Takahashi M, Motohashi K et al. (2007) Large-area pulsed-laser deposition of dielectric and ferroelectric thin films. J Vac Sci Technol A 25:903–907 Samoilova T B et al. (2005) Microwave Up-Converter Based on a Nonlinear Ferroelectric Capacitor. Technical Physics 50:1335–1342 Scheel H (2000) Historical aspects of crystal growth technology. J Cryst Growth 211: 1–12 Scheele P et al. (2004) Phase-Shifting Coplanar Stubline-Filter on Ferroelectric-Thick Film Proc EuMC’2004:1501–1504 Scheele P et al. (2005) Continuously Tunable Impedance Matching Network Using Ferroelectric Varactors. IEEE MTT-S:603–605 Schreiter M et al. (2004) Electro-acoustic hysteresis behaviour of PZT thin film bulk acoustic resonators. Journal of the European Ceramic Society 24:1589–1592 Schwartz R W et al. (1999) Control of Microstructure and Orientation in Solution-Deposited BaTiO3 and SrTiO3 Thin Films, J Am Ceram Soc 82(9):2359–67 Semenov A A (2006) Ferrite-ferroelectric layered structures for electrically and magnetically tunable microwave resonators. Appl Phys Lett 88:033503 Semiconductor Wafer Inc. http://www.semiwafer.com/index.htm. Accessed 13 August 2008 Sherman V et al. (2001) Digital reflection type phase shifter based on a ferroelectric planar capacitor. IEEE Micr Wireless Comp Letters 11:407–409 Sigman J et al. (2008) Fabrication of Perovskite-Based High-Value Integrated Capacitors by Chemical Solution Deposition. J Am Ceram Soc 91:1851–1857 Spirito M et al. (2005) Surface Passivated Hig-resisitivity Silicon as a true Microwave Substrate. IEEE Trans. Microwave Theory Techn 53 (7):2340–2347 Stauf G T et al. (1999) BaSrTiO3 thin films for integrated high frequency capacitors. Proc 10th IEEE Int Symp Applications of Ferroelectrics 1:103–106 Su B et al. (2003) Dielectric and microwave properties of barium strontium titanate (BST) thick films on alumina substrates. J European Ceramic Society 23:2699–2703 Tageman O, Falk K, Hallbjörner P et al. (2003) Ferroelectric Beam Steering Plate. Proc of Workshop on Tunable Ferroelectric Materials and devices for Microwave Applications, EuMC2003 Tan C Y and Ong C K (2006) Planar tunable HTS microwave filter with patterned ferroelectric thin film Supercond. Sci Technol 19:1–5 Teo P T et al. (2000) Design and Development of Tunable Multi-Layer Smart Antennas Using Ferroelectric Materials. J Intelligent Material Systems and Structures 2000 11:294–299 Tombak A et al. (2003) Voltage-Controlled RF Filters Employing Thin-Film Barium-StrontiumTitanate Tunable Capacitors. IEEE Trans Microwave Theory and Tech 51:462–576 Ustinov A B et al. (2006) Electric field tunable ferrite-ferroelectric hybrid wave microwave resonators: Experiment and theory. J Appl Phys 100:093905 Varadan et al. (1992) Ceramic Phase Shifters for Electronically Steerable Antenna Systems. Microwave Journal 34:116–125 Varatharajan R, Madeswaran S, Jayavel R (2001) Nb:BST: Crystal growth andferroelectric properties. J Cryst Growth 225:484–488 Vinoy K J et al. (1999) Gain Enhanced Electronically Tunable Microstrip Patch Antenna. Microwave and Optical Technology Letters 23:368–370 Vorobiev A, Berge J, Gevorgian S (2007) Thin film Ba0.25Sr0.75TiO3 voltage tuneable capacitors on fused silica substrates for applications in microwave microelectronics. Thin Solid Films 515:6606–6610 Vorobiev A, Gevorgian S (2007) Large area BaxSr1–xTiO3 thin films grown by magnetron sputtering. MRS Fall Meeting 2007, Boston Vorobiev A, Gevorgian S (2008) Development of processes for heterogeneous integration of ferroelectric films and devices in microwave systems. Electroceramics XI, Manchester, 31st August – 3rd September 2008 Vorobiev A, Rundqvist P, Khamchane K et al. (2003) Microwave properties of SrTiO3/ SrRuO3/CeO2/YSZ heterostructure on low-resistivity silicon. J Eur Cer Soc 23(14):2711 Wang P et al. (2007) Planar tunable high-temperature superconductor microwave broadband phase shifter with patterned ferroelectric thin film. Supercond Sci Technol 20:77–80

References

113

Waser R (2005) Nanoelectronics and information technology: advanced electronic materials and novel devices. Wiley-WCH, Weinheim Waser R et al. (2001) Advanced chemical deposition techniques-from research to production. Integrated Ferroelectrics 36:3 Xu H (2005) MMICs using GaN HEMTs and Thin-Film BST Capacitors, PhD thesis, University of California, Santa Barbara Yan L et al. (2004) Ba0.1Sr0.9TiO3–BaTi4O9 composite thin films with improved microwave dielectric properties. Eur Phys J B 41:201–205 Yeo K S K et al. (2004) High Frequency Thick Film BST Ferroelectric Phase Shifter. Integrated Ferroelectrics 61:65–70 Yeo K S K et al. (2004) Thick Film Ferroelectric Phase Shifters using Screen Printing Technology. Proc EuMC’2004:1489–1492 York B (2008) Tunable Dielectrics for RF Circuits. In: Steer M (Ed) Multifunctional Adaptive Microwave Circuits and Systems. Scitech, Raleigh York R A et al. (2000) Microwave integrated circuits using thin-film BST. Proc 12th Intl Symp on Applications of Ferroelectrics (ISAF) 1:195 York, B et al. (2000) Thin-Film Ferroelectrics: Deposition Methods and Applications, presented at Workshop Ferroelectric materials and their applications Int. Microwave Symposium IMS’2000 Yoshimura J, Sakamoto T, Usui S et al. (1998) X-ray perfection study of Verneuil-grown SrTiO3 crystals. J Cryst Growth 191: 483–491 Zimmermann F et al. (2004) Ba0.6Sr0.4TiO3 and BaZr0.3Ti0.7O3 thick films as tunable microwave dielectrics. J European Ceramic Society 24:1729–1733 Zinck C et al. (2004) Design, Integration and Characterization of PZT tunable FBAR. IEEE International Ultrasonics, Ferroelectrics, and Frequency Control Joint 50th Anniversary Conference: 29–32

Chapter 4

Substrates, Varactors and Passive Components Spartak Gevorgian and Andrei Vorobiev

Abstract This chapter looks at basic designs of ferroelectric varactors. Thin film and thick film varactors with coplanar-plate and parallel-plate electrodes on different substrates are considered. The dielectric properties of high resistivity silicon are addressed having in mind the heterogeneous integration possibilities. Special sections are devoted to the aspects of optimization, equivalent circuit models, I-V, C-V, tuning speed and microwave performances. The last sections look at varactors with increased power handling capability and applications of ferroelectrics as non-tunable high permittivity dielectrics in high density capacitors, MEMs and field effect transistors.

4.1 Introduction Varactors are one of the basic components used in agile microwave devices. The overall performance of these devices largely depends on the parameters of the used varactors. This chapter looks at the complex materials and design issues that define the performances of the ferroelectric varactors. The selection of the right substrate is important not only from the varactor performance standpoint but also from the integration possibility. In this respect the high resistivity silicon is regarded as one of the most promising since it allows cost effective heterogeneous integration of ferroelectric components with the other high performance microwave components, MEMs etc. All aspects of the optimization of parallel-plate and coplanar-plate varactors are considered taking into account the microstructure of the ferroelectric films. The considerations of the complex impedance using physics based equivalent circuit parameters allow identification of the parameters that impact the overall performance of the varactors. The chapter briefly reviews the tuning and microwave performances of some of the reported varactors. Special sections are devoted to the varactors with increased power handling capability and capacitive components using ferroelectrics as high dielectric materials. 115

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4.2 Substrates 4.2.1 Common Substrates The substrate materials considered for tunable ferroelectric devices include metal (e.g. Pt as bottom electrode), glass (Acikel et al. 2001), ceramics (e.g. alumina) (Delpat et al. 2003), semiconductors (Si, GaAs) (Abadei et al. 2002), (Erker et al. 2000), single crystal dielectrics MgO (Kirchoefer et al. 1998), Al2O3 (sapphire) (Acikel et al. 2001), LaAlO3 (Van Keuls et al. 1997) etc. Gennum (Koutsaroff et al. 2002) compared BST MOD film on SiO2/Si(111), r-plane sapphire, polycrystalline alumina Al2O3 (99.6%), zirconia/yttria stabilized alumina (ZYSA) and glazed polycrystalline alumina substrates. The BST films of the same thickness and under the same processing conditions exhibit different properties. They possess higher capacitance on all types of alumina-based substrates compared to those on SiO2/Si substrates. In these experiments the higher capacitance on alumina is always associated with larger losses, and lower or similar leakage current densities. The lowest achieved leakage current density of Pt/BST/Pt capacitor (500 × 500 µm2) on glazed alumina is 2.8 × 10–9 A/cm2 at 200 kV/cm with capacitance per unit area of 27 fF/µm2. Single crystal substrates (MgO, LaAlO3, Sapphire etc.) have been extensively considered for fabrication of tunable ferroelectric devices, since they allow epitaxial growth of ferroelectric films such as SrTiO3 and BaxSr1–xTiO3. The good crystalline quality of the ferroelectric films is the main advantages of the single crystal substrates (e.g. MgO, LaAlO3, Al2O3) used in tunable ferroelectric devices. However, they are not cost effective to use, partly due to the small sizes and cost of the available crystalline wafers. On the other hand, largescale applications of the ferroelectric components and devices depend on the integration possibilities of microwave ferroelectric components with semiconductors (fabrication processes). In this respect the ferroelectrics are not new in silicon technology. Considerable efforts have been concentrated on the development of CMOS based memory cells for dynamic random access memory (DRAM) and nonvolatile memory (FRAM) applications, where ferroelectric capacitors are integrated with MOS transistors. In DRAM memory cells the ferroelectrics, preferably in paraelectric, non-polar phase, are used as high permittivity dielectrics in passive capacitors, while in nonvolatile memory FRAM cells the two opposite polarization states in the hysteresis loop of the polar (ferroelectric) phase are used to utilize “0” and “1” memory states. Most of the material problems associated with the integration ferroelectrics with standard silicon processes are solved. In addition, there is considerable progress in developing CMOS based MMICs. Thus, there seems to be no major problems in the development of SiMMICs integrating ferroelectric films, where some useful features of ferroelectrics are utilized. However, this requires a substantial investment which, at least at present, is not justified due to the relatively small market of the CMOS MMICs. In this respect the heterogeneous integration of ferroelectrics with other microwave devices on a common carrier/substrate seems to be more attractive.

4.2 Substrates

117

1 MgO

0,9

LaAlO3 Sapphire

0,8

Quartz 0,7

HR Si Glass

0,6

Alumina

0,5 0,4 0,3 0,2 0,1

A lu m in a

G la ss

Si H R

Q ua rtz

La A lO 3 Sa pp hi re

M gO

0

Fig. 4.2.1 Relative cost of the substrates

The substrates should withstand high temperatures used in the growth of the ferroelectric films. The relative cost of the commonly used substrates suitable for ferroelectric devices is shown in Fig. 4.2.1. The main dielectric properties of the substrates are show in Table 4.2.1. For commercial applications low cost substrates as sapphire, quartz, high resistivity (HR) silicon, glass and alumina are preferable. The simple soda-lime glass is not suitable in this case since its softening at temperatures is close to the temperature of deposition (>600°C) of good quality (textured/polycrystalline) ferroelectric films. For these applications the fused silica with its high softening/melting temperature (>1000°C) is preferable and its microwave losses are extremely small. This substrate is also more suitable for devices based on ferroelectric varactors (especially coplanar-plate), where the shunt capacitance in parallel with ferroelectric varactor is low in comparison with the other higher permittivity substrates. Fused quartz and fused silica types of glasses contain primarily silica in amorphous (non-crystalline) form. Fused quartz is made by melting high-purity naturally occurring quartz crystal at around 2000°C using either an electrically heated furnace (electrically fused) or a gas/oxygen-fueled furnace (flame fused). They are normally transparent. The naturally occurring form of fused quartz is known as Metaquartzite and is formed under metamorphic conditions. Due to increased heat the crystals within the quartz become fused together. Fused silica is produced using high purity silica sand as the feedstock. It is normally melted using an electric furnace, resulting in a material that is translucent or opaque due to very small air bubbles trapped within the material. Alumina or aluminum oxide (Al2O3) in its pure form is a white, high hardness ceramic. Fully dense alumina can be translucent. Alumina has found wide application due to its versatility and a relatively low raw material cost. Depending on the purity and density, alumina is widely used for dielectric substrates. Alumina’s main drawback is its relatively poor thermal shock resistance due to its higher coefficients of thermal expansion and lower thermal conductivity compared to other

118

4 Substrates, Varactors and Passive Components

pure ceramic materials. The high grade alumina substrate has good dielectric features. This substrate is also available as processed substrate, having via-halls and/or grooves. It may have excellent surface roughness, high bending strength. Substrates in thickness as thin as 0.1 mm are commercially available. They are used both for thin film and thick film ferroelectrics. Table 4.2.1 Main substrate materials used in ferroelectric devices Substrate LaAlO3 MgO

Permittivity 24@295°K (18–35 GHz) 9.8

Loss tangent –4

3⋅10 @ 300 K –3

9⋅10 @10.0 GHz

Structure

CTE⋅106

Single crystal

10@25C

Single crystal

8.0@ 100C

–5

Fused Silica (SiO2)

[email protected] MHz 3.82 @ 24 GHz

1.5⋅10 @1.0Mz Amorphous 3.3⋅10–4 @24 GHz

0.55@ (20–320) C

Sapphire (Al2O3)

11.5/[email protected] MHz

8.6⋅10–4/3⋅10–4 (@1.0 MHz)

Single crystal

5.3 @25C

9.9 @1.0 MHz Alumina (Al2O3, 99.6%)

10–[email protected] GHz

Poly-crystalline 8.1@ (25–600) C

Silicon

( ωρ o ε o ε L ) −1

Single crystal

11.7(ρο>1.0 Ohm cm

2.6@25C

4.2.2 Silicon as a Microwave Substrate High resistivity silicon is a cost effective and potentially low loss material for application as substrate for microstrip and coplanar circuits, especially at millimeter wave frequencies. As substrate material in microwave integrated circuits (IC) it has several advantages in comparison with the other dielectrics. It allows low loss monolithic integration of both active (i.e. transistors) and passive (i.e. inductor coils) microwave components in SiMMICs (RFICs). The HR silicon may be used for hybrid integration, in the form of multichip modules (MCM), of a number of emerging microwave components, yet not compatible with the standard silicon (foundry) processes such as TFBARs, MEMs, micromachined cavities, antennas, tunable ferroelectric components etc. Additionally, it reduces (eliminates) thermal expansion mismatch problems when it comes to flip-chipping of silicon IC chips on silicon MCM substrates. The first attempts to use the low resistivity (Czochralski) silicon as a substrate for microwave IC dates back to early 1960s (Guckel et al. 1967). In ordinary dielectrics the microwave losses are associated only with phonon processes. In silicon the phonon related losses are negligible in comparison to the losses associated with the free charge carrier absorption. Due to extremely high microwave losses in microstrip lines the early attempts to use low resistivity silicon have not been successful. Using compensated high resistivity (Czochralski) silicon was not successful either. Upon thermal treatments, used in IC fabrication processes, the compensated silicon drastically reduces its resistivity and may change the type of the conductivity.

4.2 Substrates

119

The availability of the high resistivity (nearly intrinsic) float zone silicon makes it possible to reconsidered silicon as a substrate for microwave circuits. However, recent experiments show that the microwave losses in passive components, such as transmission lines and inductor coils, are much higher than one expects from the high resistivity of silicon. For example, in microwave measurements, a wafer with resistivity 10 kOhm cm may appear as having resistivity slightly higher than 1 kOhm cm (Deleniv et al. 2003). Additionally, the device parameters (e.g. losses, capacitance) depend on DC bias which, in some cases, is not desirable (as a parasitic tuning), and changing the DC bias in one component affects the DC bias in other components on the common HR silicon substrate. Furthermore, the nonlinearities (i.e. harmonic generation (Kerr et al. 2008) are rather high as compared with dielectric substrates. It is now well established that high conductivity accumulation an inversion surface layers build up at the SiO2/Si interface as a result of charged defects (most probably oxygen vacancies) in SiO2 or/and at the SiO2/Si interface. Since bulk losses are negligible, losses associated with surface accumulation or inversion layers become dominant. Due to the high resistivity the surface space charge (depletion) layers are wider and sensitive to the electric fields. The electrical isolation of integrated devices becomes difficult due to the wider spacecharge regions associated with the very light doping level of the HR Si. Fortunately the negative effects associated with the surface conductivity of silicon may be practically eliminated as it is shown below.

4.2.3 High Resistivity Silicon 4.2.3.1 Dielectric Properties In contrast to the dielectric substrates the complex permittivity of semiconductor silicon also depends on its conductivity (i.e. density of the free charge carriers). ρo Above Maxwell (dielectric) relaxation frequency ( f dr = ) the real and 2πε oε L imaginary parts of permittivity and the loss tangent may be presented as:

ε′ = εL , ε" =

(4.2.1)

1

(4.2.2)

ε o ρ oω

tan δ =

1

ωρ oε oε L ,

(4.2.3)

where εo=8.85·10–12 F/m is the dielectric constant of vacuum, εL=11.7 is the lattice dielectric constant, ω=2πf is the circular frequency, ρo is the static (DC) resistivity (=1/σo). The dependences of the real, ε’=Re(ε), and imaginary, ε’’=Im(ε), parts of the permittivity are shown in Fig. 4.2.2 (a) (Gevorgian 1998).

120

4 Substrates, Varactors and Passive Components

20

10 5 5

ε''(ρo\)@1.0GHz

1000

-10 10

-20 -30 -40

0.1

ε''(ρo\)@100.0GHz

1000

1

0.001 0.1

10

0.1

-50 0.0001 0.001 0.01

100

1

10

Good dielectric

fr

Lossy "metal" with negative permittivty

0

10 4

Frequency, GHz

ε'('ρo)

Imaginary part of prmittivity, ε''

Real part of permittivity, ε'

10

10

fr

f

dr

Lossy dielectric

0.01

100

0.0001 0.001 0.01

DC resisitivity (ρo), Ohm m

0.1

1

10

100

DC resisitivity (ρo ),O hm m

(a)

(b)

Fig. 4.2.2 Imaginary and real parts of the dielectric constant vs. DC resistivity (a) and frequency-resistivity (λ) chart for an n-type silicon (b). Reprinted with permission from Wiley©1998

The real part of the permittivity is independent of resistivity above 1.0 Ohm cm, including CMOS grade silicon. It decreases with decreasing resistivity, and even becomes negative below resistivity ρ + = ( 2πfτ ε o ε L ) − 1 , where silicon may be regarded as a lossy metal. fτ is the scattering frequency (=1/2πτ, τ is the scattering time). 1000 106

ρo =1.0 O hm m

10

100

10 Loss tangent

Loss tangent, ε''/ε'

100 4

f=1.0GHz 10.0

1

0.01

10.0 Ohm m

1 0.1

100.0 O hm m

0.01

100.0

0.001

0.0001

0.0001

0.00010.001 0.01

0.1

1

DC resisitivity (ρo), Ohm m

(a)

10

100

1

10

100

Frequency, GHz

(b)

Fig. 4.2.3 DC (static) resistivity (a) and frequency (b) dependencies of microwave losses. Reprinted with permission from Wiley©1998

In fact, the low resistivity (ρ<0.2 Ohm cm) silicon is used as a (lossy) ground plane in low frequency and digital ICs. A rather good application assessment of silicon as a lossy ground plane, lossy or good dielectric substrate may be done using the frequency-resistivity chart presented in Fig. 4.2.2 (b). A similar chart may

4.2 Substrates

121

be generated for a p-type silicon. In the dashed area, above ρ + = ( 2πfτ ε o ε L ) − 1 and below about 200 GHz silicon may be regarded as a lossy substrate with loss tangent inverse proportional to resistivity and frequency (Fig. 4.2.3) as it follows from (4.2.3). At THz and infrared frequencies silicon is a good, transparent dielectric with extremely low losses regardless its resistivity. The theoretical frequency dependence of tanδ is shown in Fig. 4.2.3 are rather correct and useful for bulk silicon with uniform distribution of free charge carriers. In reality, the measured loss tangent is substantially larger then one expects from the bulk resistivity. Figure 4.2.4. shows measured frequency dependence of the loss tangent of a n-type silicon with bulk resistivity 5 kOhm cm. It fits well with the theoretical prediction ω–1 (4.2.3). However, due to the high surface conductivity the measured effective resistivity is only 1.0 kOhm cm, i.e. 5 times lower than the bulk resistivity 5 kOhm cm. In contrast to low resistivity, for high resistivity silicon (i.e. float zone silicon), the flat-band potential is very low and the difference between the bias voltages required for accumulation and inversion conditions is rather small. The charged defects at Si/SiO2 interface and/or in the bulk of SiO2 attract mobile charge carriers in the silicon inducing highly conductive layers. Oxygen vacancies in ferroelectric films may induce similar layers. In the case of p-type silicon these positive charges induce inversion, and in the case of n-type silicon accumulated layers with conductivity much larger than the conductivity in the bulk of substrate. For this reason the measured microwave resistivity, Fig. 4.2.4, is smaller. Additionally, in HR silicon the thickness and the conductivity of these interfacial (accumulation, inversion, depletion) layers are large and DC bias dependent, which causes undesirable “substrate coupling” between the components.

Effective loss tangent, tanδ

0,1 0,08 0,06 0,04 M easured 0,02 M odelled 0 0

5

10 15 20 25 Frequency, G Hz

30

35

Fig. 4.2.4 Measured and modeled using (4.2.3) loss tangent. Reprinted with permission from EuMA©2003

Different methods are proposed to “passivate” and reduce the negative impact of the low resistivity surface layers. If not passivated the MOS capacitance is connected in parallel with the capacitance of the ferroelectric varactor causing extra

122

4 Substrates, Varactors and Passive Components

microwave losses. Additionally, it distorts the C-V dependence of the ferroelectric varactor. In some cases, where the parasitic shunt MOS capacitance dominates it may lead to (especially for coplanar-plate varactors) enhanced tuneability at low frequency, i.e. the parasitic MOS capacitance “screens” the main ferroelectric varactor. Removing (etching) silicon in the slot in coplanar and coplanar strip waveguides and in spiral inductors, Fig. 4.2.5, is considered to reduce the microwave losses. This method can not be used for effective elimination of the parasitic substrate couplings. A more effective way to use additional surface layers with high density of recombination centers are considered in the next section.

(a)

(b)

Fig. 4.2.5 Surface micromachined CPW (a) and CPS (b)

4.2.3.2 Surface Passivation Passivation Methods The problems of the surface passivation and DC isolation of the components are successfully solved in standard low resistivity silicon industry (Martin et al. 2001, Voz et al. 2003). For obvious reasons the methods of the traditional DC isolation do not work for isolation of the microwave components. The traditional surface passivation is accomplished by covering the surface of the semiconductor with dielectric layers such that they protect the surface (devices) from the harmful effects of the environment, and at the same time keep the surface (interface) recombination velocity low. Note that the term passivation has an opposite meaning when it comes to photodetectors and optically controlled microwave devices. In this case the passivation is intended to reduce the surface recombination velocity allowing for high density of photogenerated carriers. At present several methods are demonstrated to reduce or eliminate the negative effects in HR silicon substrate microwave devices associated with the charged defects in SiO2 and/or at SiO2/Si interfaces (Fig. 4.2.6). Making trenches between the components (strips) by surface micromachining of the silicon (Fig. 4.2.5) somehow helps to reduce microwave losses in coplanar microwave devices (i.e. CPW), however in many cases the micromachining is not a part of the standard fabrication processes and perhaps may not be applicable in all circuit topologies and processes including planarization steps. More efficient passivation is achieved by introducing high density recombination centers in the bandgap at the surface of silicon. High trap density may be achieved by a high-dose implantation using a neutral impurity, such as argon (Spirito et al. 2005). Ar ion implantation assisted amorphization of the Si surface is also reported (Spirito et al. 2005). It has been shown that the re-crystallization, by rapid thermal annealing (RTA), of the depos-

4.2 Substrates

123

ited at the low temperature (525oC) amorphous silicon layers result in passivation layers smoother and higher stability of the resistivity (Lederer and Raskin 2005). The traps in deposited or damaged surface layers (Fig. 4.2.6 (b)) cause high recombination rate preventing formation of accumulation, depletion, and inversion layers, hence reducing the associated negative effects-extra microwave losses and parasitic couplings. The passivation technique is somehow similar to SI GaAs, where the density of the surface recombination centers is many orders of magnitude larger as compared to Si, which prevents generation of accumulation and inversion layers. It seems the first time this technique was used by Fusco and co-workers (Fusco 2000). One expects the negative effects of surface conductivity (accumulation/inversion) to be even more severe in the case of ferroelectric films on top of SiO2. In this case the positive charge of oxygen vacancies in ferroelectric film will add-up with those in the SiO2. This may require thicker polysilicon layers in comparison with the Si passivation with only SiO2 films. Simplified Model of Passivation MOS structure before passivation (Fig. 4.2.6 (a)): In the surface layer of silicon the space charges may be induced by an external DC field or/and by the difference in work functions between metal and silicon. However, any charges in SiO2 (eventually in the ferroelectric film on top of it) and SiO2/Si interfaces may also cause space charge layers in silicon. Perhaps there are both negative and positive charges in SiO2 (eventually in the ferroelectric film on top of it) and SiO2/Si interfaces. Some of them are fixed; some of them are mobile, although the mobility and the density of the mobile charges are very low. They do not make a substantial contribution in the DC leakage current; however, they may cause relaxation effects and extra microwave losses. The experiments show that the net charge in SiO2 and SiO2/Si interfaces is positive. They attract electrons and repel holes in silicon causing inversion or accumulation depending on the type of conductivity. In a simplified qualitative analysis the positive charges in SiO2 and SiO2/Si interface may be regarded as a net charge Qo (Fig. 4.2.6 (b)) sheet located at the SiO2/Si interface. The attracted by these positive charges electrons form an inversion layer, i.e. decrease the surface resistivity of silicon and according to (4.2.3) increase the microwave losses. MOS structure after passivation (Fig. 4.2.6 (c) and (d)): Amorphous, polysilicon or Ar implanted layers are used for passivation. The defects in these layers introduce extra trap and recombination levels in the bandgap of silicon. Electrons, from the conduction, and holes, from the valence bands, are trapped and recombined at the recombination centers. The density of the recombination centers is high and their capture cross section (recombination velocity) is large resulting in negligible densities of free charge carriers (Fig. 4.2.6 (d)). A comparison of different passivation methods is given in (Norling et al. 2007). Figure 4.2.7 shows the frequency dependent losses in a CPW on SiO2/Si substrate before and after passivation (Kuylenstierna et al. 2007). The microwave losses are

124

4 Substrates, Varactors and Passive Components

Metal

Metal

SiOx

SiOx

Passivation layer

HR p-Si

HR p-Si

(a)

(c)

ρ(x) Qo

ρ(x) Qmetal

(Wi+Wm) x

−d

-d

Oxyde

0 Wi

Poly-Si

Qmetal

-qNA -Qn

0

x

-Qs

(b

(d)

Fig. 4.2.6 p-Si MIS structures without (a) and with (c) passivation layers and the corresponding charge distributions (b, d)

0

-1

Loss [dB/cm]

Loss [dB/cm]

0

-20 V -2 -3

-1

+ 20 V -20 V

-2 -3

+ 20 V -4

5

10

15

Freq. [GHz] (a)

20

25

-4

5

10

15

20

25

Freq. [GHz] (b)

Fig. 4.2.7 Frequency dependent losses in CPW on SiO2/Si substrate before (a) and after (b) passivation. Reprinted with permission from IEEE©2007

4.3 Varactors. Basic Designs and Figure of Merit

125

substantially reduced and the DC bias dependence is practically eliminated, i.e. silicon acts as a good “dielectric” substrate. The experiments show that the passivation remains effective even after deposition of the BSTO layers. The effective permittivity and microwave losses of the CPW on passivated samples are practically bias independent at all microwave frequencies (Fig. 4.2.7) indicating that no charged inversion layers are available at any bias voltage. It is shown (Kerr et al. 2008) that the passivation results in a substantial reduction of nonlinearities of high resistivity silicon.

4.3 Varactors. Basic Designs and Figure of Merit 4.3.1 Basic Designs of Ferroelectric Varactors Ferroelectric varactors used in tunable microwave devices have two basic designs: parallel-plate (Fig. 4.3.1 (a)) and coplanar-plate (Fig. 4.3.1 (b)). In both designs the tuning (change in capacitance) is achieved by applying DC voltage to the plates which causes a reduction of the permittivity, ε, of the ferroelectric film and hence the capacitance, provided that it has single crystal or polycrystalline structure. In microwave devices the ferroelectric varactors are used as lumped element components where the sizes of the varactors are much smaller than the wavelength of the microwave signal in the ferroelectric (λg =λo/√(ε), where λo is the wavelength in the free space), and as distributed varactor structures. In the latter case the sizes of the ferroelectric components are comparable (as in a resonators) or much larger (as in delay lines) then the wavelength λg. The coplanar-plate design is more suitable in these applications since the impedance of the lines sections with ferroelectric films may be tailored by changing the slot width between the electrodes. This is in contrast to MEM and semiconductor varactors. The designs of the MEM varactors simply do not allow their implementation as distributed elements, at least at microwave frequencies. The semiconductor varactors in principle may be implemented as distributed elements, for example in the form of coplanar waveguides. However, due to the high leakage currents their application may be extremely limited. On the other hand distributed circuit implementation of the ferroelectric varactors in the form of delay line type CPW phase shifters is one of the most popular implementation reported in the literature. They are considered in Chap. 5. In parallel-plate varactors the maximum tuneability of the capacitance, TC ( E ) =

C ( 0) − C ( E ) , C ( 0)

(4.3.1)

practically is the same as the tuneability of the permittivity (2.5.6). The parallelplate varactors based on the thicker ferroelectric films require higher tuning DC voltages and have better power handling capability. The thickness of the films

126

4 Substrates, Varactors and Passive Components

may be tailored to have low tuning voltages-compatible with CMOS technology, i.e. below 3–5 V. The ferroelectric films in these varactors are fabricated using thin film processes (laser ablation, RF Magnetron sputtering etc., see Chap. 3). The maximum thickness of the films fabricated using thin film technologies may be in the range of 0.05–1.5 μm with the required tuning voltages in the range of 3–100 V. The thicker films are fabricated using thick film technologies. In some circuit implementations two parallel-plate varactors may be cascaded as shown in Fig. 4.3.1 (c). In this case the common bottom electrode may be used to apply the DC voltage, for example in balanced circuits (Aspemyr et al. 2007), where the circuit has an RF virtual ground coinciding with the common bottom electrode (Fig. 4.3.1 (e)). Alternatively it may be “floating” if the floating is not prohibited by the circuit (i.e. noise associated with uncontrollable charge accumulation). The main performance advantage of this design is its symmetric C-V and I-V dependences (provided the structure is symmetric) regardless the potential barrier heights at the bottom and top electrodes.

Ferroelectric

(a)

(b) Ferroelectric

(c)

(d)

-VDC +VDC

+VDC

Virtual RF ground

(e)

(f)

Fig. 4.3.1 Cross-sectional view of parallel-plate (a, c) and coplanar-plate (b, d, f) varactors

The coplanar-plate varactors have relatively simple design and fabrication (single mask) process. In these varactors, typically, the plates are on top of the ferroelectric films (Fig. 4.3.1 (b)). In contrast to parallel-plate varactors, the field (both DC and RF) is of fringing nature. Its confinement in the ferroelectric film is small. In most of the cases the non-tunable partial capacitances associated with the fring-

4.3 Varactors. Basic Designs and Figure of Merit

127

ing field in the substrate, Csub, and air, Cair, are substantial. They are in parallel with the capacitance associated with the ferroelectric film. This “screening” results in capacitance tuneability smaller than the tuneability if the permittivity of ferroelectric film, i.e. Tc(E)
C f ( 0) − C f ( E ) C f (0) + C sub + C air

,

(4.3.2)

In parallel-plate varactors the effect of the similar non-tunable parasitic capacitances is considerably smaller since the main capacitance is typically larger. To increase the field confinement in the ferroelectric film the plates are partially (Fig. 4.3.1 (d)) or completely buried in the ferroelectric film. This somehow helps to increase the field confinement. For further increase in the field confinement, hence the capacitance and tuneability, the ferroelectric film has to be quite thick and/or the slot between the electrodes has to be as small as possible. Thicker (>2.0 μm) films are made using LTCC or HTCC processes. However, fabrication of the small gaps (slots) between the electrodes is limited. To achieve higher capacitances for applications at lower microwave frequencies the length of the slot between the electrodes is increased and it is meandered to keep the sizes of the varactor smaller (Fig. 4.3.2 (b)). In this interdigital design, a slight increase of the field confinement is possible due to extensive fringing at the ends of fingers. However the parasitic inductance associated with the long fingers reduce the self resonant frequency of the varactor (Kirchoefer et al. 1998). At higher microwave and millimeter wave frequencies the required in circuits capacitances are smaller, typically tens of fF. These values are achievable using interdigital plates with very short fingers. The short fingers allow reduction of the parasitic inductances and shifting the self resonant frequencies up. At the same time it maintains higher fringing fields confined in the ferroelectric film. This types of varactors with the narrow (<1.0 μm) slots fabricated by nanolithography demonstrated by Velu et al. (2007) allow increasing the field confinement/tuneability and reduce the tuning voltage. Typical designs of experimental ferroelectric varactors are shown in Fig. 4.3.2. For a given film quality (tuneability of permittivity and loss tangent) the ferroelectric varactors may be designed allowing trading the low tuning against higher Q-factor. In the case of parallel-plate varactor, at least in theory, very thin dielectric spacers (buffer layers) between the plates and ferroelectric film substantially decrease the effective permittivity and tuneability. At the same time the Q-factor may be substantially increased due to layered composite and also due to reducing current density in the plates. The same effect may also be achieved in coplanarplate varactors. However, the dielectric spacers drastically increase the required tuning voltages and this method is hardly acceptable. The tuneability vs. Q-factor trade-off is relatively easy for coplanar-plate varactors by simply changing the slot width between the plates.

4 Substrates, Varactors and Passive Components

Electrode

(b)

Electrode

l

2g

(a)

(c)

2g

128

Electrode w

2s

Electrode

Fig. 4.3.2 Microphotos of typical parallel-plate (a) and coplanar-plate (b, c) varactors

4.3.2 Figure of Merit, Structure and Performance of Ferroelectric Films The number of parameters used to characterize the quality of the ferroelectric films depends on applications. The tuneability of permittivity (2.5.6) and loss tangent are main parameters regardless the application. A useful figure of merit (commutation quality) to characterize ferroelectric material was introduced by Vendik et al. (2000) which takes into account the DC field induced changes both in permittivity and loss tangent, and may be represented as: Kε ( E ) =

[ε (0) − ε ( E )]2

ε (0)ε ( E ) tan δ (0) tan δ ( E )

(4.3.3)

ε ( 0) Tε2 ( E ) = ε ( E ) tan δ (0) tan δ ( E )

where Tε(E) is the tuneability of the permittivity as defined above (2.5.6), tanδ(0) and tanδ(E) are the loss tangents of the ferroelectric with and without DC bias. Sometimes the ratio ε(0)/ε(E) is regarded as fractional tuning (nr). Notice that this figure of merit characterizes the material itself regardless the design of the ferroelectric varactors and devices. It helps to estimate the usefulness of the ferroelectric material for varactor and other microwave device applications. Materials should have as high as possible figure of merit, Kε(E), typically >1000. The performance of the ferroelectric varactors depends on the figure of merit of the used films and on the design of the varactor itself. It is worth to mention once more that (4.3.3) characterizes the ferroelectric material itself, regardless the design of the varactor it is used for. In general, a figure of merit similar to (4.3.3) may be used for the varactors, including the losses in the plates: KC (E) =

TC2 ( E ) C ( 0) C ( E ) tan δ C (0) tan δ C ( E )

(4.3.4)

4.3 Varactors. Basic Designs and Figure of Merit

129

In this figure of merit both the losses in the ferroelectric, tanδ(E), and in the plates, tanδσ(E), are included: tan δ C ( E ) = tan δ ( E ) + tan δ σ ( E )

(4.3.5)

The loss tangent of the ferroelectric is defined in Sect. 2.5.1, while tanδσ (E) is the loss tangent associated with the plates (equivalent resistance rm) and it depends on their shape, the used metal and their thickness: tanδσ (E)=ω rmC(E). The cut-off frequency, fc= [1/C(E)–1/C(0)]/2πr (r is series loss resistance), is another figure of merit often used for semiconductor varactors (Dillner et al. 1998). It may be represented as: fc = f

C (0) TC ( E ) C ( E ) tan δ C (0)

(4.3.6)

The relationship between fc and figure of merit (4.3.2) is: KC (E) =

f c TC ( E ) f tan δ ( E )

(4.3.7)

4.3.3 Correlation of the Design with the Film Structure 4.3.3.1 Granular and Columnar Structures The figure of merit depends not only on the chemical composition and stoichiometry (i.e. x in BaxSr1–xTiO3) but also on its fabrication method and crystalline structure. As it is indicated in Chap. 2 the ferroelectric used in microwave devices may be in the form of single crystals (bulk, epitaxial) and ceramics (bulk, thin film, LTCC, HTCC). The films epitaxially grown on well oriented crystalline substrates (LaAlO3, MgO etc.) have, in general, strained single crystal structure (textured or large grains). The films grown on polycrystalline (alumina, Au, Pt, etc.) have granular or columnar structure depredating on the growth conditions. The microphotos of typical ceramics are shown in Fig. 4.3.3. AO

Au

l Ba0.5SriO3

Ba0.3Sr0.7TiO3 3µm 10 μ m

(a)

Al2O3

E Pt

(b)

0.1µm

(c)

Fig. 4.3.3 Micro-structure of bulk ceramics (a), granular (b) and columnar (c) films

130

4 Substrates, Varactors and Passive Components

The cores of the grains typically have the same crystal structure as the bulk single crystal counterparts and, in principle, should have similar dielectric and acoustic properties. For example, the core of a grain in ceramic (bulk and film) BaTiO3 should have the same tuneability and losses as its bulk single crystal counterpart. This was proven in the experiments with 70 nm thick bulk single crystal considered in (Morrison et al. 2005). The most drastic effect on the overall performance of the ferroelectric ceramics is associated with the grain boundaries and misfit strains. The grain boundaries are responsible for the higher (than bulk single crystal counterparts) losses, lower permittivity and tuneability, high leakage current, reduced reliability etc. In fact the mixture of the grain cores and grain boundaries behaves as a composite ceramic and the models available for the dielectric properties of the composite ceramics are applicable to them. 4.3.3.2 Parallel-Plate vs. Coplanar-Plate Besides the difference in tuneabilities reflected in (4.3.1) and (4.3.2) the performance of the parallel-plate and coplanar-plate varactors depends also on the design of the varactors; the same film may result in different dielectric properties, as it fellows from the electric field configurations schematically depicted in Fig. 4.3.4 (Rundqvist et al. 2006). In parallel-plate varactors the electric field is perpendicular to the ferroelectric film, while in coplanar-plate varactors it is predominantly in the plane of the film. The overall performance of the varactors depends on the microstructure (columnar, granular etc.) of the film and on the orientations of the applied electric field (RF and DC) relative to the grains. Top electrode

Interface/grain bondary

Bottom electrode

Electrode

E-field lines

Electrode

BSTO film

BSTO film

E-field lines

Substrate

Substrate

(a)

(b)

Fig. 4.3.4 Columnar ferroelectric films in parallel-plate (a) and coplanar-plate (b) varactors. Reprinted with permission from AIP©2006

In a parallel-plate varactor utilized on columnar ferroelectric film (Fig. 4.3.4 (a)) the column boundaries are nearly parallel the electric field lines. The electric field lines cross only the interfacial dead layers. The columns form individual capacitors connected in parallel (Rundqvist et al. 2006). Since the cross sectional areas of the columns are larger than the cross sectional areas of the column boundaries the negative effect of these column boundaries have a minor effect on overall per-

4.3 Varactors. Basic Designs and Figure of Merit

131

formance of the varactor. Contrarily, in a coplanar-plate design (Fig. 4.3.4 (b)) the electric field lines cross the column boundaries. The local capacitors formed between the columns are now in series with the capacitances of the column boundaries. This results in a reduction of the varactors capacitance and its tuneability. At the same time it may increase the losses if the column boundaries are lossy. The above consideration indicates that the parallel-plate design should have advantages over the coplanar-plate, provided that the ferroelectric films on bottom electrodes have columnar structure. Similarly, the layered films, including the ferroelectric superlattices (i.e. BTO/BSTO) are expected to have preferred performance in coplanar-plate varactors where the electric field lines are predominantly in the plane of the layers, at least in the area below the gap.

Cinterface1

Cgc1

Cgc2

CgcN

Cgci Cgb2

Cgb1

(a)

Cgbi

Cinterface2

(b) Cinterface1

Cinterface2

Cgb1 Cgc1

Cgbi

Cgb2 Cgc2

Cgci

CgcN

Fig. 4.3.5 Simplified equivalent circuits of varactors based on columnar films with parallel-plate (a) and coplanar-plate (b) electrodes. Reprinted with permission from AIP©2006

Typically the columnar films consist of columns with different crystal orientations, and they are subject of interfacial strains, causing changes in dielectric properties (permittivity and losses). The columns with different crystal orientation experience different interfacial stress and hence different changes in the Curie temperatures and permittivity. In contrast to the bulk samples, in the films, under interfacial strains, the columns with the different orientations have anisotropic and unequal permittivity. As result different columns will have different permittivity and the peak in the temperature dependent of the apparent permittivity will be diffused. For this reason and due to the interfacial/intercolumnar dead layers the permittivity of the film in the varactors appears to be substantially different from the bulk single crystal of the same composition. Additionally, columns with different orientations have different growth rates, hence different heights – causing a substantial roughness of the surface of the film. As a result the interface with the top electrode is not conformal, and the applied voltage induces different electric fields in the columns with different heights/orientations.

132

4 Substrates, Varactors and Passive Components

In the ferroelectric ceramics with granular structure, including the composite ceramics (both bulk and film) the external field lines cross the grain boundaries regardless the design of the varactors as shown in Fig. 4.3.6. Hence both parallelplate and coplanar-plate varactors may have poorer performances. Electrode

Electrode

Top electrode

Bottom electrode

Substrate

Substrate

(a)

(b)

Fig. 4.3.6 Granular ferroelectric films in parallel-plate (a) and coplanar-plate (b) varactors. The electric field lines are model by the arrows. Reprinted with permission from AIP©2006

4.3.3.3 Apparent Permittivity and Tuneability For a parallel-plate varactor based on a columnar film the effective capacitance and the apparent permittivity that may be calculated from the measured capacitance are given (Fig. 4.3.5) as:

(

−1 Ceff = ∑ Cbi + ∑ Cgbi

)−1 + ∑ Cint−1erfacej

parallel ε app = (Ceff t ) /(ε o A)

(4.3.8)

(4.3.9)

Here Cgci, Cgbi, and Cinterfacej represent equivalent capacitances of the grain core, grain boundary and electrode/ferroelectric interfaces. For a coplanar-plate varactor:

(

−1 Ceff = (∑ Cbi ) )−1 + ∑ C gbi

)−1 + ∑ Cint−1erface

coplanar ε app = (Ceff t ) /(ε o A)

(4.3.10)

(4.3.11)

Now it should be clear that the apparent permittivity of the same columnar film measured using parallel-plate electrodes may be higher than that measured using parallel coplanar ≥ ε app . Figure 4.3.7 (Hoffmann et al. 1996) coplanar-plate electrodes: ε app demonstrates the drastic effect the grain structure on the apparent permittivity measured using parallel-plate capacitors. For a columnar film the measured apparent permittivity is less than that of the single crystal counterpart mainly due to the interfacial dead layers. In the case of the granular films the smaller the grain size (more grain boundaries) the smaller the apparent permittivity. Recently simple and rather effective models for the apparent permittivity for columnar, layered and

4.3 Varactors. Basic Designs and Figure of Merit

133

Fig. 4.3.7 Temperature dependences of the apparent permittivity of the BaTiO3 films in parallelplate capacitors

granular ferroelectric films are proposed, including granular films with different grain shapes (Tagantsev et al. 2005). Since the permittivity of the grain boundaries and interfacial dead layers is lower, the applied DC and RF fields in these layers is higher that in the bulk of the grains. This results in a reduced tuneability which, again, has different magnitude for columnar/layered and granular films. These dependences of the tuneability for columnar, layered and granular composites (mixture of grain boundaries and cores) are modeled and compared with the results of the dedicated experiments. Figure 4.3.8 (Setter et al. 2004) depicts the dependence of the tuneability of columnar (“parallel”), layered (“in-series”) and granular (spherical) composites on the apparent permittivity (i.e. density of the grain boundaries!). It is shown that the apparent permittivity and the losses of a columnar film in parallel-plate varactor may be reduced substantially by increasing the non-ferroelectric constituent (e.g. grain boundary) without reducing it tuneability.

Fig. 4.3.8 Tuneability εmax /εmin of SrTiO3 columnar composite vs. its apparent permittivity under DC field 1.7 V/μm

134

4 Substrates, Varactors and Passive Components

Thus, the parallel-plate and coplanar-plate varactors based on the films with the same composition and nanostructure may have drastically different performances in terms of tuneability and loss (Setter et al. 2004). Additionally the grain boundaries have crucial affects on the leakage current, reliability and lifetime.

4.3.4 Varactor Design Issues Typically the parameters of the ferroelectric film are optimized for certain thicknesses. For a given ferroelectric film, apart from the varactor design-film structure correlation issues discussed in the previous section, the selection of the metals for the electrodes, adhesion and buffer layers is another issue to address in order to ensure the best possible performance of the varactors. These issues are considered in Chap. 3. For an established film fabrication processes the ferroelectric film thicknesses and other parameters (permittivity, tuneability, loss tangent) are fixed. Then, for circuit applications, the main task is to design varactors with the specified capacitance, tuneability and Q-factor using the given film parameters. It includes optimization the shape of the electrodes aiming at reduction of the losses in the plates, parasitic capacitances and inductances. To keep the overall microwave losses low, the thickness of the electrodes has to be at least three skin depths. Additionally, especially in the case of the varactors with the parallel-plate electrodes, the thickness of the electrodes and other interfacing layers have to be selected so that the losses associated with the microwave to acoustic transformations are minimized. The latter problem is discussed in Sect. 4.6. 4.3.4.1 Coplanar-Plate Varactors

In the case of a coplanar-plate varactor (Fig. 4.3.1) for a given ferroelectric film the capacitance is defined by the shape of the electrodes and the gapwidth (g) between them. The electrodes of a coplanar-plate varactor may have two basic designs: straight gap (Fig. 4.3.2 (b)) and interdigital (Fig. 4.3.2 (c)). In both cases the selection of the width of the gap (2g) between the plates is based on trading the tuneability against the total losses (Q-factor) of the varactor. For small gapwidths the required tuning voltage is small and the tuneability is large since more DC and microwave fields are confined in the ferroelectric film. For small gapwidths the “screening” (i.e. reduction of tuneability according to (4.3.2)) is also smaller. A further reduction of the screening may be achieved if substrates with smaller permittivity (MgO, Al2O3 or even glass) are used. For small gapwidths the Q-factor of the varactor, associated with the loss tangent of the ferroelectric film, is smaller. Typically the ferroelectric films with higher permittivity have higher losses and higher tuneability (Tagantsev et al. 2005). For a given (i.e. high losses and high tuneability) ferroelectric film one may increase the Q-factor by increas-

4.3 Varactors. Basic Designs and Figure of Merit

135

ing the gapwidth. The increased tuning voltage and/or decreased tuneability are the price to pay. Typically the interdigital design allows more fields (DC, microwave) to confine in the ferroelectric film, and the highest degree of the confinement is achieved if the gapwidths and finger widths are nearly the same (s≈g). However, the too narrow fingers may increase the ohmic losses. In general, the application of the interdigital varactor in microwave circuit is limited by the parasitic inductance of the fingers. The parasitic inductance and the varactor capacitance form a lumped element LC resonator with resonant frequencies in the range 5–20 GHz depredating on the length of the fingers and the capacitance of the varactor. For higher microwave frequencies interdigital capacitors with shorter fingers or straight gap layouts may be used. For millimeter wave applications the varactor capacitances required in circuits are small and the straight gap layout is preferable. In coplanar-plate varactors, one expects to have enhanced current/charge crowding at the electrodes/plates facing the gap between them. Due to enhanced electric field confinement in the ferroelectric film the charge/current crowding effect, typical for all structures with coplanar electrodes, becomes enhanced (Carlsson and Gevorgian 1999). It results in slightly higher losses in the plates, reduced permittivity (locally, adjacent to the plate edge) and tuneability, and higher nonlinearity. Similar effects occur in ferroelectric devices with coplanar-plate electrodes, like coplanar-strip (CPS) waveguide and coplanar waveguide (CPW) devices. In the case of single step patterning of both plates the reproducibility of the capacitance depends on the reproducibility of the film parameters (permittivity, thickness etc.), and on the tolerances of the lithographic processes. For small gapwidths (<1–2 μm) the surface roughness of the films has to be small which is possible for the films grown epitaxially on crystalline substrates. In the case the plates are patterned separately (using separate masks), the reproducibility depends also on the mask alignment process. 4.3.4.2 Parallel-Plate Varactors

In parallel-plate varactors the ferroelectric film is sandwiched between two electrodes and, for the given ferroelectric film, the capacitance is defined by the thickness and overlap area between the top and bottom plates: A=wl (Fig. 4.3.9). In microwave circuit applications the capacitances of the varactors are in the range of several pF and less. Thus, due to the extremely high permittivity of the ferroelectric film, typically >100, the required overlapping area of the plates are very small. A small misalignment (±Δl) leads to substantial changes in the capacitance. Moreover, the desire to reduce the series resistance of the plates forces to have aspect ratio of the plates as high as possible (w/l>1, (Deleniv et al. 2008)) as shown in Fig. 4.3.10 (a), leading to strict fabrication/alignment tolerances. The design shown in Fig. 4.3.10 (b) and Fig. 4.3.10 (c) are insensitive to misalignments and offers a better capacitance prediction. However, the designs include narrow interconnect strips contributing in the parasitic inductance and resis-

136

4 Substrates, Varactors and Passive Components

tance as one may expect from the simulated current distribution shown in Fig. 4.3.10 (d). Figure 4.3.10 (e) compares the Q-factors of varactors with solid (not patterned) bottom and circular top plates (inset in upper right corner) and varactor with patterned plates similar to the one shown in Fig. 4.3.10 (c) (inset in lower left corner) to demonstrate the drastic effect of the interconnect strips. Ferroelectric

(a)

M2 M1 Substrate

(b)

w

l

Fig. 4.3.9 Simple design of a parallel-plate varactor

In an alternative design an extra low permittivity (ε<10) film between the top electrode and ferroelectric film is used to define the overlap area (Fig. 4.3.11 (a)). At the same time the extra dielectric film (SiO2, SiN4 etc.) reduces any possible negative effect from the etched step (increased leakage current, losses etc.) of the ferroelectric film. This design requires more masks and fabrication processes, and is less sensitive to misalignments. The capacitance of the varactor is defined mainly by the overlap area: A=wl. To reduce the series resistances of the top plate the length l of the late has to be minimum, limited by the processing tolerances, while the desired capacitance is achieved by changing the width (w) of the overlap area (“window” in SiO2 layer, Fig. 4.3.11 (b)). The C-V performance of this design may suffer some imprint due to asymmetricity (different barriers at the top and bottom interfaces). The design shown in Fig. 4.3.11 (c) provides a symmetric, imprint free, C-V performance even if the top and bottom potential barriers of the plates with the ferroelectric film are different. It has two identical back-to-back connected varactors and has even lower leakage currents due to in series connected potential barriers. The gapwidth g is selected by trading the low parasitic capacitance (between two bottom plates), against low series resistance (length of the common top electrode). The power handling capability of this design also is higher. The disadvantage of this design is that it requires twice as higher DC bias to reach the same tuneability. The common bottom electrode may be “floating” or may be used as a third terminal as shown in Fig. 4.3.11 (d), where it is used for DC bias supply.

4.3 Varactors. Basic Designs and Figure of Merit

Bottom plate

137

Ground plane (Pt+Au/Pt) Inductive strip

Top plate

STO/Silicon Signal strip

40

Varactors

40

STO/Silicon Ground plane

(a)

(b)

Top plate

Bottom plate

(d)

(c)

(e) Fig. 4.3.10 Typical designs of parallel-plate varactors (a, b, c), simulated current distribution in a design with narrow interconnect strips, and comparison of the Q-factors of the varactors with prepatterned and solid bottom plates (d)

138

4 Substrates, Varactors and Passive Components

(a)

(b)

(c)

(d) Fig. 4.3.11 Single (a, b) and double back-to-back connected varactors (c) with the overlap areas defined by windows opened in additional dielectric layers

4.4 Equivalent Circuit Model of the Varactors

139

4.4 Equivalent Circuit Model of the Varactors 4.4.1 Equivalent Circuit 4.4.1.1 Parallel-Plate

Equivalent circuit: The varactors may have rectangular and circular shapes as shown in Fig. 4.4.1. Figure 4.4.2 (a) shows the equivalent circuit of a varactor in circuit applications. Besides the core it includes the parasitic inductance (Lc) capacitance (Cc) and resistance (rc) of the interconnecting strips, representing the “cladding” of the varactor. The varactor core consists of the plates and the ferroelectric film. The inductor (L) and resistor (rm) represent the plates, while the dielectric losses and permittivity of the ferroelectric film are represented by the equivalent resistor (Rd(V)) and capacitor (C(V)) respectively. The parasitic parameters of the cladding (Lc, Cc, and rc) depend on the specifics of the circuit where the varactors are used. These parameters should be considered (may be available) while developing the layouts of the circuits incorporating the varactor. They may be modeled using electromagnetic simulators, for example Momentum and Sonnet. A more detailed scalable circuit model for parallel-plate varactors may be found in (Gevorgian et al. 2008). l tpl 1’

r

t

w

tpl t

ε, tanδ

2’

ε, tanδ

(a)

(b)

Fig. 4.4.1 The core of a parallel-plate (a) and circular (b) varactors

rm

rc Cc

L

Lc

re C(V) R(V,ω)

Cladding

Ce(V)

Core

(a)

(b)

Fig. 4.4.2 Equivalent circuit model the varactor including the core and cladding (a) and simplified representation of the core (b). Reprinted with permission from Wiley©2008

140

4 Substrates, Varactors and Passive Components

Capacitance: The area (A) of the top plate and the required capacitance are related as: C pp (V ) = 8.85ε ap (V )

A , pF t

(4.4.1)

t is the thickness of the ferroelectric film, V is the applied DC voltage. The apparent permittivity of a columnar film considered in Chap. 2 (2.4.12) is useful for analysis and optimization of the fabrication process. However, for modeling and circuit applications a simpler formula for the apparent permittivity may be deduced from (Chase et al. 2005, Gevorgian et al. 2008):

ε ap (V ) = ε c +

ε ap (0) ⎡2 ⎛ 2V 2 cosh ⎢ a sinh ⎜⎜ 3 ⎝ V2 ⎣⎢

(4.4.2)

⎞⎤ ⎟⎟⎥ − 1 ⎠⎦⎥

where the first term εc takes into account several contributions from background (Noeth et al. 2007), i.e. the permittivity due to the possible soft mode contribution at extremely high temperatures (2.4.10) and possible effects due to the grain boundaries. In (4.4.2) εc, εap(0) and V2 are fitting parameters obtained from the measured test capacitors fabricated using the given/available process (laser ablation, RF magnetron sputtering etc.). While for large area electrodes (A> 10 μm2) the contribution of the fringing field may be neglected, it has to be taken into account the smaller area varactors and for varactor with very narrow and elongated (large aspect ratio l/w) electrodes. The normalized fringing capacitance C fr P (where P is the perimeter of the inner electrode) may be calculated using C fr (V ) = ε 0ε ap (V )

0.2

π

ln(2 ) , fF/μm

(4.4.3)

Then the total capacitance is: C(V)=Cpp(V)+Cfr(V). Equivalent shunt resistance R(V,ω) (Gevorgian et al. 2008): For a given varactor (sizes) the resistance of the equivalent shunt resistor (Fig. 4.4.2) is: R (V , ω ) =

1 t ωε ap (V )ε o tan δ ap (V , ω ) A

(4.4.4)

where ω=2πf, the apparent permittivity εap(V) is given by (4.4.2), εo=8.85 10–12 F/m. The apparent loss tangent of the ferroelectric film may be given as: tan δ ap (V , f ) = Ff nε ap (V ) + Bf

p

(4.4.5)

4.4 Equivalent Circuit Model of the Varactors

141

where εap(V) is the apparent permittivity (4.4.2). The fitting parameters F, p and n are obtained from the same measured test capacitor as indicated above. For a columnar film considered in Chap. 2 F=6.2510–15, B≈0, p=0, n=1. Equivalent resistance of the plates: The equivalent series resistance of the pleats (Fig. 4.4.1 (a)) with length l , and width w is given by (Gevorgian et al. 2008) (see also Sect. 7.4: rm (ω ) =

l ⎛⎜ ρtop ρbot ⎞⎟ + ⎜ 3w ⎝ δ ttop , ω δ (tbot , ω ) ⎟⎠

(

)

(4.4.6)

where 2

2

⎞ ⎛ t ⎞ cosh ⎛⎜ t δ (ω )⎟⎠ − cos⎜⎝ δ (ω )⎟⎠ ⎝ , δ (t , ω ) = 2δ ⎞⎟ ⎞⎟ + sin ⎛⎜ 2t sinh ⎛⎜ 2t ⎝ δ (ω )⎠ ⎝ δ (ω )⎠

δ (ω ) =

2

ωμ 0σ

,

(4.4.7)

(4.4.8)

where ρ top (bot ) is the DC resistivity of the top(bottom) electrode, and ttop (bot ) is the thickness of the top(bottom) electrode (Fig. 4.4.1), δ(ω) is the standard skin depth. For the given sizes (w and l, Fig. 4.4.1) the resistance of the plates depends on the location of the terminals. An example of a rectangular varactor with the plate area 5 × 10 μm 2 is depicted in Fig. 4.4.3. In one case the terminals are located on the broad sides of the plates, i.e. w = 10μm and l = 5μm , while in the other case the terminals are located on the narrow sides: w = 5μm and l = 10 μm . Although the varactor area (capacitance) in both cases is the same, 50 μm 2 , the resistance of the plates are considerably different.

( )

0.08

w=5μm; l=10μm

m

Electrode resistance r , Ohm

0.1

0.06 0.04 w=10μm; l=5 μm

0.02 0

5

10

15 20 25 30 35 Frequency, GHz

40

45

Fig. 4.4.3 The equivalent resistance rm(ω) for 0.5um thick Au( σ Au = 4.1 × 10 7 (S m ) electrodes. ttop=tbot= 0.5μm . Reprinted with permission from Wiley©2008

142

4 Substrates, Varactors and Passive Components

Equivalent inductance of the plates: The inductance of the plates comprises of two contributors-the geometric and internal inductances: L = Lg + Li

(4.4.9)

The geometric inductance takes into account the magnetic field outside the conductor: Lg ≈

μotl

(4.4.10)

2w

The internal inductance represents the energy of the magnetic field stored inside the conductor. For the electrically thick electrodes ( t > 3 ⋅ δ (ω ) ), and w >> t one may use the incremental inductance rule: Li (ω ) =

rm (ω )

ω

=

μ 0lδ (ω )

(4.4.11)

3w

[

]

For a varactor with sizes w=l=10 μm, 2πf L g + Li (ω ) ≤ 0.05Ohm up to 50 GHz, i.e. in many circuit application it may be ignored below these frequencies. 4.4.1.2 Coplanar-Plate

The equivalent circuit of the coplanar-plate varactors are similar to the one used for parallel-plate ones (Fig. 4.4.2). The main difference is that one needs to take into account the parasitic shunt capacitances and (microwave) conductance due to the substrate and the air (or any other dielectric) above the plates. The RF and microwave fields in both straight and interdigital coplanar-plate varactors (Fig. 4.3.2 (b) and (c)) are highly inhomogeneous and the DC field induced change in permittivity distribution in the ferroelectric film is also inhomogeneous. Even the field dependent tuning is expected to be different from that one has for a parallel-plate varactor given by (4.4.2). The numerical models of the capacitances and other circuit parameters using commercially available software’s often are limited by the extremely high permittivity of the ferroelectric films, the nanoscale thickness of these films and non-uniform/nonlinear distribution of the permittivity and the loss tangent of the films under applied DC and RF fields. Simple analytical models of the capacitances of coplanar-plate varactors (lumped element and distributed), using conformal mapping technique, may be given ignoring nonuniform distribution of the permittivity (see Chap. 7).

4.4 Equivalent Circuit Model of the Varactors

143

4.4.2 Impedance of Parallel-Plate Varactors The impedance measured between the two terminals of the varactor is usually represented as a simple RC circuit shown in Fig. 4.4.2 (b). The apparent series resistance and capacitance of this circuit may be expressed in terms of parameters given in Fig. 4.4.2 (a):

re ( E ) = r +

Ce ( E ) =

R( E )

(4.4.12)

1 + [ωC ( E ) R( E )]2

1 + [ωC ( E ) R( E )]2

[ωR( E )]2 C ( E ) − ω 2 L{1 − [ωC ( E ) R( E )]2 }

(4.4.13)

where E=V/t. Alternatively, the equivalent parameters of the series circuit may be given in terms of losses (loss tangents) of the ferroelectric and metal strips:

re ( E ) =

1 tan δ m ( E ) + [1 + tan δ m ( E ) tan δ d ( E )] tan δ d ( E ) (4.4.14) ωC ( E ) 1 + tan 2 δ d ( E ) Ce ( E ) =

[

C ( E ) 1 + tan 2 δ d ( E ) 2

[

]

⎛ ω ⎞ ⎟⎟ 1 + tan 2 δ d ( E ) 1 − ⎜⎜ ⎝ ωo ( E ) ⎠

]

(4.4.15)

with tan δ d ( E ) =

1

(4.4.16)

ωC ( E ) R( E )

tan δ m ( E ) = ωC ( E )rm

(4.4.17)

(LC ( E ))

(4.4.18)

ωo ( E ) = 1 /

The effective loss tangent of the circuit shown in Fig. 2.4.2 (b) is

tan δ e ( E ) = ωR( E )C ( E ) =

{

R( E ) + rm 1 + [ωC ( E ) R( E )]2

{[

}

(4.4.19)

]}

ωC ( E ) R ( E ) − ωL [ωC ( E ) R( E )] + 1 2

2

In terms of loss tangents of the dielectric and metal strips:

tan δ e ( E ) =

tan δ m ( E ) + [1 + tan δ m ( E ) tan δ d ( E )] tan δ d ( E ) 2

[

⎡ ω ⎤ 2 1− ⎢ ⎥ 1 + tan δ d ( E ) ω ( E ) ⎦ ⎣ o

]

(4.3.20)

144

4 Substrates, Varactors and Passive Components

For low frequencies and/or L=0:

ω ( E ) << One has:

ωo 1 + tan 2 δ d ( E )

[

]

Ce ( E ) = C( E ) 1 + tan 2 δ d ( E )

tan δ e ( E ) = tan δ m ( E ) + [1 + tan δ m ( E ) tan δ d ( E )] tan δ d ( E ) ≈ tan δ m ( E ) + tan δ d ( E )

(4.4.21)

(4.4.22) (4.3.23)

The expressions above are very helpful for interpretation of the measurements of the varactors circuit and materials parameters. The capacitance C(E) is frequency independent (if the fringing field capacitance may be ignored) since the permittivity of the ferroelectric is frequency independent below soft mode frequency. Hence the frequency dependence of the measured effective capacitance Ce(E), well below resonant frequency ωo, should have similar frequency dependence as the frequency dependence of the loss tangent of the ferroelectric film, tanδd. For films with the dominating loss mechanism associated with the charged defects (oxygen vacancies) tanδd ~ω1 (Tagantsev et al. 2005). Hence, the effective capacitance should have ω2 frequency dependence as it follows from (4.4.22) above; it should slightly increase with the increased frequency. However, the parasitic inductance L may cause a substantially increased Ce with increased frequency, especially near the self resonant frequency. On the other hand in simple reflection measurements of varactors using VNAs and standard calibration kits often the measured Ce appears to be decreasing with increased frequency. As it follows from (4.4.13), this may be associated with a negative inductance involved in calibration procedure based on standard calibration substrate (i.e. from Cascade Microtech, www.cascademicrotech.com). A simple scalable circuit model for the parallel-plate varactors taking into account the apparent permittivity, the composite effect associated with the grain boundaries, electrode ferroelectric interfaces and loss tangent is given in (Gevorgian et al. 2008).

4.5 Low Frequency and Tuning Performances 4.5.1 C-V and P-V Performances 4.5.1.1 Parallel-Plate Varactors

The performance of a ferroelectric varactor depends not only on the composition of the film, but also on the strain, defects, electrode/ferroelectric interface chemistry, fabrication method, design etc. A simple scanning of the recent publications

4.5 Low Frequency and Tuning Performances

145

shows that depending on these factors the varactors based on the same ferroelectric composition (i.e. BaxSr1–xTiO3) have performance ranging from rather good to totally unacceptable. Shown in Fig. 4.5.1 are the cross section and the typical C-V and Q-factor of a BST/Pt/Au varactor at 1.0 MHz (Vorobiev et al. 2003). The varactor is fabricated on an n-type silicon ((100)Si, ρ = 5 kΩ⋅cm) substrate with adhesive TiO2 (15 nm) and Pt (100 nm) layers. BST films (560 nm thick) are grown by laser ablation of Ba0.25Sr0.75TiO3 target using KrF excimer laser operating at 10 Hz and 1.5 J⋅cm–2. The bottom electrode and top electrodes are made of a 0.5 μm thick Au film and 50 nm Pt layer. For comparison, Pt(200 nm)/TiO2/SiO2/Si structures are used as substrate to form BST/Pt varactors. Use of thicker Au bottom electrode substantially increases the Q-factor of the varactor in comparison with a varactor with only Pt bottom electrode (Fig. 4.5.1 (b)) provided that the fabrication processes optimized to grow high quality ferroelectric films. Both C-V and Q-V curves in Fig. 4.5.1 (b) are given for one cycle of full reversal of the DC bias field. In this experiment the tuning voltage changes linearly in time. On the other hand, if the fabrication process is not optimized and the film is in polar, ferroelectric phase, the C-V have two peaks (“butterfly” shape), and the capacitance at given DC bias depends on the prehistory of biasing. The polar phase can be easily detected by measuring the P-V performance. In some cases the C-V dependence may have the form shown in Fig. 4.5.2 (a). In this case the capacitance does not return to its initial value after a full cycle bias reversal. There is no polarization related hysteresis in P-V performance and the P-V is essentially linear (Fig. 4.5.2 (b)). The magnitude of the none-return capacitance ΔC is associated with charged defects in the film and not desirable for device applications. The imprint in C-V observed in varactors may be partly due to the asymmetric structure, i.e. potential barriers at the bottom and top plates. These barriers may 2.4

300

BST/Pt/Au

2.2

Au

250 2

Pt Ba0.25Sr0.75TiO3 film

1.8

200

Pt/Au/Pt/TiO2 bottomelectrode

SiO2

1.6

BST/Pt

Si substrate

150

1.4 1.2 -30

-20

-10

0

10

20

100 30

Voltage (V)

(a)

(b)

Fig. 4.5.1 Cross section (a) and C-V dependence (b) of a parallel-plate varactor with diameter of the top plate 30 μm. Reprinted with permission from AIP©2003

146

4 Substrates, Varactors and Passive Components 80

15

20

Cc4-1MHz-26V 13_32_54 2002-04-29

15

ΔC 14

10

70 12

65 11

10 -30

P (µC/cm2)

13 1/tan(δ)

Caoacitance (pF)

75

5 0 -5 -10 -15

60 -20

-10

0

10

20

30

-20 -15

-10

-5

0

5

10

15

Bias (V)

voltage, V

(a)

(b)

Fig. 4.5.2 The effect of charged defects on C-V performance of a Pt/STO/Pt varactor (a), and its P-V performance (b)

have different heights even of both bottom and top electrodes are made of the same metal, i.e. Pt. The reason for this is that while growing the film at elevated temperatures the lower interface becomes heavily affected by the dead layer, while the top interface, fabricated at relatively lower temperatures is sharper. In addition, even for ideally symmetric potential barriers, one may still expect some imprint associated with the misfit strains (Basceri et al. 1997) briefly discussed in Sect. 2.8. In a varactor consisting of two back-to-back connected parallel-plate varactors (Fig. 4.3.11 (c)) the potential barriers under both top and over both bottom electrodes are identical since they are prepared under the same conditions. Similarly the misfit strain related electric fields are also identical. Hence the C-V performance of these varactors is always symmetric provided that the areas of both plates are identical. In case where the area of one of the plates is much larger one still may observe imprint since the large area results in much larger capacitance equivalent to short circuiting the top and bottom electrodes of this varactor. 4.5.1.2 Coplanar-Plate Structure

In coplanar-plate varactors too, the potential barriers under both electroded are identical since they are prepared under the same conditions. Similarly the misfit strain related electric fields are also identical. Hence the C-V performance is expected to be symmetric.

4.5.2 I-V Performance The low leakage currents, or in other words the low control power consumption is one of the most important advantages of the ferroelectric varactors. The currents in

4.5 Low Frequency and Tuning Performances

147

these devices are limited by the high resistivity of the ferroelectric and by the barrier heights at the ferroelectric/electrode interfaces. The experimental I-V studies of very thin (77 nm) barium titanate single crystals show that it may support DC fields up to 1300 V/μm (Morrison et al. 2005). Thus to reduce the leakage currents the ferroelectric used in the devices should have structural and dielectric properties as close to single crystals as possible. The other task is selection of the metals for electrodes that have highest potential barrier with the ferroelectrics and do not interact chemically and do not diffuse in the ferroelectric. Table 4.5.1 summarizes the electrode materials that are used in ferroelectrics and the height of Schottky barrier with SrTiO3 (Eg,STO =3.3 eV, Robertson and Chen 1999). Pt may be considered as the best in terms of higher work function/barrier height, lower leakage currents and longer time-to-breakdown. It is good as the bottom plate since has no chemical interactions and allows epitaxial growth of the high quality ferroelectric films. However, it has a poor adhesion where used as a top plate. Gold is characterized with similar properties but the lower barrier height results in higher leakage currents and shorter lifetime. Although Ni has even lower barrier height it has relatively good adhesion and is widely used in industry in multilayer capacitors. SRO and YBCO are considered favorable for the lattice matched growth of ferroelectric films with a better crystallinity (Boikov and Claesson 2002, Rundqvist et al. 2003). The varactors with these interfaces have higher tuneability. Unfortunately the high leakage currents and loss tangent make them less interesting for most of the device application. Especially in parallel-plate varactors the microwave loss tangent of the ferroelectric varactors is very high perhaps due to the inter diffusion between the SRO and BSTO. Besides the potential barriers at the electrode/ferroelectric interfaces the I-V performance and microwave losses of the ferroelectric varactors is closely correlated with the defects in the film and at the interfaces. In the case of coplanar-plate varactors the surface leakage currents may be rather high for small gaps/slots between the plates. Table 4.5.1 Work functions of the electrode metals and barrier heights on SrTiO3 Electrode material

Work function, eV

Barrier height, eV

Reference

Pt

5.3

0.89

Robertson

Au

5.1

0.84

Robertson

Ni

5.01

Pd

4.79–5.28

0.97

Robertson

Ti

4.35

0.63

Robertson

Si (VB/CB)

4.0/5.1

(–0.14/2.3)

Robertson

YBCO

5.2–6

0.4

SRO

5.21

1.2?

148

4 Substrates, Varactors and Passive Components

(a)

(b)

Fig. 4.5.3 A qualitative I-V performance (a) and of parallel-plate varactors with Au(Pt)/ Ba0.25Sr0.75TiO3/(Pt)Au interfaces. Reprinted with permission from AIP©2005 and AIP©2004

To achieve highest tunings the DC field developed in ferroelectric varactors should be as high as possible. Different conduction mechanisms become active with the increased DC field. Figure 4.5.3 (a) shows a quantitative I-V dependence of a parallel-plate structure based on BaTiO3 at elevated DC fields. This shape is reproduced experimentally in (Morrison et al. 2005). Figure 4.5.3 (b) (Vorobiev et al. 2004) shows an example of I-V curve for a parallel-plate varactor. A careful examination shows that the most probable mechanisms controlling the nonlinear dc current through perovskite films are Schottky emission, Pool-Frenkel emission, and SCLC. The capacitances of the varactors used in microwave and millimeter wave circuits are in the range of several tens of pF and less. Given the high permittivity of the ferroelectrics the areas of the plates are less than hundreds of μm2. As a result the maximum leakage currents are in nA to pA range. Table 4.5.2 Leakage current comparison Type

Material

Capacitance Q factor (at 10 GHz) pF

μA/pF

Schottky (UMS) Abrupt junction Heterostructure barrier Parallel-plate (Chalmers) Coplanar-plate (Chalmers)

GaAs Si GaAs based BSTO NKN

250 32 38 100 10

0.1 25 240 8·10–4 1.5·10–3

Leakage current μA 0.095 (@0V) 0.01(@–4V) 0.4(@–4 V) 10(@–30 V) 0.05(@0 V) 7(@12V) 0.25(@0 V) 2·10–4 (@20V) 0.1 (@0V) 1.5·10–4 (@20V)

Typically the (leakage) currents in ferroelectric varactors are much smaller in comparison with the currents in the competing semiconductor and magnetic technologies. This is one of the heaviest advantages of tunable the ferroelectric technology. In terms of device performance the small leakage currents mean small control power consumption which is an important issue for power hungry systems

4.5 Low Frequency and Tuning Performances

149

such as the portable and space based microwave systems, and the systems where large arrays of the devices are densely packed and the heating and heat sink is a serious issue. For example, current through a 10 µm (in diameter) BST/Pt/Au varactor at 20 V is about 5⋅10–11 A which is 3 orders of magnitude less than reverse current through dual Schottky diode at 5 V. Table 4.5.2 gives a brief comparison of the leakage currents of several competing technologies. The negligible leakage currents combined with the high tuning speed makes the ferroelectric varactors outstanding when it comes to microwave systems using large numbers varactors, such as phased array antennas and metamaterials (Gevorgian and Vorobiev 2007).

4.5.3 Tuneability and Response Time The soft mode frequency of BSTO, depending on the Ba content and temperature, is in the changes from 100 GHz to 3.0 THz (Ostapchuk et al. 2007, Kozyrev et al. 2007). Hence, the changes in the permittivity below at least several hundred GHz, should almost instantaneously follow the in the changes of the applied electric (DC and RF) fields, i.e. one may expect sub-nanosecond scale tuning speeds in paraelectric phase. The measurements of intermodulation products seem to confirm this statement (Mateu et al. 2006, Soldatenkov et al. 2006), indicating that the permittivity tuning under fast changing microwave voltages is similar to C-V measured using slow (“DC”) tuning voltages. The tuning voltage may have any shape and the tuning speed of a ferroelectric device may be limited by several extrinsic factors: • time constants associated with the parasitic RLC circuit parameters; • charged defects in the bulk of the film, grain boundaries and at the interfaces with the electrodes; • residual/local ferroelectric polarization in paraelectric phase. The latter two have to do with the crystalline quality of the used ferroelectrics and interfaces. An extensive response time measurement of the ferroelectric varactors is carried out by Kozyrev et al. (2005). The none-retune capacitance ΔC (see Fig. 4.5.2 (a)) is one of the ways the charged defects affect the performance (tuneability) of the varactor. Figure 4.5.4 shows the measured non-return capacitance for coplanar-plate and parallel-plate varactors under unipolar pulses (Kozyrev et al. 2005). The drastic effect of the film quality (fabrication method) is clearly seen. The effect is very low for the films prepared by RF magnetron sputtering. The electric field induced charging (trapping/detrapping) of the charged defects may have more drastic effect on the tuning speed. The trapped/detrapped charges change the local fields about the defects (trapping centers) thereby changing the permittivity of the films. Injection of the charge carriers from the electrodes and their trapping on local centers (Stolichnov and Tagantsev 1998), redistribution of the oxygen vacancies under the bias electric field (Boikov et al. 2001, Maruno et al. 2000), and the space charge relaxation at the near electrode and grain bound-

150

4 Substrates, Varactors and Passive Components

∆C/C0,%

16

Ceramic coplanar plate varactor

14 12

Constant tunability line Cmax/Cmin=1.6

10 8

Parallel-plate (MOD)

6 4

Parallel-plate (magnetron sputtering)

2 0

0

10

20

30 E, V/ μ m

40

60

50

Fig. 4.5.4 Dependences of none-return capacitances on the field of rectangular control pulses. Reprinted with permission from EuMA©2006

ary areas are considered as the main mechanisms responsible for the observed relaxation times. Figure 4.5.5 depicts the time response of the ferroelectric varactors under different levels of the unipolar electric fields. In all experiments (Kozyrev et al. 2005) the time duration of the leading front is limited by the applied pulse which indicates that the change in permittivity takes place in sub-nanosecond scale, as one expects from an ideal paraelectric. On the other hand, depending on the film quality and the field strength, the relaxation time of the capacitance may be up to 10s. The relaxation times are much shorter in the films with the better crystalline structure.

Capacitance, pF

0.8 0.7 10 V/μm

0.6 0.5 0.4 0.3

100

200

(a)

0.9

12 % 2.5 V/μm

0.8 0.7 0.6

0.5 E ~ 15 V/μm

E~ 60 V/μm 0

Capacitance, pF

1.0

6%

300 Time, s

0

100

200

300 Time, s

(b)

Fig. 4.5.5 Time responses of the capacitances to the control pulses for a 0.8 μm thick textured BSTO (a) and a 6 μm thick ceramic BSTO/MgO (b) films in coplanar-plate varactors. Pulse duration is about 60 s. Reprinted with permission from EuMA©2005

4.6 Microwave Performance

151

The effective screenings of the local fields about the trapping centers may be achieved by ultra violate radiation (Alford et al. 2005). This experiment clearly shows that the relaxation time may and should be reduced by improving the crystalline quality of the ferroelectrics. It should be also clear that the relaxation times are expected to be longer in ceramics (Fig. 4.5.5 (b)) where the density of the defects associated with the rain boundaries is very high.

4.6 Microwave Performance 4.6.1 Parallel-Plate Varactors Chalmers varactors: The Q-factor of a varactor is limited by the losses in the ferroelectric and in the plates/interconnect strips. Distinguishing between these contributions based on the measurements is a difficult, if possible at all, task. For given film (fabrication process) one of the main design tasks is to reduce the losses in the plates and interconnect strips. In this sense the test structure with circular patch and unpatented bottom plate has no interconnect strips in the top plate and the annular interconnect strip (outside the overlap area) in the bottom plate offers the smallest losses associated with the plates interconnects (Fig. 4.3.10). In fact this test varactor is used for the assessment of the possible highest Q-factor of the varactors based on a given film/varactor preparation technologies. Typical frequency dependencies of the capacitance and loss tangent of parallel-plate ferroelectric varactors are shown in Fig. 4.6.1 (Vorobiev 2008). In this case the 350 nm thick Ba0.5Sr0.5TiO3 film is grown by RF magnetron sputtering at rather low temperature (550°C). For this reason the apparent permittivity is rather low (190 at zero field). Due to the low (in comparison with Pt) Schottky barrier at top Ni/BSTO interface the loss tangent and the leakage current are relatively high at positive polarity of the top plate. Negative polarity allows applying higher voltage. The voltage 25 V corresponds to the field 70V/μm. At this field tuneability is 32%.

(a)

(b)

Fig. 4.6.1 Capacitance (a) and loss tangent (b) of a Au/Ni/B0.5Sr0.5TO3/Au/Pt/TiO2/Si varactor

152

4 Substrates, Varactors and Passive Components

The oscillations of the capacitance in Fig. 5.6.1 (a), and the resonant absorption peaks in loss tangent seen in Fig. 4.6.1 (b) are associated with induced by the DC bias piezoelectric effect (Gevorgian et al. 2006). This may limit the applications of ferroelectric varactors at low microwave frequencies if the effect is not eliminated. An efficient method of elimination/reduction of the acoustic resonance proposed in (Gevorgian et al. 2006). The proposed method is verified experimentally (Fig. 4.6.2). An acoustic Bragg reflector consisting of 5 pairs of quarter (acoustic) wavelength thick AlN/SiO2 layers are deposited on Si substrate (Fig. 4.6.2 (a)). At frequency where the thicknesses of these layers correspond to the quarter wavelength the multilayer acts as Bragg reflector resulting in a resonant absorption peak seen in Fig. 4.6.1 (b). Away from the resonance the interference of the acoustic waves is not constructive and does not cause resonant absorption of microwave signals. Away from the resonance an applied DC field reduces the loss tangent. Above and below the Bragg frequency bandwidth the acoustic waves pass through the reflector and damp in the substrate. The relatively high loss in this case is associated with the small thickness of the electrodes (Fig. 5.6.2 (a)). 0.5 tan-S22-ubr1-C51-1-10GHz+0+15V Au (20 nm)

0.4

B0.5Sr0.5TiO3 (200 nm) Pt (100 nm) 5 pairs of SiO2/AlN (280/540 nm) Si

Loss tangent

Al (110 nm)

0.3 0.2 0V 0.1 15 V 0

(a)

2

4 6 Frequency, GHz

8

10

(b)

Fig. 4.6.2 Cross section (a) and loss tangent (b) of a B0.5Sr0.5TiO3 varactor based on acoustically transparent AlN/SiO2 layers. Reprinted with permission from EuMA©2006

In an example shown in Fig. 4.6.3 (Vorobiev et al. 2003) the thickness of the B0.25Sr0.75TiO3 film is 0.56 μm and the diameter of the top circular plate is 10 μm. As it can be seen the capacitance and the tuneability are fairly frequency independent, the tuneability at 20 V, Tc(20), is more than 40% in the frequency range 1 MHz–45 GHz. In the frequency range 5–40 GHz the Q-factor of BST varactors fabricated on thick bottom Au/Pt electrode is more then 50 which is comparable or larger then Q-factors of the best semiconductor analogs (Fig. 4.6.3 (b)). With these parameters the BST varactors may outcompete semiconductor varactors in tunable microwave devices above 10–20 GHz. These experimental results show that the

4.6 Microwave Performance

153

permittivity of paraelectric B0.25Sr0.75TiO3 films is about 200, and the loss tangent is an order of magnitude larger than in single crystals (e.g. SrTiO3), indicating that there is a room for further improvement of the films/varactors. GaAs-Schottky 100

BST/Pt

BST/Pt/Au Si

GaAs-HBV 10 1

10

Frequency (GHz)

(a)

(b)

Fig. 4.6.3 Frequency dependencies of the capacitance (a) and Q-factor (b) of parallel-plate varactors. Reprinted with permission from AIP©2003

w

(a)

(b)

Fig. 4.6.4 Cross-section (a) and frequency dependent Q-factor (b) of UCSB back-to-back varactor. tPt=1000 Å, tBST=750 Å, ε=250

UCSB varactors: UCSB in collaboration with Agile RF developed a commercial process for fabrication of microwave devices based on parallel-plate varactors. The bottom plate in these designs is made of Pt and the 30/78 BST films are prepared by RF sputtering. The Q-factor of one of the earlier back-to-back varactors developed by UCSB group is shown in Fig. 4.6.4 (b) (Nagra et al. 2000). It can be easily shown that the overall Q-factor is limited mainly by the losses in thin Pt plates, especially by the losses in floating common bottom electrode

154

4 Substrates, Varactors and Passive Components

(Fig. 4.6.2 (a)). The effect of the floating electrode is shown in Fig. 4.6.2 (b). Increasing its length (w) from 2.0 μm to 5.0 μm leads to a drastic decrease in Q-factor. The results presented in (Chase et al. 2005) show some reduction of the tuneability for the varactors with the small sizes. It is concluded, based on 2D simulations, that the redaction can not be explained by fringing field since its tuneability is almost the same as the tuneability of the ideal parallel-plate varactor (see (4.4.3)). The details of the varactor design are not reported in (Chase et al. 2005). However, one may speculate that the used 2.8 fF/μm correction term is associated with the parasitic capacitance of the gap (w) between the lead electrodes. In case this parasitic capacitance is independent of the overlap area its relative contribution will increase with the reduction of the overlap area (main capacitance). The parasitic capacitance will reduce the tuneability as it follows from (4.3.2). (a)

(b)

Fig. 4.6.5 Micro photo (a) and schematic cross-section of a parallel-plate varactor by UCSB

Figure 4.6.5 (see also Fig. 3.6.4) depicts the basic varactor structure used by UCSB group (York 2009). A window in a low permittivity dielectric layer is used for the contact to the ferroelectric film. This “interlayer” dielectric (SiO2, SiN, Al2O3) separates the top electrode away from the edge of the bottom electrode and helps to increase the breakdown field. Besides it serves as a passivation layer to reduce the harmful environmental impact on the varactor performance. Gennum compared the performances of the parallel-plate Ba0.7SrO0.3TiO3 varactors with Pt/Ti electrodes on SiO2/Si(111), r-cut sapphire, polycrystalline alumina Al2O3 (99.6%), zirconia/yttria stabilized alumina (ZYSA) and glazed polycrystalline alumina wafers (Koutsaroff et al. 2002). In this work the BST films of the same thickness and under the same processing conditions are grown by metal-organic decomposition (MOD). It is observed that the BST possess higher permittivity and higher losses when grown on all types of alumina-based substrates compared to those on SiO2/Si substrates. The lowest achieved leakage current density (2.8 × 10–9 A/cm2 at 20.0V/μm) is observed in Pt/BST/Pt varactors on glazed alumina. The investigation of the morphology of the BST films revealed that regardless of the processing temperature the grain sizes and surface roughness are larger on Si substrate as compared with the alumina. The screen printing of thick ferroelectric films (Hu et al. 2005) and especially LTCC are the most cost effective technologies considered for tunable ferroelectric devices. Due to the low resolution of these technologies, gap/slot widths between

4.6 Microwave Performance

155

Bottom Pt plate

BSTO film

Top Pt plate

the plates, the coplanar-plate varactors require very high tuning voltages. The parallel-plate design seems to be more favorable since the thickness of the ferroelectric films may be small allowing low tuning voltages. The possibilities of the screen printing technology are limited by its low resolution, typically 150–200 μm. Figure 4.6.6 (a) shows an example of a screen printed varactor. A group in Oulu University (Deleniv et al. 2005) is believed to be the first successfully integrating doped (to reduce the sintering temperature) BSTO film based varactors in LTCC compatible process. The group has used an advanced gravure printing technology allowing increasing the resolution and making printed circuits with linewidth/spacing of 10 μm (Fig. 4.6.6 (b)).

(a)

(b)

Fig. 4.6.6 Screen printed (Courtesy of T. Button, University of Birmingham) (a) and LTCC (Courtesy of H. Jantunnen, Oulu University) compatible ferroelectric varactors

ETU varactors: ETU group develop both coplanar-plate and parallel-plate varactors (Gagarin et al. 2005). A chip with typical design of a parallel-plate varactor is shown in Fig. 4.5.7 (a). ETU had close collaborations with Paratek and a large number of phase shifters, filters, and delay lines developed by ETU are based on varactor chips similar to those shown in Fig. 4.6.7. The smallest gapwidth in coplanar-plate design based on thick (8 μm) ferroelectric films (Fig. 4.6.7 (b)) is limited by the surface roughness where a standard photolithography is used for patterning the electrodes.

(a)

(b)

Fig. 4.6.7 Parallel-plate (a) and coplanar-plate (b) varactor designs by ETU

156

4 Substrates, Varactors and Passive Components

4.6.2 Coplanar-Plate Varactors For a given film thickness it is easy to control the capacitance by proper patterning of the gap between the plates, and the metallization of the both plates may be rather thick. Additionally, for a given ferroelectric film the Q-factor tuneability may be easily traded against tuneability by changing the spacing between the fingers. 4.6.2.1 Varactors Based on Dielectric Substrates

Crystalline (MgO, LaAlO3, Al203) Substrates The ferroelectric film grown in crystalline substrates, such as MgO, LaAlO3 and Al2O3 (sapphire) have very smooth surfaces (nanometer scale surface roughness) allowing fabrication of coplanar-plate varactors with the sub-micrometer gaps (slot) between the electrodes, hence requiring low tuning voltages, higher degree of confinement of the electric field in thin (< 1.0 μm) ferroelectric films, thus higher tuneability. Georgia Tech, in collaboration with nGimat has developed interdigital capacitors (IDCs) for use in phase-shifters for phased-array applications (Kenney et al. 2006, Kim and Kenney 2003). Combustion chemical vapor-phase deposition (CCVD) is used to deposit BSTO films on an r-cut sapphire substrate. Figure 4.6.8 (a) shows an example of an IDC device where thick Cu films are used to pattern interdigital electrodes.

Fig. 4.6.8 Microphoto (a), DC bias dependent tuneability (b) and Q-factor (c) of Georgia TechnGimat IDC varactor. Reprinted with permission from IEEE©2006

With decreasing the spacing between the fingers the electric field confinement in the 350 nm thick ferroelectric film increases leading to higher tuneability (Fig. 4.6.8 (b)). At the same time the Q-factor has wreaker dependence on the finger spacing (Fig. 4.6.8 (c)). Due to the relatively low Q-factor (10 to 100) these varactors are not useful for narrow bandwidth, low loss filter applications. On the

4.6 Microwave Performance

157

other hand the Q-factor of these varactors is in line with traditional semiconductor varactors, and is used for medium loss applications (Kim et al. 2003). The losses in the sapphire substrate and Cu electrodes are low and they do not depend on the DC bias. Hence the performances shown in Fig. 4.5.8 (c) indicate that most of the losses in these varactors are due to the ferroelectric film. The tuneability of the Q-factor is in the same range as the tuneability of the capacitance. Murata reported IDC varactors based on Ba0.6Sr0.4TiO3 thin films on sapphire substrate deposited by chemical solution deposition method (CSD) (Kageyama et al. 2005). Interdigital e-beam evaporated 2.0 μm thick Cu electrodes are formed on the surface of the BST film using lift-off process (Fig. 4.6.9 (a)). Finite element method simulation is used to check the effect of the permittivity on the capacitance for a fixed IDC geometry (finger spacing). The capacitance increases linearly with increased permittivity (Fig. 4.6.9 (b)). As it is seen from Fig. 4.6.9 (b), for fixed spacing between the fingers and permittivity of the film the capacitance of the varactor increases for the thicker films, which is associated with the increased confinement of both DC and microwave field confinement in the ferroelectric film.

(a)

(b)

Fig. 4.6.9 Coplanar-plate interdigital varactor by Murata Manufacturing Co., a) layout, and b) capacitance vs. permittivity of the ferroelectric film. Reprinted with permission from IEEE©2005

A careful microstructure analysis is carried out in view to correlate the measured varactor performance with the microstructure of the ferroelectric films. The AFM analysis shows that the grains grow bigger with the increased film thickness. The grain growth is constrained for the thicknesses below 300 nm, which was explained by the interaction between the substrate and BST film at the initial stage of film growth and crystallization. The results of the XRD analysis show that the fabricated BST thin films have perovskite structures and a random growth orientation. It is observed that above 300 nm the measured lattice constants are practically independent of the film thickness. The trend in changes of the grain sizes and lattice constants are in line with the film growth dynamics considered in Chap. 3.

158

4 Substrates, Varactors and Passive Components

The measured film thickness dependent dielectric permittivity at microwave frequencies shown in Fig. 4.6.10 (a) does not decreases significantly below 200 nm whereas the measured tuneabilities decrease with the thickness of BST thin films (Fig. 4.6.10 (b)).

(a)

(b)

Fig. 4.6.10 Measured at 3.0 GHz permittivity at zero DC bias permittivity (a) and tuneability under 20 V/μm DC field (b) of IDC varactor shown in Fig. 4.6.9. Reprinted with permission from IEEE©2005

Polycrystalline (Al2O3) Substrates Tunable devices based on thick film ferroelectrics and polycrystalline substrates are regarded as cheaper alternatives to thin films. The surface roughness of the polycrystalline substrates is high and the ferroelectric film have to be thicker in order to be uniform and without pinholes. The pinholes are not acceptable for the parallel-plate varactors and may cause reliability issues in coplanar-plate varactors. In (Nath et al. 2006) Ba0.6Sr0.4TiO3 thin-films 0.6 μm thick are deposited on polished alumina substrate using a RF magnetron sputtering. Ex-situ post deposition annealing in air at 900°C for 20 hours is used to fully crystallize and densify the BST films. Cr (20 nm) is used as an adhesion layers. 0.5μm thick Cu with a capping layer of 30 nm thick Pt (on top of the Cu layer to prevent ambient oxidation of copper) is used as electrode. A lift-off process is used to complete the IDC fabrication. The fingers of the BST interdigital varactor have a length of 195 μm and width of 10 μm. The finger spacing is 3 μm and the number of fingers is 16. A tuneability of 33% at 35 V bias (11.6 V/μm) and loss tangent of 0.015 at zero bias is measured. The ETU (Fig. 4.6.7) and Darmstadt groups (Fig. 4.6.11) have demonstrated a number of quite successful devices on thick film ferroelectrics. Figure 4.6.11 (Scheele et al. 2005) shows the C-V performance and the measured power handling capability of one of the varactors. The tuneability is T(100V)=35.7%, and the Q-factor is [email protected] GHz.

4.6 Microwave Performance

32.5

56 54

30.0

0.8

Q

27.5

0.7

25.0

0.6 22.5 -100 -80 -60 -40 -20 0 20 40 60 80 100

UDC / V

(a)

IP3 / dBm

C / pF

0.9

32 IP3 Pdiss

30

52

28

50

26

48

24

46

22

44

20

42

18

40 22

Pdiss / dBm

1.0

159

24

26

28

30

32

16 34

Pin / dBm

(b)

Fig. 4.6.11 C-V, Q-V (a) and power handling performances (b) of a thick film interdigital BST varactor. Reprinted with permission from IEEE©2005

4.6.2.2 Varactors Based on Semiconductor Substrates

The progressive downscaling of the gate lengths and development of CMOS transistors with the cut-off frequencies well above 100 GHz makes this cost effective MMIC technology competitive with the III-V (GaAs etc.) based MMICs. Similar progress is achieved in SiGe based MMICs. In both of these technologies introduction of the dedicated processes for fabrication of high performance varactors requires more masks and process steps making these processes not cost effective. Instead the available transistor designs are modified to adopt for varactor application. The tuneability of the MOS structures is very small at elevated microwave frequencies, and they cannot be used as varactors at millimeter wave frequencies. In principle, the ferroelectrics have the potential to fill in the “varactor” gap. The material problems associated with the integration ferroelectrics with standard silicon processes are solved; ferroelectric capacitors integrated with MOS transistors are used commercially in FRAM. Thus, there seems to be no major problems in the development of SiMMICs integrating ferroelectric films, where some useful features of ferroelectrics may be utilized. High dielectric permittivity, electric field dependence of permittivity and piezoelectric effect are the main features of ferroelectrics making them attractive for applications in SiMMICs. Currently the main limitation seems to be associated with the limited market of the MMICs (in comparison to digital/memory IC) which makes it economically unjustified for the semiconductor foundries to consider SiMMICs with ferroelectrics. Ferroelectric films integrated with coplanar-plate MOS structures (Fig. 4.6.12 (a), may be useful for varactor applications and offer added functionality in ferroelectric (polar) phase. Figure 4.6.12 (b) shows a simplified equivalent circuit of the metal-ferroelectric-oxide-semiconductor (MFOS) varactor, where C⊥2 and C⊥2 represent the capacitances between the electrodes and SiO2 layer, in the direction normal to the interface. Cox1 and Cox2 are the capacitances of the ox-

160

4 Substrates, Varactors and Passive Components

C||

1

1

2

2

C⊥1

C⊥2

Cox1

Cox2

Ferroelectric Silicon substrate

COS1

SiO2

(a)

100

~(1/COS1+1/COS2)-1

Microwave

Tuneability, %

Low frequency

(c)

COS2

(b) C

~C||

RSi

MFOS 10 1.0

MOS

~C|| 0.1 V

(d)

10

20

30

40

50

Frequency, GHz

Fig. 4.6.12 MFOS varactor (a), its equivalent circuit (b), C-V (c) and comparison of the tuneability with the CMOS varactor (d). Reprinted with permission from IEEE©2001

ide film between the ferroelectric film and silicon substrate. COS1 and COS2 are the equivalent capacitances of oxide-silicon interface including the potential barrier at the silicon surface. The capacitance between the electrodes associated with the inplane electric field in the ferroelectric film is denoted by C||, and Rsi represents the losses in the silicon substrate. In fact, there are two back-to-back connected MFOS capacitors. Each of these capacitors should have C-V dependence typical for MOS capacitors (Nicollian and Brews 1982). It can be easily shown that the C-V performance of MFOS varactor has the shape shown in Fig. 4.6.12 (c). The performance depicted in Fig. 4.6.12 (c) is observed in experiments (Gevorgian et al. 2001) at frequencies as high as 30–40 GHz. In this experiment Na0.5K0.5NbO3 (NKN) films deposited by RF sputtering are used. The results presented in (Gevorgian et al. 2001) show that NKN/Si structures have a number of advantages for applications in practical tunable microwave devices at f>10– 20 GHz. The most distinguishing features for such applications is the high Q-factor (Q=15–80 at 40 GHz, depending on the NKN film quality). Varactors based on NKN/Si films are also characterized by sufficient tuneability, low dispersion and low frequency dependence of the tuneability. The analysis of these ex-

4.6 Microwave Performance

161

periments also show that at low microwave frequencies (below about 10 GHz) the tuneability of the capacitance is dominated by the surface barrier at the SiO2/Si interface, while at millimeter wave frequencies the tuneability is due to the ferroelectric film (Fig. 4.6.12 (d)). Little is known about the microwave properties of NKN in polar phase. Recently more experiments have been published with NKN films deposited on oxidized silicon substrates (Abadei et al. 2002). Bulk NKN is characterized by a ferroelectric phase transition at about 600 K, i.e. one should expect that the films at room temperature are in a polar phase. Indeed, thin films on silicon substrate have distinct hysteresis loops with remnant polarization about 10 μCoul/cm2. This may be used to make MFOS based bi-stable microwave switches where up and down remnant polarizations in NKN film are used to induce highly conductive or dielectric (depleted) surface channels between the plates of the varactor.

4.6.3 Distributed Varactors The extremely low leakage currents in ferroelectrics (e.g. BSTO) used in tunable microwave devices allow fabrication of transmission line sections uniformly loaded with ferroelectrics. The transmission lines with coplanar electrodes, such as CPW, CPS and coupled microstrips, are suitable for distributed ferroelectric varactors. In this respect MEMs, due to design, and semiconductors, due to leakage currents, have very limited possibilities. The distributed varactors extensively used in room temperature delay lines considered in Sect. 5.3.5. The NASA group considered coupled microstrip lines with HTS (Van Keuls et al. 1997) and normal metal electrodes (Van Keuls et al. 1999).

60

1450 1400 1350

4/18

effective dielectric constant

Thin film dielectric constant

1500

6/25

1300 1250 1200

strip width (µm)/ gap width (µm)

1150 1100 -5

0

5 10 15 Electric field (kV/cm)

(a)

20

g 2s g

55 50

LAO

45

Au YBCO or Au STO

Sample 2s/g (µm)

40

#3 4/18

35 30

#3 6/25 #1 4/18

25

#1 6/25

20

0

10

20 30 40 Frequency (GHz)

50

(b)

Fig. 4.6.13 The voltage dependence of the thin film dielectric constant of sample 3 at 20 GHz and 20 K (a) and frequency dependence of the effective dielectric constant measured for sample 1 and sample 3. Reprinted with permission from AIP©1998

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4 Substrates, Varactors and Passive Components

The integration of the ferroelectrics with high temperature superconductors is due to the low losses in HTS electrodes and structural/chemical compatibility of these materials. Figure 4.6.13 depicts the performance of a coplanar waveguide on LaAlO3 substrate (Petrov et al. 1998). The STO film is 400 nm thick. There is no YBa2Cu3O7–x (YBCO) in sample 1 and gold film is 1.0 μm thick. In sample 3 YBCO is 250 nm thick with a 20 nm Au on top if it (see inset in Fig. 4.6.13 (b)). Higher field confinement in STO and higher tuning is obtained for narrow gapwidth (Fig. 4.6.13 (a)). It is interesting to compare the frequency dependences of the effective dielectric permittivity for the CPWs with the identical cross sections but with YBCO and Au electrodes (Fig. 4.6.13 (b)). The strong frequency dependence for the gold electrodes (sample 1) is due to the skin effect associated internal inductance (Gevorgian et al.1997). The kinetic inductance (London penetration depth) is frequency independent which explains the frequency independent effective permittivity observed for the CPW with YBCO electrodes (sample 3). Unfortunately the losses in STO grow at cryogenic temperature which does not allow full utilization of the advantages of the HTS electrodes (low losses) in microwave devices.

4.7 Power Handling Capability and High Power Varactors High levels of the microwave power cause overheating of the varactor due to the dissipation of the microwave power both in electrodes and in the ferroelectric. The overheating affects the permittivity/capacitance, tuneability and the losses. Additionally, at high microwave power levels the voltage swing of the microwave signal may be comparable with the maximum tuning DC voltage causing a parasitic modulation of the device capacitance and generation of high order harmonics. While the latter may be a useful feature for applications in nonlinear devices (see Sect. 5.8) it results in unwanted harmonic generation and intermodulation distortion in other applications. The intermodulation distortion may be characterized (Mueller et al. 2001) by the ratio: IMD∼VRF/VDC and it should be below certain limit specified by the system application. A measurement procedure and the results of the nonlinear measurements for the parallel-plate varactors are given in Chap. 8. For increasing the power handling capability, i.e. reducing the heating and the levels of the generated higher order harmonics the thickness of the ferroelectric film in the parallel-plate varactors and the gapwidth in coplanar-plate varactors have to be increased. This straightforward approach inevitably leads to the increased levels of the DC voltages required for controlling the capacitance. This is not always acceptable, especially in microwave circuits (i.e. CMOS based) and systems where the DC supply is below 5 V. A more elegant solution takes the advantage of the excellent dielectric properties of the ferroelectrics. Due to the negligible leakage currents the ferroelectric varactors offer a unique way for utilization of DC biasing networks. A technique of increasing power handling capability of the semiconductor varac-

4.7 Power Handling Capability and High Power Varactors

163

tors is proposed in (Knights and Kelly 1999) is based on stacking junction varactors using a combination of series back-to-back and parallel combinations of diodes. Recently the concept is applied to the ferroelectric varactors. For three cascaded ferroelectric varactors it is shown in Fig. 4.7.1. Since the leakage current in the varactor is negligible, no current flows in the resistors R, and the potentials of the terminal 1 and node 4 are practically the same. The same is applied to terminal 2 and node 3. Thus the DC voltage over any of the varactors is the same as the voltage applied between the terminals 1 and 2. The resistor’s resistance is very high, so that it does not shunt the RF current flowing in the varactor. As a result, for the RF signal all varactors are connected in series, while for the DC bias they are in parallel. One may increase the number of the varactors thus reducing the RF voltage over each varactor while the DC tuning voltage remains small and the same on each of the varactors. This allows controlling high microwave powers by small DC voltages and effectively increases the power handling capability. R

1

4 3

2

R

Fig. 4.7.1 The concept of increasing the power handling capability

The main features of the concept: the RF and DC terminals are common, odd number of varactors may be cascaded. It may be easily shown that the tuneability and the Q factor of the resulting high power varactor is the same as one of the consisting varactors. The reduced tuning speed is the price to pay. The resistance of the resistors is selected using three basic conditions: • The resistors should not shunt microwave current: R>(ωC)–1, • The resistance should be larger than the shunt/loss resistance of the two varactors R>(1/G)–1, where G is given via loss tangent: G=1/(εεotanδ) • The time constant of the RC circuit, τ=RC, has to be small enough to keep the tuning speed high: (in case R is the main de-charging circuit). Both parallel-plate and coplanar-plate varactors based on this principles are demonstrated.

4.7.1 Parallel-Plate Varactors Agile RF Inc. and Kyocera (Katta et al. 2006) developed high power parallel-plate ferroelectric varactors using high resistivity DC bias networks. Similar results are reported by Mortazavi’s group (Fu et al. 2006). Shown in Fig. 4.7.2 is the varactor

164

4 Substrates, Varactors and Passive Components

Single varactor

1.1

140

1.0

120

0.9

100

0.8

80

0.7

60

0.6

40

0.5

20

0.4

0 0

TaNx DC Bias

Q Factor

Normalized Capacitance C(V)/C(0V)

developed by Kyosera. The 1.0 × 0.5 mm2 device consists of 11 cascaded BST parallel-plate varactors fabricated on sapphire substrate. The tuneability of the varactor is 40% at 3.6 V, the Q-factor (at 2 GHz) is better than 60, and the leakage current is less than 10 nA at 3.6 V. The power handling capability of a similar design measured in (Fu et al. 2006) is depicted in Fig. 5.7.2 (c).

1

2

3

4

5

6

Applied Voltage[V]

(a)

(b)

(c)

Fig. 4.7.2 Microphotograph (a) and C-V performance (b) of 11 cascaded varactors Kyocera’s (Katta et al. 2006), and dependence of the intermodulation product on the number of cascaded varactors at 1.35 GHz (Fu et al. 2006). Reprinted with permission from IEEE©2006

4.7.2 Coplanar-Plate Varactors The concept is proved for the coplanar-plate varactors (Fig. 4.7.3, Yoon et al. 2003). In this work oxide electrodes made of indium tin oxide (ITO) or lanthanum strontium cobalt oxide (LSCO) of 3–10-nm thickness, are used for the highresistivity DC-bias (called attached bias electrodes, ABE) electrodes. Obviously this may be done on nanometrically smooth ferroelectric films grown epitaxially on crystalline substrates (e.g. sapphire, MgO). The sheet resistance of these films is in the range of (2–3)104 Ohm/sq. According to the authors a lightly doped silicon or polysilicon may also be used. Fig. 4.7.3 (c) shows the frequency dependence of the capacitance of the varactors with short (Fig. 4.7.3 (a)) and long (Fig. 4.7.3 (b)) high resistivity ITO DC bias electrodes (ABE). In the low-frequency region, the capacitance of the varactor with the long high resistivity electrodes is the sum of

4.8 Ferroelectrics in Passive Devices as High Permittivity Dielectric

165

the capacitance from high resistivity bias and RF electrodes (Fig. 4.7.3 (c)). Above 10 MHz, the overall impedance of this varactor is dominated by the RF electrodes with an equivalent frequency independent capacitance defined by the wide gap between the RF electrodes. The applied DC bias effectively changes the permittivity of the ferroelectric film due to the small gap between the high resistive bias electrodes and at the same time these electrodes do not contribute in the total capacitance- they are not “visible” for the microwave field.

Fig. 4.7.3 Coplanar-plate varactor with short (a) and long (b) Attached Bias Electrodes and the capacitance dependences of these structures with and without ABE (C). Reprinted with permission from IEEE©2003

4.8 Ferroelectrics in Passive Devices as High Permittivity Dielectric 4.8.1 High Density Capacitors High permittivity not only reduces the footprint (real estate) of the high density capacitor but also the parasitic inductance of the plates due to the small sizes of the plates thus shifting the self resonant frequency upwards which is important for

166

4 Substrates, Varactors and Passive Components

microwave applications. Ceramic BaTiO3 is traditionally used in large capacitors. Although some ceramics companies (American Ceramics, Murata, Temex Ceramics etc.) market ceramic BaTiO3 based capacitors (know as high K dielectric capacitors) as a commercial product, the large temperature and voltage dependences of these capacitors is not acceptable for some applications. In some of these capacitors the ferroelectric is in polar phase with a rather large piezoelectric effect, which is supposed to cause noise problems. In this sense use of the ferroelectrics in paraelectric phase is preferable. In this section thin film high density capacitors based on paraelectric films are considered. Incipient ferroelectrics (SrTiO3, KTaO3, TiO3, TiO2) seem to be the best candidates. Since they do not have ferroelectric phase, the temperature dependence of the permittivity is very week near the room temperature. The permittivity slope at room temperature is of the order 10–4 K–1, (Lemanov et al. 1999) and microwave losses are negligible. Gennum (Bernacki et al. 2004) developed mesa type multi layer BST capacitors where the alternating layers of Pt and paraelectric phase BST are deposited on 4” alumina wafer to form a four-layer capacitor stack, Fig. 4.8.1. BST films are deposited by metal-organic decomposition (MOD) or RF reactive sputtering. Each layer, in sequence from the top down, is patterned until the entire mesa structure is defined. An interlayer dielectric (ILD) is deposited over the entire wafer surface and cured at high temperatures followed by formation of vias using standard photolithography and reactive ion etching. Gold or aluminum layers are used for interconnect. Silicon nitride is used for passivation. The BST capacitor process in full-scale high volume manufacturing yields approximately 90%. 4-inch wafers typically contain between 400 and 5000 dice, depending on the design. The achieved total capacitance density is in the range of 144 to 256 nF/mm2, depending on the deposition method used. For a device with tuneability of approximately 2:1 Q factor of over 200 at 1 GHz, and over 160 at 3 GHz is reported. When the BST composition is tailored to favor tuneability over quality factor, tuneabilities of over 4:1 is achieved, with Q factors over 60 at 1 GHz. Time-domain dielectric breakdown (TDDB) studies indicate that the capacitors have lifetimes of greater than 10 years under a continuous bias of 3.3 V.

Fig. 4.8.1 Gennum’s multilayer BSTO varactor

SrTiO3 is most considered for high density capacitor applications. It has extremely high resistivity (undoped ρ >108–1010 Ohm cm) and frequency independent permittivity up to several THz. Ion beam sputtered SrTiO3-based MIM capacitors

4.8 Ferroelectrics in Passive Devices as High Permittivity Dielectric

167

for above IC technology is considered by ST Microelectronics (Guillan et al. 2004). The MIM capacitors are fabricated on thermally oxidized silicon wafers. A 10 nm-thick Ti layer was sputtered and fully oxidized, 15 minutes in oxygen at 600°C, to get TiO2 adhesive layer. A 100 nm-thick platinum layer was used as a bottom electrode. Process conditions and STO characterization are described in (Defaÿ et al. 2003). As-deposited STO films are amorphous (ε= 18). The film is annealed 30 minutes in air. The top electrode is made of 100 nm-thick sputtered Pt. The complete structure is annealed for curing. MIM capacitors with 20 nm and 50 nm thick STO film are fabricated and measured. The measured permittivity of 50 nm STO films is 95 and 116 respectively for 450°C and 550°C annealing temperatures. The permittivity and capacitance are not DC bias dependent up to 75 V/μm. The breakdown field is less than 100 V/μm. After annealing, the 20 nm STO capacitor exhibited leakage currents of 10-7 A/cm² at 100V/μm. The films with lower crystalline (more amorphous) structure are smoother and have lower leakage current. The leakage is associated with the conductivity of the grain boundaries. Fujitsu considered ferroelectric decoupling capacitors for high frequency applications (Imanaka et al. 2002). BSTO is considered in passive/decoupling capacitors in GaAs (Ueda 1999) and GaN (Xu et al. 2004) ICs. You1 et al. (2007) designed and fabricated embedded capacitors in 8-layered printed circuit board employing standard PCB processes. Composites of BaTiO3 powder and epoxy resin are employed for dielectric materials in embedded capacitors. The PCB integrated diplexer is remarkably reduced in size by using embedded high Q circular stacked spiral inductors and MIM capacitors with high dielectric BaTiO3 composite film (Park et al. 2007).

4.8.2 MEMs with Ferroelectric Spacers In the traditional MEM switches the used low dielectric permittivity material (e.g. Si3N4) limits its application at lower frequencies. To further improve the performance of MEM switches, higher ratio Con/Coff and thus larger down state capacitance is required. High permittivity ferroelectrics (e.g. BSTO) are used in digital RF MEMs, instead of SiO2 (Fig. 4.8.2) to increase the on/off ratio of the capacitance (Liu et al. 2002, Berland et al. 2003). Bridge

Substrate

Ferroelectric

Bottom plate

(a)

Substrate

(b)

Fig. 4.8.2 Off (a) and on (b) states of a MEM switch using ferroelectric film

168

4 Substrates, Varactors and Passive Components

A ferroelectric MEM switch may offer and extra functionality analog tuning of the on state capacitance due to bias dependent permittivity of the ferroelectric film. A compact and low-loss capacitive cantilever MEMS switch with extra analog tuned tuning is proposed in (Wang et al. 2005). It uses BSTO film as the dielectric layer and a separate actuation electrode. Figure 4.8.3 shows the switch in both up and down switch states. The BSTO films are prepared by using nGimat’s CCVD process. Sapphire substrate is used to deposit 200 nm BST films on Ti/Pt (200 Å/1000 Å) base metal and the Au membrane is 1.2 mm thick. The pull-down voltage is measured to be 45 to 50 V. At down state the capacitance changes from 130 to 71.2 pF when the applied voltage ranges from 1 to 5 V. The measured Q-factor is 260 and the isolation is –25 dB at 20 GHz. In the down state the insertion loss is 0.6 dB up to 40 GHz. It is not indicated in the paper if there is a thin metal layer deposited on top of the BST film. The negative effects of the dead layers, discussed throughout this chapter and other chapters in this book, show that a possible air gap between the bridge/cantilever and ferroelectric film in down state will reduce the analog tuneability of the discussed MEM. An extra conducting film deposited on top of the BST film may help to avoid this problem.

(a)

(b)

Fig. 4.8.3 Up (a) and down (b) states of the cantilever switch with analog tuning features using BST thin film and separate actuation electrode (Wang et al. 2005). Reprinted with permission from IEEE©2005

4.8.3 MOS Transistors with Ferroelectrics as Gate Dielectric Since the MOS transistors have been introduced in early 1960s SiO2 is used as gate dielectric. However, SiO2 based IC technology is approaching fundamental limits. The size reduction imposes scaling constraints on gate oxide thickness (Feldman et al. 1998). The thickness of the SiO2 less than 50 Å is limited by tunneling currents. The excessive tunneling currents force to look for alternative gate dielectrics. Perovskite ferroelectrics as SrTiO3 and BaTiO3 are discussed for these applications. It is suggested that they maintain a one-to-one correspondence between physical and electrical structure preserving translational symmetry to atomic dimensions (McKee et al. 1988). By virtue of high dielectric constants,

4.9 Conclusions

169

these ferroelectrics offer changes in the scaling laws for silicon-based transistor technology. The effective thickness: teq =

ε oε SiO2 (C / A)

(4.8.1)

For these applications SrTiO3 is considered as one of the most attractive materials. It has extremely high bulk dielectric constant and can be grown epitaxially on Si (Eisenbeiser et al. 2000). A110 Å thick SrTiO3 layer grown epitaxially on Si is electrically equivalent to a SiO2 film of less than 10 Å (Eisenbeiser et al. 2000). The MOSFETs using this gate dielectric show excellent performance with inversion layer electron mobility of 221 cm2/V s and hole mobility of 62 cm2/Vs. The leakage current in these devices is over 2 orders of magnitude lower than an electrically comparable SiO2 gate dielectric. Using BSTO as a gat dielectric in GaN HEMT transistors is reported in (Hansen et al. 2004). Other possibilities of the MFOS structure are discussed in Sect. 4.6.2.

4.9 Conclusions Today tunable microwave components are utilized using semiconductor devices (p-n, Sckottky HBV, transistors etc.); micro- and nano-electromechanical switches; ferromagnetic/ferrite components etc. The accumulated experience and knowledge in materials science allows optimization of the ferroelectric films for applications in high performance ferroelectric varactors and passive components like high density capacitors, MEMs with improved on/off ratio, MOS structures etc. The ferroelectric varactors available today have superior parameters (tuning speed, Q-factor, leakage current, power handling capability etc.) in comparison with the competing technologies (see Sect. 1.4), and the developed scalable circuit models allow their applications in complex agile microwave devices and systems. The low leakage currents, small sizes, low losses, easy integration and other advantages of the ferroelectric varactors make them attractive for applications in large 2D and 3D arrays of agile microwave systems like phased arrays and metamaterials. Using Si carriers may allow implying new functionalities of the MFOS structures and open up possibilities for heterogeneous integration of the ferroelectrics with the other advanced components (MEM, TFBAR etc.). The temperature stabilization, hysteresis, reliability etc. are considered in Chap. 10 where it is show that these issues do not hinder the large scale practical applications of the ferroelectric varactors. No publications dealing with the noise performance of ferroelectric varactors are available. However, it follows from general considerations that one may expect very low 1/f noise, since it is directly related to the leakage currents.

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4 Substrates, Varactors and Passive Components

References Abadei S et al. (2002) Low frequency and Microwave Performances of Laser Ablated Epitaxial

Na0.5K0.5NbO3 Films on High Resistivity SiO2/Si Substrates. J Appl Phys 91:2267–2276 Acikel B et al. (2001) Phase shifters using (BaSr)TiO3 thin films on sapphire and glass substrates. IEEE MTT-S’2001 International Microwave Symposium Digest Volume 2:1191– 1194 Alford N McN et al. (2005) Improving electrical properties of ferroelectric films by ultraviolate radiation. Appl Phys Lett 87: 22204 Aspemyr L et al. (2007) 25 GHz and 28 GHz Wide Tuning Range 130 nm CMOS VCOs with Ferroelectric Varactors. The 2nd IEEE International Workshop on RF Integration Technology, Singapore, Dec. 2007 Basceri C et al. (1997) The dielectric response as a function of temperature and film thickness of fiber-textured (Ba,Sr)TiO3 thin films grown by chemical vapor deposition. J Appl Phys 82 (5):2497–2504 Berland E et al. (2003) 4th Workshop on MEMS for Millimeterwave Communications, Toulouse:F59–F62 Bernacki T A et al. (2004) Barium Strontium Titanate Thin-Film Multi-Layer Capacitors. Passive Component Industry, September/October: 11–13 Boikov Yu A et al. (2001) Slow capacitance relaxation in BaSrTiO3 thin films due to the oxygen vacancy redistribution. Appl Phys Lett 78 (24):366–3868 Boikov Yu, Claesson T (2002) c-axis oriented epitaxial Ba0.25Sr0.75TiO3 films display CurieWeiss behavior. Physica B 311:250–262 Carlsson E and Gevorgian S (1999) Conformal Mapping of the Field and Charge Distributions in Multilayered Substrate CPWs. IEEE Trans. Microwave Theory Tech 47:1544–1552 Chase D R et al. (2005) Modeling the Capacitive Nonlinearity in Thin Film BST Varactors. IEEE Trans Micr Theory Tech 53 (10):3215–3220 Defaÿ E et al. (2003) Deposition and Characterisation of SrTiO3 Thin Films Deposited by Ion Beam Sputtering on Platinized Silicon Substrates. Ferroelectrics 288:121–132 Deleniv A et al. (2005) LTCC compatible phase shifters. Digest IMS’2005 Deleniv A, Abadei S, and Gevorgian S (2003) Microwave Characterization of Thin Ferroelectric Films. Proc. EuMC’2003 1:483–486 Deleniv A, Gevorgian S (2008) Modelling of Conductor Losses in Capacitors with Rectangular and Circular Plates. RFMiCAE, Published on-line August 20, 2008 Delpat S et al. (2003) Voltage and Frequency Dependent Dielectric Properties of BST-0.5 Thin films on Alumina Substrate. IEEE Microwave and Wireless Components Letters 13:211213 Dillner L, Stake J and Kollberg E (1998) Analysis of symmetric varactor frequency multipliers. Microwave and Optical Technology Letters 15:26–29 Eisenbeiser K et al. (2000) Field dielectric in CMOS Field effect transistors with SrTiO3 gate dielectric on Si. Appl Phys Lett 76 (10):1324–1326 Erker E G et al. (2000) Monolithic Ka-band phase shifter using voltage tunable BaSrTiO3 parallelplate capacitors. IEEE Microwave and guided Weave Letters 10:1012 Feldman L C et al. (1998) Ultrathin Dielectrics in Silicon Microelectronics. In: Garfunkel E et al. (Ed) Fundamental Aspects of Ultrathin Dielectrics on Si based Devices. Kluwer, Dordrecht Fu J S et al. (2006) A Linearity Improvement Technique for Thin-film Barium Strontium Titanate Capacitors. Dig. IMS 2006:560–563 Fusco V F (2000) Topical meeting on silicon integrated circuits in RF systems:5–28 Gevorgian S (1998) Surface Impedance of Silicon Substrates and Films. Int Journal of RF and Microwave Computer Aided Design 8:433–440 Gevorgian S and Vorobiev A (2007) Tunable Metamaterials Based on Ferroelectric Varactors. Proc. EuMC 2007:404–407 Gevorgian S et al. (1997) A Simple and Accurate Dispersion Expression for the Effective Dielectric Constant of Coplanar Waveguides. IEE Proc Antennas and Propagation 144 (2):145–148

References

171

Gevorgian S et al. (2001) MOS Varactors with Ferroelectric Films. IEEE MTT-S2001 Dig 2:1195–1197 Gevorgian S et al. (2006) DC field and temperature dependent acoustic resonances in parallelplate capacitors based on SrTiO3 and Ba0.25Sr0.75TiO3 films. Experiment and modeling. J Appl Phys 99:124112 Gevorgian S et al. (2006) Electromechanical Modelling and Reduction of the Electroacoustic Losses in Parallel-Plate Ferroelectric Varactors. Proc EuMC:851–853 Gevorgian S, Deleniv A, Vorobiev A et al. (2008) CAD Oriented Frequency, temperature and DC bias dependent small-signal, scalable circuit model of parallel-plate paraelectric varactors. RFMiCAE. Published on-line November 3, 2008 Guckel H et al. (1967) A Parallel-Plate Waveguide Approach to Microminiaturised, Planar Transmission Linens for Integrated Circuits. IEEE Trans Micr Theory Tech MTT-15:468–476 Guillan J et al. (2004) Optimization of surfacic capacitance and leakage currents on Ion Beam Sputtered SrTiO3-based MIM capacitors for above IC technology. Iteg Ferroelectrics 67:93/1025-102/1034 Hansen P J et al. (2004) AlGaN/GaN Metal-oxide-semiconductor Heterostructure Field Effect Transistors using barium strontium titanate. J Vacuum Science and Technology B 22(5): 2479–2485 Hoffmann F (1996) Grain size effect on the permittivity of CSD prepared BaTiO3 Thin Films. IWE/RWTH and EKM Report 199:62–63 Hu W et al. (2005) Cost effective ferroelectric thick film phase shifter based on screen-printing technology. Dig Int Microwave Symp IMS’2005 Imanaka Y et al. (2002) Decoupling Capacitor with Low Inductance for High-Frequency Digital Applications. Fujitsu Sci Tech J 38 (1):22–30 Kageyama K et al. (2005) Thickness Dependences on Microwave Tunable Properties for (Ba, Sr)TiO3 Thin Films in Planar Capacitor Structure. Dig Int Microwave Symp IMS’2005 Katta H et al. (2006) Tunable Power Amplifier Using Thin-Film BST Capacitors. Dig Int Microwave Symp IMS’2006:564–567 Kenney J S et al. (2006) Low-Voltage Ferroelectric Phase Shifters from L- to C-Band and Their Applications. Aerospace Conference 2006 Kerr D C et al. (2008) Identification of RF harmonic distortion on Si substrates and its reduction using a trap-rich layer. SiRFIC Dig:151–154 Kim D S et al. (2003) 2.4 GHz Continuously Variable Ferroelectric Phase Shifters Using AllPass Networks. IEEE Microwave and Wireless Component Lett 13 (10):434–36 Kim D S, Kenney J S (2003) Tunable Ba0.6Sr0.4TiO3 Interdigital Capacitors for Microwave Applications. Proc 2003 Asia-Pacific Microwave Conf Nov. 4–7, 2003, Seoul, South Korea Kirchoefer S W et al. (1998) Microwave properties of Sr0.5Ba0.5TiO3 thin-film interdigitated capacitors. Microwave and Optical Technology Letters 18(3):169–171 Knights A P and Kelly M J (1999) Laterally stacked varactor formed by ion implantation. Electronics Letters 35 (10):846–847 Koutsaroff I P et al. (2002) Dielectric Properties of (Ba,Sr)TiO3 MOD Films Grown on Various Substrates. Proc 13th IEEE Intern Symp on Applications of Ferroelectrics, Nara, Japan, May 28–June 1:347–250 Kozyrev A B et al. (2007) Time tuning of ferroelectric film varactors under pulse voltages. Appl Phys Lett 91:022905–022907 Kozyrev A et al. (2003)14 GHz tunable filter base on ferroelectric films. Itegr Ferr 55:905–913 Kozyrev A, Gagarin A, Kosmin D et al. (2005) Residual polarization in paraphase BSTO structures and its impact on parameters of microwave devices. Workshop, EuMC, 2005 , Paris Kuylenstierna D et al. (2007) Performance of Coplanar Waveguides on Surface Passivated Highly Resistive Silicon Covered by Ferroelectric Thin Film. Dig. Int. Microwave Symp. IMS’2007:2055– 2058 Lederer D and Raskin J-P (2005) New Substrate passivation Method Dedicated to SOI Wafer Fabrication with Increased Stability of Resistivity. IEEE Electron Device Lett 26 (11): 805–807

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Lemanov V V et al. (1999) Perovskite CaTiO3 as an incipient ferroelectric. Solid State Communications 110:611–614 Liu B et al. (2002) High Isolation BST MEM Switches. Dig Int Microwave Symp IEEE MTT-S 2002 Martin I et al. (2001) Surface passivation of p-type crystalline Si by plasma enhanced chemical vapor deposited amorphous SiCx:H films. Appl Phys Lett 79:2199–2201 Mateu J et al. (2006) Measurement and analysis of microwave nonlinearities in ferroelectric thin film transmission lines. Dig IEEE Int Microwave Symp:1622–1625 McKee R A et al. (1988) Crystalline Oxides on Silicon: The First Five Monolayers. Phys Rev Lett 81:3014–3017 Morrison F D et al. (2005) High-field conduction in barium titanate. Appl Phys Lett 86:152903152905 Mueller C H et al. (2001) Ferroelectric thin film and broad-band satellite systems. IEEE Potentials 20:36–39 Nagra A. S (2000) (2000) Applications of Ferroelectrics in Military Systems. IMS 2000 Workshop WFE: Ferroelectric Materials and Microwave Applications Nath J et al. (2006) Discrete Barium Strontium Titanate (BST) Thin-Film interdigital Varactors on Alumina: Design, Fabrication, Characterization, and Applications. Dig IEEE Int Microwave Symp:552–555 Nicollian E H and Brews J R (1982) MOS physics and technology, Wiley Noeth A et al. (2007) DC bias-dependent shift of the resonant frequencies in BST film membranes. IEEE Utrasonics, Ferroelectrics and Frequency Control 54:2487–2492 Norling M et al. (2007) Comparison of High-Resistivity Silicon Surface Passivation Methods. Proc EuMC2007:215–218 Ostapchuk T et al. (2007) Far Infrared Spectroscopy of Sr1−xBaxTiO3 (0.01≤x≤0.2) Ceramics. Ferroelectrics 353:70–77 Park D. J et al. (2007) Fully Embedded Compact Diplexer into Organic Package Substrate for Dual-mode (GSM/DCS) Handset Applications. ISIF 2007 Petrov P Kr et al. (1998) Improved SrTiO3 multilayers for microwave application: Growth and Properties. J Appl Phys 84: 3134–3140 Robertson J, Chen C W (1999) Schottky barrier height tantalum oxide, barium strontium titanate, lead titanate, and strontium bismuth tantalite. Appl Phys Let 74:1168–1170 Rundqvist P, Vorobiev A, Gevorgian S (2006) The effect of SiO2, Pt and Pt/Au templates on microstructure and permittivity of Ba0:25Sr0:75TiO3 films. J Appl Phys 100:114116 Rundqvist P et al. (2003) DC and microwave resistivities of SrRuO3 films deposited on SrTiO3. J Appl Phys 92:1291–1297 Scheele P et al. (2005) Continuously Tunable Impedance Matching Network Using Ferroelectric Varactors. Dig IEEE Int Microwave Symp IMS’2005:6003–6006 Setter N et al. (2004) Polar Ceramics in RF-MEMS and Microwave Reconfigurable Electronics: A Brief Review on Recent Issues. Journal of Electroceramics 13:215–222 Shigemitsu M et al. (2000) Effects of Oxygen Vacancy Diffusion on Leakage Characteristics of Pt/(Ba0.5Sr0.5)TiO3/Pt Capacitor. Jap J App Phys 39:L416 Soldatenkov O et al. (2006) Nonlinear properties of thin ferroelectric film based capacitors at elevated microwave power. Appl Phys Lett 89:232901 Spirito M et al. (2005) Surface Passivated Hig-resistivity Silicon as a true Microwave Substrate. IEEE Trans. Microwave Theory Techn 53:2340–2347 Stolichnov I and Tagantsev A (1998) Space-charge influenced-injection model for conduction in PbZrxTi12xO3 thin films. J Appl Phys 84:3216 Tagantsev A K et al. (2005) Permittivity, tuneability and losses in ferroelectrics for reconfigurable high frequency electronics. In: Setter N (Ed) Electroceramic Based MEMs. Springer Ueda D (1999) Implementation of GaAs Monolithic Microwave Integrated Circuits with On-Chip BST Capacitors. J Electroceramics 3:105–113

References

173

Van Keuls F et al. (1999) Ku-Band Gold/BaxSr1-xTiO3/LaAlO3 Conductor/Thin Film Ferroelectric Microstripline Phase Shifter for Room Temperature Operation. Microwave and Optical Tech Lett 20:53–56 Van Keuls F W et al. (1997) YBCO, Au/STO/LAO thin film conductor/ferroelectric coupled microstrip phase shifters for phased array applications. Appl Phys Lett 71:3075–3077 Velu G et al. (2007) A 360o phase shifter with moderate bias voltage at 30 GHz. IEEE Trans Micr Theory Techn: 52:438–444 Vendik I B et al. (2000) Commutation quality factor of two-state switchable devices. IEEE Transactions Microwave Theory and Techniques 48:802–808 Vorobiev A (2008) Unpublished Vorobiev A et al. (2003) Silicon substrate integrated high Q-factor parallel-plate ferroelectric varactors for microwave/millimeterwave applications. Appl Phys Lett 83:3144–3146 Vorobiev A et al. (2004) Microwave Loss Mechanisms in Ba0.25Sr0.75TiO3 Thin Film Varactors. J Appl Phys 96 (8):4642–4649 Vorobiev A, Rundqvist P, Khamchane K et al. (2004) Microwave Loss Mechanisms in Ba0.25Sr0.75TiO3 Thin Film Varactors. J Appl Phys 96:4642–4649 Voz C et al. (2003) Surface passivation of crystalline silicon by Cat-CVD amorphous and nanocrystalline thin silicon films. Thin Solid Films 430:270–273 Wang G et al. (2005) A High Performance Tunable RF MEMS Switch Using Barium Strontium Titanate (BST) Dielectrics for Reconfigurable Antennas and Phased Arrays. IEEE Anat Wireless Prop. Lett 4:217–220 Xu H et al. (2004) Low Phase-Noise 5 GHz AlGaN/GaN HEMT Oscillator Integrated with BaxSr1–xTiO3 Thin Films. Digest IEEE International Microwave Symposium IMS2004: 1509–1512 Yoon Y K et al. (2003) A Reduced Intermodulation Distortion Tunable Ferroelectric Capacitor— Architecture and Demonstration. IEEE Trans Micr Theory Techn 51:2568–2576 York B (2009) Tunable Dielectrics for RF Circuits. In: Steer M (Ed) Multifunctional Adaptive Microwave Circuits and Systems. Scitech, Raleigh You1 H-W et al. (2007) Simulation and Fabrication of Embedded Capacitors for System on Packaging Applications. ISIF 2007

Chapter 5

Ferroelectric Devices Spartak Gevorgian and Anatoli Deleniv

Abstract Tunable devises based on ferroelectric varactors is the subject of this chapter. It includes delay lines and delay line type phase shifters with frequency independent tunable delay time and phase shifters with frequency independent tunable phase shift. These devices along with tunable resonators, filters, matching networks, tunable power splitters and antennas are the most representative components considered for applications in microwave systems. Applications of the ferroelectric varactors in nonlinear devices like harmonic generators, frequency converters, power limiters, pulse shapers and parametric amplifiers are briefly reviewed. A new type of device – a tunable thin film bulk acoustic resonator using induced piezoelectric effect in paraelectric film concludes the chapter.

5.1 Introduction Applications of the ferroelectric varactors in different microwave devices are considered in this chapter. The tunable phase shifters and delay lines are the typical devices where the potential of the ferroelectrics is most demonstrated. It is important to distinguish between the phase shifters and delay lines. Ideally a phase sifter is supposed to provide frequency independent differential phase shift in a given frequency range. An ideal delay line is expected to provide a frequency independent group delay time in a given frequency range while its differential phase shift linearly depends on the frequency. In reality (and often) the delay lines are also regarded as phase shifters or delay line type phase shifters. The high power handling capability of the ferroelectric varactors is an important feature considered for tunable matching networks used in power amplifiers and antennas. The tunable filters are one of the most considered devices where the high Q-factor of the ferroelectric varactors may be exploited. However, in some applications (i.e. front ends of the modern multi-channel and multi-standard microwave communications systems) the loss/selectivity/tuning/cost requirements to these filters are very strin175

176

5 Ferroelectric Devices

gent. Hardly any available technology may meet these requirements! Apart from these devices tunable power splitters and antennas are the other representative components considered for applications in microwave systems. The applications of the ferroelectric varactors in nonlinear devices like harmonic generators, frequency converters, power limiters, pulse shapers and parametric amplifiers are relatively less studied. Tunable thin film bulk acoustic resonators TFBARs) using induced piezoelectric effect in paraelectric films are essentially new components. These tunable TFBARs are in their infancy and have great potential when it comes to tunable filters and switches.

5.2 Tunable Delay Lines and Delay Line Type Phase Shifters 5.2.1 Figure of Merit The delay lines have considerable applications in modern microwave and digital technologies. Delay locked loops (DLL, Jung et al. 2001), and Voltage controlled oscillators (VCO, Koo and Long 2003), feed-forward amplifiers (Seo 2003), are typical examples, not to mention the phased array antennas, radars, measurement (Seo 2003) systems etc. (Kirchner 1969). Delay lines are also used in digital circuits such as time to digital converters (Rubin and Singh 2000), and computer printed circuit boards to minimize the skew of the clock (Dudek et al. 2000). The absolute value of the delay time, the losses and the sizes are the main parameters of the delay lines. To be able to do assessment of the performance the delay lines are characterized by a figure of merit defined as: FoM τ (V ) =

Lmax (V ) , dB/s Δτ max (V )

(5.2.1)

where Lmax(V) is the maximum loss (typically at V=0), Δτ is the maximum differential delay time: Δτmax(V)=τ(0)–τ(Vmax). For a transmission line based delay line a good merit is the ratio (differential delay time)/(line length), (s/m ns/mm, ps/μm), which allows assessment of the geometrical features. In contrast to none tunable delay lines the tunable delay lines are also characterized by tuneability of the delay time: Tτ (V ) =

( ) 100%

Δτ V

τ (0)

(5.2.2)

In case the delay line is treated as a phase shifter its performance is assessed by: FoM φ (V ) =

Δφmax (V ) , degree/dB Lmax (V )

(5.2.3)

5.2 Tunable Delay Lines and Delay Line Type Phase Shifters

177

Δφ is the maximum differential phase shift: φmax(V)=φ(0)–φ(Vmax). This figure of merit is also used for the performance assessment of the phase shifters with constant (dispersionless) differential phase shifts. FoM of a phase shifter is related to the figure of merit (K) of varactor (4.3.3): FoMφ(V)= m(Δφ)K(V)1/2 (Vendik et al. 2005). The coefficient m(Δφ) depends on the maximum phase shift: m(Δφ) = 6.6 for Δφ=180.

5.2.2 Periodically Loaded Lines 5.2.2.1 Simplified Theoretical Background Periodically loaded delay lines are often regarded as delay line type phase shifters. In this case a standard transmission line (i.e. coplanar, microstrip) is periodically loaded by ferroelectric varactors. The equivalent circuit of a lossless transmission line is shown in Fig. 5.2.1 (a), where the dx is much smaller than the wavelength in the line and L’ and C’ are the per-unit length inductance and capacitance. In principle, the regular line is a delay line itself, characterized by the delay time τ and impedance Z:

τ = dx L'C ' Z=

(5.2.4)

L' C'

(5.2.5)

By loading the line periodically with ferroelectric varactors one increases the delay time and makes it tunable. The unit cell equivalent circuit of a line periodically loaded by varactors delay line is shown in Fig. 5.2.1 (b), where the length dx should still be much smaller than the wavelength in the loaded line., LL is the extra inductance which may be parasitic, i.e. associated with the electrodes of the loading varactor and/or it may be introduced deliberately for increasing the delay time. Cv is the capacitance of the varactor. Both of them are scaled to the length (dx i.e. LL=LL/dx and Cv=Cv/dx). Below the Bragg frequency, fB=1/[π√(L’+LL)(C’+Cv]), the delay time and the impedance of the loaded line may be approximated as: (a) L’

LL

C’

dx

(b)

L’

Cv C’

dx

Fig. 5.2.1 Equivalent circuit of a regular (a) and periodically loaded by inductor LL and varactor Cv (b) transmission line

178

5 Ferroelectric Devices

τ (V ) = ndx ( L'+ LL )[C '+Cv (V )] Z (V ) =

(5.2.6)

L'+ LL C '+Cv (V )

(5.2.7)

where n is the number of the cells, i.e. varactors and ndx is the total length of the loaded line. The delay time (5.2.6) and the differential time delay caused by the tuning of the capacitance: Δτ (V )

[

= ndx ( L'+ LL )[C '+Cv (0)] − ( L'+ LL )[C '+Cv (V )]

]

(5.2.8)

is frequency independent below Bragg frequency. The propagation constants of the unloaded and loaded lines are:

β = ω L'C '

(5.2.9)

β (V ) = ω ( L'+ LL )[C '+Cv (V )]

(5.2.10)

And the phase shift is: Δφ (V ) = ndx[β (0) − β (V )]

[

= ωndx ( L'+ LL )[C '+C v (0)] − ( L'+ LL )[C '+C v (V )]

]

(5.2.11)

i.e. the differential phase shift of the periodically loaded line type phase shifters has linear frequency dependence. As it is evident from (5.2.6) and (5.2.7) along with the tuning of the delay time the impedance of the line also is tuned where the varactor capacitance changes under the applied DC voltage. While designing tunable delay lines one may need matching networks at the input and output ports. In a simple case it may be implemented as cascaded quarter wavelength transformers with characteristic impedance: Z λ / 4 = Z (0) Z (Vmax )

(5.2.12)

5.2.2.2 Varactor Loaded Delay Line (type phase shifters)

Figure 5.2.2 shows a Ku-band delay line type phase shifter (Park et al. 2006) implemented as a CPW (Fig. 5.2.2 (a)) periodically loaded by Bi1.5Zn1.0Nb1.5O7 (BZN) based thin film parallel plate varactors (Fig. 5.2.2 (b)).

5.2 Tunable Delay Lines and Delay Line Type Phase Shifters

179

Fig. 5.2.2 Photograph/layout (a), varactor design (b), measured S-parameters (c) and phase shift (d) of the delay line type phase shifter. L=dx=340 µm, w=30 µm, g=70 µm). Reprinted with permission from IEEE©2006

The 150 nm thick BZN film is deposited by RF magnetron sputtering on sapphire substrate. A nine-section distributed coplanar waveguide provides a differential phase shift of 175 degrees (Fig. 5.2.2 (c) with a maximum insertion loss of 3.5 dB (Fig. 5.2.2 (d)) at 15 GHz, giving a figure of merit 50 degree/dB. The linear frequency dependence of the phase and differential phase shift (Fig. 5.2.2 (d)) is what one expects from this type of devices (5.2.10). A similar device, based on B0.2Sr0.8TiO3 film is reported by Acikel et al. (2002). Agile RF developed a series of this type of true time delay lines (phase shifters) to cover frequency band 1–45 GHz (http://www.agilematerials.com/pdf/ PhaseShifter_WhitePaper.pdf). For comparison, the estimated figure of merit of a periodically loaded synthetic delay line (type phase shifter) implemented in 0.6 μm GaAs MESFET technology (Ellinge et al. 2003) is about 70 degree/dB. This phase shifter is based on low pass filter topology and consist of 16 Π-unit cells with deep depletion-type FETs (G-FETs) used as varactors (0.3 pF). These varactors provide a capacitance ratio of approximately three, Q-factor in the range 14 (at V=0) to 32 (V=5V) at 5.5 GHz. The Q-factor of the 1.2 nH lumped element inductors is 23. The sizes of

180

5 Ferroelectric Devices

the device are 1.4 × 0.6 mm2, and the matching is better than 10 dB. This result seems to be the best reported for the semiconductor passive phase shifters. A high-temperature superconductor phase shifter based on a coplanar strip (CPS) transmission line periodically loaded with planar varactors is reported by Wang (2007). The coplanar-plate YBa2Cu3O7−δ (YBCO) electrodes are deposited on patterned ferroelectric thin film. Baluns are used at the input/output of the balanced CPS to facilitate transitions to input/output microstrip ports. The operation bandwidth of the phase shifter is between 7 to 11 GHz and an average phase shift of 20 degree is achieved under 200 V DC bias. The losses are 0.5 dB and matching is better than 20 dB at center frequency 9 GHz. Attempts are made to develop cost effective delay line type phase shifters using thick ferroelectric films, both HTCC and LTCC compatible (Deleniv et al. 2005). In this work two phase shifters with novel topologies are presented. The phase shifters are based on LTCC compatible ferroelectric films with ε=200, and tanδ=0.04 at 10 GHz. A Ku band phase shifter is designed to provide DC bias independent 15 dB matching in 50% bandwidth with a figure of merit 15 degree/dB. To reduce the DC bias voltages it is implemented as a microstrip design where the ferroelectric film is used as substrate. In an X band phase shifter (Fig. 5.2.3, Deleniv et al. 2005), the ferroelectric film is deposited on the back side of the low permittivity substrate. Coplanar-plate varactors are included in the ground plane and connected with the microstrip using vias (Fig. 5.2.3 (b) and (c)). A DC bias applied between the microstrip and ground plane changes the permittivity of the

Matching network

Vias

Strip

(a) 200μm

~12mm

250 μm Vias

Slots

(b)

Ground plane

Strip Alumina

BSTO, 20 μm 500μm

(c) Via

Slot in ground plane

Fig. 5.2.3 Top (a), bottom (b) views and cross section (c) of LTCC compatible delay line type phase shifter. Shown are photographs of the vias seen in the strip (a) and ground plane (b). Reprinted with permission from IEEE©2005

5.2 Tunable Delay Lines and Delay Line Type Phase Shifters

181

0

(a)

140

(b) 10 GH z

120

-2

Phase shift Δφ, deg

-6

250V -8

-10

0V 2

4

6

8

10

12

Frequency, GHz

14

16

80

g/ dB

700V 600V 500V

600V

∼2 2d e

-4

60 40

500V

20 0

700V

at

100

FO M

Insertion Losses S21, dB

ferroelectric film in the slot, i.e. the capacitance of the concentric coplanar-plate varactor which in this design is integrated in the ground plane. Due to the limitations in screen printing technology the slot is rather wide, 250 μm, and the required tuning voltages are rather high. The BSTO tape is 20 μm thick with εr≈200, tanδ≈0.04@10 GHz. Tuneability is 30% at 4 V/μm. Electrodes are 5 mm thick made of Ag (σ=1.5·107 (S/m)). This design allows reduction in the loss due to reducing the loss contribution associated with the varactors. The measured performance of the devices is shown in Fig. 5.2.4. The figure of merit of this phase shifter is 20 degree/dB at 10 GHz. Matching is better than 10 dB.

250V 0

2

4

6

8

10 12 14 16

Frequency, GHz

Fig. 5.2.4 Transmission losses (a) and FoM (b) of the device show in Fig.5.2.3. Reprinted with permission from IEEE©2005

5.2.2.3 Lumped Inductor and Varactor Loaded Delay Lines

The temptation to increase the delay time by increasing the capacitance of the loading varactors (5.2.6) inevitably leads to reduction of the impedance of the periodically loaded line (5.2.7). Inclusion of lumped element inductors, LL, periodically loading the transmission line (Fig. 5.2.1 (b)) increases the available delay time (phase shift) and allows flexibility in selection of the impedance. An example of this type of delay line developed by Agile RF (Watson 2007) is shown in Fig. 5.2.5. The maximum bias voltage of these parallel-plate varactor based devices is 15 V. The sizes of the devices are of the order of 1.0 mm2. They are designed for flip chip mounting and do not require hermetic packaging. The delay lines using multi turn inductors, as the one shown in Fig. 5.2.5 are practical for lower frequencies, typically below 10 GHz and the bandwidth is limited by the self resonance frequency of the inductors. An ultra wideband delay line reported in (Kuylenstierna et al. 2005) is implemented as a synthetic coplanar-strip (CPS) line loaded by single turn U-shaped inductors (Fig. 5.2.6 (a) and (b)). This type of delay line offers lower dispersion, i.e. frequency dependence of the delay time and good matching. By increasing both LL and Cv, the delay time (5.2.6) may be increased while keeping the impedance (5.2.7) on a desired level.

182

5 Ferroelectric Devices

Fig. 5.2.5 Periodically inductor/varactor loaded delay line. Reprinted with permission from Agile RF Inc.

The equivalent circuit of the unit cell is similar to Fig. 5.2.1 (b). The photographs of the zoomed unit cells are shown in Fig. 5.2.6 (b), where the parallel-plate varactor formed between the bottom and top Au layers sandwiching the ferroelectric films is indicated. Typically the per unit length inductance L’ and capacitance C’ are much smaller than the lumped inductance LL and varactor capacitance Cv, and the delay time and impedance of the synthetic line are given by τ≈√(LLCv), Z≈√(LL/Cv). More than 25% frequency independent tuneability is achieved in the frequency band 45 MHz–25 GHz with a figure of merit 45 dB/ns (Fig. 5.2.6 (c)). 140

Varactor

(b)

Delay time, nanoseconds

(a)

(c)

120 100

0V

80 20 V

60 40 20 0

5 10 15 20 25 30 35 40 Frequency, GHz

Fig. 5.2.6 Synthetic CPS delay line (a), its zoomed unit cell (b) and ultra-wideband performance at 0 and 20 V DC bias. The total length of the device is 2.0 mm. Reprinted with permission from IEEE©2005

5.2.3 Uniformly Loaded Delay Lines The delay lines utilizing sections of the transmission lines including ferroelectrics uniformly distributed along the propagation directions may be regarded as the limiting case of the periodically loaded lines considered in the previous section. In

5.2 Tunable Delay Lines and Delay Line Type Phase Shifters

183

this case the length of the varactors increase and/or the distance between them vanishes. Small size ultra-wideband delay lines are easily implemented using microstrip, coplanar and coplanar strip line sections of length l incorporating ferroelectric films (distributed varactors) as shown in Fig. 5.2.7. In the equivalent circuit of the device (Sect. dx, Fig. 5.2.1 (b)) L’ and C’ are the per-unit line inductance and capacitance of the line without ferroelectric film, and Cv is the per unit length capacitance associated with the ferroelectric film (distributed varactor). Typically C represents the partial capacitances due to the substrate and air, and is much smaller than Cv. As a first approximation the delay time is given as:

τ (V ) =

l ε eff (V ) = L' Cv (V ) co

(5.2.13)

where co is the velocity of the light in vacuum, l is the length of the line section uniformly loaded by ferroelectric (the length of the distributed varactor), εeff(V) is the DC field dependent effective permittivity. The delay time tuning and the associated differential phase shift may be given in terms of effective dielectric permittivity:

[ε

Δτ (V ) =

l co

Δφ (V ) =

2πfl co

Strip

eff

[ε

(a)

(0) − ε eff (V )

eff

]

(0) − ε eff (V )

(5.2.14)

]

(5.2.15)

Strip

Strip

(b)

BaxSr1-xTiO3 B 0 0 T

B xSr Ba 0 1-xSTiO 03T Ground plane (e.g. Au) Substrate (e.g. Si)

Substrate (e.g. Si)

(c)

(d) BaxSr1-xTiO3

BaxSr1-xTiO3 B 0 0 T Substrate (e.g. Si)

B 0

0 T

Substrate (e.g. Si)

Fig. 5.2.7 Cross section of high capacitance microstrip (a) coplanar-strip line (b), and coplanar waveguides (c, d) with ferroelectric films uniformly distributed along the propagation direction

184

5 Ferroelectric Devices

Cv(V) and the effective dielectric permittivity εeff(V) may easily be calculated using conformal mapping technique (Gevorgian et al. 2003). The tuneability of the delay time is given by (5.2.2), and the figure of merit by (5.2.3). The advent of the thin ferroelectric film delay line type phase shifters is closely associated with the discovery of HTS (Vendik et al. 1994). Given the chemical and structural compatibilities (both perovskite) the first YBCO films have been grown on STO substrates and soon the low losses in YBCO electrodes and the DC field dependent permittivity of STO at cryogenic temperatures triggered considerable activities in tunable integrated YBCO/STO and YBCO/BSTO microwave devices. In fact the delay line type of phase shifters based on coplanar YBCO electrodes are one of the first devices demonstrated, (Fig. 5.2.7 (c) DeGroot et al. 1995, Carlsson et al. 1997). After the first experiments with the HTS electrodes the center of the gravity has shifted towards the devices with the normal metal (e.g. Au) electrodes. Superconductor electrodes (Carlsson et al. 1997, DeGroot et al. 1995) may be used if the cryocooling is acceptable. However, one has to keep in mind that along with increased permittivity and tuneability upon cooling the losses also increase in STO. The disadvantage of this delay line is that to reduce the tuning voltages, increase the delay time and its tuneability the width of the slot between the ground plane and signal line need to be as small as possible. The reduction of the slot width inevitably leads to increased losses both in metal strips and ferroelectric film. For a given geometry the delay lines based on distributed varactors are shorter in comparison with the periodically loaded line. This statement is valid for CPW, CPS, slot (fin) lines and coupled microstrip lines. They are intrinsically ultrawideband and more compact. In the case of a coupled microstrip lines, which in fact is a single pole bandpass filter, the bandwidth is limited by the length of the coupled line section. As such the devices based on coupled microstrip lines with distributed varactors have to be designed for the desired frequency band. These devices are filter-phase shifters where the phase shift at a given frequency is associated with the steepness of the filters phase frequency dependence. (b) (a) Z~6Ohm

λ/4

Fig. 5.2.8 Thick film microstrip line [Reprinted with permission from IEEE©2007] (a) and parallel-plate waveguide (b) delay line phase shifters. Reprinted with permission from EuMA©2005

5.2 Tunable Delay Lines and Delay Line Type Phase Shifters

185

0

(a)

S21(0V) S21(330V) S21(650V) S21(900V)

-5

Reverse matching S11, dB

Transmission Losses S21, dB

Microstrip lines based on thick ceramic ferroelectric substrate are considered in the past (Varadan et al. 1992, Varadan et al. 1995). These delay lines require very high voltages to tune and are useful for low frequencies where the substrate surface waves are not exited. Microstrip and parallel-plate waveguide using thick ferroelectric films based chip delay lines (Fig. 5.2.8 (a)) offer lower tuning voltages they are easy to fabricate and integrate in microwave circuits as surface mounted components. The BSTO substrate (prepared by standard bulk ceramic technology) in microstrip line is 100 μm thick and the strip is 50 μm wide. The design shown in Fig. 5.2.8 (b) demonstrated 55 degree/dB at 2.4 GHz under 250 V. The performance of this parallel-plate waveguide based phase shifter is shown in Fig. 5.2.9. This delay line chip is fabricated by TEMEX using standard multilayer capacitor processing technology (Deleniv et al. 2005). (b)

0

-5

-10

-10

S11(0V) S11(330V) S11(650V) S11(900V)

-15

-15

2

2.5

3

3.5

4

Frequency, GHz

4.5

-20

5

2

2.5

3 3.5 4 Frequency, GHz

4.5

5

100

300 Diff_phase(330V) Diff_phase(650V) Diff_phase(900V)

250 200 150 100 50 0

(d)

3

3.2

3.4

3.6

Frequency, GHz

3.8

4

Figure of merit F, deg/dB

Differential phase shift ϕ, deg

(c)

measured simulated

80 60 40 20 0

0

0.5

1

1.5

2 2.5 E, V/μm

3

3.5

4

Fig. 5.2.9 Measured S-parameters (a,b), differential phase shift (c) and FoM at 3.5 GHz (d) of the thick film parallel-plate delay line shown in Fig. 5.2.8 (b). Reprinted with permission from EuMA©2005

In a uniformly loaded delay line one has the possibility to trade between the low losses and high tuneability by selecting the slot width between the coplanarplate electrodes. Additionally, by periodically loading the line by series inductors one may gain extra delay times and achieve desired impedance levels for the specified slotwidths. For example, this may be done in a CPW with uniform ferro-

186

5 Ferroelectric Devices

electric films by periodically loading it with the inductive slot stubs made in the ground plane electrodes in a CPW delay line (Kim 2006). A delay line type phase shifter using a section of uniformly loaded by ferroelectric film fin-line is reported in (Kozyrev et al. 2002). The BaxSr1 –xTiO3 ferroelectric films with thickness 0.5–1.0 μm are deposited by RF magnetron sputtering on alumina substrate at substrate temperature of 905°C. The ferroelectric films are characterized by a loss tangent of 0.04 and tuneability Cmax/Cmin≈1.7. The 1.0 μm thick Cu slotline – waveguide phase shifter operates around 60 GHz with a figure of merit 32 deg/dB and provides a continuous phase shift up to 255 deg. A slot line phase shifter implying interdigital electrodes is reported in (Karmanenko et al. 2007). The distributed interdigital electrodes along the slot form a multislot line and help to reduce the tuning fields (Fig. 5.2.10). The figure of merit is les then 5deg/dB at 30 GHz.

Fig. 5.2.10 Slot line phase shifter with distributed multislot DC bias electrodes. Courtesy of A.B. Kozyrev, LETI, S. Petersburg, Russia

5.2.4 Other Delay Lines In (Kozyrev et al. 2003) a microstrip delay line is proposed using broadband directional couplers with the reflecting ports loaded by two tunable reflective loads including ferroelectric coplanar-plate varactors. A delay variation of 1 ns over frequency range from 1.8 GHz to 2.2 GHz is demonstrated. The device is implemented as a copper microstrip on a 1 mm thick alumina substrate. The delay line consists of a 3 dB 90o hybrid (broadband quadrature directional coupler). Each of the reflection ports of the hybrid is loaded by two series LC resonators connected in parallel (Fig. 5.2.11). The capacitance of each of the varactors is controlled individually. For simplicity the DC bias circuits of the varactors are not shown in Fig. 5.2.11. Under the applied control voltages the resonance frequencies of the LC tanks are derived apart or closer causing changes in the slope of the phase-frequency dependence of the device thereby the group velocity. Experimentally under the DC bias the tunable delay line demonstrated delay time tuning from 3.0 to 2.0 ns (33%) with phase deviation of less than ±5 degrees over frequency

5.3 Phase Shifters

187

range 1.8 GHz to 2.2 GHz. In this frequency band the insertion loss is about 2.5 dB with deviation less than 0.2 dB and return loss is better than –13 dB. The FoM is more than 1.0 ns/dB. Substantial delay times (up to 10 ns at 2.0 GHz) have been achieved in cascaded delay lines of this type. The delay lines have relatively small size. Due to the used resonator circuits they have relatively narrow bandwidth (about 50%) in comparison with the periodically loaded delay lines (Kylenstierna et al. 2006). Output

Input 90o hybrid

Fig. 5.2.11 Simplified circuit topology of the delay line

5.3 Phase Shifters 5.3.1 Figure of Merit of an Analog Phase Shifter Phase sifters are essential in phased array antennas, radars and other microwave systems (Koul and Bhat 1991). They are used for controlling the phase of the signals in microwave systems. Phase shifters with stepwise (digital), continuous (analog) and mixed digital-analog tuning of the phase are considered. Frequency independent phase shift in a wide frequency band, low microwave losses and power consumption, high power handling capability, high tuning speed and low cost; these are some of the common requirements the phase shifters have to meet. Attempts to make phase shifters based on ferroelectrics are reported in already 1962 (Didomenico et al. 1962). A stripline circuit (Varadan et al. 1992) a BST capacitor provided a differential phase shift of 11° at X band under DC bias of 7.0 V/μm. A microstrip phase shifter reported in (Varadan et al. 1995) provides 20°/kV at 2.65 GHz. A phase shifter using thick sol-gel BSTO film provided 55°/dB figure of merit at 2.4 GHz under of 250 V (DeFlaviis 1997). Ferroelectric based phase shifters are basically analog devices. Most of the analog phase shifter topologies considered in (Koul and Bhat 1991) may be realized on ferroelectric varactors. Attempts also are made to develop digital phase shifters based on ferroelectric varactors (Sherman et al. 2001, Kozyrev et al. 2004).

188

5 Ferroelectric Devices

The losses and the differential phase shift are the main parameters of the phase shifters. In most of the system applications the phase shift Δφ needs to be frequency independent in a given frequency range of operation while the losses L have to be independent of the DC bias. The figure of merit of an analog phase shifter is defined in (5.2.3). It is DC bias dependent and usually is taken the maximum when making assessment of the phase shifter performance. Again, it requested that in the frequency range of operation the FoM is frequency independent. Typically the phase shifters are compared by the maximum figure of merit: FoM(V)=Δφmax/Lmax (degree/dB). The figure of merit of a digital phase shifter takes in to account the losses in two phase states (Vendik et al. 1999, Vendik 2000). Figure 5.3.1 gives an estimation of the FoM of ferroelectric phase shifters (Vendik et al. 2003) including the losses in the ferroelectric film and plates. Theoretical estimation

F, degree/dB 300 200

1

100

2

50

4

3

5

20 10

6 1

3

10

30

100

FREQUENCY, GHz

Fig. 5.3.1 Figure of merit – comparison of the experimental results with the theoretical limits (Courtesy of O.G. Vendik). 1, 3, 4 – Ferroelectric phase shifter based on reflection type lumped network, 2, 5 – Transmission line periodically loaded with lumped ferroelectric capacitors, 6 – Transmission line type ferroelectric phase shifter. Courtesy of O.G. Vendik, LETI, S. Petersburg, Russia

5.3.2 Periodically Loaded Line Phase Shifters 5.3.2.1 Traditional Topologies

Periodically loaded line type phase shifters are essentially delay line type phase shifters. In this case a standard transmission line (i.e. coplanar, microstrip) is periodically loaded by ferroelectric varactors. The periodically loaded delay line type phase shifters considered in the previous section have linear phase frequency dependence with substantial change in the differential phase shift in a bandwidth of interest. On the other hand for many applications, especially in phase shifter based

5.3 Phase Shifters

189

and wide band phased array antennas, the differential phase shift within operation frequency bandwidth should be constant. A careful selection of the topology and special design efforts are required for achieving such performance. To generate a flat phase-frequency dependence the microstrip line is periodically loaded by parallel LC resonators approximately λ/4 apart (Fig. 5.3.2 (a)) incorporating coplanar plate straight gap ferroelectric varactors (Kozyrev et al. 2001). In this work the 0.7μm-thick film Ba0.3Sr0.7TiO3 films 3, Fig. 5.3.2 are deposited by RF sputtering on 125 μm thick alumina substrate 7. About 1μm thick copper is used for the electrodes. (a)

(b)

(c) Fig. 5.3.2 Layout (a), unit cell (b) and equivalent circuit (c) of the loaded line phase shifter. Courtesy of A.B. Kozyrev, LETI, S. Petersburg, Russia

In this device a 50 Ohm line is periodically loaded by 20 parallel LC resonators (Fig. 5.3.2 (a)). Each resonator consists of an inductor and a coplanar-plate varactor 4 grounded using radial stubs 5 as shown in Fig. 5.3.2 (b). The inductance is implemented as open circuited shunt microstrip stubs (2) with a length exceeding λ/4. The capacitances are formed by a gap (4) between the microstrip line and λ/4 radial stubs (5). The DC control voltage is applied to the capacitive gap (4) between the microstrip line and the radial λ/4 stubs. The radial stabs are connected by a 30 μm wide strip facilitating connection to the DC bias pad 1.

f, GHz

f, GHz

Fig. 5.3.3 Transmission losses (a) and phase shift (b) under 100, 200, 250, and 320 V DC bias. Courtesy of A.B. Kozyrev, LETI, S. Petersburg, Russia

190

5 Ferroelectric Devices

The measured performance of the phase shifter is depicted in Fig. 5.3.3. A figure of merit of 22 degree/dB at a maximum phase shift of 220 degree at frequencies near 60 GHz is achieved. 5.3.2.2 Phase Shifters Based on Metamaterials Concept

Phase shifters with both positive and negative slopes of phase-frequency dependence may be obtained by taking advantage of recently explored right handed (RH) and left handed (LH) transmission line (TLs) concept (Caloz and Itoh 2006, Eleftheriades and Balmain 2005). A first demonstration on how the nature of RH and LH TLs may flatten the group delay of phase shifting lines was given in (Antoniades and Eleftheriades 2003). Recently a purely left handed (PLH) synthetic TL phase shifter is demonstrated (Kim et al. 2005). The design, modeling, and realization of a tunable left handed (LH) phase shifter using thin film Ba0.25Sr0.75TiO3 ferroelectric varactors is presented in (Kuylenstierna et al. 2006). The LH transmission line metamaterials enables reduced size, compared to conventional loaded line phase shifters realized as right handed (RH) TLs. The phase shifter includes 9 LH unit cells. At 10 GHz the phase advance is about 1000 degrees without applied bias. Under applied 20 V DC bias it reduces to750 degrees resulting in a FoM better than 30 degree/dB over a 22% bandwidth in X band. A thick ferroelectric film based LH phase shifter presented in (Giere et al. 2006) is implemented as a high-pass filter and makes use of thick film BSTO interdigital varactors. The screen-printed and sintered Ba0.6Sr0.4TiO3 layer is on top of a 635 µm Al2O3 ceramic Alumina substrate. The IDC has 8 fingers, each 200 µm long and 10 µm wide. The gaps between the fingers are 10 μm wide. The tunability of the varactors is 32% and the Q-factor is larger than 23 at 2.8 GHz. The measured figure of merit is 29 degree/dB at 2.8 GHz. The bandwidth of the realized circuit, using 3unit cells, is 10%. The simulations show that a 180 degree phase shifter based on the same components may be achieved with a bandwidth of 27% and a figure of merit 31.5 degree/dB. Even though the sizes are very small, the LH transmission line phase shifters produce differential phase shifts with a negative slope, i.e. the phase shift decreases with the increasing frequency. Kuylenstierna et al. (2006) reported a composite right/left handed (CRLH) transmission line phase shifter, using Ba0.25Sr0.75TiO3 parallel-plate varactors (Fig. 5.3.4). The unique features of CRLH TLs (negative slope due to LH and positive slope due to RH sections) enable a differential phase shift with flat frequency dependence around a specified center frequency. The transition from RH performance to LH performance takes place at frequency:

ω o (V ) = ω R (V )ωC (V )

(5.3.1)

5.3 Phase Shifters

191

Where the RH and LH cut-off frequencies are given by

ω R (V ) =

ω L (V ) =

2

(5.3.2)

LR CR (V ) 1

(5.3.3)

2 LL C L (V )

The differential phase shift and impedance are rather well approximated by: Δφ (V ) ≈ n

2ω L (0) ⎡ 2ω ⎡ C (0) ⎤ C (V ) ⎤ ⎢1 − ⎥−n ⎢1 − ⎥ , rad ω R (0) ⎢⎣ ω ⎢⎣ C (V ) ⎥⎦ C (0) ⎥⎦

(b)

(a)

(c)

(5.3.4)

(e)

(d)

Fig. 5.3.4 Equivalent circuit (a), layout (b), measured and simulated differential phase shift (c) and S-parameters (d, e) of CRLH phase shifter. Reprinted with permission from IEEE©2006

where n is the number of the unit cells. C(0)/C(V) is the ratio of the capacitances for both RH and LH varactors at zero bias and under voltage V. The matched at zero bias impedance is: ⎡ C (Vmax ) ⎤ Z R , L (0) = Z o ⎢ ⎥ ⎣ C (0) ⎦

0.25

(5.3.5)

The experimental CPW design is integrated on a high resistive Si substrate. The 3850 μm long device includes four CRLH T-unit cells (Fig. 5.3.4 (b) with the

192

5 Ferroelectric Devices

equivalent circuit of the unit cell shown in Fig. 5.3.4 (a). The design includes DC bias pads 1 and 2. The shunt inductors are “hidden” in the openings in the ground planes of the CPW with one of the ends RF grounded via large area ferroelectric capacitors. The nods of the inductors are connected with the DC bias pads 1 and 2. The parallel-plate varactors, CR, are formed between the overlapping shunt inductor strips and narrow strips in the ground planes. The latter also provide continuous edges of the ground plains and helps avoiding slot line modes. The narrow center strips of the CPW provide series inductors cascaded with the series varactors CL. Under 15 V DC bias applied over each varactor a differential phase shift of 50 degrees is produced which is rather flat about 17 GHz in a 30% bandwidth (Fig. 5.3.4 (c)). For this not completely optimized design the matching and loses are fairly good (Fig. 5.3.4 (d) and (e)). Further reduction of the losses is possible if the varactor design is optimized for example by replacing the used design (Fig. 4.3.10 (b)) with the design shown in Fig. 4.3.11 and passivating the high resistivity substrate as described in Sect. 4.2.3.

5.3.3 Reflection Type Phase Shifters Reflection-type phase shifters typically consist of a 3-dB coupler (Sherman et al. 2001, Kim et al. 2002), rat-race coupler (Kozyrev et al. 1998) and reflective loads. They provide relatively large phase shifts and wide bandwidths. However in this topology the coupler contributes directly to the insertion loss of the phase shifter, and takes a large portion of the substrate. A reflection type ferroelectric phase shifter based on a lumped element hybrid is demonstrated by Serraiocco et al. (2003). Even though the sizes are smaller this device has higher losses due to the low Q-factor of the passive lumped elements. In all reported reflection type phase shifters the differential phase shift has substantial deviations. See also Sect. 5.3.5. The reflection type phase shifters (modulators) used as RFID backscatterers are reported in (Scheele et al. 2005). The resonators are implemented as printed lumped element coils in parallel or in series with thick film Ba0.6Sr0.4TiO3 based varactors. The circuit area is less than 2.4 mm2. In these devices the achieved reflection phase shift is more than 70 degrees under 100 V DC bias and at about 3.0 GHz.

5.3.4 Phase Shifters Based on All Pass Filter Topology In comparison with the loaded line and reflection type phase shifters the phase shifters based on all-pass networks have smaller sizes. An integrated all-pass network based ferroelectric phase shifter (Fig. 5.3.5, Kenney et al. 2006) is designed to operate in the frequency band 0.7–6 GHz. The phase shifter uses BSTO thin-film varactors on a sapphire substrate. Thick copper metallization is used to allow inte-

5.3 Phase Shifters

193

gration of the ferroelectric varactors with the high-Q inductors and other passive microwave elements. The phase shifters are designed for flip-chip mounting. They have sizes less than 4.0 × 4.0 mm2, require 20 V for a phase shift of more than 100 degree over a 30% fractional bandwidth. The coplanar-plate varactors in this phase shifter are fabricated by combustion chemical vapor-phase deposition and make use of high resistivity interdigital electrodes in the gap allowing reduction of the DC bias voltages and increasing the power handling capability (see Sect. 4.7.2). Figure 5.3.6 shows the performance of one of the phase shifters. The highest figure of merit at 2.2 GHz is about 60 deg/dB and the matching is fairly good.

(a)

(b)

Fig. 5.3.5 nGimat- Georgia Tech phases shifter circuit topology (a) and photo (b). Reprinted with permission from IEEE©2006

Similar phase shifters are reported in (Kim et al. 2003). A two-tone cancellation setup (Kim and Kenney 2005) is used to measure the IMD performance of two different phase shifters with the identical layouts but 2 and 4 µm gaps between the fingers of the used interdigital varactors. The IIP3 is 35 dBm for the structure with 4 μm gap: about 8 dB higher then for 2 μm gap.

(a)

(b)

Fig. 5.3.6 Phase shift (a) and S-parameters (b) of nGimat’s nPS1726 phase shifter. Reprinted with permission from IEEE©2006

194

5 Ferroelectric Devices

5.3.5 Other Phase Shifters 5.3.5.1 Phase Shifters Using Distributed Varactors

Distributed coplanar-plate varactors in the form of coupled microstrip lines (Miranda et al. 2008, Romanofsky 2007) and Lange couplers (Serraiocco et al. 2002, Subramanyam et al. 2000) are used in phase shifters. These devices have single pole passband filter response and provide dispersionless (flat) differential phase shift vs. frequency.

(a)

(b)

Fig. 5.3.7 NASAs ferroelectric-semiconductor (a) and Ku-band (b) phases shifters. Reprinted with permission from IEEE©2007

To meet the low cost, energy efficient beam-steering requirements, NASA in its Glenn Research Center developed phase shifters based on ferroelectrics (Miranda et al. 2008, Romanofsky 2007). One of the phase shifters use coupled microstrip lines on top of about 0.4 μm thick ferroelectric Ba1–xSrxTiO3 film. At room temperature, using Au electrodes a figure of merit of 70 degree/dB is demonstrated (Van Keuls et al. 1999). With YBa2Cu3O7–δ electrodes and 2.0 μm thick SrTiO3 films, this phase shifter produces a figure of merit approaching 120 degree/dB at 40 K (Van Keuls et al. 1997). NASAs hybrid ferroelectricsemiconductor phase shifter consists of coupled microstrip line ferroelectric phase shifters and a beam lead GaAs diode switch (Fig. 5.3.7 (a), Romanofsky 2004). The 400 nm thick Ba0.5Sr0.5TiO3 film is laser ablated on a 0.5x10 × 10 mm3 lanthanum aluminate substrate. The cascaded four coupled line sections printed on the ferroelectric film provide up to 180° of analog phase shift under 350 V. A GaAs switch appended to the last coupled section by a quarter wavelength radial stub, switches between an open and virtual short circuit, provides “digital” phase shift between 0° and 180° allowing coverage of a full 360° analog phase shift with 3.2 dB losses in a 10 percent bandwidth. The unmatched beam-lead diode contributed 0.5 to 0.75 dB to the overall insertion loss. In a recent publication (Miranda et al. 2008) NASA reports experimental performance of coupled microstrip line phase Ku-band (near 16 and 18 GHz) shifters

5.3 Phase Shifters

195

using BST films with Ba:Sr ratios of 30:70 and 20:80. The films are grown by pulsed laser deposition. Each of the seven coupled microstrip line sections are 400 μm long with 7.5 μm spacing between the coupled lines (Fig. 5.3.7 (b)). The coplanar metal layers on top the BST films consist of a 15-nm-thick chromium (adhesion layer), followed by 1.6 μm of gold. The BST films are typically 300– 370 nm thick deposited by pulsed laser deposition at a commercial foundry. The films exhibited typical relative dielectric constants of 800 at 300 K and 1 MHz.

Fig. 5.3.8 Room temperature performance of the phase shifter shown in Fig. 5.3.7 (b). Reprinted with permission from IEEE©2007

Figure 5.3.8 (a) depicts the performance of the phase shifter at 300 K and 16 GHz. Hysteresis is negligible. The insertion loss versus frequency (Fig. 5.3.8 (b)) shows shifts of the reject band with voltage. The marked points, a, b, c, d, show how tuning and loss are affected by the position of the reject band. The dip in the insertion loss in Fig. 5.3.8 (a) is intrinsic to the design of the phase shifter which, in fact, consists of seven single pole band pass filters connected in series. For this reason the operating (and rejection) band is narrow and shifts as a function of applied bias. The points a–d in the Fig. 5.3.8 (b) indicate how tuning and loss are affected by the position of the reject band. In applications these types of phase shifters should be designed such that optimal operation is achieved in the pass band, where the insertion loss does not change drastically with the applied DC bias. As it may be seen in Fig. 5.3.8 (b) between 50 V and 200 V, the losses from 13 to 14.5 GHz are within 2.0–2.5 dB. The performance of the phase shifter is measured as function of temperature in the paraelectric as well as in the ferroelectric phases of the film. The phase shifters using BST films, with Ba:Sr ratio of 30:70, have phase shift up to 400° and insertion losses of about 3 dB (figure of merit 133°/dB). In addition, they are hysteresis-free in the paraelectric phase. The phase shifters made with Ba:Sr ratios of 20:80 exhibited very good phase shift and a mild hysteresis both in the paraelectric and ferroelectric phases. Elimination of the hysteresis in phase shift is essential in many practical microwave applications since voltage controlled oscillators and electronically steerable phased array antennas rely on accurate phase shift versus

196

5 Ferroelectric Devices

tuning voltage profiles. A superconducting version of this design is demonstrated earlier (Van Keuls et al. 1997). Chai et al. (2002) developed a switching line phase shifter using BSTO (0.5 μm)/MgO(500 μm) substrates. Three cascaded tunable coupled microstrip lines, similar to (Romanofsky 2004), are used in each branch of the phase shifter. A figure of merit 29 degree/dB is achieved in the frequency band 15 GHz to 17 GHz. 5.3.5.2 Active Phase Shifter

An active phase shifter using ferroelectric Ba0 5Sr0 5TiO3 parallel plate varactor (Mahmud et al. 2006) consists of two bipolar junction transistors coupled with a feedback network containing a varactor which produces a transfer function that can be varied with a control voltage. The active circuit allows for signal gain, while the BST varactor provides a high tuning. According to the authors this phase shifter offers an improvement over strictly passive ferroelectric. The phase shifter provides a true all-pass response over the frequency band 200–1100 MHz and demonstrates 100 degree phase shift with a gain of about 0.6 dB at 1 GHz. The tuneability of the used parallel-plate varactor is 2.75:1. The ferroelectric phase shifters are fairly compact, low loss, consume extremely low DC power and easy to fabricate. They may enhance conventional phased array performance or enable a new type of reflectarray antenna (Romanofsky 2007, Romanofsky et al. 2000).

5.4 Tunable Filters 5.4.1 Tunable Resonators Use of HTS electrodes is considered for high Q-factor integrated (Van Keuls et al. 1998) and disk (Vendik et al. 1995, Gevorgian et al. 1996) resonators. In both cases the Q-factor is limited by the dielectric losses on ferroelectrics. In the case of HTS electroded parallel-plate disk resonators rather high Q-factors may be achieved by using bulk single crystal paraelectrics like SrTiO3 (Eriksson et al. 2003) and KTaO3 (Gevorgian et al. 1998). These type of resonators are considered for high power (>100 W CW) applications, for example in base stations of mobile phones. Unfortunately the Q-factor of these resonators degrades under applied DC bias. This is a fundamental property of the ferroelectrics associated with quasiDebye loss mechanism (Tagantsev et al. 2005). Eriksson et al. (2003) measured the orientation and DC field dependent dielectric properties of bulk single crystal SrTiO3 at microwave frequencies. Circular disk shaped parallel plate resonators with epitaxially grown YBa2Cu3O7 and with

5.4 Tunable Filters

197

evaporated Cu/Ti electrodes are measured. The disks are 0.5 mm thick, 7.0 and 10.0 mm in diameter with [100], [110] and [111] orientations. The dielectric properties are measured in the temperature range 30–300 K, under relatively low DC field 0–1.0 V/μm at 1.0 kHz and in the frequency range 0.3–2.0 GHz. No peculiarities in field dependent dielectric permittivity are detected for STO with smaller densities of impurities. For samples with larger impurity densities double loop hysteresis is observed in the DC field dependent permittivity. For all orientations the losses are minimum at temperatures about 50–55 K. The losses at microwave frequencies increase with the applied dc field regardless of the orientation of the STO crystal. At relatively high DC fields, depending on the temperature, the losses start decreasing. The DC filed dependence is explained by qusi Debye mechanism (Tagantsev et al. 2005). The tuning voltages required for high power disk resonators are high. In contrast, depending on the thickness, in thin films rather high fields and thus permittivity tuning may be achieved at very low voltages. At the same time the loss tangent of the films, depending on the film quality may be much higher as compared with the bulk single crystal analogs. In developing tunable resonators and filters based on film ferroelectrics one may trade between tuneability and Q-factor. In a simple case a “composite varactor” consisting of a high quality non tunable capacitor in series with the varactor allows to increase the Q-factor at the coast of reduced tuneability. In what follows, a simple theory is given, allowing trading between the tuneability and Q-factor. Consider a tunable lumped LC resonator as shown in Fig. 5.4.1. The reactive elements of a hosting resonator are denoted as Lres and Cres , while their losses are represented by R and G respectively. The resonator is loaded by a ferroelectric varactor with the tuneability n and loss factor tan δ , capacitance Cv and conductance Gv . The Q-factor of such a loaded resonator is given by: 1 1 1 − k0 k0 = + + , Ql Qind Qcap Qv

k0 =

Cv (0 ) . Cv (0 ) + Cres

(5.4.1)

(5.4.2)

where Qind , Qcap and Qv are respectively Q-factors of the resonator, inductor, capacitor and ferroelectric varactor, while k0 holds for the inclusion rate of the unbiased ferroelectric varactor. Under applied DC voltage the capacitance of the ferroelectric varactor drops leading to increase in the resonance frequency. At the fixed voltage ( Vmax ) the new/tuned resonant frequency is: ωV max = ω0 + Δω . The tuneability of the resonator, T , is defined as: Tres =

ωV max ω0

(5.4.3)

198

5 Ferroelectric Devices

It is easy to show that for the known inclusion rate k0 and the tuneability n of the ferroelectric varactor, the tuneability of the resonator, T , is given by: Tres =

n . (1 − k 0 )n + k 0

(5.4.4)

The Q-factors of the loaded resonator as defined by (5.4.1) is valid only for the case without DC bias. Under DC bias the inclusion rate and the loss factor of the ferroelectric varactor change resulting in a related change in the loaded Q-factor of the resonator. To keep things simple an averaged loss factor: tan δ = QV

−1

= tan δ0 tan δV max

and average inclusion rate

k = k0 kV max

are used while calculating the averaged loaded Q-factor of the resonator. Obviously, the accuracy of the estimated Q-factor will degrade for higher tuneability ( n ) and also for large difference between the unbiased ( tan δ0 ) and biased ( tan δV max ) losses of the varactor. It follows from (5.4.4) that for a fixed tuneability ( n ) the tuneability of the resonator ( T ) is higher for higher inclusion rates ( k0 ) of the varactor. For the inclusion rate k0 = 1 , Tres = n . It works the other way round for the Q-factor of the varactor loaded resonator ( Ql ). This Q-factor is higher for lower inclusion rates. Hence the Q-factor of the varactor loaded resonator ( Ql ) may be traded against its tuneability ( Tres ). The above formulas are correct for the considered lumped equivalent circuit. However, the accuracy will degrade if the host resonator can not be represented by a simple equivalent circuit shown in Fig. 5.4.1 with the frequency independent Lres and Cres elements. Ferroelectric varactor

Cv Gv

Cres

G

Lres

R

Fig. 5.4.1 A lumped equivalent circuit of the tunable resonator

5.4 Tunable Filters

Resonator

199

(a)

-30

(b)

120MHz

Transmission S21, dB

-35 -40

Varactors

-45

DC bias strip

-50 S21(0V) S21(15V) S21(30V) S21(40V)

-55 -60 14.5

14.6

14.7

14.8

14.9

15

Frequency,GHz

Fig. 5.4.2 Dielectric (fused quartz) resonator loaded with ferroelectric varactors (a) and its performance (b)

The principle described above is demonstrated experimentally (Buslov et al. 2003, Deleniv 2006). Shown in Fig. 5.4.2 (a) is dielectric (fused quartz) resonator loaded by ferroelectric varactors (Deleniv et al. 2006). The ferroelectric Ba0.25Sr0.75TiO3 film is 560 nm thick. The inset in Fig. 5.4.2 (a) shows the design of two cascaded parallel-plate varactors. The Q-factor and the tuneability of the varactor are 50 and 42% correspondingly at about 15 GHz. The measured resonant curves of the resonator enclosed in a metal cavity are shown in Fig. 5.4.2 (b). The loaded Q-factor, as it may be calculated from Fig. 5.4.2 (b) is about 200. The unloaded Q-factor (without DC bias circuit) and the tuneability of the resonator are Q(0V)=530 and 9% correspondingly.

5.4.2 Bandpass Filters 5.4.2.1 General Considerations

Tunable microwave filters used today in commercial and defense microwave systems are mechanical, magnetic (ferrite, YIG) or based on semiconductor varactors. Mechanically tunable filters are used where no fast tuning is required or the adjustment (trimming) of the center frequency of the filter is done rarely. Although MEM switches have relatively high Q-factor, the analog tuned MEM varactors and filters based on them still have high losses, they are slow, have small tuning range, rather complex design and require vacuum packaging (Rebeiz 2003, Entesari et al. 2007, Lee et al. 2006). Commercially, semiconductor varactor based filters are available below several GHz (Tunable Filters, Pole/Zero Corp). They have rather high losses and the selectivity (number of poles, steepness of the skirts) is not high due to the low Q-factor of the semiconductor varactors. The selectivity (Q-factor) of YIG filters is rather high. Unfortunately they are hard to impedance match. YIG filters with

200

5 Ferroelectric Devices

HTS electrodes (Oats and Dionne 1999) have substantially smaller losses; however, the filters need to be cooled to below 90 K. In terms of power handling capability, mechanically tuned (bulk) filters have no competitors. YIG filters are next to handle rather high power levels. Both these technologies are quite complex and not cost effective. Ferroelectrics offer relatively simple solutions (Paratek 2004). Thin film ferroelectric tunable filters are one of the most discussed, but perhaps relatively less successful components. The reason is that for most applications the loss requirements are quite strict and practically no tunable components meet these requirements. In most of the system applications filters should have very low losses in the passband and high selectivity, i.e. steep skirts, which is not easy to fulfill, especially in the case of narrow band (bandwidth less than 5%) filters. Resonators are the main building blocks of the filters. In general, for a bandpass filter the fractional bandwidth BW, the insertion losses (IL) and the unloaded Q-factor of the resonators used are related as (Matthaei et al. 1964):

ILdB = 4.34

∑ gi BW ⋅ Q

(5.4.5)

where gi represents capacitances (scaled) and inductance in the low frequency prototype of the filter. For a given Q-factor of the resonators (and hence varactor included in the resonator) this formula sets the limits of achievable losses and filter bandwidth. Narrow bandwidth and high selectivity filters may only be realized on high Q resonators. 5.4.2.2 Planar (Microstrip) Filters

Tunable filters with ferroelectric films partly filling the gap between the coupled microstrip lines have been demonstrated in (Miranda et al. 2002). In most of the reported cases the applied DC field changes not only the center frequency of the filter, but also the bandwidth, which is a reflection of the fact that the applied field changes the impedance of the resonators and the coupling between them. An original method to design tunable ferroelectric filters with constant fractional bandwidth is proposed in (Matthaei et al. 1964). In system applications the size/cost of the filters is a critical issue. While selecting the filter design this issue has to be addressed properly. For example, for communications applications the tunable filters based on lumped elements are preferable since they offer integration and size/cost reduction possibilities, especially at relatively low microwave frequencies (typically below 10 GHz). In this case the filter performance is limited by Q-factor of lumped inductor coils. For frequencies above 10 GHz the waveguide designs offer low loss and high selectivity at the cost of limited tuneability. These types of filters usually are not cost effective.

5.4 Tunable Filters

201

5.4.2.3 Lumped Element Filters

Both lumped element (i.e. capacitor and inductor coils with sizes much smaller than the wavelength of microwave signal) and waveguide resonators incorporating ferroelectric varactors are considered in tunable filters. In lumped element resonators, (Tombak et al. 2003, Moeckly and Zhang 2001), the ferroelectric varactor is the main part of the resonator capacitor. The Q-factor of the resonator may be given as 1/Q=1/QL+1/Qv, where QL and Qv are the Q-factors of the inductor coil and ferroelectric varactor respectively. Below 10.0 GHz the Q factor of the varactors is usually higher (>100) than the Q-factor of thin film lumped inductor coils (QL <100), and the performance of the resonators, matching networks, filters etc. based on lumped element ferroelectric LC resonators is limited by the losses in metals strips of the coils. A possible way to reduce the losses is to use superconductor strips instead of normal metal. Figure 5.4.3 shows equivalent circuit, layout and the performance of a superconducting filter with STO varactors (Moeckly and Zhang 2001). The flip-chip varactors are made of 2.0 μm thick STO on LaAlO3 substrate. Both STO and superconducting (YBa2Cu3O7) films are prepared by reactive co-evaporation technique. The bandwidth is about 3.5%. The tuning, about 1.0% at E<2.0 V/μm field, may be increased by increasing the bias DC field. (a)

(c)

(b)

Fig. 5.4.3 Equivalent circuit (a), layout (b) and performance (c) of a superconductor filter with interdigital (coplanar-plate) ferroelectric (STO) varactors at T=65 K. Reprinted with permission from IEEE©2001

A third order lumped element tunable ferroelectric filter using parallel-plate BST varactors (0.2 μm thick Pt bottom electrodes) operating at room temperature is demonstrated by Tombak et al. (2003). The center frequency of the filter tuned from 176 to 276 MHz (57% under DC bias 6.0 V). The insertion loss of the filter is 3.0 dB, of which only 1.5 dB is attributed to the STO varactors. A tunable bandpass filter reported by Yun et al. (2007) to have bandwidth of 3% with insertion and the return losses 2.0 dB and 16.6 dB, respectively. The cen-

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5 Ferroelectric Devices

ter frequency of the suggested ferroelectric BPF is moved from 5.81 GHz to 6.06 GHz at 50 V bias. The filter is based on BSTO films on MgO substrate. 5.4.2.4 Hollow Waveguide Based Filters

The Q-factor of waveguide (Microstrip, CPW, hollow) resonators incorporating ferroelectric varactors (1/Q=1/Qr+k/Qv) depends on the varactor inclusion rate: k<1.0 (see Sect. 5.4.1). The unloaded Q-factor of waveguide resonators is usually higher than the Q-factor of the varactors. For microstrip/coplanar type resonators it is in the range of several hundreds, while for hollow waveguide resonators it is even higher. In contrast to lumped element resonators, in the case of hollow waveguide resonators the Q-factor of tunable resonator (i.e. resonator with a varactor) is limited by the Q-factor of varactors. In waveguide based tunable filters the varactor may be only a part of the resonators. For applications in low loss, narrow band filters with high selectivity (i.e. multipole filters) the Q-factor of the tunable resonator may be kept rather high by keeping the inclusion rate very small: k<<1. In this case the varactor acts as a perturbation and the changes in the resonant frequency (tuning) are small, although the tuneability of the varactor may be high. DC bias

Metal

Quartz plates

Varactor Regular waveguide

Cut-off waveguide

(a)

(b)

Fig. 5.4.4 Design (a) and measured transmission coefficient (b) of ferroelectric varactor tuned filter. Courtesy of A.B. Kozyrev, LETI, S. Petersburg, Russia

Room temperature hollow waveguide tunable filters with commercially acceptable performances are demonstrated. Tunable filters with center frequencies 14 GHz (Fig. 5.4.4) and 32 GHz, bandwidths about 0.9%, and tunings about 1.8% had insertion losses 3dB and 4.5 dB respectively (Buslov et al. 2003). The varactors used in these filters have coplanar-plate design and require rather high tuning voltages (about 300 V) due the large gap between the electrodes.

5.4 Tunable Filters

203

5.4.2.5 High Power Tunable Filters

A number of tunable filters based on parallel-plate resonators using single crystal paraelectrics are reported in the past. In (Eriksson et al. 2001) an experimental two-pole tunable filter is realized using two KTO disk resonators, where a transmission pole is introduced at the high frequency skirt making the filter useful for high power duplexer applications. The filter is designed utilizing TM020 modes to operate at 77 K with a pass-band 1.5% and center frequency 0.9 GHz. Deleniv et al. (2002) utilized the degeneracy of TM110 mode in STO circular disk resonators to design a four-pole filter with improved skirts (Fig. 5.4.5). (a) 5

L

4 3

2

1 W 0

500 V

-10 0V

-20

Reflection coefficient, S21 (dB)

Transmission coefficient, S21 (dB)

0

-30 -40 -50 -60

300

-5

0V

-10

500 V

-15 300 V

-70 -20 0.4

-80 0.4

0.45

0.5

0.55

Frequency, GHz

0.6

0.65

(b)

0.45

0.5

0.55

Frequency, GHz

0.6

0.65

(c)

Fig. 5.4.5 Layout (a), measured transmission (b) and reflection coefficients of a four-pole filter based on dual mode resonators. Reprinted with permission from EuMA©2002

5.4.3 Notch Filters Choi and Troiler-McKinstry (2001) reported a tunable thin film distributed RC notch filter. It is based on a distributed TaN resistor deposited on Y-doped BaTiO3. Both films are grown by pulsed laser deposition. A notch frequency of 2.8 MHz and notch depth of –76.7 dB are measured with a notch resistance (RN) of 34 Ω. The experimental optimum notch parameters of α=R/RN =19.7 and xn=ω/ω0=33.0

204

5 Ferroelectric Devices

are obtained. The tunable notch filter reported by Lourandakis at al. (2008) includes two inductors with inductances L1=L2=2.7 nH. To facilitate a simple biasing the varactor is split into two parts as shown in Fig. 5.4.6 (a). The total zero bias capacitance of these two varactors is 5 pF. The measured stopband is tuned from 1.5 GHz to 2.1 GHz under applied DC bias 9 V with a minimum attenuation of 17 dB (Fig. 5.4.6 (b)). The measured return loss for each operating state is not exceeding 1.1 dB within the rejection band. (a)

(b)

Fig. 5.4.6 Circuit topology (a) and measured tuning of the rejection band (b) of a stopband filter based on ferroelectric varactors. Reprinted with permission from EuMA©2008

5.5 Matching Networks (Impedance Tuners) Recently tunable matching networks (MN) based on ferroelectric varactors are extensively considered for applications in power amplifiers (PA) for efficiency and linearity improvement, multi-band transceivers, antennas for impedance variation compensation etc. (Fu et al. 2008, Scheele et al. 2006). For these applications the ferroelectric varactors have several advantages over the competing technologies, such as low bias voltage and high power handling capability (especially for cascaded varactors discussed in Chap. 4), no forward biased problem (as in the case of semiconductor varactors) low leakage current and high tuning speed. A comprehensive study of ferroelectric varactor based matching network is reported in (Tombak 2007). In PA the NM may be used as pre/post-distorters to improve the linearity, as impedance tuners to improve the power efficiency under different power levels and different load impedance. For example, the impedance of a mobile phone antenna changes due to different environments, proximity to human body etc. (de Mingo et al. 2004).

5.5 Matching Networks (Impedance Tuners)

205

(a)

(b)

Fig. 5.5.1 Π-MN terminated with R L (a), and T-MN terminated with R L (b). Reprinted with permission from EuMA©2007

MN based on thick film ferroelectric varactors reported by Scheele et al. (2005) provides insertion loss 1.15 dB @ 1.95 GHz. Fu et al. (2008) achieved 6.5:1 impedance transformation ratio at 1.8. GHz using all-pass networks. A comparison of tunable ferroelectric Π- and T-matching network is reported in (Schmidt et al. 2007). Two dual circuits (Fig. 5.5.1) using ferroelectric varactors are theoretically and experimentally analyzed. It is shown by Schmidt et al. (2007) that Π- and T-networks show a mirror inverted small-signal behavior and the capacitors C 1 and C 2 must be identical, which is valid for the lossless case. In the case of losses C 1 and C 2 must be properly adjusted. The requirements for the insertion loss of a MN imply that its added insertion loss is smaller than the mismatch loss of a detuned load (in this case this is an antenna) without the network. Since a matching network does not work in a 50 Ohm environment the transducer power gain, GT , needs to be calculated to determine the loss: G=

S 21

2

1 − S 11

2

(5.5.1)

In a simulated and measured MN at the operating frequency 850 MHz the ferroelectric varactors have Q-factors in the range of Q=35 at a bias voltage 0 V up to Q=65 at 25 V. The tuneability of the varactors is 70% at 25 V. 1pF and 2pF varactors where used in the T-MN, while 16pF and 22pF varactors in the Π-MN respectively. The experiments reveal that the loss in Π-MN is 2dB higher as compared to the T-MN. It is attributed to the parasitic influence of the bond wires and may be eliminated by using a flip-chip mounting technique. The nonlinear measurements (Schmidt et al. 2007) reveal an IP3 of 30dBm and 20dBm for Π- and T-MN respectively which is due to the low break-down voltages (about 30 V) of the used varactors. The problem may be resolved by using (cascaded) high power varactors discussed in Chap. 4.

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5 Ferroelectric Devices

(a)

(b)

M1

M2

Z 2 ,θ 2

Z 1,θ 1

Z ,θ Fig. 5.5.2 Equivalent circuit (a) and photo (b)of the tunable MN using ferroelectric LTCC. Reprinted with permission from IEEE©2003

An attempt to realize MNs using cost effective LTCC is reported by Deleniv et al. (2003). These MNs are based on CPS and have traditional double stub topology shown in Fig. 5.5.2 (a). The tuneability is achieved by changing the electric length (and also the impedance) of the two short circuited stubs connected in series. The stubs are deposited on top of the ferroelectric film i.e. they are in metal layer M2. The bias voltages are applied separately to two ground patches in bottom metal layer M1 (Fig. 5.2.2 (b). The ferroelectric film is sandwiched between the short circuited stubs in metal layer M2 and bottom patch in M1. At present tunable MNs are commercially available from Agile RF (http://agilematerials.com) and Paratek (www.paratek.com).

5.6 Power Splitters In a tunable power divider using chip ferroelectric varactors (Lourandakis et al. 2008) the output branches are implemented as low pass filters consisting of λ/4 sections of microstrip lines shunted at both ends by ferroelectric varactors. The prototype is implemented on a Rogers RO3010 substrate where the ferroelectric varactors are soldered to the microstrip lines. The center frequency of the divider is tuned from 1.7 to 2.1 GHz with the additional losses changed from 1.2 to 0.6 dB. The achieved isolation between the output ports is 25 dB. The worst case misbalance between the output amplitudes and phases are 0.5 dB and 9 degrees correspondingly. The tuneability of this device helps to avoid the inherent narrow band performance (while maintaining its small size) of the divider by dynamically changing the operation frequency. An attempt to develop LTCC compatible power splitters with tunable splitting ratio is done by Deleniv et al. (2003).

5.7 Antennas

207

5.7 Antennas Patch antennas are widely used in modern microwave systems for transmitting and receiving microwave signals. They may have any shape, the rectangular being the most used one. The on-board, on-wafer and on-chip integration of the antennas require reduction of their sizes. Attempts to reduce the sizes lead to gain-bandwidth limitations. Tunable antennas allow avoiding the fundamental gain-bandwidth limitation (Chu 1948) of electrically small antennas. A small and highly efficient antenna with a narrow instantaneous bandwidth may be tuned over a wide bandwidth. A single tunable antenna may eliminate the need for multiple antennas covering several wireless standards. The cost reduction requires simplifications and high degree of integration in terms of functionality and design. Typically semiconductor (Alkanhal et al. 2007, US patent 5943016) devices (varactors, P-I-N diodes etc.), and MEMs (Jackson et al. 2007) are considered for tunable antenna applications. The advantages of the ferroelectric varactors make them attractive for tunable antenna and antenna array applications (Lovat et al. 2006). Support by NASA, QorTek and in collaboration with North Carolina State University considers (www.qortek.com), BSTO and BZN as DC field tuned permittivity dielectrics for application in tunable printed patch antennas (Shuch 2004, Shuch 2005). Microstrip antennas on high permittivity ferroelectric substrate (Jose et al. 1999) suffer from poor efficiency which is associated with the energy loss due to the excitation of surface modes, and they have narrow bandwidth. Attempts are done to solve these problems by multilayer structures incorporating tunable ferroelectric plates (Vinoy et al. 2000, Teo et al. 2001). To avoid most of the problems indicated above tunable antennas using thin ferroelectric films on low permittivity substrate are proposed (Castro-Vilaró and Soils 2003). In this work, the performance of a Au/Ba0.6Sr0.4TiO3/MgO twolayered tunable coplanar waveguide (CPW) fed folded-slot antenna (FSA) is modeled using finite difference time domain (FDTD) method. The antenna designed for operational at Ka-band, matched at 50 Ohms. A minimum reflections and tunable bandwidth of 7.1 GHz for 23.33% around 30.47 GHz is predicted. Upon application of a DC voltage between the CPW ground plane and antenna the induced field in the thin ferroelectric film changes the permittivity in the slot causing a total frequency shift of 4 GHz. The simulated input resistance shift is 28.54 Ohms and the gain is approximately 2.98 dBi. Another tunable antenna using 0.4 μm thick BSTO films on MgO substrate operating at around 30 GHz is analyzed in (Amador-Perez and Rodrigez-Solis 2006). A tuneability of 14.78% when the dielectric permittivity of BSTO is varied from 600 to 1200 and a directivity of –8.8 dB is predicted. Recently an experimental tunable antenna using ferroelectric varactor is reported (Buslov et al. 2007). In these devices the VCO and the ferroelectric varactor tuned antenna are connected via a section of a transmission line.

208

5 Ferroelectric Devices

5.8 Nonlinear Devices In the devices considered in the previous sections of this chapter, the dependence of the permittivity and losses on microwave power, i.e. the dynamic nonlinearity, is an undesirable effect. Typically it is avoided by increasing the thickness of the ferroelectric in parallel-plate devices (gapwidth in coplanar-plate devices). Alternatively, for high power application the varactors are cascaded as it is described in Sect. 4.7. On the other hand the dynamic nonlinearity may be used to utilize a number of useful microwave devices. In contrast to high power varactors described in Sect. 4.7, for nonlinear applications the varactors are designed for higher dynamic nonlinearity. Particularly, the thickness in parallel-plate, and the gapwidth in coplanar-plate devices are reduced so that the electric field induced by microwave power causes highest possible changes in the permittivity in the ferroelectric.

5.8.1 Harmonic Generators The harmonic generators are one of the earlier nonlinear applications experimentally tested in the past where along with the nonlinearity the advantage of symmetric C-V dependence is employed to demonstrate a high power tripler from 3 GHz to 9 GHz (DiDomenico et al. 1962). In this experiment a ceramic post (0.5 mm height, 0.25 mm in diameter) consisting of 73% BaTiO3 and 37% SrTiO3 is used in a coaxial arrangement. 8.5% conversion efficiency is achieved at input power of 2200 W.

5.8.2 Frequency Up-Converters An up-conversion experiment using 2μm thick Ba0.5Sr0.5TiO3 and SrTiO3 films with correspondingly Au and YBa2Cu3O7–d CPW electrodes is demonstrated by Findikoglu et al. (1995). The slotwidth between the electrodes of 6 mm long CPWs are 40 and 20 μm. In these experiments a 50 MHz signal is mixed with a 4 GHz CW pump signal and the up-converted power is measured using a spectrum analyzer. The output up-converted power is measured depending on the DC bias applied between the central strip and ground plane of the CPW. At zero DC bias the converted power is very week (about –8dBm). With increasing DC bias the converted power rapidly increases peaking at the inflection point (voltage) of the C-V curve and gradually decreases upon further increased DC bias. An experimental up-converter from 0.8 to 4.4 GHz using BaxSr1–xTiO3 varactors is reported by Samoilova et al. (2005). The coplanar-plate and parallel-plate chip varactors used in the experiment are fabricated on alumina based ceramic

5.8 Nonlinear Devices

209

substrate using RF magnetron sputtering. The hybrid design is implemented on a 48×30×0.64 mm3 Rogers 3010 substrate (ε =10.2, tanδ=3.5×10–3). The layout of the converter and its frequency spectrum are shown in Fig. 5.8.1. The simulated spectrum is given for correspondingly pump and input powers Pp =+30 dBm, Pin= –20 dBm, and varactor bias 27 V. The input power dependence of the up-converted signal powers for parallel-plate and coplanar plate varactors for different DC bias are shown in Fig. 5.8.1 (c). The film thickness in the parallel-plate and coplanar-plate varactors are correspondingly 0.5 mm 0.8 μm, the gapwidth in coplanar-plate varactor is 30 μm. The estimated conversion gain is in the range of 2.5–8 dB depending on the Q-factor of the varactor. In the case of using parallelplate varactor the conversion gain is limited by overheating of the varactor.

(a)

(b)

(c)

Fig. 5.8.1 (a) layout, (b) output frequency spectrum of the converter, and (c) measured dependence of the output power for parallel-plate (circles) and coplanar-plate (dots) varactors. 1-shorted stubs, 2, 3-open stubs serving as rejection filters for signals at frequencies fp and 2fp, respectively; 4-contact pad

5.8.3 Power Limiters A limiter based on Pb0.315Sr0.685TiO3 is reported in 1967 by Horton and Donaldson (1967). It uses the RF field dependence of the dielectric constant of a ferroelectric material to achieve power limiting performance. The electric field, E, of the input microwave power changes the permittivity and loss tangent of the ferroelectric resulting in nonlinear change of capacitance Cf(E) and microwave conductance G(E) of the varactor (Fig. 5.8.2 (a)). Paraelectric (Curie temperature 23°C) phase (Pb0.135Sr0.685)TiO3 is used in this experiment with no hysteresis and low loss tangent (tanδ = 0.05). The sizes of the ferroelectric chip are 0.011x0.013x0.020 (inches).

210

5 Ferroelectric Devices

(a)

(b)

Fig. 5.8.2 Equivalent circuit (a) and experimental performance (b) of power limiter. Reprinted with permission from IEEE©1967

In this experiment the ferroelectric varactor is a part of the detuning circuit which is implemented as a shunt stub shown in Fig. 5.8.2 (a). The varactor is located at quarter-wavelength distance from the main transmission line, and terminated by a shorted inductive stub. The capacitance of the varactor Cf(E) is larger than the value necessary for resonating with the inductive stub. The magnitude of the mismatch in the main transmission line increases with the increase of applied power. At a specified microwave power the capacitance of the varactor decreases to a level that forms a parallel resonance with the inductive stub producing a maximum mismatch in the main transmission line. Further increase of power causes a further reduction of the capacitance, breaking the resonance condition and the mismatch starts decreasing. Since the insertion loss of the main transmission line is a function of mismatch, the shunt stub loaded by a nonlinear varactor offers a means of producing attenuation, the magnitude of which is controlled by the input power. In Fig. 5.8.2 (b) the duty factor is defined as DF=(microwave pulsewidth)/(time between pulses), and peak power is defined as (average power)/DF. The small signal insertion loss is about 3.6 dB. The limiting occurs at approximately 200 watts input peak power with only a small change of output power up to 800 watts input.

5.8.4 Pulse Shapers The first pulse shaping experiment using barium titanate based ceramic capacitors is reported by Wilson et al. (1991). The peak permittivity of the used BTO based ceramic is 8000 at 25 C with loss tangent about 0.05 at 15 MHz. The LC ladder network consists of 15 sections with 1.5 μH inductors. The 1.2 nF disk capacitor is 18 mm thick. Under the electric field of the propagating pulse the capacitance drops causing increased pulse velocity, i.e. the time delay in the LC ladder net-

5.8 Nonlinear Devices

211

work is amplitude dependent. It causes the rest of the pulse to catch up with the low amplitude part of slow propagating leading front. In this experiment the rise time of the leading edge of a 28 kV pulse is reduced from 280 ns to 50 ns. The performance of a pulse shaper reported by Mikhailov et al. (2007) is shown in Fig. 5.8.3.

Fig. 5.8.3 Pulse shaping in a nonlinear transmission line periodically loaded by ferroelectric varactors. Reprinted with permission from EuMA©2008

In a 25 mm wide air filled stripline periodically loaded by 5.5 mm thick and 3 mm long Ba0.6Sr0.4TiO3 ceramic bricks a pulse is converted an array of microwave solitons (Ikezi et al. 1991). In another pulse shaping experiment by Findikoglu et al. (1999) an 8 cm long CPW based on 1.0x10x10 mm3 SrTiO3 single crystal substrate and 400 nm thick YBa2Cu3O7–d electrodes is used. The slotwidth in the CPW is 15 μm. At low temperature and under certain relationship between the dispersion and nonlinearity a waveform is generated which may be identified as a soliton.

5.8.5 Parametric Amplifiers Applications of the dynamic nonlinearity of ferroelectrics for the parametric amplification of microwave signals have been considered in 1950s (Tien 1958) and later (Aoki 1960) since at that time there was only a limited number of possibilities for the utilization of amplifiers. In the past this and some of the other nonlinear applications have been limited by the high losses in the available ferroelectric ceramics. Currently, the application of the dynamic nonlinearity in parametric amplifiers and frequency converters in microwave range, i.e. up to 100–200 GHz, is not motivated (except for some special cases). The cut-off frequencies of both silicon and III-V transistors are well above 100 GHz and for these applications they can easily, in most cases, outcompete ferroelectric parametric amplifiers. At THz frequencies these devices are still welcome.

212

5 Ferroelectric Devices

5.9 TFBARs 5.9.1 Basic Designs and Resonant Frequencies The thin film bulk acoustic wave resonators (TFBAR) attracted much attention for applications in small size low loss filters (Ruby et al. 2001) and oscillators (Zhang et al. 2005) at frequencies below 10 GHz. Most of the TFBARs considered today, are based on piezoelectric films (i.e. ZnO, AlN). Since the ferroelectrics in polar (ferroelectric) phase are piezoelectric, they are also considered for TFBAR applications (i.e. PZT by Hanajima et al. (1997)). Two basic designs of TFBARs considered so far are show in Fig. 5.9.1. Membrane mounted (MM) TFBARs are fabricated either by bulk micromachining of the substrate (typically silicon) or by surface micro aching. The Bragg reflectors (“mirrors”) are used in surface mounted TFBARs (SMR) to acoustically isolate the resonator from the substrate (Fig. 5.9.1 (c)). In an ideal case of infinitely thin electrodes the thickness mode series (fs) and parallel (fp) resonant frequency of the TFBAR is given by the velocity of the acoustic waves (vac) and thickness of the ferroelectric (piezoelectric) film, t, and electromechanical coupling coefficient kt (k33):

fp =

c 33D

vac 1 = 2t 2t

fs = f p 1 −

ρ

8

π

2

,

kt2 ,

(5.9.1)

(5.9.2)

where ρ is the density of the ferroelectric/piezoelectric film, c 33D is its stiffness coefficient in orientation normal to the surface of the piezoelectric film, and

kt =

2 e33 D s c33 ε 33

,

(5.9.3)

ε33 is the permittivity and e33 is the piezoelectric stress coefficient. For simple piezoelectrics like ZnO and AlN the acoustic parameters and permittivity in the above formulas are not DC field dependent. DC field dependences of these parameters for ferroelectric films in polar and paraelectric phases are considered in Chap. 2. It is worthwhile to indicate that in paraelectric phase the ferroelectrics, in general, are nor piezoelectric. The piezoelectric effect in this phase is external DC field induced (see Chap. 2).

5.9 TFBARs

213

Bragg reflector

Sacrificial layer

t

t

t

Ferroelectric (piezoelectric)

Membrane

Membrane

Micromachined (etched)

(a)

(b)

(c)

Fig. 5.9.1 Bulk (a), surface (b) micromachined membrane, and Bragg reflector based (c) TFBARs

For TFBAR applications AlN and ZnO are the most investigated materials because of high quality factor and stability despite small electromechanical coupling coefficient. Because of its high coupling coefficient PZT is also considered for TFBAR applications. The AlN TFBARs are commercially available and widely used (e.g. cell phones) components. The possibility of developing tunable SM TFBARs using ferroelectrics in paraelectric phase (i.e. Ba0.25Sr0.75TiO3) is demonstrated recently by Gevorgian and Vorobiev (2005). These types of TFBARs make use of electrostriction and field dependent piezoelectric effects to achieve tunable resonant frequencies. Similar tunable resonators may be developed using other ferroelectric materials, even in polar/ferroelectric phase (i.e. NaxK1–xNbO3), characterized by electric field dependent acoustic parameters. Tunable TFBARs open up possibilities for the development of tunable filters and VCOs for adaptive microwave communications systems. These VCOs promise to have lower phase noise due to the high Q-factor of TFBARs – in contrast to the semiconductor varactor based VCOs, where the phase noise is limited by low Q-factor of the resonator (inductor coil). Having higher Q-factor (in comparison with varactor based resonators) these resonators are promising for applications in low loss tunable filters in front ends of microwave communications systems. For applications in microwave communications systems using the solidly mounted TFBARs seem to have advantages. If properly designed, they may not require vacuum packaging and may be integrated in multichip modules and, in the future, in silicon based MMICs in a cost effective way. A 2 GHz fixed frequency oscillator using a solidly mounted TFBAR is reported in (Norling et al. 2006). The oscillator makes use of AlN based SM TFBAR chip developed earlier.

5.9.2 Tunable TFBARs 5.9.2.1 Ferroelectric Phase

The DC bias dependences of the resonance frequency and electro-mechanical coupling constant in solidly mounted TFBARs based on Pb(ZrxTi1–x)O3 (x=0.25 to 0.6)

214

5 Ferroelectric Devices

is reported by Schreiter et al. (2004) and Gabl et al. (2002). The 2 GHz parallelplate resonators are arranged on a planar acoustic mirror (Bragg reflector) using Pt as a base electrode. The PZT thin films are deposited in a planar multi target sputtering system using three metallic targets in a reactive Ar/O2 mixture. The Zr content x of Pb(ZrxTi1–x)O3 is varied between 0.25 (PZT25/75) and 0.6 (PZT60/40) by changing the power delivered to the individual targets. The top Au plate is 100 nm thick with different sizes (30×30 μm2 up to 500×500 μm2).The films of the tetragonal and rhombohedral phase show significant differences in self polarization, permittivity and hysteresis.

(a)

(b)

Fig. 5.9.2 DC bias dependences of the series and parallel resonances for tetragonal (a) and rhombohedral (b) PZT compositions. Reprinted with permission from IEEE©2002

Figure 5.9.2 shows the series and parallel resonance frequencies vs. bias voltage for tetragonal and rhombohedral PZT resonators. As the films are self polarized (piezoelectric) in the virgin state, the resonators show resonance behavior even without DC bias. The tuning of the resonant frequency is due to the ferroelectric properties of the PZT thin film. For tetragonal PZT25/75 film the parallel resonance shows a strong bias dependence, whereas the series resonance is nearly unaffected (Fig. 5.9.2 (a)). An opposite behavior is observed for rhombohedral PZT58/42 film (Fig. 9.2 (b)) where the series resonance frequency is mainly controlled by the bias, whereas the tuning of the parallel resonance is rather weak. A rather strong hysteresis (“butterfly” dependencies, Fig. 5.9.2) is observed for both series and parallel resonances. For smaller sizes spurious responses appear under higher DC fields. For larger resonators the series resonance degrades due to series resistances. The measured Q-factors are about 220 for the series resonance of the virgin 70×70 μm2 resonator. Under DC bias the effective coupling constant changes between zero (no piezoelectric response due to a zero net polarization) and a maximum value of about 0.21. For higher Zr-content (PZT58/42) the maximum is about 0.3. The maximum frequency tuning is in the range of 2–3%. As a potential application, a bandwidth-tunable or programmable RF filter based on PZT FBARs is proposed. Membrane based tunable PZT TFBARs are presented by Zinck et al. (2004). As in the previous case, the tuning in this material is associated with it ferroelectric (polar) nature and inherent piezoelectricity. The resonators are based on mem-

5.9 TFBARs

215

branes made by deep reactive ion etching of silicon. The 200–800 nm thick Pb(Zr0,52Ti0,48)O3 films deposited by RF magnetron sputtering at room temperature. The amorphous films are annealed for crystallization at 675C in N2+O2 atmosphere. The fundamental thickness mode frequency is 1.4 GHz and the 2nd harmonic is measured at 2.1 GHz. The DC bias dependence of the series and parallel resonant frequencies are measured in the range of –25 to 25 V/μm. Butterfly dependencies are both observed for series and parallel resonances. The frequency tuning of the series resonance, 2%, is higher than that of the parallel one, consistent with Schreiter et al. (2004). The maximum coupling coefficient (7.3%) is measured which become null for non symmetrical values of bias fields of 1.5 V/μm and –5.5 V/μm. A Q-factor of 85 is measured for the parallel resonance. It was very small and not measurable for the series resonance. The low Q is explained by the losses in top and bottom Pt electrodes. 5.9.2.2 Paraelectric Phase

In paraelectric phase BaxSr1–xTiO3 (x<0.5–0.6) is not ferroelectric/piezoelectric. In some cases, under interfacial misfit stress caused by the substrate (or other interfacing films), and due to oxygen vacancies and other defects the symmetry of the crystal lattice reduces resulting in a strong background piezoelectric effect. Even in a paraelectric center symmetric film the external electric DC field (E3) induces piezoelectricity (see Sect. 2.8.3) and the microwave signal “sees” a crystal with a DC field dependent effective piezoelectric coefficient. In the case of field induced and background piezoelectric effects an effective piezoelectric coefficient may be defined as (Rupprecht and Winner 1967): d*33= d33+2g33E3, where d33 is the piezoelectric coefficient of the background piezoelectric effect induced (distortion of the crystal lattice) by misfit strain, g33 is the electrostriction coefficient. This concept is used to develop a simplified model of tenability in TFBARs (Gevorgian et al. 2006). The results of complete electromechanical treatment published recently are summarized in Sect. 2.8.3. In the case of the nearly ideal films with no misfit strain, d33=0, the resonances in ferroelectric varactors are explained by electrostriction only (Tappe et al. 2004). The essential difference between the paraelectric film based and ferroelectric film based TFBARs is absence of the hysteretic in DC field dependent resonant frequency in the former case. Figure 5.9.3 (c and d) depict the measured DC field dependences of the resonant frequencies and electromechanical coupling coefficient for TFBARs (Berge et al. 2008). The dependences are shown for DC bias reversals. They are practically hysteresis free in comparison with the similar dependences for piezoelectric PZT shown in Fig. 8.9.2. In this case the Bragg reflector consists of two pairs of Au (150 nm) and SiO2 (280 nm) layers with quarter acoustic wavelength thickness, Fig. 8.9.3 (a). The bottom and top electrodes are made of Au (80 nm) and Al/Au (110/20 nm), respectively. The layout of the resonator is designed to facilitate measurements using 150 μm pitch ground-signal-ground microprobes. The laser ablation deposited BSTO film is 350 nm thick.

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(b)

(a) Al/Au

BSTO Reflector / Bottom el.

Au Substrate

(c)

(d) 4 3.5

fp

3 2.5

fs

4.15

k2 (%)

Resonance frequency (GHz)

4.2

2 1.5 1 0.5

4.1

0

5

10 Bias (V)

15

0

0

5

10

15

Bias (V)

Fig. 5.9.3 Cross section (a), layout (b), DC field dependent resonant frequencies (c) and electromechanical coupling coefficient (d) of a Ba0.25Sr0.75TiO3-based TFBAR. Reprinted with permission from AIP©2008

At room temperature the tuneability of the series and parallel resonances are 1.7% and 0.3% respectively for 15 V bias voltage applied over the 350 nm thick ferroelectric film (43 V/μm). The electromechanical coupling coefficient increases with DC bias up to 3.7% at 15 V. The ferroelectric film may withstand fields as high as 1000 V/μm (Morrison et al. 2005). This indicates that by improving the film quality and hence the breakdown field one may anticipate substantially increased tuneability under higher applied voltages. The relatively low Q-factor, about 100, is also expected to increase with the improvement of the film quality since the acoustic Q-factor of the bulk single crystal SrTiO3 is above 4000–1000 depending on the crystal orientation. Further improvement of the Q-factor is associated with the optimization of the electrodes and the Bragg reflector. In spite of relatively low Q-factors and tuneabilities the tunable TFBARs are considered for applications in switches (Zhu et al. 2007, Gevorgian et al. 2008) and filters (Schreiter et al. 2004). Due to small sizes, in comparison, for example, with the tunable LC resonators based on lumped element inductors and varactors, the tunable TFBARs are promising candidates for applications in VCOs. Current experimental results indicate (Fig. 5.9.3, (Berge et al. 2008)) that there is a complex relationship between the crystalline structure and tuneability on one hand and film quality and Q-factor on the other hand. It is expected that the recently developed theory of the tunable TFBARs (Noeth et al. 2007, Vendik et al. 2008) is going to be extended to take into account these complex relationships – paving a way for further optimization of the ferroelectric based tunable TFBARs.

References

217

5.10 Conclusions The advances in both thin epitaxial and thick ferroelectric varactor technologies allow development of a large number of agile microwave devices. The analysis of the performances of the published, and partly discussed, devices mentioned in this chapter show that considerable progress is achieved in devices based on ferroelectric varactors and some of the devices are being marketed. On the other hand some of the devices considered in this chapter are concept demonstrators rather than devices with the best performances, i.e. they merely show the potential of the ferroelectric varactors in device application. In some of the reported devices the full potential of the ferroelectric varactors, first of all in terms of high Q-factor, are not fully utilized. Although there is some room for further reduction of the dielectric losses in ferroelectrics, the relatively poor performance of some of the devices seems to be associated with the design specifics. The performance improvement of these devices require a careful optimization of the design/layout of the devices so that the parasitics (i.e. losses in the plates) associated with the integration (interconnects) of the varactors are minimized. While the “standard” devices such as tunable delay lines, phase shifters filters and matching networks etc. are being commercialized, a new component – the tunable TFBAR based on paraelectric phase ferroelectrics is attracting considerable attention. When completely understood and optimized it may found a wide range of microwave circuits and systems – VCO, frequency selective switches, filters etc.

References Acikel B et al (2002) A new high performance phase shifter using BaxSr1–xTiO3 thin films. IEEE Microwave and Wireless Components Letters 12:237–239 Alkanhal M A and Sheta A F (2007) A novel dual-band reconfigurable square-ring microstrip antenna. Progress in Electromagnetic Research. PIER 70:337–349 Amador-Perez A and Rodrigez-Solis R A (2006) Analysis of a CPW fed annular slot ring antenna using DOE. Dig. IEEE AP-S Int Symp:4301–4304 Antoniades M and Eleftheriades G (2003) Compact linear lead/lag metamaterial phase shifters for broadband applications. IEEE Antennas and Wireless Propagation Letters 2:103–106 Aoki Y (1960) Proposed Parametric Amplifier Utilizing Ferroelectric Substance. IRE Trans Micr Theory Techn 8:465–466 Berge J et al. (2008) Field and temperature dependent parameters of the dc field induced resonances in Ba0.25Sr0.75TiO3-based tunable thin film bulk acoustic resonators. J Appl Phys 103:064508-064508-8 Buslov O Yu et al. (2007) VCO/radiator module tuned by ferroelectric varactor,19th International Symposium of Integrated Ferroelectric, May 8–11, 2007 Buslov O Yu et al. (2003) 14 GHz tunable filter based on waveguide-dielectric resonators. (CriMiCo’ZOO3), 8–12 September, Sevastopol, Crimea, Ukraine: 493–494 Caloz C, Itoh T (2006) Electromagnetic Metamaterials: Wiley Carlsson E F et al. (1997) Experimental study of thin film HTS/ferroelectric CPW phase shifters for microwave applications. Inst Phys Conf Ser.158:339–342

218

5 Ferroelectric Devices

Castro-Vilaró A M, Soils R R (2003) Tunable folded-slot antenna with thin ferroelectric film material. IEEE AP-S Int Symp 2:549–552 Chai D, Linh M, Yoon G (2002) Wideband microstrip line 45o phase shifter. 2002 Asia pacific Microwave Conference: 598–601 Chang C C et al. (2001) True time phased antenna array systems based on nonlinear delay line technology. APMC 2001. Asia-Pacific Microwave Conference 2:795–800 Choi W-Y and Troiler-McKinstry S (2001) A voltage-controlled tunable thin-film distributed RC notch filter. IEEE Transactions on Components and Packaging Technologies, 24:33–37 Chu L J (1948) Physical limitations of omnidirectional antennas. J Appl Phys 19:1163–1175

De Flaviis F (1997) Planar Microwave Integrated Phase Shifter Design with High Purity Ferroelectric Material. IEEE Trans MTT 45:963–969 de Mingo J et al(2004) An RF electronically controlled impedance tuning network design and its application to an antenna input impedance automatic matching system. IEEE Trans. Microwave Theory Tech 51:489–498 DeGroot D C et al. (1995) Tunable Microwave properties of YBCO/STO thin film transmission lines. IEEE Appl Supercond 5:2272–2275 Deleniv A et al. (2003) Tunable ferroelectric components in LTCC technology. Digest IEEE Int Microwave Symposium 2:1997–2000 Deleniv A et al. (2005) Parallel-plate waveguide bulk ceramic ferroelectric phase shifters. Proc. EuMC2005 Deleniv A, Eriksson A, Gevorgian S (2002) Four-Pole Tunable Band-Pass Filters Based on Two Dual Mode SrTiO3 Disc Resonators. Proc EuMC 1:215–218 Deleniv A, Abadei S, Gevorgian S (2003) Tunable Ferroelectric Filter-Phase Shifter. Dig., IEEE Int Microwave Symposium IMS2003 2:1267–1270 Deleniv A, Emanuelsson T and Tageman O (2006) Unpublished Deleniv A, Gevorgian S (2003) Tunable Power Splitters and Matching Networks based on LTCC Ferroelectrics. Proc of Workshop Tunable Ferroelectric Materials and devices for Microwave Applications, EuMC2003 Deleniv A Eriksson A, Gevorgian S (2002) Design of Narrow Band Tunable Bandpass Filters Based on Dual Mode SrTiO3 Disc Resonators. Dig IEEE MTT Symposium 2:1197–2000 Deleniv A etc (2005) LTCC Compatible Ferroelectric Phase Shifters. IEEE IMS’2005 Deleniv A, Gevorgian S, Jantunnen H et al. (2004) Microwave characterization of ferroelectric ceramic films. Proc EuMC 2004:541–544 DiDomenico M et al. (1962) An ferroelectric phase shifter. IRE Transactions on Microwave Theory and Techniques MTT-10:179–185 DiDomenico M et al. (1962) Ferroelectric harmonic generator and large-signal microwave characterization of a ferroelectric ceramic. J Appl Phys 33:1697–1706 Dudek P et al. (2000) A high resolution CMOS time-to-digital converter utilizing a vernier delay line. IEEE J Solid State Circ 35:240–247 Eleftheriades G V, Balmain K G (2005) Negative-Refraction Metamaterials: Fundamental Principles and Applications. John Wiley & Sons, IEEE Press Ellinge F R et al. (2003) Varactor-Loaded Transmission-Line Phase Shifter at C-Band Using Lumped Elements. IEEE Trans Micr Theory Tech 51:113–1140 Entesari K, Rebeiz G M (2008) RF MEMS, BST, and GaAs Varactor System-Level Response in Complex Modulation Systems. International Journal of RF and Microwave Computer-Aided Engineering 18:86–98 Eriksson A, Deleniv A, Gevorgian S (2003) Orientation and direct current field dependent dielectric properties of bulk single crystal SrTiO3 at microwave frequencies. Journal of Applied Physics 93:2848 Eriksson A, Deleniv A, Gevorgian S (2004) Two-pole tunable band pass filter based on YBCO plated single crystal KTO disk resonators. IEEE Appl Supercond 14:1–5 Findikoglu A T et al. (1995) Tunable microwave mixing in nonlinear dielectric thin films of SrTiO3 and Ba0.5Sr0.5TiO3. Electron Lett 31:1814–1815

References

219

Findikoglu A T et al. (1999) Pulse shaping using nonlinear dielectric SrTiO3. Appl Phs Lett 74:1770–1772 Fu J-S, Zhu X A, Phillips J D et al. (2008) A Ferroelectric-Based Impedance Tuner for Adaptive Matching Applications. IEEE Int Microwave Symp IMS2008 Gabl R, Schreiter M, Primig R et al. (2002) Hysteresis properties of Pb(ZrxTi1–x)O3 thin-film bulk acoustic resonators. Proceedings of the 13th IEEE International Symposium on Applications of Ferroelectrics, ISAF 2002:355–358 Gevorgian S et al. (1996) Lower Order Modes of YBCO/STO/YBCO Circular Disk Resonators. IEEE Trans. Microwave Theory Techn 44:1738–1741 Gevorgian S et al. (2003) Basic Parameters of Coplanar-Strip Waveguides on Multilayer Dielectric/Semiconductor Substrates. Part 1: High Permittivity Superstrates. IEEE Microwave Magazine: 60–70 Gevorgian S et al. (2006) A Tunable resonator. International Application No.: PCT/SE2004/ 001099, International Filing Date: 06.07.2004, Publication Date:12.01.2006 Gevorgian S et al. (2006) DC field and temperature dependent acoustic resonances in parallelplate capacitors based on SrTiO3 and Ba0.25Sr0.75TiO3 films. Experiment and modeling. J Applied Physics 99:124112-124112-11 Gevorgian S, Carlsson E, Wikborg E et al. (1998) Tunable Microwave Devices Based on Bulk and Thin Film Ferroelectrics. Integrated ferroelectrics 22:245–257 Gevorgian S, Norling M, Berge J et al. (2008) Frequency Selective Switches Based on Tunable TFBARs. PCT patent application (Ericsson) P24542 WO1 Gevorgian S, Vorobiev A (2005) Tuneable TFBARs based on BaxSr1–xTiO3 films. Ferroelectrically Tuneable Microwave Devices. Workshop at 35th European Microwave Conference, Paris, 3–7 October, 2005 Giere A et al. (2006) LH Phase Shifter using Ferroelectric Varactors, Proceedings. 2006 IEEE Radio and Wireless Symposium IMS2006:403–405 Hanajima N et al. (1997) Ultrasonic Properties of Lead Zirconate Titanate Thin Films in UHFSHF Range. Jpn J Appl Phys 36:6069–6072 Horton J B and Donaldson M R (1967) A One GHz Ferroelectric Limiter. IEEE Trans. Microwave Theory Tech MTT-15:517–523 Ikezi H et al. (1991) Soliton generation at 10 MW level in the very high frequency band. Appl Phys Lett 58:986–987 Jackson R and Ramadoss R (2007) A MEMS-based electrostatically tunable circular microstrip patch antenna. J. Micromech. Microeng 17:1–8 Jose K A et al. (1999) Experimental Investigations on Electronically Tunable Microstrip Antennas. Microwave and Optical Technology Letters 20:166–169 Jung Y J et al. (2001) A dual loop delay locked loop using multiple voltage controlled delay lines. IEEE J Solid State Circuits 35:784–791 Karmanenko S F et al. (2007) Multislot transmission lines and microwave phase shifters based on (Ba,Sr)TiO3 films. ISIF 2007 Kenney J S et al. (2006) Low-Voltage Ferroelectric Phase Shifters from L- to C-Band and Their Applications. Aerospace Conference, IEEEAC Paper 1530 Kim D et al. (2002) A wide-band reflection-type phase shifter at S-band using BST coated substrate. IEEE Trans. Microwave Theory Tech 50:2903–2909 Kim D et al. (2003) 2.4 GHz Continuously Variable Ferroelectric Phase Shifters Using All-Pass Networks. IEEE Microwave and Wireless Comp Lett 13:434–436 Kim D et al. (2005) Linear tunable phase shifter using a left handed transmission line. IEEE Microwave and Wireless Components Letters 15:366–368 Kim D, Kenney J S (2005) Experimental Investigations of Intermodulation Distortion in Tunable Ferroelectric Phase Shifters. IEICE Trans Electron. E88-C:2310–2315 Kim K-B et al. (2006) Integration of Coplanar (Ba,Sr)TiO3 Microwave Phase Shifters onto Si Wafers Using TiO2 Buffer Layers. IEEE Transactions Ultrasonics, Ferroelectrics, and Frequency Control 53:518–524 Kirchner E K (1969) Microwave delay lines. IEEE Trans. Micr Theory Techn MTT-17:986–997

220

5 Ferroelectric Devices

Koo R C, Long J R (2003) An inductively tuned quadrature oscillator with extended frequency control range. Proc IEEE Int Symposium on Circuits and Systems 1:709–712 Koul S K, Bhat B (1991) Microwave and Millimeter Wave Phase Shifters. Artech House Kozyrev A B et al. (2001) Ferroelectric (Ba,Sr)TiO3 Thin-Film 60-GHz Phase Shifter. Technical Physics Letters 27:1032–1034 Kozyrev A B et al. (2002) A Finline 60-GHz Phase Shifter Based on a (Ba,Sr)TiO3 Ferroelectric Thin Film. Technical Physics Letters 28: 239–241 Kozyrev A et al. (1998) Ferroelectric films: Nonlinear properties and applications in microwave devices. Dig IEEE MTT-S’1998:985–988 Kozyrev A et al. (2004) Digital-Analog phase shifters using tunable dielectric capacitors. Proc EuMC’2004:813–815 Kozyrev A et al. (2004) Tunable ferrelectric Microwave Devices. IMS’2004 Workshop on New Technologies for Frequency-or Phase-Agile Microwave Circuits and Systems Kozyrev A B et al. (2003) Electrically controlled ferroelectric delay line. 13th Int Crimean Conference Microwave & Telecommunication Technology, 8–12 September, Sevastopol, Crimea, Ukraine CriMiCo’ZOO3:481–482 Kozyrev A B et al. (2003) Electrically controlled ferroelectric delay line. Microwave and Telecommunication Technology. 13th International Crimean Conference, 8–12 Sept. 2003 CriMiCo 2003:481–482 Kuylenstierna D et al. (2004) Ferroelectrically Tunable Delay-lines. Proc.- EuMC 2004:157–160 Kuylenstierna D et al. (2005) Ultrawideband tunable true-time delay lines using ferroelectric varactors. IEEE Trans Microwave Theory Tech 53:2164–2170 Kuylenstierna D et al. (2006) Composite Right/Left Handed Transmission Line Phase Shifter using Ferroelectric Varactors. IEEE Microwave and Wireless Components Letters 16:167–169 Kuylenstierna D et al. (2006) Tunable Left Handed Phase Shifter using Thin Film Ba0.25Sr0.75TiO3 Ferroelectric Varactors. Proc EuMC:847–850 Lee H-S, Yun S-W (2006) Microwave Planar Varactor Tuned Bandpass Filters: Historical Overview, IEICE Trans. Electron E89-C:1806–1813 Lourandakis E et al. (2008) A tunable and reduced size power divider using ferroelectric film varactors. Dig IEEE IMS 2008 Lourandakis L, Schmidt M, Seitz S et al. (2008) Tunable Lumped Element Filters With BST Thin-Film Varactors. Proc EuMC:1691–1694 Lovat G et al. (2006) A Tunable Ferroelectric Antenna for Fixed-Frequency Scanning Applications. IEEE Antennas and Wireless Propag Letters 5:353 Mahmud A et al. (2006) A 1-GHz Active Phase Shifter with a Ferroelectric Varactor. IEEE Micr Wireless Comp Lett 16:261–263 Matthaei G L et al. (1964) Microwave Filters, Impedance Matching Networks, and Coupling Structures. McGraw-Hill. New York Mikhailov A K, Samoilova T B, Kozyrev A B (2008) The Non-Uniform Non-Linear Transmission Line Based on Parallel-Plate Ferro-Electric Capacitors. Paper EuMC/EuRAD:1–5 Miranda F et al. (2002) Performance enhancement of Tunable Bandpass Filters using Ferroelectric Thin Films. Integrated Ferroelectrics 50:121–131 Miranda F A et al. (2008) BaxSr1–xTiO3 Thin Film Ferroelectric-Coupled Microstripline Phase Shifters with Reduced Device Hysteresis. J Am Ceram Soc 91:1864–1868 Moeckly B H and Zhang Y (2001) Strontium Titanate Thin Films for Tunable YBa2Cu3O7 Filters. IEEE Trans Appl Supercond 11:450–453 Morrison F D et al. (2005) High-field conduction in barium titanate Appl Phys Lett 86:152903 Nagra A and York R (1999) Distributed analog phase shifters with low insertion loss. IEEE Transactions on Microwave Theory and Techniques 47:1705–1711 Noeth A et al. (2007) Tuning of direct current bias-induced resonances in micromachined Ba0.3Sr0.7TiO3 thin-film capacitors. J Appl Phys 102:114110 Norling et al. (2006) A 2 GHz oscillator based on a solidly mounted thin film bulk acoustic wave resonator. Dig IEEE 2006 International Microwave Symposium IMS’2006

References

221

Oats D E and Dionne J F (1999) Magnetically tunable resonators and filters. IEEE Trans Appl Supercond 9:4170–4175 Paratek Microwave Inc (2004) Columbia, MD, Thin film electronically tunable pre-selectors for software defined radios. Microwave Journal, October 2004 Park J et al. (2006) Distributed Phase Shifter with Pyrochlore Bismuth Zinc Niobate Thin Films. IEEE Microwave and Wireless Components Letters 16:264–266 Rebeiz G (2003) RF MEMS Theory, Design, and Technology. Wiley Romanofsky R (2004) Broadband, Low-Loss K- and Ka-Band Phase Shifters Based on Thin Ferroelectric Films. IEEE MTT Symposium Workshop WMC Romanofsky R (2007) Array Phase Shifters: Theory and Technology. Glenn Research Center, Cleveland, Ohio, NASA/TM 2007-214906 (http://gltrs.grc.nasa.gov) Romanofsky R (2007-1) Advances in Scanning Reflectarray Antennas Based on Thin Ferroelectric Film Phase Shifters. Proc IEEE Special Issue on Technical Advances in Deep Space Communications and Tracking 95:1968–1975 Romanofsky R et al. (2000) Phased Array Antennas Based on Ba0.60Sr0.40TiO3 Thin-Film Phase Shifters. IEEE Trans MTT-48:2504–2510 Romanofsky R. R (2007) Array Phase Shifters: Theory and Technology, NASA report NASA/TM 2007-214906 Rubin B J and Singh B (2000) Study of meander line delay in circuit boards. IEEE Trans. Microwave Theory Tech 48:1452–1460 Ruby R et al. (2001) Ultra-Miniature High-Q Filters and Duplexers Usung FBAR Technology. IEEE International Solid-State Circuits Conference Digest of Technical Papers. ISSCC2001:120–121 Rupprecht G, Winner W H (1967) Electromechanical Behavior of Single-Crystal Strontium Titanate. Phys Rev155:1019–1028 Samoilova T B et al. (2005) Microwave Up-Converter Based on a Nonlinear Ferroelectric Capacitor. Technical Physics 50:1335–1342 Scheele et al. (2005) Passive ferroelectric phase modulators for RFID backscatter transponders. Proc. EuMC 2005:645–648 Scheele P, Goelden F, Giere A et al. (2006) Continuously Tunable Impedance Matching Network Using Ferroelectric Varactors. Workshop (http://www.hf.e-technik.tu-darmstadt.de) Scheele P et al. (2005) Continuously tunable impedance matching network using ferroelectric varactors. IEEE Int Microwave Symp MTT-S2005:603–606 Schmidt M, Lourandakis E, Leidl A et al. (2007) A comparison of tunable ferroelectric Π- and T-matching networks. Proc 37th EuMC:98–101 Schreiter M et al. (2004) Electro-acoustic hysteresis behaviour of PZT thin film bulk acoustic resonators. Journal of the European Ceramic Society 24:1589–1592 Seo C (2003) Novel phase shift line in feedforward circuit using photonic bandgap. Microwave and Optical technology Lett 38:357–359 Serraiocco J et al. (2002) Tunable Passive integrated circuits Using BST Thin Films. Integrated Ferroelectrics 49:161–170 Serraiocco J L et al. (2003) Compact ferroelectric reflection phase shifter. Dig. IEEE IMS’2003:1993–1996 Sherman V et al. (2001) Digital reflection type phase shifter based on a ferroelectric planar capacitor. IEEE Micr Wireless Comp Letters 11:407–409 Shuch P (2004) Multiband Reconfigurable Synthetic Aperture Radar Antenna. Proc 2004 Earth Science Technol Confer (B1P1, NASA):1–5 Shuch P (2005) Updating the Multiband Reconfigurable Synthetic Aperture Radar Antenna. Proc. 2005 Earth-Sun Systemtechnology Conference (B5P1, NASA):1–5 Subramanyam G et al. (2000) Performance of a K band voltage controlled Lange coupler using a ferroelectric microstrip configuration. IEEE Micr. Guided Wave Lett 10:136–138 Tagantsev A K et al. (2005) Permittivity, tunability and losses in ferroelectrics for reconfigurable high freauency electronics. In: Setter N (Ed) Electroceramic Based MEMs. Springer

222

5 Ferroelectric Devices

Tappe S et al. (2004) Electrostrictive resonances in BaSrTiO thin films at microwave frequencies. Appl Phys Lett 85:624–626 Teo P et al. (2000) Beam scanning of array using ferroelectric phase shifters. Electronics Letters 36:1624–1626 Teo P T et al. (2001) Design and Development of Tunable Multi-Layer Smart Antennas using Ferroelectric Materials. Journal of Intelligent Material Systems and Structures 11:294–299 Tien P K (1958) Parametric amplification and frequency mixing in propagating circuits. J Appl Phys 29:1347–1357 Tombak A (2007) A ferroelectric-capacitor-based tunable matching network for quad-band cellular power amplifiers. IEEE Trans Microwave Theory Tech 55:370–375 Tombak A et al. (2003) Voltage-Controlled RF Filters Employing Thin-Film Barium-StrontiumTitanate Tunable Capacitors. IEEE Trans Microwave Theory and Tech 51:462–576 Tunable Filters, Pole/Zero Corp (http://www.polezero.com/) Van Keuls F et al. (1997) YBa2Cu3O7–δ, Au/SrTiO3/LaAlO3 Thin Film Conductor/Ferroelectric Coupled Microstripline Phase Shifters for Phased Array Applications. Appl Phys Lett 71:3075–3077 Van Keuls F et al. (1999) Ku-Band Gold/BaxSr1–xTiO3/LaAlO3 Conductor/Thin Film Ferroelectric Microstripline Phase Shifter for Room Temperature Operation. Microwave and Optical Tech Letters 20:53–56 Van Keuls F W et al. (1998) Influence of the biasing scheme on the performance of Au/SrTiO3/LaAlo3 thin film conductor/ferroelectric tunable ring resonators. Integrated Ferroelectrics 22:883 Varadan V et al. (1992) Ceramic Phase Shifters for Electronically Steerable Antenna Systems. Microwave Journal January:116–127 Varadan V et al. (1995) A Novel Microwave Planar Phase Shifter. Microwave Journal April: 244–253 Vendik I B et al. (1999) Criterion for a switching device as a basis of microwave switchable and tunable components. Proc 29th Eur Microwave Conf EuMC’1999:3187–190 Vendik I B et al. (2008) Modeling tunable bulk acoustic resonators based on induced piezoelectric effect in BaTiO3 and Ba0.25Sr0.75TiO3 films. J Appl Phys 103:014107 Vendik I et al. (2001) Design of Tunable Ferroelectric Filters with a Constant Fractional Bandwidth. IEEE Int Microwave Symposium IMS2001:1461–1464 Vendik I, Pleskachev V, Vendik O (2005) Figure of Merit and Limiting Characteristics of Tunable Ferroelectric Microwave Devices Progress. Electromagnetics Research Symposium 2005, Hangzhou, China, August 22–26: 327–330 Vendik I B, Vendik O G, Kollberg E L (2000) Commutation quality factor of two-state switchable devices. IEEE Trans Microwave Theory and Techniques 48:802–808 Vendik O G, Zubko S P, Nikolski M A et al. (2003) Theoretical estimation of achievable figure of merit of microwave ferroelectric phase shifters. Int Ferroel 55:991–999 Vendik O G et al. (1995) 1 GHz Tunable Resonator on Bulk single Crystal SrTiO3 Plated with YBa2Cu3O7–x Films. Electron Lett 31:654–656 Vendik O, Mironenko I, Ter-Martirosyan L (1994) Superconductors Spur Applications of Ferroelectric Films. Microwaves & RF July:67–70 Vinoy K J et al. (1999) Gain Enhanced Electronically Tunable Microstrip Patch Antenna. Microwave and Optical Technology Letters 23:368–370 Vorobiev A et al. (2003) Silicon substrate integrated high Q-factor parallel-plate ferroelectric varactors for microwave/millimeterwave applications. Appl Phys Lett 83:3144–3146 Wang P et al. (2007) Planar tunable high-temperature superconductor microwave broadband phase shifter with patterned ferroelectric thin film. Supercond Sci Technol 20:77–80 Watson T (2007) Agile RF Inc (Privat communication) Wheeler H A (1947) Fundamental limitations of small antennas. Proc IRE 35:1479–14881 Wilson C R et al. (1991) Pulse shaping in uniform LC ladder network containing nonlinear ferroelectric capacitors. IEEE Trans Electron Devices 38:767–771

References

223

Zhu X et al. (2007) A DC Voltage Dependant Switchable Thin Film Bulk Wave Acoustic Resonator Using Ferroelectric Thin Film. Dig. IEEE IMS2007:671–674 Yun T S et al. (2007) Ferroelectric Tunable Band-pass Filter with Tapped-line Input. ISIF 2007 Zhang H et al. (2005) 5 GHz Low-phase-noise oscillator based on FBAR with low TCF. 13th Int Conf Solid State Sensors TRANSDUCER’2005:1100–1101 Zinck C et al. (2004) Design, Integration and Characterization of PZT tunable FBAR. IEEE International Ultrasonics, Ferroelectrics, and Frequency Control Joint 50th Anniversary Conference: 29–32

Chapter 6

Circuit and System Applications of Tunable Ferroelectric Devices

Abstract This chapter looks at circuit and systems applications of ferroelectrics. Voltage Controlled Oscillators (VCO) based on ferroelectric varactors with low phase noise, extended tuning range and linear dependences of the oscillation frequency on the DC bias are discussed. Use of ferroelectric varactors in power amplifiers is reviewed where they allow increasing in the efficiency, linearity and help reducing the current consumption. Representative electronically scanning cost effective beamformers and phased array antennas are presented.

6.1 Introduction Recent improvements in the quality of the ferroelectric thin films and ceramics have led to successful development of varactors and devices. In many cases, especially in thin film varactors, the Q-factor is limited rather by the losses in the plates and interconnects than in the ferroelectric itself. These achievements triggered considerable activities in the development of agile devices (phase shifters, matching networks etc.) considered in the previous chapter. This chapter reviews higher level circuit and system applications of the ferroelectrics and devices based on them. VCOs are one of the circuits where the application of the ferroelectric varactors is most promising. The low phase noise, high linearity of the DC bias voltage dependence frequency tuning, and the larger tuning range of the oscillation frequency are the main advantages of the VCOs based on ferroelectric varactors. The first integrated demonstration of a ferroelectrically controlled VCO is reported in (Romanofsky et al. 1998). In this cryogenic GaAs PHEMT/ferroelectric Ku-Band VCO a side-coupled Au/SrTiO3 3λ long ring resonator provides over 500 MHz tuning where the DC bias changes between 0 and 250 V. Several ferroelectrically controlled VCOs operating at room temperature, discussed below, demonstrate the actual potential of the technology. A number of applications of the ferroelectric varactors in amplifiers are proposed and demonstrated. As an example, a ferroelectric impedance tuner (match225

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6 Circuit and System Applications of Tunable Ferroelectric Devices

ing network) improves the load performance in multi-band reconfigurable systems (Katta et al. 2006). Recently phased arrays based on ferroelectric phase shifters with 1D (Romanovsky et al. 2000, Buslov et al. 2006) and 2D (Ingram et al. 2008) electronic beam scanning are demonstrated. The lens type ferroelectric 2D scanning beam formers (Rao et al. 1999, Tageman et al. 2003) seem to be quite attractive and promising both in terms of small sizes, simplicity and low cost.

6.2 Voltage Controlled Oscillators The first room temperature ferroelectric varactor based VCO is reported in (Victor 2004). The potential of the high power VCOs employing BST is explored in (Victor et al. 2006). For comparison purposes two identical 50-MHz VCO’s, one using a semiconductor junction varactor and the other a BST varactor are designed fabricated and measured. The phase noise of the VCOs based on BST ferroelectric varactor is analyzed and compared with the phase noise of an identical VCO based on a silicon semiconductor junction varactor. The analysis shows that the phase noise has the expected Q-factor dependence. The BST-based oscillator demonstrates reduced phase noise degradation near zero volts. The greater phase noise degradation when operated near breakdown may be explained by the increased leakage current near the breakdown voltages which is relatively low for the parallel-plate ferroelectric varactor used in this particular experiment (Victor et al. 2006). This negative effect may be reduced and completely eliminated by improving the quality of the ferroelectric film used in the varactor. In the case of semiconductor varactor based VCO the poor phase noise may only be reduced by avoiding DC voltages close to zero which essentially reduces the tuning ranges provided by semiconductor varactors. A Ba0.5Sr0.5TiO3 varactor based VCO using cross-coupled discrete RF BJTs is reported in (Jamil et al. 2007). It has a tuning range from 205 MHz to 216.3 MHz with a power consumption of 5.1 mW. The measured phase noise is –90 dBc/Hz at 100 kHz and –140 dBc/Hz at 1 MHz offset. Another VCO, a GaN-on-Si heterostructure field effect transistor (HFET) based 1.6 GHz power VCO using an interdigital ferroelectric varactor is reported in (Victor et al. 2006). The surface-mount BST varactor is fabricated on alumina using sputtering and copper metallization. An output power of 1.6 W (32 dBm) is obtained with a DC conversion efficiency of 25.5%. Tuning sensitivity of the VCO is 500 kHz/V. A 49 MHz linear frequency tuning and power flatness of better than 0.5 dB are obtained with 0–100 V tuning voltage. The phase noise is –81.4 dBc/Hz at 100 kHz offset. Recently two K-band VCOs based on parallel-plate BSTO varactors have been demonstrated (Norling et al. 2007, Aspemyr et al. 2007). Norling et al. (2007) report a K-band VCO utilized as a hybrid module where the cross-coupled SiGe transistors (Fig. 6.2.1) are flip-chip mounted on a silicon carrier (Fig. 6.2.1 (b)) incorporation integrated parallel-plate ferroelectric Ba0.25Sr0.75TiO3 varactors (Fig. 6.2.1 (c)) and other passive circuits. The parallel-plat varactors are formed

6.2 Voltage Controlled Oscillators

227

between the patterned bottom (M1) and top (M2) electrodes. The non-patterned BSTO film is sandwiched between bottom and top electrodes. The sizes of the module (Fig. 6.2.1 (b)) including the output balun and the DC bias network, are 4.7×2.2 mm2. A linear tuneability of 6.7% and an output power of 3 dBm±1 dB over the tuning range are measured at center frequency 16.5 GHz. The phase noise at center frequency is –95 dBc/Hz at 100 kHz offset. A similar VCO, operating at 19.6 GHz, demonstrates a tuneability of 3.3% and a phase noise of –102 dBc/Hz at 100 kHz offset. The voltage dependence of the oscillation frequency (Fig. 6.2.1 (d)) is nearly linear thanks to nearly quadratic voltage dependence of the varactor capacitance: f∼[LC(V)]–0.5. Due to the processing tolerances the complete tuning (>40%) of the varactors is not utilized in this experiment. However a good linearity in f(V) dependence and fairly constant output power may be observed (Fig. 6.2.1 (d)). (a)

(b)

(d)

(c)

Balun

DC bias network Fig. 6.2.1 Equivalent circuit (a), photos of the VCO assembly and varactors (b, c), and measured performance (d) of the K-band VCO. Reprinted with permission from IEEE©2007

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6 Circuit and System Applications of Tunable Ferroelectric Devices

In advanced versions the VCO’s cross coupled transistors are implemented as IC chips and the external LC tanks, consisting of lumped inductors and ferroelectric varactors, are integrated with the high resistivity silicon carrier. In these VCOs the IC chips carry two 130 nm CMOS transistors (Aspemyr et al. 2007). The cross-coupled VCO-cores (Fig. 6.2.2 (a)) are flip-chip mounted on the silicon carrier with integrated inductor and ferroelectric varactor (Fig. 6.2.2 (b)). The output frequency of one of the VCOs is tunable from 23.4 GHz to 26.1 GHz, corresponding to a tuning range of 11 % (Fig. 6.2.2 (c)). The phase noise of this VCO, at its

Vdd

CVAR CVAR

M1A

M1D

LS

(b)

27 Phase noise (dBc/Hz)

Oscillation frequency (GHz)

(a)

26 25 24 23 –20

–10

–15

Tuning voltage (V)

(c)

–5

0

–20 –30 –40 –50 –60 –70 –80 –90 –100 –110 –120 1kHz

10kHz

100kHz

1 000kHz

Offset frequency

(d)

Fig. 6.2.2 Circuit topology (a), Si-carrier with passives and flip-chipped ICs (b), measured bias dependences of the frequency (c) and phase noise (d) performances. Reprinted with permission from IEEE©2007

6.3 Amplifiers

229

center frequency, measures –117 dBc/Hz at 1 MHz offset. A second VCO is demonstrated with tuning from 25.8 GHz to 30.5 GHz, corresponding to a tuning range of 17%. The phase noise at center frequency for this design measures –109 dBc/Hz and the power consumption is 5.3 mW. Experimentally, a Ka-band tunable Gunn diode based active antenna module is demonstrated in (Buslov et al. 2007). It includes a planar dielectric resonator tuned by a ferroelectric varactor. The tunable resonator stabilizes the VCO and at the same time acts as a radiator (Fig. 6.2.3). The operation frequency of the module is about 17 GHz. (a)

(b)

Fig. 6.2.3 Schematics (a) and photo (b) of the active radiator module. Reprinted with permission from IEEE©2007

6.3 Amplifiers In (Katta et al. 2006) the low tuning voltage high power ferroelectric varactors (see Fig. 4.7.2, Sect. 4.7.1) are developed for power amplifier applications (Fig. 6.3.1). The measured adjacent channel leakage power ratio (ACPR1) is about

230

6 Circuit and System Applications of Tunable Ferroelectric Devices

–48 dBc and the current consumption (Icc) is 519mA. In this experiment the load impedance is 50 ohm and the output power is +28 dBm at center frequency of 1880 MHz. The ACPR1’s load performance of tunable PA is improved by 4 dB, compared to fixed-impedance PA. V1

V2

Output MN L

DC block

DC block

DC block

Input MN Ct1 Ct1

Ct2

-40

550

-44

530

-48

510 Out MN Ct1 C

-52

490

Icc[mA]

ACPR1[dBc]

(a)

Ct2 C

-56 -60 1840

470

1850

1860

1870

1880

1890

1900

1910

450 1920

(b)

Frequency[MHz] Fig. 6.3.1 Circuit topology (a) and performance (b) of Kyosera’s tunable power amplifier using high power ferroelectric varactors. Reprinted with permission from IEEE©2006

Agile RF Inc. (http://www.agilematerials.com) offers similar matching networks for power amplifiers operating at 1.5 GHz. The chips of the devices, designed for flip-chip mounting, are about 1 mm2 in size. The devices tune the load to get minimum current drain regardless the power level – thus yielding a maximum power added efficiency. According to Agile RF, in a power amplifier using variable bias and a tuning network allows reduction of the current consumption more then 60% and substantially increases the talk time in mobile hand sets. According to Agile RF application of the ferroelectric phase shifters in Doherty amplifiers provide RF linearization.

6.4 Steerable Phased Array and Beam Antennas

231

6.4 Steerable Phased Array and Beam Antennas The adaptable/reconfigurable antennas provide radiation pattern (beams) that are electronically controlled allowing tunable beam width/gain, 1D and 2D scanning, etc. Today the most common types of the scanning antennas are mechanical. Usually they are heavy, slow and scan fixed beamshapes. More advanced antennas are in the form of phased arrays based on semiconductor and ferrite phase shifters (Parker 2002, Koul and Bhat 1999). In the case of large arrays the power consumption, heating, the sizes of Tx/Rx modules and the cost cause serious problems forcing to look for alternative technologies. In this respect scanning antennas based on ferroelectrics have been considered since early 1960s (Vendik 1965, Vendik et al. 1979), and first experimental demonstrator was proposed 1982 (Vendik et al. 1994).

6.4.1 Phased Arrays The advanced/future commercial microwave communications systems, including cellular (mobile) systems, tend to be reconfigurable and adaptable with tunable beamshapes and scan angles. Simplified (4 element 1D array) schematic diagrams of traditional phased arrays based on phase shifters and delay lines are shown in Fig. 6.4.1. For military and space applications 2D phased arrays may consist of up to several thousand phased shifters or delay lines. For such arrays the speed, power consumption and sizes of the phase shifters and delay lines are critical issues. In this respect ferroelectric phase shifters and delay lines have no competitors. In a phase shifter based beam scanner (Fig. 6.4.1 (a) the scanning of the beam is achieved by controlling the phase shift. The maximum required phase shift for full Θ=90°scan angle is 2π, which is easily achievable using ferroelectric technology. The delay line type phase shifters with linear phase frequency response may be used in phased arrays operating in narrow frequency band. For wide band (narrow pulse) phased array antennas (PAA) the phase shift needs to be frequency independent in the required frequency band of operation. In time delay scanning systems (Fig. 6.4.1 (b)) the delay lines should provide non-dispersive (i.e. frequency independent) delay time in a wide frequency range. For example, for a 1D array consisting of 8 elements with the inter element spacing a=λo/2, where λo is the free space wavelength, the total length of the array is about 4λo. At f=23 GHz and scan angle Θ=90o, the required incremental delay time is ΔΤ=a/co=1/(2f)=0.02 ns. Hence the maximum delay time to be provided by a delay line should be about n ΔΤ= 8·0.02=0.16 ns, which is easy to achieve in the delay lines discussed in the previous chapter. At present ferroelectric technology based phased array antennas for space (Romanofsky et al. 2000) and commercial (Kozyrev 2000, Kozyrev et al. 2004, Purden et al. 2005) applications are reported.

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6 Circuit and System Applications of Tunable Ferroelectric Devices

(a)

3Δφ

2Δφ Θ

Δφ a

Δφ=a(ω/co)SinΘ

0

Radiator

Tunable phase shifter

(b)

3ΔΤ

2ΔΤ Θ

a

ΔΤ

Tunable delay line

ΔΤ=(a/co)SinΘ

0

Radiator

Fig. 6.4.1 4 element 1D phased arrays based on phase shifters (a) and delay lines (b)

6.4.2 Steerable Beamformers and Phased Arrays A simple phased array antenna based on a power splitter, phase shifters and radiators is reported in (Fig. 6.4.2, DeFlaviis and Alexopoulos 1998). The 2.1 GHz microstrip prototype is fabricated on a Duroid substrate with thickness 1.5 mm and permittivity 2.33. The delay line type microstrip phase shifters are based on a 100 μm thick ceramic BSTO substrate (DeFlaviis et al. 1997). The width of the microstrip is 50 μm. A total beam scan of 36o is achieved under 450 V and matching is better than 20 dB. The drive power (4 mW) is about an order of magnitude less then those for comparable ferrite phase shifters.

6.4 Steerable Phased Array and Beam Antennas

233

Patch radiator

Patch radiator To DC bias

DC block

Microstrip ferroelectric phase shifter

Power splitter

Fig. 6.4.2 4 Ferroelectric phase shifter based two element phased array beam scanner. Reprinted with permission from IEEE©1997

A similar 1D array has been reported by Romanovsky (2000). In this array 16 microstrip patch antennas are fed by a 16 channel passive parallel feed network via 16 ferroelectric phase shifters. The phase shifters are based on coupled microstrip lines (see inset, Fig. 6.4.3) patterned on thin heteroepitaxial Ba0:6Sr0:4TiO3 films grown on MgO substrates. The figure of merit of the phase shifters is about 70 degrees/dB at 19 GHz and at 46 V/μm DC field.

Coupled microstrips

Fig. 6.4.3 Parallel fed 16 element 1D phased array. Reprinted with permission from IEEE©2000

234

6 Circuit and System Applications of Tunable Ferroelectric Devices

In contrast to the microstrip power splitters (Fig. 6.4.3) the 16 element 1D array (Fig. 6.4.4, Golovkov et al. 2001) employs a Ka band waveguide serial feed power splitter. Microstrip probes inserted via a-side of the waveguide couple the microwave signals into the serially fed microstrip patch antennas via ferroelectric phase shifters. The serially fed patches allow shaping the beam in the vertical directions. In horizontal plane this array scans the beam in a ±40° sector. A similar array is reported by Kozyrev et al. (2000). Using hollow waveguide power splitters (Buslov et al. 2006, Kozyrev et al. 2008) allow a substantial reduction of the microwave losses and improving the overall performance of the array at the expenses of reduced flexibility, i.e. dynamic control of amplitude distribution. In one of the designs developed in collaboration with Paratek (Buslov et al. 2006) the power splitter consists of an H-plane Ka-band waveguide horn, split in the output section into sectors. The slot line ferroelectric phase shifters, in each of the output sectors, consist of input and output ports in the form of Vivaldi radiators. One of the Vivaldi antennas is coupled with the H-plane horn, while the other radiates into the free space.

Radiator array

DC bias

Ferroelectric phase shifters Array port

Fig. 6.4.4 1D 16-element serially fed phased array. Courtesy of A. B. Kozyrev, LETI, S. Petersburg, Russia

A low cost 24 GHz automotive phased array by Agile RF and Delphi Electronics and Safety (Purden et al. 2005) is shown in Fig. 6.4.5. The BST phase shifters are implemented as distributed CPS transmission line with thirty three BST varactors evenly distributed along the line. The 50 Ohm input impedance phase shifter provides a differential phase shift of 360 degrees where the DC bias voltage is changed from 0 to 20 volts. The input and output ports of the phase shifters are connected to the microstrip feeding lines and radiators using baluns. The quarter wavelength CPS

6.4 Steerable Phased Array and Beam Antennas

235

transformers used between the baluns and phase shifters provide impedance matching. The measured insertion loss (including the phase shifter, matching networks and the baluns) is less than 6 dB and the return loss is about 15 dB. The phased array shown in Fig. 6.4.5 is fabricated on a 100 mm sapphire wafer using a simple sixmask process. It makes use of 12 phase shifters based on CVD deposited BST thin film varactors. A field of view greater than ±45 degrees is demonstrated. The antenna is designed for applications in automotive radar collision warning systems that require fast beam scanning in large scan angles and low cost.

Fig. 6.4.5 Automotive phased array by Agile RF and Delphi Electronics and Safety. Reprinted with permission from IEEE©2005

Fig. 6.4.6 NASA’s 615 element, 19 GHz ferroelectric prototype array. The diameter is 28 cm (http://esto.gsfc.nasa.gov/conferences/estc2005/papers/a1p3.pdf)

A scanning reflectarray proposed by NASA (Ingram et al. 2008), consists of a flat surface with diameter D containing N integrated phase shifters and N patch radiators that are illuminated by a single feed at a virtual focus located a distance f from the surface with f/D≈1 (Fig. 6.4.6). The incident on the radiators signal passes through the N reflection type phase shifters and is re-radiated as a focused beam. The control voltages applied to the phase shifters scan the reflected beam in

236

6 Circuit and System Applications of Tunable Ferroelectric Devices

a preferred direction. The hybrid X-band phase shifters consist of four cascaded coupled microstrip lines patterned over 400 nm thick Ba0.5Sr0.5TiO3 film deposited by laser ablation. At the ends the phase shifters are loaded by silicon P-I-N diodes switches, as it was discussed previously (see Sect. 5.3.5). Each of the ferroelectric phase shifters provide nominally 180 degrees of analog phase shift as the DC bias, applied across the coupled line electrodes, changes from 0 to 350 V. The silicon P-I-N diodes are switched between on and off states resulting in a digital transition between a reflection coefficient with magnitude near unity and phase of ≈ 0 degrees and ≈180 degrees, respectively providing a full 360 phase shift. Arrays with the number of elements 2832 are considered by Romanofsky (2000). The proposed array is very cost effective due to integration simplicity and reduced phase shifter cost. The radiators may be fabricated on soft substrates. Thus, the implementation of the phased arrays with large number of radiators/phases shifters becomes possible due to the unique properties of ferroelectric phase shifters-virtually no controlling power consumption. The low control power consumption by the phase shifters prevent the heat generation and removal issues. In spite of the reduced sizes, power consumption, cost, and increased scanning speeds, the ferroelectrically scanning beamformers based on traditional phased array architectures still feature some of the problems, may be to a smaller extent, typical for non-ferroelectric analogs, such as the complexity of the design and cost. On the other hand (in contrast with the competing technologies) the ferroelectrics offer extra possibilities in terms of development of new architectures with reduced complexity and cost. Some of the published and potential architectures are discussed below.

6.4.3 Nontraditional and Lens Type Steerable Beamformers An electronically steerable traveling wave antenna based on thick ferroelectric ceramics film reported in (Vendik et al. 1994). It is based on a 48×7x0.5 mm MgO substrate with a 3.5 μm thick BSTO ceramic film (Fig. 6.4.7). The substrate is mounted on a copper ground plane and a rectangular waveguide is used to launch traveling along the ferroelectric film waves. A number of interdigital electrodes, deposited on the surface of the ferroelectric film and separated by slots, act as phase shifters. The DC applied field changes the permittivity of the film under the interdigital electrodes changing the phase of the traveling waves. The slots between the interdigital electrodes act as radiators. The distance between the radiating slots is chosen to be about half wavelength. Thus, the whole structure forms a linear array of radiators fed via interdigital phase shifters. The phase shifters being connected in series provide the incremental phase shifts that are needed for the radiating slots. The slot that is closer to the input experiences the smallest phase shift, while the phase shift is largest for the last radiating slot. A DC bias applied to the phase shifting interdigital electrodes causes scanning of the antenna beam. This 1D scanning antenna is proposed for operation at 40 GHz.

6.4 Steerable Phased Array and Beam Antennas

237

Fig. 6.4.7 Traveling wave 1D scanning array antenna

(a) Plane waves

φ

Wavefront

E

(b)

Ferroelectric

λo/2

Matching transformer

DC

Fig. 6.4.8 Parallel-plate phase shifters (a) in a phased array lens (b) of Naval Research Laboratory. Reprinted with permission from IEEE©1999

A 1D voltage controlled ferroelectric phased array lens is proposed by Rao et al. (1999). This array makes use of phase shifters based on parallel-plate waveguides with ferroelectric ceramics feeling (Fig. 6.4.8). The parallel-plate delay line type phase shifters are provided with the input/output horns and dielectric matching transformers. The phase shifters are stacked to form the lens. An adequate DC bias network is used to control the phase in each phase shifter. The incident plane waves experience different phase shits in different parallel-plate delay

238

6 Circuit and System Applications of Tunable Ferroelectric Devices

lines forming the scanning beam as shown in Fig. 6.4.1 (b). An experimental phase shifter based on Ba0.55Sr0.45TiO3 ceramics (with 60% addition of a low permittivity non-ferroelectric oxide, e.g. MgO) demonstrated 180 degree/dB figure of merit at 9 GHz. In this first experiment the drive power at 10 kV DC voltage was 0.5 W. A similar lens is proposed by Peng et al. (2007). The ferroelectric lens proposed by Ericsson (Tageman et al. 2003) is by far the simplest and most cost effective among all other ferroelectric lenses published today. The core of the lens consists of a ferroelectric plate with typical sizes 10x10 mm2. The thickness may be in the range 1–5 mm depending on the permittivity of the plate (typically from 100 to several hundred) and operation frequency. The plate is covered on both sides by high resistivity films (Fig. 6.4.9 (a) and (c)).

Fig. 6.4.9 Ferroelectric plate with high resistivity films and electrodes (a, c) the electric field and refractive index distribution for 1D beam scanning (b)

Simplified structures of the ferroelectric plate for 1D and 2D beam steering are shown in Fig. 6.4.9. The high resistivity films and conducting strips (electrodes) are used for applying DC field. To ensure low losses of the electromagnetic waves, the resistivity of the resistive films is chosen so that the thickness of the film is much smaller than the skin depth. A DC field applied between the electrodes, as shown in Fig. 6.4.9 (a), generates a linear distribution of the potential along the left resistive film resulting in electric field and refractive index, √ε, distributions in the ferroelectric plate, schematically shown in Fig. 6.4.9 (b). Tuning the applied DC field causes changes in the gradient in the refractive index (Fig. 6.4.9 (b) and introduces changes in the gradient (phase front) in the phase after the ferroelectric plate, which leads to a steering of the beam, as shown in Fig. 6.4.10. The concept may be extended to 2D scanning of the microwave beam by orthogonal arrangement of the electrodes on the opposite surfaces of the ferroelectric plate (Fig. 6.4.9 (c)).

6.4 Steerable Phased Array and Beam Antennas

239

l BW

SA

L

ERF

Wave front

EDC

x SA/2

Ferroelectric plate

y

z

Fig. 6.4.10 The beam steering concept. SA-scanning angle, BW-beamwidth. Reprinted with permission from EuMA©2003

The photograph of the lens, including quarter wavelength transformer plates (permittivity 34 and thickness 0.32 mm), and free space measurement setup are shown in Fig. 6.4.11. In this experiments the 100×100×1 mm3 core plate made of Ba0.46Sr0.63Ti0.37O3+0.54MgO ceramic, sintered at 1425°C for 8 hours. The composition of the BaxSr1–xTiO3 and the content of the MgO are optimized to achieve high tuning of the permittivity and low microwave losses. From a 10 kHz LCR measurement its permittivity is determined to be 1057 at 22°C and zero bias. The thickness of the ferroelectric plate, 1.0 mm, is selected by trading between the low control voltages and large phase shift. To ensure large phase shift the thickness of the plate has to accommodate as many wavelengths as possible, i.e. the plate needs to be electrically thick. On the other hand, to completely utilize the available from the used ferroelectric composition tuneability, electric fields up to 15 kV/mm are required. Avoiding the extremely high DC bias voltages required for the generation of such high field strengths, the thickness of the ferroelectric plate has to be as small as possible. A special high resistivity composition, based on LaMnO3:SrTiO3, was developed to facilitate the application of the DC bias. The resistivity (~100 MOhm/sq) and the thickness (~ 10 μm) of the resistive film are selected from low microwave loss and low DC current considerations. The free space measurement setup is shown in Fig. 6.4.11 (b) and the measured losses and differential phase shift under different bias fields are shown in Fig. 6.4.12. The phase shift is defined in (5.2.15) with l being the thickness of the ferroelectric plate. The S21 “reflect” trace, indicated in Fig. 6.4.12 (a), is for the measurements where the ferroelectric plate is replaced by a blank Al plate. It is a part of measurement calibration procedure. The results shown in Fig. 6.4.11 and Fig. 6.4.12 are obtained for uniform field (permittivity) distribution across the ferroelectric plate, i.e. in the free space phase shifter/modulator regime where both electrodes on each side of the plate (Fig. 6.4.9) are under the same potential. No beam scanning is reported in these preliminary measurements. The figure of merit of the plate at about 30 GHz (operation frequency with matching, S11, about –20 dB) is more then 60 degree/dB.

240

6 Circuit and System Applications of Tunable Ferroelectric Devices

(a)

(b)

Fig. 6.4.11 The lens with λ/4 transformers (a) and the measurement setup. Reprinted with permission from EuMA©2003

As it is indicated in Fig. 6.4.10, the applied DC filed (EDC) is normal to the plate surface. As result the change in permittivity in orthogonal x-direction, i.e. parallel to the RF field (ERF) is less than that in z-direction (Tagantsev 2003):

1 1 1⎡ 1 1 ⎤ − = ⎢ − ⎥ ε x (E DC ) ε (0 ) 3 ⎣ ε z (E DC ) ε (0) ⎦

(6.4.1)

Then the tuneability which will “see” the RF field is lower: 1 ε (E ) T x ( E DC ) = T z x DC 3 ε z (E DC )

(a)

(6.4.2)

(b)

Fig. 6.4.12 Measured S21 at 0, 8 and 15 kV/mm (a) and the differential phase shifts under different DC-fields (b). Reprinted with permission from EuMA©2003

6.5 Conclusions

241

To increase the tuneability the applied DC and RF fields have to be collinear, as in Fig. 6.4.8. Figure 6.4.13 shows a design (Gevorgian et al. 2004) meeting this requirement. In contrast to the horns and matching networks shown in Fig. 6.4.8 this lens uses quarter wavelength “corporate” matching plates attached to the faces of the stack of the parallel-plate phase shifters.

Fig. 6.4.13 Alternative design of a lens with collinear RF and DC fields and corporate quarter wave matching plates. (a) parallel-plate phase shifter, (b) packed lens with matching plates, an (c) fragment of fabricated 5 layer structure.

6.5 Conclusions The circuit and system application examples discussed in this chapter demonstrate the potential and the advantages of the ferroelectrics in terms of high Q-factor and high tuneability (e.g. in VCOs), high power handling capability (e.g. in VCOs, impedance tuners, delay lines in power amplifiers), low leakage currents and high tuning speeds (e.g. steerable beamformers), unique and cost effective system solutions (e.g. lens type steerable beamformers). Even though not discussed in this chapter, the ferroelectrics in polar phase used in commercial piezoelectric transducers offer cost effective solutions for microwave devices and systems (Gevorgian 2002). Given the advantages and the current progress in materials, i.e. drastic reduction of the dielectric losses and increased tuneabilities, it is anticipated that the ferroelectrics will have more applications in commercial and defense circuits and systems. Application of the phase shifters in adaptive duplexers allowing improvement of the system performance is only one of the examples to mention (O’Sullivan et al. 2005).

242

6 Circuit and System Applications of Tunable Ferroelectric Devices

References Aspemyr L et al. (2007) 25 GHz and 28 GHz Wide Tuning Range 130 nm CMOS VCOs with Ferroelectric Varactors. The 2nd IEEE International Workshop on RF Integration Technology, Singapore, Dec. 2007 Buslov O Y, Golovkov A A , Keis V N et al. (2007) Active Integrated Antenna Based on Planar Dielectric Resonator With Tuning Ferroelectric Varactor. IEEE Trans Microwave Theory and Techniques 55:2951–2956 Buslov O Y, Keis V N, Kotelnikov I V et al. (2006) Slot-line ferroelectric phase-shifters and phase-array antenna on their base. Int Ferroelectrics 86:125–130 DeFlaviis F, Alexepolous N G, Staffsudd M (1997) Planar Microwave Integrated Phase Shifter Design with High Purity Ferroelectric Material. IEEE Trans Micr Theory 45:963–969 DeFlaviis F, Alexopoulos N G (1998) Thin Ceramic Ferroelectric Phase shifters for Steerable Microstrip Patch Antenna Array. Proc EuMC’98:678–681 Deleniv A, Eleftheriades G. J. Wong (2008) Beam Steering in Planar Anisotropic TransmissionLine Metamaterial. 2nd International Congress on Advanced Electromagnetic Materials in Microwaves and Optics, Pamplona, Spain, September 21–26 Gevorgian S, Vorobiev A (2007) Tunable metamaterials based on ferroelectric varactors. EuMC’2007:404–407 Gevorgian S, Deleniv A, Tageman O et al. (2004) A ferroelectric lens. European Patent EP1825562. Publication Date: 05/14/2008 Filing Date:12/08/2004 Gevorgian S Sh (2002) Tunable ferroelectric/piezoelectric microwave devices. In: Setter N (Ed) Pizoelectric Materials and Devices, EPFL, Lausanne Golovkov A A et al. (2001) Investigation of a Ka range FAA using ferroelectric phase shifters (in Russian). Proc 11th Int Conference Microwave&Telecommunication Technology, Sevastopol, Crimea, Ukrain CriMiCo2001:339–340 Ingram M A et al. (2008) LEO Download Capacity Analysis for a Network of Adaptive Array Ground Stations: http://www.esto.nasa.gov/conferences/estc2005/papers/a1p3.pdf Ingram M A et al. (2008) Optimizing Satellite Communications With Adaptive and Phased Array Antennas. http://eo1.gsfc.nasa.gov/new/validationReport/Technology/SensorWebs/EO-1%20 Optimizing%20Satellite%20Communications_PPT.pdf Jamil A, Kalkur T S, Cramer N (2007) Tunable ferroelectric capacitor-based voltage-controlled oscillator: IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control l54:222– 226 Katta H, Kurioka H, Yashima Y (2006) Tunable Power Amplifier Using Thin-Film BST Capacitors. IEEE IMS’2006:564–567 Koul S K and Bhat B (1999) Microwave and Millimeter Wave Phase Shifters. Artech House Kozyrev A et al. (2004) Tunable Ferrelectric Microwave Devices. IMS’2004 Workshop on New Technologies for Frequency-or Phase-Agile Microwave Circuits and Systems Kozyrev A B et al. (2000) 30 GHz steerable beam antenna based on ferroelectric phase shifters. Proc Progress In Electromagnetics Research Symposium, July 5–14, 1: 48 Kozyrev A B, Buslov O Yu, Golovkov A A et al. (2008) VCO/radiator module tuned by ferroelectric varactor. Integr Ferroelectrics 97:38–49 Miranda F A et al. (2000) Design and Development of Ferroelectric Tunable Microwave Components for Ku- and K-Band Satellite Communication Systems. IEEE Trans Microwave Theory Techn 48:1181–1189 Norling M et al. (2007) A Low-Noise K-Band VCO Based on Room-Temperature Ferroelectric Varactors. IEEE Trans On Microwave Theory and Techniques 55:361–369 O’Sullivan T, York R A, Noren B et al. (2005) Adaptive Duplexer Implemented Using SinglePath and Multipath Feedforward Techniques With BST Phase Shifters. IEEE Trans Micr Theory Techn 53:106–114 Parker D, Zimmermann D C (2002) Phased Arrays- Part II: Implementations, Applications, and Future Trends. IEEE MTrans Microwave Theory Techn 50: 688–698

References

243

Peng L, Ran L, Zou Y. K et al. (2007) A miniaturized phased array aperture antenna based on bulk ferroelectric material. Micr Opt Techn Letter 49:37–40 Purden S Shi, Jin J, York R A (2005) A 24 GHz Wafer Scale Electronically Scanned Antenna Using BST Phase Shifters for Collision Avoidance Systems. IEEE Ant Prop Symp 1B:84–87 Rao J B L, Patel D P, Krichevsky V (1999) Voltage-Controlled Ferroelectric Lens Phased array, IEEE Trans Antennas and Propagation 47: 458–468 Romanofsky R R, Van Keuls F W, Miranda F A (1998) A cryogenic GaAs PHEMT/ferroelectric Ku-band tunable oscillator. Journal de Physique IV 8:171 Romanovsky R et al. (2000) A K-Band Linear Phased Array Antenna Based on Ba0.60Sr0.40TiO3 Thin Film Phase Shifters. Dig IEEE MMT-S’2000:1351–1354 Romanovsky R et al. (2000) K-band Phased Array Antennas Based on Ba0.60Sr0.40TiO3 Thin-Film Phase Shifters. IEEE Trans Microwave Theory Techn 48:2504–2510 Tagantsev A (2003) Private communication Tageman O, Falk K, Hallbjörner P et al. (2003) Ferroelectric Beam Steering Plate. Proc Workshop Tunable Ferroelectric Materials and Devices for Microwave Applications, EuMC2003 Vendik O G (1965) Antenny s nemekhanicheskim kachaniem lucha, (Antennas with NonMechanical Scanning). Sovetskoe Radio, Moscow (in Russian) Vendik O G (1979) Segnetoelektriki v Tekhnike SVCh (Ferroelectrics at Microwaves). Sovetskoe Radio, Moscow (in Russian) Vendik O G, Mironenko I G, Ter-Martirosyan L T (1994) Superconductors spur application of ferroelectric films. Microwave & RF 33:67–70 Victor A, Nath J, Ghosh D et al. (2006) Voltage Controlled GaN-on-Si HFET Power Oscillator Using Thin-Film Ferroelectric Varactor Tuning. Proc EuMC2006:87–90 Victor A, Nath J, Ghosh D et al. (2006) Noise Characteristics of an oscillator with a Barium Strontium Titanate (BST) Varactor. IEE Proc Micr Antennas Propagation 153:96–102 Victor A, Nath J, Ghosh D et al. (2004) A voltage controlled oscillator using Barium Strontium Titanite (BST) thin film varactor. Proc IEEE Radio and Wireless Conference RAWCON 2004:91–94

Chapter 7

Modeling

Abstract This chapter provides simple closed form analytical models of coplanarplate transmission lines and capacitors incorporating ferroelectric layers. Coplanar-Strip (CPS), Coplanar Waveguides (CPW), and coplanar-plate capacitors with straight, interdigital and annular slots on multilayer substrates including ferroelectric layers are considered. The simple analytic formulas are mainly based on a conformal mapping technique and assume uniform dielectric permittivity distribution in ferroelectrics layers. They are useful for device optimization and measurements of the dielectric properties of the ferroelectric layers. An accurate closed form analytic formula for the losses in the plates of parallel-plate capacitors is also provided.

7.1 Introduction Commercially available software (Momentum, Sonnet, etc.) may be used for the analysis of the complex microwave structures. In some cases, where ferroelectric films with extremely small thicknesses and extremely high permittivity (i.e. several hundreds to several thousands) are involved, one encounters computational problems/accuracy problems. On the other hand closed form analytic expressions for the basic parameters of the devices, such as capacitance, impedance, effective dielectric permittivity and losses are still preferable, since they are computationally more efficient and allow time efficient optimization of complex circuits. In this chapter, the partial capacitance technique is used to deal with the basic parameters of the main coplanar-plate devices including ferroelectric layers. In contrast to the parallel-plate devices, in coplanar-plate devices the electric field distribution in the ferroelectric film and hence the induced changes in the permittivity are non uniform. The accurate modeling of the performances of these devices, taking into account the non-uniform distribution of the permittivity, involves heavy computations (Giraud et al. 2005, Berg and Gevorgian 2002). 245

246

7 Modeling

Assuming uniform distribution of the permittivity and using conformal mapping technique results in simple and closed form analytic approximations. These formulas (approximations) are rather correct without DC bias and allow an estimation of the device parameters and performance with acceptable, for most of the applications, accuracy. The provided models include the dielectric losses and allow calculation of complex impedances of the devices. They are useful for extraction of the dielectric properties of the ferroelectric layers using the measured impedances of the devices. The detailed conformal transformations given in the appendices may help an interested reader to deal with their own designs/devices.

7.2 Coplanar-Plate Transmission Lines 7.2.1 The Equivalent Circuit of the Lines 7.2.1.1 The Physical Model and Equivalent Circuit The structures of the CPS and CPW based on multilayer substrates are shown in Fig. 7.2.1 (a) and b accordingly. In general, the substrate may have more dielectric layers. The analysis in this chapter is based on low loss assumption, so that the quasi-TEM approximation is applicable. The equivalent circuit of the lines is given in Fig. 7.2.1 (c). For the given per unit length line parameters the line impedance and propagation constant are presented in a standard way: Z=

r + jωL G + jωC

,

γ = (r + jωL)(G + jωC )

(7.2.1) ,

(7.2.2)

with commonly used notations: γ=α+jβ, εeff=(β/ko)2, ko=2πf/co, co=3·108 m/s, ω=2πf. The conformal mapping and partial capacitance techniques are extensively used to derive closed form analytical expressions for the parameters C, L, and G. Though the conformal mapping also may be used to take into account the thickness of the strips (Ghione et al. 1999) here a closed form approximation is used to keep the formulas simpler. The line inductance and its frequency dependence associated with the skin effect (internal inductance) are modeled using conformal mapping where the equivalent width of the strip is reduced by two skin depths, Fig. 7.2.2 (b). A simple approximation is used for r. The CPS model considered below is valid below the cut-off frequencies of any possible higher order or leaky waves. For a single layer substrate with permittivity ε and thickness h these frequencies are below f
7.2 Coplanar-Plate Transmission Lines

247

tilayer dielectric substrate the wave propagation dynamics is more complex. For example, it has been shown (Liu et al. 1993) that a thin dielectric layer with a higher (than the substrate) dielectric permittivity just below or above the strips may drastically reduce the possibilities of coupling into the substrate leaky waves. ε5

(a) ε3, σ3, tanδ3 h3

s

s

2g

h1

h2

ε2, σ2, tanδ2

ε1, σ1, tanδ1 ε4 ε5

(b) ε3, σ3, tanδ3 h3

g

2s

g

h1

h2

ε2, σ2, tanδ2

ε1, σ1, tanδ1 ε4

(c) L

r C

G

Fig. 7.2.1 Cross section of CPS (a) and CPW (b) and their quasi-TEM equivalent circuit (c). Reprinted with permision from IEEE©2003

248

7 Modeling

Δ

s

Δ

2(g-Δ)

s

Δ

(a)

Δ t

s+2Δ

s+2Δ H

s–2δs

δs

s-2δs

δs

δs

(b) δs t<3δs

s

s

2g

Fig. 7.2.2 Cross section of the strips including thickness dependent width increments (a) and frequency dependent equivalent strip width (b). Reprinted with permision from IEEE©2003

In the case where the thickness of the metal layers is of the order of a couple of micrometers or less, i.e. for widely used metals (Al, Cu, Ag, Au) it is comparable with the skin depth in a wide frequency range. Having this in mind the effect of the film thickness (t) on the line capacitance is taken into account as an increment 2Δ in the strip width (Fig. 7.2.2 (a)) using a simple approximation:

Δ=

t 2πε e

⎡ ⎛ 8πs ⎞⎤ ⎟⎥ ⎢1 + ln⎜ ⎝ t ⎠⎦ ⎣

(7.2.3)

εe is the mean value of permittivity of the layers in contact with the strips. This simple approximation was proven to work well in many cases. In modeling of the capacitances (only) the cross sectional dimensions of the strips width increments shown in Fig. 7.2.2 (a) will be used. Furthermore, for film thickness less than three skin depth (t<3δ) conformal mapping is used to take into account the internal inductance of the strips (Gevorgian et al.1997). Figure 7.2.2 (b) shows the strip geometry used in inductance modeling. 7.2.1.2 Equivalent Resistance and Inductance

For t<3δ limit the equivalent line resistances due to the losses in metal strips may be approximated by (Rautio 2000): r=

1 , sσ mδ s {1 − exp(− t / δ s )}

(7.2.4)

where s is the strip width, σm is conductivity of the strip metal, and δs is skin depth: δs=1/√(πμοσmf). μο is the magnetic constant of vacuum, σm (S/m) is conductivity of the strip.

7.2 Coplanar-Plate Transmission Lines

249

The low frequency dispersion associated with the internal inductance of the strip is evaluated using conformal mapping technique. The analysis is similar to that reported earlier for CPW (Gevorgian et al. 1997). In this analysis the thickness of the strips is assumed to be less than 2–3 skin depths, so that the current distribution across the thickness of the strips is nearly uniform at all frequencies of interest. In other words, this means that the part of the internal inductance due to the penetration of magnetic field from top and bottom surfaces of the strips is not frequency dependent and may be ignored: L=Lg+Lint~(t–2δs)/(s–2δs) ≈ t/(s–2δs). The skin depth is give by δs=1/√(πμοσmf). For s>>2δs the geometrical inductance dominates Lg>>Lin, and L≈ Lg, while for narrow strips and/or low frequencies the skin depth may be comparable with the strip width leading to substantial frequency dependence of total line inductance of CPS. At very low frequencies (practically below microwave region), the total inductance approaches to its DC limit (Klingbeil and Heinrich 1994). Schematically the magnetic field lines in CPS are shown in Fig. 7.2.2 (b), where the penetration depth of magnetic field at the edges of the strips is assumed same as the skin depth δs. The geometric (external) inductance of the CPS is given by the width s of the strips and the spacing between them 2g. A simple conformal mapping procedure may be employed to derive a closed form expression for the total line inductance L=Lg+Ltnt. Instead of separating the Lg and Lint the total line inductance is represented as part of the effective geometrical inductance, i.e. the edges of the strips are moved inwards by skin depth δs as shown in Fig. 7.2.2 (b). For the magnetic field the strips are s’=s–δs wide and the slotwidth is 2g’=2g+2δs. For an air filled CPS a conformal transformation of this geometry leads to the following expression for the lone inductance L=Lg+Ltnt: L = μo

K( k L ) K ( k 'L )

(7.2.5)

with the modulus of the complete elliptic integrals: kL =

g +δs ; k L' = 1 − k L2 s + g −δs

(7.2.6)

7.2.2 Coplanar-Strip Waveguides CPS, like CPW, allows a simple way of shunt and series connection of the microwave components. In these lines, in contrast to microstrips, the desired impedance may be achieved by adequate selection of the strip and gap/slot widths regardless the thickness of the substrate. In comparison with CPW the CPS offers additional design flexibility due to the smaller cross sectional dimensions, especially where the substrate includes high permittivity ferroelectric layers. Symmetric (two strips

250

7 Modeling

are identical) CPS is inherently balanced, i.e. the currents in the strips are opposite and have similar distributions across the strips. Due to the balanced nature, the lines are less sensitive to induced noises and are widely used in low noise amplifiers, oscillators etc. They are especially useful as transmission lines/interconnects for high loss substrates, e.g. silicon. If the cross sectional dimensions are chosen properly these lines provide lower substrate losses since the currents induced in the substrate are partially canceled. 7.2.2.1 CPS on a Finite Thickness and Infinite Thick Substrates

For a CPS based on a single layer substrate (Fig. 7.2.1, assuming h=h1, ε3=ε5=1 and/or h3=0, ε2=ε1 and/or h2=0), the conformal transformations (see Appendix A) result in the following line capacitance: C = ε o ε eff 1

K ( k o' ) , K ( ko )

(7.2.7)

and static impedance: Z=

120π K ( k o )

ε eff 1 K ( k o' )

,

(7.2.8)

where the effective dielectric permittivity is given by:

εeff1=1+(ε–1)q

(7.2.9)

The filling factor and the modulus of the complete elliptic integers are defined as: q=

1 K ( k' ) K ( k o ) 2 K ( k ) K ( k o' )

(7.2.10)

⎛π( g − Δ )⎞ tanh⎜ ⎟ 2h ⎝ ⎠ k= ⎛π( s + g + Δ )⎞ tanh⎜ ⎟ 2h ⎝ ⎠,

ko =

g −Δ ; s+g+Δ

k'= 1− k 2

k 'o = 1 − k o2

(7.2.11) (7.2.12)

The above formulae may be used for calculation of the line parameters of, for example, CPS based on ferroelectric membranes. For a CPS with an infinite thickness substrate, i.e. h=∞ limit, k≈ ko, from (7.2.10) q=1/2 and the effective dielectric permittivity, εeff=(ε+1)/2.

7.2 Coplanar-Plate Transmission Lines

251

7.2.2.2 Multilayer Substrates Including Ferroelectric Films. ε2>ε1 Line Capacitance

The results of the previous section may be easily extended to multilayer substrate CPS with dielectric layers on top and below the strips. The case of the three-layer CPS shown in Fig. 7.2.3 (a) is considered here assuming the top 4 and bottom 5 layers to be infinitely thick, e.g. air or other dielectrics. The main condition is that the permittivity of the layers decrease going away from the strips: ε2>ε1> ε4 and ε3>ε5 (Fig. 7.2.3 (b)) so that the field components are predominantly parallel to the dielectric/dielectric interfaces, and all dielectric/dielectric interfaces may be approximated as magnetic walls looking from the strips. The total line capacitance of this CPS is the sum of partial capacitances due to the different layers connected in parallel: C=Ca+C1+C2+C3, where Ca is the capacitance of the CPS in the absence of dielectric layers, and C1, C2, are the partial capacitances of the layers shown in Fig. 7.2.3 (a). Each of these partial capacitances is found using the procedure given in Appendix A: C1 =

K ( k 1' ) 1 ε o ( ε1 − ε 4 ) , 2 K ( k1 )

(7.2.13)

C2 =

K ( k '2 ) 1 ε o ( ε 2 − ε1 ) , 2 K( k2 )

(7.2.14)

C3 =

K ( k 3' ) 1 εo(ε3 − ε5 ) , 2 K( k3 )

(7.2.15)

Ca = ε o

K (k o' ) , K (k o )

(7.2.16)

where (ε1–ε4), (ε2–ε1), and (ε3–ε5) are the equivalent permittivity of the layers (Gevorgian et al. 2003). The dielectric permittivity of the spaces below and above, ε4 and ε5 (Fig. 7.2.3 (a)) are assumed to satisfy the conditions ε4<ε1 and ε5<ε3. In a particular case, one of them or both these spaces may be air filled: ε4 = 1 and/or ε5 = 1. By taking the sum of these capacitances and the capacitance (7.2.13) to (7.2.16) one arrives at the following expression for the line capacitance of a CPS on a three layer substrate: C = ε o ε eff 3

K ( k o' ) K ( ko )

εeff3=1+(ε1–ε4)q1+(ε2–ε1)q2+(ε3–ε5))q3,

(7.2.17) (7.2.18)

252

7 Modeling

s

s

2g

ε2,

Ex Ey

ε1 ,σ1

E

ε2,> ε1 or/and σ2 > σ1

(a) ε5=ε4=1

y

σ=εοεωtanδ

y

(ε3-1)

h3

0

1

ε2

ε1

σ3 0

σ1

σ σ2

h1

h2

ε

ε3

(σ2-σ1)

(ε2-ε1)

(ε1-1)

(b)

(c)

Fig. 7.2.3 Schematics of the electric field lines for (a) permittivity (b) and conductivity (c) distribution in the layers. ε2>ε1, σ2>>σ1. Reprinted with permision from IEEE©2003

The filling factors, qi, and the modulus of the elliptic integrals, ki, are given as: qi =

1 K (ki' ) K (ko ) ; i=1,2,3 2 K (ki ) K (ko' )

⎛ π ( g − Δ) ⎞ ⎟ tanh⎜⎜ 2hi ⎟⎠ ⎝ ki = ; k i' = 1 − k i2 ;i=1,2,3 ⎛ π ( s + g + Δ) ⎞ ⎟ tanh⎜⎜ ⎟ 2hi ⎝ ⎠

(7.2.19)

(7.2.20)

The static impedance of this three-layer substrate CPS is: Z=

120π K ( k o )

ε eff 3 K ( k o' )

(7.2.21)

7.2 Coplanar-Plate Transmission Lines

253

Shunt Conductance

Besides the dielectric losses, characterized by a loss tangent, tanδε=εε''/ εε', there could be extra losses associated with the conductivity, as in the case of semiconductor layers. Formally, these losses may be represented by an equivalent loss tangent, tanδσ=(εσ''/εσ')=σ/εοε'ω, where σ is the electrical conductivity of a substrate layer and ε is its dielectric permittivity. It is suggested that the overall line losses are small and the quasi-TEM approximation is applicable. The partial conductance formality and the conformal mapping technique are employed to evaluate the shunt conductance of the CPS. In this procedure the loss tangent of the dielectric layers, formally, are represented via an equivalent conductivity: σ=εοεωtanδ. A schematic distribution of conductivity is shown in Fig. 7.2.3 (c). The conformal transformations required for evaluation of the partial conductivities due to different layers are the same (Appendix A) as in the case of partial capacitances described above. Following the same procedure one arrives at: 1 K (k1' ) ε1 2 K (k1 )

(7.2.22)

G2 =

K (k 2' ) 1 (σ 2 − σ 1 ) 2 K (k 2 )

(7.2.23)

G3 =

K (k 3' ) 1 (σ 3 − σ 5 ) 2 K (k 3 )

(7.2.24)

G1 =

The total line conductance is then the sum of all partial conductancies: G=

K (k 3' ) ⎤ K (k 2' ) 1 ⎡ K (k1' ) + (σ 2 − σ 1 ) + (σ 3 − σ 5 ) ⎢σ 1 ⎥ K (k 2 ) K (k 3 ) ⎦⎥ 2 ⎣⎢ K (k1 )

(7.2.25)

σ4=σ5=0 is assumed (i.e. air for the layers 4 and 5) in this expression. In terms of loss tangents: ⎡ K (k1' ) K (k 2' ) ⎤ + (ε 2 tan δ 2 − ε 1 tan δ 1 ) ⎢ε 1 tan δ 1 ⎥ K ( k1 ) K (k 2 ) ⎥ ωε o ⎢ G= ⎥ ' 2 ⎢ ⎢+ (ε 3 tan δ 3 − ε 5 tan δ 5 ) K (k 3 ) ⎥ ⎢⎣ ⎥⎦ K (k 3 )

(7.2.26)

254

7 Modeling

The Complex Line Impedance and Propagation Constant

Using the equivalent capacitance C (7.2.17), inductance L (7.2.5), shunt conductance G (7.2.26), are and resistance r (7.2.4) the complex impedance and propagation constant are easily obtained from (7.2.1) and (7.2.2). Using these results one may easily distinguish between the line losses associated with the strips and losses associated with the static conductivity of the semiconductor substrate. For rather small losses the total loss of the line may be approximated as α=r/(2Z)+GZ/2= αc+αd. The dielectric losses, using (7.2.26), take a simple form:

αd =

30πωε o ⎡ε 1 q1 tan δ 1 + (ε 2 tan δ 2 − ε 1 tan δ 1 )q 2 ⎤ ⎢ ⎥ ε 3eff ⎣+ (ε 3 tan δ 3 − ε 5 tan δ 5 )q 3 ⎦

(7.2.27)

with ε3eff and filling factors qi defined above. The model of CPS with ε2>ε1 work well for a wide range of ε2, starting withε2=ε1. However, one may expect higher order modes for extremely largeε2 and wide slotwidths 2g. Interestingly, the losses decrease with increasing ε2, which is explained by the fact that the field is “pulled out” from the lossy substrate into the high permittivity layer 2, where the losses are smaller (Gevorgian et al. 2003). For the same reason the imaginary part of the impedance, which is inductive due to the high losses in the substrate, decrease with increasing ε2. For smaller ε2 the impedance is rather high, which is typical for CPS, since CPS is an inherently high impedance line. At given line geometry a high permittivity layer helps to keep impedance smaller. The dispersion in line parameters at low frequencies is associated with the internal inductance of the strips while the dispersion at high frequency is due to substrate leaky waves (Gevorgian et al. 2003). For a CPS withε3, ε2>ε1 the phase velocity of the fundamental and leaky waves are quite different and the coupling into the leaky waves is substantially reduced. A more efficient way to reduce the effects of leaky waves is to use high permittivity layers on top of strips (ε3>ε1). This reduces the coupling into the leaky waves, and at the same time, the losses associated with the substrate and parasitic couplings between circuit components. 7.2.2.3 CPS with a Backside Ground Plane (Coupled Microstrip Lines)

The even and odd mode capacitances (Ce and Cod) of the coupled microstrip lines (Fig. 7.2.4) are obtained using conformal mapping (Appendix B): C e = ε o (ε 2 − 1)

K (k e' ) K (k e )

,

(7.2.28)

7.2 Coplanar-Plate Transmission Lines

s

2g

255

s

ε2,σ2 Ce

Cod

Fig. 7.2.4 CPS with backside ground plane (coupled microstrip lines). Reprinted with permision from IEEE©2003

with ⎛π( g − Δ )⎞ ⎟ cosh⎜ ⎜ 2h2ef ⎟ ⎝ ⎠ ; ke = ⎡ π (s + g + Δ ) ⎤ cosh ⎢ ⎥ ⎣⎢ 2 h2ef ⎦⎥

k e' = 1 − k e2

(7.2.29)

The odd mode capacitance Cod of a coupled microstrip line (see Appendix B) is: Cod = ε o (ε 2 − 1)

K (k od' )

(7.2.30)

K (k od )

where ⎡π ( g − Δ ) ⎤ sinh ⎢ ⎥ ⎢⎣ 2 h2ef ⎥⎦ ; k od = ⎡ π (s + g + Δ ) ⎤ sinh ⎢ ⎥ ⎣⎢ 2h2 ef ⎦⎥

' k od = 1 − k e2

(7.2.31)

7.2.2.4 Multilayer Substrates Including Ferroelectric Layers: Case ε2<ε1, Fig. 7.2.5

Partial Capacitances

Derivation of the close form analytic formulae, for the cases where the adjacent to the strips layers have dielectric permittivity lower then the substrate itself, is a little bit more complicated. In a substrate consisting of three dielectric layers, so that ε2<ε1 (Fig. 7.2.5 (b)) the electric field component in layer 2 normal to the interface is larger than the component parallel to the interface (Fig. 7.2.5 (a)). The dielectric/dielectric interface cannot be modeled as a magnetic wall. Instead, the interface behaves more like an imperfect electric wall. A ferroelectric film deposited on SiO2/Si substrates is a typical example for this case.

256

7 Modeling

The partial capacitance of the dielectric layer 2 may be decomposed into two components, as it is shown in Fig. 7.2.6 (a). C21 represents the field lines normal to the interface. The component C22 represents the field lines parallel to the interfaces which take care of the energy in the layer 2. Shown in Fig. 7.2.6 (c) is the equivalent circuit of the shunt admittance Y=G+jB of the line in terms of partial capacitances and conductance. For computation of the partial capacitance C11 associated with the substrate layer 1 “image strips” as shown in Fig. 7.2.6 (a) and Fig. 7.2.6 (b) are assumed. s

s

2g

ε2,σ2

Ex

ε1 ,σ1 Ey

E

ε2< ε1 or/and σ2 <<σ1

(a)

ε5=ε4=1

y

y

h3

(ε3-1)

ε2

ε1

0

σ1

σ

σ2

h1

h2

0 1

σ3

ε

ε3

(ε2-ε1)

(ε1-1)

(b)

σ=ωεοεtanδ

(c)

Fig. 7.2.5 Cross section of a CPS with ε2<ε1 and/or σ2<σ1 (a), dielectric permittivity (b) and conductivity (b) distributions. Note that (ε2–ε1) and (σ2–σ1) are negative. Reprinted with permision from IEEE©2003

For CPS with 2g>>h2, and ε2<ε1, the electric field lines in layer 2, under the strips, are predominantly normal to the interfaces of the layers 1 and 2 and the strips are “projected” on the interface, as shown in Fig. 7.2.6 (b). The numerical analysis shows that using an effective layer thickness, h2ef=h2(1– ε2/ ε1), helps to reduce the errors associated with the imperfect electric wall approximation at the interface. The relationship h2ef=h2(1– ε2/ε1) is valid for ε2≤ε1 and takes into account energy redistribution between the substrate and layer 2.

7.2 Coplanar-Plate Transmission Lines

257 ε4=ε5=1

jy

(a)

C3 s

g C22

C21

C22

(ε2–1)

x h2

C21

(ε3–1)

s

g

h

(ε1–1) “Image stripe”

C11 Electric wall for C21 Magnetic wall for C22

Electric wall for C22 Magnetic wall for C21

s

s

2g

(b) ε2,σ2

“Image strips”

ε1 ,σ1

ε2< ε1 or/and σ2 <<σ1 Ca

(c)

C3 G3 0.5C22

G21

0.5G22 G21

C21

C21

C11 G11

Fig. 7.2.6 CPS with ε2<ε1. Identification of the equivalent capacitances (a) and image strips (b), and its equivalent circuit (c). Reprinted with permision from IEEE©2003

The capacitance Ca is available readily (7.2.16). The partial capacitance C21 is identical with even mode capacitance of a coupled microstrip line Ce, i.e. C21=Ce. (7.2.28), while the capacitance C22 is: ⎡ K ( k' ) K( k' ) ⎤ od e ⎥ C 22 = C od − Ce = ε o ( ε 2 − 1 )⎢ − ⎢ K ( k od ) K ( k e ) ⎥ ⎣ ⎦

(7.2.32)

258

7 Modeling

The capacitance C11 is obtained the same way as the capacitance of a single layer substrate, Appendix A: C11 = ε o ( ε 1 − 1 )

' ) 1 K ( k 11 2 K ( k 11 )

(7.2.33)

The module is computed for image strips setting the substrate thickness h11=h1–h2ef:

k11

⎛π( g − Δ )⎞ ⎟ tanh⎜⎜ 2h11 ⎟⎠ ⎝ ; = ⎛π( s + g + Δ )⎞ ⎟⎟ tanh⎜⎜ 2h11 ⎝ ⎠

2 k '11 = 1 − k11 ;

(7.2.34)

The partial capacitance of layer 3, C3, is given by (7.2.15) Partial Conductances

Partial conductances shown in Fig. 7.2.6 (c) are found from (7.2.28), (7.2.32), (7.2.33) and (7.2.15) where the permittivities are replaced by corresponding specific conductances: G21 = σ 2

K (k e' ) K (k e )

⎡ K (k ' ) K (k ' ) ⎤ od e ⎥ − G22 = σ 2 ⎢ ⎢⎣ K (k od ) K (k e ) ⎥⎦ G11 =

G3 =

' ) σ 1 K ( k11

2 K ( k11 )

σ 3 K (k 3' ) 2 K (k 3 )

(7.2.35)

(7.2.36)

(7.2.37)

(7.2.38)

The line shunt admittance of the CPS Y=G+jB (Fig. 7.2.1 (c)) is found from the equivalent circuit Fig. 7.2.6 (c) by using partial capacitances and partial conductances considered in this subsection. This admittance together with readily available resistance r and inductance L of the strips is used to calculate the complex impedance (1) and propagation (2) constant of the line.

7.2 Coplanar-Plate Transmission Lines

259

The model of CPS with ε2<ε1 works well for smaller ε2, such as SiO2 or polymer films between the strips and silicon substrate. However its accuracy degrades slightly at ε2=ε1 limit. The relationship h2ef=h2(1– ε2/ε1) is valid for ε2≤ε1 and (h2<2g), and rather correctly characterizes the correction in the balance of the energy conserved in the substrate and layer 2. The model gives a rather correct results in ε2< 0.8ε1 limit. The accuracy may be slightly increased in ε2=ε1 limit if the asymptotic approximation ke=kodd=exp(–πg/2h2eff) is used in computations. At this limit, the partial inductance method (Berg and Gevorgian 2002) seems to be a better approximation for line parameter computation. As in the case with ε2>ε1 the dispersion at low frequencies is associated with the internal inductance of the strips, which is rather large for stripwidths comparable with the skin depth. The models of CPS (line inductance) given above are rather accurate for stripwidths s>6δs, where δs is the skin depth in the strip. The thickness of the strips is supposed to be smaller than δs. The dispersion at high frequency is due to substrate leaky waves. For the lines with ε2<ε1 the leaky substrates waves cause substantial frequency dependences at lower frequencies. In contrast to CPS with ε2>ε1, in this case the field tends to be confined more in the high permittivity substrate, enhancing conditions for the slab (substrate) mode propagation. One way to reduce the effects of the substrate leaky waves is to use substrates with smaller thickness. The cut-off frequency of lowest TE mode may be estimated using fTE=co/(4h1√ε1−1). A more efficient way to reduce the effects of leaky waves is to use high permittivity layers on top of the strips (ε3>ε1). This will reduce the coupling into the leaky waves, and at the same time, the losses associated with the substrate and parasitic couplings between circuit components. Two more dispersion mechanisms need to be taken into account where semiconductor substrates (layers) are used. Maxwell (dielectric) relaxation frequency, fM=σ1/(2πεoε1) sets the frequency below which the conduction currents dominate over the displacements currents. In the substrates, including dielectric and semiconductor layers, the interfacial relaxation (Maxwell-Wagner) cause substantial dispersion and losses at very low frequencies. The frequency of Maxwell-Wagner relaxation may be estimated using a simple relationship: fMW=(1/2π)·(2G11+G21)/(C21+2C11). The peak at frequency fr=( f2M + f2 MW)1/2 in the imaginary part of the impedance is result of Maxwell and MaxwellWagner relaxations.

7.2.3 Coplanar Waveguides Coplanar waveguides are the most considered in the literature coplanar-plate structures dealt with conformal mapping (see Gevorgian et al. (1995) and references therein). In this section a CPW with a ferroelectric superstrate is considered (Fig. 7.2.1 (b)) where ε3=1 is assumed. The ferroelectric layer with the thickness h2 and permittivity ε2>ε1 is sandwiched between the coplanar strips and the sub-

260

7 Modeling

strate. The equivalent circuit of the CPW in TEM approximation is shown in Fig. 7.2.1 (c)). For a CPW the parameters of this equivalent circuit may be modeled in a similar (not identical) manner as it was done for CPS. In a simple case, for a CPW without taking into account the thickness of the metal and frequency dependence, the line capacitance and impedance are: C = 4ε o ε e

Z=

K (k o )

(7.2.39)

K (k o' )

30π K ( k o' )

(7.2.40)

ε e K (k o )

where the effective permittivity and filling factors are given by

ε e = 1 + (ε 1 − 1)q1 + (ε 2 − ε 1 )q 2

(7.2.41)

and qi =

1 K (k i' ) K (k o' ) ; 2 K (k i ) K (k o )

i = 1,2

(7.2.42)

The modules of the elliptic integrals:

ko =

s ; k o' = 1 − k o2 , i = 1,2 ; s+g

⎛ πs ⎞ ⎟ sinh ⎜⎜ 2hi ⎟⎠ ⎝ ; k i' = 1 − k i2 , i = 1,2 ; ki = ⎛ π (s + g ) ⎞ ⎟ sinh ⎜⎜ ⎟ ⎝ 2hi ⎠

(7.2.43)

(7.2.44)

7.3 Multilayer Substrate Coplanar-Plate Capacitors 7.3.1 Coplanar Plate Capacitors with the Straight Gap (Slot) 7.3.1.1 Physical Model

In this section closed form analytic approximations are given for the capacitance and Q-factor of coplanar plate capacitors sandwiched between dielectric layers (Fig. 7.3.1). Analytic approximations for the coplanar-plate capacitors on two

7.3 Multilayer Substrate Coplanar-Plate Capacitors

261

layer substrates proposed in (Vendik et al. 1999) are useful only for large aspect ratios, i.e. W/g (=(gap length)/(gapwidth)) since they do not take into account the fringing fields at the ends of the gap.

Fig. 7.3.1 Multilayer substrate coplanar-plate capacitor. Reprinted with permision from IEEE©2003

The electric field about the plates has large fringing components and the application of the conformal mapping may be in question, since, in general, it is applicable to planar fields. However, exploitation of the symmetry results in rather correct closed form approximations, as it has been shown in the past for a gap in the signal strip of a coplanar waveguide (Deleniv et al. 2000) and an open end in a coplanar strip waveguide (Gevorgian et al. 2001).

z

x

(a)

(b)

x

y

Fig. 7.3.2 Schematics of the electric field lines in the planes of magnetic walls

The formulas take into account the entire fringing field (Fig. 7.3.2) about the patches. The main condition used is that the dielectric permittivity (and losses) of the layers decrease going away from the metal strips, as shown in Fig. 7.2.3. This condition is associated with the magnetic wall approximation at dielectric/dielectric interfaces used for the evaluation of partial capacitances and conductances.

262

7 Modeling

7.3.1.2 Single Layer Substrate Capacitor

In the case of a single layer substrate the capacitance is given as (see Appendix C): C = 2ε e1ε o

K (k a ' ) AK (k o' ) K (k a )

(7.3.1)

where ko and ka are: ko =

ka =

g ; s+g

ko ' = 1 − ko 2

(7.3.2)

1 ⎛π W ⎞ ⎟⎟ cosh⎜⎜ ⎝ 2 AK (k o ) ⎠

ka ' = 1 − ka 2

(7.3.3)

The integration constant is set to be A=g, i.e. half the gap between the coplanar plates. The effective dielectric permittivity is:

ε e1 = 1 + (ε 1 − 1)q1

(7.3.4)

with a filling factor: q1 =

k11 =

' 1 K (k11 ) K (ka ) K (k1' ) 2 K (k11 ) K (ka' ) K (ko ' )

1 ⎛π W ⎞ ⎟⎟ cosh⎜⎜ ⎝ 2 AK (k1 ) ⎠

;

⎛ πg ⎞ ⎟ tanh⎜⎜ 2h1 ⎟⎠ ⎝ k1 = ; ⎡ π (s + g ) ⎤ tanh ⎢ ⎥ ⎣ 2h1 ⎦

(7.3.5)

k11' = 1 − (k11 )2

(7.3.6)

k1' = 1 − k12

(7.3.7)

7.3 Multilayer Substrate Coplanar-Plate Capacitors

263

7.3.1.3 Three Layer Substrate Capacitor

Capacitance

The results obtained above may be extended to a more general case. As an example capacitors having three and two dielectric layers are considered, so that ε2>ε1, ε4=ε5=1, and the thickness of the layers 1, 2 and 3 (h1, h2, h3) are finite (Fig. 7.3.1 and Fig. 7.2.3 (a)). Once more, the condition ε2>ε1 is imposed due to the magnetic wall approximation enabling evaluation of the partial capacitances. The capacitance of this structure is represented as a sum of partial capacitances of all layers, see Appendix C, C = 2ε e3ε o

K (ka ' ) AK (ko' ) K (k a )

(7.3.8)

with effective dielectric constant

ε e3 = 1 + (ε1 − 1)q1 + (ε 2 − ε1 )q2 + (ε 3 − 1)q3

(7.3.9)

and filling factors qi =

1 K (kii' ) K (ka ) K (ki' ) ; 2 K (kii ) K (ka' ) K (ko ' )

i = 1,2,3

(7.3.10)

where ko, ka, k1 and k11 are given in the previous section, while the other modules of the complete elliptic integrals of the first kind are defined as: k 22 =

1 ⎛π W ⎞ ⎟⎟ cosh⎜⎜ ⎝ 2 AK (k 2 ) ⎠

k 22 ' = 1 − k 22 2

;

(7.3.11)

with ⎛ πg ⎞ ⎟ tanh⎜⎜ 2h2 ⎟⎠ ⎝ k2 = ; ⎡ π (s + g ) ⎤ tanh ⎢ ⎥ ⎣ 2h2 ⎦ k33 =

1 ⎛π W ⎞ ⎟⎟ cosh⎜⎜ ⎝ 2 AK (k3 ) ⎠

k2 ' = 1 − k22

(7.3.12) ;

k33' = 1 − k33 2

(7.3.13)

264

7 Modeling

with ⎛ πg ⎞ ⎟ tanh⎜⎜ 2h3 ⎟⎠ ⎝ k3 = ; ⎡ π (s + g ) ⎤ tanh ⎢ ⎥ ⎣ 2h3 ⎦

k3' = 1 − k32

(7.3.14)

As first approximation one may assume A=g. To increase the accuracy, A has to be regarded as a fitting parameter to be adjusted to fit the calculated by (7.3.8) capacitance with the measured or numerically evaluated capacitance. The difference in (7.3.1) and (7.3.8) is only in the effective dielectric permittivity. For ε2=ε1 and ε3=1 one has εe3=εe1 and the capacitances (7.3.1) and (7.3.8) are identical. The capacitances of the two layer capacitors are also easily deducible from (7.3.9)– (7.3.10): • In the case ε3=1 one has a capacitor with plates on top of two layer substrate; • In the case ε2=ε1 or ε1=1 the plates of the capacitor are sandwiched between layers 3 and 1 or 2. Dielectric Losses

In this model perfect conducting plates with no Ohmic losses are assumed and only the dielectric losses are taken into account. The dielectric losses are associated with the dielectric layers (partial capacitors) discussed above. These losses are taken into account via partial conductances Gi. The partial conductances are evaluated the same way as the partial capacitances, see Appendix C. The resulting total conductance is: ' ' ⎤ ⎡ K (k11 ) K (k 22 ) G = σ 1 A⎢ K (k1' ) − K (k 2' )⎥ + K (k 22 ) ⎦⎥ ⎣⎢ K (k11 ) ' ' K (k 33 ) K (k 22 ) σ2 AK (k 2' ) + σ 3 AK (k 3' ) K (k 22 ) K (k 33 )

(7.3.15)

In (7.3.15) the conductivity of the layer 1 is assumed to be larger than the conductivity of the layer 2, σ1>σ2, as in Fig. 7.2.3 (c). Formally the loss tangent and conductivity of a dielectric (semiconductor) layer are related as σi=εοεωtanδi, i=1, 2, 3. Using (7.3.8) and (7.3.15) one can compute the effective loss tangent and/or the Q-factor of the capacitor at a given frequency, ω=2πf: tan δ e =

G 1 = Q ωC

(7.3.16)

7.3 Multilayer Substrate Coplanar-Plate Capacitors

265

Inverse Problem: Computations of the Dielectric Permittivity and Loss From Known Capacitance Values

For a measured capacitance C and Q-factor the dielectric permittivity and loss tangent of any of the layers are determined from (7.3.9), (7.3.15), and (7.3.16). For example, assuming the thickness of the layer 2 and parameters of all other layers known, the measured capacitance may be used to compute εe3 from (7.3.8), and the dielectric permittivity of the layer 2 from (7.3.9):

ε 2 = ε1 +

ε e3 − 1 − (ε1 − 1)q1 − (ε 3 − 1)q3 q2

(7.3.17)

⎡ K (k 22 ) ⎤ C ⎥ tan δ e + tan δ 2 = ⎢ ' ⎢⎣ ε o ε 2 AK (k 2 ) K (k '22 ) ⎥⎦ ' ' ⎤ σ1 [1 − K (k11 ) K (k 22' ) K (k1' ) ⎥ ωε o ε 2 K (k11 ) K (k ) K (k ) ⎥ 22 2 ⎦

−

(7.3.18)

' σ 3 K (k 33 ) K (k 22 ) K (k 3' ) 1 ωε o ε 2 K (k 33 ) K (k 22 ) K (k 2' )

Again, the loss tangents may be replaced the conductance of the substrate layers, σi=εοεωtanδi, i=1, 2, 3, where the substrate consists of ordinary dielectrics instead of semiconductors. The conformal mapping based model given above, and the formulas, are useful for frequencies, where the sizes of the plates, the gap between them and the thicknesses of the dielectric layers are much smaller than the wavelength of the microwave signal. As a first approximation the wavelength may be estimated using λc=λo/√εeff, where λo is the wavelength in free space, and the effective permittivity is given by (7.3.9).

7.3.2 Interdigital (IDC) Coplanar-Plate Capacitors In this section the model of the interdigital capacitor on a multilayer substrate (Fig. 7.3.3) reported in (Gevorgian et al. 1996) is given in a simplified form, without taking into account the fringing capacitance associated with the ends of the strips. For a three finger (n=3) IDC C3 = 4ε e3ε o

K (k o' 3 ) K (k o3 )

(7.3.19)

266

7 Modeling

(a) gend

(b)

ε3

2g

2s

l

h3

2g

h1

2s

h2

ε2 ε1

Fig. 7.3.3 Layout (a) and cross section (b) of an interdigital capacitor

where the with effective dielectric permittivity

ε e3 = 1 + (ε 1 − 1)q13 + (ε 2 − ε 1 )q 23 + (ε 3 − 1)q33

(7.3.20)

and the filling factors are: qi 3 =

1 K (k i 3 ) K (k o' 3 ) ; 2 K (k i'3 ) K (k o3 ' )

i = 1,2

(7.3.21)

ko, ka, k1 and k11 are given in the previous section, while the other modules of the complete elliptic integrals of the first kind are defined as:

k o3 =

k i3

⎛ πs ⎞ sinh ⎜ ⎟ 2hi ⎠ ⎝ = ⎛ π (s + 2g ) ⎞ ⎟ sinh ⎜⎜ ⎟ ⎝ 2hi ⎠

i=1, 2.

s s + 2g

⎤ 1 − ⎡(s + 2 g ) (3s + 2 g )⎥⎦ ⎢⎣ ⎤ 1− ⎡ s ⎢⎣ (3s + 2 g )⎥⎦

2

2

(7.3.22)

⎡ ⎤ 2 ⎛ π (s + 2 g ) ⎞ ⎟ ⎢sinh ⎜⎜ ⎥ ⎟ ⎝ 2hi ⎠ ⎥ 1− ⎢ ⎢ 2 ⎛ π (3s + 2 g ) ⎞⎥ ⎟⎥ sinh ⎜⎜ ⎢ ⎟ 2hi ⎢⎣ ⎝ ⎠⎥⎦ ⎡ ⎤ 2 ⎛ πs ⎞ ⎟ ⎢sinh ⎜⎜ ⎥ ⎟ ⎝ 2hi ⎠ ⎥ 1− ⎢ ⎢ 2 ⎛ π (3s + 2 g ) ⎞⎥ ⎟⎥ sinh ⎜⎜ ⎢ ⎟ 2hi ⎢⎣ (7.3.23) ⎝ ⎠⎥⎦

7.4 Parallel-Plate Capacitor

267

For an IDC with three and more fingers, n ≥ 3: ⎡ K (k o' 3 ) ⎤ K (k o ) ⎥ + 4 C n = ε o l ⎢(n − 3)ε en ε e3 K (k o3 ) ⎥ K (k o' ) ⎢⎣ ⎦

(7.3.24)

the effective dielectric permittivity εen is given by:

ε en = 1 + (ε 1 − 1)q1n + (ε 2 − ε 1 )q2 n + (ε 3 − 1)q3n

(7.3.25)

and the filling factors qin =

1 K (k in ) K (k o' ) ; 2 K (k in' ) K (k o ' )

i = 1,2,3

(7.3.26)

The modules the complete elliptic integrals of the first kind are defined as: ko =

k in

⎛ πs ⎞ sinh ⎜ ⎟ ⎝ 2hi ⎠ = ⎛ π (s + g ) ⎞ ⎟ sinh ⎜⎜ ⎟ ⎝ 2hi ⎠

s s+g

(7.3.27)

⎛ π (s + g ) ⎞ ⎛ π (s + g ) ⎞ ⎟ + sinh 2 ⎜ ⎟ cosh 2 ⎜⎜ ⎟ ⎜ 2h ⎟ h 2 i i ⎝ ⎠ ⎝ ⎠ ⎛ ⎞ ⎛ ⎞ πs) π (s + g ) ⎟ + sinh 2 ⎜ ⎟ cosh 2 ⎜⎜ ⎟ ⎜ 2h ⎟ h 2 i (7.3.28) ⎝ i⎠ ⎝ ⎠

' With k in = 1 − k in2 . In the case s/hi>>1:

⎛ πg k in = 2 exp⎜⎜ ⎝ 2hi

⎞ ⎟ ⎟ ⎠

(7.3.29)

It is assumed that h1≥h2, and the accuracy of the above formulas for l>>gend limit is within 10%. In the case the finger length, l, is comparable with the finger end gapwidth, gend, the end capacitance has to be taken into account for a higher accuracy.

7.4 Parallel-Plate Capacitor The model of the parallel-plate varactor is considered in Chap. 4, where the losses in the ferroelectric film are treated in detail. In this section the model of the losses

268

7 Modeling

in the plates of a parallel-plate capacitor are considered (Deleniv and Gevorgian (2008). The model is given for the core of the capacitor (Fig. 7.4.1 (a)) delimited by two reference planes. The sizes of the plates are given by the width w and the length l . For the purpose of modeling, the core of the capacitor is represented as a section of a TEM waveguide (Fig. 7.4.1 (b)) with the equivalent circuit shown in Fig. 7.4.2 (a) which is defined as a two port network with the terminals 1–4. Due to the symmetry of the structure, the equivalent circuit may be represented with the one shown in Fig. 7.4.2 (b). Except for the equivalent resistance of the electrodes rm all the elements of the equivalent circuit can be defined using the known (Matthaei et al. 1980) identities: B = Y sin(θ ) ≈ ω

ε 0 ε r wl d

(7.4.1)

lμ d X = Z tan θ ≈ ω 0 , 2 2w 2

( )

(7.4.2)

G eq = B ⋅ tan δ ε

(7.4.3)

where Z ( Y ) and θ = kl ε r are the real part of characteristic impedance and the electric length of the WG section respectively, while tan δ ε is the loss tangent of the dielectric (ferroelectric film).

Fig. 7.4.1 The structure of an integrated parallel-plate capacitor (a) and its core used in modeling. (b). Reprinted with permision from Wiley©2008

7.4 Parallel-Plate Capacitor

269

The plate inductance is typically very small ( ωL << (ωC )−1 ) and in most cases may be neglected. The loss tangent of the capacitor comprises of two contributors ( tan δ ε and tan δ σ ) with the latter representing the electrode loss. The dielectric losses in ferroelectrics are considered in Chap. 2. Here only tan δ σ is considered. Assuming an ideal dielectric ( tan δ ε = 0 ), the equivalent loss tangent of the capacitor, tan δ σ , is only due to conductive losses: (a)

(b)

ωL rm

ωC

Fig. 7.4.2 Equivalent lumped element network of a section of the TEM WG (a), and the equivalent circuit of the varactor core (b). Reprinted with permision from Wiley©2008

( )

~ tan δ σ = ωCrm = − Re Z in

( )

~ Im Z in

~ ~ Z in = Z coth(γ~l )

(7.4.4) (7.4.5)

~ where Z in is the complex input impedance of the open circuited TEM waveguide with the length l and the complex propagation constant γ~ . Using small argument approximation in (7.4.4), the following expression for tan δ σ is obtained: tan δ σ =

θ 2 Rs1 + Rs2 , 3d ωμ 0

(7.4.6)

d is the thickness of the ferroelectric film (Fig. 7.4.1 (b)) and Rsi =

1

σ iδ i

,

i=1,2

(7.4.6)

270

7 Modeling

In (7.4.6), Rs1 and Rs2 are the surface resistances of the top and the bottom plates, while σ i and δ i hold respectively for their conductance and bulk skin depth. Using (7.4.4) and (7.4.6), the equivalent resistance of the electrodes is defined as rm =

tan δ σ l ⎛ 1 1 ⎜ = + ωC 3w ⎜⎝ σ 1δ 1 σ 2δ 2

⎞ ⎟⎟ ⎠

(7.4.7)

The formula (7.4.7) is valid only for thick electrodes with t1 and t 2 thicker than three skin depths. In practice, however, one often deals with electrically thin plates. The utility of (7.4.7) is extended by replacing the skin depth of the bulk material ( δ 1(2 ) ) by an equivalent thickness dependent skin depth δ (t ) . The latter is considered in (Eo and Eisenstadt 1993) where the following two assumptions are made: i) the current is crowded on one conductor surface; ii) away from the conductor surface the current decays exponentially. The result is: ⎛ ⎝

δ (t ) = δ ⎜ 1 − e

−t

δ

⎞ ⎟. ⎠

(7.4.8)

(7.4.7) in combination with (7.4.8) is identical to that derived by (Xiong and Fusko 2002). The alternative approach for the equivalent skin depth reported in (Deleniv and Gevorgian 2008) utilizes the following identity: Rs = Re(Z~s (t )) =

1

σδ (t )

(7.4.9)

with

( )

~ ~ Z~s (t ) = Z Cond . coth k t

(7.4.10)

~ ~ In (7.4.9) and (7.4.10) Z Cond . and k are respectively the wave impedance and the wave-number in the conductor. It is noted that Z~ s (t ) holds for the surface impedance of thin conductor sheet with one side terminated by a magnetic wall. This allows accounting for the field interference between two electrode surfaces. Using (7.4.9), the equivalent skin-depth δ (t ) is represented as: δ (t ) = 2δ

( δ )2 − cos( t δ )2 sinh (2t ) + sin(2t ) δ δ

cosh t

(7.4.11)

where δ is the bulk skin depth (δ1 or δ2). Figure 7.4.3 compares the Q-factor for

the capacitor, Q = (tan δ σ )−1 , with the rigorous Sonnet simulations.

7.5 Conclusions

271

900 Electrodes Q-factor

800

F=20GHz

700 600 500 400 300 200

Model Xiong & Fusco Sonnet

100

0 0.5 1 1.5 2 2.5 3 Normalized electrode thickness t/δ

Fig. 7.4.3 Thickness dependent Q-factor of the electrodes.

w = 5 μm , l = 10 μm ,

t1 = t 2 = 0.58μm , ε r = 280

The discussed approach (Deleniv and Gevorgian 2008) produces distinctly different from (Eo and Eisenstadt 1993) results for the electrodes with the thickness in the range δ ≤ t ≤ 2δ . The Q-factor of the capacitor has a maximum recaptured in Sonnet simulation and also by equivalent skin depth formula (7.4.11) which is not observed in the case of (7.4.7). Clearly, the Q-factor maximum is due to interference of the current inside the electrically thin electrode, which can not be predicted using a monotonic, exponential decay of the current away from the conductor surface. It is, therefore, expected that the equivalent skin-depth formula (7.4.11) produces more accurate results.

7.5 Conclusions The conformal mapping technique based on closed form analytic models for the devices with coplanar plate electrodes considered in this chapter are rather correct for the cases where no DC control field is applied to the ferroelectric layers. These models are especially useful if dielectric layers with extremely high permittivities (e.g. ferroelectrics with ε>100) are involved, where the simulation accuracy for some of commercial software (i.e. Momentum) is not guaranteed. They may be used for the analysis, design and optimization of the devices based on multilayer lossy dielectric (semiconductor) substrate incorporating ferroelectric layers. They may be, and have been, used extensively for the extraction of the effective dielectric permittivity of the ferroelectric layers using measured capacitances (impedances). Even though the analytic models are derived for the uniform distribution of the permittivity in the ferroelectric layers they have been widely used for the measurement of the DC bias dependent effective dielectric

272

7 Modeling

permittivity and loss tangent of the ferroelectric layers. One has to keep in mind that the measured in this way permittivity and loss tangent and their DC field dependences are heavily affected by the non uniform distribution of the electric field, permittivity and loss tangent. In this sense the measured permittivity and loss tangent are some averaged, effective parameters and their DC bias dependences are not identical with the DC dependences of the bulk counterparts. While using the conformal mapping based models it is instructive to check carefully the accuracy of the calculations of the involved complete elliptic integrals of the first kind. The integrals may be computed numerically using their standard definitions: 1

K (k ) = ∫

0

dt 2

(

(1 − t ) 1 − k 2t 2

)

Alternatively one may use any available series expansion. Simple approximations for the ratio of the elliptic integrals is given in Appendix D.

Appendix A

273

Appendix A CPS on a Finite Thickness Substrate The sequence of the conformal transformations for a CPS is shown in Fig. A.1. First, the partial capacitance due to the substrate with an equivalent dielectric permittivity (ε–1) is evaluated. The symmetry plane of the CPS at x=0 is regarded as an equivalent electric wall, while all dielectric/air interfaces are approximated by magnetic walls. Then the capacitance between the strips of the CPS is the capacitance of series connected capacitors between the strips and the electric wall Fig. A.1 (a). To evaluate the capacitance of one of these capacitors the semiinfinite right hand side of the substrate in the Z-plane (Fig. A.1 (a)) is mapped on a lower part of T-plane (Fig. A.1 (b)), using the transformation t = cosh 2 ( πz / 2 h ) . This mapping results in the following vortex coordinates in T-plane: t1 = 1;

t 2 = cosh 2 (πg / 2h) ;

t 4 = t5 = ∞ ;

t 3 = cosh 2 (π ( s + g ) / 2h);

t6 = 0

(A.1)

Next, the lower part of the T-plane is mapped onto a rectangle in W-plane, shown in Fig. A.1 (c), using a Christoffel-Schwartz transformation: t

W(t ) = A ∫

t3

dt ( t − t1 )( t − t 2 )( t − t 3 )( t − t6 )

+B

(A.2)

For t>t3>t2>t1>t6 the solution of (A.2) is an elliptic integral. By using the T-plane coordinates given above the modulus of the elliptic integral take the form: ⎛π( g − Δ )⎞ tanh⎜ ⎟ 2h ⎝ ⎠ , k= ⎛π( s + g + Δ )⎞ tanh⎜ ⎟ 2h ⎝ ⎠

(A.3)

The substitution of the T-plane coordinates in the elliptic integral leads to the following coordinates of the vortex in W-plane w1=K(k)+jK(k’), w3=0, w6=K(k). Then the capacitance of the parallel-plate capacitor shown in Fig. A.1 (c) is written as: C = εo(ε − 1)

K( k' ) K( k )

(A.4)

274

7 Modeling

(a)

Z-plane jy

Electric wall

g

(s+g)

C

6

4 →∞

3

1 2

ε

x

C

5 →∞

-j h jt

(b) T-plane

t5=∞ 5

t6

t1

6

1

jv

t2 2

t3

t4=∞

3

4

x

(c)

W-plane

2

K(k’)

1

3

4 5

6

u

K(k)

Fig. A.1 Sequence of conformal transformations for a single dielectric layer. The width increment Δ is not shown here for simplicity. Reprinted with permision from IEEE©2003

K(k) and K(k’) are complete elliptic integrals of the first kind with k’=√(1–k2). An identical series connected capacitance is due to the left-hand side of Fig. A.1 (a), hence the total partial capacitance due the substrate is: Cs = ε o ( ε − 1 )

1 K( k' ) 2 K( k )

(A.5)

The partial capacitance between the two strips shown in Fig. A.1 (a) in the absence of the substrate is readily available from (A.5) for h=∞ limit if we replace (ε–1) by 1, i.e. the dielectric permittivity of the air, and double it to take into account the air above and below the strips: Ca = ε o

K ( k o' ) K ( ko )

(A.6)

Appendix A

275

where

ko =

g −Δ ; s+g+Δ

k 'o = 1 − k o2

A simple expression for the correction Δ of strip width is given in (7.2.3).

(A.7)

276

7 Modeling

Appendix B Capacitances of a CPS with a Backside Ground Plane (Same as Coupled Microstrip Lines), Fig.7.2.4 The even and odd capacitances of the coupled microstrip lines, Ce and Cod, obtained by assuming a magnetic wall at the symmetry plane (interval (y1y6), Fig. B.1) and electric wall at the interface of layers 2 and 1 (interval (y5y6), Fig. B.1). To evaluate Ce the semi-infinite right hand side of the layer conveniently represented in the Z-plane (Fig. B.1 (a)) is mapped onto the lower part of

Te-plane (Fig. B.1 (b)) using transformation t = cosh 2 ( πz / 2 h ) . The vortex coordinates in Te-plane are: t1 = 1;

t 2 = cosh 2 (πg / 2h) ;

t 3 = cosh 2 (π ( s + g ) / 2h);

t 4 = t5 = ∞ ;

t6 = 0

(B.1)

In the next step the upper half of the Te-plane plane is mapped onto the interior of the rectangle in We-plane (Fig. B.1 (c)) using the function: t

We( t ) = A ∫

t3

dt ( t − t 3 )( t − t 2 )( t − t6 )

+B

(B.2)

By using Te-plane (Fig. B.1 (b)) vortex coordinates t3, t2, t6 (B.1) in the solutions of this integral lead to the following vortex coordinates in the We-plane (Fig. B.1 (c)): w3=0 and w6 = K ( k e ) + jK ( k e' ) , and the modulus of the complete elliptic integrals: ⎛π( g − Δ )⎞ ⎟ cosh⎜ ⎜ 2h2ef ⎟ ⎝ ⎠ ; ke = ⎡ π (s + g + Δ ) ⎤ cosh ⎢ ⎥ ⎣⎢ 2 h2ef ⎦⎥

k e' = 1 − k e2

(B.3)

Then the even mode capacitance Ce, is found from Fig. B.1 (c): C e = ε o (ε 2 − 1)

K (k e' ) K (k e )

A simple expression for the correction Δ of strip width is given in (7.2.3).

(B.4)

Appendix B

277

(a)

Z-plane jy

Magnetic wall

ε2−1

g

(s+g)

1 2

3 C21

C

4 →∞ 5 →∞

6 -j h

x

Electric wall

jt

(b) Te-plane

t6

t5=∞

6

5

jv

t3

x

2

1

t4=∞ 4

3

We-plane 1

(c)

6 K(k’e)

2

t2

t1

4

3

5 u

K(ke)

Fig. B.1 Sequence of conformal mapping for even mode capacitance. Reprinted with permision from IEEE©2003

In the case of Cod an electric wall is assumed at the symmetry plane and interface between layers 1 and 2 as shown in Fig. B.2 (a). To find this capacitance the same mapping function t = cosh 2 ( πz / 2 h ) and sequence is used to arrive at the Tod-plane (Fig. B.2 (b)) where, in contrast to the previous case, an electric wall is also assumed in the interval (t1t6). A Christoffel-Schwartz transformation results in a rectangle in Wod-plane (Fig. B.2 (c)): t

Wod ( t ) = A ∫

t3

dt ( t − t 3 )( t − t 2 )( t − t1 )

+B

(B.5)

278

7 Modeling

(a)

Z-plane jy

Electric wall

g

4 →∞ 5 →∞ Electric wall

C22

6

x

3

2

1

ε2−1

(s+g)

-j h

(b)

jt Tod-plane

6

5

t1

t2

jv

t4=∞

3

4

x

2

1

t3

Wod-plane

2

(c)

1 6

K(k’od

t6

t5=∞

4 5

3

u K(kod)

Fig. B.2 Sequence of conformal transformations for evaluation of odd mode capacitance. Reprinted with permision from IEEE©2003

This integral has a solution similar to the previous one. However in this case we have to use Tod-plane vortex coordinates t3, t2, t1 (B.1) in the solution of the integral, which leads to the following vortex coordinates in the Wod-plane ' (Fig. B.2 (b)): w3=0 and w1 = K ( kod ) + jK ( kod ) . The modulus of the elliptic integrals is:

k od

⎡π ( g − Δ ) ⎤ sinh ⎢ ⎥ ⎢⎣ 2 h2ef ⎥⎦ = ; ⎡ π (s + g + Δ ) ⎤ sinh ⎢ ⎥ ⎣⎢ 2h2 ef ⎦⎥

' k od = 1 − k e2

(B.6)

Appendix B

279

And the odd mode capacitance (Fig. B.2 (c)) is: Cod = ε o ( ε 2 − 1 )

K ( k 'od ) K ( k od )

(B.7)

280

7 Modeling

Appendix C Capacitance of the Coplanar Plate Capacitor with a Straight Gap Consider two symmetric coplanar plates (length 2 W, width s) separated by a gap 2g on a substrate with thickness h1 and dielectric permittivity ε1 (Fig. C.1). For evaluation of the capacitance between the plates magnetic walls are assumed at all dielectric/dielectric (air) interfaces. A magnetic wall may be assumed at y=0 plane and electric wall at x=0 plane since the structure is symmetric. The capacitor shown in Fig. C.1 has a symmetric coplanar-plate structure, where the symmetry planes are indicated as electric (z0y) and magnetic (x0y) walls. The conformal mapping is applied to the x0z plane where the field is planar. Beyond this plane the field is not planar, and the conformal mapping applied to the symmetry plane transforms the filed distribution beyond symmetry plane the same way as in the symmetry plane, i.e. as if the fields are planar. This distortion of the actual field distribution is the source of the error in this model which, as the comparison with the numerical simulations show, is in reasonable limits, given the simplicity of the closed form approximations. The total capacitance is presented as a sum of capacitance in the absence of the substrate Ca and capacitance C1 due to dielectric layer with thickness h1 and equivalent dielectric permittivity (ε1–1): C=Ca+C1.

Fig. C.1 Symmetry planes with the electric field magnetic walls in a coplanar-plate capacitor. Reprinted with permision from IEEE©2003

The transformations start with the evaluation of C1. The cross section in y=0 plane (Z-plane) is shown in Fig. C.2 (a). To evaluate these capacitances the semiinfinite right hand side of the substrate in the Z-plane (Fig. C.2 (a)) is mapped on a

Appendix C

281

lower part of T-plane (Fig. C.2 (b)) using transformation t = cosh 2 (πz / 2h) . This mapping results in the following T-plane vertex coordinates: t0 = 1;

t 2 = cosh 2 (πg / 2h) ;

t3 = cosh 2 (π ( s + g ) / 2h);

(C.1)

t 4 = t9 = ∞ ;

In the next step the upper half of the T-plane is mapped onto the interior of the rectangle in W-plane (Fig. C.2 (c)) using Christoffel-Schwartz transformation: t

W (t ) = A ∫

t3

dt (t − t3 )(t − t 2 )(t − t0 )(t − t8 )

+B

(C.2)

For t>t3>t2>t0>t8 the solution of (C.2) is given as an elliptic integral, F(ϕ, k1). By using vertex coordinates (C.1) in this solution we arrive at the following W-plane coordinates, W(t3)=0, W(to)= A[ K(k1) +jK(k’1)] (Fig. C.2 (c)) and modulus for the complete elliptic integrals of the first kind: ⎛ πg ⎞ ⎟⎟ tanh⎜⎜ ⎝ 2h1 ⎠ ; k1 = ⎡ π (s + g ) ⎤ tanh ⎢ ⎥ ⎣ 2h1 ⎦

k1' = 1 − k12

(C.3)

Selecting the lower limit at t=t3 in the above integral sets the origin at w3=0 in the W-plane, in i.e. B=0 in (C.2). Shown in Fig. C.2 (c) is also the accompanying transformation of the structure in the third y-direction and the electric wall corresponding to line section 08 of the electric wall (see Fig. C.2 (a)). Note that conformal transformations in Z- and T-planes do not change the lengths in y-direction. To simplify the further transformations the semi-infinite rectangular tube (Fig. C.2 (c)) is represented as shown in Fig. C.2 (d), i.e. to the left of u=0 plane. A similar symmetric structure is added to the right, at u=0 plane to simplify the further transformations. Note that in this representation the magnitudes of all actual dimensions are conserved. Now the function P=sin[πU/2AK(k1)] is used to map the interior of the triangle (vertex 5 in the infinity) onto the upper half of the P-plane (Fig. C.2 (e)). By using in this formula, the U-plane vertex coordinates u0=0, u2= –AK(k1) and u6= –AK(k1)+jW one gets, after simple arithmetic, the following P-plane coordinates: p0=0, p2= –1, and p6=1/k11, where k11 =

1 ; ⎛π W ⎞ ⎟⎟ cosh⎜⎜ ⎝ 2 AK (k1 ) ⎠

k11' = 1 − (k11 )2

(C.4)

282

7 Modeling

Electric wall

jz

0

(ε1-1)

h1

Z-plane

g

(s+g)

2

3

x 5

8

9

(a)

–jh1 T-plane

t9=∞

t8

t0

t2

t3

t4=∞

9

8

0

2

3

4

t

(b)

W-plane (u0v) y

ju

6 ∞ ∞

AK(k1’)

2

0

7 W

3

4, 9

0 jy

5

8

(c)

v

AK(k1) U-plane (u0y)

∞

7

W

6

AK(k’1) 0

AK(k1)

AK(k1)

(d)

u

v

Fig. C.2 The sequence of the conformal transformations. Reprinted with permision from IEEE©2003

Appendix C

283

∞

P-plane

jq

7

3

AK(k’1) 2 -p6

0

–p2

p2

p

p6

(e) jg F-plane

7

5

AK(k11’)

6

3 2

AK(k’1)

0

(f)

–AK(k11)

AK(k11)

f

Fig. C.2 (Continued)

The next Christoffel-Schwartz transformation maps the upper half of the P-plane onto the interior of the rectangle in the F-plane (Fig. C.2 (f)) with the modulus of the complete elliptic integral give in (C.4). Finally, the capacitance C1 is: C1 = (ε1 − 1)ε o

K (k11 ' ) AK (k1' ) K (k11 )

(C.5)

Note that a similar capacitance due to the left hand side in Fig. C.2 (a) is connected in series with this one, making the total capacitance of the structure shown in Fig. C.2 (a) C1/2. This is the capacitance of the right hand side in Fig. C.2, i.e. half of the total partial capacitance between the plates due to the substrate. The capacitance in the absence Ca of the substrate is found from (C.5) at h1=∞ limit by replacing (ε1−1) by 1, and taking into account the air above and below the strips: Ca = 2ε o

K (ka ' ) AK (ko' ) K (ka )

(C.6)

284

7 Modeling

where ko and ka are found from (C.3) and (C.4) at h1=∞ limit: ko = k1 h

k a = k11 h

1 =∞

1 =∞

=

=

g ; s+g

ko ' = 1 − ko 2

1 ⎛π W ⎞ ⎟⎟ cosh⎜⎜ ⎝ 2 AK (ko ) ⎠

(C.7)

ka ' = 1 − ka 2

(C.8)

Taking the sum of partial capacitances (C.6) and (C.8) we get the total capacitance between the plates: C = 2ε e1ε o

K (k a ' ) AK (k o' ) K (k a )

(C.9)

where the effective dielectric permittivity is:

ε e1 = 1 + (ε1 − 1)q1

(C.10)

with a filling factor: q1 =

' 1 K (k11 ) K (ka ) K (k1' ) 2 K (k11 ) K (ka' ) K (ko ' )

(C.11)

The arbitrary constant in above expressions is set to be A=g, i.e. half the gap between the coplanar plates.

References

285

Appendix D Approximations for the Complete Elliptic Integrals of the First Kind In some cases, the modulus of the elliptic integrals take extreme values, k→0 or k→1 causing computational problems (overflow) in simulations of the ratios of the elliptic integrals using standard build in functions of the commercial software (i.e. MATCAD). Fortunately, in those extreme cases, the asymptotic approximations take simple, highly accurate, and computationally more effective forms. A possible form of this type is given below: ⎧ ⎪ 2 ⎛4⎞ ⎪ ln⎜ ⎟ ; ⎪ π ⎝k⎠ ' K (k ) ⎪⎪ 1 ⎛⎜ 1 + 1 − k 2 = ⎨ ln 4 K (k ) ⎪ π ⎜ 1 − 1 − k 2 ⎝ ⎪ π ⎪ ; ⎪ ln⎛ 4 1 + k ⎞ ⎜ ⎟ ⎪⎩ ⎝ 1 − k ⎠

for ⎞ ⎟; ⎟ ⎠

0 < k < 10 − 5

for 10 −5 < k ≤ for

k≥

1 2 1 2

In the above expressions k has to be replaced by k’ [i.e. √(1–k2)] for computation of K(k)/K(k’).

References Berg H, Gevorgian S (2002) Partial Capacitance and Partial Inductance Techniques for Multilayer Substrate Coplanar-Strip and Coplanar Waveguides. Proc Workshop on Conformal Mapping EuMC2002 Berg H, Gevorgian S (2002) A Simple Method for Evaluation of the Transmission Line Capacitance on Nonlinear and Non-Homogeneous Substrates. Proc EuMC 1:709–712 Deleniv A, Gevorgian S (2008) Modelling of Conductor Losses in Capacitors with Rectangular and Circular Plates. RFMiCAE, Published on-line August 20, 2008

Deleniv A, Vendik I, Gevorgian S (2000) Modeling gap discontinuity in coplanar waveguide using quazi-static spectral domain method. Int J RF Microw CAE 10:150–158 Eo Y, Eisenstadt W R (1993) High-speed VLSI Interconnect Modeling Based on S-Parameter Measurements. IEEE Trans Components, Hybrids, and Manufacturing Technology 16:555– 562 Gevorgian S, Linnér P, Kollberg E (1995) CAD Models for Shielded Multilayered CPW. IEEE Trans Micr Theory Tech, 43:772–779

286

7 Modeling

Gevorgian S, Berg H, Jacobsson H et al. (2003) Basic Parameters of Coplanar-Strip Waveguides on Multilayer Dielectric/Semiconductor Substrates. Part 1: High Permittivity Superstrates. IEEE Microwave Magazine, June:60–70 Gevorgian S, Berg H, Jacobsson H et al. (2003) Basic Parameters of Coplanar-Strip Waveguides on Multilayer Dielectric/Semiconductor Substrates. Part 2: Low Permittivity Superstrates. IEEE Microwave Magazine, September:59–78 Gevorgian S, Linner P, Kollberg E (2001) An Analytic Approximation for Open-End Capacitance in a Finite Thickness Substrate Coplanar-Strip Waveguide. Electronics Letters 37: 1226–1228 Gevorgian S, Martinsson T, Deleniv A et al. (1997) A Simple and Accurate Dispersion Expression for the Effective Dielectric permittivity of Coplanar Waveguides. IEE Antennas and Propagation 144:145148 Gevorgian S, Martinsson T, Linnér P et al. (1996) CAD Models for Multilayered Substrate Interdigital Capacitors. IEEE Trans Microwave Theory Techn 44:896–904 Ghione G, Goano M, Madonna G L et al. (1999) Microwave Modelling and Characterization of Thick Coplanar Waveguides on Oxide-Coated Lithium Niobate Substrates for Electrooptical Applications. IEEE Trans. Microwave Theory Techn 47:2287–2293 Giraud S et al. (2005) Characerisation of ferroelectric thin film planar microwave devices using the Method of Lines (MoL). 35 EuMC:513–516 Klingbeil H, Heinrich W (1994) Calculation of CPW A.C. Resistance and Inductance Using a Quasi-Static Mode Matching Approach. IEEE Trans Microwave Theory Techn 42:1004– 1007 Liu Y, Cha K, Itoh T (1993) Non-Leaky Coplanar Waveguides with Conductor Backing. IEEE Trans Micr Theory Techn 43:1067–1072 Matthaei G, Jones E M T, Young L (1980) Microwave Filters, Impedance-Matching Networks, and Coupling Structures. Artech Rautio J C (2000) An Investigation of Microstrip Conductor Loss. Microwave December:60–67 Vendik O G, Zubko S P, Nikolskii M A (1999) Modeling and calculation of the capacitance of a planar capacitor containing a ferroelectric thin film. Technical Physics 44:349–355 Xiong X Z, Fusko F (2002)A comparison study of EM and physical equivalent circuit modelling for MIM CMOS capacitors. Microwave and Opt Technology Letters 34:177–181

Chapter 8

Measurements of the Dielectric Properties Anatoli Deleniv and Spartak Gevorgian

Abstract Microwave characterization of bulk, thin and thick film ferroelectrics is considered in this chapter. Both single crystals and ceramics are discussed. The resonant techniques include disk, Courtney and composite resonator methods for characterization of the bulk ferroelectrics. The open resonator and split post dielectric resonator methods are considered for thick films. Resonator techniques for on-wafer characterization of the thin films and varactors include: microprobe resonator, transmission line resonator, and the near field scanning microscope. The broadband techniques include transmission/reflection method and methods based on coplanar lines and coupled microstrip lines. The methods for the measurement of the nonlinearities and tuning speeds also are considered.

8.1 Introduction Microwave measurements of the dielectric permittivity and loss tangent of a ferroelectric material is used i) as initial data for the device design, ii) for the dielectric spectroscopy e.g. for the analysis of the loss mechanisms, and iii) feedback information for the optimization of the composition and fabrication process. In principle, any technique used for microwave characterization of the dielectrics may be considered for measurements of the dielectric properties of the ferroelectrics. However, the extremely high permittivity of the ferroelectrics limits usefulness of some of the well known techniques. Additionally, the electrodes used for application of the DC bias fields may drastically affect the measured permittivity and losses. In contrast to the ordinary dielectrics, the sizes of the material under test (MUT) and its crystalline structure (single crystal, ceramic) strongly affect the measured complex permittivity. Due to the complex dependence on the mechanical strains and internal electric fields the distribution of the permittivity in the MUT may be non uniform. In this sense the measured microwave permittivity and loss tangent have to be regarded as effective parameters. 287

288

8 Measurements of the Dielectric Properties

In the following sections a number of resonator techniques are discussed which are specifically useful for measurement of the ferroelectrics. Using the resonant technique requires a careful consideration of the electric field configuration. The disk resonator approach (Vendik et al. 1995) makes use a family of TM modes with the angular symmetry. This is a simple and useful techniques that allows measurement of the dependence of the material properties on the applied DC field. The Courtney (Courtney 1970) method, also known as Hakki and Colleman (Hakki and Coleman 1960) method, and the composite resonator method (Krupka et al. 2006) make use of TE modes with the angular symmetry is useful for measurement of the bulk ferroelectric materials. As compared to Courtney method, the composite resonator method is more versatile, although somewhat more complex. The resonant frequency of the Courtney resonator is defined only by the parameters of the measured material which, considering the high permittivity of the ferroelectrics, limits its use to lower frequencies. In the composite resonator, the ferroelectric is only one of the dielectrics that define the parameters of the resonator. This allows measurements of the materials with extremely high losses and dielectric permittivities. The DC electric field may be applied in the direction orthogonal to its microwave counterpart. For this reason, Courtney and the composite resonator methods are suitable for studying field dependent cross polarization effects. The split-post dielectric resonator method (Krupka et al. 2000, Krupka 2004) is an accurate and well established technique for measurements of the thick ferroelectric films below 20 GHz. The open resonator technique (Deleniv and Gevorgian 2005) is useful for the higher frequencies. Neither of the above two methods allow application of DC fields. The majority of measurement techniques dealing with the thin films use test capacitors. This seems to be the only practical way to confine electric field in quantities sufficient for reliable measurements. Two resonator techniques are considered that allow application of the DC field for characterization of thin ferroelectric films. The first method uses a resonator consisting of a coaxial line-microprobe assembly (Deleniv et al. 2008). It is convenient for on wafer measurements. Another resonant technique uses a microstrip resonator loaded by a ferroelectric film (Galt et al. 1995) or by a test capacitor in the form of flipped chip (Kozyrev et al. 1998b). The near field scanning microscope method (Cho et al. 1996, Steinhauer et al. 2000) is useful for local characterization of the linear/nonlinear dielectric properties of ferroelectrics. The resolution of the technique is limited by the size and the shape of the probe tip. The nm resolution of this technique (Cho et al. 1999) allows observation of the ferroelectric domain structure. The broadband measurement techniques provide materials parameters in a rather wide frequency range. However, the accuracy of these measurements is not as high as the accuracy of the resonant methods. Most of the broadband techniques use sections of the transmission lines (TRL) partly or completely filled by ferroelectric materials. The latter affects the impedance and the complex propagation constant of the TRL and, therefore, may be used for the measurement of the complex permittivity of the ferroelectrics, (Nicolson and Ross 1970), (Weir 1974). The method is instable at frequencies where the electric length of the line section is an integer multiple of the half-wavelength. However this problem may be eliminated

8.2 Resonant Techniques

289

(Boughriet et al. 1997). The measurements using coplanar waveguide (Lue and Tseng 2001) and coupled microstrip lines (Deleniv et al. 2003b) are suitable for on wafer microprobe measurements. In the first case a CPW with a ferroelectric film deposited on the top of high-Q dielectric substrate is used. The accuracy of this technique needs careful consideration before planning the measurement. Methods of the measurements of the nonlinearities and response time conclude this chapter. In the further discussions a ferroelectric film is considered to be thin if its electric thickness Θ satisfies the condition Θ≤0.1 rad. The film is thick if 0.1≤Θ≤1 rad.

8.2 Resonant Techniques 8.2.1 Disk Resonator Technique In measurements of the DC field dependent dielectric properties of the bulk ferroelectrics the external bias is applied between the top and bottom electrodes of the disks made of the MUT (Fig. 8.2.1 (a)). An experimental setup used in transmission type resonant measurements (Vendik et al. 995) is schematically shown in Fig. 8.2.1 (b). The disk resonator is in the gap of the central wire of the coaxial line. The coupling of the 50 Ohm line with the resonator is achieved by using a number of quarter-wavelength impedance transformers. The DC bias is applied to the resonator electrodes using two external bias tees. Electrodes

(a)

(b)

Quater-wavelength impedance transformers

h

2r Disk resonator

z

ρ

λ/4

L

λ/4 R

Z0

Z1

Z2

Z3

λ/4

λ/4

Z2

Z1

(c)

C

G

Z3

Z0

Fig. 8.2.1 The disk resonator (a), design (b) and the equivalent circuit (c) of the measurement setup

290

8 Measurements of the Dielectric Properties

From the measured resonant frequency and the Q-factor, the dielectric permittivity and the loss tangent of the ferroelectric are extracted. The model of the resonator is obtained assuming a magnetic wall at the cylindrical surface. This allows defining eigen-fields of the resonator analytically, making the retrieval procedure simpler. The modal solutions, which are in the forms of TMmnp modes use the following index nomenclature, m and n are reserved for the axial and radial field variation, while p holds for that along the disk axe. Due to angular symmetry of the structure and the excitation field, only axially symmetric modes TM0np modes can be exited. It is required that the disk is electrically thin, which implies p=0. The equivalent circuit of the setup is shown in Fig. 8.2.1 (c)) where, R holds for the resistance of the electrodes, while C, L, and G stand for the lumped equivalents of the resonator. From the solution of Maxwell equations, the dielectric permittivity and loss tangent for the first TM0n0 mode are than evaluated using the following equations (Vendik et al. 1995): ⎛k c ε = ⎜⎜ 0 n o ⎝ 2πrf 0 tan δ =

2

⎞ ⎟ , ⎟ ⎠

(8.2.1)

Rsur co 1 − , Q0 120π 2 hf 0

(8.2.2)

where k 0 n is the n-th root of the zero-th order Bessel function, c o = 3 × 10 8 m/s, r is the radius of the cylinder, R sur is the surface resistance of the electrode, h is the thickness of the resonator, f0 is the resonance frequency, and Q0 is the unloaded quality factor. In some cases, due to the roughness of the surface and/or reduced density, the surface resistance of the metal electrodes is known only approximately. It is then useful to measure two resonators of the same diameter but with different thickness, h1 and h2 . It helps to eliminate the contribution of the conductor loss. Then the loss tangent of the ferroelectric is given by: ⎛h h ⎞ 1 tan δ = ⎜⎜ 2 − 1 ⎟⎟ ⎝ Q2 Q1 ⎠ h2 − h1

(8.2.3)

where Q1 and Q2 are the unloaded Q-factors measured for the resonators with the thickness h1 and h2 respectively. A simpler setup (Fig. 8.2.2) may be used for the reflection type measurements. The test fixture comprises a cylindrical package, where the position of the disk resonator is fixed by using a spring-loaded contact. The internal sizes of the package are selected so that no parasitic package modes are exited. The design of the package allows a good thermal contact between the disk and the package and

8.2 Resonant Techniques

291

eventually between the package and the “cold finger” of the vacuum cryocooller which is required in the measurements. Sometimes the other modes with no axial symmetry, m>0, also are used for the measurements. However, using the modes with angular symmetry is always preferred, since the magnetic wall approximation works best for them. A magnetic wall enforces a tangential component of the magnetic field to be zero at the cylindrical surface of the disk. For the modes with axial symmetry there is only one component of the magnetic field ( H φ ) which is due to radial currents, Jρ. At the electrode edges the radial current vanish and so does the magnetic field. The only parasitic effect is due to fringing electric field, which is minimized by choosing the size of the disk to be identical to that of the electrodes. The modes with no angular symmetry have a large radial component of the magnetic field ( H ρ ) close to the electrode periphery. The ferroelectric-air interface does not represent any discontinuity for magnetic field causing increased eddy currents. It leads to reduced accuracy of the formula for the electrode loss obtained under ideal magnetic wall assumption. Additionally it results in a shift of the resonance frequency, which is due to the fringing magnetic field. Both the above effects degrade the accuracy of the method. 1 2 3 4

5

Fig. 8.2.2 Reflection type measurement of a disk resonator. 1-SMA connector; 2-cylinder-shaped package; 3-spring; 4-contact pad; 5-disk resonator

As the loss of the ferroelectric material increase, the resonators Q-factor degrades. Below a certain threshold the Q-factor can not be measured with the confidence. Therefore, the utility of the method for characterization of ferroelectric is limited by materials with tan δ ≤ 0.01 ÷ 0.02.

8.2.2 Courtney Resonator The resonator was originally proposed by Hakki and Coleman (Hakki and Coleman 1960). Courtney has significantly contributed to developing this method (Courtney 1970). The resonator comprises a dielectric rod made of the MUT

292

8 Measurements of the Dielectric Properties

placed in between two parallel conducting plates (Fig. 8.2.3). The resonator is considered as a section of a shorted at both ends dielectric waveguide supporting TE, TM and hybrid (HEM) modes. The field configurations of TE and TM modes are symmetrical and independent of ϕ, i.e. their nomenclature is limited by TEmnp and TMmnp with m = 0 . The index m is reserved for the angular, while n and p hold for the radial and longitudinal field variations. The fields having angular dependence are combinations of TM and TE modes and are usually designated as HEMmnp. However, these are also referred to as EH or HE modes depending TM or TE mode is dominating. The measurement of the dielectrics relies on the use of TE0np modes having only one component of electric field, Eϕ . This makes the resonator insensitive to the small air gaps that may exist between the dielectric rod and conducting plates. This specific feature of TE0np modes defines high accuracy of the method, especially for the materials with high dielectric permittivity.

Fig. 8.2.3 The dielectric rod between two parallel conducting plates

For the purpose of modeling it is assumed that the conducting plates are infinitely large. Than, the characteristic equation for the TE0np modes is (Hakki and Coleman 1960): J 0 (α ) K (β ) , = −β 0 J1 (α ) K1 (β )

(8.2.4)

πD ε r − ( pλ 2L )2 , λ

(8.2.5)

α where

α=

β=

πD λ

( pλ

2 L )2 − 1 ,

(8.2.6)

where J1 (α ) , and J 0 (α ) are the Bessel functions of the first kind, while K1 (α ) and K 0 (α ) are the modified Bessel functions of the second kind of first and zero orders respectively, λ is the free space wavelength, D is the diameter, L is the length of the MUT rod and p=1, 2, 3…, corresponds to the multiple halfwavelength in the cavity along the axial direction of the cylinder. The characteristic equation (8.2.4) is a transcendental; hence it is solved numerically or graphi-

8.2 Resonant Techniques

293

cally. For each fixed value of β there exists an infinite set of {α n } which satisfies (8.2.4). For the TE011 mode the relationship between α and β is given by 2

(

)

⎛ λ ⎞ 2 2 ⎟ α 1 + β1 , ⎝ πD ⎠

εr = 1 + ⎜

(8.2.7)

where α 1 and β 1 are the first roots of the characteristic equation with m = 0 , p = 1 and λ is the resonant wavelength. For the dielectric resonator with known dimensions and the resonant frequency of the TE011 mode, the real part of dielectric permittivity is found using (8.2.5). The loss tangent tan δ of the MUT is obtained using (Courtney 1970): tan δ =

A − BRS Q0

(8.2.8)

where A = 1+

B=

1

1 2πf13 μ 02ε 0 L3ε r

F (α 1 ) = G (β1 ) =

F (α 1 )G (β1 ) ,

(8.2.9)

[1 + F (α1 )G(β1 )]

(8.2.10)

εr

J 12 (α 1 )

(8.2.11)

K 0 (β1 )K 2 (β1 ) − K12 (β1 )

(8.2.12)

J 12 (α 1 ) − J 0 (α1 )J 2 (α 1 ) K12 (β1 )

RS =

πf1μ σ

(8.2.13)

where Q0 is unloaded Q-factor of the dielectric resonator and σ is the conductivity of the metal plates. For the materials with small losses, the terms A Q0 and BR S may be of the same order of magnitude leading to high sensitivity of tan δ to the errors in RS . To exclude the conductor loss from consideration one need to measure two rods with identical diameter and the length of the second rod being k times longer than that of the first one. In this case the resonant frequencies of the TE011 mode of the first sample and the TE01 k mode of the second sample are the

294

8 Measurements of the Dielectric Properties

same and the loss due to conductor plates can be removed. The loss tangent of the MUT is than calculated using (Kobayashi and Katoh 1985): tan δ =

A ⎛ k 1 ⎞ ⎜⎜ ⎟, − k − 1 ⎝ Q0 k Q01 ⎟⎠

(8.2.14)

where Q01 and Q0 k are the unloaded Q-factors of the TE011 and TE01 k modes of the first and second rods respectively. The model of the resonator assumes infinite conducting plates. The effect of the non-ideal plates on the resonance frequency and Q-factor is insignificant, since the field outside the dielectric rod decays rapidly. This is especially pronounced for ferroelectric materials having high dielectric permittivity. For the ratio d D ≈ 6 (Fig. 8.2.3) the measurement error is less than 0.1%. In the measurements the identification of TE011 mode may be difficult. Based on the approximate knowledge of the dielectric permittivity and the rod size it is possible to estimate the expected resonance frequency. This, along with the fact that TE011 mode is the second low-frequency mode, should be sufficient to locate it on the frequency axe. To identify the mode, one should use the low sensitivity of TE mode family to the thickness of the air gap between the rod and plates. This is achieved by raising and lowering the upper plate. As the plate is raised, the TM modes move rapidly to higher frequencies while the TE011 mode remains unaffected. The excitation of the resonator for transmission type measurements is typically made using two E-field probes, Fig. 8.2.4. With minor rearrangements the measurement set up shown in Fig. 8.2.4 may allow application of the DC bias between the top and the bottom conducting plates without using bias tees to study the cross-polarizing effects. In (Kobayashi and Katoh 1985) the effect of the air gap on the measurement accuracy is experimentally studied for the MUT with dielectric permittivity ε r ≈ 33 . Measurements with the air gap 0.2 mm revealed ∼0.1% error in the di-

Fig. 8.2.4 The dielectric post resonator showing the rod made of the MUT and probes (Courtney 1970). Reprinted with permission from IEEE©1970

8.2 Resonant Techniques

295

electric permittivity. The effect of the loss in MUT on the resonance frequency is rather small. For a MUT with tan δ = 0.1 the resulting shift in the resonance frequency is about 0.1%. However the high losses lead to degradation of the resonator Q-factor.

8.2.3 Composite Resonator Method A composite resonator for characterization of lossy ferroelectrics is proposed in (Krupka et al. 2006). In contrast to Courtney resonator it allows measurement of the MUT with extremely high dielectric loss. The resonator consists of a cylinder cavity loaded by a hollow high Q dielectric resonator. The ferroelectric MUT is loaded into the Teflon sleeve as it is shown in Fig. 8.2.5. By controlling the size of the hole 2r3 in the dielectric resonator and the thickness of the Teflon sleeve one may control a fraction of the energy stored in the ferroelectric MUT at the resonance frequency. In measurement the first non sensitive to the air gap TE0n1 axially symmetric modes are used. The model is based on the solution of Maxwell`s equations, where it is assumed that the height of all dielectric regions are identical. The metallization of the cavity enclosure is assumed to be ideal. Then, for each region, i = 1,2 … 5 , the electric and magnetic field components may be written as (Krupka et al. 2006):

[ ( )

( )]

[ ( )

( )]

Eϕi = ωμ 0 Ai J1 k ρi r + BiY1 k ρi r sin (k z z ) H zi = k ρi Ai J 0 k ρi r + BiY0 k ρi r sin (k z z ) ,

where k ρi =

(ω c )2 ε i − k z2

(8.2.15) (8.2.16)

. J n and Yn are Bessel functions of the first and

second kind of the order of n and k z = (π L ) . In the above equations the permittivity and angular frequency may be complex. For the first dielectric layer B1 = 0 , since the Bessel function of the second kind is infinite at ρ = 0 .

Fig. 8.2.5 Composite resonator used for the complex permittivity measurements of ferroelectrics. Reprinted with permission form IEEE©2006

296

8 Measurements of the Dielectric Properties

To find the solution of the Maxwell equations the following continuity conditions are enforced at each dielectric interface: Eϕ1 = Eϕ2 and H 1z = H z2 at ρ = r1

(8.2.17)

Eϕ2 = Eϕ3 and H z2 = H z3 at ρ = r2

(8.2.18)

Eϕ3 = Eϕ4 and H z3 = H z4 at ρ = r3

(8.2.19)

Eϕ4 = Eϕ5 and H z4 = H z5 at ρ = r4

(8.2.20)

Eϕ5 = 0 at ρ = r5

(8.2.21)

This leads to the eigenvalue matrix equation:

[W ]⋅ [X ] = 0 ,

(8.2.22)

where

[X ] = [A1

A2

B2

A3

B3

A4

B4

A5

B5 ] .

(8.2.23)

A nontrivial solution to (8.2.22) exists only if the determinant of the matrix vanishes. Hence, the complex resonant frequencies for all TE0n1 modes are given by a set of complex frequencies ω~n that satisfies:

[W ]

det W (ω~n ) = 0

(8.2.24)

Then the Q-factor due to dielectric losses is: ~ ) (2 Im(ω ~ )) Qd = Re(ω n n

(8.2.25)

For the Q-factor due to conductor loss one may use the perturbation approach which is valid for most of the high conductivity metals. Qc = G RS ,

(8.2.26)

where R S is the surface resistance and G is a geometric factor of the metal enclosure defined as:

∫∫∫ μ G =ω

0H

⋅ H * dv

Vt

∫∫ S

H τ ⋅ H τ* ds

(8.2.27)

8.2 Resonant Techniques

297

where S and Vt holds for the surface of the metal enclosure and volume of the resonator respectively. For TE0n1 modes the geometric factor may also be found using the incremental frequency rule (Kobayashi et al. 1985). The unloaded Q-factor of the resonator is then defined as: Q −1 = Q d−1 + Qc−1

(8.2.28)

Retrieval of the complex permittivity of the MUT is made iteratively. It is assumed that the other losses in the resonator are not changed due to insertion of the MUT. When the complex permittivity of the MUT is found, it is used to compute a more accurate conductor Q-factor using (8.2.27). In the next step a new value of the permittivity is computed using a more accurate estimate of the parasitic loss. The procedure is repeated if necessary. In practice the MUT volume is small and the resonant frequency of the resonator loaded by MUT is very close to that without the sample. According to Krupka et al. (2006), one iteration step provides results with accuracy better than the level of other systematic errors. The sample diameter is chosen in such a way that Q-factor for one of the TE011 or TE021 modes is measurable. Practically it means that it is larger than 100 for the expected range of the permittivity. The composite resonator method is recommended for characterization of bulk materials with extremely high losses.

8.2.4 Split-Post Dielectric Resonator Method for Thick and Thin Films The split-post dielectric resonator (SPDR) technique is a well established and accurate method for characterization of the dielectrics in the laminar, thick and thin film forms up to 20 GHz (Krupka et al. 2001, Krupka 2004). Since no electrodes are involved this method allows measurements not affected by electrode/ferroDielectric resonators

Metal encloser

hr

ha

dr Support

MUT

Dc

Fig. 8.2.6 Split-post resonator fixture. Modified after (Krupka 2004). Reprinted with permission form IEEE©2004

298

8 Measurements of the Dielectric Properties

electric interfacial effects (i.e. dead layer). The split-post resonator (Fig. 8.2.6) consists of two low loss dielectric packs in a metal enclosure. The resonator uses TE01δ mode of the electromagnetic field, which is insensitive to the presence of air gaps between the tested sample and the dielectric resonator. The characterization of a thick film is made in three steps, i.e. by measurements of the resonant frequency and quality factor of the i) empty resonator, ii) resonator with the substrate which is supposed to have low dielectric permittivity and low loss and, finally, iii) resonator with the substrate and the tested thick film deposited on its top. The first two measurements provide the input for calculation of the dielectric permittivity and the loss of the blank substrate. The real part of the complex permittivity is computed from the measured resonant frequencies of SPDR with and without the substrate using the following equation (Krupka et al. 2001):

ε r′ = 1 +

f0 − f s hf 0 K ε (ε r′ , h )

(8.2.29)

where h is the thickness of the measured substrate, f 0 is the resonant frequency of the empty SPDR, f S is the resonant frequency of the SPDR with the dielectric sample, K ε is a function of ε r′ and h . The latter is calculated for a number of ε r′ and h using the Rayleigh-Ritz technique. To evaluate the values of K ε and ε r′ from (8.2.29) one uses an iterative procedure. The loss tangent of the substrate is computed using: tan δ =

1 p es

⎛ 1 1 1 ⎜ ⎜Q − Q − Q DR c ⎝ 0

⎞ ⎟ ⎟ ⎠

(8.2.30)

where p es is the filling factor representing the fraction of the energy in the substrate, Q0 is the unloaded quality factor of the resonator containing the sample(substrate), Qc is the quality factor representing the conductor loss of the SPDR and Q DR is a quality factor representing the loss of the dielectric parts of SPDR. The values of p es , Qc and Q DR are slowly varying functions of ε r′ and h . Therefore, their accurate values are obtained by interpolating the tabulated data. The thick film to be measured is deposited on the top of the characterized substrate, which must satisfy the following requirements:

(

)

Δh ε f − 1 h f ≤ h εr −1

(8.2.31)

where h f and ε f are respectively the thickness and relative permittivity of the tested layer, Δh is the maximum tolerance in the substrate thickness in the tested area. The cross-section of the two layered sample is shown in Fig. 8.2.7. This

8.2 Resonant Techniques

299

measurement step produces a new pair of the resonant frequency and unloaded Q-factor. The real part of the permittivity, ε f , and the loss tangent, tan δ f , are then computed iteratively using full-wave analysis. tested layer

hf h

Low loss low permittivity substrate

Fig. 8.2.7 Thick film deposited on the top of the premeasured substrate

The SPDR technique may also be used for characterization of thin ferroelectric films (Krupka et al. 2006) with the thicknesses in the range 200 nm to 2000 nm and permittivity in the range 100–10000. The uncertainties of the measurements are dominated by the measurement uncertainties of the film thickness. The experimental procedure is identical to the one discussed above for thick films. However, extra care is required to ensure the accuracy of measurements. To compensate for possible temperature drift, the empty resonator is repeatedly characterized before measurement of the thin films. It also requires identical location (placement) of the dielectric substrate with and without thin film. This is made to mitigate the non-uniform thickness of the dielectric substrate that may introduce significant measurement error. Extraction of the film properties is based on mode-matching and Reyleigh-Ritz analysis of SPDR. In (Krupka et al. 2006) thin ferroelectric films with ε=50÷300 and tanδ=0.04÷0.26 are experimentally characterized with less than 6% error. The resolution of the loss tangent is defined by uncertainty of Q-factor measurement, which is within 2%. The theoretical study showed that for the films with high permittivity (ε>800) the loss tangent in access of 10–4 can still be measured. The accuracy of the dielectric permittivity measurement is defined by accuracy of the resonance frequency shift due to thin film. In principle this can be measured very precisely, however practically it is limited by 0.5–1% of 3dB resonance curve bandwidth. For the films considered in (Krupka et al. 2006), this is estimated to be 0.2 MHz leading to errors comparable with those of loss tangent measurement.

8.2.5 Open Resonator Technique The open resonator (OR) is a type of cavity without side walls (Kogelnik and Li 1966). The OR has a number of advantages as compared to traditional cavities making it specifically useful for measurements at millimeter-waves:

300

8 Measurements of the Dielectric Properties

• OR is more accessible than closed cavities; • the mode spectrum of OR is sparse reducing the likelihood of error due to mode coincidences; • their Q-factors are higher than those of closed cavities of similar volume; • only the cross section of MUT is critical, provided its radius is greater than that of the beam. The schematic view of an open resonator with two hemispherical mirrors is shown in Fig. 8.2.8. With respect to the symmetry plane the fields are classified as symmetric and antisymmetric. For symmetric modes the tangential components of the magnetic field vanish on S1 (magnetic wall), while for antisymmetric modes the tangential components of the electric field are zero on S1 (electric wall). Electric wall is easy to realize with any good conductor (copper, silver, etc.), making the symmetric half of the OR practically meaningful. The microwave field of the OR is in the form of a beam with a waist located at the symmetry plane (Fig. 8.2.8). The electromagnetic field has Gaussian distribu2

2

tion (∼ e− ρ w ) in the plane normal to z-axe. The size of a MUT should be large enough to intercept the beam completely in its waist. The measurements utilize TEM modes having nearly planar phase front at the lower plane mirror. x

2 w0

w0

w (z )

z

y

S1

2D

Fig. 8.2.8 OR with two hemispherical mirrors

Using OR for characterization of the thick ferroelectric films is reported in (Buslov et al. 2003), where a simplified theory – the transverse resonance technique is used to model OR loaded by multilayered dielectric plates. A more accurate model based on the vector field theory (Yu and Cullen 1982) is extended for multilayered dielectric plates in (Deleniv and Gevorgian 2005). The detailed derivation of the formulas is given in Appendix E, where the model and the measurement procedure are considered. The model of the loaded OR allows prediction of the resonant frequency ωres based on the sizes and parameters of the dielectric MUT (loading). The reverse problem of finding the parameters of the dielectric MUT with known resonance frequency is solved iteratively, i.e. using the model one searches the values of dielectric permittivity and loss tangent that result in the measured resonance frequency and Q-factor. Here the model of the loaded OR is based on the variational

8.2 Resonant Techniques

301

“mixed-field” formula (Rumsey 1954, Harrington 1961) for the resonant frequency of the cavity. First, the trial fields are chosen for each layer of the dielectric sample. These are used to obtain an initial estimate of the resonance frequency ωin . Considering the effect of imperfectly matched electromagnetic field, the initial estimate of ωin is corrected to define more accurate value of ωres .

(2) (3)

(1)

Fig. 8.2.9 The photo of the OR. 1-digital micrometer, 2-lower plane mirror, 3-upper hemispherical mirror

The photo of an OR is shown in Fig. 8.2.9. The MUT is placed on the lower plane mirror. The shift of its position with respect to the upper hemispherical mirror is accurately measured using a digital micrometer. The identification of the TEM mode is done as follows. At a fixed frequency of measurement the length Dq of the resonator (see Fig. 8.2.8) for the dominant TEM00q mode is calculated solving the transcendental equation: f =

⎞ 2D ⎞ ⎛ c ⎛⎜ (q + 1)π + 1 arccos⎜⎜ 1 − q ⎟⎟ − 1 ⎟⎟ ⎜ 2πDq ⎝ 2 R0 ⎠ 4 kR0 ⎠ ⎝

(8.2.32)

where R0 is the curvature radius of the hemispherical mirror. To set the value of q unambiguously, one needs to approximately measure D q . Assuming that the resonance obtained belongs to the TEM0,0,q “reference” mode, the TEM0,0,q–1 mode resonance is searched by shifting the lower plane mirror upwards Δlqq −1 :

Δlqq −1 = Dq − Dq −1 .

(8.2.33)

302

8 Measurements of the Dielectric Properties

The absence of TEM0,0,q–1 resonance indicates that a wrong mode is identified as the “reference” TEM0,0,q and, therefore, the procedure is repeated again with another “reference” until the TEM0,0,q–1 mode is found. This is a quick and straightforward way to identify the mode to be used. The correct curvature radius, R0 , of the upper mirror is defined following the procedure developed in (Komiyama et al. 1991). With the obtained sizes of the OR, its Q-factor at the chosen frequency is measured. This is used to calculate the conductivity (skin depth) of the mirrors (Jones 1976), see Appendix E. The measurement of the ferroelectric film is made in two steps. In the first step one characterizes the high-Q dielectric substrate so its dielectric permittivity, ε sub , and the loss tangent, tan δ , are known at the measurement frequency. Inserting the MUT into OR makes it electrically longer shifting its resonance frequency down. Following the length variation method (Yu and Cullen 1982) the length of the OR is shortened by Δl to reestablish the resonance of TEM0,0,q mode at the measurement frequency. With the parameters of the empty ( Dq , Q0 ) and loaded ( Dq − Δl , Ql ) resonator known, the dielectric permittivity of the substrate, ε sub , and its dielectric loss tangent, tan δ , are computed. In the second step the characterized substrate with the thick ferroelectric film on its top is measured. Using the model of the loaded OR the parameters of the ferroelectric film are retrieved in the similar fashion. The utility of the OR technique may be limited by the thickness of the sample. For the samples which are thicker than few half-wavelengths, an approximate knowledge of the dielectric permittivity is required to identify unambiguously the operating mode TEM0,0,q.

8.2.6 Resonant Technique for on Wafer Characterization of the Ferroelectric Varactors and Films The resonator methods described in the previous sections are useful for bulk and thick/thin film (without electrodes) characterization. This and the next two sections consider methods useful for thick and mostly for the thin ferroelectric film characterization. The resonator: A resonance technique reported in (Deleniv et al. 2008) allows on wafer characterization of ferroelectric varactors. The resonator shown in Fig. 8.2.10 comprises of a section of a coaxial line connected with a microprobe. The coupling to VNA is provided by a small gap in the inner electrode of the coaxial line.

8.2 Resonant Techniques

303

Coupling gap R1 Coaxial line

Microprobe

Fig. 8.2.10 The microprobe-resonator arrangement. Reprinted with permission form IEEE©2008

The measurement is done in three steps. The unloaded coaxial-line-microprobe resonator is measured first with the microprobe lifted above the substrate. This n measurement produces a number of resonant frequencies ωopen and associated n Q-factors Qopen , where the index n holds for the number of half-wavelengths

( n = 1,2 … ). In the next step the resonator is loaded by a test varactor and new data

{

}

n n , Qload set is measured ωload . Finally, the resonator is measured with the microprobe contacting metallization identical to the varactor electrodes. A number

m m of resonant frequencies ωshort and Q-factors Qshort are measured, with m being

the resonance index ( m = 1,2 … ). Modeling: The coaxial line-probe arrangement is represented by a uniform section of TEM transmission line with the admittance Y = 0.02 (S), Q-factor, and the frequency dependent electric length θ (hereafter this is referred to as a coaxial line). The loaded resonator arrangement at the resonant frequency is shown in Fig. 8.2.11 (a), while its lumped equivalent is shown in Fig. 8.2.11 (b). In Figure 8.2.11 G and CV are the equivalent conductance and capacitance of the varactor, Rct is a microprobe-to-varactor contact resistance, Leq , Ceq and Req are the equivalent inductance, capacitance and resistance of the coaxial line with the length θload . The dielectric loss in the coaxial line is ignored.

(a)

(b)

Fig. 8.2.11 A varactor loaded coaxial resonator (a), and its equivalent circuit about the resonance frequency (b). Reprinted with permission form IEEE©2008

304

8 Measurements of the Dielectric Properties

The fraction of electric field energy in the varactor is given by the inclusion rate kV . In terms of the equivalent circuit it is defined as:

(

)

kV = CV CV + C eq .

(8.2.34)

The inclusion rate may also be defined in terms of the electric length of the coaxial line at resonance frequency: kV =

2 . 1 − 2θ load csc(2θ load )

(8.2.35)

with ω θload = πn load . n ωopen

(8.2.36)

The identity (8.2.36) defines θload using the resonance frequencies ωload and n ωopen of the loaded and unloaded resonators respectively. The resonance index of

the loaded re sonator is intentionally unspecified, although a better accuracy is exn are close. pected if ωload and ωopen

With the inclusion rate known, the Q-factor of the loaded resonator is calculated as: k 1 . = V + Qload QV Q* 1

(8.2.37)

In (8.2.37) QV is the Q-factor of the varactor, while Q* is that of the coaxial line at the loaded resonance frequency ω load . Since the Q-factor of the coaxial line is proportional to

ω (dielectric loss in the coaxial line are neglected), the

following identity holds for Q* : n ω load Q* = Qopen

n ωopen

.

(8.2.38)

The accuracy of expression (8.2.38) is verified experimentally in (Deleniv et al. 2008). Using (8.2.37) and (8.2.38) one arrives at: QV =

Q* ⋅ Qload ⋅ kV Q* − Qload

.

(8.2.39)

8.2 Resonant Techniques

305

(a)

(b)

Fig. 8.2.12 A quarter-wavelength resonator (a), and its equivalent circuit in the neighborhood of the resonance frequency (b). Reprinted with permission form IEEE©2008

The value obtained using (8.2.39) is effected by a microprobe-to-varactor contact resistance Rct (Fig. 8.2.11) and needs to be deembedded. The contact resistance is measured with the microprobe contacting a metallization identical to that of the varactor. The lumped equivalent circuit of the shorted coaxial line resonator (Fig. 8.2.12 (a)) is shown in Fig. 8.2.12 (b). The slope parameter x and the Q-factor of the resonator are defined as: m x = ω short Leq =

1 m Qshort

=

(2m − 1)πZ 4

Rct 1 + n x Qopen

, m = 1,2…

n ωopen m ω short

,.

(8.2.40)

(8.2.41)

resulting in: ⎛ 1 ⎜ 1 Rct = x⎜ m − n ⎜ Qshort Qopen ⎝

n ⎞ ωopen ⎟

⎟. m ω short ⎟

(8.2.42)

⎠

With the contact resistance known, the “de-embedded” Q-factor of the varactor is computed by:

(Q )

* −1 V

CV = −

= (QV )−1 − ω load CV Rct , Y

ω load

tan(θ load ) .

(8.2.43) (8.2.44)

The obtained Q-factor and the capacitance CV of the varactor are then used as the input data to retrieve the parameters of ferroelectric film. For the given design/sizes of the varactor the parameters of the film may be extracted by using electromagnetic simulations using the measured QV and CV . In the cases where the analytic models of the varactors are available, one may use QV and CV to ex-

306

8 Measurements of the Dielectric Properties

tract the permittivity and the loss tangent analytically. Simple analytic models for the parallel-plate and coplanar plate (strait gap and interdigital) varactors are given in the previous chapter. A simple and accurate model for varactors with the annular slot is given in the Appendix F.

8.2.7 Transmission Line Resonator Method The transmission line resonators with the higher Q-factor provide higher sensitivity and accuracy of the measurements of the ferroelectric varactors and films. Next to the hollow and dielectric waveguides the stripline and microstrip resonators have relatively high Q-factors acceptable for the ferroelectric film characterization. Besides, they have relatively simpler design and are more suitable for thin film characterization. A stripline split resonator is used under elevated power levels in (Kozyrev et al. 1998b). A typical resonator arrangement using a microstrip line is shown in Fig. 8.2.13. The test varactor is mounted as a flip-chip element over the gap splitting the resonator on two symmetric halves. Alternatively the ferroelectric film may cover the gap below or above the strips (Galt et al. 1995). The equivalent circuit of the resonator is shown in Fig. 8.2.14. The symmetry of the resonator implies even and odd mode resonances with the magnetic (MW) and electric wall (EW) respectively in the symmetry plane. Test varactor

Fig. 8.2.13 A microstrip resonator with a flip-chipped test varactor MW for even mode EW for odd mode C

Z0

Z0

l

Fig. 8.2.14 Equivalent circuit of the resonator shown in Fig. 8.2.13

8.2 Resonant Techniques

307

The resonant frequency and Q-factor of the even modes are not affected, since no current flows via the test varactor. In contrast, the current passing through the test capacitor is high for the odd modes. Therefore, the resonant frequency and Q-factor of the odd mode depend on the parameters of the test varactor. The capacitance C of the test varactor is calculated from the measured resonant frequencies of the odd and even modes ( f1 and f 2 ) respectively (Kozyrev et al. 1998b): C=−

tan (π f1 f 2 ) 4 f 1 Z 0π

(8.2.45)

The dielectric permittivity of the film may be extracted from the measured capacitance using suitable model of the test varactor as it is indicated at the end of the previous section. The Q-factor of the test varactor may be obtained from (Kozyrev et al. 1998b): 1 1⎛ 1 1 ⎞ ⎟, = ⎜⎜ − (8.2.46) QV ξ ⎝ Q1 Q0 ⎟⎠ with

ξ=

2 , 1 − 2ϕ sin (2ϕ )

(8.2.47)

f1 . f2

(8.2.48)

and

ϕ =π

The Q-factors ( Q1 and Q0 ) are those measured at f1 using the test varactor and lossless capacitor with identical capacitances. The lossless capacitor is an additional standard that may be difficult to find/realize. Fortunately, there is a simpler way to obtain Q-factor of the transmission line at f 1 . For high-Q dielectric substrates (MgO, Al2O3, LaAl2Os, etc.) the electrode loss dominates. This implies that the dependence of Q-factor on the frequency is governed by skin-depth dependence, i.e. Q ≈

f . A more accurate result for the

test capacitor loss can be calculated using a modified version of (8.2.46), using Q-factor of the even mode, Q2 : 1 1⎛ 1 1 = ⎜ − ⎜ QV ξ ⎝ Q1 Q2

f2 f1

⎞ ⎟. ⎟ ⎠

(8.2.49)

Although the above formulas are given for the first (odd) and the second (even) modes, the approach can be extended to higher order modes, although their identi-

308

8 Measurements of the Dielectric Properties

fication can be difficult. In (Galt et al. 1995) the first six modes are identified and used for the measurements. For the discussed above resonator the DC voltage may be applied to the two halves of the microstrip resonator at the voltage nodes using RF chokes. Galt et al. (1995) used adjustable DC probes to bias the varactor.

8.2.8 Near Field Scanning Microscope The near field scanning is used for measurements of the spatial distribution of the dielectric permittivity and nonlinearities in thin/thick films and bulk ferroelectrics. The microscope includes a coaxial resonator terminated at one end with an openended coaxial probe (Fig. 8.2.15). The other end is coupled to a microwave source. The probe has a sharp-tipped center electrode which is in contact with the measured MUT. Typically, the contact is controlled by a small force (50 μN) exerted from the sample side (Steinhauer et al. 2000). While the probe is held in a fixed position, the film is raster scanned in X-Y plane. The RF fields are concentrated in small volume next to the probe tip. The Q-factor of the resonator and its resonant frequency depend on the film properties near the tip. A combination of DC and low frequency AC bias may be applied to the sample allowing measurement of nonlinear polarization effects in ferroelectrics.

To microwave source

z

Resonator

ρ

∼

~ Vb Vbdc

Probe Film X-Y stage Counter-electrode

Fig. 8.2.15 Schematic diagram of the near field scanning microscope. Reprinted with permission from AIP@2000

8.2 Resonant Techniques

309

For measurements, the microscope is first calibrated using samples with known parameters. The resonator is than loaded with a test sample leading to changes in Q-factor and the resonance frequency. The obtained data are than translated into parameters of the test film using perturbation theory. For better accuracy the dielectric permittivity of the calibration sample has to be closer to that of the measured MUT. The perturbation formula for the resonance frequency is (Sucher and Fox 1963):

ε Δf ≈ 0 ∫ (ε r 2 − ε r1 )E1 ⋅ E 2 dv , f 4W Vs

(8.2.50)

where W is the energy stored in the resonator, and the integral is over the volume VS of the sample. The dielectric permittivities ε r1 and ε r 2 are the permittivities of the calibration and test sample respectively. The electric fields, required in (8.2.50), are calculated in static approximation which, considering small size of the tip, is justified. An important factor affecting the accuracy is the geometry/shape of the probe tip and also the area, which is in contact with the test sample. Two commonly used tip configurations are shown in Fig. 8.2.16. The tip in the form of the topped cone is shown in Fig. 8.2.16 (a), where r and θ are the two parameters (Steinhauer et al. 2000) defining its shape. In Fig. 8.2.16 (b) the geometry of the tip is defined by an ellipsoid of revolution with a blunt end (Qi et al. 2007). Here, three parameters are used to define the tip shape: long axis a, short axis b and blunt end width c. For the chosen tip geometry, the parameters are defined experimentally, i.e. by comparing the resonance frequencies obtained with a number of calibration samples and those predicted by perturbation formula (8.2.50) using the field distribution obtained for the fixed set of the parameters.

a b

θ 2r Sample

(a)

c Sample

(b)

Fig. 8.2.16 Probe tips in the form of a topped cone (a) (Steinhauer et al. 2000), an ellipsoid of revolution (b) (Qi et al. 2007)

A theory of nonlinear measurements using scanning microscope is presented in (Cho et al. 1996). In this case a signal, which is a superposition of DC and low frequency AC field (one may also use only one component), is applied to the probe. DC bias is applied using a counter-electrode (Fig. 8.2.15). Depending on

310

8 Measurements of the Dielectric Properties

design of the latter different components of nonlinear permittivity may be measured. Use of a high resistivity electrode for biasing is reported in (Steinhauer et al. 2000). It is transparent for RF field, while at low frequencies it acts as a good electrode. The RF field is dominated by in-plane ρ -component, whereas the biasing field is oriented along z-axe mostly. The electric displacement D is then expanded in powers of the electric field E (Cho et al. 1999): D1 (E ) = ε 11E1 +

1 1 ε113 E1E3 + ε1133 E1E32 + … , 2 6

(8.2.51)

where E1 is the RF field in the ρ direction, and E3 = Eb is the applied bias field ~

in the z direction. Since the biasing field is Eb = Ebdc + Eb cos(ωbt ) , the effective RF permittivity is in the form (Steinhauer et al. 2000, Cho et al. 1996):

⎛ε ε E dc + ⎜ 113 + 1133 b ⎜ 2 3 ⎝

( ) + (E~ )

⎛ E dc b 6 ⎝

1 2

ε rf = ε 11 + ε 133 Ebdc + ε 1133 ⎜⎜

2

⎞ ⎟ 12 ⎟ ⎠ 2

b

⎞~ ⎟ E b cos(ω b t ) + 1 ε 1133 E~b2 cos(2ω b t ) + … ⎟ 12 ⎠

(8.2.52)

The Taylor expansion of the resonant frequency about f0 (ε rf = ε 11 ) with (8.2.52) results in the resonant frequency of the microscope, (Steinhauer et al. 2000): f0 (t ) ≈ cons tan t +

1 ~ df ε 113 Eb 0 2 dε rf

cos(ωbt ) + ε 11

1 ~ df ε 1133 Eb2 0 12 dε rf

cos(2ωbt ) (8.2.53) ε 11

It follows from (8.2.53) that the nonlinear terms ε 113 and ε1133 can be measured using ωb and 2ωb components of the frequency. The DC bias may also be applied in ρ direction (in-plane) with the electrodes deposited on the top of the ferroelectric film. In this case both, the RF and biasing fields, will be aligned enabling measurement of the diagonal nonlinear permittivity tensor component, such as ε11 and ε 111 . The reported/achieved resolution of the scanning microscope is in nm scale. This allows observation/study of the domain size, orientation, etc. (Cho et al. 1999).

8.2 Resonant Techniques

311

8.2.9 Uncertainty of Resonant Measurements 8.2.9.1 Transmission Type Measurements The accuracy of the resonant methods depends on many factors which, in general, may be classified as sample and measurement related. The impact of the fabrication accuracy (sizes) on the final result is specific for each test sample and chosen resonant technique. In this section the uncertainty/accuracy of Q-factor measurements is analyzed. It is applicable to all methods considered above. The detailed analysis of uncertainties for transmission type measurements is developed in (Kaifez et al. 1999). The equivalent circuit of the transmission type microwave resonator embedded between two ports of a VNA is shown in Fig. 8.2.17.

Fig. 8.2.17 Equivalent circuit of transmission type microwave resonator embedded between VNA ports

Two impedance invertors K1 and K 2 define the input and output coupling of the resonator ( k 1 and k 2 ): ki =

K i2 , i = 1,2 R0 Rc

(8.2.54)

The response of the transmission type resonator is shown in Fig. 8.2.18. The loaded Q-factors is given by 3dB bandwidth of the resonance curve centered at f 0 : QL =

f0 BW

(8.2.55)

The unloaded Q-factor is then found assuming that the input and output couplings k 1 and k 2 are identical:

Q0 = QL (1 + 2k ) =

QL 1 − S 21e

(8.2.56)

Hence, the uncertainties in bandwidth ΔBW and the insertion loss Δα ( α is S 21e in decibels) at the resonance frequency are the two quantities that affect the

312

8 Measurements of the Dielectric Properties

accuracy of unloaded Q-factor. The error propagation formula for the unloaded Q-factor results in:

(ΔQ0 )2 =

2

∂Q0 2 (ΔBW )2 + ∂Q0 ∂α ∂BW

(Δα )2

(8.2.57)

It is shown by Kaifez et al. (1999) that the relative uncertainty of the unloaded Q is: 2

ΔQ0 ⎛ ΔBW ⎞ 2 2 = ⎜ ⎟ + Cα (Δα ) , Q0 ⎝ BW ⎠

(8.2.58)

with ΔBW =

Δf

2

+ ΔBW (α ) , 2

(8.2.59)

and α

Cα2 =

ln (10) 10 20 ⋅ α 20 1 − 10 20

2

.

(8.2.60)

In (8.2.59) Δf is the instrumentation uncertainty of frequency reading, while ΔBW (α ) is the bandwidth uncertainty caused by the inaccuracy of the amplitude reading.

S21e

S21w BW fo Fig. 8.2.18 The transmission curve

8.2 Resonant Techniques

313

For the bandwidth measured between 3 dB points and insertion loss expressed in decibels the bandwidth uncertainty is defined as (Kaifez et al. 1999):

ΔBW (α ) = 0.23 BW ⋅ Δα .

(8.2.61)

The measurement uncertainty Δα has three different contributors:

(Δα )2 = (Δα 1 )2 + (Δα 2 )2 + (Δα 3 )2 ,

(8.2.62)

where Δα 1 is due to instrument limitations, Δα 2 is due to unequal coupling and Δα 3 is caused by coupling losses. As it is shown in Fig. 8.2.19, for tightly coupled cavities (small insertion loss α), Cα grows rapidly and may exceed unity. For Cα > 1 , and an insertion loss uncertainty Δα = 0.1dB (8.2.58) leads to larger than 10% uncertainties in Q-factor. This is the reason why the tightly coupled cavities are not well suited for transmission type measurements of Q-factor. 2

C

α

1.5

1

0.5

0 -5

-4

-3

-2

α(dB)

-1

0

Fig. 8.2.19 Factor Cα to be used in (8.2.58)

As it was mentioned, the Eq. 8.2.56 is valid for the cavities with the identical input and output couplings k 1 and k 2 which is difficult to achieve in practice. The error due to unequal input and output coupling coefficient is given by: ⎛2 r ⎞ ⎟, Δα 2 (dB ) = 20 log⎜ ⎜1+ r ⎟ ⎝ ⎠

r = k2

k1

.

(8.2.63)

(8.2.64)

There is no additional insertion loss error, i.e. Δα 2 = 0 where the couplings are identical. However, if the output coupling coefficient is 35% larger, the contribution of Δα 2 into loss uncertainty budget is Δα 2 ≈ 0.1dB .

314

8 Measurements of the Dielectric Properties

The coupling losses (resistive loss of loops, probes etc.) are modeled using a resistance R s in series with the external load Rc . The uncertainty due to coupling losses is: ⎛ R 1+ k ⎞ ⎟ Δα 3 (dB ) = −20 log⎜⎜1 + 2 s ⋅ Rc 1 + 2k ⎟⎠ ⎝

(8.2.65)

For 1% of the total power dissipated in each of the input and output coupling circuits, the uncertainty in Q0 caused by such coupling loss is Δα 3 = 0.09 dB . In summary two conditions are essential for accurate measurements of the unloaded Q-factor (Kaifez et al. 1999): • the input and output couplings should be well balanced so that similar return loss is obtained for both ports of the VNA; • the measurement must be done under small coupling. Provided the above two conditions are fulfilled, the typical uncertainty of Q-factor in transmission-type measurements is ∼1%. 8.2.9.2 Reflection Type Measurements

An uncertainty analysis for Q-factor using reflection-type measurements is developed by Deleniv et al. (Deleniv et al. 2008). It is based on the measurement procedure for unloaded Q-factor given in (Ginzton 1957). The equivalent circuit of the measurement set-up is shown in Fig. 8.2.20.

L VNA

Z

K Zin

C R

R1

Fig. 8.2.20 Equivalent circuit of a reflection type microwave resonator. Reprinted with permission form IEEE©2008

The impedance locus in the Smith chart is shown in Fig. 8.2.21. The unloaded Q-factor of the resonator is defined using two half power frequency points corresponding to the intersection of the impedance locus and the circles with the radius

2 passing through the endpoints of the resistive axis. These circles correspond to x = ± r lines in the impedance plane. The amplitude of the reflection coeffi-

8.2 Resonant Techniques

315

cient, Sω0 , at the resonance frequency ω0 , is measured first. It is used to compute ~

the amplitude of the reflection coefficient at half-power points, S H .P . : S H .P . = 1 + 4 ⋅ sin(ξ )2 − 2 ⋅ sin(2ξ ) ,

(8.2.66)

where ⎛

ξ = a tan⎜ 1 − ⎝

~ S (ω 0 ) ~ S (ω 0 )

⎧1 + ⎪ d =⎨ ⎪⎩1 −

d⎞ ⎟, 2⎠

(8.2.67)

d >1

(8.2.68)

d <1

A

Impedance locus

ω δ1

r=x

R =0

ξ

S ω0

S

R =∞

H .P .

δ2

B

d

Fig. 8.2.21 Measured impedance locus in the Smith chart. Reprinted with permission form IEEE©2008

The relative half-power bandwidth RBW is then measured taking two frequency readings ω1 and ω2 at half power points. The unloaded Q-factor is Q=

1 1 , = δ 2 − δ1 RBW

(8.2.69)

where δ is a detuning parameter defined as:

δ=

ω − ω0 . ω0

(8.2.70)

316

8 Measurements of the Dielectric Properties

The worst case uncertainty is calculated assuming that the errors due to both measurements contribute “in phase”: ΔQ =

(

)

dQ ΔRBWω0 + ΔRBWH .P. , dRBW

(8.2.71)

where ΔRBWω0 an ΔRBWH .P. are the relative bandwidth errors due to uncertainty of the reflection loss measured at the resonance frequency Δρω0 and at half-power points Δρ H .P . respectively. In Fig. 8.2.21 these uncertainties are visualized by the small shaded circles delimiting the possible locations of the useful signals. The errors due to inaccurate frequency readings are neglected. The formula for the Q-factor uncertainty is derived as: ⎛ Δρ ⎞ Δρ H .P ω0 ⎜ ⎟ 1 + tan(ξ )2 =⎜ + , ⎟ Q ⎜ 1 + tan(ξ )2 cos(ξ ) − sin(ξ ) ⎟ 2 tan(ξ ) ⎝ ⎠

ΔQ

(8.2.72)

where Δρω 0 and Δρ H .P. are the residual systematic uncertainties. They depend on the magnitude of the reflection coefficient at the frequencies of the interest. The above uncertainties are specific for the chosen calibration technique and accuracy of the used calibration standards. The uncertainty of the reflection type measurements of Q-factor in the frequency band 2–20 GHz is shown in Fig. 8.2.22. It is computed for HP85107B VNA (Option 005) using the uncertainty data provided by Agilent Technologies (2006). The smallest worst case uncertainty ( ∼2%) is achieved using a coupling close to the critical, i.e. k ≈ 1 . The above estimation is derived assuming coherent (“in phase”) effect of the measurement errors. Hence, smaller values (∼1%) are expected in practice. 0.08

ΔQ/Q

0.06

0.04

0.02

0 0.1

1

Coupling coefficient, k

10

Fig. 8.2.22 Worst case uncertainty for the resonators with high-Q-factor

8.3 Broadband Techniques

317

8.3 Broadband Techniques 8.3.1 Transmission/Reflection Method. Bulk Samples in Waveguides For the transmission/reflection measurement a section of a transmission line is partly or completely filled by ferroelectric material. The method discussed in this section is based on Nicolson-Ross-Weir (NRW) procedure (Nicolson and Ross 1970, Weir 1974). The explicit equations for the dielectric permittivity and permeability are derived from the measured scattering parameters. For low loss materials, however, the method diverges at frequencies corresponding to integer multiples of one half wavelength in the sample. Different approaches have been proposed to eliminate these instabilities using electrically thin samples and iterative processing procedures (Barker-Jarvis et al. 1990). In this section, however, the formulation proposed by Boughriet et al. (1997) is discussed which resolves the instability of NRW procedure. A transmission line/waveguide section filled by ferroelectric material is shown in Fig. 8.3.1. L1

L1

L

E Inc. Port 1

E Re fl .

ETrans .

Port 2

Fig. 8.3.1 Transmission line section including ferroelectric MUT

The procedure initially proposed by Nicolson and Ross (1970) and Weir (1974) is deduced from the following equations:

(

)

(8.3.1)

(

)

(8.3.2)

S11 =

Γ 1−T 2 , 1 − Γ 2T 2

S 21 =

T 1 − Γ2 , 1 − Γ 2T 2

Γ=

Z − Z0 , Z + Z0

T = exp(− γL ) ,

(8.3.3) (8.3.4)

318

8 Measurements of the Dielectric Properties

γ = j

2π

λ0

γ0 = j

Z=

Z0 =

2

⎛λ ⎞ ε r μ r − ⎜⎜ 0 ⎟⎟ , ⎝ λc ⎠

2π

λ0

⎛λ 1 − ⎜⎜ 0 ⎝ λc

jωμ 0 μ r

γ

jωμ 0

γ0

2

⎞ ⎟⎟ , ⎠

,

(8.3.5)

(8.3.6)

(8.3.7)

.

(8.3.8)

where S11 and S 21 are the reflection and transmission scattering coefficients, Γ is the first reflection coefficient (i.e. reflection coefficient from the left MUT interface (Fig. 8.3.1) assuming that its length is infinite) and T is the transmission coefficients between the faces of the MUT, γ 0 , Z 0 , and γ , Z holds for the propagation constant and the impedance of the empty and filled sections of the waveguide respectively, λ0 and λc correspond to the free-space and the cutoff wavelength, ε r and μ r are the real permittivity and the permeability of the MUT. The Eqs. 8.3.5–8.3.8 are specific for the rectangular waveguide and should be replaced by appropriate expressions if the procedure is to be extended for the lines with TEM mode. Following Boughriet et al. (1997) the dielectric permittivity ε r and the permeability μ r of the sample are obtained in two steps. First, the effective quantities, ε e and μ e are calculated from the measured S-parameters: K=

2 2 S11 − S 21 +1 , 2 S11

Γ = K ± K 2 −1 , T=

2 2 S11 + S 21 −Γ , 1 − (S11 + S 21 )Γ

(8.3.9)

(8.3.10) (8.3.11)

2

1 ⎤ ⎡ j =⎢ ln (T )⎥ , 2 Λ ⎦ ⎣ 2πL

(8.3.12)

8.3 Broadband Techniques

319

εe =

λ0 g ⎛ 1 − Γ ⎞

μe =

⎜ ⎟, Λ ⎝1+ Γ ⎠

(8.3.13)

λ0 g ⎛ 1 + Γ ⎞

⎜ ⎟, Λ ⎝1− Γ ⎠

(8.3.14)

with 1

λ0 g =

(1 ) − (1 λ ) λ20

2 c

.

(8.3.15)

In (8.3.10) the sign is chosen so that Γ ≤ 1 . The Eqs. 8.3.9–8.3.12 are borrowed from the original NRW procedure, while ε e and μ e , as given by (8.3.13) and (8.3.14), are introduced by Boughriet et al. (1997). These effective parameters presuppose a TEM propagation mode and are determined from the first reflection Γ and the transmission T coefficients respectively: Γ=

(μe (μe

εe ) −1

(8.3.16)

εe ) +1

⎛ 2π T = exp⎜ − j ⎜ λ 0g ⎝

⎞ ⎟ ⎠

μ eε e L ⎟

(8.3.17)

The dielectric permittivity of the MUT is found from the following identities:

γ = γ 0 ε eμ f , Z = Z0

(8.3.18)

μe , εe

(8.3.19)

where γ and Z are defined by (8.3.5) and (8.3.7). For a ferroelectric material μ r = μ e = 1 , hence the dielectric permittivity is defined as:

( (

))(

) (

ε r = 1 − λ20 λ2c λ20 g Λ2 + λ20 λ2c

)

(8.3.20)

As compared to the original NRW procedure, the final expression for the dielectric permittivity does not contain the term [(1 − Γ ) (1 + Γ )] . This is shown to be responsible for instability of the original NRW procedure. It is eliminated in the approach discussed by Boughriet et al. (1997).

320

8 Measurements of the Dielectric Properties

Notice the ambiguity of (8.3.12), which has an infinite number of roots: ln (T ) = T + jϕ ± j 2πn ,

(8.3.21)

with n being an integer and ϕ = Im(−γL ) is the phase of T in radians. In practice the phase measurements are limited by −π < ϕ ≤ π , i.e. the phase of the propagation factor T does not change when the length of the sample is increased by a multiple of wavelength. For the lines with TEM-mode the phase can be resolved unambiguously. This requires measurement at low frequencies, where the phase approaches zero and a solid “reference” can be established. Unwrapping of the measured phase is illustrated in Fig. 8.3.2, where the proper shifting ( 2πn ) is applied to each section of the curve delimited by the phase jumps. ϕ

π ω

0 -π

2π 4π

Measured Unwrapped phase

Fig. 8.3.2 An illustration to phase wrapping in measurement systems

The discussed above unwrapping procedure, however, can not be applied to hallow/rectangular waveguide measurement, since the measurement is limited to the frequencies above waveguide cut off. In this case, the phase ambiguity can be resolved by finding a solution for ε r that produces the value of group delay identical to the measured one (Weir 1974). The latter is defined from the slope of the phase of the propagation factor versus frequency: τg = −

1 dϕ 2π df

(8.3.22)

For each n-th solution of ε r the group delay can also be computed.

τ gn = L

d df

12

⎡ε 1 ⎤ ⎢ r − ⎥ 2 2 ⎣⎢ λ0 λc ⎥⎦ n

(8.3.23)

8.3 Broadband Techniques

321

The correct solution, n = k , is found when τ gk − τ g ≈ 0 .

(8.3.24)

It seems important to mention the problem of the air gap where hollow waveguides are used in the measurements. Even though the MUT is machined to completely fill the cross-section of the rectangular waveguide, in practice the air gaps are unavoidable. These may cause large errors while measuring the material with high dielectric permittivity (Champlin and Glover 1966). For ferroelectrics, even a gap of a few microns in the millimeter wave range causes large errors in measurements of the dielectric parameters. Therefore, the sample should be electroded with sputtered gold or coated with silver around the faces of flange contact (Grigas 1996).

8.3.2 Film Measurements Using Coplanar Waveguide (CPW) 8.3.2.1 Permittivity and Loss Tangent

The discussed in the previous section broad-band transmission type measurements can be adopted for characterization of thin/thick ferroelectric films using planar lines. The cross-section of a CPW with a ferroelectric film is shown in Fig. 8.3.3. Simple close form formulas for a two layer substrate CPW is given in Chap. 7. For convenience, some of the formulas are reproduced here. The purpose of the measurement is to obtain a complex propagation constant γ which is then translated into the dielectric permittivity and loss factor of the ferroelectric layer. With the complex propagation constant of CPW available, the effective dielectric permittivity of CPW is calculated using:

εe =

β2 k 02

=

Im(γ )2 , k 02

(8.3.25)

where β and k 0 ( rad ⋅ m −1 ) are the wave propagation constants in CPW and free space, respectively. The effective dielectric permittivity (8.3.25) is a combination of those of the air above the CPW, the ferroelectric film and the substrate material. Using the measured εe and the sizes of the CPW, the permittivity of the ferroelectric film may be calculated from (7.2.41):

ε2 =

[ε e − 1 − q1 (ε 1 − 1) + q 2ε 1 ] q2

(8.3.26)

322

8 Measurements of the Dielectric Properties

2s

g h2

g

h1

ε2 ε1

Fig. 8.3.3 Cross-section of a CPW on two-layered substrate

In (8.3.26) q1 and q2 are the dielectric filling factors of the substrate and ferroelectric film (7.2.42) respectively. The dielectric loss tangent tan δ1 of the ferroelectric film is retrieved from the measured attenuation constant α : α = α d + α c = Re(γ ) ,

α=

β 2Q

=

β 2

(tan δ d + tan δ c ) ,

(8.3.27) (8.3.28)

where α d (c ) ( Np ⋅ m −1 ) is the attenuation constant due to dielectric(electrode) and tan δ d (c ) is the effective loss tangent of the two-layered substrate (electrodes). To obtain the electrode loss α c one needs an additional measurement of a CPW on a blank substrate. This is a perturbation approach that puts some limitations on CPW`s geometry (discussed later). The contribution of a two-layered dielectric substrate into loss budget ( tan δ d ) is fixed by the following formula: tan δ d = k1 tan δ1 + k2 tan δ 2 ,

(8.3.29)

where k1 and k2 are the inclusion rates of the substrate and the ferroelectric film respectively. The inclusion rate holds for the fraction of electric field energy confined in specific layer. In the static limit ki for the i-th layer is equal to the normalized capacitance of this layer: ki =

Ci C

(8.3.30)

where C is the per unit length capacitance of CPW line. The latter is defined as a sum of the partial capacitances of the substrate layers. It can be shown that the inclusion rates ki and the dielectric filling factors qi are inter-related via the following identities: k1 =

ε1 (q1 − q2 ) , εe

(8.3.31)

8.3 Broadband Techniques

323

k2 =

ε 2 q2 . εe

(8.3.32)

The Eqs. 8.3.31–8.3.32 are sufficient for extraction of the loss tangent, tan δ 2 of the ferroelectric film. 8.3.2.2 The Sensitivity of the Loss Measurements

It follows from (8.3.27) that the electrode loss is the main factor limiting the utility of the method. Indeed, it is very difficult to expect accurate measurements of substrate loss for α c >> α d . For this reason superconductor electrodes are often preferred. For the electrodes made of normal metals, the conductor loss tangent is typically limited to tan δ c ≥ 0.01 ÷ 0.02 . Therefore, to obtain accurate data for the substrate loss, its part in the loss budget must be at least comparable with that of the electrode loss. The electrode loss in CPW with ferroelectric film is estimated by measuring an identical line on a blank substrate (without ferroelectric film). This perturbation method under certain conditions looses its accuracy since the ferroelectric film has strong impact on the current distribution in the electrodes (Carlsson and Gevorgian 1997). It is therefore important to ensure that the geometry of the CPW chosen for measurements does not alter it significantly. To verify this, preliminary simulations are required for the chosen CPW geometry using an estimated permittivity for the ferroelectric film. It follows from (8.3.29) that the other two factors affecting the accuracy of dielectric loss tangent measurements are the loss of the substrate ( tan δ 1 ) and the filling factor of the ferroelectric layer q 2 . Hence, to achieve better accuracy, the following conditions should be fulfilled: • use low-loss substrate (LaAl2O3, MgO, Al2O3, etc), so its contribution does not screen the loss of the ferroelectric film; • use CPW with high dielectric filling factor of the ferroelectric film, q2 , which requires narrow slots (comparable to the film thickness), signal electrode and/or thicker films.

While using narrower slots/signal electrode, the estimation of conductor loss looses its accuracy (discussed above). It is, therefore, important to keep a reasonable balance between the high filling factor q 2 (this defines the part of the ferroelectric film in the loss budget) and accurate measurement of conductor loss using the perturbation approach. The properties of the ferroelectric film can also be studied under DC bias using bias tees. It is, however, noted that application of the constant voltage produces uneven change in permittivity due to inhomogeneous field distribution in ferroelectric film. Hence, a nonlinear problem should be solved to correctly extract the values of field dependent permittivity and loss tangent.

324

8 Measurements of the Dielectric Properties

8.3.2.3 Measurement Procedure

Typically for the on-wafer measurements the CPW is provided with pads. The sizes of the pads are dictated by the pitch size of the microprobes. Matching a narrow CPW to wide probing pads requires use of tapers, which may lead to serious errors if they are not properly compensated. One of the methods allowing removal of their effect uses so-called TRL (thru-reflection-line) calibration (Engen and Hoer 1979, Rubin 1990). The calibration standards required for measurements are shown in Fig. 8.3.4. The reference plane (R) is in the middle of the thru standard consisting of two identical tapers A and B (Fig. 8.3.4 (a)). The distance between the tapers should be long, so that their fringing fields do not reach the reference plane R. The “reflection” standards are identical for both ports (Fig. 8.3.4 (b)). These are typically realized by removing equal sections from both sides of the reference position. In Fig. 8.3.4 (c) the “line” standard with the length L is shown. This method for measurement of the thin ferroelectric film was first demonstrated byLue and Tseng (2001) where all three standards where used to calculate the complex propagation constant and impedance of the CPW. The knowledge of the complex propagation constant is sufficient to retrieve the dielectric permittivity and the loss tangent. This can be accomplished by measuring only the thru” and “line” standards shown in Fig. 8.3.4 (a) and Fig. 8.3.4 (c) respectively. It is supposed that before measurements the VNA is calibrated using standard SOLT (short-open-loadthru) procedure. The description of this simplified procedure (Engen and Hoer 1979, Rubin, 1990) is given in the Appendix G. It is, however, noted that retrieval of the CPW impedance with the above procedure is impossible.

A

A

B

R

B

(a) A

(b) L

B

(c)

Fig. 8.3.4 The standards for TRL calibration

8.3 Broadband Techniques

325

8.3.3 Film Measurements Using Coupled Microstrip Lines In the case of thick films the tuning DC bias voltages are quite high, up to several hundred volts. Using external bias tees and microprobes for the measurements requires development of the special setups in order to avoid damaging the microprobes. Coupled microstrip lines (Fig. 8.3.5) may be used for microwave characterization of thick ferroelectric films. In this case the ferroelectric film with the thickness h (typically h ≥ 25 μm ) is used as the substrate; therefore the line is extremely sensitive to the film parameters. The coupled lines support even and odd modes with respectively magnetic and electric walls in the symmetry plane. For on-wafer microprobe measurements one uses the odd mode excited with a pair of signal-ground (SG) and ground-signal (GS) microprobes (Fig. 8.3.6). In the measurement set-up (Deleniv et al. 2003) the signal (S) and ground (G) electrodes of both microprobes are under the same DC potential (“grounded”), since they are connected via bias tee and strips of the coupled microstrip lines. The “+” potential of the DC bias is applied to the ground plane using a via as shown in Fig. 8.3.6. Hence, no high voltage is applied between the tips of the microprobes. The only factor limiting the applied DC voltage is dielectric strength of the ferroelectric film. This makes the structure well suited for studying thick film parameters under high DC bias fields. Additionally, there is no risk to damage the VNA in the case of DC voltage breakdown in the ferroelectric film. sw

h 2g

ws

h

ε1 Ground plane

Fig. 8.3.5 Cross-section of the coupled microstrip lines l

2g

s

S G

s

G

Microprobe

Microprobe

S

Via to the ground plane

Bias tee

Bias tee

Rlim VDC

VNA Port1

VNA Port2

Fig. 8.3.6 Layout of the test structure and the measurement set-up. Reprinted with permission form EuMA©2003

326

8 Measurements of the Dielectric Properties

However, using the discussed method has a drawback. Since the ferroelectric films have high dielectric permittivity ( ε 1 = 100 ÷ 1000 ) it results in a low impedance of the guided mode and, as consequence, high electrode losses. This limits the sensitivity of the measurements with respect the ferroelectric film loss.

8.3.4 Measurements Using Test Varactors Coplanar plate capacitors (especially IDC) are the most common structures used for microwave and low frequency characterization of the ferroelectric films. 8.3.4.1 Reflection Measurements Using Interdigital and Straight Gap Varactors

IDC and straight gap capacitors are used for in plane dielectric characterization of the ferroelectric films deposited on dielectric substrates. Closed form formulas for calculating the permittivity and loss tangent of a ferroelectric film, using the measured complex admittance of a test interdigital capacitor incorporating a ferroelectric film of a given thickness, is provided by Gevorgian et al. (1996). Particularly, using the measured capacitance, the thickness of all substrate layers, including the ferroelectric film and the permittivity of the substrate, the permittivity of the measured ferroelectric film may be calculated using (7.3.19) and (7.3.20). First the measured capacitance is used to calculate the effective permittivity (εe3) using (7.3.19), and then εe3 is used in (7.3.20) to calculate the permittivity ε2 of the film. The IDC is a useful tool for low frequency (in MHz range) and microwave measurements in low GHz range, i.e. well below self resonant frequency. Its application at elevated microwave frequencies is limited by self resonant frequency associated with the parasitic inductance of the “fingers”. For these measurements a coplanar-plate capacitor with a straight gap (Fig. 7.3.1) is more suitable. The dielectric permittivity and the loss tangent of the ferroelectric films may be estimated using (7.3.17) and (7.3.18) correspondingly, provided that the thicknesses of all substrate layers (including the ferroelectric film) and the permittivity of all other layers are given. 8.3.4.2 Reflection Measurements Using Coplanar-Plate Test Capacitors with Annular Slot

The coplanar-plate test capacitors with the annular gaps shown in Fig. 8.3.7 are widely used for microwave and low frequency in-plane and out-of plane characterization of the ferroelectric films. For in-plane measurements the ferroelectric film is deposited directly on the substrate without bottom plate shown in

8.3 Broadband Techniques

327

Fig. 8.3.7. In this case (corresponding to the films in coplanar-plate varactors) the width of the annular gap has to be rather small. This structure is used in Sect. 8.2.6 (see Appendix F). For out-off plane dielectric characterization the ferroelectric films are deposited on a bottom electrode, as shown in Fig. 8.3.7 (a). This corresponds to using the films in parallel-plate varactors. In this case the circular patch with a diameter d forms a parallel-plate capacitor (C) with the bottom electrode (plate). The top outer electrode, with inner diameter D and the bottom electrode (ground plane) form another parallel-plate capacitor (Cg). This test structure, originally proposed by Ma et al. (1998) does not require etching the ferroelectric film to open the bottom electrode (ground plane) for contacting (Rundqvist et al. 2004) and uses only one step lift-off process to fabricate. A coplanar G-S-G microprobe is used to measure the impedance between the central circular patch (S) and top outer electrode (“Ground plane”). The equivalent circuit of the test structure is shown in Fig. 8.3.7 (b). The capacitors C and Cg are connected in series and r represents the resistance of the top and bottom plates and the resistance of the bottom ground plane under the annular gap. To simplify the measurements, the area of the top outer electrode is set to be much larger, i.e. Cg>>C, which results in an even simpler equivalent circuit shown in Fig. 8.3.7 (c). S

(a)

Annular gap between top coplanar electrodes

G

C

(b) Cg

r Cg>>C

D d

(c)

Ferroelectric film, thickness t

S

Bottom plate

Substrate

G

C r

Fig. 8.3.7 Coplanar-plate test capacitor with annular gap (a) and its equivalent circuits (b, c)

The measured complex impedance, Z = r–j/ωC, is used to calculate the permittivity and the loss tangent of the ferroelectric film. As a first approximation the permittivity of the ferroelectric is:

ε=

4Ct

ε o πd 2

,

(8.3.33)

328

8 Measurements of the Dielectric Properties

where C is the measured capacitance, and t is the thickness of the ferroelectric film. The loss tangent of the varactor is given by: tan δ eff = tan δσ + tan δ f = rωC + tan δ f ,

(8.3.34)

where tan δσ is the effective loss tangent of the electrodes (r is resistance of the electrodes), while tan δ f is an intrinsic loss tangent of the ferroelectric film. For the considered structure the resistance of the electrodes can be estimated using the formula: r=

⎞ Rs ⎛ 1 ⎛D⎞ ⎜ + ln⎜ ⎟ + Router ⎟⎟ 2π ⎜⎝ 4 ⎝d⎠ ⎠

(8.3.35)

In (8.3.35) Router holds for the resistance of the outer electrode which can not be defined analytically. Typically the resistance Router of the outer electrode is small and for D d ≈ 1.5 one can estimate the resistance of the varactor electrodes as: r=

Rs ⎛ 1 ⎛ D ⎞⎞ ⎜ + ln⎜ ⎟ ⎟⎟ 2π ⎜⎝ 4 ⎝ d ⎠⎠

(8.3.36)

In measurements the probe-electrode contact resistance may be comparable or even larger than the series resistance of the plates (electrodes). Thus care should be taken to estimate and remove (de-embed) it from measured results otherwise the loss tangent of the film may appear higher than it is in reality. 8.3.4.3 Transmission Type Measurements of Test Varactors

The two port measurements techniques are often claimed to be more accurate as compared to the reflection type measurements. Zhu et al. (2005) proposed a two port measurement technique that uses a CPW test structures for measurement of ferroelectric film parameters in parallel-plate varactors. In this experiment the test varactor is monolithically integrated in the gap of a CPW test structure (Fig. 8.3.8 (a)) and two additional CPWs with identical pad/taper sections and different lengths of the regular lines (Fig. 8.3.8 (b and c)) are used for deembedding the parameters of the ferroelectric film. Simple equivalent circuits consisting of lossy inductors (Fig. 8.3.9) in combination with measured ABCD matrix are used to facilitate the extraction of the film parameters. For short lengths (relative to wavelength) and low frequencies these equivalent circuits provide a reasonable accuracy. To increase the accuracy, especially at higher frequencies, more advanced circuit models and/or numerical treatment of the measured S-parameters (ABCD matrix) should be considered.

8.3 Broadband Techniques

329

a3

a1

a2

a1

(a)

a2

2 a1 + 2 a2 + a3

2 a1 + a3

(b)

(c)

Fig. 8.3.8 Test CPW (ground planes are not shown) structure including the varactor (a) and additional CPW (b, c) used for de-embedding. Reprinted with permission from IEEE©2005

Fig. 8.3.9 Equivalent lumped element circuits of the CPW structures shown in Fig. 8.3.8. Reprinted with permission from IEEE©2005

8.3.4.4 Accuracy Analysis

The discussed above reflection and transmission measurements of test varactors are two commonly used broadband measurement techniques. A generalized uncertainty analysis of the reflection and transmission measurements is developed by

330

8 Measurements of the Dielectric Properties

Deleniv and Gevorgian (2006). This analysis considers the worst case uncertainty scenarios where all error contributors are added “in phase”. In reality one should examine their effect independent of each other. In general, the accuracy of these measurements may be insufficient when it comes to high-Q (>100) varactors. Furthermore, one should remember that the discussed uncertainties result from systematic calibration residuals and are repeatable for a fixed measurement set-up and the test structure. Removal of the measurement uncertainties would be possible using a standard with known losses and the capacitance-identical to that of the test capacitor. In practice it is sufficient to use a high Q-factor standard based on low loss dielectrics (MgO, LaAl2O3, etc.) with the capacitance that matches that of the test capacitor within ±10–15%. This allows significant improvement in the measurement accuracy of the thin film parameters.

8.4 Nonlinear Measurements of Ferroelectrics Ferroelectrics are nonlinear dielectrics. Tunable devices, such as phase shifters, delay lines etc., use ferroelectrics in small signal regime, i.e. the tuning (changes) in permittivity is caused only by the applied DC field. The microwave signal is small. In other words the dynamic nonlinearity is low and it does not cause generation of the additional spectral components. As the amplitude of the microwave signal grows it changes the permittivity resulting in generation of the additional spectral components with substantial powers. This effect limits the use of the device below a certain level of input powers and may also reduce the dynamic range of the whole system. On the other hand the dynamic nonlinearity may be used for frequency conversion (i.e. multipliers and harmonic generators), pulse shaping, soliton generation, etc. (see Sect. 5.7). Thus, for applications in linear devices (e.g. phase shifter, filter) the dynamic nonlinearity has to be lower than a specified level, while for nonlinear applications it has to be as high as possible. For these applications the nonlinear properties of the ferroelectric devices should be properly quantified. The harmonic balance analysis or another equivalent technique is a way to quantify the nonlinear performance of a component. As the input, the harmonic balance requires the C-V dependence of ferroelectric varactor, which is conveniently measured at low frequencies. Based on this dependence one may predict the performance of the device/component under elevated microwave powers. For the parallel-plate varactors the C-V dependence is identical with ε − E dependence. In the case of the coplanar-plate varactors the microwave field is strongly inhomogeneous and C-V dependence should be measured separately for two varactors with different gap sizes. Direct measurements of the harmonic and/or intermodulation distortions (IMD) are alternative way used for assessment of the nonlinearities. A simple measurement set-up for IMD measurements is shown in Fig. 8.4.1. The signals from two

8.4 Nonlinear Measurements of Ferroelectrics

331

sources with the close frequencies ω1 and ω 2 = ω1 ± Δω are combined and applied to the DUT. The DUT may be a single varactor or a section of a transmission line (Kozyrev et al. 1998, Kozyrev et al. 2000, Findikoglu et al. 2002). The output signal consists of a number of intermodulation products measured using a spectrum analyzer (SA). ω1

∼ ω2

DUT

SA

∼ Fig. 8.4.1 A set-up for IMD measurements

Fig. 8.4.2 2-port test structure including a parallel-plate varactor

An example of a DUT used in measurements is shown in Fig. 8.4.2. It comprises a section of CPW with thin film parallel-plate ferroelectric varactor in the central signal strip (Deleniv et al. 2007). The thickness of the Ba0.25Sr0.75TiO3 film is 0.56 μm. It is sandwiched between top and bottom Pt/Au plates. Shown in Fig. 8.4.3 are the results of the measurements. In the case of harmonic generation a CW microwave signal at frequency 6.8 GHz is applied directly to the input of the DUT and the output at 20.4 GHz (Fig. 8.4.3 (a)) measured using a spectrum analyzer. To measure the intermodulation distortion two CW signals at frequencies 6.8 GHz and 6.85 GHz are applied to the DUT as shown in Fig. 8.4.1. The measured output power at frequency 6.75 GHz is shown in Fig. 8.4.3 (b). As already mentioned, the microwave field in a parallel-plate varactor is highly homogeneous, which implies that the measurements are useful not only for assessment of the varactor performance (i.e. power handling capability, etc.), but also for the ferroelectric film. A comparison of the measured third order harmonic and intermodu-

332

8 Measurements of the Dielectric Properties

lation distortion and data predicted by harmonic balance using low frequency C-V dependence are shown in Fig. 8.4.3. The good agreement of experimental and simulated (harmonic balance, HB) data demonstrates the utility of quasi-static C-V dependence. 20

40

P P

1out

1out

HB simul. using C-V

0

P1out, P3out , dBm

20

0 HB simul. using C-V

-20

-20

-40

-40

P 3out

-80

P3out

-60

-60

5

10

P

15 1inc

20 , dBm

25

30

-80

0

(a)

5

10 P1inc, dBm

15

20

(b)

Fig. 8.4.3 Comparison of measured third order harmonic (a) and intermodulation products (b) with simulations based on the measured static C-V dependence of the ferroelectric varactor. Reprinted with permission form IEEE©2007

For most the systems the third order harmonic generation is of special concern. The system applications set the limits of the power levels for the higher order harmonics. In Fig. 8.4.3 the 3rd order intercept point is at about 40dBm. As it is shown in Sect. 4.7 the power level of the higher order harmonics may be decreased either by increasing the thickness of the ferroelectric film (gapwidth in the coplanar-plate devices) or/and by cascading varactors in a special way where the required DC voltages are kept low.

8.5 Switching Time of Ferroelectric Films The measurements of the 3rd order harmonics discussed in the previous section is an indirect way for estimation of the tuning speed of a ferroelectric device. The results shown in Fig. 8.4.3 indicate that the permittivity is being changes at subnanosecond speed.

8.5 Switching Time of Ferroelectric Films

1

(a)

(b)

2

2

3

333

4

Fig. 8.5.1 Simplified layout of the microstrip resonator (a) and changes in the amplitudefrequency characteristic under an applied DC voltage pulse (b). 1-microstrip resonator, 2-lowpass filters, 3-control pulse, 4-connection point for the varactor, ΔS21-change in the transmission coefficient at fixed microwave frequency ( f s )

A direct procedure for measurement of the response time of the permittivity of a ferroelectric film is developed by Kozyrev et al. (1998). In this work the measurement is done using a resonator arrangement shown in Fig. 8.5.1. The thin ferroelectric film capacitor is in the gap of the microstrip resonator close to its shorted end. The other end of the microstrip resonator is not loaded. A train of the voltage pulses is supplied to the varactor via low-pass filters with the cut-off frequency ∼2 GHz. It is important to keep the cut off frequency relatively high so the shape of the driving pulses is not distorted. To avoid loading of the microstrip resonator, the low pass filters are connected at the points, where the microwave electric field is minimum. Under the applied DC control voltage, the capacitance of the varactor changes, and so does the resonance frequency: ⎛ ω0 ε e ⎞ le ⎟ , ⎜ c ⎟ ⎝ ⎠

ω 0 Z 0 C (Vb ) = tan⎜

(8.5.1)

where Z 0 and ε e are the wave impedance and the effective permittivity of the microstrip line, l e is the effective length of the microstrip resonator, and c = 3 × 10 8 m/s is the velocity of light.

The shift of the resonance frequency leads to change in the transmission coefficient (ΔS21) at the fixed frequency (Fig. 8.5.1 (b)). A comparison of the applied voltage pulse and the detected microwave response reveal the tuning speed of the cavity including the varactor. As it follows from the signal form shown in Fig. 8.5.2 (b) the response time of SrTiO3 can not be measured since it is smaller than the rise time of the applied pulse (∼30 ns). However, two different relaxation mechanisms are detected for the

334

8 Measurements of the Dielectric Properties

(Ba,Sr)TiO3 varactors (Fig. 8.5.2 (c)). A fast variation in the permittivity over a time less than the rise time of the control pulse and a slower variation with a response time of the order of 20μs. The slow relaxation time is detected after the signal drops below 5–10% level of the total pulse amplitude.

Fig. 8.5.2 100μs control pulse (a), pulse shape for SrTiO3 (b) and (Ba,Sr)TiO3 (c) varactors. The scales of the pulse durations of the microwave response for the SrTiO3 and (Ba,Sr)TiO3 varactors are different to reveal the “slow” (∼20μs) relaxation mechanism

8.6 Conclusions For the bulk single crystals and ceramics with the sizes of the MUT much larger than the characteristic lengths (correlation, screening, surface layer etc.) the measured small signal complex dielectric permittivity (without applied DC field) is useful for optimization of the composition and the fabrication processes. It follows from the theory discussed in Chap. 1 that both the loss tangent and the tuneability of a ferroelectric are proportional to the dielectric permittivity. Theoretically, an ideal (intrinsic) ferroelectric with higher dielectric permittivity has both higher tuneability and loss tangent. On the other hand there is a large number of relaxation processes (see Chap. 1) that increase the losses and to some extent reduce the tuneability. For a given composition the intensity of these processes and their effect on the losses, permittivity and tuneability depend on the fabrication/processing conditions. The resonant measurements without electrodes are useful for establishing correlations between the MUT dielectric properties on one hand and composition,

8.6 Conclusions

335

crystalline structure (e.g. sizes of the grains, doping) and MUT fabrication conditions on the other hand. The OR measurements are recommended for higher microwave and millimeter wave frequencies. The near field scanning microwave microscope is another resonant techniques that is recommended for the dielectric characterization of thin ferroelectric films without electrodes and with high spatial resolution. These measurements also may be used for investigation of the power handling capability of the MUT without electrodes. Measurement of the agility requires electrodes for application of the DC bias. For DC bias dependent microwave measurement of a bulk ferroelectric material the disk resonator method, with HTS and normal metal plates, may be recommended. The disk resonator method is rather simple though it requires very high voltages to reach reasonably high fields and tunings. Sometime these measurements are limited by breakdown voltages. The on-wafer measurement, using resonant microprobes, is a unique way for the accurate characterization of the dielectric properties of the thin ferroelectric films under applied DC filed. The highest Q-factor that may be measured using this method is limited by the low Q-factor of resonant microprobe. However, it is useful for practical ferroelectric films and varactors. Although the resonant methods provide higher accuracy (in comparison with the broadband methods) they are more complex/time consuming when it comes to measurements in a wide frequency band. The test varactors and sections of the transmission lines (CPW, CPS etc.) are most used in broadband measurement techniques. These techniques are relatively simple but require special care in selecting the designs of the test structures (capacitance of the test varactor, transmission line cross section and DC biasing network etc.) for the frequency band of interest to ensure highest possible accuracy of the measurements. Distinguishing between the losses in the plates and in the ferroelectric film is a very complicated, if even possible. A simple way to estimate the dielectric losses is possible by extrapolation procedure proposed by Vorobiev et al. (2007) Apart from the microwave measurements these test structures are widely used for low frequency C-V, I-V and P-V measurements. Typically these measurements are carried out using standard RLC meters, semiconductor device analyzers (or similar) and ferroelectric material/device characterizers. These measurements are rather simple and are not covered in this chapter. The large signal (dynamic nonlinearity) measurements are rather straightforward. Apart form the power handling capability; these measurements also give indirect information about the potential tuning speed. The generation of the third order and intermodulation harmonics at microwave frequencies is a direct indication that the permittivity of the ferroelectric changes at the same speed as the microwave signal. On the other hand the measurement of the response time to the controlling (tuning) pulses show that there are some slow processes, most probably associated with the charged defects (i.e. film quality).

336

8 Measurements of the Dielectric Properties

Appendix E Model of the OR Loaded by a Multilayered Plate The cross-section of the loaded resonator is given in Fig. E.1. Each of the i = 1… m + 1 layer is characterized by thickness hi and refractive index ni . This resonator is analyzed using the variational “mixed-field” formula for the resonant frequency (Rumsey 1954, Harrington 1961):

ωres = j

∫ (E ⋅ ∇ × H + H ⋅ ∇ × E )dv + ∫ nˆ ⋅ E × Hds

V

S

∫ (μH ⋅ H − ε rε 0 E ⋅ E )dv

.

(E.1)

V

By splitting the volume of the resonator into i partial volumes and introducing m + 1 surfaces between the dielectric layers (E.1) may be rewritten in a more convenient form: ωres =

I1 + I 2 + I 3 J

(E.2)

with I1 = j

m +1

∑ ∫ (E ⋅ ∇ × H i

i

)

+ H i ⋅ ∇ × E i dv ,

i =1 Vi

∑ ∫ nˆ ⋅ (E × H m

I2 = j

i

i

i +1

)

− E i + 1 × H i ds ,

i =1 S i

I 3 = − j ∫ nˆ ⋅ E m + 1 × H m + 1ds ,

(E.3)

(E.4)

(E.5)

S m +1

J =

m +1

∑ ∫ (μH i =1 V p

i

)

⋅ H i − ε ri ε 0 E i ⋅ E i dv .

(E.6)

The surface integrals (E.4) are added to the original formula to support the discontinuous trial fields at each interface of the multilayered dielectric stack. The first order matching of the electric and magnetic fields at the interfaces delimiting the layers is accomplished first. Consider a traveling beam wave incident

Appendix E

337

on the dielectric stack. In general, for the i − th layer the beam wave form can be written, using the standard notations:

ψi =

⎛ ρ2 ⎞ ⎛ ⎞ jn kρ 2 + jΦ i ⎟ exp⎜ − 2 ⎟ exp⎜ − jni kz − i ⎜ ⎟ ⎜ ⎟ wi 2 Ri ⎝ wi ⎠ ⎝ ⎠

w0(i )

(E.7)

where ρ ( ρ 2 = x 2 + y 2 ) is the transverse distance from the beam axe, and ⎫ ⎪ ⎪ wi2 (z ) = w02(i ) ⎛⎜ 1 + (z − zi )2 z02(i ) ni2 ⎞⎟⎪ ⎝ ⎠⎬ Ri (z ) = z − zi + z02(i )ni2 (z − zi ) ⎪ ⎪ Φ i (z ) = arctan (z − zi ) z0 (i ) ni ⎪⎭ z0 (i ) = kw02(i ) 2

(

(E.8)

)

Here, z i and w0 (i ) denote the coordinate of the beam waist and its radius, respectively, and k = ω c . The first order matching of the fields across the interfaces is done in two steps. The matching of the radial variation of amplitude and phase requires ⎞ ⎫ ⎛ i ⎞ ⎛ i wi ⎜ h p ⎟ = wi +1 ⎜ h p ⎟ ⎪ ⎟ ⎪ ⎜ ⎟ ⎜ ⎝ p =1 ⎠ ⎪ , i = 1… m . ⎝ p =1 ⎠ (E.9) ⎬ ⎞⎪ ⎛ i ⎞ ⎛ i ni +1Ri ⎜ h p ⎟ = ni Ri +1 ⎜ h p ⎟⎪ ⎟ ⎜ ⎟ ⎜ ⎝ p =1 ⎠⎪⎭ ⎝ p =1 ⎠ (E.9) is satisfied if

∑

∑

∑

∑

w0 = w0 (i ) ≡ z0 = z0 (i ) ⎫ ⎪ ⎛ i ⎞ ⎜ h ⎟(n − n ) + n z ⎪ , i = 1… m p⎟ i i +1 i +1 i ⎬ ⎜ ⎪ p =1 ⎝ ⎠ zi + 1 = ⎪ ni ⎭

∑

(E.10)

which also results in Φ i = Φ i +1 at all interfaces. To calculate z 0 , which is related to scale radius w0 , the equality, Rm +1 (D ) = R0 is used: z0 =

(R0 − D + zm +1 )(D − zm +1 )

,

(E.11)

where R0 is the upper mirror curvature radius. The recursive formula for z i +1 in (E 10) is initialized with z1 = 0 .

338

8 Measurements of the Dielectric Properties

z

nˆ

Sm+1

d D

nm+1

Sm nm m

nm − 1 m −1

S1

∑ hp

n1

h1

∑ hp

p=1

p=1

nˆ Fig. E.1 Cross-section of the open resonator loaded with a multilayered sample. Reprinted with permission form IEEE©2005

Next, general expressions for the E x and H y components of the trial fields for the dielectric layers are defined: E xi (z ) = Ai

H iy (z ) = jAi

⎛ ρ 2 ⎞⎛ ⎞ w0 2 ⎞ ⎛ n kρ 2 +Ψ i ⎟ (E.12a) exp⎜ − 2 ⎟⎜ 1 − 2 2 2 ⎟ sin⎜ ni kz − Φ i + ζ i + i ⎟ ⎜ ⎜ w ⎟⎜ ⎟ wi 2 R n k w i i ⎠⎝ i i ⎠ ⎝ ⎝ ⎠

⎛ ρ 2 ⎞⎛ ⎞ 2 ⎞ ⎛ n kρ 2 ε i w0 exp⎜ − 2 ⎟⎜⎜ 1 − 2 2 2 ⎟⎟ cos⎜ ni kz − Φ i + ζ i + i +Ψ i ⎟ (E.12b) ⎜ w ⎟ ⎜ ⎟ 2 R μ0 wi n k w i i ⎠⎝ i i ⎠ ⎝ ⎝ ⎠

E xm +1 (z ) =

⎛ ρ 2 ⎞⎛ w0 2 ⎞ exp⎜ − 2 ⎟⎜⎜ 1 − 2 2 ⎟⎟ ⎜ ⎟ wm +1 k wm + 1 ⎠ ⎝ wm + 1 ⎠⎝

⎛ kρ 2 ⎞⎟ × sin⎜ k (z − D ) − Φ m + 1 (z ) + Φ m +1 (D ) + ζ m + 1 (z ) − ζ m +1 (D ) + ⎜ 2 Rm + 1 ⎟⎠ ⎝

(E.13a)

Appendix E

339

H ym + 1 (z ) = j

⎛ ρ 2 ⎞⎛ ε 0 w0 2 ⎞ exp ⎜ − 2 ⎟⎜⎜ 1 − 2 2 ⎟⎟ ⎟ ⎜ μ0 wm + 1 k wm + 1 ⎠ ⎝ wm + 1 ⎠⎝

⎛ kρ 2 ⎞⎟ × cos ⎜ k (z − D ) − Φ m + 1 (z ) + Φ m + 1 (D ) + ζ m + 1 (z ) − ζ m + 1 (D ) + ⎜ 2 Rm + 1 ⎟⎠ ⎝

(E.13b)

where

ζ i (z ) = arctan(1 ni kRi (z )) .

(E.14)

Expressions (E.12a and b) hold for the first m layers, while (E.13a and b) are given for the m + 1 layer. The phase shift, Ψi , in (A.12) is chosen to match the field components across the first m − 1 interfaces and is given by the recursive formula: ⎛n i ⎛ ⎞⎞ ⎛ i ⎞ ⎛ i ⎞ Ψi +1 = arctan⎜ i +1 tan⎜⎜ ni k ∑ h p − Φ i ⎜⎜ ∑ h p ⎟⎟ + ζ i ⎜⎜ ∑ h p ⎟⎟ + Ψi ⎟⎟ ⎟ ⎟ ⎜ ni p =1 ⎝ p =1 ⎠ ⎝ p =1 ⎠ ⎝ ⎠⎠ , ⎝

(E.15)

⎛ i ⎞ ⎛ i ⎞ − ni +1 k ∑ h p + Φ i +1 ⎜⎜ ∑ h p ⎟⎟ − ζ i +1 ⎜⎜ ∑ h p ⎟⎟ p =1 p p = 1 = 1 ⎝ ⎠ ⎝ ⎠ i

which is initiated with Ψ 1 = 0 . The eigenvalue equation is obtained by matching the fields at the m − th interface: ⎛ ⎞ ⎛ m ⎞ 1 (E.16) tan⎜⎜ nm k ⎜ hp ⎟ − ΦT ⎟⎟ = − tan(kd − Φ D ) ⎜ ⎟ nm ⎜ ⎟ ⎝ p =1 ⎠ ⎝ ⎠

∑

⎛ m ⎞ ⎛ m ⎞ with ΦΤ = Φ m ⎜ h p ⎟ − ξ m ⎜ h p ⎟ −Ψ m , and ⎜ ⎟ ⎜ ⎟ ⎝ p =1 ⎠ ⎝ p =1 ⎠

∑

⎛

∑

⎞ ⎛ m ⎞ h p ⎟ − ξ m + 1 (D ) + ξ m + 1 ⎜ hp ⎟ ⎜ ⎟ ⎜ ⎟ ⎝ p =1 ⎠ ⎝ p =1 ⎠

Φ D = Φ m + 1 (D ) − Φ m + 1 ⎜

m

∑

∑

(E.17)

(E.18)

Equations E.16–A.18 together with (E.10) and (A.15) contain the required information to obtain the initial value of the resonance frequency ω in . The energy stored in the resonator is represented by (E.6), which in analytic form (Deleniv and Gevorgian 2005) is: ⎛ m ⎞ 1 J = − πw02ε 0 ⎜ hi Δi + d ⎟ , ⎜ ⎟ 2 ⎝ i =1 ⎠

∑

(E.19)

340

8 Measurements of the Dielectric Properties

with Δi = ni2 Ai2 . Here, Δi is calculated using the recursive formula (A.20), which is initialized with Δm +1 = 1 :

( )

( ) )

2 2 ni2 ⎛⎜ ni2+1 cos α i*+1 + sin α i*+1 ⎞⎟ ⎠, Δi = Δi +1 ⎝ 2 2 ni +1 ni cos(α i )2 + sin(α i )2

(

with

α i*+1

(E.20a)

− (khm +1 − Φ D ) i+1= m+1 ⎧ ⎪ i i i ⎛ ⎞ ⎛ ⎞ , (E.20b) =⎨ n k h p − Φ i + 1 ⎜ h p ⎟ + ζ i + 1 ⎜ h p ⎟ +Ψ i + 1 i +1≤ m ⎪ i +1 ⎜ ⎟ ⎜ ⎟ p =1 ⎝ p =1 ⎠ ⎝ p =1 ⎠ ⎩

∑

∑

∑

and

α i = ni k

i

∑h p =1

p

⎛ i ⎞ ⎛ i ⎞ − Φ i ⎜ h p ⎟ + ζ i ⎜ h p ⎟ +Ψ i . ⎜ ⎟ ⎜ ⎟ ⎝ p =1 ⎠ ⎝ p =1 ⎠

∑

∑

(E.20c)

The upper mirror surface correction (A.5) is defined as below (Yu and Cullen 1982): 3πw02 (E.21) I3 = − 8ωμ0 R0 The effect of imperfect field matching at the substrate interfaces is given by (E.4), where the integrals are defined analytically: I2 =

w02π 2

ε0 m ∑ Ai Ai +1 μ 0 i =1

⎡ ⎛ ⎜ ⎢ ⎜ ⎢ ni + ni +1 * ×⎢ sin α i − α i +1 + (ni +1 − ni ) Im⎜ 2 ⎜ ⎢ ⎜⎜ 2 − ⎢ ⎝ ⎣

(

)

⎞⎤ , (E.22a) ⎟⎥ ⎟⎥ exp j α i + α i*+1 ⎟⎥ ⎛ 2⎛ i ⎞ ⎛ i ⎞ ⎞ ⎟⎥ ⎜ ⎟ j ⎜ wi ⎜⎜ ∑ h p ⎟⎟kni Ri ⎜⎜ ∑ h p ⎟⎟ ⎟ ⎟⎥ ⎝ p =1 ⎠ ⎠ ⎟⎠⎦ ⎝ ⎝ p =1 ⎠

((

))

with 1 i = m+1 ⎧ ⎪ Ai = ⎨ Ai +1 sin α i*+1 i≤m ⎪ sin α i ⎩

(E.22b)

Finally, the integral (E.3) is given by the following identity (Yu and Cullen 1982): (E.23) I 1 = ωin J

Appendix E

341

From (E.16), (E.19), (E.21), (E.22) and (E.23), the final expression for the resonance frequency of a loaded open resonator: ⎛

ωres = ωin ⎜⎜ 1 + ⎝

I2 + I3 ⎞ ⎟. Jωin ⎟⎠

(E.24)

Here, ω in is the initial estimate of the resonance frequency obtained with (E.16), and ω res is an accurate value that accounts for imperfect field matching at the dielectric interfaces (E.22) and at the upper mirror surface (E.21) of the loaded open resonator. Computation of the Losses: A generalized expression for the quality factor of the loaded open resonator is in the following form:

1 1 1 = + , Ql Qσ Q d

(E.25)

where Qσ is a quality factor associated with the finite conductivity of the lower and upper mirrors, while dielectric loss of the sample is represented by Q d . The coupling losses are very low and are not considered here. The quality factor of the empty open resonator for the TEM 0 ,0 ,q mode is defined (Jones 1976): Qσ0 =

Dq

(E.26)

δ1 + δ 2

where δ 1 and δ 2 designate the skin depths of the lower and upper mirrors, respectively. The length of the open resonator at TEM 0 ,0 ,q mode is denoted by Dq , Fig. E.1. For the resonator loaded by a multilayered plate, the following formula is derived (Deleniv and Gevorgian 2005): Qσ =

Deff

Δ1δ 1 + δ 2

D eff =

, Δ1 = n12 A12

(E.27)

m

∑h Δ + d i i

(E.28)

i =1

Deff is the effective length of the resonator. Dielectric loss of the multilayered

plate are defined using the formula:

342

8 Measurements of the Dielectric Properties

Qd =

m

(

D eff

2 ∑ WEi tan δ i Δi hi i =1

WEi = ⎛

α i = 2⎜⎜ ni k ⎜ ⎝

⎛

βi = 2⎜⎜ ni k ⎜ ⎝

(

)

,

(E.29)

1⎛ sin(α i ) − sin(β i ) ⎞ ⎜1 + ⎟ ⎟ 2 ⎜⎝ 2ni khi ⎠

(E.30a)

⎞ ⎛ i −1 ⎞ ⎛ i −1 ⎞ − Φ i ⎜ h p ⎟ + ζ i ⎜ h p ⎟ +Ψ i ⎟⎟ ⎜ ⎟ ⎜ ⎟ ⎟ ⎝ p =1 ⎠ ⎝ p =1 ⎠ ⎠

(E.30b)

⎞ ⎛ i ⎞ ⎛ i ⎞ h p − Φ i ⎜ h p ⎟ + ζ i ⎜ h p ⎟ +Ψ i ⎟⎟ ⎜ ⎟ ⎜ ⎟ ⎟ p =1 ⎝ p =1 ⎠ ⎝ p =1 ⎠ ⎠

(E.30c)

i −1

∑h p =1

i

∑

p

∑

∑

∑

∑

)

−1

is the normalized electric field energy in the i-th diwhere WEi = WEi WEi + WHi electric layer. In practice it is necessary to obtain the loss tangent for the specific layer with the measured quality factor of the loaded open resonator and the parameters of the other layers available. For the j-th layer being measured: tan δ j =

D eff ⎛⎜ 1 1 2WEi tan δ i Δi hi − − j 2WE Δ j h j ⎜ Ql Qσ i (i ≠ j ) D eff ⎝

∑

⎞ ⎟ ⎟ ⎠

(E.31)

Appendix F

343

Appendix F Model of the Test Capacitor with Annular Slot It is assumed that the complex permittivity ε~i and thickness hi of all substrate layers, except for the MUT, are specified. From bottom and top the structure is terminated by an arbitrary impedance condition, i.e. electric/magnetic wall or infinitely extended media. The capacitor is formed on top of a substrate with dimensions d and D as it is shown in Fig. F.1. The analysis starts with a stationary formula for the admittance (Harrington 1961): Yin =

a ,a V2

= − ∫∫

H a ⋅ M a ds V2

,

(F.1)

where a , a is a self-reaction or the reaction of the field on its own voltage source V. The latter is defined as two sheets of inversely directed magnetic currents M a , impressed beneath and above the perfectly conducting ring interface complementing the metal free area (slot) of the test structure. The upper surface of such a voltage source is shown schematically in Fig. F.2. Being inserted into aperture such voltage source produces a positively directed terminal filed E ρa = − M φa as it is shown in Fig. F.1 (b). Then the expression (F.1) may be rewritten in a rather accommodative form: Yin =

a ,a V

2

J a ⋅ E a ds , = ∫∫ V2

(F.2)

where J a is an induced current through the voltage source and integration is over the aperture.

Yin

2r

2R

(a) Fig. F.1 The layout (a) and cross-section (b) of the test capacitor

(b)

344

8 Measurements of the Dielectric Properties

2R

Ma Fig. F.2 Equivalent voltage source representation using inversely directed sheets with magnetic current

In the next step the field-current relation in the Hankel transform domain (HTD) is defined. Considering no angular dependence the fields obviously have TM-to-z configuration. Thus, the following relationship holds in the HTD:

( )

(

) ( )

~ ~ ~ J ρ k ρ = Ye ω ,k ρ Eρ k ρ ,

(F.3)

where Y~ e (ω , kρ ) is a TM-to-z wave admittance seen from the interface with the ~ impressed electric field E ρ (kρ ) : R ~ Eρ k ρ = ∫ Eρ (ρ )J1 k ρ ρ ρ dρ .

( )

( )

r

(F.4)

J1 in (F.4) is a first order Bessel function of the first kind. In the next step the trial

fields are defined using the following basis functions:

E ρn (ρ ) =

⎛ ρ − 0.5(R + r ) ⎞ ⎟⎟ Tn⎜⎜ ⎝ 0.5(R − r ) ⎠ 1 2 ⎛ ρ − 0.5(R + r ) ⎞ 2 ⎟⎟ ρ 1 − ⎜⎜ 0.5(R − r )

⎝

,

(F.5)

⎠

where Tn is the n-th order Chebyshev polynomial, R and r are the sizes of the test structure (Fig. F.1). With the above selection of the trial functions, analytic ex~ pressions can be derived for the large argument of E ρ (k ρ ) leading to a rather efficient numerical routine. Since the varactors size is considerably smaller than the wavelength, the following equality holds for any n: a a ∫∫ J ⋅ En ds = I inV n ,

(F.6)

Appendix F

345

where I in is the input current and Vn is the voltage of the n-th trial field basis function at the input. Therefore, the following relationship is derived for the self reaction (Deleniv et al. 2003): ⎡V1 ⎤ ⎢ ⎥ a , a = I in ⎢ ⎥ ⎢⎣Vn ⎥⎦

~1 T ⎡ J~ 1 , E ρ ρ

or

⎢ ⎢ ⎢ ~n ~n ⎢ J ρ , Eρ ⎣

… …

−1 ~ ~ J ρ1 , E ρn ⎤ ⎡V1 ⎤ ⎥ ⎥ ⎢ ⎥I , in ~ n ~ n ⎥ ⎢⎢ ⎥⎥ J ρ , E ρ ⎥ ⎣Vn ⎦ ⎦

2 [ ]T [ a , a = Iin V Matr ]−1[V ] .

~

(F.7)

(F.8)

~

In (F.7) the reactions J ρi , Eρj are defined in HTD as: ∞~ ~ ~ ~ ~ J ρi , E ρj = 2π ∫ Y e ω , k ρ E ρí k ρ E ρj k ρ k ρ dk ρ 0

(

) ( ) ( )

(F.9)

Inserting (F.8) into (F.2) the following expression for the input admittance is found: Yin = ⎛⎜ [V ]T [Matr ]−1 [V ]⎞⎟ ⎠ ⎝

−1

(F.10)

For the test structure with the known thicknesses and parameters of the layers, the capacitance may be calculated using (F.10). It may be used for computing the unknown parameters of one layer based on the experimentally measured impedance and known thicknesses and parameters of the other layers. The configuration of test capacitor shown in Fig. F.1 is often used without metallization M1 under the ferroelectric film. It is then recommended to use a smaller aperture, R − r . This increases the inclusion rate of the ferroelectric film and reduces the impact of the measurement errors on the retrieved film parameters. In another configuration metallization M1 isolates the ferroelectric film from the substrate. The inclusion rate of the film is then close to 1, and the test capacitor is ideally suited for characterization of the ferroelectric films. For an electrically thin metallization M1 (thickness is less than the skin depth), some fraction of the electric field may penetrate into the substrate. It is important to note that the test structure admittance as it is given by (F.10) is defined for the circularly shaped terminals delimiting the aperture boundaries (Fig. F.1 (a)).

346

8 Measurements of the Dielectric Properties

Appendix G Measuring of the Complex Propagation Constant of CPW The complex propagation constant of a CPW (with the effect of the tapers removed) is obtained by measuring the structures indicated in Fig. 8.3.4 (a) and Fig. 8.3.4 (c) as explained below. b2

a1

2-Port Network

b1

a2

Fig. G.1 To definition of the R matrix (sometimes this is also called transmission matrix)

For a two-port network in Fig. G.1, the scattering parameters are converted to transmission parameters: ⎛ b1 ⎞ 1 ⎛ − Δ ⎜⎜ ⎟⎟ = ⎜⎜ ⎝ a1 ⎠ S21 ⎝ − S 22

S11 ⎞⎛ a2 ⎞ ⎛a ⎞ ⎟⎟⎜⎜ ⎟⎟ = [R ] ⋅ ⎜⎜ 2 ⎟⎟ 1 ⎠⎝ b2 ⎠ ⎝ b2 ⎠

(G.1)

where Δ is a determinant of the measured S-matrix. From the measured S-parameters RT = R A R B and R L = R A R CPW R B

[ ] [ ][ ]

[ ] [ ][

][ ]

[ ]

are calculated for the “thru” and the “line” standards respectively where R A ,

[R ] and [R ] are the R-matrices of the taper A, taper B and the section of the B

CPW

CPW line with the length L (Fig. 8.3.4). In the next step the matrix [T ] is defined:

[T ] = [R L ][RT ]−1 = [R A ][RCPW ][R A ]−1

(G.2)

The CPW line is non-reflective (the same impedance as at the end of the tapers), therefore ⎡e−γL 0 ⎤ (G.3) R CPW = ⎢ ⎥, eγL ⎦⎥ ⎣⎢ 0

[

]

γ is the complex propagation constant of the CPW. In the next step the following identity is formulated:

[T ][R A ] = [R A ][RCPW ],

(G 4)

References

347

which is then expanded into the following four equations: A A A −γL T11 R11 + T12 R21 = R11 e

(G.5)

A A A −γL T21 R11 + T22 R21 = R21 e

(G.6)

A A A γL T11 R12 + T12 R22 = R12 e

(G.7)

A A A γL T21 R12 + T22 R22 = R22 e

(G.8)

The following convention is used in n (G.5)–(G.8): the sub-indexes in Tij and RijA

hold for the position of the elements within related matrices. The combining

pairs (G.5)–(G.6) and (G.7)–(G.8) yields (Rubin 1990): e −2γL − e −γL (T11 + T22 ) + (T11T22 − T12T21 ) = 0 e 2γL − eγL (T11 + T22 ) + (T11T22 − T12T21 ) = 0

(G.9) (G.10)

The coefficients in quadratic equations (G.9) and (G.10) are identical, hence −γL and e −γL are the two solutions of the complex equation: e+

G 2 − G (T11 + T22 ) + (T11T22 − T12T21 ) = 0

(G.11)

It is noted that all the elements of matrix [T ] are known, hence (G.11) can be solved for G1( 2 ) = e ±γL . The identification of solutions is based on the sign of arg (G1(2 ) ) , which for e −γL should be negative and positive for eγL .

References Agilent 8510C network analyzer data sheet. Agilent Technologies, Inc. http://cp.literature.agilent.com/litweb/pdf/5091-8484E.pdf Barker-Jarvis J, Vanzura E, Kissick W (1990) Improved technique for determining complex permittivity with the transmission/reflection method. IEEE Trans Microw Theory and Tech 38:1096–1103 Boughriet A, Legrand C, Chapoton A (1997) Noniterative stable transmission/reflection method for low-loss material complex permittivity determination. IEEE Trans Microw Theory and Tech 45:52–57

348

8 Measurements of the Dielectric Properties

Buslov O, Keys V, Kozyrev A et al. (2003) Procedure of measurement of ferroelectric film parameters using open resonator method. Microwave and Telecommunication Technology CriMiCo2003:683–684 Carlsson E, Gevorgian S (1997) Effect of enhanced current crowding in a CPW with a thin ferroelectric film. Electron Lett 33:145–146 Champlin K, Glover G (1966) ”Gap effect” in measurement of large permittivities. IEEE Trans Microw Theory and Tech MTT-14:397–398 Cho Y, Kazuta S, Matsuura K (1999) Scanning nonlinear dielectric microscopy with nanometer resolution. Appl Phys Lett 75:2833–2835 Cho Y, Kirihara A, Saeki T (1996) Scanning nonlinear dielectric microscope. Rev Sci Instrum 67:2297–2303 Courtney W (1970) Analysis and evaluation of a method of measuring the complex permittivity and permeability of microwave insulators. IEEE Trans Microw Theory Tech 14:476–485 Deleniv A, Abadei S, Gevorgian S (2003a) Microwave Characterization of Thin Ferroelectric Films. Proc EuMC’2003:483–486 Deleniv A, Gevorgian S (2005) Open resonator technique for measuring multilayered dielectric plates. IEEE Trans Microw Theory Tech 53:2908–2916 Deleniv A, Hu T, Jantunen H et al. (2003b) Tunable ferroelectric components in LTCC technology. Dig IEEE IMS’2003:1997–2000 Deleniv A, Rundqvist P, Vorobiev A et al. (2007) Experimental characterization of the 3rd order nonlinearities in thin film parallel-plate ferroelectric varactors. Dig IEEE IMS’2007:683–686 Deleniv A, Vorobiev A, Gevorgian S (2008) On-wafer characterization of varactor using resonating microprobes. IEEE Trans Micr Theory Tech 56: 1105–1111 Engen G, Hoer C (1979) Thru-reflect-line: An improved technique for calibrating the dual sixport automatic network analyzer. IEEE Trans Micr Theory Tech MTT-27:987–993 Findikoglu A, Camassa R, Lythe G et al. (2002) Dielectric nonlinearity and stochastic effects in strontium titanate. Appl Phys Lett 80:3391–3393 Galt D, Price J, Beall J et al. (1995) Ferroelectric thin film characterization using superconducting microstrip resonators. IEEE Trans Appl Supercond 5:2575–2578 Gevorgian S, Carlsson E, Wikborg E et al. (1998) Tunable microwave devices on bulk and thin ferroelectrics. Integr Ferroelectr 22:245–257 Gevorgian S, Martinsson T, Linnér P et al. (1996) CAD Models for Multilayered Substrate Interdigital Capacitors, IEEE Trans Microw Theory Tech 44:896–904 Ginzton E (1957) Microwave measurements. McGraw-Hill Book Company Grigas J (1996) Microwave dielectric spectroscopy of ferroelectrics and related materials. Ferroelectricity and Related Phenomena, vol.9. Gordon and Breach Hakki B, Coleman P (1960) Adielectric resonator method of measuring inductive capacities in the millimeter range. IRE Trans Micr Theory Tech 8:402–410 Harrington R (1961) Time-Harmonic Electromagnetic Fields. McGraw-Hill Book Company Jones R (1976) Precise dielectric measurements at 35 GHz using an open microwave resonator. Proc IEE 123:285–290 Kaifez D, Chebolu S, Abdul-Gaffoor M et al. (1999) Uncertainty analysis of the transmission type measurement of Q-factor. IEEE Trans Micr Theory Tech 47:367–371 Kobayashi Y, Katoh M (1985) Microwave measurement of dielectric properties of low-loss materials by the dielectric rod resonator method. IEEE Trans Micr Theory Tech MTT-33:586– 592 Kogelnik H, Li T (1966) Laser beams and resonators. Proc IEEE 54:1312–1329 Komiyama B, Kiyokawa M, Matsui T (1991) Open resonator for precision dielectric measurements in the 100 GHz band. IEEE Trans Mic Theory Tech 39:1792–1796 Kozyrev A, Ivanov A, Samoilova T et al. (2000) Nonlinear response and power handling capability of ferroelectric BaxSr1–xTiO3 film capacitors and tunable microwave devices. Journal of Appl Phys 88:5334–5342 Kozyrev A, Soldatenkov O, Ivanov A (1998) Switching time of planar ferroelectric capacitors using strontium titanate and barium strontium titanate films. Tech Phys Lett 24:755–757

References

349

Kozyrev A, Soldatenkov O, Samoilova T et al. (1998b) Response time and power handling capability of tunable microwave devices ferroelectric films. Integr Ferroelectrics 22:329–340 Krupka J (2004) Complex permittivity measurements with split-post dielectric resonator. Workshop on the broadband characterization of dielectric substrates. In IEEE MTT-S Int. Microwave Symp. Dig., Forth Worth, USA. Krupka J, Gregory A, Rochard O et al. (2001) Uncertainty of Complex Permittivity Measurements by Split-Post Dielectric Resonator Technique. Journal of the European Ceramic Society 21: 2673–2676 Krupka J, Huang W-T, Tung M-J (2006) Complex permittivity measurements of thin ferroelectric films employing split post dielectric resonator. Ferroelectrics 335:89–94 Krupka J, Zychovicz T, Bovtun V et al. (2006) Complex permittivity measurements of ferroelectrics employing composite dielectric resonator technique. IEEE Trans Ultrasonics, Ferroelectrics, and Frequency Control 53:1883–1888 Lue H, Tseng T (2001) Application of on-wafer TRL calibration on the measurement of microwave properties of BaSrTiO thin films. IEEE Trans Ultrasonics, Ferroelectrics Frequency Control 48:1640–1647 Ma Z, Becker A, Polakos P et al. (1998) RF measurement technique for characterizing thin dielectric films. IEEE Trans Electron Devices 45:1811–1816 Nicolson A, Ross G (1970) Measurement of the intrinsic properties of materials by time-domain techniques. IEEE Trans Instrumentation Measurement 19:377–382 Qi Yi, Anlage S M, Zheng H et al. (2007) Local dielectric measurements of BaTiO3-CoFe2O4 nano-composites through microwave microscopy. Journal of Materials Research 22:1193– 1199 Rubin D (1990) De-embedding mm-wave MICs with TRL. Microwave Journal 33:141–150 Rumsey V (1954) The reaction concept in electromagnetic theory. Phys Rev Ser.2 94:1483–1491 Rundqvist P, Vorobiev A, Gevorgian S et al. (2004) Non-Destructive Microwave Characterisation of Ferroelectric Films on Conductive Substrates. Integrated Ferroelectrics 60:1–19 Steinhauer D, Vlahacos C, Wellstood F et al. (2000) Quantitative imaging of dielectric permittivity and tunability with a near-field scanning microwave microscope. Rev Scientific Instruments 71:2751–2758 Sucher M, Fox J (1963) Handbook of Microwave Measurements II. Polytechnic Inst. Of Brooklyn, Brooklyn, New York Vendik O, Kollberg E, Gevorgian S et al. (1995) 1 GHz tunable resonator on bulk single crystal SrTiO3, plated with YBa2Cu3O7–x films. El Lett 31:654–656 Vorobiev A, Berge J, Gevorgian S (2007) Thin film Ba0.25Sr0.75TiO3 voltage tunable capacitors on fused silica substrates for applications in microwave microelectronics. Thin Solid Films 515:6606–6610 Weir W (1974) Automatic measurement of complex dielectric constant and permeability at microwave frequencies. Proc IEE, l.62:33–36 Yu P, Cullen A (1982) Measurement of permittivity by means of an open resonator. I. Theoretical. Proc R Soc Lond A.380:49–71 Zhu X, Chen D-Y, Jin Z et al. (2005) Characterization of thin film BST tunable capacitors using a simple two port measurement technique. Dig IEEE IMS’2005:611–614

Chapter 9

Potentials and Perspectives

Abstract New promising agile materials, like multiferroics, ferroelectric and ferromagnetic nanotubes, pyrochlores, oxides with resistive switching, and liquid crystals are reviewed in this chapter. Potentials for applications in metamaterials and THz technology are considered. New effects in ferroelectrics, like resistivity switching in doped SrTiO3, nanoscale effects, integration with semiconductors and high temperature superconductors (HTS), are reviewed.

9.1 Introduction A number of new complementing and competing materials are being considered for agile microwave applications. Multiferroics, depending on temperature and composition are characterized both by ferroelectric, ferromagnetic and piezoelectric/ piezomagnetic properties. Current research activities are directed towards understanding, modeling and synthesis of multiferroics with both ferroelectric and ferromagnetic spontaneous polarizations for applications in electrically controlled magnetic memory. For microwave applications multiferroics in paraelectric/paramagnetic phase and tunable at room temperature seems to be attractive, for example, in electric field condoled magnetic and nonreciprocal devices. Some of non-ferroelectric pyrochlores demonstrate rather high tuneabilities and low microwave losses. Pyrochlores are not ferroelectrics, i.e. they should not have hysteresis effects typical for ferroelectrics below and close to phase transition temperatures. Besides these complex metal oxides (i.e. multiferroics, ferroelectrics and pyrochlores) another class of metal oxides having resistive switching properties may be considered for applications in microwave switches integrated with ferroelectric/multiferroic tunable devices. Currently these oxides are extensively investigated for memory applications. Among these oxides VO2 has been successfully demonstrated as a microwave switch. In recent years liquid crystals (LC) also are considered for microwave applications. They demonstrate very low losses 351

352

9 Potentials and Perspectives

especially at high microwave/millimeter wave frequencies. However, the compatibility/integration issues and low tuning speeds make LCs less favorable in some applications in comparison with ferroelectrics.

9.2 Multiferroics Multiferroics are, perhaps, the most multifunctional and agile materials with a rich variety of effects, such as: • • • • • •

Electrical tuning of magnetic permeability; Magnetic tuning of dielectric permittivity; Magnetic tuning of magnetic permeability; Electric tuning of dielectric permittivity; Electrostrictive and magnetostrictive effects; Piezomagnetic and piezoelectric effects etc.

These effects may be used in microwave devices with enhanced performances and radically new functionalities. The negative refractive index is the most extraordinary feature, which in multiferroics may be tunable and may allow development of new class of microwave devices with new functionalities. Multiferroics combine both ferroelectric and ferromagnetic (antiferromagnetic, ferrimagnetic) properties. So far the main interests and research efforts have been directed towards multiferroics with double ordering, i.e. both electric and magnetic spontaneous polarizations-useful for memory applications. On the other hand for microwave applications multiferroics in non-polar phase, i.e. both in paraelectric and paramagnetic phases may be of great practical interest. Some of antiferromagnetic multiferroics are insulators (Spaldin et al. 2003) and they may have both ferroelectric and antiferromagnetic resonances in THz range. Above ferroelectric (soft mode) resonance the real part of the ferroelectric’s permittivity is negative. Similarly, above the antiferromagnetic resonance the real part of the antiferromagnet is negative. Below these frequencies the real parts of the permittivity and permeability are positive. Thus, they may provide enhanced permittivity, permeability and, at least in theory, both negative permittivity and negative permeability-hence negative refractive index at THz frequencies (Ward et al. 2004). The definition of the negative refractive index is given in the Sect. 9.4. The dielectric permittivity of a multiferroic my be controlled by external electric field the same way us it is done with ferroelectrics considered in this book. Additionally, since they also have ferromagnetic properties, their magnetic permeability may be controlled by external magnetic field. Thus a multiferroic offers tuning flexibility in microwave device applications. One of the prominent features of the multiferroics is the cross controlling possibility, i.e. the possibility of controlling its magnetic permeability by electric field and magnetic field control of permittivity. The magnetic field tuning of the dielectric permittivity is demonstrated experimentally: in BiFeO3 by Kamba et al. (2007), in GdMnO3 and TbMnO3 by Pimenov et al.

9.2 Multiferroics

353

(2006). High-resolution room temperature images of both antiferromagnetic and ferroelectric domains in (001)-oriented multiferroic BiFeO3 films revealed a strong coupling between the ferroelectric and antiferromagnetic orders indicating the possibility of electric field control of the magnetic state and vice versa (Zhao et al. 2006). Only a limited number of single phase multiferroic materials exist. This, amongst other reasons, is because the classical ferroelectric perovskites (BaTiO3, etc.) contain d ions with empty shells (e.g. Ti4+) and thus bear no magnetic moment. Exceptions include some orthorhombic manganites, like TbMnO3, and Bi-based perovskites like BiFeO3 and BiMnO3. In addition, most multiferroics are antiferromagnetic or weak-ferromagnets (e.g. BiMnO3). Some multiferroics, like TbMnO3, exhibit magnetoelectric effect. Currently the single phase intrinsic mutiferroics are in their infancy, i.e. this is a “hot” research topic (Cheong and Mistook 2007, Pimenov et al. 2006). So far true (single phase, intrinsic) multiferroics with practically useful properties are not reported. The artificial, composite (multiphase) multiferroics are based on nanostructured and well characterized antiferromagnetics and ferroelectrics and their properties may be relatively easy tailored by controlling the composition and the nanostructure. Typically the sizes of the ferroelectric and ferromagnetic constituents are much smaller than the wavelengths of the electromagnetic waves in microwave, terahertz and optical frequency ranges and the nanocomposite “pretends” to be a quasi-homogeneous medium with effective dielectric permittivity and magnetic permeability. Examples of artificial multiferroics are shown in Fig. 9.2.1.

(a)

(b)

Fig. 9.2.1 Layered (a) and columnar (b) artificial multiferroics based on ferroelectric and ferromagnetic constituents

Artificial multiferroics based on ferroelectric (BaxSr1–xTiO3)-antiferromagnetic (NiCoO) composites are considered experimentally (Kirby et al. 2007) where the negative permittivity in ferroelectric BaxSr1–xTiO3, is used, in combination with the negative permeability in NiO, to demonstrate negative refractive index at THz frequencies (Fig. 9.2.1 (a)). Potentially one may expect multiferroic properties in self assembled nano-columnar (Fig. 9.2.1 (b)) composites like BiFeO3–CoFe2O4

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(Ramesh and Spaldin 2007, Zheng et al. 2004), PbTiO3–CoFe2O4 ( Li 2006) and BaFe12O19/Ba0.5Sr0.5TiO3 (Heindl et al. 2007). Growth and microwave characterization of BaxSr1–xTiO3–CoFe2O4 is reported in (Qi et al. 2006). In artificial, engineered nano-composites the effective dielectric and magnetic properties may be tailored both by the structural diversity the ferromagnetic-ferroelectric composite and by the physical properties of the used ferromagnetic and ferroelectric materials. The “marriage” of these rather mature technologies (ferroelectric and ferromagnetic) allows developing dual tunable materials for applications in a wide frequency range (microwave to optics) and for a wide range of devices. The intrinsic and artificial multiferroics as well as the ferromagnets and antiferromagnets may be used below their characteristic resonant frequencies as high permeability and high permittivity materials. Possible implementation of artificial multiferroics based on ferroelectric nano-tubes and ferromagnetic nanowires is considered in the next section, while the possibilities of using multiferroics as negative refractive metamaterial are addressed in Sect. 9.4. One may expect a rich variety of ultra-fast effects (microwave, THz and optical) associated with ferroelectric/ferromagnetic interfaces (Galatsis 2006, Zhuravlev et al. 2005, Tsymbal and Kohlstedt 2006, Zhuravlev et al. 2005, Chau et al. 2007, Gonzalez-Diaz et al. 2007) especially where the permittivity of the ferroelectric film is negative.

9.3 Ferroelectric Nanotubes. Ferromagnetic Nanowires Ferroelectric nanotubes with different external and internal electrodes have been considered mainly for memory application (Scott et al. 2005). At this instance no microwave applications/experiments are reported. However the enhanced dielectric (and optical) properties observed in ferroelectric nanotubes (Morozovska et al. 2006) potentially may be used in microwave devices. It is shown by Morozovska and Glinchuk (2006), that by changing the ratio of external/internal radiuses (hence the radial stress) the ferroelectric (i.e. BaTiO3) nanotube may be driven into paraelectric phase. For memory applications ferroelectric nanotubes offer size reduction (Morrison et al. 2003). So far ferroelectric nanotubes fabricated in porous alumina and silicon (Ottow et al. 1996) is demonstrated. Highly ordered nanotubes in anodized porous alumina are produced by a two step process (Masuda and Fukuda 1995), nanoimprint (Choi et al. 2003) and by using silicon nitrite mask (Vlad et al. 2006). Fabrication of nano pores with highly controllable locations and sizes in silicon is a relatively easy task and is based on standard silicon technology, although the minimum diameter of the nonporous is limited. Ferroelectric nanotubes in porous alumina with the external diameter up to 400 nm and in porous silicon from 400 nm up to several micrometers (Scott et al. 2005, Morrison et al. 2003, Luo et al. 2003) are demonstrated. Ferroelectric nanotubes in standard Whatman anodic 50 μm thick alumina membranes are fabricated using a sol-gel process by

9.3 Ferroelectric Nanotubes. Ferromagnetic Nanowires

355

dipping the membrane in solution (Hernandez et al. 2002) and by spin coating (Morrison et al. 2003). The integration of the ferroelectrics with ferromagnetic nanowires seems to be attractive for microwave device applications. Due to the ferromagnetic resonance (without DC bias) the ferromagnetic (Ni, Co, Fe etc.) nanowires are considered for microwave (Spiegel et al. 2007, Sklyuyev et al. 2006) and optical (Melle et al. 2003) applications. Ferromagnetic nanowires are fabricated mainly by electroplating using porous alumina. Successful fabrication of ferromagnetic nanowires in porous alumina with thin oxide layer at the pore bottom is reported. The 100% nickel-filled nano-pores are fabricated by pulsed electroplating (Nielsch et al. 2000). Growth of ferroelectric (BaxSr1–xTiO3) films on alumina substrates is a rather well established process (Nath et al. 2006, Razumov et al. 2002). Additionally Ni, as electrode material, has been commonly used in commercial multilayer ferroelectric capacitors. As buffer/adhesion layer Ni is used in thin BaxSr1– xTiO3film varactors (Vorobiev and Gevorgian 2007). Hence both alumina and Ni allow high temperature deposition process of BaxSr1–xTiO3film and no problems are anticipated for fabrication of composites. A possible integration concept is shown in Fig. 9.3.1 (a). In fact, these types of ferroelectric/ferromagnetic nanocomposites including ferroelectrics films grown on top of nanowire (Co, Ni) impregnated alumina films are reported by Evans et al. (2007). Alternatively, the ferroelectric film may be grown (and patterned) on bottom electrode before deposition and anodic oxidization of aluminum as shown in Fig. 9.3.1 (c). The anodic alumina films, typically 0.5–5.0 μm thick, are impregnated by ferromagnetic nanowires, typically 30–100 nm in diameter, and the BSTO films, typically are 100–500 nm thick. In Fig. 9.3.1 no Al is possible in case (a) due to high deposition temperature of ferroelectric films and the loss resistors are not shown for simplicity. The main issues to be addressed include selection of the film thicknesses and buffer/adhesion layers to control the interfacial strains and sticking of the films. A 2D film consisting of unit cells shown in Fig. 9.3.1 will have effective refractive index tunable by external electric or magnetic fields. The film, the top and bottom electrodes (Au, Pt) may be patterned in micrometer scale to form microwave circuits consisting of LC networks, including “traditional microwave metamaterials” like left and right hand transmission lines. The tunable equivalent circuits of the unit cells are shown in Fig. 9.3.1 (b) and Fig. 9.3.1 (d). Preliminary measurements at microwave frequencies seem promising in terms of microwave losses (Deleniv et al. 2007). In more advanced nanocomposites the ferromagnetic nanowires may be fabricated inside ferroelectric nanotubes. In these structures the concentric electrodes (nanotubes) sandwich the ferroelectric nanotubes. Fabrication of both inside (nano-tube) and outside (nano-tube) electrodes are considered by wetting (no electroplating) using Pt (Seo et al. 2006), and Ru (Scott 2006) as the electrode materials. No reports are available where ferromagnetic nanowires are fabricated inside the ferroelectric films. Fabrication of ferromagnetic nanowires inside carbon nanotubes in anodized alumina substrate is demonstrated in (Kim 2005). Successful

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fabrication of ferromagnetic Ni nanowires inside alumina nano-tubes with alumina barrier layer at the bottom (i.e. no ohmic contact at the bottom of the nanopore) of the pore (Nielsch et al. 2000) indicates that a pulsed electroplating may be used to grow ferromagnetic nanowires inside ferroelectric nanotubes. A simple consideration of this transient (charging) current supported electroplating process shows that it may be even easier in the case of ferroelectric nanotubes with much larger permittivity (i.e. transient current). Furthermore, for an aspect ratio (tube diameter/tube length) lower than 10 a conformal deposition of ferromagnetic (i.e. Ni) inside a ferroelectric nano-tube may be achieved by magnetron sputtering. a<<λ Unit cell

Ni

Al2O3

Al2O3

Top electrode Ferroelectric CF

C

Bottom electrode L

Si or SiO2(silica glass) a substrate

(a)

(b)

a<<λ

BSTO

Ni

Al2O3

Al

Unit cell

Al2O3

Top electrode

Bottom electrode Si or SiO2 (silica glass)

(c)

CF

C

L

(d)

Fig. 9.3.1 Ferroelectric-ferromagnetic nano-composites integrating ferroelectric films and ferromagnetic nanowires (a, c) and equivalent circuits of their unit cells (b, d)

In fact, the ferroelectric-ferromagnetic nanowire composite films may be regarded as artificial multiferroics. These films have enhanced dielectric permittivity due to ferroelectric constitute which may be controlled by external electric field.

9.4 Metamaterials

357

The effective magnetic permeability is also higher due to ferromagnetic nanowires. The permeability may be controlled by external magnetic field (Spiegel et al. 2007, Sklyuyev et al. 2006). The composite films are also integration friendly allowing utilization of MCM integration of tunable inductors and nonreciprocal devices like circulators (Saib et al. 2005).

9.4 Metamaterials In a wider sense a metamaterial should provide average (effective) properties not readily available from natural materials. This may include materials with higher permittivity and/or permeability. However, the negative refractive index is the most striking feature allowing extraordinary effects to happen: negative angle of refractions (see third quadrant, Fig. 9.4.1), reversed Doppler effect, backward wave propagation etc. A material may have negative refractive index if both the real part of its dielectric permittivity (ε<0) and the real part of the magnetic permeability (μ<0) are negative:

n = εμ = − ε

− μ = j ε j μ =− ε μ

(9.4.1)

Negative refractive index materials may be used for utilization of devices with extraordinary performances. Figure 9.4.1 shows the possible combinations of the materials with the different signs of the real parts of the permittivity and permeability. In Fig. 9.4.1 in all quadrants the refractive index in the upper plane (upcoming waves) is positive. Materials with negative permittivity are readily available in the nature: SrTiO3 and similar ferroelectrics are examples. Their permittivity is negative above soft mode frequency (ωTO, Fig. 9.4.1, second quadrant). Typically the soft mode frequency is in THz range. The permeability of ferromagnets above ferromagnetic (typically in GHz range) resonance is also negative. The negative permeability of the antiferromagnetic materials (NiO, BiFeO3 etc.) above antiferromagnetic resonance (ωAFM) is in THz range, Fig. 9.4.1 forth quadrant. No wave propagation is possible in these materials, i.e. in second and forth quadrants where the refractive indices are imaginary. However, under certain conditions they may support surfaces (interfacial) waves where interfaced with other materials having positive permittivity and permeability, as indicated by horizontal dashed arrows in Fig. 9.4.1. Furthermore, if a material with negative permittivity (imaginary refractive index, second quadrant, Fig. 9.4.1) is impregnated with negative magnetic permeability inclusions, like split ring resonators (SRR), it pretends to be a medium with an effective negative refractive index and supports backward waves (Engheta and Ziolkowski 2006).

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Fig. 9.4.1 Refractive index chart indicating propagation of the electromagnetic waves in ferroelectric, multiferroic and (anti)ferromagnetic materials

Similarly, a material with negative permeability impregnated with negative permittivity inclusions like metal strips (Engheta and Ziolkowski 2006) exhibits negative refractive index and again supports propagation of backward waves. Metamaterials with negative refractive index supporting backward waves are also known as left handed (LH) materials. In the forth quadrant in Fig. 9.4.1 a natural material (if exists) has negative refractive index, thus supports backward wave propagation. In the race for negative refractive index, along with using SRR, (Engheta and Ziolkowski 2006) and other metal-dielectric structures (Caloz and Itoh 2006, Eleftheriades and Balmain 2005), attempts of using natural materials are being made. Intrinsic (true) multiferroics are considered as natural materials with natural negative refractive index (at least in theory). Both the intrinsic and artificial multiferroics may be considered for negative refractive index. In contrast to the “traditional” metamaterials, based on, for example, SRRs these metamaterials gain their properties both from their structure and the composition of the materials they are made of. In addition to negative refractive index both intrinsic and artificial multiferroics offer dual (by electric and/or magnetic fields) tunable properties. The effective negative refraction in traditional metamaterials (Engheta and Ziolkowski 2006, Caloz and Itoh 2006, Eleftheriades and Balmain 2005) based on microwave components is observed in relatively narrow frequency bands limiting their systems applications. Avoiding these limitations and increasing the functionality of the metamaterials urge investigation of tunable metamaterials (Landy et al.

9.4 Metamaterials

359

2007, Kotsuka et al. 2007). In tunable metamaterials the frequency band with the negative refractive index (or extreme permittivity and permeability) may be shifted (tuned) to cover wider frequency bands. Furthermore, for applications in agile devices and systems the tuneability/reconfigurability is one of the main desirable features. In large tunable metamaterial arrays the DC powers required for tuning, the tuning speed, and the dissipation of the generated heat are critical issues. Although a considerable progress in metamaterials is reported, the losses still remain one of the main issues in implementations of the metamaterials with industrially adequate performances. Most of the reported tunable metamaterials use semiconductor devices. Metamaterials controlled by P-I-N diodes (Kotsuka et al. 2007) operating about 4– 5 GHz, and by Schottky contacts operating at 1–2 THz frequencies (Chen et al. 2006, Landy et al. 2007) are demonstrated. The semiconductor varactor tuned scanning leaky wave antenna with back firing capability is typical examples of 1D tunable metamaterials (Lim et al. 2005–2004). Tunable metamaterials based on MEMs (Hand et al. 2007), liquid crystals (Zhao et al. 2007), ferromagnets (He et al. 2007) and ferromagnetic nanowires (Saib et al. 2003) is demonstrated. The possibility of magnetic tuning of ferromagnetic nanowire based metamaterials, including negative permeability, is demonstrated in (Spiegel et al. 2007). Semiconductor device based metamaterials may be tuned optically (Degiron et al. 2007). Each of these tuning mechanisms has its advantages and disadvantages. Magnetic ad optical tunings are contactless, i.e. they do not require DC bias networks integrated with the microwave circuit. Hence they introduce no extra parasitics in the circuit. However both of these methods use high control powers. Optical control potentially may be high speed, while there is a speed limitation for magnetic control. The other methods: MEM, P-I-N diode, varactor (semiconductor, ferroelectric) etc., require DC biasing networks which causes wiring problems in tunable metamaterials consisting of large numbers of unit cells. MEMs control has additional disadvantages of being slow and requiring vacuum packaging. The ferroelectric varactors have extremely low leakage currents, as their MEM counterparts. On the other hand the tuning speed they offer is much higher (subnanosecond). A comparison of the available tunable technologies shows (Gevorgian et al. 2006) that the ferroelectric varactors are best suited for tunable metamaterial applications. Photonic bandgap structures using ferroelectric varactors are reported in the past (Kuylenstierna et al. 2003). Examples of 1D and 2D tunable metamaterials based on ferroelectric varactors are briefly summarized in (Gevorgian and Vorobiev 2007). The potential of the ferroelectric varactors in an experimental tunable 2D array integrated with silicon substrate is demonstrated at Ka-band (Gevorgian et al. 2007). The flexibility and functionalities of the tunable metamaterials may be further expanded by using, along with ferroelectrics, ferromagnetic materials. In microwave and terahertz frequency ranges the negative refractive index may be achieved by using composites consisting of natural negative permittivity and negative permeability occurring above ferroelectric and ferromagnetic resonances (Ward et al. 2005). In SrTiO3, above soft mode frequency (Ostapchuk et al. 2002)

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the real part of permittivity is negative. The results of explicit measurement of electric field controlled negative (Misra et al. 2005) and positive (Kuzel et al. 2007) permittivity in SrTiO3 are reported. In ferroelectrics, the permittivity and the frequency range where the permittivity is negative may be controlled by temperature (Ostapchuk et al. 2007, Petzelt et al. 2007, Sirenko et al. 2000) composition (Kirby et al. 2007, Ostapchuk et al. 2007, Shen et al. 2006), electric field (Fleury and Worlock 1968), and stress (Kamba et al. 2008). Negative permittivity in ferroelectric films associate with the resonant motion of the domains is reported at low microwave frequencies (Shen et al. 2006). It, in combination with SRRs, was used in experiments (Bai et al. 2007) for demonstration of negative refractive index in the frequency range 2.5–3.0 GHz. No independent experiments are reported to confirm these results. The results of these experiments need independent confirmation since no negative permittivity associated with ferroelectric domains have been reported in the past. The artificial (multiphase) multiferroics discussed in Sect. 9.2 and 9.3 may be considered as metamaterials. In multiferroics the negative refractive index may be achieved by using composites consisting of natural negative permittivity and negative permeability occurring above the ferroelectric and ferromagnetic resonances (Ward et al. 2005). The main problem here is selection of the ferroelectric and ferromagnetic materials with overlapping frequency ranges where both permittivity and permeability are negative. Special care has to be taken while using negative permittivity ferroelectrics and negative permeability ferromagnetic as host mediums, since the host medium, if not properly “isolated”, destroys the negative permeability and permittivity generated by the SRR (for example) and the negative permittivity generated by thin metallic strips (Dewar 2005), (Maraues and Smith 2004). These metamaterials need structural optimization based on the deep theoretical analysis and modeling of the interaction at the i) interfaces of different phases in nanocomposites (e.g. ferroelectric-ferromagnetic), and ii) between the host medium and ferromagnetic/ferroelectric inclusions. The structural diversity may be achieved by arrangement of the nano-circuit LCR elements, while the tuneability is associated electric field dependent permittivity of the ferroelectrics and/or magnetic field dependent permeability of ferromagnetic materials. Due to the physical nature of the ferroelectric and ferromagnetic materials, the artificial multiferroics may have dual tuning properties, i.e. the dielectric permittivity may be controlled by external electric field and at the same time its magnetic permeability may be tuned by external magnetic field. More importantly, they may offer cross-tuning possibility-tuning of the permittivity by magnetic field (magnetodielectric effect) and/or tuning of the magnetic permeability by electric field.

9.5 Bridging the “THz Gap” The potential applications of THz technology in medicine, imaging/security/ safety, spectroscopy, environmental monitoring, communication etc. are well

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known (Tonouchi 2007). In contrast to microwave and optical technologies the practical implementation/commercialization of the THz technology is largely limited by the lack of adequate natural materials and cost effective components. The quantum cascade lasers (QCLs) discovered recently (Faist et al. 1994, Kohler et al. 2002) open up new possibilities. As compared to the previous µW powers available from the other CW techniques, the QCLs provide power level in the 10 mW range. QCLs partly fill the “THz gap”. On the other hand there is need in cost effective passive and agile THz components, especially in integrated form. In this sense the metamaterials, especially based on ferroelectrics and multiferroics have a great potential to fill up the THz gap. BaxSr1–xTiO3 is the main ferroelectric to be considered since it is well understood, has lowest microwave losses and is widely used in tunable microwave devices. In THz range the ferroelectrics have high and electric field dependent permittivity which is positive below and negative above the soft mode frequency (Petzelt et al. 2007). In SrTiO3, the tunable negative (Misra et al. 2005) and positive (Kuzel et al. 2007) permittivity in THz range has been measured explicitly. The electric field controlled permittivity, especially if it is negative, may be used to develop agile THz components with enhanced performances. For example, by employing surface (interfacial) waves at the boundaries of two dielectrics one of which has negative permittivity (Engheta and Ziolkowski 2006). Most of the multiferroic antiferromagnets are expected to have antiferromagnetic resonance at THz frequencies (Cazayous et al. 2007, Pimenov et al. 2006, Kamba et al. 2007). Hence they offer both positive (below resonance) and negative (above resonance) enhanced magnetic permeability which is also tunable i.e. depends on the external magnetic field. Even more flexibility and enhanced functionalities are expected from exploiting tunable permittivity and permeability potentially offered by intrinsic and artificial multiferroics. These materials may be used to develop agile THz components with enhanced and new functionalities. THz beam formers/scanners, phase and amplitude modulators are only a few to mention.

9.6 Other Tunable Materials The oxide electronics, mainly based on perovskite ferroelectrics is gaining ground. Complex metal oxide perovskite ferroelectrics offer a large spectra of physical phenomena. Depending on the transition metal contained in the structure, perovskite oxides offer metallic, semiconductor, tunable permittivity dielectric, superconducting, colossal magnetoresistive, ferromagnetic/antiferromagnetic piezoelectricity and many other properties. The integration of oxide perovskites with the other oxide materials (i.e. ZnO, (E. Bellingeri et al.)) may lead to a wide variety of new electronic/optoelectronic/spintronic devices.

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9.6.1 Pyrochlores Pyrochlores are another large group of complex metal oxides (Smolenskii 1984) that have moderately high permittivity (50–200) and potentially may be used in tunable microwave devices. They offer better temperature stability, low sintering and crystallization temperatures which is important in tunable LTCC devices and thin film devices integrated with semiconductor substrates containing prefabricated ICs. Additionally, they have low losses, and the moderate permittivity makes the sizes of the varactors based on them compatible with the rest of integrated microwave components. Some of them are not ferroelectric hence potentially no hysteresis and lower losses may be expected. Recently BZN is considered for tunable microwave applications (Kamba et al. 2002, Ren et al. 2001, Park et al. 2005). Two main phases of BZN are distinguished: Bi1.5Zn1.0Nb1.5O7 with cubic pyrochlore structure, and Bi2(Zn1/3Nb2/3)2O7 which has a pyrochlore related (monoclinic) structure. The temperature coefficient of permittivity is negative for the cubic Bi1.5Zn1.0Nb1.5O7, while the monoclinic Bi2(Zn1/3Nb2/3)2O7 has a positive temperature coefficient of permittivity. Non-ferroelectric bismuth zinc niobate (Bi1.5Zn0.5 )( Zn0.5Nb1.5)O7 with the cubic pyrochlore structure is considered by Ren et al. (2001) and Park et al. (2005) and varactors and phases shifters are demonstrated by Hongt et al. (2002 and Park et al. (2006). The temperature and frequency dependences of the real part of the permittivity are negligible at near room and higher temperatures (Kamba et al. 2002). Figure 9.6.1 shows DC bias dependent permittivity and loss tangent of a BZN film measured at 1.0 MHz by Lu and Stemmer (2003). For this film tanδ ~ 0.0005, ε is 180 and the tuneabilities about 55% at 250 V/μm. The shape of the ε(E) dependence is similar but not as steep as for BSTO.

Fig. 9.6.1 Measured permittivity and loss tangent for an RF sputter deposited BZN film. Reprinted with permission from AIP©2003

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Different thin film technologies are used to prepare BZN films. The Bi1.5ZnNb1.5O7 pyrochlore is prepared by the polymeric precursor method deposited by dip coating on fluorine-doped tin oxide coated glass, fused quartz, and Pt/Ti/SiO2/Si(100) substrates (Zanettia and Silvab 2006). The films deposited on glass are annealed at temperatures ranging from 400 to 550°C and from 500 to 800°C, for fused quartz and Pt/Ti/SiO2/Si(100) substrates. The films treated above 450°C are cubic pyrochlore. Full crystallization occurs at 700°C. The films show a high [111] orientation independently of the substrate. The films deposited on fused quartz show the highest orientation. The optical band gap, calculated from the transmission measurements, is in the range 3.9 to 3.2 eV depending on the temperature and the crystallite size. The BZN thin films deposited on platinized Si substrates using a reactive RF magnetron sputtering (Hongt et al. 2002) have a cubic pyrochlore phase and secondary phases of zinc niobate and bismuth niobate when crystallized at 600–800°C. The dielectric constant and tuneability of thin films depend on O2/Ar ratio and post-annealing temperature. The BZN thin films sputtered in 15% O2 and annealed at 700°C have a dielectric constant of 153, tanδ of 0.003 and maximum tuneability of 14% at 100V/μm of DC bias field at 1.0 MHz. It seems BZN, in comparison with BSTO, is less sensitive to the negative effects associated with the electrode interface, i.e. the permittivity of thin BZN films is not affected by thickness (Ren et al. 2001). The dielectric properties of BZN are quite sensitive to its structure and misfit strain. The origin of the low-temperature dielectric relaxation of ceramic Bi1.5ZnNb1.5O7 is studied by Wu et al. (2006). It is found that the Bi1.5ZnNb1.5O7 is not composed of a single phase pyrochlore. It consists of Bi1.5Zn0.92Nb1.5O6.92 and ZnO where the ZnO is distributed evenly in the grain and at the boundary of the Bi1.5Zn0.92Nb1.5O6.92 structure. The observed voids (<1μm) are associated with the loss of volatile Bi during sintering. The Bi1.5Zn0.92Nb1.5O6.92 exhibit a broad dielectric relaxation between 100 and 400 K at 1.8 GHz, with a maximum around 230 K. The Fourier transformation IR spectra predict that dielectric relaxation may occur near room temperature during extremely high frequencies (THz). The substitutional point defects in Bi1.5Zn0.92Nb1.5O6.92 are assumed to be responsible for dielectric relaxation at microwave frequencies and low quality factor (Q × f<520 GHz). A periodically loaded delay line type phase shifter based on parallel-plate BZN varactors reported by Park et al. (2006) exhibit figure of merit 50 degree/dB at 15 GHz. In this work the BZN films are deposited by RF magnetron sputter on Pt bottom electrode. The tuning fields required for BZN are substantially higher than that needed for BSTO. At this instance this is the main disadvantage of the BZN films and they are much less studied. The structure of the BZN films is not completely understood and hence the optimization of the fabrication processes and the film quality still is a challenging problem. Microwave and tuning performances (hysteresis due to oxygen vacancies etc.), lifetime and reliability tests etc. are some of the research challenges for the nearest future.

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9.6.2 Resistive Switching in Oxides Change in resistivity eunder temperature, electric or magnetic fields is widely investigated for memory applications. Electrical switching is observed in a great variety of materials (Madan and Shaw 1988). Chalcogenide glass (e.g. GeSbTe (GST)) in the past (Ovshinsky and Fritzsche 1973), and even more energetically today, are considered for memory applications. Most probably in the nearest future they will appear in the market (Greene 2008). The voltage-current dependence in these materials is either S-or N-shaped with negative differential resistance (NDR). Some of them may be considered for microwave applications. Large changes in resistivity (Rmax/Rmin>1000) is one of the main requirement for microwave applications. Electric field (current) induced change (switching) in resistivity also is preferable. Additionally, in a view of possible integration the compatibility (chemical) with complex oxides (i.e. ferroelectric and multiferroic perovskites) is preferable. Oxides with resistive switching, TiO2, CuxO, CoO, NiOx, Fe2O3, SrZrO3, LaCoCuO4, SrTiO3, etc. considered for memory applications may also be considered for microwave applications provided they have large changes in resistivity. Several mechanisms of resistivity switching are proposed. Experimental evidence available in the literature shows that the resistivity of the interface is higher in switched state. Changing the polarity increases the resistance of the other interface and reduces the resistance of the former. The switching is then due to electromigration of the defects (i.e. oxygen vacancies) from the interface to the bulk of the film and to the other interface (Rozenberg, Inoue and Sanchez 2004). Switching due to local domains-electroformation-generation of conducting channels (Szot 2006) is another widely accepted mechanism. Three main resistive switching mechanisms (phase change, creation/annihilation of metallic protrusion, and oxygen vacancies in metal oxides) are nicely summarized by Meijer (2008). Figure 9.6.2 depicts the I-V performance of NiO (Kim et al. 2007). The measurements show that the switching is accompanied with a negative differential resistance. The experiment shows multiple memory resistance states and anomalous resistance fluctuations between resistance states. The authors indicate that the memory switching in NiO is from percolative formation and rupture of filamentary conducting paths. Pulse experiments are performed to see the dynamics of filament formation and rupture. It is suggested that during the electroforming process, which initialize the memory switching with the first formation of filamentary conducting paths, by voltage pulses, an intermediately formed state showing threshold switching behaviors in micro-second time scale is observed. It is explained in terms of the filamentary conduction model as the tunneling transport between incompletely formed filament segments. The local filamentary conduction model in consideration of the Joule heating effect is considered. A similar I-V is reported for CoO (Kim et al. 2007).

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365

Fig. 9.6.2 I-V curves of memory switching in NiO. RESET means the resistive transition from a low resistance state to a high resistance state, whereas SET means the transition vice versa

A qualitatively different switching performance from high to low resistive state is reported in Cu doped SiO2 films (Choi et al. 2007), Fig. 9.6.3. The device switches around 0.5 V from an “off” (Roff close to 109 Ω) to an “on” state with Ron more than two orders of magnitude lower. A similar switching is reported in CuxO films (Lv et al. 2007).

Fig. 9.6.3 Current-voltage (a) and resistance-voltage (b) curves of 15 nm thick Cu–SiO2 films with various photo diffusion times

The oxides discussed above and VO2 may be used in integrated circuits operating at room temperatures. In VO2 the phase transition from crystalline to amorphous phase takes place at about 68C (for single crystal). This is a very fast process (< 1.0 μs) leading to 3–4 orders of magnitude changes in resistivity. It is widely accepted that the electric current induced switching in VO2 films is associated with heating and monoclinic to tetragonal phase transformation. The electric current induced switching speed is reported to be in nanosecond range (Stefanovich et al. 2000). However, experiments indicate that some non-thermal, electronic switching processes may be involved. The subpicosecond insulator-to-metal tran-

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sition under high interband electronic excitation suggests that, in this regime, the structural transition may not be thermally initiated (Cavalleri et al. 2001). In parallel-plate vanadium dioxide structures high electric fields (105–106 V/cm) may be easily induced, which increases the charge carrier density screening of the Coulomb interactions resulting in elimination of the Mott-Hubbard energy gap at T < Tt. The S-shaped I-V dependence is associated with the development of an electrothermal instability in the switching channel. Under applied voltage the channel is heated up to phase transition temperature (T = Tt at V = Vth) and the VO2 in the channel undergoes a transition from insulating high resistive to a low resistive metallic phase. The parallel-plate devices studied in (Stefanovich et al. 2000) are fabricated by anodic oxidation of the vanadium films deposited in vacuum. Gold top electrodes are evaporated onto the surfaces of the oxide films to form MOM structure. Channels in the vanadium dioxide are formed in the process of electroforming (Chudnovskii et al. 1996). In microwave applications the switches or variable resistors may have parallel-plate or coplanar-plate metal-oxide-metal (MOM) configuration. Figure 9.6.4 (a) shows a typical temperature dependent resistivity of VO2 (Crunteanu et al. 2007), while Fig. 9.6.4 (b) shows the switching performance of this film in a coplanar waveguide in a wide frequency range. A rather good switching performance may be observed.

Tetragonal VO2 film

Moniclinic

(a)

(b)

Fig. 9.6.4 Temperature dependence of the resistivity (a) and microwave switching performance (b) of a VO2 film. Reprinted with permission from EuMA©2007

Single-pole-double-throw (SPDT) switches based on VO2 films operating at 25 GHz are demonstrated earlier (Stotz et al. 1999). Due to the high temperature coefficient of resistance VO2 films are used in uncooled room temperature bolometers (Gonzalez et al. 2003, Chen et al. 2001) with responsivity over 10 kV/W, thermal time constant 11 ms at 300 K and at frequency 30 GHz.

9.6 Other Tunable Materials

367

9.6.3 High Temperature Superconductors (HTS) High temperature superconductors based on complex oxides are chemically and structurally compatible with most of the oxide ferroelectrics. In fact the HTS activities in 1990s considerably boosted the interest in tunable microwave devices based on ferroelectrics (Vendik et al. 1994). The successful synthesis of YBCO films on SrTiO3 single crystal substrates and the tuneability of SrTiO3 at cryogenic temperatures triggered rather extensive activities in developing integrated HTS/ferroelectric tunable devices. On the other hand, attempts have been done to develop microwave devices utilizing superconducting phase transition and the associated change in the resistivity of HTS films. In contrast to DC, at microwave frequencies the YBCO films have finite resistivity below phase transition temperature (93K). The phase transition from the low microwave resistance (superconducting) phase to the high resistive (normal) phase may be initiated by heating, external magnetic field and DC currents above certain critical fields/currents.

9.6.4 Liquid Crystals Dielectric anisotropy in liquid crystals (LC) is also considered for tunable microwave applications. The nematic and smectic LCs are uniaxially symmetric. Due to the week bonding between the molecules they are easily rotated and aligned along the externally applied electric and magnetic fields. The dielectric permittivity of the molecules along the axis ε// and normal to it ε⊥ are different. The dielectric anisotropy is defined as Δε=ε//–ε⊥, where the first term is the permittivity parallel to electric/magnetic field, whereas the second is normal to field direction (Fig. 9.6.5 (a)). Δε may be positive or negative depending on the type of the LC. Most commonly used for microwave devices is the nematic phase LC characterized by a high degree of long range orientational order but no translational order. Molecules in a nematic phase spontaneously order with their long axes roughly parallel. A schematic diagram of a nematic phase is shown in Fig. 9.6.5 (b). Above a certain temperature Tc the liquid crystal is isotropic, with an average permittivity εisotropic (Fig. 9.6.5 (c)). To fully employ the anisotropy the LC molecules without external bias have to be aligned. The alignment on the surface of the substrate depends on dipole interaction, chemical bonding, van der Waals force, steric factor, surface topology, and the elasticity of LC molecule. In the case of the homeotropic alignment the LC molecules align perpendicular to the surface using silane (compound of hydrogen and silicon). The pre-tilt angle is strongly related to the fabrication of LC. The pretilt angle in the devices is generated by the interaction between LC molecules and alignment material. For parallel alignment rubbing the substrate with linen cloth and lens paper is used which results in uniform and unidirectional tilt of the dangling bonds on the surface and the LC molecules align in the direction of rubbing. The tuning in microwave devices is associated with the reorientation of the LC

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9 Potentials and Perspectives

molecules under the applied DC electric and magnetic fields leading to changes in the dielectric permittivity of the mixture along the electric field. The maximum change in the dielectric permittivity (tuneability) is then limited by the dielectric anisotropy Δε (Fig. 9.6.3 (c)) T(E)max= Δε/ε//. As an example, to facilitate alignment of the liquid crystal, the aluminum slats used in microwave phase shifters (Yang and Sambles 2004) are individually coated with a polyimide (AL 1254) film on both sides. They are then baked and the polyimide is unidirectionally rubbed, with a soft cloth, along the short axis direction of the slats to provide homogeneous alignment of the liquid crystal director (the average orientation of the long axis of the nematic molecules). In this work the polyimide layers also act as ion barriers preventing ions entering the thin liquid crystal when an electric field is applied.

ε //

ε

ε Δε > 0

ε⊥

ε isotropic

ε⊥ Tc

(a)

(b)

T

(c)

Fig. 9.6.5 Schematic diagram of the molecule (a) structure (b) and temperature dependence for a nematic LC

A considerable number of tunable microwave devices based on LC are reported. A Q-factor of 310 with a control voltage of 5 V is achieved at 4 GHz in an LC varactor (Yeh et al. 2005). A tuning range of 25.3% for the control voltages from 0 to 5 V was obtained at 5 GHz. Figure 9.6.6 shows the measured DC bias dependent capacitance and Q-factor of the varactor at different frequencies. (a)

(b)

Fig. 9.6.6 E7 liquid crystal based varactor C-V (a) and Q-V (b). Spacing is 5 μm, overall sizes 500x500 μm2. Reprinted with permission from IEEE©2005

9.6 Other Tunable Materials

369

LC tunable filters (Bernigaud 2006), wavelength selectors (Yang and Sambles 2002), beam former/scanner (Kamod et al. 2005) etc. are demonstrated in the past. A tunable coplanar waveguide phase shifter using ferroelectric liquid crystal with floating DC control electrodes is presented in (Moritake et al. 2007). In the frequency range from 10 to 30 GHz the measured phase shift increases with increasing applied voltage. The response time of this phase shifter is less than 1 ms above 120 V. The commercially available nematic LC K15 (5CB) is useful in the temperature range15 to 35C, and its dielectric anisotropy is not sufficiently high for many tunable microwave device applications. To avoid these limitations novel liquid crystals with higher dielectric anisotropy and low microwave is developed by Merck (Weil et al. 2003). The melting point of the novel LC is well below room temperature and the clear point of the nematic phase is close to150C. The measured (Muller et al. 2004) microwave permittivities and loss tangent of this novel LC is shown in Fig. 9.6.7 (a and b). A continuously voltage-tunable invertedmicrostrip phase shifter is demonstrated (Weil et al. 2002).

(a)

(b)

(c) Fig. 9.6.7 Frequency dependences of the permittivity (a) and loss tangent (a) for the new LCs (Reprinted with permission from EuMA©2007), and W-band phase shifter performance based on them (c) (Reprinted with permission from IEEE©2006)

W-band phase shifters based on standard K15 and new highly anisotropic mixture MDA-03-2844 and MDA-05-1132 are reported by Mueller et al. (2006), Fig. 9.6.7 (c)). The return loss is below –10 dB, the figure-of-merit of is 78 degree/dB at 108 GHz. A 35 GHz reflectantenna array also is reported (Moessinger et al. 2006). LC layers at most tens of micrometers thick are used in the visible domain. This is many wavelengths at optical frequencies. The alignment of the LC molecules by appropriate surface treatment of the two glass plates coated on their inner surfaces with transparent conducting layers (indium tin oxide) is not a problem.

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9 Potentials and Perspectives

Moreover, the light is generally incident at close to normal angles. The polarization state of the light is controlled by the LC where a control voltage is applied across the layer. Scaling this up to the microwave domain makes the LC layer several millimeters thick which makes the surface and voltage alignment of the molecules problematic. Thus, the normal incident scenario, with transparent electrodes, is not an option for low microwave frequencies. Perhaps it may be useful at THz frequencies (Chen et al. 2004). Thick layers require high control voltages. Furthermore the required larger amounts LC may make the tunable microwave devices less cost effective. The tunable LC microwave devices considered in this section have parallelplate design where the signals propagate in the LC along the conducting electrodes. This design allows smaller thicknesses of the LC layers and lower tuning voltages. The main advantage of the tunable LC microwave devices is the low losses, especially at high microwave (Mueller et al. 2008) and THz frequencies. The tuning speed is limited by the viscosity, i.e. internal resistance of the LC to flow, resulting from the intermolecular forces. The viscosity, defined as the ratio of shearing stress to the rate of shear, is higher at lower temperature due to lower molecular kinetic energy. The rotational viscosity coefficient γ is a measure of resistance to the rotational motion. The LC switching time ~γ/d, where d is the thickness of the LC layer. The tuning speed, temperature range, integration possibility and the cost are the main issues to be considered where the LC is selected for the development of tunable microwave devices.

9.7 Other/New Effects 9.7.1 Resistivity Switching in Doped SrTiO3 In contrast to tunable microwave applications, the ferroelectric oxides (e.g. SrTiO3) considered for resistive switches are either doped or are intrinsically conductive. Doped semiconducting SrTiO3 is widely used in the industry in voltage dependent resistors-varistors (H. K. Industry Co., LTD), and as a transparent electrode (Pellegrino 2004). The electrical properties of strontium titanate strongly depend on its oxygen content; the oxygen reduced phase (SrTiO3–δ) is metallic, while when stoichiometry is recovered (SrTiO3) the compound turns into a dielectric. The oxygen stoichiometry of SrTiO3 thin films can be tuned by depositing films at different background oxygen pressure. Conductivity of transparent SrTiO3 thin films is controlled by doping with La or Nb. Currently the resistivity switching in doped/conducting SrTiO3 is considered for applications in memory cells. Figure 9.7.1 (a) shows the I-V performance of Nb doped single crystal SrTiO3 (Lee 2007). No sharp switching between the high and low resistive states is observed. However, the resistance ratio of the two current states is about two orders of magnitude at low voltage. The switching is explained by variation of the Schottky barrier height due to charge trapping at the metal/STO interface (Fujii et al. 2005).

9.7 Other/New Effects

371

The I-V performance of the Cr doped SrTiO3 (Phan et al. 2007) is radically different. It changes from high to resistance, Fig. 9.7.1 (b). The variable range hopping (VRH) and the space charge limit current (SCLC) conduction are regarded responsible as a transport mechanism. In the positive voltage region, the leakage current is due to VRH conduction. The transition from the VRH to the SCLC conduction is explained by localized traps.

Fig. 9.7.1 I-V dependences of the conductive SrTiO3 doped by Nb (a) and Cr (b)

The Cr-doped (0.2 mol %) SrTiO3 single crystals exhibit an electrical-fieldinduced insulator-to-conductor transition with a resistive memory effect. The resistivity measurements on the electrically conducting state is shown to be metallic, while he insulator-to-metal transition is accompanied by an increase of the Cr valence underneath the anode from Cr3+ to approximately Cr4+ (Meijer et al. 2005). It is assumed that the insulator-to-metal transition is associated with internal doping due to a change of the Cr valence, thereby providing free carriers to the Ti 3d band. No microwave applications of doped SrTiO3 have been reported so far. The exploration of the conducting/doped SrTiO3 for microwave switch and tunable resistor applications seems to be an interesting research topic for the nearest future.

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9 Potentials and Perspectives

9.7.2 Nanoscale Effects Exploiting oxide interfaces to generate new functions: The emerging nanoscale phenomena at the interfaces between complex non-magnetic oxides associated with the high mobility 2D electron gas, like interfacial superconductivity, ferromagnetism, metal-insulator transition (Chen et al. 2008) etc. For example, it is established that these effects appear at the interface of 3 unit cell thick films of LaAlO3 and isolating SrTiO3 substrate. Based on the room temperature experiments and local density of state simulations Chen et al. (2008) suggest that the switching between the metallic and isolating states of the interfacial layers between the 3 unit cell thick LaAlO3 and SrTiO3 substrate is associated with the oxygen vacancies in 3 unit cell thick LaAlO3 film. Adding and removing oxygen vacancies leads to drastic changes in the density of 2D electron gas at the interface. This and similar experiments show that i) at nano-scale the physical properties are extremely sensitive to the number of unit cells involved (more or less than 3 unit cell in the examples considered in (Chen et al. 2008) and point defects (e.g. oxygen vacancies); ii) for practical implementations of these extraordinary effects industrial scale fabrication processes of the nanoscale devices have to be developed. Toroidal ordering the low-temperature ground state instead of conventional parallel or antiparallel atomic displacements of dipoles (Scott 2005) may open up new possibilities, if it is experimentally proven. Theoretical investigation shows (Zhuravlev et al. 2005) that by switching the polarization in a ferroelectric film the spin of the tunneling through it spin polarized current may be may be controlled. This effect may be used for developing of new types of spintronic and microwave devices.

9.7.3 Integration with Semiconductors The heterogeneous integration of the ferroelectrics with semiconductors, for example by heteroepitaxial growth of ferroelectrics (e.g. SrTiO3) on semiconductor substrate, is yet another possible scenario promising new physical effects (Li et al. 2003). SrTiO3 is considered as a high permittivity dielectric in MOS transistors (Eisenbeiser et al. 2000, McKee et al. 1998). Ferroelectric films in coplanar-plate varactors allow tailoring the C-V performance of the MOS varactors by setting the polarized state of the ferroelectric film (Gevorgian et al. 2001). SrTiO3 films are proposed as buffer layers to integrate GaAs with silicon (Motorola 2002). Utilization of the functional properties of ferroelectrics (tunable permittivity, piezoelectric effect) integrated with GaAs and Si devices has a great potential in terms of development of ICs with enhanced functionalities. Perhaps the other III-V semiconductors also (InP, GaN, InAs etc.) may be integrated with silicon. A successful integration of BST films on AlGaN/GaN High Electron-Mobility Transistor (HEMT) monolithic microwave integrated circuits on sapphire substrates reported

9.8 Conclusions

373

in (Xu et al. 2004). The main problem in the nearest future is to develop industrial processes of fabrication of ferroelectric films on large area semiconductor, first of all Silicon, substrate followed by exploitation of the possibilities of the new technology-development of integrated III-V and silicon active devices, photonic circuits, ICs and MMICs.

9.8 Conclusions After successful utilization of the tunable dielectric properties one may think of using the other properties of the ferroelectrics in microwave devices. One of the new functionalities of ferroelectrics, the induced piezoelectric effect in paraelectrics is already being considered for applications in tunable TFBARs and devices based on them. The semiconductor properties of SrTiO3 used in the voltage dependent resistors-varistors (H. K. Industry Co., Ltd) may be considered for application in tunable microwave loads. The resistive switching in the doped ferroelectrics considered for memory application may be used in microwave switches etc. Integration of the devices based on these properties with the tunable microwave devices (on a common substrate/carrier) seems possible and needs further investigations. The multiferroics with their ferroelectric and ferromagnetic properties offer even a richer variety of functionalities, including cross controlling of the dielectric and magnetic properties. While the intrinsic multiferroics still are in their infancy, the artificial multiferroics have a greater potential to be utilized in microwave devices. In this sense the nanosize effects in ferroelectrics and heterogeneous integration of ferroelectrics with ferromagnets and semiconductors in the form of the nanostructured metamaterials is quite promising and may lead to materials with the designed properties. Alternative agile materials are being considered for microwave applications. The pyrochlores are the most possible competitors to paraelectrics in terms of tuning speed and low losses. Additionally they do not have polar (ferroelectric) state and associated hysteresis effects. Pyrochlores for agile microwave applications are still on a research stage. Even though the liquid crystals have been considered in the past, only the recently synthesized new composition with higher anisotropy and relatively high tuning make it possible to consider them for application in devices with acceptable performance. The main disadvantages of the liquid crystals are their very slow response time and poor integration capability. The nonperovskite (non-ferroelectric) oxides and chalcogenides extensively considered for memory application may, potentially, be useful for agile microwave applications too.

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References Bai Y et al. (2007) Left-handed material based on ferroelectric medium. Optics Express 15:8284 Bellingeri E et al. (2005) High mobility ZnO thin film deposition on SrTiO3 and transparent field effect transistor fabrication. Superlattices and Microstructures 38:446–454 Bellingeri E et al. (2005) Oxide devices for transparent electronics. Thin Solid Films 486:186 Bernigaud J F (2006) Liquid Crystal Tunable Filter Based On DBR Topology. Proc EuMC’2006:368–371 Caloz C, Itoh T (2006) Electromagnetic Metamaterials. Wiley Cavalleri A et al. (2001) Femtosecond Structural Dynamics in VO2 during an Ultrafast SolidSolid Phase Transition. Phys Rev Lett 87:237401 Cazayous M et al. (2007) arXiv:0712.3044v1 arXiv:0712.3044v1 (cond-mat.str-el) Chau K J et al. (2007) Electron-spin-dependent terahertz light transport in spintronic-plasmonic media. Phys Rev Lett 98:133901-1 Chen C et al. (2001) Characterisation of VO2 uncooled microbolometer linear array. Sens Actuat A 90:212–214 Chen C et al. (2008) Nanoscale control of an interfacial meta-insulator transition at room temperature. Nature Materials 7:298–302 Chen C-Y et al. (2004) Magnetically tunable room-temperature 2π liquid crystal terahertz phase shifter. Optics Express 12:2630–2635 Chen H-T et al. (2006) Active terahertz metamaterial devices. Nature 444:597–600 Cheong S W, Mostovoy M (2007) Multiferroics: A magnetic twist for Ferroelectricity. Nature Materials l6:13–20 Choi J, Wehrspohn R B, Gösele U (2003) Moiré pattern formation on porous alumina arrays using nanoimprint lithography. Advanced Materials 15:1531–1534 Choi K-J et al. (2007) Characterization of copper doped silicon oxide films for programmable metallization cell memory applications. ISIF 2007 Chudnovskii F A et al. (1996) Electroforming and Switching in Oxides of Transition Metals: The Role of Metal–Insulator Transition in the Switching Mechanism. J Solid State Chem 122:95– 99 Crunteanu A et al. (2007) Microwave Switching Functions Using Reversible Metal-Insulator Transition (MIT) in VO2 Thin Films. Proc EuMC’2007:12–15 Degiron A et al. (2007) Modulating and tuning the response of metamaterials at the unit cell level. Optics Express 15:1115 Deleniv A et al. (2007) Silicon Substrate Integrated Ferromagnetic Nanowires for Microwave. Proc EuMC:1310–1313 Dewar G. (2005) A thin wire array and magnetic host structure with n<0. J Appl Phys 97:10Q101 Eisenbeiser K et al. (2000) Field effect transistors with SrTiO3 gate dielectric on Si. Appl Phys Lett 76:1324–1326 Eleftheriades G V and Balmain K G (2005) Negative-Refraction Metamaterials: Fundamental Principles and Applications. John Wiley & Sons, IEEE Press Engheta N and Ziolkowski R (2006) Metamaterials. Wiley Evans P R et al. (2007) Toward Self-Assembled Ferroelectric Random Access Memories: HardWired Switching Capacitor Arrays with Almost Tb/in Densities. Nano Lett 7:1134–1137 Faist J et al. (1994) Quantum cascade laser. Science 264:553–556 Fleury P A and Worlock J M (1968) Electric-Field-Induced Raman Scattering in SrTiO3 and KTaO3. Physical Review 174:613–623 Fujii T et al. (2005) Hysteretic current-voltage characteristics and resistance switching at an epitaxial oxide Schottky junction SrRuO3/SrTi0.99Nb0.01O3. Appl Phys Lett 86:0123107 Galatsis K (2006) International Technology Roadmap for Semiconductors: Strongly correlated electronic materials for beyond CMOS logic. Workshop summary Stanford University, November 15, 2005 (http://www.galatsis.com/publications/Report%20ERM%20v7 mg.pdf)

References

375

Gevorgian S and Vorobiev A (2007) Tunable Metamaterials Based on Ferroelectric Varactors. Proc EuMC:404–407 Gevorgian S et al. (2001) MOS Varactors with Ferroelectric Films. Dig IMS’2001 2:1195–1198 Gevorgian S et al. (2006) The Potential of Thin Film Ferroelectric Varactors for Applications in Large Microwave Arrays. IEEE Radio and Wireless Symposium RWS 2006, San Diego Gevorgian S et al. (2007) 1D and 2D Tunable Metamaterials Based on Ferroelectric Varactors. Metamaterails’2007, Rome Gonzalez F J et al. (2003) Antenna-coupled VOx thin-film microbolometer array. Micr Opt Techn Lett 38:235–237 Gonzalez-Diaz J B et al. (2007) Enhanced magneto-optics and size effects in ferromagnetic nanowire arrays. Advanced Materials 19:2643 Greene K (2008) A Memory Breakthrough. Two firms have doubled the capacity of phasechange memory, a likely replacement for flash. Technology review published by MIT, February 04, 2008 (http://www.technologyreview.com/read_article.aspx?ch=specialsections&sc=storage&id=20 148&a=f) Hand T et al. (2007) Characterization of Tunable Metamaterial Elements Using MEMS Switches. IEEE Antenn Wireless Prop Let 6:401–404 He Y et al. (2007) Tunable negative index metamaterial using yttrium iron garnet. J. Magnetism and Magnetic Materials 313: 187 Heindl R et al. (2007) Structure, magnetism, and tunable microwave properties of pulsed laser deposition grown barium ferrite/barium strontium titanate bilayer films. J Appl Phys 101:09M503 Hernandez B A et al. (2002) Sol-gel synthesis and characterization of BaTiO3 and PbTiO3 nanotubes Chem Mater 14:480–482 Hongt Y P et al. (2002) RF Sputtered BZN Pyrochlore Thin Films for Voltage Tunable Dielectric Device Applications. Mat Res Soc Symp Proc:720 Hongt Y P et al. (2002) Voltage tunable dielectric properties of rf sputtered Bi2O3–ZnO–Nb2O5 Pyrochlore thin films. Thin Solid Films 419 (1–2):183–1881 Kamba et al. (2002) Anomalous broad dielectric relaxation in Bi1.5Zn1.0Nb1.5O7 Pyrochlore. Phys Rev B 66:054106.1-054106.8 Kamba S et al. (2007) Infrared and terahertz studies of polar phonons and magnetodielectric effect in multiferroic BiFeO3 ceramics. Phys Rev B 75:024403–024408 Kamba S et al. (2008) Near room temperature ferroelectric phase transitions in SrTiO3 and EuTiO3 strained thin films: Polar phonon properties. ISIF’2008 Kamod H et al. (2005) Conductor loss reduction for liquid crystal millimeter wave beam former. IEICE Electronics Express 2 (18):471–446 Kim D C et al. (2007) Investigation on resistive memory switching mechanism of NiO. ISIF 2007 Kim K H (2005) Radio Frequency Applications of Carbon Nanotube Coated Permalloy Nanorod Array. Proc APMC’2005 Kim S H et al. (2007) Properties of CoO thin films as alternative RRAM materials. ISIF 2007 Kirby S D et al. (2007) An approach to achieve a negative index of refraction using coincident resonances. J. Physics D: Applied Physics 40:1161–1167 Kohler R et al. (2002) Terahertz semiconductor-heterostructure laser. Nature 417:156–159 Kotsuka Yet al. (2007) Novel computer controllable metamaterial beyond conventional configurations and its microwave absorber application. IMS’2007:1627 Kuylenstierna D et al. (2003) Tunable Electromagnetic Bandgap Performance of Coplanar Waveguides Periodically Loaded by Ferroelectric Varactors. Microwave and Optical Technology Letters 39:79–86 Kuzel P et al. (2007) Highly tunable SrTiO3/DyScO3 heterostructures for applications in the terahertz range. Appl Phys Lett 91:232911.1-232911.3 Landy N I et al. (2007) Terhertz metamaterials for active, tunable, and dynamic devices. Proc SPIE 6581:65810P

376

9 Potentials and Perspectives

Lee B (2007) Resistive Switching Behavior of SrTiO3 Single Crystals for Nonvolatile Memory Application. ISIF 2007 Li H et al. (2003) Two-dimensional growth of high-quality strontium titanate thin films on Si. J Appl Phys 93:4521–4525 Li J (2006) PhD thesis. University of Maryland Lim S et al. (2004) Electronically-controlled metamaterial-based transmission line as a continuous-scanning leaky-wave antenna. Dig IEEE IMS’2004 1:313 Lim S et al. (2005) Metamaterial-Based Electronically Controlled Transmission-Line Structure as a Novel Leaky Wave Antenna With Tunable Radiation Angle and Beamwidth. IEEE Trans Microwave Theory Tech 53:161–173 Lu W, Stemmer S (2003) Low-loss, tunable bismuth zinc niobate films deposited by rf magnetron sputtering. Appl Phys Lett 83:2411–2413 Luo Y et al. (2003) Nanoshell tubes of ferroelectric lead zirconate titanate and barium titanate. Appl Phys Lett 83:440–442 Lv H B et al. (2007) Resistive Switching of CuxO Films for Nonvolatile Memory Application. ISIF 2007 Madan A and Shaw M P (1988) The Physics and Applications of Amorphous Semiconductors. Academic Press, New York Maraues R, Smith R (2004) Comment on “Electrodynamics of metallic photonic crystals and the problem of left-handed materials”. Phys Rev Lett 92:059401 Masuda H and Fukuda K (1995) Ordered Metal Nanohole Arrays Made by a Two-Step Replication of Honeycomb Structures of Anodic Alumina. Science 268:1466–1468 McKee R A et al. (1998) Crystalline Oxides on Silicon: The First Five Monolayers. Phys Rev Lett 81 (14):3014–3017 Meijer G I (2008) Who Wins the Nonvolotile Memory Race? Science 319:1625–1626 Meijer G I et al. (2005) Valence states of Cr and the insulator-to-metal transition in Cr-doped SrTiO3.Phys. Rev B 72:155102 Melle S et al. (2003) Magneto-optical properties of nickel nanowire arrays. Appl Phys Lett 83:4547–4549 Misra M et al. (2005) Observation of TO1 soft mode in SrTiO3 films by terahertz time domain spectroscopy. Appl Phys Lett 87:182909 Moessinger A et al. (2006) Electronically reconfigurable reflectarrays with nematic liquid crystals. Electron Letters 42:899–900 Moritake H et al. (2007) Fast-Switching Microwave Phase Shifter of Coplanar Waveguide Using Ferroelectric Liquid Crystal. Japn J Appl Phys 46 (21):L519–L521 Morozovska A N and Glinchuk M D (2006) Phase diagrams and polar properties of ferroelectric nanotubes and nanowires. arxiv:astro-phys/0608578v1(cond-mat.mtrl-sci) Morozovska A, Glinchuk M and Eliseev E (2006) Ferroelectrisity enhancement in ferroelectric nanotubes. arXiv:cond-mat/0608681v1 (cond-mat.mtrl-sci) Morrison F D et al. (2003) Ferroelectric nanotubes. Rev Adv Sci 4:114–122 Morrison F D et al. (2003) Use of the “Mist” (Liquid-Source) Deposition System to Produce New High-Dielectric Devices: Ferroelectric-Filled Photonic Crystals and Hf-Oxide and Related Buffer Layers for Ferroelectric-Gate FETs. Microelectron Eng 66:591-9 Motorola Starts a GaAs-on-Si Company; Invests in IQE, III-V review 15 (1) 2002 Mueller S (2006) Passive Phase Shifter for W-Band Applications using Liquid Crystals. EuMC’2006:3006–3009 Mueller S et al. (2008) W-band characterization of anisotropic liquid crystals at room temperature. EuMC’2008 Müller S et al. (2004) Novel Liquid Crystals for Tunable Microwave Components. IEEE IMS workshop 2004 Nath J et al. (2006) Discrete Barium Strontium Titanate (BST) Thin-Film Interdigital Varactors on Alumina: Design, Fabrication, Characterization, and Applications. IEEE Int Microwave Simp IMS’2006:552–555

References

377

Nielsch K et al. (2000 Uniform nickel deposition into ordered alumina pores by pulsed electrodeposition. Adv Mater 12:582 Ostapchuk T et al. (2002) Origin of soft-mode stiffening and reduced dielectric response in SrTiO3 thin films. Phys Rev B 66:235406 Ostapchuk T et al. (2007) Far Infrared Spectroscopy of Sr1−xBaxTiO3 (0.01≤x≤0.2) Ceramics. Ferroelectrics 353:70–77 Ottow S, Lehmann V, Foell H (1996) Development of Three-Dimensional Microstructure Processing Using Macroporous n-Type Silicon. Appl Phys A63:153–9 Ovshinsky S R, Fritzsche H (1973) Amorphous semiconductors for switching, memory, and imaging applications. IEEE Trans Electron Devices 20:91–105 Park J et al. (2005) Microwave dielectric properties of tunable capacitors employing bismuth zinc niobate thin films. J Appl Phys 97:084110 Park J et al. (2006) Distributed Phase Shifter with Pyrochlore Bismuth Zinc Niobate Thin Films. IEEE Microwave Wireless Comp. Lett 16:264–267 Pellegrino L (2004) PhD thesis. Genoa University Petzelt J et al. (2001) Dielectric, infrared, and Raman response of undoped SrTiO3 ceramics: Evidence of polar grain boundaries. Phys Rev B 64:184111–184120 Petzelt J et al. (2007) Infrared and Raman studies of the dead grain-boundary layers in SrTiO3 fine-grain ceramics. J Physics: Cond Matter19:196222 Phan B T et al. (2007) Electrical conduction of Cr-Doped SrTiO3 thin films. ISIF’ 2007 Pimenov A et al. (2006) Possible evidence for electromagnons in multiferroicmanganites. Nature Physics 2:97 Qi Yi et al. (2006) Local Dielectric Measurements of BaTiO3–CoFe2O4 Nano-composites Through Microwave Microscopy. arXiv:cond-mat/0601059 (cond-mat.mtrl-sci) Ramesh R, Spaldin N (2007) Multiferroics: progress and prospects in thin films. Nature Materials 6:21–29 Razumov S V et al. (2002) Characterization of quality of BaxSr1–xTiO3 thin film by the commutation quality factor measured at microwaves. Appl Phys Lett 81:1675–1678 Ren W et al. (2001) Tuneability of Bi-Rich BZN Cubic Pyrochlore Thin Films by Reactive Sputtering. J Appl Phys 89:767 Rozenberg M J, Inoue I H and Sanchez M J (2004) Nonvolatile memory with multilevel switching: A basic model. Phys Rev Lett 92:178302-1 Saib A et al. (2003) Magnetic photonic band-gap material at microwave frequencies based on ferromagnetic nanowires. Appl Phys Lett 83:2378–2380 Saib A et al. (2005) An Unbiased Integrated Microstrip Circulator Based on Magnetic Nanowired Substrate. IEEE Trans. Microwave Theory and Techniques 53(6):2043–2049 Scott J F (2005) Novel geometric ordering of ferroelectricity. Nature Materials 4:13–14 Scott J F (2006) Nanoferroelectrics: Statics and dynamics. J Physics: Condensed Matter 18:R361–R386 Scott J F et al. (2005) Recent Materials Characterizations of [2D] and [3D] Thin Film Ferroelectric Structures. J Am Ceram Soc 88:1691–1701 Seo B I et al. (2006) Growth of ferroelectric BLT and Pt nanotubes for semiconductor memories. J Crystal Growth 292:315–319 Shen J et al. (2006) Ferroelectric and dielectric properties of {Pb(Ni1/3Nb2/3)O3– PbTiO3}/{Ni0.2Cu0.2Zn0.6)Fe2O4} composites. Materials Letters 60:1071 Sirenko A et al. (2000) Soft-mode hardening in SrTiO3 thin films NATURE 404:373–376 Sklyuyev A et al. (2006) Measurement of complex permeability of ferromagnetic nanowires using cavity perturbation techniques. IEEE CCECE/CCGEI:1486–1489 Smolenskii G A (1984) Ferroelectrics and related materials. Gordon and Breach Spaldin N A et al. (2003) Journal of Solid State Chemistry 176:615–632 Spiegel J et al. (2007) Ferromagnetic material with negative permeability for tunable left handed devices EuMC’2007:1–4 Stefanovich G et al. (2000) Electrical switching and Mott transition in VO2. J Phys: Condens. Matter 12:8837–8845

378

9 Potentials and Perspectives

Stotz M et al. (1999) Thermally controlled coplanar microwave switches. EuMC’1999:415–418 Szot et al. (2006) Nanoscale resistive switching in SrTiO3 thin films. Physica Status Solidi (RRL) – Rapid Research Letters 1:R86–R88 Tonouchi M (2007) Cutting-edge terahertz technology. Nature Photonics 1:97105 Tsymbal E Y and Kohlstedt H (2006) Tunneling across a ferroelectric. Science 313:181 Vendik O, Mironenko I, Ter-Martirosyan L (1994) Superconductors Spur Applications of Ferroelectric Films. Microwaves & RF July:67–70 Vlad A et al. (2006) Controlled growth of single nanowires within a supported alumina substrate. Nanotechnology 17: 4873–4876 Vorobiev A, Gevorgian S (2007) Large area BaxSr1–xTiO3 thin films grown by magnetron sputtering. MRS’2007 Ward D W et al. (2005) On the physical origins of the negative index of refraction. New J Phys 7:213 Ward D W et al. (2004) The Role of Multiferroics in the Negative Index of Refraction. http://arxiv.org/ftp/cond-mat/papers/0401/0401046.pdf

Weil C et al. (2002) Tunable inverted-microstrip phase shifter device using nematic liquid crystals. Dig IEEE IMS’2002:367–370 Weil C et al. (2003) Highly-anisotropic liquid-crystal mixtures for tunable microwave devices. El Lett 39:1732–1734 Wu M-C et al. (2006) Comparison of microwave dielectric behavior between Bi1.5Zn0.92Nb1.5O6.92 and Bi1.5ZnNb1.5O7. J Eur Ceram Soc 26 (10–11):1889–1893 Xu H et al. (2004) Integration of BaxSr1–xTiO3 Thin Films With AlGaN/GaN HEMT Circuits. IEEE El Dev Lett 25:49–51 Yang F, Sambles J R (2002) A liquid crystal microwave wavelength selector. Liquid Crystals Today 11:1–2(2) Yang F, Sambles J R (2004) Microwave liquid-crystal variable phase grating. Appl Phys Lett 85(11): 2041–2042 Yeh J A et al. (2005) Microwave Characteristics of Liquid-Crystal Tunable capacitors. IEEE Electr Dev Lett 26:451–453 Zanettia S M, Silvab S A da (2006) Structural and optical properties of Bi1.5ZnNb1.5O7 Pyrochlore thin films prepared by chemical method. Thin Solid Films 497(1–2):72–76 Zhao Q et al. (2007) Tunable Metamaterials Based on Nematic Liquid Crystals. PIERS’2007:302 Zhao T et al. (2006) Electrical control of antiferromagnetic domains in multiferroic BiFeO3 films at room temperature. Nature Materials 5:823–829 Zheng H et al. (2004) Three-dimensional heteroepitaxy in self-assembled BaTiO3-Fe2O4 nanostructures. Appl Phys Lett 85:2035–2037 Zhuravlev M Ye et al. (2005) Ferroelectric switch for spin injection. Appl Phys Lett 87:222114– 222116 Zhuravlev M Ye et al. (2005) Giant electroresistance in ferroelectric tunnel Junctions. Phys Rev Lett 94:246802

Chapter 10

Concluding Remarks

Abstract This chapter summarizes the main performance features of the ferroelectric devices including temperature stabilization, nonlinearity and power handling capability, hysteresis, long term stability etc. It is shown that these and other “traditional” concerns pose no limitations on commercialization and wide scale applications of ferroelectrics in tunable microwave devices.

10.1 Introduction When it comes to practical applications of ferroelectric devices some concerns are expressed and questions are asked. What about the temperature stability, nonlinearity, power handling capability, hysteresis, reliability etc? It is shown, in the next sections of this chapter, that these and other concerns are somehow exaggerated and they pose no limitations on commercialization and wide scale applications of ferroelectrics in tunable microwave devices.

10.2 Stabilization of the Temperature Dependences The inherent property of ferroelectrics – the strong temperature dependence of permittivity (and losses) was one of the major concerns for their practical applications in agile microwave components. Several methods proposed recently indicate that the problem is not as severe as it appears from the first glance, i.e. from the simple consideration of the ε(T) dependences of ferroelectrics. The following subsections give a brief summary of temperature stabilization methods.

379

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10 Concluding Remarks

10.2.1 Intrinsic Temperature Dependences of Permittivity and Tuneability In general for a displacive ferroelectric, in paraelectric phase, the tuneability is proportional to the permittivity which at low fields is given by (Tagantsev 2008): 2 Tε ( E DC , T ) = ADC [ε (0, T )]3 E DC

(10.2.1)

where ADC is a material specific constant. Typical dependences of the capacitance and tuneability of a parallel-plate Ba0.25Sr0.75TiO3 varactor in a wide temperature range are shown in Fig. 10.2.1. The capacitance and the tuneability are higher close to the Curie temperature, and decreases with increased temperature. As it is seen from Fig. 10.2.1 the temperature dependence of the capacitance is rather low near room temperature with a substantial tuneability at relatively low DC fields. In a tunable microwave device the temperature dependence has to be within the specified limits. The proposed methods of temperature stabilization may be classified as physics based and circuit based. The physics (material) based methods include controlling the composition and nanostructure. The circuit based methods are external and include electronic feedback, Peltier element, capacitive voltage divider based DC bias compensation etc. 15

1 E=30 V/μm T(E)=[C(0)-C(E)]/C(0)

Capacitance, pF

0 V/μm 10

5

7.5

15 V

22.5

100

200

300

22.5 0,4 0,2

15

0

400

Temperature, K

(a)

0,6

7.5

30 V/μm

0

0,8

500

100

200

300

400

500

Temperature, K

(b)

Fig. 10.2.1 Temperature dependencies of the capacitance (a) and tuneability (b) of a thin film parallel-plate Ba0.25Sr0.75TiO3 varactor

10.2 Stabilization of the Temperature Dependences

381

10.2.2 Materials and Device Design Based Methods of Stabilization 10.2.2.1 Utilizing the Intrinsic Potential of a Ferroelectric in Paraelectric Phase The simplest method is based on trading temperature stability against tuneability, i.e. by choosing the temperature interval of operation well above the temperature corresponding to the permittivity maximum. By selecting a BSTO composition with a smaller content of Ba, the temperature of the peak permittivity is set well below the range of the operation temperatures so that the slope of ε(Τ) dependence is in the desired limit. As it follows from temperature dependence shown in Fig. 10.2.1, the applied DC filed provides an additional reduction of the slope. Under higher DC fields the temperature dependence becomes even smaller. One may select the controlling bias fields in the range of higher fields, utilizing only a part of the available tuning. As a result, for some applications, the temperature dependence of a ferroelectric varactor may be set within some acceptable limits. Working in the range of higher DC fields offer an extra benefit for free; the Q-factor of thin ferroelectric film varactors is higher at higher DC fields. A more advanced method is demonstrated in (Prudan et al 2005). 10.2.2.2 Tailoring Temperature Stabilization in Layered Paraelectric/Ferroelectric Composites For some applications one may need even lower temperature coefficient of capacitance (TCC) and higher tuneability at the same time. An alternative way to increase the temperature stability of a ferroelectric varactor, (US patent 6,563,153 B2, Gevorgian et al. 2001), suggests use of layered ferroelectric films consisting of polar and paraelectric phases as shown in Fig. 10.2.2 (a). In the proposed method a coplanar-plate varactor is made of two ferroelectrics with different Curie temperatures. One of the ferroelectrics (Ba0.25Sr0.75O3) is in paraelectric phase (permittivity peak at about 150K), and the other (Ba0.75Sr0.25O3) is in polar phase (permittivity peak above 320K). In the temperature interval between the peaks, the permittivity of the polar phase increases with increasing temperature, while the permittivity of the paraelectric phase decreases. In the experiment with coplanarplate electrodes (Fig. 10.2.2 (a)) the gapwidth is mach larger than the thickness of the ferroelectric layers. Due to this fact, and high permittivity of the films, the electric field between the plates is practically in the plane of the films, i.e. the two ferroelectric layers are “connected in parallel”. The TCC (=ΔC/CΔT) of the varactor between the dielectric permittivity peaks (temperature range 150–250 K), Fig. 10.2.2, is less than 2×10–4, which is comparable with the TCC of the best commercial non-tunable capacitors. At the same time in this temperature range the

382

10 Concluding Remarks

Q-factor and the tuneability are high. Depending on the geometry, the temperature interval and the material used, the capacitor may be designed to have a desired TCC. A similar approach may be used in parallel-plate varactors based on columnar ferroelectric films.

Fig. 10.2.2 The cross section (a) and the temperature dependences of the capacitance and Q-factor (b) of a temperature compensated coplanar-plate varactor. Layer thicknesses: top Ba0.75Sr0.25TiO3 –0.2 μm, bottom Ba0.25Sr0.75TiO3 – 0.2 μm, middle MgO – 0.03 μm, YBCO – 0.3 μm, Au electrodes – about 1.0 μm. Reprinted with permission from AIP©2001

10.2.2.3 Nanostructured Ferroelectric Films As a limiting case of the method described in the previous section, one may use superlattices (Tabata et al. 1994) and graded (Jeon et al. 01) ferroelectric films with continuous or quasi-continuous increasing/decreasing of the Ba content in the BaxSr1–xTiO3 films. However, the method of reducing the temperature dependence by using layered paraelectric/ferroelectric (or graded) composites may suffer from hysteresis due to the involved polar phases. On the other hand within the superlattice stuck a ferroelectric film with normally ferroelectric (polar) phase may be in a misfit strain induced paraelectric phase (Haeni et al. 2004) leading to reduction/elimination of the hysteresis. The effect of the strain becomes dominant with decreasing the film thickness (grain sizes). 10.2.2.4 DC Bias and Temperature Controlled Stabilization Electronic Temperature Stabilization The temperature dependence of the permittivity and hence the capacitance of the ferroelectric varactors may be compensated by adjusting the DC bias applied to the devices. In circuit and system applications with built in microprocessors this may be easily achieved which may require slightly complicated control circuits. The electronic system may become even more complex and in some cases not cost

10.2 Stabilization of the Temperature Dependences

383

effective in systems without microprocessors. Use of Peltier elements to control the temperature of ferroelectric varactors and devices may also be considered. The extra cost of temperature stabilization/control electronics may limit the application of these methods. Use of Capacitive Voltage Dividers A simple and cost effective way of temperature stabilization is shown in Fig. 10.2.3 (Setter 2005). The bias network consists of a capacitive voltage divider, and a DC decoupling network. Ferroelectric varactors and microwave devices based on them have extremely low leakage currents. Hence, to bias (control/ derive) them, a simple capacitive voltage divider may be used, Fig. 10.2.3. The voltage divider consists of a fixed capacitor, C, based on a conventional dielectric, preferably with good temperature stability, and a temperature sensitive capacitor, CT, made of the same ferroelectric as the one used in the varactor. At given bias voltage VDC, the voltage drops on capacitors C and CT are:

VC = VT =

CT V DC C + CT

(10.2.2)

C V DC C + CT

(10.2.3)

The temperature dependence of the capacitor CT is similar to that of the varactor itself. Due to this dependence a voltage drop redistribution takes place in the capacitive voltage divider where the temperature changes. The voltage on CT decreases where its capacitance increases with the changing temperature. In a simple case the DC decoupling network may be a resistor or an inductor. However, the achieved temperature stabilization is very limited for these simple networks. More complex networks (i.e. buffer amplifier) may be used to increase the efficiency of the stabilization. VDC CT Vv

Varactor

Decoupling network

C

VT

VC

Fig. 10.2.3 The concept of the temperature stabilization using capacitive voltage dividers

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10 Concluding Remarks

10.3 Nonlinearity and Power Handling Capability In Sect. 2.6 two aspects of the nonlinearity are distinguished. The DC field dependent permittivity constitutes the static nonlinearity used in tunable microwave devices. The microwave power dependence of the permittivity constitutes the dynamic nonlinearity. Dynamic nonlinearity as a useful effect is used in nonlinear devices (see Sect. 5.8). For these applications the varactors need to be designed so that the microwave field induced changes of the capacitance are as high as possible The dynamic nonlinearity has a negative impact on the performance of the tunable microwave devices in the form of harmonic generation, intermodulation distortion and power handling capability. The power handling capability of ferroelectric varactors and devices is limited by two main factors: dynamic nonlinearities and heating (RF leakage currents and breakdown voltages). There are several ways to decrease dynamic nonlinearity and increase power handling capability (see Sect. 4.7). In fact, the nonlinear and power handling performances of ferroelectric varactors are superior to competing technologies-provided they are properly designed. This is not an issue for ferroelectric varactors. Moreover, the recent developments of matching networks for the power amplifiers indicate that ferroelectric varactors are the best choice for high power applications.

10.4 Hysteresis, Retention, Long Term Stability and Noise Hysteresis has negative impact in a tunable device, Fig. 10.4.1. In bulk ferroelectrics it is associated with domains in polar phase (see Fig. 2.3.2 (b), Chap. 2). In thin films it may be suppressed by controlling the misfit strain, i.e. optimization of the structure of devices and their fabrication process which lead to the downward shift of the Curie temperature. Ferroelectrics with hysteresis may be used in analog tunable microwave devices provided that the losses are small, and the hysteresis (Fig. 10.4.1 (a, and b)) is stable and repeatable at the DC bias reversals. In this case the desired capacitance may be unambiguously defined by applying control voltages of special shapes, as shown in Fig. 10.4.1 (c). The disadvantages of these types of tunable devices are the somehow complex electronics, and longer switching/tuning time. In paraelectric phase thin films the distorted “butterfly” shape with two typical peaks in C-V dependence is associated with the misfit strain induced ferroelectricity (upward shift of the Curie temperature), remnant polar phase (near the Curie temperature) and/or interfacial charges. Again, hysteresis in paraelectric thin films may be eliminated by optimization of the structure and the fabrication processes of the devices. Figure 10.4.2 depicts the C-V performance of a Ba0.5Sr0.5TiO3 varactor fabricated by RF magnetic sputtering. The films have a single layer columnar structure with column diameters in the range of 15–100 nm and column heights

10.4 Hysteresis, Retention, Long Term Stability and Noise

385

P

(a)

E

n m

(b)

E

E n

m t

(c)

Fig. 10.4.1 Ferroelectric hysteresis in P-E (a) and C-V (b) curves and an example of control voltage (field)

2.8 10

-11

0.14 Plate diamater: 40 μm V =100 mV

2.6 10

-11

2.4 10

-11

2.2 10

-11

0.08

2 10

-11

0.06

1.8 10

-11

0.04

1.6 10

-11

0.02

1.4 10

-11

1

0.12

-5

-4

-3

-2

-1

0

DC voltage (V)

(a)

1

2

0

Hysteresis, H(20V), %

0.1 Dissipation

Capaciatnce, F

AC

1.0 MHz

0.5

0 Plate diamater: 40 mm V =100 mV AC

f=1.0 MHz -0.5 -5

-4

-3

-2 -1 0 DC bias (V)

1

(b)

Fig. 10.4.2 C-V (a) and hysteresis (b) of a varactor with Au/Ni/BSTO/Au structure

2

386

10 Concluding Remarks

(film thickness) 90 nm. The bottom plate (interface) is made of a 0.5 μm thick gold. To ensure a good adhesion a Ni layer is used between the top gold plate and the ferroelectric film. The C-V and dissipation factor are recorded during up to 10 hours. The imprint (the peak in C-V shifted by about 1.0 V!) seen in Fig. 10.4.2 (a) is due to the asymmetric interfaces, i.e. Au/BSTO at the bottom and Ni/BSTO at the top. Hysteresis is defined as the difference in capacitance between the two successive (n and (n–1)) DC bias reversals: Hn,(n–1)(V)=[Cn(V)–C(n–1)(V)]/Cn(V). As it is seen from Fig. 10.4.2 (b) for the considered test varactor H(20V)<1.0%, i.e. it is much smaller then the tuneability at 20 V. The retention is defined as the relative capacitance difference between the nth and 1st bias reversal: R(V,n)=[Cn(V)–C1(V)]/C1(V). For the varactor shown in Fig. 10.4.2 R(20, 2000)< 2%. The long-term stability, i.e. the drift of the parameters of the ferroelectric devices is caused by trapping, detrapping, diffusion and electromigration uncontrollable charges (typically oxygen vacancies). They may be in the bulk of the ferroelectric film (grains, columns), at the electrode/ferroelectric interfaces, and at the grain/column boundaries and dislocations. The density of these vacancies depend on the film fabrication process. The density of the oxygen vacancies may be reduced by post fabrication annealing in an oxygen atmosphere. However, this requires a careful selection of the buffer layers. The buffer layers should not take the oxygen from the ferroelectric film and should not introduce defects and diffuse into the film. Additionally, the buffer and other interfacing (i.e. top electrode) layers have to ensure growth of ferroelectric films without stresses. The density of the oxygen vacancies is partly controlled by the partial pressure of the oxygen at the deposition/operation temperature and stresses within the film. To minimize its free energy the film may “expel” some of the oxygen ions. This condition may best be met if the films are grown on lattice and thermal expansion matched substrates/buffer layers or alternatively on the substrates and buffer layers which initiate a growth process controlled by minimum surface energy. In well optimized films the density of the oxygen vacancies may be reduced to practically acceptable levels (see for example Fig. 4.5.1 (b), Fig. 10.4.2 (a)). In case the devices are not optimized the oxygen vacancies, and perhaps other charged defects, cause extra microwave losses and leakage currents, non-return capacitance (see Fig. 4.5.2 (a), Fig. 4.5.4) and slow response time (e.g. Fig. 4.5.5), noise etc. The noise in microwave ferroelectric devices is the less investigated topic. In polar phase, besides causing hysteresis, the domains may cause extra noise, known as Barkhausen noise. In good quality films the leakage currents are very small and the expected 1/f noise is also small.1/f noise studies in semi-conducting BSTO date back to 1970s (Mytton and Benton 1972, Agawal et al. 1977). It is shown (Ambrozy 1981) that BSTO behaves as semiconductor below Curie temperature (110K), while above this temperature the resistivity increases steeply which is explained by a high level of acceptor state at the grain boundaries. These states are

10.5 Reliability

387

filled by electrons from the grains resulting in depleted layers at the grain boundaries. The other theoretically expected noise sources in paraelectric phase are: • Thermal Nyquist noise may be negligible for smaller for the films with low losses/power dissipation; • Besides causing hysteresis, the local polar phase in paraelectric films may cause extra (Barkhausen) noise. The noise associated with Barkhausen jumps have very low frequencies and may be eliminated in devices by eliminating local polar regions; • Additional noise may appear at high microwave power due to the parametric effects. Experiments with the VCOs based on ferroelectric varactors (Aspemyr et al. 2007, Norling et al. 2007, Victor et al. 2006) show that these noises are negligible.

10.5 Reliability Not much is reported on the reliability tests on thin film tunable ferroelectric devices. The studies of time dependent dielectric breakdown and stress induced leakage current studies under 1.0V bias field show (Yamamichi et al. 1997) that the lifetime of thin Ba0.5Sr0.5TiO3 films for applications as a passive dielectric may be longer than 10 years. Some indirect reliability judgment about the thin films may be done based on the data available for the BaTiO3 based ceramic capacitors. These capacitors have been in the commercial market for more than 30 years, and a large number of dedicated/detailed reliability experiments are reported (Lefkowitz and Mitsui 1959) for the BaTiO3 based ceramic capacitors (X7R, Z5U etc., USA Electronic Industries Alliance (EIA) standard). The reliability tests (Rawal et al. 1988) on BaTiO3 based X7R and Z5U capacitors, after a number accelerated treatments (thermal treatment with and without NaCl water solution, life and 85C/85%RH), show a very low failure rate. A detailed explanation of the failure mechanisms in BaTiO3 based ceramics capacitors is given in (Rawal and Chen 1989). These mechanisms are related to the intrinsic (oxygen vacancies, dislocations, grain boundaries, presence of the second phase etc.), and extrinsic (porosity, de-lamination, thin spots, cracks, local contaminations and voids etc.). Accelerated lifetime measurements of sol-gel grown Pt/BSTO/Pt capacitors under elevated temperatures (210–290oC) show (Roest et al. 2007) that the resistance degradation is a thermally activated with activation energy 1.1–1.6 eV. The lifetime of the capacitors based on ferroelectric films with permittivity 960 and at fields up to 25 V/μm is estimated to be more than ten years. Figure 10.5.1 shows that the tuneability dependence of the time-to-failure for the parallel-plate varactors based on columnar Ba0.5Sr0.5TiO3 films under constant tuning voltage (Vorobiev et al. 2008). The lifetime depends on the height of the potential barrier at the ferroelectric/electrode interface and the film quality. Clearly, the lifetime of the varactors with the Pt electrodes is longer.

388

10 Concluding Remarks

10

11

10

10

Plate diamater: 40 μm V =100 mV AC

f =1.0 MHz

Time-to-failure (sec)

Pt 10

9

10

8

10

7

10

6

10

5

10

4

AC

10 years

Au

1000

0

5

10

15

20

25

30

35

40

Tunability T(V), %

Fig. 10.5.1 Time-to-failure vs. tuneability for parallel-plate varactors fabricated by RF magnetron sputtering

10.6 Integration Trends Current trends indicate that within the forthcoming 5–10 years silicon technology will dominate, successively utilizing 65, 45 and 22 nm nodes. More circuits with enhanced performances based on III-V semiconductors, InP, GaN, and even SiC are used in advanced systems. Along with semiconductor devices, devices based on new materials and technologies are being developed. Some of these are listed below: • Micro and nanomachining, microelectromechanical (MEM) and nanoelectromechanical (NEM) switches; • nanoelectronic devices (carbon nanotubes, nanowires) • spintronic devices; • microwave photonics (intrachip and on chip optical interconnects, optically controlled microwave devices etc.); • devices based on new materials (ferroelectrics, ferrites); • acousto-electronic (TFBAR etc.); • etc. Hybrid Heterogeneous Integration Most of the high performance devices based on new materials and new physical phenomena are not compatible with mature industrial semiconductor technologies

References

389

(Si, III-V etc.). The market of the analog microwave devices is much smaller as compared with digital circuits. Monolithic integration of these advanced materials and technologies with the standard silicon/semiconductor process is not justified economically. The integration of these new technologies with standard semiconductor chips, at least in a foreseeable 5–10 years, will take place in the form of hybrid modules (MCM, SoC, SiP). Hybrid, heterogeneous integration (multichip modules, system-in-package, system-on-chip etc.) will be widely used to utilize available technologies with enhanced performances and new functionalities. The hybrid heterogeneous integration allows combining, in a single module, besides microwave circuits, also digital circuits for signal processing, in some cases also sensors and activators. Monolithic Heterogeneous Integration Recent integration attempts of GaAs with silicon (Motorola 2002) opens up enormous possibilities for the development of advanced components for future communications systems, based on cost effective silicon technology. Perhaps the other III-V semiconductors also (InP, GaN, InAs etc.) may be considered for integration with silicon. Along with III-V semiconductors, other new materials are being integrated with silicon. It is worthwhile to note that IQE/Motorola (Motorola 2002) used ferroelectric films as buffer layers to integrate GaAs with silicon. Utilization of functional properties of ferroelectrics (tunable permittivity, piezoelectric effect) integrated with GaAs and Si devices have great potential in terms of development of ICs with enhanced functionalities.

References Agawal R P, Ambrozy A, Hartnagel H (1977) Excess noise in semiconducting BaTiO3. IEEE Trans Electron Devices ED-24:1337–1341 Ambrozy A (1981) 1/f Noise in (BaSr)TiO3 (Barrier-Dominated Contact Noise). IEEE Trans Electron Devices, ED-28:344–346 Aspemyr L, Kuylenstierna D, Sjöland H et al (2007) 25 GHz and 28 GHz Wide Tuning Range 130 nm CMOS VCOs with Ferroelectric Varactors. The 2nd IEEE International Workshop on RF Integration Technology, Singapore, Dec. 2007 Gevorgian S, Petrov P K, Ivanov Z et al (2001) Tailoring the temperature coefficient of capacitance in ferroelectric varactors. Appl Phys Lett 79:1861–1863 Haeni J H et al (2004) Room-temperature ferroelectricity in strained SrTiO3. Nature, 430:758– 761 Jeon J-H, Hahn Y-D, Kim H-D (2001) Microstructure and dielectric properties of bariumstrontium titanate with functionally graded structure. J Europ Cer Soci 21:1653–1656 Lefkowitz I, Mitsui T (1959) Effect of g-Ray and pile Irradiation on the Coercive Field of BaTiO3. J Appl Phys 39:269 Motorola Starts a GaAs-on-Si Company; Invests in IQE, III-V review, vol. 15, No. 1, 2002 Mytton R J, Benton R K (1972) High 1/f noise anomaly in semiconducting barium-strontium titanate. Phys Lett 39A:329–330

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10 Concluding Remarks

Norling M, Vorobiev A, Jacobsson H et al (2007) A Low-Noise K-Band VCO Based on RoomTemperature Ferroelectric Varactors. IEEE Trans Microwave Theory Techniques 55:361–369 Prudan A M, Kozyrev A B, Osadchy V N et al (2005) Electric field for temperature driven variation of permittivity in ferroelectric devices. Appl Phys Lett 87:212909(1–3) Rawal B S, Chen N H (1989) Conduction and Failure Mechanisms in Barium Titanate based Ceramics Under High Accelerated Conditions. Proc 34th Electroceramics Conference, New Orlean:184–188 Rawal R S, Childs M, Cooper A et al (1988) Reliability of Multilayer Ceramic Capacitors After Thermal Chock. Proc 38 Electronic Components Conference: 371–375 Roest R, Reimann K, Klee M (2007) Accelerated lifetime measurements on thin film ferroelectric materials with a high dielectric constant. 37th Europ Solid-State Device Research Conf ESSDERC’2007:402–405 Setter N (2005) Electroceramic-Based MEMS. Fabrication-Technology and Applications. Springer

Tabata H, Tanaka H, Kawai T (1994) Formation of artificial BaTiO3/SrTiO3 superlattices using pulsed laser deposition and their dielectric properties. Appl Phys Lett 65:1970–1972 Tagantsev A (2008) Private communication Victor A, Nath J, Ghosh D et al (2006) Noise Characteristics of an oscillator with a Barium Strontium Titanate (BST) Varactor. IEE Proc Micr Antennas Propagation 153:96–102 Vorobiev A, Nik S M, Boustedt K et al 2008) Room temperature dynamic life time measurements of ferroelectric varactors”, ISIF 2008 Yamamichi S, Yamamichi A, Park D et al (1997) IEDM’97:10.5(1–4)

Index

A Ablation, 66, 88 Acoustic, 5, 52 impedance, 95 losses, 134 resonance, 54, 91, 152, 212 velocity, 43 wave, 42, 54, 152 ACRT, accelarated crucible rotation technique, 63 Admittance microwave, 256, 343 AFM, 97 Agile, 4, 169, 351, 359, 373 Amplifier, 9, 175, 204 Parametric, 211 Anisotropy, 30, 46, 47 Anneal, 64, 68, 78, 80, 89 Antenna, 1, 72, 149, 175, 187, 207 active, 229 tunable, 207 Antiferroelectric, 3 B Balun, 180 Bandgap photonic, 2, 8, 359 Barkhausen noise, 386 Beam, 9, 78, 80, 87, 101, 231 former, 225, 226, 232, 236 lens type, 226, 236 reflectarray, 235 scanner, 226, 231, 238 steerable, 194, 235, 238 Biaxial strain, 31, 54

Bolometer, 366 Bragg frequency, 177, 178 reflector, 10, 91, 152, 212 Breakdown, 6, 101, 105, 166, 226, 325, 335, 384 C Capacitor, 4, 36, 66, 82, 86, 99 coplanar-plate, 99, 261 even mode, 254, 307 high density, 165 IDC, 156, 265 MFOS, 159 MIM, 21, 167 Multilayer, 147, 166, 185 non-return, 149 odd mode, 254, 307 parallel-plate, 101, 116, 132, 260, 267, 327 partial, 274 test, 307, 326, 327 CCVD, combustion chemical vapor-phase deposition, 62 Centrosymmetric, 52, 54 Chart frequency-resistivity, 120 refractive index, 357 Chemical composition, 27, 129 deposition, 81, 94, 156 etching, 93, 100 formula, 22 solution, 83, 157 vapor, 81, 94, 107, 156 391

392 CIS, crystal ion slicing, 66 CMOS, 8, 126, 159, 228 Co-fire, 74, 78 Cognitive radio, 12 Column, 21, 32, 34 Composite, 21, 32, 130, 133, 167, 359 columnar, 32, 33 granular, 32, 33 layered, 32, 33, 127 resonator, 287, 288, 295 right/left, 190, 220 Conformal coating, 81 coverage, 104 deposition, 356 film, 108 mapping, 246, 277 transformation, 249, 253 Coplanar plate, 77, 89, 99, 125, 130, 134, 142, 146, 155, 156, 164, 246, 260, 265, 280, 326 strip, 249 waveguide, 106, 259, 321 Core, 32, 34 column, 36 grain, 36, 86, 130, 132 varactor, 139 Curie constant, 24, 50 temperature, 24, 29, 32 -von Schweidler, 42 -Weiss low, 24, 36 Current, 17, 57, 135, 148, 162 DC, 70, 123 leakage, 6, 66, 116, 125, 136, 146, 148 SCL, 57 Cut-off frequency, 129, 159, 191, 259, 333 D Damping, 28, 29 Delay line, 9, 90, 91, 104, 161, 175 fom, 176 loaded, 177, 181, 182, 184 other, 186 tunable, 176 time, 176, 177, 183 Digital, 8, 12, 14, 84, 120, 187, 194 Dipole, 23, 29, 40, 42, 367, 372 Discontinuity, 291

Index Dispersion, 29, 31, 40, 160, 181, 211, 249, 254, 259 Distortion, 44, 162, 219, 280, 330, 331 Domain, 6, 7, 65, 80, 166, 207, 288, 310, 344, 349, 384 Doping, 32, 69, 73, 119, 335, 370 E Effect Doppler, 357 electrostriction, 5, 40, 49, 215, 352 magnetoelectric, 353 magnetostriction, 352 piezoelectric, 41, 48, 54, 55, 212 piezomagnetic, 352 Pool Frenkel, 56 skin, 246 Electromechanical coupling coefficient, 212 switch, 9, 169 transducer, 5 Electrostriction, 3, 41, 50, 215, 352 Elliptic integral, 249, 260, 273 first kind, 263, 266, 285 modulus, 252, 260, 276, 281 Evaporation, 66, 72, 82, 87, 88, 91, 93, 99, 102, 105 Expansion thermal, 46, 48, 50, 54, 66, 95 F Failure, 387 Figure of merit (FOM), 89, 93, 177, 185, 188 Filling factor, 250, 252, 260, 262, 266, 298, 322, 323 Filter bandpass, 184, 199, 201 lumped element, 201 notch, 203 rejection, 204, 209 Flip-chip, 118, 193, 201, 205, 226 Fringing field, 127, 140, 144, 154, 291, 324 FWHM, full width at half Maximum, 67, 96 G Gate, 8, 14, 159, 168 Grain, 32, 73, 78, 85, 96, 129 boundary, 34, 47, 56, 80, 85, 132 core, 34, 36, 132

Index Green sheet, 78 tape, 74, 76 H Harmonic Balance, 330, 332 Generation, 119, 162, 176, 208, 331 HBV, heterojunction barrier Varactor, 17, 169 HEMT, high electron mobility transistor, 169, 225 Heterogeneous, 12, 62, 84, 115, 169, 372 HR, high resistivity, 117, 119 HTCC, high temperature co-fired ceramics, 62, 74 Hysteresis, 3, 4, 72, 116, 145, 161, 214, 362, 384 I IDC, interdigital capacitor, 156, 265 IDL, interlayer dielectric, 166 IMD, intermodulation distortion, 330 Impedance, 56, 143, 177, 178, 191, 230, 246, 249, 252, 260, 268, 289, 314 acoustic, 95 complex, 115, 327 surface, 65 tuner, 204 Inclusion rate, 197 Insertion loss (IL), 179, 187, 194, 200, 235, 297, 311 Interface, 32, 34, 36, 62, 65, 119, 121, 130, 132, 147, 149, 291, 296, 336, 354, 357, 360, 364, 370 Inversion, 52, 107, 119, 121, 123, 125 Isolation, 94, 119, 122, 168, 206 L Lattice, 22, 40, 46, 48, 52, 54, 64, 79, 97, 119, 157, 215 Lifetime, 56, 147, 166, 387 Line admittance, 258 capacitance, 248, 251 conductance, 254 impedance, 246, 254 inductance, 246, 249 periodically loaded, 177, 178, 181 propagation constant, 254 resistance, 248

393 synthetic, 182 transmission, 176, 180, 188, 246, 288, 306 Liquid Crystal (LC), 16, 351, 367 Loss, 37, 38 conductor, 269, 293, 323 dielectric, 46, 47, 196, 264, 304 electrode, 269, 307, 322, 341 extrinsic, 42, 43 intrinsic, 38, 39 ohmic, 264 M Memory, 4, 14, 23, 63, 87, 116, 159, 351, 354, 364, 370 Metamaterial, 8, 149, 169, 190, 355 MFOS, Metal-Ferroelectric-OxideSemiconductor, 160 Microprobe, 215, 288, 302, 305, 324, 327, 335 MIM, Metal-Insulator-Metal, 21, 167 MMIC, Microwave Monolithic Integrated Circuit, 1, 8, 14, 116, 213 MN, matching network, 175, 178, 201, 204 MOCVD, metal organic chemical vapor deposition, 81 MOD, Metal Organic Decomposition, 84 Multichip module (MCM), 15, 118, 213 Multiferroic, 3, 351 Multilayer, 70, 74, 78, 82, 147, 152, 166, 185, 207, 246, 251, 261 MUT, material under test, 287, 292, 293, 294, 300, 308, 309, 317, 334, 343 N Nanotube, 354 Nanowire ferromagnetic, 355 NDR, negative differential Resistance, 364 Near field microscope, 288 NEM, nanoelectromechanical, 15 O Optical, 16, 353, 369 OR, open resonator, 299 Oscillator, 176, 212, 213, 226 P PAA, phased array antenna, 231

394 Passivation, 106, 107, 122, 123 Permeability, 352, 360 negative, 352, 353, 357 Permittivity, 4, 22, 25, 28, 117, 261, 321 apparent, 33, 36, 132 background, 36, 55 complex, 28, 119, 287, 295, 343 effective, 36, 125, 265, 326 equivalent, 251 nonlinear, 310 Phase noise, 225, 226, 229 Phase shift differential, 175, 177, 179, 185 Phase shifter, 175, 187 active, 196 all-pass, 192, 196, 205 digital, 187, 188 filter, 184 loaded line, 178 metamaterial, 190 other, 194 reflection type, 192 switching line, 196 transmission line, 190 Phased array, 226, 231, 237 1D, 231, 233, 237 2D, 231, 238 lens, 237 reflectarray, 235 Photolithography, 72, 75, 84, 90, 92, 104 Power amplifier, 175, 204 divider/splitter, 176, 206 handling capability, 175, 187, 193, 204 high, 203 limiter, 176, 209 Pulse shaper, 176, 210 PVD, physical vapor deposition, 95 Q QCL, quantum cascade lasers, 361 Quantum paraelectric, 6 Quartz, 117 Quasi-Debye, 39 R Refractive index, 357 effective, 355 imaginary, 357 negative, 352, 357 Relaxation time, 334 Resonator acoustic (TFBAR), 213

Index composite, 295 Courtney, 291 dielectric, 199 disk, 196, 289, 291 LC, 186, 189, 197 lumped element, 197, 201 microprobe, 303 microstrip, 306 open, 299 split-post, 297 RTA, rapid thermal annealing, 107 S SCLC, space charge limited current, 57 SDR, software defined radio, 12 Self propagation high temperature Synthesis (SHS), 68 SEM, scanning electron Microscopy, 34, 73, 79, 91 Silica fused, 117 SiP, system-in-package, 15 SoC, system-on-chip, 14 Sol-gel, 62, 68, 81, 84 Solidly mounted (FBAR), 213 Sputter, 62, 91, 92 Stabilization temperature, 379 Substrate, 115 Switch microelectromechanical, 15 resistive, 364 T Tape-casting, 68 TFBAR, 5, 42, 54, 213 Trap, 56, 107, 122 TSSG, top seeded solution growth, 63 Tuneability, 240 capacitance, 125, 127 permittivity, 41, 46, 240 resonant delay time, 176 U Uncertainty broadband method, 329 resonator method, 311, 314 V Varistor, 370 Voltage controlled oscillator (VCO), 226