the squid handbook (fundamentals and technology of squids and squid systems) || front matter

J. Clarke, A. I. Braginski (Eds.)

The SQUID Handbook

Vol. I

The SQUID Handbook, Volume 1. Edited by J. Clarke, A. I. BraginskiCopyright � 2004 WILEY-VCH Verlag GmbH & Co. KGaA, WeinheimISBN: 3-527-40229-2

J. Clarke, A. I. Braginski (Eds.)

The SQUID Handbook

Vol. I Fundamentals and Technology of SQUIDsand SQUID Systems

Editors

Prof. Dr. John ClarkeUniversity of CaliforniaDepartment of Physics366 LeConte HalBerkeley, CA 94720-7300USA

Prof. Dr. Alex I. BraginskiResearch Center J6lichISG-2D-52425 J6lichGermany

& This book was carefully produced. Nevertheless,editors, authors and publisher do not warrant theinformation contained therein to be free of errors.Readers are advised to keep in mind that statements,data, illustrations, procedural details or other itemsmay inadvertently be inaccurate.

Library of Congress Card No. applied for

British Library Cataloguing-in-Publication DataA catalogue record for this book is available from theBritish Library.

Bibliographic information published by

Die Deutsche BibliothekDie Deutsche Bibliothek lists this publication in theDeutsche Nationalbibliografie; detailed bibliographicdata is available in the Internet at<http://dnb.ddb.de>.

� 2004 WILEY-VCH Verlag GmbH & Co. KGaA,Weinheim

All rights reserved (including those of translationinto other languages). No part of this book may bereproduced in any form – nor transmitted or trans-lated into machine language without written permis-sion from the publishers. Registered names, trade-marks, etc. used in this book, even when notspecifically marked as such, are not to be consideredunprotected by law.

Printed in the Federal Republic of Germany.

Printed on acid-free paper.

Typesetting K'hn & Weyh, Satz und Medien,FreiburgPrinting betz-druck GmbH, DarmstadtBookbinding Großbuchbinderei J. Sch3ffer GmbH& Co. KG, Gr'nstadt

ISBN 3-527-40229-2

V

Preface XI

1 Introduction 1

1.1 The Beginning 2

1.2 Subsequent Developments 5

1.3 The dc SQUID: A First Look 7

1.4 The rf SQUID: A First Look 12

1.5 Cryogenics and Systems 16

1.6 Instruments: Amplifiers, Magnetometers and Gradiometers 17

1.7 Applications 21

1.8 Challenges and Perspectives 24

1.9 Acknowledgment 26

2 SQUID Theory 29

2.1 Josephson Junctions 30

2.1.1 RCSJ Model 31

2.1.2 Thermal Noise 37

2.1.3 The 1/f Noise (I0, R fluctuations) 41

2.2 Theory of the dc SQUID 43

2.2.1 Introduction 43

2.2.2 Basic Equations, dc SQUID Potential 44

2.2.3 Thermal Fluctuations 50

2.2.3.1 General Considerations 50

2.2.3.2 Numerical Simulations (Langevin Equation) 53

2.2.3.3 Analytical Theory of the dc SQUID 59

2.2.4 Effect of Asymmetry 65

2.3 Theory of the rf SQUID 70


2.3.2 SQUID Potential and the Equation of Motion for the PhaseDifference 72

2.3.3 Unitary Theory for Output Signal and Noise 76

2.3.4 Noise as a Small Perturbation 83

2.3.4.1 Introduction 83

Contents


VI

2.3.4.2 Adiabatic Operation; Hysteretic Phase Diagram 84

2.3.4.3 Non-adiabatic Regime 86

3 SQUID Fabrication Technology 93

3.1 Junction Electrode Materials and Tunnel Barriers 94

3.2 Low-temperature SQUID Devices 96

3.2.1 Refractory Junction Electrodes 96

3.2.2 Tunnel Barrier Technology 97

3.2.3 Deposition Techniques 98

3.2.4 Junction Definition 101

3.2.5 Dielectric Insulation 102

3.2.6 Patterning Techniques 103

3.2.7 Passive Components for Device Fabrication 105

3.2.8 Integrated SQUID Fabrication Process 105

3.3 High-temperature SQUID Devices 107

3.3.1 General Requirements and Problems 107

3.3.2 Thin-film Deposition 108

3.3.3 Patterning Techniques 110

3.3.4 Junction Fabrication 112

3.3.5 Fabrication of Single-layer Devices 115

3.3.6 Fabrication of Multilayer Devices 116

3.3.7 Device Passivation and Encapsulation 118

3.4 Future Trends 118

4 SQUID Electronics 127

4.1 General 128

4.2 Basic Principle of a Flux-locked Loop 128

4.2.1 Linearization of the Transfer Function 128

4.2.2 Noise and Dynamic Behavior 131

4.2.3 Integrator Types 135

4.3 The dc SQUID Readout 137

4.3.1 Fundamentals 137

4.3.2 Methods to Suppress Preamplifier Noise 139

4.3.2.1 Flux Modulation 139

4.3.2.2 Additional Positive Feedback 141

4.3.3 Methods to Suppress 1/f Noise 143

4.3.4 Further Readout Concepts 148

4.3.4.1 Two–stage Configuration 148

4.3.4.2 Series SQUID Arrays 149

4.3.4.3 Relaxation Oscillation SQUIDs 150

4.3.4.4 Digital SQUIDs 152

4.4 The rf SQUID Readout 155

4.4.1 General 155

4.4.2 Basic Building Blocks of rf SQUID Readout Electronics 155

4.4.3 Construction of the Tank Circuit 157

Contents

VII

4.4.4 Coupling of the Tank Circuit to the Transmission Line 159

4.4.5 Cryogenic Preamplifiers 160

4.4.6 Optimization for Maximum Sensitivity 162

4.4.7 Multiplexed Readouts for Multichannel rf SQUID Systems 164

4.5 Trends in SQUID Electronics 165

5 Practical DC SQUIDS: Configuration and Performance 171

5.1 Introduction 172

5.2 Basic dc SQUID Design 175

5.2.1 Uncoupled SQUIDs 175

5.2.2 Coupled SQUIDs 177

5.3 Magnetometers 186

5.3.1 Overview 186

5.3.2 Magnetometers for High Spatial Resolution 187

5.3.3 Magnetometers for High Field Resolution 188

5.4 Gradiometers 193

5.4.1 Overview 193

5.4.2 Thin-Film Planar Gradiometers 195

5.4.3 Wire-Wound Axial Gradiometers 198

5.5 1/f Noise and Operation in Ambient Field 200

5.5.1 General Remarks on 1/f Noise 200

5.5.2 Critical Current Fluctuations 200

5.5.3 Thermally Activated Motion of Vortices 201

5.5.4 Generation of vortices 203

5.5.5 Reduction of 1/f Noise Generated by Vortex Motion 205

5.5.5.1 Overview 205

5.5.5.2 Vortex pinning 205

5.5.5.3 Narrow Linewidth Device Structures 206

5.5.5.4 Flux Dams 207

5.6 Other Performance Degrading Effects 208

5.6.1 Hysteresis 208

5.6.2 Radio-Frequency Interference 209

5.6.3 Temperature Fluctuations and Drift 210

6 Practical RF SQUIDs: Configuration and Performance 219


6.2 Rf SQUID Magnetometers 220

6.2.1 Practical Device Optimization 220

6.2.2 Low-Temperature rf SQUID Magnetometers 223

6.2.2.1 Low-Temperature Bulk Magnetometers 223

6.2.2.2 Low-Temperature Thin-Film Magnetometers 226

6.2.3 High-Temperature rf SQUID Magnetometers 228

6.2.3.1 Technological Limitations 228

6.2.3.2 Bulk High-Tc Magnetometers 229

6.2.3.3 Early Thin-Film High-Tc Magnetometers 229

Contents

6.2.3.4 Magnetometers with Coplanar Resonators 230

6.2.3.5 Magnetometers with Dielectric Resonators 234

6.2.3.6 Thin-Film HTS Magnetometers with Flux Transformers 235

6.3 Rf SQUID Gradiometers 236

6.3.1 Low-Temperature Gradiometers 236

6.3.2 High-Temperature Gradiometers 236

6.3.2.1 Hardware rf SQUID Gradiometers 236

6.3.2.2 Electronic rf SQUID gradiometers 237

6.4 Low-Frequency Excess Noise in rf SQUIDs 237

6.5 Response of rf SQUIDs to High-Frequency ElectromagneticInterference 239

6.6 Characterization and Adjustment of rf SQUIDs 241

6.7 The rf SQUID versus the dc SQUID 244

6.8 Concluding Remarks and Outlook 246

7 SQUID System Issues 251


7.2 Cryogenics 255


7.2.2 Liquid Cryogen Cooling (Cryostats) 256

7.2.3 Cryogenic Refrigerators (Cryocoolers) 258


7.2.3.2 Joule–Thomson Coolers 259

7.2.3.3 Stirling Coolers 260

7.2.3.4 Gifford–McMahon Coolers 261

7.2.3.5 Pulse-tube Coolers 262

7.2.3.6 Comparison of Cryocoolers 264

7.2.3.7 Trends in Cryocooling 265

7.2.4 Cryostat or Cryocooler? 266

7.2.5 Cryocooler-interference Reduction 267

7.2.5.1 Interference Mechanisms 267

7.2.5.2 Time Separation 268

7.2.5.3 Space Separation 268

7.2.5.4 Low-noise Coolers 269

7.2.5.5 Noise Suppression Techniques 269

7.2.6 Material Properties 270

7.3 Cabling and Electronics 272

7.3.1 Shielding and Filtering of Noise Sources 272

7.3.1.1 Introduction to Shielding Effectiveness 272

7.3.1.2 Absorption 273

7.3.1.3 Reflection 274

7.3.1.4 High-frequency Shielding 276

7.3.1.5 Low-frequency Shielding 277

7.3.1.6 Filtering in an Unshielded Urban Environment 281

ContentsVIII

7.3.1.7 Determination of Low-frequency Shielding, Filtering or NoiseCancellation Requirements 281

7.3.2 Electronics and Cables 283

7.3.2.1 RF Screening of Electronics 283

7.3.2.2 Cables and Conductors 284

7.3.2.3 Cable Junctions, Terminations, Connectors and Grounding 285

7.3.2.4 Crosstalk 286

7.3.2.5 Power Consumption and Supply 287

7.3.2.6 Choice of SQUIDs and Electronics 289

7.4 Data Acquisition and Rudimentary Signal Processing 289


7.4.2 Hardware Considerations 290

7.4.3 Dynamic Range, Accuracy and Linearity 290

7.4.4 Sampling Rate and Signal Conditioning 291

7.4.5 Digital Signal Conditioning and Storage 292

7.5 Characterization, Calibration and Testing 292


7.5.2 Characterizing SQUIDs 293


7.5.2.2 Transfer Coefficient 293

7.5.2.3 Effective Area of a Magnetometer 294

7.5.2.4 Effective Volume of a Gradiometer 294

7.5.2.5 SQUID Noise and Bandwidth Measurements 295

7.5.2.6 Dynamic Range 296

7.5.2.7 Slew Rate 296

7.5.2.8 Nonlinearity 297

7.5.3 Characterization in Various Magnetic Field Situations 298


7.5.3.2 Field-applied (FA) Characterization 299

7.5.3.3 Field-removed (FR) Characterization 299

7.5.3.4 Hysteresis 301

7.5.4 Calibration 301

7.5.4.1 Setting up Calibration Fields 301

7.5.4.2 Magnetometer and Gradiometer Calibration 305

7.5.5 Testing and Practical Tips 305

7.5.5.1 Drifts and Offsets 305

7.5.5.2 SQUID or Flux Jumps 305

7.5.5.3 Excess Noise 307

7.5.5.4 Electronic Noise from Other Systems 307

7.5.5.5 Adequate Shielding of the Cryostat 307

7.5.5.6 Consequences of Cryogen Boil-off 308

7.5.5.7 Mechanical Vibration 308

7.5.5.8 Increase in Noise of the System Compared to a SQUID 309

7.6 Conditions Imposed on SQUID Systems by the Environment andApplications 309

Contents IX


7.6.2 Signals Acting on SQUID Systems 310

7.6.3 Noise Acting on a SQUID System 311

7.6.3.1 Environmental Noise in Stationary Applications 311

7.6.3.2 Additional Noise in Mobile Instrumentation 315

7.7 Noise Suppression 315


7.7.2 Active Shielding 315

7.7.3 Noise Cancellation by Primary Sensors 316

7.7.4 Noise Cancellation Using References 319


7.7.4.2 Static Systems 323

7.7.4.3 Mobile Systems 330

7.7.5 Noise Cancellation Without the References 332

7.8 Signal and Noise Implications for the SQUID System Design 335


7.8.2 Static SQUID Systems 335

7.8.3 Mobile SQUID Systems 339

7.8.4 Summary of Parameters 342

7.9 Concluding Remarks and System Trends 344

Appendix 1 357

Appendix 2 367

Index 383

ContentsX

XI

We hope that this Handbook will provide an in-depth, systematic treatment ofSuperconducting QUantum Interference Devices (SQUIDs) and their many applica-tions. Extended reviews of this subject have appeared previously in journals, booksand textbooks devoted to broader aspects of superconductivity, and several proceed-ings of NATO Advanced Study Institutes (ASI) covering various aspects of supercon-ducting electronics. In particular, the NATO proceedings,1) “SQUID Sensors: Fun-damentals, Fabrication and Applications”, the most comprehensive review pre-viously available, has become the “bible” for those in the field. However, NATOproceedings are written by individual summer school lecturers, so that some aspectsof the subject may be omitted while there may be unavoidable overlaps in others.Furthermore, most of the material in this book was written almost a decade ago.

Our intent is to offer the reader a reasonably complete, balanced and up-to-datepresentation of the entire field, with as few omissions and duplications as possible.Initially, our publisher suggested that one or two of us write the book, but wepointed out that this was an impossible workload for anyone actively working in thefield. Furthermore, many aspects of SQUIDs, especially applications, have becomeso specialized that no one person is likely to be able to provide adequate coverage.For these reasons, we invited many colleagues collectively to write a comprehensivetreatise. Virtually all of those who were asked graciously agreed. This team com-prises many of the leading specialists who have been involved in all aspects ofSQUIDs and their applications; many of them are former NATO lecturers who con-tributed to the “bible”.

The Handbook is organized into two volumes, the first being devoted to the fun-damentals and technology of SQUIDs and SQUID systems. The second volume isconcerned with applications using SQUIDs as sensors and readout devices, with aninevitable emphasis on magnetometers. SQUIDs as building blocks for digital cir-cuits are beyond our scope.

In Chapter 1 of the first volume we offer a broad, phenomenological introductionto SQUIDs and their operation as sensors and readout devices. We include somehistorical highlights and an overview of existing and future applications. Our intro-

Preface


1) SQUID Sensors: Fundamentals, Fabrication and Applications, Ed. Harold Weinstock, Kluwer Aca-demic Publishers (1996).

duction is aimed mainly at readers who are unfamiliar with SQUIDs, and whohopefully will benefit from reading this chapter before delving into the more ad-vanced material in subsequent chapters.

In Chapter 2, Chesca, Kleiner and Koelle present the theoretical foundations ofdirect-current (dc) and radio-frequency (rf) SQUIDs, starting with a discussion ofthe Josephson junction. The authors include analytical theories for low and highlevels of thermal fluctuations for both kinds of SQUIDs. They address numericalsimulations only for the dc SQUID, since no such work yet exists for the rf SQUID.

Subsequently, in Chapter 3, Cantor and Ludwig discuss the fabrication of Joseph-son junctions and SQUIDs using low-temperature-superconducting (LTS) and HTSthin films, dielectric insulators and normal metals.

In Chapter 4, Drung and M�ck give the essentials of analog and digital room-temperature readout electronics for dc and rf SQUIDs with broad bandwidth, highdynamic range and low noise. They present several approaches to the flux-lockedloop, as well as issues such as the suppression of low-frequency noise in a dcSQUID and the coupling of an rf SQUID to its readout preamplifier.

In Chapter 5, Cantor and Koelle describe practical LTS and HTS dc SQUIDs,beginning with a brief historical overview. They include the analytical and numericaldesign of SQUID parameters, and the performance of typical devices. Many of theexpressions introduced are also applicable to rf SQUIDs. They discuss magnet-ometers and gradiometers, including thin-film and wire-wound pickup coils.

In Chapter 6, Braginski and Zhang describe practical thin-film rf SQUIDs withan emphasis on HTS devices, since LTS rf SQUIDs are rarely used today. Their his-torical overview includes bulk rf SQUIDs, which dominated the first decade ofSQUID research and application. In contrast to Chapter 5, they do not address ana-lytical and numerical design issues, since HTS rf SQUIDs were developed empiri-cally, with little recourse to simulations.

In Chapter 7, Foley, Keene, ter Brake and Vrba address SQUID system issues,beginning with such requirements as cryogenics and cabling. They briefly discussdata acquisition and processing as well as methods of testing and calibration. Theyconsider situations in which one needs to measure very low-level signals in an openenvironment where the ambient noise levels are high. This case requires sophisti-cated techniques for noise suppression, for example, synthetic gradiometry. Theydiscuss design and noise considerations for both static and mobile SQUID systems.

Finally, in Appendix A.1, Kleiner and Koelle give a brief overview of the relevantproperties of superconductors.

The second volume begins with a description of SQUID amplifiers, followed by achapter on the applications of SQUIDs to standards. The next chapter outlines theinverse problem, which is of central importance in imaging applications. Subse-quent chapters deal with practical applications in biomagnetism, nondestructiveevaluation of materials and structures, geophysical exploration and gravity andmotion sensors.

The handbook would be suitable as a textbook for graduate students in physicsand engineering, and hopefully will serve as a general reference for professionalsworking on SQUIDs and their applications. We hope that researchers who are not

PrefaceXII

SQUID specialists – for example, physicians working in neuromagnetism and mag-netocardiography – will also study relevant chapters.

In concluding, we express our heartfelt thanks to all the contributors to this vol-ume, not least for their patience and persistence during the editing process. We owean enormous debt of gratitude to Dr. Michael B�r, Mrs. Vera Palmer and Mrs. UlrikeWerner of Wiley-VCH, without whose expert guidance and extraordinary patiencethis book would never have surfaced.

Alex Braginski and John Clarke

Preface XIII

Alex I. Braginski(Chapters 1 and 6)Forschungszentrum J�lich, ISG-2,D-52425 J�lich, Germany, (retired)andFachbereich C, Fachgruppe Physik,Bergische Universit�t Wuppertal,D-42097 Wuppertal, [email protected]

Robin Cantor(Chapters 3 and 5)STAR Cryoelectronics,25-A Bisbee Court,NM 87508 Santa Fe, [email protected]

Boris Chesca(Chapter 2)Physikalisches Institut,Universit�t T�bingen,Auf der Morgenstelle 14,D-72076 T�bingen, [email protected]

John Clarke(Chapter 1)Department of Physics, University ofCalifornia, 366 LeConte Hall,Berkeley CA 94720-7300, USA,andMaterials Science Division,Lawrence Berkeley NationalLaboratory, One Cyclotron Road,Berkeley CA 94720, [email protected]

Dietmar Drung(Chapter 4, Appendix 2)Physikalisch-TechnischeBundesanstalt, Abbestrasse 2–12,D-10587 Berlin, [email protected]

C. P. Foley(Chapter 7)CSIRO Telecommunicationsand Industrial Physics, P.O. Box 218,Lindfield, NSW 2070 [email protected]

M. N. Keene(Chapter 7)QinetiQ Ltd., St. Andrews Road,Malvern, Worcestershire WR14 3PS,United [email protected]

XV

List of Contributors


Reinhold Kleiner(Chapter 2, Appendix 1)Physikalisches Institut,Experimentalphysik II,Universit�t T�bingen,Auf der Morgenstelle 14,D-72076 T�bingen, [email protected]

Dieter Koelle(Chapter 2, Appendices 1 and 2)Physikalisches Institut,Experimentalphysik II,Universit�t T�bingen,Auf der Morgenstelle 14,D-72076 T�bingen, [email protected]

Frank Ludwig(Chapter 3)Institut f�r elektrische Meßtechnikund Grundlagen der Elektrotechnik,Technische Universit�t Braunschweig,D-38092 Braunschweig, [email protected]

Michael M�ck(Chapter 4)Institut f�r Angewandte Physik,Justus-Liebig-Universit�t Gießen,Heinrich-Buff-Ring 16,D-35392 Gießen, [email protected]

H. J. M. ter Brake(Chapter 7)Twente University of Technology,Department of Applied Physics,P.O. Box 217, 7500AE Enschede,The [email protected]

Jiri Vrba(Chapter 7) CTF Systems Inc.,VSM MedTech Ltd, 7 Burbridge StreetCoquitlam, B.C., [email protected]

Yi Zhang(Chapter 6)Forschungszentrum J�lich, ISG-2,D-52425 J�lich, [email protected]

List of ContributorsXVI

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