Edited by

Takao Someya

Stretchable Electronics

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Stretchable Electronics

Edited by Takao Someya

The Editor

Prof. Takao SomeyaUniversity of TokyoDepartment of Electrical Engineering7-3-1 Hongo, Bunkyo-kuTokyo 113-8656Japan

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Printed in SingaporePrinted on acid-free paper

V

Contents

Preface XV ListofContributors XVII

PartI Theory 1

1 TheoryforStretchableInterconnects 3 JizhouSongandShuodaoWang1.1 Introduction 31.2 Mechanics of Stretchable Wavy Ribbons 51.2.1 Small-Deformation Analysis 51.2.2 Finite-Deformation Analysis 81.2.3 Ribbon Width Effect 121.3 Mechanics of Popup Structure 151.4 Mechanics of Interconnects in the Noncoplanar Mesh

Design 191.4.1 Global Buckling of Interconnects 191.4.2 Adhesion Effect on Buckling of Interconnects 211.4.3 Large Deformation Effect on Buckling of Interconnects 241.5 Concluding Remarks 27 References 27

2 MechanicsofTwistableElectronics 31 YewangSu,JianWu,ZhichaoFan,Keh-ChihHwang,YonggangHuang,

andJohnA.Rogers2.1 Introduction 312.2 Postbuckling Theory 312.3 Postbuckling of Interconnect under Twist 332.4 Symmetric Buckling Mode 342.5 Antisymmetric Buckling Mode 362.6 Discussion and Concluding Remarks 38 References 38

VI Contents

PartII MaterialsandProcesses 41

3 GrapheneforStretchableElectronics 43 ChaoYan,Seoung-KiLee,HoukJang,andJong-HyunAhn3.1 Introduction 433.2 Production of Graphene Films 443.2.1 Large-Area Graphene Synthesis by CVD 443.2.2 Exfoliation Methods 473.2.3 Epitaxial Growth Methods 483.3 Fabrication of Graphene Films on Substrates 503.3.1 Solution-Based Method 503.3.2 Transfer Printing 523.4 Applications in Flexible and Stretchable Electronics 543.4.1 Interconnect for Integrated Circuits 573.4.2 Flexible Electronics 603.4.2.1 Graphene Electrodes for Flexible FETs  603.4.2.2 Graphene Electrodes for Flexible OPVs  643.4.2.3 Graphene Electrodes for OLEDs  663.4.2.4 Graphene Film for Flexible Touch Screen Panels  703.4.3 Stretchable Electronics 713.5 Concluding Remarks 75 References 76

4 StretchableThin-FilmElectronics 81 StéphanieP.Lacour4.1 Introduction 814.2 Silicone Rubber as a Substrate 824.2.1 Elastomers 824.2.2 Silicone Rubber – Polydimethylsiloxane (PDMS) 834.2.2.1 PDMS Surface Chemistry  834.2.2.2 PDMS Mechanical Properties  844.2.2.3 Dielectric Properties  854.2.2.4 Other Properties  864.2.3 Photosensitive Silicones 864.3 Mechanical Architecture 874.3.1 Preserving the Mechanical Integrity of Thin-Film

Structures 884.3.1.1 Small Platforms (<500 µm Side)  894.3.1.2 Large Platforms (>500 µm Side)  904.3.2 Ensuring Smooth Strain Gradient across Interconnects 914.4 Stretchable Metallization 934.4.1 Morphology of Thin Gold Films on PDMS 944.4.2 Electromechanical Response 954.4.2.1 Uni-axial (1D) Stretching  964.4.2.2 Multi-axial (2D) Stretching  98

Contents VII

4.4.3 Printed Films on PDMS Substrate 994.5 Integrated Stretchable Thin-Film Devices 1004.5.1 Soft Neural Electrode Arrays 1004.5.2 Stretchable Capacitive Sensors 1014.5.3 Stretchable Antennas 1024.5.4 Stretchable Thin-Film Transistors 1034.5.5 Stretchable Organic Lasers 1054.6 Outlook 106 References 107

5 StretchablePiezoelectricNanoribbonsforBiocompatibleEnergyHarvesting 111

YiQi,ThanhD.Nguyen,PrashantK.Purohit,andMichaelC.McAlpine5.1 Energy Harvesting and Piezoelectric Materials 1115.1.1 Introduction to Biomechanical Energy Harvesting 1115.1.2 Piezoelectric Materials and Lead Zirconate Titanate (PZT) 1125.2 PZT Nanofabrication and Interfacing with Stretchable

Substrates 1165.2.1 Wafer-Scale PZT Nanowire Fabrication 1165.2.2 Transfer Printing onto Stretchable Substrates 1175.2.3 Stretchable Wavy and Buckled PZT Nanoribbons 1205.3 Piezoelectric Characterization and Electrical Measurements 1265.3.1 Piezoelectric Characterization 1265.3.2 Electrical Measurements 1305.4 Summary 133 References 134

PartIII CircuitBoards 141

6 ModelingofPrintedCircuitBoardInspiredStretchableElectronicSystems 143

MarioGonzalez,Yung-YuHsu,andJanVanfleteren6.1 Technology Development Considerations 1436.2 Modeling and Simulation 1456.2.1 Optimization of Metal Conductor Shape 1466.2.1.1 Description of the Model  1466.2.1.2 Material Properties  1466.2.1.3 Stress/Strain Comparison of Different Conductor Shapes  1476.2.1.4 Optimization of the Horseshoe Shape of Conductor  1496.2.2 Influence of Substrate Stiffness on the Plastic Strain of the

Conductor 1516.2.3 Induced Mechanical Interaction on Multitracks 1526.2.4 Polyimide-Supported Stretchable Interconnect 155 References 158

VIII Contents

7 MaterialsforStretchableElectronicsCompliantwithPrintedCircuitBoardFabrication 161

MatthiasAdler,RuthBieringer,ThomasSchauber,andJürgenGünther7.1 Introduction 1617.1.1 Silicones 1617.1.1.1 Fundamentals of Silicones  1617.1.1.2 Silicone Elastomers  1637.1.1.3 Durability  1667.1.1.4 Processing  1687.1.1.5 Fields of Application  1707.1.2 Polyurethanes 1717.1.2.1 Fundamentals of Polyurethanes  1717.1.2.2 Properties of Polyurethanes  1757.1.2.3 Thermoplastic Polyurethanes  1767.1.2.4 Cast Polyurethanes  1777.1.2.5 Commercial Raw Materials  1797.1.2.6 Applications of Polyurethanes  1817.1.2.7 Excursion Conductive Pastes (Developed during the STELLA

Project)  182 References  184 Further Reading 185

8 TechnologiesandProcessesUsedinPrintedCircuitBoardFabricationfortheRealizationofStretchableElectronics 187

FrederickBossuytandThomasLöher8.1 Lamination Technology 1878.1.1 Process Concept 1878.1.2 Polyurethane Films 1888.1.3 Printed Circuit Board Cu Foils 1898.1.4 Lamination of Copper Foils to Polyurethane Films 1898.1.5 Substrate Fabrication 1908.1.6 Component Assembly and Interconnection 1938.1.7 Encapsulation of Components 1948.1.8 Outline Cutting of Circuits on the Fabrication Board and Release 1958.1.9 Lamination to Textiles or Other Substrates 1958.2 Molding Technology 1968.2.1 General Introduction of the Process 1968.2.2 Copper as Electrical Conductor 1978.2.3 Polyimide as Mechanical Support 1998.2.4 Lamination of Polyimide–Copper Sheet on Rigid Substrate Using a

Temporary Adhesive 1998.2.5 Copper Patterning 2008.2.6 Solder Mask Application 2008.2.7 Copper Finish Application 2018.2.8 Assembly of Components 2018.2.9 Encapsulation by Molding 202

Contents IX

8.2.10 Application to Textiles 203 References 205

9 ReliabilityandApplicationScenariosofStretchableElectronicsRealizedUsingPrintedCircuitBoardTechnologies 207

JanVanfleteren,FrederickBossuyt,ThomasLöher,Yung-YuHsu,MarioGonzalez,andJürgenGünther

9.1 Application Considerations 2079.2 Reliability 2099.2.1 Results and Discussion of Single and Cyclic Elongation Tests 2099.2.2 One-Time Stretch Tests 2109.2.3 Cyclic Endurance Tests of Laminated and Molded Test Samples 2119.2.3.1 Pure Copper Tracks 2119.2.3.2 PDMS Encapsulated Parallel PI Supported Meander Tracks 2129.2.4 Failure Analysis 2149.2.4.1 In Situ Observation of the Deformation Behavior and Failure

Mechanism of Encapsulated/Nonencapsulated Stretchable Interconnects 214

9.2.4.2 In Situ Electromechanical Measurement for One-Time-Stretching Reliability 216

9.2.4.3 Correlation between Numerical and Experimental Results 2189.2.4.4 Fatigue Failure of Copper Meanders 2199.2.4.5 Lifetime Prediction by FEM 2219.2.5 Washability – An Introduction 2229.3 Application Scenarios 2239.3.1 Temperature Sensor 2239.3.2 Wireless Power Circuit 2249.3.3 Fitness Sensor 2259.3.4 Pressure Senors in a Shoe Insole 2269.3.5 Bandage Inlay for Compression Therapy 2279.3.6 Baby Respiration Monitor Demonstrator 2279.3.7 LED Matrix 2299.3.8 RGB Led Matrix (SMI by Laser) 2309.3.9 Thermoforming of Printed Conductors – Single Stretching 231 Reference 233 Further Reading 233

PartIV DevicesandApplications 235

10 StretchableElectronicandOptoelectronicDevicesUsingSingle-CrystalInorganicSemiconductorMaterials 237

Dae-HyeongKim,NanshuLu,andJohnA.Rogers10.1 Introduction 23710.1.1 Materials Selection for High-Performance Stretchable Electronics 237

X Contents

10.1.2 Monocrystalline Inorganic Semiconductors in Stretchable Designs 238

10.1.3 Bio-integrated Electronics 24010.2 Stretchable Circuits 24010.2.1 Wavy Electronic Devices and Circuits 24010.2.2 Noncoplanar Electronic Devices and Circuits 24210.2.3 Electronic Circuits with Serpentine Interconnects 24410.2.4 Stretchable Electronic Devices on Unconventional Substrates 24410.3 Application of Stretchable Designs to Microscale Inorganic Light

Emitting Diodes (µ-ILEDs) 24710.3.1 Stretchable µ-ILED Arrays 24710.3.2 Lighting Devices on Substrates of Unconventional Materials and

Shapes 24910.4 Biomedical Applications of Stretchable Electronics and

Optoelectronics 25310.4.1 Encapsulation Strategy 25310.4.2 Bio-applications of µ-ILEDs: Suture Threads and Proximity

Sensors 25310.4.3 Minimally Invasive Surgical Tools: Instrumented Balloon

Catheters 25610.4.4 Epidermal Electronic System (EES) 25910.5 Stretchable Digital Imagers and Solar Modules 26110.5.1 Hemispherical Electronic Eye Camera 26110.5.2 Curvilinear Imagers and Stretchable Photovoltaic Modules with High

Fill Factors 26310.5.3 Hemispherical Electronic Eye Camera with Adjustable Zoom

Magnification 26410.6 Conclusions 265 References 267

11 StretchableOrganicTransistors 271 TsuyoshiSekitaniandTakaoSomeya11.1 Introduction 27111.2 Perforated Organic Transistor Active Matrix for Large-Area,

Stretchable Sensors 27211.2.1 Simultaneous Sensing of Pressure and Temperature 27411.3 Rubber-Like Stretchable Organic Transistor Active Matrix Using

Elastic Conductors 27511.3.1 Integration of Elastic Conductors with Printed Organic

Transistors 27611.3.1.1 Integration Process  27611.3.2 Electrical and Mechanical Performances 27811.4 Rubber-Like Organic Transistor Active Matrix Organic Light-Emitting

Diode Display 28011.5 Future Prospects 283

Contents XI

Acknowledgments 283 References 283

12 PowerSupply,Generation,andStorageinStretchableElectronics 287

MartinKaltenbrunnerandSiegfriedBauer12.1 Introduction 28712.2 Radio Frequency Power Supplies 28712.3 Power Generation 28912.3.1 Dielectric Elastomer Generators 29012.3.2 Piezoelectric Energy Generation 29212.3.3 Solar Cells 29412.4 Power Storage 29712.4.1 Supercapacitors 29712.4.2 Batteries 29912.5 Summary 301 Acknowledgments 301 References 301

13 SoftActuators 305 KinjiAsaka13.1 Introduction 30513.2 Conducting Polymers 30613.3 Ionic Polymer Metal Composites (IPMCs) 30813.4 Nanocarbon Actuators 31013.4.1 Carbon Nanotube (CNT) Actuators 31013.4.2 CNT Actuators Based on Ionic-Liquid-Based Bucky-Gels 31113.4.3 Materials of Bucky-Gel Actuators 31313.4.4 Modeling of the Nanocarbon Actuators 31513.5 Applications 31913.6 Conclusion 319 References 320

14 Elastomer-BasedPressureandStrainSensors 325 BenjaminC.K.Tee,StefanC.B.Mannsfeld,andZhenanBao14.1 Introduction 32514.2 A Brief Elastomers Overview 32614.3 Important Sensor Characteristics 32714.3.1 Sensitivity 32814.3.2 Hysteresis 32914.3.3 Temporal Resolution 32914.3.4 Sensitivity to Environmental Factors 33014.3.5 Mechanical Durability 33014.4 Elastomeric Force Sensors 33014.4.1 Piezoresistive Sensors 331

XII Contents

14.4.1.1 Conductive Fillers in Elastomeric Composites  33114.4.2 Elastomer as a Dielectric Material 33514.4.2.1 Plain Elastomers  33614.4.2.2 Foam  33814.4.2.3 Microstructured Elastomers  33914.4.3 Piezoelectric Films 34114.4.4 Optical Pressure Sensors 34214.5 Active Pressure/Strain Sensors Systems 34314.6 Applications 34814.7 Outlook 348 References 350

15 ConformableActiveDevices 355 RobertA.StreetandAnaClaudiaArias15.1 Introduction 35515.2 Printing Processes for Organic TFTs 35615.2.1 Printing Considerations for Metals, Semiconductors, and

Dielectrics 35615.2.2 Printed Organic CMOS TFTs 35915.2.3 Alternative Material Choices 36015.2.4 Self-Assembly of TFTs from Solution 36115.3 Sensing and Memory Devices Based on Piezoelectric Polymer 36315.3.1 Pressure Sensor and Accelerometer 36315.3.2 Chemical Sensors 36415.3.3 Nonvolatile Printed Memory 36515.3.4 Printed Memristor 36615.3.5 Photodiodes and Other Devices 36715.4 Electronic Circuits 36815.4.1 All-Printed Organic TFT Display 36915.4.2 Inverter, Ring Oscillator, and Shift Register 37115.4.3 Self-Stabilized Amplifier Circuits 37215.5 Curved Conformal Devices by a Cut-and-Bend Approach 37415.6 Summary 375 Acknowledgments 376 References 376

16 StretchableNeuralInterfaces 379 WooHyeunKang,WenzheCao,SigurdWagner,andBarclayMorrison,III16.1 Introduction 37916.2 Overview of MEAs 38016.2.1 Advantages of Stretchable MEAs 38116.3 Classes of SMEAs 38216.3.1 Planar SMEAs 38216.3.2 Cuff SMEAs 38916.4 Common Limitations for All SMEAs 394

Contents XIII

16.5 Future Directions in Stretchable Neural Interfaces 39416.6 Conclusion 395 References 396

17 Bio-basedMaterialsasTemplatesforElectronicDevices 401 ChristianMüllerandOlleInganäs17.1 Introduction 40117.2 Polysaccharide-Based Templates 40217.2.1 Cellulose: Paper Substrates 40217.2.2 Cellulose: Nanofiber Networks 40317.2.3 Cellulose Fibers: Cotton, Lyocell, and Viscose 40717.2.4 Vascular Bundles 40717.2.5 Polysaccharide Hydrogels 40817.3 Protein-Based Templates 40917.3.1 Wool and Silk Fibers 40917.3.2 Silk Fibroin Films 41017.3.3 Protein Fibrils: Rhapidosomes, Microtubules, Actin Filaments, and

Amyloid Fibrils 41317.3.4 Collagen and Gelatin 41517.4 DNA Templates 41517.4.1 Intrinsic Electrical Properties of DNA 41517.4.2 Decorated DNA 41617.5 Virus Templates: Tobacco Mosaic Virus and M13 Bacteriophage 41817.6 Summary 419 References 420

18 OrganicIntegratedCircuitsforEMIMeasurement 431 MakotoTakamiya,KoichiIshida,TsuyoshiSekitani,TakaoSomeya,

andTakayasuSakurai18.1 Introduction 43118.2 Stretchable EMI Measurement Sheet 43218.2.1 Overview of Stretchable EMI Measurement Sheet 43218.2.2 2 V Organic CMOS Decoder 43418.2.3 Stretchable Interconnects with CNTs 43618.3 Silicon CMOS LSI for EMI Detection 43718.4 Experimental Results and Discussion 44018.4.1 Direct Silicon–Organic Circuit Interface 44018.4.2 Comparison of Conventional and Proposed EMI Measurements 44218.4.3 Calibration for EMI Measurement LSI 44318.5 Conclusion 446 Acknowledgments 447 References 447

Index 449

XV

Today’s electronics are bulky and rigid since they are manufactured on rigid sub-strates such as glass and/or silicon; however, the next-generation electronics will be manufactured on polymeric foils, subsequently going to be flexible and even stretchable.

Objects that surround our everyday life have very complicated shapes. In fact, most ambient tools are composed of round/curvy surfaces rather than flat glass/silicon wafers. Imagine overlaying a machine such as a humanoid robot with a skin-like sensor sheet. For a joint part of a robot, the sensor sheet needs to be extremely stretchable to accommodate the twisting or bending motion of the joint. In order to mask the sensor sheet to a surface with complex, intricate curves, “stretchability” is the key. As a result, electronics that are as flexible as films, and as stretchy as rubber sheets, will soon replace the traditional solid electronics. Future electronics will be highly deformable and will adapt their shapes by stretching, shrinking, and wrinkling as desired. Expectations are unlimited and abundant. Emerging applications will be realized when new elec-tronics adopt their stretchability.

This book, which has four parts, comprises 18 chapters. Part I introduces the theory of stretchable electronics and mechanics of twistable electronics. Here, deformation analysis and postbuckling theory are described. Part II puts together materials and processes. Graphene-based stretchable electrodes, polydimethyl-siloxane (PDMS) substrates, and stretchable piezoelectric nanoribbons are pre-sented as candidate materials for stretchable electronics. In Part III, stretchable circuit boards and related technologies ranging from modeling, materials, pro-cesses, device reliability, and applications are reported. Part IV covers novel stretchable applications of stretchable electronics which are made of inorganic and organic semiconductors. In addition to stretchable transistor integrated circuits and other conformable active devices, stretchable actuators, sensors, and stretch-able power sources are described. Bio-inspired and bio-medical applications are important and bio-based materials are introduced for electronics devices. Novel applications include stretchable systems to measure electromagnetic interference and signals from neurons.

Preface

XVI Preface

I would like to express my sincere gratitude to all our colleagues and friends involved in the realization of this book. I greatly appreciate them for agreeing to devote their time and effort to submitting and reviewing chapters to ensure its success. I am also indebted to Wiley-VCH for publication of this book.

Takao SomeyaTokyo, October 2012

XVII

Matthias AdlerFreudenberg Forschungsdienste SE & Co. KGHöhnerweg 2-469469 WeinheimGermany

Jong-Hyun AhnSungkyunkwan UniversitySchool of Advanced Materials Science and EngineeringSuwon, 440-746Korea

Ana Claudia AriasUniversity of CaliforniaEECS DepartmentBerkeley, CA 94720USA

Kinji AsakaNational Institute of Advanced Industrial Science and Technology (AIST)Health Research Institute1-8-31 MidorigaokaIkedaJapan

ListofContributors

Zhenan BaoStanford UniversityDepartment of Chemical Engineering381 North South MallStanford, CA 94305USA

Siegfried BauerJohannes Kepler University LinzSoft Matter PhysicsAltenbergerstraße 694040 LinzAustria

Ruth BieringerFreudenberg Forschungsdienste SE & Co. KGHöhnerweg 2-469469 WeinheimGermany

Frederick BossuytUniversity Ghent9052 Gent-ZwijnaardeBelgium

Frederick BossuytCentre for Microsystems TechnologyGhent University and Interuniversity Microelectronics CentreTechnology Park, Building 914-A9052 Gent-ZwijnaardeBelgium

XVIII ListofContributors

Wenzhe CaoPrinceton UniversityDepartment of Electrical Engineering and Princeton Institute for the Science and Technology of MaterialsF310 Engineering QuadOlden StreetPrinceton, NJ 08544USA

Zhichao FanTsinghua UniversityDepartment of Engineering MechanicsBeijing, 100084China

Mario GonzalezThe Interuniversity Microelectronics Center IMECKapeldreef 753001 LeuvenBelgium

Jürgen GüntherFreudenberg Forschungsdienste SE & Co. KGHöhnerweg 2-469469 WeinheimGermany

Yung-Yu HsuThe Interuniversity MicroElectronics Center IMECKapeldreef 753001 LeuvenBelgiumPresent address: MC10 Inc.36 Cameron Ave.MA 02140USA

Yonggang HuangNorthwestern UniversityDepartments of Civil and Environmental Engineering and Mechanical EngineeringEvanston, IL 60208USA

Keh-Chih HwangTsinghua UniversityDepartment of Engineering MechanicsBeijing, 100084China

Olle InganäsLinköping UniversityBiomolecular and Organic ElectronicsDepartment of Physics, Chemistry and Biology58183 LinköpingSweden

Koichi IshidaUniversity of TokyoTokyo 153-8505Japan

Houk JangSungkyunkwan UniversitySchool of Advanced Materials Science and EngineeringSuwon, 440-746Korea

Martin KaltenbrunnerJohannes Kepler University LinzSoft Matter PhysicsAltenbergerstraße 694040 LinzAustria

ListofContributors XIX

Woo Hyeun KangColumbia UniversityDepartment of Biomedical Engineering351 Engineering TerraceMC 89041210 Amsterdam AvenueNew York, NY 10027USA

Dae-Hyeong KimSeoul National UniversitySchool of Chemical and Biological EngineeringSeoul, 151-744Korea

Stéphanie P. LacourCenter for NeuroprostheticsEPFL | STI | IMT/IBI | LSBI Station 17CH-1015 Lausanne Switzerland

Seoung-Ki LeeSungkyunkwan UniversitySchool of Advanced Materials Science and EngineeringSuwon, 440-746Korea

Thomas LöherFraunhofer IZMGustav-Meyer-Allee 2513355 BerlinGermany

Nanshu LuDepartment of Aerospace Engineering and Engineering MechanicsUniversity of Texas at Austin405 N Mathews St.Austin, TX 78712USA

Stefan C.B. MannsfeldStanford UniversityDepartment of Chemical Engineering381 North South MallStanford, CA 94305USA

Michael C. McAlpinePrinceton UniversityDepartment of Mechanical and Aerospace EngineeringEngineering QuadOlden StreetPrinceton, NJ 08544USA

Barclay Morrison, IIIColumbia UniversityDepartment of Biomedical Engineering351 Engineering TerraceMC 89041210 Amsterdam AvenueNew York, NY 10027USA

Christian MüllerDepartment of Chemical and Biological Engineering/Polymer TechnologyChalmers University of Technology41296 GöteborgSweden

Thanh D. NguyenPrinceton UniversityDepartment of Mechanical and Aerospace EngineeringEngineering QuadOlden StreetPrinceton, NJ 08544USA

XX ListofContributors

Prashant K. PurohitUniversity of Pennsylvania Department of Mechanical Engineering and Applied Mechanics220 South 33rd Street Philadelphia, PA 19104-6391USA

Yi QiPrinceton UniversityDepartment of Mechanical and Aerospace EngineeringEngineering QuadOlden StreetPrinceton, NJ 08544USA

John A. RogersUniversity of IllinoisDepartment of Materials Science and EngineeringUrbana, IL 61801USA

John A. RogersUniversity of Illinois at Urbana-ChampaignDepartment of Materials Science and EngineeringBeckman Institute for Advanced Science and Technology and Frederick Seitz Materials Research LaboratoryUrbana, IL 61801USA

Takayasu SakuraiUniversity of TokyoTokyo 153-8505Japan

Thomas SchauberFreudenberg Forschungsdienste SE & Co. KGHöhnerweg 2-469469 WeinheimGermany

Tsuyoshi SekitaniThe University of Tokyo Department of Electrical Engineering and Information Systems 7-3-1 Hongo Bunkyo-ku Tokyo 113-8656Japan

Takao SomeyaThe University of TokyoDepartment of Electrical Engineering and Information Systems 7-3-1 HongoBunkyo-kuTokyo 113-8656Japan

Jizhou SongUniversity of MiamiDepartment of Mechanical and Aerospace EngineeringCoral Gables, FL 33146USA

Robert A. StreetPalo Alto Research Center3333 Coyote Hill RoadPalo Alto, CA 94304USA

Yewang SuTsinghua UniversityDepartment of Engineering MechanicsBeijing, 100084China

ListofContributors XXI

Makoto TakamiyaUniversity of TokyoTokyo 153-8505Japan

Benjamin C.K. TeeStanford UniversityDepartment of Electrical EngineeringDavid Packard Building350 Serra MallStanford, CA 94305USA

Jan VanfleterenCentre for Microsystems TechnologyGhent University and Interuniversity Microelectronics CentreTechnology Park, Building 914-A9052 Gent-ZwijnaardeBelgium

Thomas VervustCentre for Microsystems TechnologyGhent University and Interuniversity Microelectronics CentreTechnology Park, Building 914-A9052 Gent-ZwijnaardeBelgium

Sigurd WagnerPrinceton UniversityDepartment of Electrical Engineering and Princeton Institute for the Science and Technology of MaterialsB422 Engineering QuadOlden StreetPrinceton, NJ 08544USA

Shuodao WangNorthwestern UniversityDepartment of Mechanical EngineeringEvanston, IL 60208USA

Jian WuTsinghua UniversityDepartment of Engineering MechanicsBeijing, 100084China

Chao YanSungkyunkwan UniversitySchool of Advanced Materials Science and EngineeringSuwon, 440-746Korea

Part ITheory

1

3

Theory for Stretchable InterconnectsJizhouSongandShuodaoWang

1.1 Introduction

A rapidly growing range of applications demand electronic systems that cannot be formed in the conventional manner on semiconductor wafers. The most promi­nent example is stretchable electronics, which has a performance equal to estab­lished technologies that use rigid semiconductor wafers, but in formats that can be stretched and compressed. It enables many application possibilities such as flexible displays [1], electronic eye camera [2–4], conformable skin sensors [5], smart surgical gloves [6], and structural health monitoring devices [7]. There are primarily two directions to make stretchable electronics. One is to use intrinsically stretchable materials such as organic materials [8–13]. However, the electrical per­formance of organic semiconductor materials is relatively poor comparing with the well­developed, high­performance inorganic electronic materials. The other direction to achieve stretchable electronics is to use conventional semiconductors, such as silicon, and make the system stretchable. The main challenge here is to make silicon­based structures stretchable since the brittleness of silicon makes it almost impossible to be stretched. Many researches bypassed this difficulty by using stretchable interconnects [14–22].

One of the most intuitive approaches to develop stretchable interconnects is to exploit out­of­plane deflection in thin layers to accommodate strains applied in the plane. Figure 1.1 illustrates some examples of this concept. In the first case (Figure 1.1a) [17, 24, 25] of stretchable wavy ribbons, the initially flat ribbons are bonded to a prestrained elastomeric substrate. The prestrain can be induced by mechanical (or thermal) stretch along the ribbon directions. Releasing the prestrain causes a compression in the ribbon, and this compression leads to a nonlinear buckling response and results in a wavy profile. When the wavy structure is subject to stretches, the amplitudes and periods of the waves change to accommodate the deformation. In the second case (Figure 1.1b) of popup structure [26], the ribbons can be designed to bond the prestretched elastomeric substrate only at certain locations. When the prestrain is released, the ribbon on the nonbonded regions delaminates from the substrate and forms popup profile. Compared to Figure 1.1a,

1

Stretchable Electronics, First Edition. Edited by Takao Someya.© 2013 Wiley­VCH Verlag GmbH & Co. KGaA. Published 2013 by Wiley­VCH Verlag GmbH & Co. KGaA.

4 1 TheoryforStretchableInterconnects

this layout has the advantage that the wavelengths can be defined precisely with a level of engineering control to have higher stretchability.

Combining the stretchable interconnects in Figure 1.1a (or Figure 1.1b) with rigid device islands, an interconnect­island structure [16, 19, 20, 22] can be developed to accommodate the deformations. Mechanical response to stretching or compression involves, primarily, deformations only in these interconnects, thereby avoiding unwanted strains in the regions of the active devices. Lacour et al. [16] and Kim et al. [19] developed a coplanar mesh design by using the wavelike interconnects, which are bonded with the substrate. Although such a coplanar mesh design can improve the stretchability to around 40%, the stretch­ability is still small for certain applications. Kim et al. [20] developed a nonco­planar mesh design (Figure 1.1c), consisting of device islands linked by popup interconnects for stretchable circuits, which can be stretched to rubber­like levels of strain (e.g., up to 100%). To further increase the stretchability, serpentine inter­connects [14, 15, 19–22] can be used. Compared to the straight interconnects, the serpentine ones can accommodate larger deformation because they are much longer and can involve large twist to reduce the strains in the interconnects.

Figure 1.1 SEM images of (a) stretchable wavy ribbons, (b) popup structure, (c) noncoplanar mesh design with straight interconnects, and (d) noncoplanar mesh design with serpentine interconnects.

(Reprinted with permission from Ref. [15] Copyright 2007 American Institute of Physics and Ref. [23] Copyright 2009 American Vacuum Society).

(a) (b)

(c) (d)

1.2MechanicsofStretchableWavyRibbons 5

Figure 1.1d shows a SEM image of serpentine interconnects used in the nonco­planar mesh design.

For serpentine interconnects, there are no theoretical work, and many research­ers have developed numerical models to study their deformations due to their complex geometries [14, 15, 19–22]. The related review is not the focus of this chapter. Here, we will review the theoretical aspects related to the designs in Figure 1.1a–c. Mechanics of stretchable wavy ribbons (Figure 1.1a) is described in Section 1.2. Analysis for small and large strains and width effect are discussed in this section. Section 1.3 describes the mechanics of popup structure (Figure 1.1b). Section 1.4 reviewed the mechanics of interconnects in the noncoplanar mesh design (Figure 1.1c). Interfacial adhesion and large deformation effect are also discussed in this section.

1.2 Mechanics of Stretchable Wavy Ribbons

The fabrication of stretchable wavy ribbons is illustrated in Figure 1.2. The flat ribbon is first chemically bonded to a prestrained compliant substrate. When the prestrain is released, the ribbon is compressed to generate the wavy layout through a nonlinear buckling response. These wavy layouts can accommodate external deformations through changes in wavelength and amplitude, which is also shown in Figure 1.2.

1.2.1 Small-Deformation Analysis

Several models [28, 29] have been developed to explain the mechanics of stretch­able wavy ribbons under small deformations. For example, Huang et al. [29] developed an energy method to determine the buckling profile. The thin ribbon is modeled as an elastic nonlinear von Karman beam since its thickness is much smaller compared with other characteristic lengths (e.g., wavelength). The sub­strate is modeled as a semi­infinite solid because its thickness (∼mm) is much larger than that (∼µm) of film. The total energy consists of the bending energy Ub and membrane energy Um in the thin film and strain energy Us in the substrate.

For a stiff thin film (ribbon) with thickness hf, Young’s modulus Ef and Poisson’s ratio vf on a prestrained compliant substrate with prestrain εpre, Young’s modulus Es, and Poisson’s ratio vs, the wavy profile forms with the out­of­plane displacement:

w A kx Ax= ( ) =

cos cos1

12πλ

(1.1)

when the prestrain is released. Here, x1 is the coordinate along the ribbon direc­tion, A is the amplitude, λ is the wavelength, and k = 2π/λ is the wave number.

6 1 TheoryforStretchableInterconnects

A and λ (or k) are to be determined by minimizing the total energy. The bending energy Ub can be obtained by

U LE h w

xx

E h ALb

f f f fd

dd=

=∫0

3 2

2

2

0

4 3 2

4 01

24 3λπ

λ

λ

(1.2)

where L0 and E Ef f f= −( )1 2ν are the length and plane­strain modulus of the thin film, respectively.

The membrane strain ε11, which determines the membrane energy in the ribbon, is related to the in­plane displacement u1 and out­of­plane displacement w by εmembrane = du1/dx1 + (dw/dx1)2/2 − εpre. The membrane force Nmembrane is given by N E hmembrane f f membrane= ε . The interfacial shear is negligible [29] and the force equilibrium equation becomes dN11/dx1 = 0, which gives a uniform membrane force and therefore a uniform membrane strain:

ε πλ

εmembrane pre= −2 2

2

A (1.3)

Figure 1.2 Schematic illustration of the process for fabricating buckled, or “wavy,” single crystal Si ribbons on a PDMS substrate. (Reprinted with permission from Ref. [27] Copyright 2009 American Vacuum Society).

Bond Si nanoribbons to prestrained PDMS

L+dLSi

PDMS

Release prestrain

L

StretchableSi device

Compress Stretch