Flexible Electronics: Theory and Method of Structural Design

Foreword
Preface
Contents
1 Structural Engineering of Flexible Electronics
1.1 Introduction
1.2 Applications of Flexible Electronics
1.2.1 Wearable Human Healthcare
1.2.2 Robotics and Haptic Interface
1.2.3 Smart Skin in Aircraft
1.3 Structural Strategies
1.3.1 Wavy Strategy
1.3.2 Island-Bridge Strategy
1.3.3 Kirigami and Origami Strategy
1.3.4 Buckling-Driven Assembly Strategy
1.3.5 Structural Designs of Substrate
1.4 Structural Opportunities by Materials
1.5 Summary
References
2 Buckling of Film-on-Substrate System in Flexible Electronics
2.1 Introduction
2.2 Formation of Film-on-Substrate Structure
2.3 Island-Bridge Structure of Stretchable Electronics
2.3.1 Mechanical Model for the Bridge Structure
2.3.2 Mechanical Model for the Island Structure
2.4 Temperature-Dependent Global Buckling Analysis and Structural Design
2.4.1 Geometrical Model and Governing Equations
2.4.2 Structure Design Based on Temperature-Dependent Properties
2.4.3 Temperature-Dependent Local Buckling Analysis and Critical Condition
2.5 Summary
References
3 Buckling of Fiber-on-Substrate System in Flexible Electronics
3.1 Introduction
3.2 Fabrication of Buckled Fibers
3.2.1 Mechano-Electrospinning (MES) Technique for In-Surface Buckled Devices
3.2.2 Direct-Writing of Fibers onto a Pre-strained PDMS
3.2.3 Materials and Experimental Set-Up
3.3 Buckling Behaviors of 1D Micro/Nanowires
3.3.1 Out-of-Plane and In-Plane Buckling
3.3.2 Mechanics of Out-of-/In-Surface Buckling
3.3.3 Competition of Buckling Modes
3.4 In-Plane Buckled, Highly Stretchable Devices
3.5 Performance of the Fabricated Stretchable Piezoelectric Device
3.6 Summary
References
4 Freestanding Fractal-Inspired Design for Stretchable Electronics
4.1 Introduction
4.2 Elasticity of Fractal Inspired Interconnects
4.2.1 Elastic Analysis of Fractal Interconnects
4.2.2 Experiments of the Fractal Structures
4.3 Fractal Designs in Stretchable Electronics
4.3.1 Mechanics and Electronics with Peano-Based Geometries
4.3.2 Fractal-Based Epidermal Electronics
4.3.3 Radio-Frequency Devices with Fractal Layouts
4.4 Summary
References
5 Fractal-Inspired Design on Substrate for Stretchable Electronics
5.1 Introduction
5.2 Mechanical Modeling of SSIs on Soft Substrate
5.2.1 Maximum Strain of Order-2 SSI
5.2.2 The Scale Law Formula
5.2.3 FEM Simulation Results
5.3 Self-Similar Design of Surface Electrodes
5.3.1 Electromechanical Design of Self-Similar Surface Electrodes
5.3.2 Electromechanical Optimization Model
5.3.3 Feasible Range of the Geometric Parameters
5.3.4 Characterization of Mechanical Performance
5.4 Self-Similar Design for Stretchable Wireless LC Strain Sensors
5.4.1 Self-Similar Design for Wireless LC Strain Sensor
5.4.2 Structural Stretchability of the Self-Similar Strain Sensor
5.4.3 Strain-Induced Tunable Inductance
5.4.4 Experimental Platform and Sensitivity Analysis
5.5 Summary
References
6 Conformal Design on Rigid Curved Substrate
6.1 Introduction
6.2 Theoretical Analysis Based on Energy Method
6.2.1 Energy Components of Thin Film
6.2.2 Energy Components of Substrate
6.2.3 Total Energy of Flexible Electronics
6.3 1D Conformability of Membranes on Rigid Wavy Substrates
6.3.1 Analytical Interface Model by Work of Adhesion
6.3.2 Analytical Interface Model by Traction-Separation Relations
6.4 2D Conformability of Island-Bridge Structures on Non-Developable Surfaces
6.4.1 Analytical Model
6.4.2 Adhesion Experiment
6.4.3 Adhesion Experiment for Island on Rigid Surface
6.5 Summary
References
7 Conformal Design on Soft Curved Substrate
7.1 Introduction
7.2 1D Conformability on Soft Substrates
7.2.1 1D Conformability of Epidermal Electronics on Soft Skin
7.2.2 1D Conformability of Epidermal Electronics on Soft Skin Under External Strain
7.3 2D Conformability on Wavy Soft Substrates
7.3.1 2D Conformability of Epidermal Electronics on Soft Skin
7.3.2 The Effects of the Roughness and Elastic Modulus of the Skin on Conformability
7.3.3 The Effects of the Substrate Thickness on Conformability
7.3.4 The Effects of the Areal Coverage of Electrode on Conformability
7.3.5 The Effects of the External Load on Conformability
7.4 2D Conformability on Complex Soft Substrates
7.4.1 2D Conformability of Island on a Bicurvature Soft Substrate
7.4.2 The Effects of Geometry Parameters on Stable Conformal Contact
7.4.3 The Effects of Materials Parameters on Conformal Contact
7.4.4 Contact Pressure in Conformal Contact
7.5 Local Failure Analysis of Island During Conformal Process
7.5.1 Conformal Strain in Island During Conformal Process
7.5.2 Wrinkling and Buckling Delamination During Conformal Process
7.5.3 Adhesion Experiment for Island on Soft Surface
7.6 Summary
References
8 In-Plane Design of Serpentine Interconnect on Substrate
8.1 Introduction
8.2 Thick Interconnects for Ultra-Large Stretchability
8.3 Transition Between Wrinkling, Buckling and Scissoring
8.3.1 Transition from Wrinkling to Buckling
8.3.2 Transition from Buckling to Scissoring
8.4 Criteria for Three Modes
8.4.1 Stretchability in the Wrinkling Mode
8.4.2 Stretchability in the Buckling Mode
8.4.3 Stretchability in the Scissoring Mode
8.5 Some Applications of Thick Interconnects
8.5.1 Interconnects for Stretchable Arrays of LEDs
8.5.2 Interconnects for Stretchable Arrays of Solar Cells
8.5.3 Traces for Stretchable RF Antennas
8.6 Summary
References
9 In-Plane Design for Serpentine Interconnect Without Substrate
9.1 Introduction
9.2 Buckling of Stretchable Serpentine Interconnects
9.3 FPD Buckling Theory of Beams
9.3.1 Geometric Relations for the Finite Deformation of 3D Beams
9.3.2 Governing Equations for the FPD Buckling Analysis
9.4 Application of Three Specific Cases
9.4.1 Lateral Buckling of a Three-Point-Bending Beam
9.4.2 Lateral Buckling of a Pure Bending Beam
9.4.3 Euler Buckling
9.5 Sample Fabrication and Experimental Verification
9.6 Summary
References
10 Self-Assembly of Self-Similar Fibers for Stretchable Electronics
10.1 Introduction
10.2 HE-Printing Technique for Fabrication of Self-Similar Nano/Microfibers
10.2.1 HE-Printing Technique
10.2.2 Fabrication of Self-Similar Nano/Microfibers
10.3 Buckling-Driven Self-Assembly of Self-Similar Fiber-Based Structures
10.3.1 Buckling of Serpentine Fibers Under Uniaxial Prestrain
10.3.2 Buckling of Serpentine Fibers Under Biaxial Prestrain
10.3.3 Self-Assembly by Tuning In-/Out-of-Surface Buckling
10.4 Hyper-Stretchable Self-Powered Sensors Based on Self-Similar Piezoelectric Nano/Microfibers
10.4.1 Hyper-Stretchable Self-Powered Sensors
10.4.2 Architecture of an HSS and HE-Printing Technique
10.4.3 Characterizations of the HSS
10.4.4 Applications of the HSS
10.5 Summary
References
11 Kirigami Strategy for Conformal Electronics
11.1 Introduction
11.2 Self-Healing Kirigami Assembly Strategy
11.2.1 Conformal Criterion for Kirigami Geometry
11.2.2 Geometrical Design Algorithm for 2D-to-3D Conformal Mapping
11.2.3 Preparation and Characterization of the Ag/PCL Self-Healing Materials
11.2.4 Kirigami-Based Conformal Heater
11.2.5 Multifunctional Wind Sensing System
11.3 Soft-Hinge Kirigami Metamaterials for Self-Adaptive Conformal Electronic Armor
11.3.1 Deformation Mechanism of Soft-Hinge Kiri-MMs
11.3.2 Stretchability, Flexibility and Conformability of Soft-Hinge Kiri-MMs
11.3.3 Electrical Enhancements with Conductive Polymer Composite
11.3.4 Functional Soft-Hinge Kiri-MM E-armor Systems
11.4 Summary
References
12 Neutral Layer Design for Flexible Electronics
12.1 Introduction
12.2 Mechanics of Neutral Mechanical Plane
12.3 The Effect of Length on Splitting of the Multiple Neutral Mechanical Plane
12.4 The Effect of Boundary Conditions on Splitting of the Neutral Mechanical Plane
12.4.1 Given Slopes Are Imposed at the Ends of the Hard Layers
12.4.2 Given Slopes Are Imposed at the End Sections
12.5 Effects of the Membrane Energy and Bending Energy of the Middle Layer
12.5.1 The Model Incorporating the Shear Energy, Membrane Energy and Bending Energy of the Middle Layer
12.5.2 The Model Neglecting the Shear Energy of the Middle Layer
12.6 Summary
References
13 Liquid Metal-Based Structure Design for Stretchable Electronics
13.1 Introduction
13.2 Microfluidic Serpentine Antennas with Designed Mechanical Tunability
13.2.1 Galium-Based Eutectic Alloys
13.2.2 The Design of Serpentine Microfluidic Antenna
13.2.3 Fabrication of the Serpentine Microfluidic Antennas
13.2.4 Characterization of the Serpentine Microfluidic Antennas
13.3 Liquid–Metal Antennas with Stable Working Frequency for RFID Applications
13.3.1 Serpentine Liquid–Metal Antennas for RFID
13.3.2 Design of Stretchable RF Antennas
13.3.3 Relationship Between Stretchability and Resonant Frequency
13.4 Liquid Metal Nanoparticles (LMNPs) for Ultrathin, Flexible Metasurface
13.4.1 Liquid Metal Metasurface
13.4.2 Sintering Process of LMNPs
13.4.3 Electromagnetic Performance
13.5 Summary
References
14 Applications of Flexible Electronics
14.1 Introduction
14.2 Application of Flexible Electronics as E-tattoos
14.2.1 Low-Cost, μm-Thick, and Tape-Free E-tattoos
14.2.2 Characterization of Wearability and Motion Artifacts
14.2.3 Applications of the Large-Area Epidermal Electrodes on Human Skin
14.3 Application of Flexible Electronics as Implantable Cardiac Membranes
14.3.1 3D Multifunctional Integumentary Cardiac Membranes
14.3.2 Design of Conformability
14.3.3 Spatiotemporal Cardiac Measurements
14.4 Application of Flexible Electronics as Aircraft Smart Skin
14.4.1 Design of the Multifunctional, Flexible Sensing Skin
14.4.2 External Airflow Multifunctional Perception
14.4.3 Internal Structural Health Monitoring
14.5 Application of Flexible Electronics as Robotic Interface
14.5.1 Design and System Architecture of 3D-Shaped E-skin
14.5.2 Fabrication of the 3D-Shaped E-skin
14.6 Summary
References