Raza Graphene Nanoelectronics

Metrology, Synthesis, Properties and Applications
2012
ISBN: 978-3-642-22984-8
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 598 Seiten

Reihe: NanoScience and Technology

Graphene is a perfectly two-dimensional single-atom thin membrane with zero bandgap. It has attracted huge attention due to its linear dispersion around the Dirac point, excellent transport properties, novel magnetic characteristics, and low spin-orbit coupling. Graphene and its nanostructures may have potential applications in spintronics, photonics, plasmonics and electronics. This book brings together a team of experts to provide an overview of the most advanced topics in theory, experiments, spectroscopy and applications of graphene and its nanostructures. It covers the state-of-the-art in tutorial-like and review-like manner to make the book useful not only to experts, but also newcomers and graduate students.

Autoren/Hrsg.

Raza, Hassan

Inhaltsverzeichnis

1;Preface;7
2;Contents;9
3;Contributors;21
4;Chapter 1: Introduction;24
4.1;1.1 Overview;24
4.2;1.2 Book Summary;30
4.3;1.3 Outlook;33
4.4;References;34
5;Part I: Metrology and Synthesis;36
5.1;Chapter 2: Raman Spectroscopy: Characterization of Edges, Defects, and the Fermi Energy of Graphene and sp2 Carbons;37
5.1.1;2.1 Introduction to the Resonance Raman Spectra of Graphene;37
5.1.1.1;2.1.1 The Raman Spectra of sp2 Carbons;38
5.1.1.2;2.1.2 Edge Structure of Graphene;40
5.1.1.3;2.1.3 The Multiple-Resonance Raman Scattering Process;40
5.1.1.4;2.1.4 Concept of the Kohn Anomaly;43
5.1.1.5;2.1.5 Introduction to Near-Field Raman Spectroscopy;44
5.1.2;2.2 Characterization of Defects;44
5.1.2.1;2.2.1 Point Defects Induced by Ion Bombardment;45
5.1.2.2;2.2.2 Model for the D-Band Activated Region;46
5.1.2.3;2.2.3 Line Defects at the Edges of Nanographene;48
5.1.3;2.3 Characterization of Edges;51
5.1.3.1;2.3.1 Overview of Graphene Edges;51
5.1.3.2;2.3.2 The Characterization of Graphene Edgesfrom Their D-Band Scattering;52
5.1.3.3;2.3.3 Mode assignments of the Raman Spectra of Graphene Nanoribbons;56
5.1.3.4;2.3.4 Polarization Dependence of the Raman Intensity;60
5.1.4;2.4 The Fermi Energy Dependence: The Kohn Anomaly;62
5.1.4.1;2.4.1 Effect of Gate Doping on the G-Band of Single-Layer Graphene;62
5.1.4.2;2.4.2 Effect of Gate Doping on the G Band of Double-Layer Graphene;64
5.1.5;2.5 Near-Field Raman Spectroscopy;66
5.1.5.1;2.5.1 The Spatial Resolution in Optical Microscopes;67
5.1.5.2;2.5.2 The Principle of TERS;67
5.1.5.3;2.5.3 Mechanism of Near-Field Enhancement;68
5.1.5.4;2.5.4 Application to Carbon Nanotubes;69
5.1.6;2.6 Summary and Perspective;71
5.1.7;References;75
5.2;Chapter 3: Scanning Tunneling Microscopy and Spectroscopy of Graphene;78
5.2.1;3.1 Introduction;78
5.2.2;3.2 STM/STS Techniques;79
5.2.3;3.3 Sample Preparation;82
5.2.4;3.4 Hallmarks of Graphene in STM/STS;82
5.2.5;3.5 Line Shape of Landau Levels;87
5.2.6;3.6 Electron–phonon Coupling;88
5.2.7;3.7 Coupling Between Graphene Layers;90
5.2.8;3.8 Twist Between Graphene Layers;92
5.2.8.1;3.8.1 Appearance of Moiré Pattern;93
5.2.8.2;3.8.2 Saddle Point Van Hove Singularities;94
5.2.8.3;3.8.3 Single Layer-like Behavior and Velocity Renormalization;94
5.2.9;3.9 Graphene on SiO2;98
5.2.9.1;3.9.1 Three Types of Corrugations;98
5.2.9.2;3.9.2 Scanning Tunneling Spectroscopy;100
5.2.9.3;3.9.3 Quantum Interference and Fermi Velocity;100
5.2.9.4;3.9.4 Trapped Charges in SiO2;101
5.2.10;3.10 Edges, Defects and Magnetism;102
5.2.11;3.11 SPM-based Nano-lithography;103
5.2.11.1;3.11.1 Signs of Invasiveness of an STM Tip;104
5.2.11.2;3.11.2 Folding Graphene Layers;104
5.2.11.3;3.11.3 Cutting Graphene Layers;105
5.2.11.4;3.11.4 Surface Modification;106
5.2.12;3.12 Summary and Perspectives;108
5.2.13;References;109
5.3;Chapter 4: The Electronic Properties of Adsorbates on Graphene;113
5.3.1;4.1 Introduction: What Are Adsorbates on Graphene Good for?;113
5.3.2;4.2 Angle-Resolved Photoemission Spectroscopy;116
5.3.2.1;4.2.1 Introduction;116
5.3.2.2;4.2.2 Band Structure Determination of Graphene;116
5.3.2.3;4.2.3 Self-energy Determination;119
5.3.3;4.3 The ``Zoology'' of Adsorbates;122
5.3.3.1;4.3.1 Adsorption of Nontransition-Metal Atoms;123
5.3.3.2;4.3.2 Adsorption of Transition Metal Atoms;127
5.3.4;4.4 Adsorbate–Graphene Interactions: General Symmetry Considerations;130
5.3.5;4.5 Hydrogen on Graphene As a Prototype Adsorbate System;132
5.3.5.1;4.5.1 Introduction;132
5.3.5.2;4.5.2 Hydrogen on Graphene: Experimental Evidence for Anderson Localization;134
5.3.6;4.6 Potassium on Graphene: The Coulomb Interactionin Graphene, Revealed;138
5.3.6.1;4.6.1 K Adsorption on Epitaxial Graphene on SiC(0001);138
5.3.6.2;4.6.2 K Adsorption on Quasi-free-Standing Epitaxial Graphene on SiC(0001);140
5.3.7;4.7 Calcium Adsorption: Superconducting Instability of Graphene;144
5.3.8;4.8 Conclusions and Outlook;148
5.3.9;References;149
5.4;Chapter 5: Epitaxial Graphene on SiC(0001);155
5.4.1;5.1 Introduction;155
5.4.2;5.2 Silicon Carbide and Its Polar Surfaces;157
5.4.3;5.3 Growth of Epitaxial Graphene on SiC(0001) in Ultra-High Vacuum;158
5.4.4;5.4 The (6363)R30 Reconstruction;160
5.4.5;5.5 Electronic Structure of Monolayer and Bilayer Graphene at the K-point;163
5.4.6;5.6 State-of-the Art Graphene Growth in Argon Atmosphere;166
5.4.7;5.7 Transport Properties of Graphene on SiC(0001);169
5.4.8;5.8 Engineering the Interface Between Graphene and SiC(0001) by Hydrogen Intercalation;172
5.4.9;5.9 Conclusion;175
5.4.10;References;175
5.5;Chapter 6: Magneto-Transport on Epitaxial Graphene;180
5.5.1;6.1 Introduction;180
5.5.2;6.2 Epitaxial Graphene Synthesis;182
5.5.3;6.3 Dielectric Integration on Epitaxial Graphene;187
5.5.4;6.4 Top-Gate Graphene Field-Effect Transistors;188
5.5.5;6.5 Half-Integer Quantum Hall-Effect in Epitaxial Graphene;191
5.5.6;6.6 Ballistic and Coherent Transport on Epitaxial Graphene;197
5.5.7;6.7 Spin Transport on Epitaxial Graphene;202
5.5.8;6.8 Summary;204
5.5.9;References;204
5.6;Chapter 7: Epitaxial Graphene on Metals;208
5.6.1;7.1 Introduction;208
5.6.2;7.2 Methods of Graphene Preparation on Metal Surfaces;212
5.6.3;7.3 Experimental Methods;213
5.6.4;7.4 Graphene on Lattice-Matched 3d-Metal Surfaces;216
5.6.4.1;7.4.1 Atomic Structure of Graphene Layer on Ni(111) and Co(0001);217
5.6.4.2;7.4.2 Electronic Structure of Grapheneon Lattice-Matched Surfaces;219
5.6.4.3;7.4.3 Magnetism of Graphene on the Ni(111) Surface;225
5.6.5;7.5 Graphene on Lattice-Mismatched 4d,5d-Metal Surfaces;228
5.6.5.1;7.5.1 Structure of Graphene on Ir(111), Ru(0001), and Rh(111);229
5.6.5.2;7.5.2 Electronic Structure of Grapheneon Lattice-Mismatched Surfaces;233
5.6.6;7.6 Hybrid Structures on the Basis of Graphene Layerson Metal Surfaces;237
5.6.6.1;7.6.1 Intercalation-like Systems;238
5.6.6.2;7.6.2 Growth of Noble Metal Clusters on Graphene Moirè;241
5.6.6.3;7.6.3 Growth of Magnetic Metal Clusters on Graphene Moirè;244
5.6.6.4;7.6.4 Chemical Functionalization of Graphene on Transition Metal Surfaces;245
5.6.7;7.7 Conclusions and Outlook;247
5.6.8;References;249
6;Part II: Electronic-structure and Transport Properties;254
6.1;Chapter 8: Electronic Properties of Monolayer and Bilayer Graphene;255
6.1.1;8.1 Introduction;255
6.1.2;8.2 The Crystal Structure of Monolayer Graphene;256
6.1.2.1;8.2.1 The Real Space Structure;256
6.1.2.2;8.2.2 The Reciprocal Lattice of Graphene;257
6.1.2.3;8.2.3 The Atomic Orbitals of Graphene;257
6.1.3;8.3 The Tight-Binding Model;258
6.1.4;8.4 The Tight-Binding Model of Monolayer Graphene;260
6.1.4.1;8.4.1 Diagonal Matrix Elements;260
6.1.4.2;8.4.2 Off-Diagonal Matrix Elements;262
6.1.4.3;8.4.3 The Low-Energy Electronic Bands of Monolayer Graphene;264
6.1.5;8.5 Massless Chiral Quasiparticles in Monolayer Graphene;266
6.1.5.1;8.5.1 The Dirac-Like Hamiltonian;266
6.1.5.2;8.5.2 Pseudospin and Chirality in Graphene;267
6.1.6;8.6 The Tight-Binding Model of Bilayer Graphene;269
6.1.7;8.7 Massive Chiral Quasiparticles in Bilayer Graphene;272
6.1.7.1;8.7.1 The Low-Energy Bands of Bilayer Graphene;272
6.1.7.2;8.7.2 The Two-Component Hamiltonian of Bilayer Graphene;273
6.1.7.3;8.7.3 Pseudospin and Chirality in Bilayer Graphene;274
6.1.8;8.8 The Integer Quantum Hall Effect in Graphene;276
6.1.8.1;8.8.1 The Landau Level Spectrum of Monolayer Graphene;276
6.1.8.2;8.8.2 The Integer Quantum Hall Effectin Monolayer Graphene;278
6.1.8.3;8.8.3 The Landau Level Spectrum of Bilayer Graphene;279
6.1.8.4;8.8.4 The Integer Quantum Hall Effectin Bilayer Graphene;280
6.1.9;8.9 Trigonal Warping in Graphene;281
6.1.9.1;8.9.1 Trigonal Warping in Monolayer Graphene;281
6.1.9.2;8.9.2 Trigonal Warping and Lifshitz Transitionin Bilayer Graphene;282
6.1.10;8.10 Tuneable Band Gap in Bilayer Graphene;284
6.1.10.1;8.10.1 Asymmetry Gap in the Band Structure of Bilayer Graphene;284
6.1.10.2;8.10.2 Self-Consistent Model of Screening in Bilayer Graphene;286
6.1.10.2.1;8.10.2.1 Introduction;286
6.1.10.2.2;8.10.2.2 Electrostatics;286
6.1.10.2.3;8.10.2.3 Layer Densities;288
6.1.10.2.4;8.10.2.4 Self-Consistent Screening;289
6.1.11;8.11 Summary;290
6.1.12;References;291
6.2;Chapter 9: Electronic Properties of Graphene Nanoribbons;294
6.2.1;9.1 Introduction;294
6.2.2;9.2 Electronic States of Graphene;296
6.2.2.1;9.2.1 Tight-Binding Model and Edge States;298
6.2.2.2;9.2.2 Massless Dirac Equation;301
6.2.2.2.1;9.2.2.1 Zigzag Nanoribbons;302
6.2.2.2.2;9.2.2.2 Armchair Nanoribbons;303
6.2.2.3;9.2.3 Edge Boundary Condition andIntervalley Scattering;303
6.2.3;9.3 Electronic Transport Properties;304
6.2.3.1;9.3.1 One-Way Excess Channel System;305
6.2.3.2;9.3.2 Model of Impurity Potential;308
6.2.3.3;9.3.3 Perfectly Conducting Channel: Absence of Anderson Localization;308
6.2.4;9.4 Universality Class;310
6.2.4.1;9.4.1 Graphene Nanoribbons with GenericEdge Structures;311
6.2.5;9.5 Transport Properties Through Graphene Nanojunction;313
6.2.6;9.6 Summary ;314
6.2.7;References;315
6.3;Chapter 10: Mesoscopics in Graphene: Dirac Points in Periodic Geometries;317
6.3.1;10.1 Graphene Ribbons;319
6.3.1.1;10.1.1 Hamiltonian;319
6.3.1.2;10.1.2 Zigzag Nanoribbons;320
6.3.1.3;10.1.3 Armchair Nanoribbons;323
6.3.2;10.2 Graphene Quantum Rings;326
6.3.2.1;10.2.1 Chirality in Armchair Nanoribbons;327
6.3.2.2;10.2.2 Phase Jumps at Corner Junctions;328
6.3.2.3;10.2.3 Numerical Results;330
6.3.3;10.3 Graphene in a Periodic Potential;333
6.3.3.1;10.3.1 Counting Dirac Points;333
6.3.3.2;10.3.2 Numerical Solutions of the Dirac Equation;336
6.3.3.3;10.3.3 Conductivity;336
6.3.4;10.4 Conclusion;338
6.3.5;References;338
6.4;Chapter 11: Electronic Properties of Multilayer Graphene;340
6.4.1;11.1 Introduction;340
6.4.1.1;11.1.1 Stacking Arrangements;341
6.4.1.2;11.1.2 -Orbital Continuum Model;342
6.4.2;11.2 Energy Band Structure;342
6.4.2.1;11.2.1 Preliminaries;342
6.4.2.2;11.2.2 Monolayer Graphene;343
6.4.2.3;11.2.3 AA Stacking;344
6.4.2.4;11.2.4 AB Stacking;346
6.4.2.5;11.2.5 ABC Stacking;348
6.4.2.6;11.2.6 Arbitrary Stacking;349
6.4.3;11.3 Landau-Level Spectrum;351
6.4.3.1;11.3.1 Preliminaries;351
6.4.3.2;11.3.2 AA Stacking;351
6.4.3.3;11.3.3 AB Stacking;352
6.4.3.4;11.3.4 ABC Stacking;354
6.4.3.5;11.3.5 Arbitrary Stacking;354
6.4.4;11.4 Low-Energy Effective Theory;356
6.4.4.1;11.4.1 Introduction;356
6.4.4.2;11.4.2 Pseudospin Hamiltonian;356
6.4.4.3;11.4.3 Stacking Diagrams;357
6.4.4.4;11.4.4 Partitioning Rules;357
6.4.4.5;11.4.5 Degenerate State Perturbation Theory;359
6.4.4.6;11.4.6 Limitations of the Minimal Model;362
6.4.4.7;11.4.7 Effects of the Consecutive Stacking;362
6.4.5;11.5 Applications;363
6.4.5.1;11.5.1 Quantum Hall Conductivity;363
6.4.5.2;11.5.2 Optical Conductivity;365
6.4.5.3;11.5.3 Electrical Conductivity;366
6.4.6;11.6 Conclusions;369
6.4.7;References;370
6.5;Chapter 12: Graphene Carrier Transport Theory;372
6.5.1;12.1 Introduction;372
6.5.2;12.2 Graphene Boltzmann Transport;375
6.5.2.1;12.2.1 Screening: Random Phase Approximation (RPA);377
6.5.2.2;12.2.2 Coulomb Scatterers;380
6.5.2.3;12.2.3 Gaussian White Noise Disorder;381
6.5.2.4;12.2.4 Yukawa Potential;382
6.5.2.5;12.2.5 Gaussian Correlated Impurities;382
6.5.2.6;12.2.6 Midgap States;383
6.5.3;12.3 Transport at Low Carrier Density;384
6.5.3.1;12.3.1 Self-Consistent Approximation;386
6.5.3.1.1;12.3.1.1 Formalism;387
6.5.3.1.2;12.3.1.2 Results;390
6.5.3.2;12.3.2 Effective Medium Theory;392
6.5.3.3;12.3.3 Magneto-Transport and Temperature Dependence of the Minimum Conductivity;396
6.5.3.4;12.3.4 Quantum to Classical Crossover;398
6.5.3.5;12.3.5 Summary of Theoretical Predictions for Coulomb Impurities;401
6.5.4;12.4 Comparison with Experiments;402
6.5.4.1;12.4.1 Magnetotransport: Dependence of xx and xy on Carrier Density;402
6.5.4.2;12.4.2 Dependence of min and Mobility on Impurity Concentration;404
6.5.4.3;12.4.3 Dependence of min and Mobility on Dielectric Environment;404
6.5.5;12.5 Conclusion;406
6.5.6;References;407
6.6;Chapter 13: Exploring Quantum Transport in Graphene Ribbons with Lattice Defects and Adsorbates;410
6.6.1;13.1 Landauer Theory of Transport;412
6.6.2;13.2 Subband Structure and Transport in Ideal Ribbons;414
6.6.3;13.3 Quantized Ballistic Conductance;417
6.6.4;13.4 Electron Transport in Graphene Ribbons;418
6.6.5;13.5 Discovery of Quantized Conductance in Strongly Disordered Graphene Ribbons;419
6.6.6;13.6 The Roles of Different Classes of Defects;420
6.6.7;13.7 Tight Binding Model of Ribbons with Edge Disorder, Interior Vacancies, and Long-Ranged Potentials;421
6.6.8;13.8 Numerical Simulations of Quantum Transport;421
6.6.8.1;13.8.1 Disorder-Induced Conductance Suppression, Fluctuations and Destruction of the Ballistic Quantized Conductance Plateaus;423
6.6.8.2;13.8.2 Conductance Dips at the Edgesof Ribbon Subbands;425
6.6.8.3;13.8.3 The Role of Temperature;426
6.6.8.4;13.8.4 From Ballistic Transport to Anderson Localization;427
6.6.8.5;13.8.5 The Quantized Conductance in Disordered Ribbons: Theory vs. Experiment;429
6.6.9;13.9 Adsorbates on Graphene and Dirac Point Resonances;431
6.6.9.1;13.9.1 Tight Binding Hamiltonian for Adsorbates on Graphene;432
6.6.9.2;13.9.2 Effective Hamiltonian for Adsorbates on Graphene;434
6.6.9.3;13.9.3 The T-matrix Formalism;435
6.6.9.4;13.9.4 Dirac Point Scattering Resonances dueto H, F, and O Atoms and OH Molecules Adsorbed on Graphene;436
6.6.10;13.10 Electron Quantum Transport in Graphene Ribbons with Adsorbates;438
6.6.10.1;13.10.1 Building Efficient Tight-Binding Models;438
6.6.10.2;13.10.2 Results of Numerical Simulations of Quantum Transport in Ribbonswith Adsorbates;441
6.6.11;13.11 Summary;446
6.6.12;References;446
6.7;Chapter 14: Graphene Oxide: Synthesis, Characterization, Electronic Structure, and Applications;450
6.7.1;14.1 Introduction;451
6.7.2;14.2 Understanding Bulk Graphite Oxide and Graphene Oxide Monolayers;452
6.7.3;14.3 Fabrication of Graphite Oxide and Graphene Oxide;454
6.7.3.1;14.3.1 Traditional Approaches to Fabricate Graphite Oxide;455
6.7.3.2;14.3.2 New Fabrication Techniques for Graphite Oxide and Graphene Oxide;456
6.7.3.2.1;14.3.2.1 Fabricating Reduced Graphene Oxide;457
6.7.4;14.4 Characterization Approaches;459
6.7.4.1;14.4.1 Optical Microscopy;459
6.7.4.2;14.4.2 Scanning Transmission Electron Microscopy;460
6.7.4.3;14.4.3 Electron Energy Loss Spectroscopy;462
6.7.4.4;14.4.4 Atomic Force Microscopy;463
6.7.4.5;14.4.5 X-ray Photoelectron Spectroscopy;464
6.7.4.6;14.4.6 Raman Spectroscopy of Graphene Oxide and Reduced Graphene;466
6.7.5;14.5 Insight from Simulations;467
6.7.5.1;14.5.1 Using Epoxy Groups to Unzip Graphene;467
6.7.5.2;14.5.2 Graphene Oxide Electronic Structure;469
6.7.5.3;14.5.3 Electron Mobility and Transport;470
6.7.6;14.6 Applications for Graphene Oxide;472
6.7.6.1;14.6.1 Graphene Oxide Electronics;472
6.7.6.2;14.6.2 Sensors;473
6.7.6.3;14.6.3 Carbon-Based Magnetism;473
6.7.7;14.7 Future Perspectives;474
6.7.8;References;475
7;Part III: From Physics and Chemistry of Graphene to Device Applications;480
7.1;Chapter 15: Graphene pn Junction: Electronic Transport and Devices;481
7.1.1;15.1 Introduction;481
7.1.2;15.2 Transport in the Absence of a Magnetic Field;483
7.1.2.1;15.2.1 Dirac Equation, Pseudospin, and Chirality;484
7.1.2.2;15.2.2 Abrupt pn Junction and Analogy with Optics;486
7.1.2.3;15.2.3 Tunneling for Dirac and Schrdinger Fermions;488
7.1.2.4;15.2.4 Quantum Transport Modeling;491
7.1.2.5;15.2.5 Experiments: Asymmetry and odd Resistances;493
7.1.3;15.3 Transport in the Presence of Magnetic Fields;496
7.1.3.1;15.3.1 Weak Magnetic Field Regime;496
7.1.3.2;15.3.2 Edge States, Snake States, and Valley Isospin;499
7.1.3.3;15.3.3 Quantum Hall Regime: The Ballistic Case;501
7.1.3.4;15.3.4 Experiments: Ballistic to Ohmic Transition;504
7.1.4;15.4 Transport in the Presence of Strain-Induced Pseudo-Magnetic Fields;508
7.1.4.1;15.4.1 Strain-Induced Pseudo-Magnetic Field;508
7.1.4.2;15.4.2 Edge States and Transport Gap;511
7.1.4.3;15.4.3 Magnetic and Electric Snake States;515
7.1.5;15.5 Discussions;517
7.1.5.1;15.5.1 Devices: Current Status and Outlook;517
7.1.5.2;15.5.2 Conclusions;519
7.1.6;References;519
7.2;Chapter 16: Electronic Structure of Bilayer Graphene Nanoribbon and Its Device Application: A Computational Study;523
7.2.1;16.1 Introduction;523
7.2.2;16.2 Methodology;525
7.2.3;16.3 Electronic Structure of Monolayer Graphene Nanoribbon;526
7.2.3.1;16.3.1 Armchair Edges;526
7.2.3.2;16.3.2 Zigzag Edges;527
7.2.3.3;16.3.3 Dopant Effect;528
7.2.4;16.4 Electronic Structure of Bilayer Graphene Nanoribbon;530
7.2.4.1;16.4.1 Armchair Edges;531
7.2.4.2;16.4.2 Zigzag Edges with Dopants;532
7.2.4.3;16.4.3 Interlayer Distance;532
7.2.5;16.5 Bilayer Graphene Nanoribbon Device;533
7.2.6;16.6 Bilayer ZGNR NEM Switch;535
7.2.7;16.7 Conclusion;538
7.2.8;References;539
7.3;Chapter 17: Field-Modulation Devices in Graphene Nanostructures;542
7.3.1;17.1 Introduction;542
7.3.2;17.2 Electronic Structure;543
7.3.3;17.3 Theoretical Framework: Extended Hückel Theory;546
7.3.4;17.4 Bilayer Graphene;548
7.3.4.1;17.4.1 –B stacking;549
7.3.4.2;17.4.2 Strain Engineering;549
7.3.4.3;17.4.3 Misalignment;551
7.3.5;17.5 Armchair Graphene Nanoribbons;551
7.3.5.1;17.5.1 Pristine Edges;552
7.3.5.2;17.5.2 Periodic edge roughness effects;556
7.3.6;17.6 Zigzag Graphene Nanoribbons with Periodic Edge Roughness ;559
7.3.7;17.7 Novel Applications;563
7.3.8;17.8 Conclusions;564
7.3.9;References;565
7.4;Chapter 18: Graphene Nanoribbons: From Chemistry to Circuits;567
7.4.1;18.1 The Innermost Circle: The Atomistic View;568
7.4.1.1;18.1.1 Flatland: A Romance in Two Dimensions;569
7.4.1.2;18.1.2 Whither Metallicity?;570
7.4.1.3;18.1.3 Edge Chemistry: Benzene or Graphene?;571
7.4.1.4;18.1.4 Whither Chirality?;573
7.4.2;18.2 The Next Circle: Two Terminal Mobilities and I–Vs;575
7.4.2.1;18.2.1 Current–Voltage Characteristics (I–Vs);575
7.4.2.2;18.2.2 Low Bias Mobility-Bandgap Tradeoffs: Asymptotic Band Constraints;578
7.4.3;18.3 The Third Level: Active Three-Terminal Electronics;581
7.4.3.1;18.3.1 Wide–Narrow–Wide: All Graphene Devices;581
7.4.3.2;18.3.2 Solving Quantum Transport and Electrostatic Equations;582
7.4.3.3;18.3.3 Improved Electrostatics in 2-D;583
7.4.3.4;18.3.4 Three-Terminal I–Vs;586
7.4.3.5;18.3.5 Pinning vs. Quasi-Ohmic Contacts;587
7.4.4;18.4 The Penultimate Circle: GNR Circuits;588
7.4.4.1;18.4.1 Geometry of An All Graphene Circuit;589
7.4.4.2;18.4.2 Compact Model Equations;591
7.4.4.3;18.4.3 Digital Circuits;591
7.4.4.4;18.4.4 How `Good' is a Graphene-based Invertor?;592
7.4.4.5;18.4.5 Physical Domain Issues: Monolithic Device-Interconnect Structures;595
7.4.5;18.5 Conclusions;595
7.4.6;References;597
8;Index;599