Graphene Nanoelectronics (eBook)

Preface 7
Contents 9
Contributors 21
Chapter 1: Introduction 24
1.1 Overview 24
1.2 Book Summary 30
1.3 Outlook 33
References 34
Part I: Metrology and Synthesis 36
Chapter 2: Raman Spectroscopy: Characterization of Edges, Defects, and the Fermi Energy of Graphene and sp2 Carbons 37
2.1 Introduction to the Resonance Raman Spectra of Graphene 37
2.1.1 The Raman Spectra of sp2 Carbons 38
2.1.2 Edge Structure of Graphene 40
2.1.3 The Multiple-Resonance Raman Scattering Process 40
2.1.4 Concept of the Kohn Anomaly 43
2.1.5 Introduction to Near-Field Raman Spectroscopy 44
2.2 Characterization of Defects 44
2.2.1 Point Defects Induced by Ion Bombardment 45
2.2.2 Model for the D-Band Activated Region 46
2.2.3 Line Defects at the Edges of Nanographene 48
2.3 Characterization of Edges 51
2.3.1 Overview of Graphene Edges 51
2.3.2 The Characterization of Graphene Edgesfrom Their D-Band Scattering 52
2.3.3 Mode assignments of the Raman Spectra of Graphene Nanoribbons 56
2.3.4 Polarization Dependence of the Raman Intensity 60
2.4 The Fermi Energy Dependence: The Kohn Anomaly 62
2.4.1 Effect of Gate Doping on the G-Band of Single-Layer Graphene 62
2.4.2 Effect of Gate Doping on the G Band of Double-Layer Graphene 64
2.5 Near-Field Raman Spectroscopy 66
2.5.1 The Spatial Resolution in Optical Microscopes 67
2.5.2 The Principle of TERS 67
2.5.3 Mechanism of Near-Field Enhancement 68
2.5.4 Application to Carbon Nanotubes 69
2.6 Summary and Perspective 71
References 75
Chapter 3: Scanning Tunneling Microscopy and Spectroscopy of Graphene 78
3.1 Introduction 78
3.2 STM/STS Techniques 79
3.3 Sample Preparation 82
3.4 Hallmarks of Graphene in STM/STS 82
3.5 Line Shape of Landau Levels 87
3.6 Electron–phonon Coupling 88
3.7 Coupling Between Graphene Layers 90
3.8 Twist Between Graphene Layers 92
3.8.1 Appearance of Moiré Pattern 93
3.8.2 Saddle Point Van Hove Singularities 94
3.8.3 Single Layer-like Behavior and Velocity Renormalization 94
3.9 Graphene on SiO2 98
3.9.1 Three Types of Corrugations 98
3.9.2 Scanning Tunneling Spectroscopy 100
3.9.3 Quantum Interference and Fermi Velocity 100
3.9.4 Trapped Charges in SiO2 101
3.10 Edges, Defects and Magnetism 102
3.11 SPM-based Nano-lithography 103
3.11.1 Signs of Invasiveness of an STM Tip 104
3.11.2 Folding Graphene Layers 104
3.11.3 Cutting Graphene Layers 105
3.11.4 Surface Modification 106
3.12 Summary and Perspectives 108
References 109
Chapter 4: The Electronic Properties of Adsorbates on Graphene 113
4.1 Introduction: What Are Adsorbates on Graphene Good for? 113
4.2 Angle-Resolved Photoemission Spectroscopy 116
4.2.1 Introduction 116
4.2.2 Band Structure Determination of Graphene 116
4.2.3 Self-energy Determination 119
4.3 The ``Zoology'' of Adsorbates 122
4.3.1 Adsorption of Nontransition-Metal Atoms 123
4.3.2 Adsorption of Transition Metal Atoms 127
4.4 Adsorbate–Graphene Interactions: General Symmetry Considerations 130
4.5 Hydrogen on Graphene As a Prototype Adsorbate System 132
4.5.1 Introduction 132
4.5.2 Hydrogen on Graphene: Experimental Evidence for Anderson Localization 134
4.6 Potassium on Graphene: The Coulomb Interactionin Graphene, Revealed 138
4.6.1 K Adsorption on Epitaxial Graphene on SiC(0001) 138
4.6.2 K Adsorption on Quasi-free-Standing Epitaxial Graphene on SiC(0001) 140
4.7 Calcium Adsorption: Superconducting Instability of Graphene 144
4.8 Conclusions and Outlook 148
References 149
Chapter 5: Epitaxial Graphene on SiC(0001) 155
5.1 Introduction 155
5.2 Silicon Carbide and Its Polar Surfaces 157
5.3 Growth of Epitaxial Graphene on SiC(0001) in Ultra-High Vacuum 158
5.4 The (6363)R30 Reconstruction 160
5.5 Electronic Structure of Monolayer and Bilayer Graphene at the K-point 163
5.6 State-of-the Art Graphene Growth in Argon Atmosphere 166
5.7 Transport Properties of Graphene on SiC(0001) 169
5.8 Engineering the Interface Between Graphene and SiC(0001) by Hydrogen Intercalation 172
5.9 Conclusion 175
References 175
Chapter 6: Magneto-Transport on Epitaxial Graphene 180
6.1 Introduction 180
6.2 Epitaxial Graphene Synthesis 182
6.3 Dielectric Integration on Epitaxial Graphene 187
6.4 Top-Gate Graphene Field-Effect Transistors 188
6.5 Half-Integer Quantum Hall-Effect in Epitaxial Graphene 191
6.6 Ballistic and Coherent Transport on Epitaxial Graphene 197
6.7 Spin Transport on Epitaxial Graphene 202
6.8 Summary 204
References 204
Chapter 7: Epitaxial Graphene on Metals 208
7.1 Introduction 208
7.2 Methods of Graphene Preparation on Metal Surfaces 212
7.3 Experimental Methods 213
7.4 Graphene on Lattice-Matched 3d-Metal Surfaces 216
7.4.1 Atomic Structure of Graphene Layer on Ni(111) and Co(0001) 217
7.4.2 Electronic Structure of Grapheneon Lattice-Matched Surfaces 219
7.4.3 Magnetism of Graphene on the Ni(111) Surface 225
7.5 Graphene on Lattice-Mismatched 4d,5d-Metal Surfaces 228
7.5.1 Structure of Graphene on Ir(111), Ru(0001), and Rh(111) 229
7.5.2 Electronic Structure of Grapheneon Lattice-Mismatched Surfaces 233
7.6 Hybrid Structures on the Basis of Graphene Layerson Metal Surfaces 237
7.6.1 Intercalation-like Systems 238
7.6.2 Growth of Noble Metal Clusters on Graphene Moirè 241
7.6.3 Growth of Magnetic Metal Clusters on Graphene Moirè 244
7.6.4 Chemical Functionalization of Graphene on Transition Metal Surfaces 245
7.7 Conclusions and Outlook 247
References 249
Part II: Electronic-structure and Transport Properties 254
Chapter 8: Electronic Properties of Monolayer and Bilayer Graphene 255
8.1 Introduction 255
8.2 The Crystal Structure of Monolayer Graphene 256
8.2.1 The Real Space Structure 256
8.2.2 The Reciprocal Lattice of Graphene 257
8.2.3 The Atomic Orbitals of Graphene 257
8.3 The Tight-Binding Model 258
8.4 The Tight-Binding Model of Monolayer Graphene 260
8.4.1 Diagonal Matrix Elements 260
8.4.2 Off-Diagonal Matrix Elements 262
8.4.3 The Low-Energy Electronic Bands of Monolayer Graphene 264
8.5 Massless Chiral Quasiparticles in Monolayer Graphene 266
8.5.1 The Dirac-Like Hamiltonian 266
8.5.2 Pseudospin and Chirality in Graphene 267
8.6 The Tight-Binding Model of Bilayer Graphene 269
8.7 Massive Chiral Quasiparticles in Bilayer Graphene 272
8.7.1 The Low-Energy Bands of Bilayer Graphene 272
8.7.2 The Two-Component Hamiltonian of Bilayer Graphene 273
8.7.3 Pseudospin and Chirality in Bilayer Graphene 274
8.8 The Integer Quantum Hall Effect in Graphene 276
8.8.1 The Landau Level Spectrum of Monolayer Graphene 276
8.8.2 The Integer Quantum Hall Effectin Monolayer Graphene 278
8.8.3 The Landau Level Spectrum of Bilayer Graphene 279
8.8.4 The Integer Quantum Hall Effectin Bilayer Graphene 280
8.9 Trigonal Warping in Graphene 281
8.9.1 Trigonal Warping in Monolayer Graphene 281
8.9.2 Trigonal Warping and Lifshitz Transitionin Bilayer Graphene 282
8.10 Tuneable Band Gap in Bilayer Graphene 284
8.10.1 Asymmetry Gap in the Band Structure of Bilayer Graphene 284
8.10.2 Self-Consistent Model of Screening in Bilayer Graphene 286
8.10.2.1 Introduction 286
8.10.2.2 Electrostatics 286
8.10.2.3 Layer Densities 288
8.10.2.4 Self-Consistent Screening 289
8.11 Summary 290
References 291
Chapter 9: Electronic Properties of Graphene Nanoribbons 294
9.1 Introduction 294
9.2 Electronic States of Graphene 296
9.2.1 Tight-Binding Model and Edge States 298
9.2.2 Massless Dirac Equation 301
9.2.2.1 Zigzag Nanoribbons 302
9.2.2.2 Armchair Nanoribbons 303
9.2.3 Edge Boundary Condition andIntervalley Scattering 303
9.3 Electronic Transport Properties 304
9.3.1 One-Way Excess Channel System 305
9.3.2 Model of Impurity Potential 308
9.3.3 Perfectly Conducting Channel: Absence of Anderson Localization 308
9.4 Universality Class 310
9.4.1 Graphene Nanoribbons with GenericEdge Structures 311
9.5 Transport Properties Through Graphene Nanojunction 313
9.6 Summary 314
References 315
Chapter 10: Mesoscopics in Graphene: Dirac Points in Periodic Geometries 317
10.1 Graphene Ribbons 319
10.1.1 Hamiltonian 319
10.1.2 Zigzag Nanoribbons 320
10.1.3 Armchair Nanoribbons 323
10.2 Graphene Quantum Rings 326
10.2.1 Chirality in Armchair Nanoribbons 327
10.2.2 Phase Jumps at Corner Junctions 328
10.2.3 Numerical Results 330
10.3 Graphene in a Periodic Potential 333
10.3.1 Counting Dirac Points 333
10.3.2 Numerical Solutions of the Dirac Equation 336
10.3.3 Conductivity 336
10.4 Conclusion 338
References 338
Chapter 11: Electronic Properties of Multilayer Graphene 340
11.1 Introduction 340
11.1.1 Stacking Arrangements 341
11.1.2 -Orbital Continuum Model 342
11.2 Energy Band Structure 342
11.2.1 Preliminaries 342
11.2.2 Monolayer Graphene 343
11.2.3 AA Stacking 344
11.2.4 AB Stacking 346
11.2.5 ABC Stacking 348
11.2.6 Arbitrary Stacking 349
11.3 Landau-Level Spectrum 351
11.3.1 Preliminaries 351
11.3.2 AA Stacking 351
11.3.3 AB Stacking 352
11.3.4 ABC Stacking 354
11.3.5 Arbitrary Stacking 354
11.4 Low-Energy Effective Theory 356
11.4.1 Introduction 356
11.4.2 Pseudospin Hamiltonian 356
11.4.3 Stacking Diagrams 357
11.4.4 Partitioning Rules 357
11.4.5 Degenerate State Perturbation Theory 359
11.4.6 Limitations of the Minimal Model 362
11.4.7 Effects of the Consecutive Stacking 362
11.5 Applications 363
11.5.1 Quantum Hall Conductivity 363
11.5.2 Optical Conductivity 365
11.5.3 Electrical Conductivity 366
11.6 Conclusions 369
References 370
Chapter 12: Graphene Carrier Transport Theory 372
12.1 Introduction 372
12.2 Graphene Boltzmann Transport 375
12.2.1 Screening: Random Phase Approximation (RPA) 377
12.2.2 Coulomb Scatterers 380
12.2.3 Gaussian White Noise Disorder 381
12.2.4 Yukawa Potential 382
12.2.5 Gaussian Correlated Impurities 382
12.2.6 Midgap States 383
12.3 Transport at Low Carrier Density 384
12.3.1 Self-Consistent Approximation 386
12.3.1.1 Formalism 387
12.3.1.2 Results 390
12.3.2 Effective Medium Theory 392
12.3.3 Magneto-Transport and Temperature Dependence of the Minimum Conductivity 396
12.3.4 Quantum to Classical Crossover 398
12.3.5 Summary of Theoretical Predictions for Coulomb Impurities 401
12.4 Comparison with Experiments 402
12.4.1 Magnetotransport: Dependence of xx and xy on Carrier Density 402
12.4.2 Dependence of min and Mobility on Impurity Concentration 404
12.4.3 Dependence of min and Mobility on Dielectric Environment 404
12.5 Conclusion 406
References 407
Chapter 13: Exploring Quantum Transport in Graphene Ribbons with Lattice Defects and Adsorbates 410
13.1 Landauer Theory of Transport 412
13.2 Subband Structure and Transport in Ideal Ribbons 414
13.3 Quantized Ballistic Conductance 417
13.4 Electron Transport in Graphene Ribbons 418
13.5 Discovery of Quantized Conductance in Strongly Disordered Graphene Ribbons 419
13.6 The Roles of Different Classes of Defects 420
13.7 Tight Binding Model of Ribbons with Edge Disorder, Interior Vacancies, and Long-Ranged Potentials 421
13.8 Numerical Simulations of Quantum Transport 421
13.8.1 Disorder-Induced Conductance Suppression, Fluctuations and Destruction of the Ballistic Quantized Conductance Plateaus 423
13.8.2 Conductance Dips at the Edgesof Ribbon Subbands 425
13.8.3 The Role of Temperature 426
13.8.4 From Ballistic Transport to Anderson Localization 427
13.8.5 The Quantized Conductance in Disordered Ribbons: Theory vs. Experiment 429
13.9 Adsorbates on Graphene and Dirac Point Resonances 431
13.9.1 Tight Binding Hamiltonian for Adsorbates on Graphene 432
13.9.2 Effective Hamiltonian for Adsorbates on Graphene 434
13.9.3 The T-matrix Formalism 435
13.9.4 Dirac Point Scattering Resonances dueto H, F, and O Atoms and OH Molecules Adsorbed on Graphene 436
13.10 Electron Quantum Transport in Graphene Ribbons with Adsorbates 438
13.10.1 Building Efficient Tight-Binding Models 438
13.10.2 Results of Numerical Simulations of Quantum Transport in Ribbonswith Adsorbates 441
13.11 Summary 446
References 446
Chapter 14: Graphene Oxide: Synthesis, Characterization, Electronic Structure, and Applications 450
14.1 Introduction 451
14.2 Understanding Bulk Graphite Oxide and Graphene Oxide Monolayers 452
14.3 Fabrication of Graphite Oxide and Graphene Oxide 454
14.3.1 Traditional Approaches to Fabricate Graphite Oxide 455
14.3.2 New Fabrication Techniques for Graphite Oxide and Graphene Oxide 456
14.3.2.1 Fabricating Reduced Graphene Oxide 457
14.4 Characterization Approaches 459
14.4.1 Optical Microscopy 459
14.4.2 Scanning Transmission Electron Microscopy 460
14.4.3 Electron Energy Loss Spectroscopy 462
14.4.4 Atomic Force Microscopy 463
14.4.5 X-ray Photoelectron Spectroscopy 464
14.4.6 Raman Spectroscopy of Graphene Oxide and Reduced Graphene 466
14.5 Insight from Simulations 467
14.5.1 Using Epoxy Groups to Unzip Graphene 467
14.5.2 Graphene Oxide Electronic Structure 469
14.5.3 Electron Mobility and Transport 470
14.6 Applications for Graphene Oxide 472
14.6.1 Graphene Oxide Electronics 472
14.6.2 Sensors 473
14.6.3 Carbon-Based Magnetism 473
14.7 Future Perspectives 474
References 475
Part III: From Physics and Chemistry of Graphene to Device Applications 480
Chapter 15: Graphene pn Junction: Electronic Transport and Devices 481
15.1 Introduction 481
15.2 Transport in the Absence of a Magnetic Field 483
15.2.1 Dirac Equation, Pseudospin, and Chirality 484
15.2.2 Abrupt pn Junction and Analogy with Optics 486
15.2.3 Tunneling for Dirac and Schrdinger Fermions 488
15.2.4 Quantum Transport Modeling 491
15.2.5 Experiments: Asymmetry and odd Resistances 493
15.3 Transport in the Presence of Magnetic Fields 496
15.3.1 Weak Magnetic Field Regime 496
15.3.2 Edge States, Snake States, and Valley Isospin 499
15.3.3 Quantum Hall Regime: The Ballistic Case 501
15.3.4 Experiments: Ballistic to Ohmic Transition 504
15.4 Transport in the Presence of Strain-Induced Pseudo-Magnetic Fields 508
15.4.1 Strain-Induced Pseudo-Magnetic Field 508
15.4.2 Edge States and Transport Gap 511
15.4.3 Magnetic and Electric Snake States 515
15.5 Discussions 517
15.5.1 Devices: Current Status and Outlook 517
15.5.2 Conclusions 519
References 519
Chapter 16: Electronic Structure of Bilayer Graphene Nanoribbon and Its Device Application: A Computational Study 523
16.1 Introduction 523
16.2 Methodology 525
16.3 Electronic Structure of Monolayer Graphene Nanoribbon 526
16.3.1 Armchair Edges 526
16.3.2 Zigzag Edges 527
16.3.3 Dopant Effect 528
16.4 Electronic Structure of Bilayer Graphene Nanoribbon 530
16.4.1 Armchair Edges 531
16.4.2 Zigzag Edges with Dopants 532
16.4.3 Interlayer Distance 532
16.5 Bilayer Graphene Nanoribbon Device 533
16.6 Bilayer ZGNR NEM Switch 535
16.7 Conclusion 538
References 539
Chapter 17: Field-Modulation Devices in Graphene Nanostructures 542
17.1 Introduction 542
17.2 Electronic Structure 543
17.3 Theoretical Framework: Extended Hückel Theory 546
17.4 Bilayer Graphene 548
17.4.1 –B stacking 549
17.4.2 Strain Engineering 549
17.4.3 Misalignment 551
17.5 Armchair Graphene Nanoribbons 551
17.5.1 Pristine Edges 552
17.5.2 Periodic edge roughness effects 556
17.6 Zigzag Graphene Nanoribbons with Periodic Edge Roughness 559
17.7 Novel Applications 563
17.8 Conclusions 564
References 565
Chapter 18: Graphene Nanoribbons: From Chemistry to Circuits 567
18.1 The Innermost Circle: The Atomistic View 568
18.1.1 Flatland: A Romance in Two Dimensions 569
18.1.2 Whither Metallicity? 570
18.1.3 Edge Chemistry: Benzene or Graphene? 571
18.1.4 Whither Chirality? 573
18.2 The Next Circle: Two Terminal Mobilities and I–Vs 575
18.2.1 Current–Voltage Characteristics (I–Vs) 575
18.2.2 Low Bias Mobility-Bandgap Tradeoffs: Asymptotic Band Constraints 578
18.3 The Third Level: Active Three-Terminal Electronics 581
18.3.1 Wide–Narrow–Wide: All Graphene Devices 581
18.3.2 Solving Quantum Transport and Electrostatic Equations 582
18.3.3 Improved Electrostatics in 2-D 583
18.3.4 Three-Terminal I–Vs 586
18.3.5 Pinning vs. Quasi-Ohmic Contacts 587
18.4 The Penultimate Circle: GNR Circuits 588
18.4.1 Geometry of An All Graphene Circuit 589
18.4.2 Compact Model Equations 591
18.4.3 Digital Circuits 591
18.4.4 How `Good' is a Graphene-based Invertor? 592
18.4.5 Physical Domain Issues: Monolithic Device-Interconnect Structures 595
18.5 Conclusions 595
References 597
Index 599