Preface .................................................... ix
1 Overview of carbon nanotubes ............................. 1
1.1 Introduction ........................................ 1
1.2 An abbreviated zigzag history of CNTs ............... 3
1.3 Synthesis of CNTs .................................. 13
1.4 Characterization techniques ........................ 16
1.5 What about non-CNTs? ............................... 17
2 Electrons in solids: a basic introduction ............... 19
2.1 Introduction ....................................... 19
2.2 Quantum mechanics of electrons in solids ........... 20
2.3 An electron in empty space ......................... 21
2.4 An electron in a finite empty solid ................ 23
2.5 An electron in a periodic solid: Kronig-Penney
model .............................................. 26
2.6 Important insights from the Kronig-Penney model .... 29
2.7 Basic crystal structure of solids .................. 32
2.8 The Bravais lattice ................................ 33
2.9 The reciprocal lattice ............................. 38
2.10 Summary ............................................ 42
2.11 Problem set ........................................ 42
3 Graphene ................................................ 47
3.1 Introduction ....................................... 47
3.2 The direct lattice ................................. 50
3.3 The reciprocal lattice ............................. 51
3.4 Electronic band structure .......................... 52
3.5 Tight-binding energy dispersion .................... 55
3.6 Linear energy dispersion and carrier density ....... 63
3.7 Graphene nanoribbons ............................... 67
3.8 Summary ............................................ 70
3.9 Problem set ........................................ 70
4 Carbon nanotubes ........................................ 73
4.1 Introduction ....................................... 73
4.2 Chirality: a concept to describe nanotubes ......... 74
4.3 The CNTs lattice ................................... 76
4.4 CNTs Brillouin zone ................................ 81
4.5 General observations from the Brillouin zone ....... 86
4.6 Tight-binding dispersion of chiral nanotubes ....... 88
4.7 Band structure of armchair nanotubes ............... 90
4.8 Band structure of zigzag nanotubes and the
derivation of the bandgap .......................... 93
4.9 Limitations of the tight-binding formalism ......... 95
4.10 Summary ............................................ 97
4.11 Problem set ........................................ 98
5 Carbon nanotube equilibrium properties ................. 102
5.1 Introduction ...................................... 102
5.2 Free-electron density of states in one
dimension ......................................... 103
5.3 Density of states of zigzag nanotubes ............. 105
5.4 Density of states of armchair nanotubes ........... 111
5.5 Density of states of chiral nanotubes and
universal density of states for semiconducting
CNTs .............................................. 113
5.6 Group velocity .................................... 116
5.7 Effective mass .................................... 117
5.8 Carrier density ................................... 119
5.9 Summary ........................................... 124
5.10 Problem set ....................................... 125
6 Ideal quantum electrical properties .................... 128
6.1 Introduction ...................................... 128
6.2 Quantum conductance ............................... 129
6.3 Quantum conductance of multi-wall CNTs ............ 134
6.4 Quantum capacitance ............................... 139
6.5 Quantum capacitance of graphene ................... 142
6.6 Quantum capacitance of metallic CNTs .............. 144
6.7 Quantum capacitance of semiconducting CNTs ........ 145
6.8 Experimental validation of the quantum
capacitance for CNTs .............................. 147
6.9 Kinetic inductance of metallic CNTs ............... 148
6.10 From Planck to quantum conductance: an energy-
based derivation of conductance ................... 151
6.11 Summary ........................................... 153
6.12 Problem set ....................................... 154
7 Carbon nanotube interconnects .......................... 157
7.1 Introduction ...................................... 157
7.2 Electron scattering and lattice vibrations ........ 158
7.3 Electron mean free path ........................... 163
7.4 Single-wall CNT low-field resistance model ........ 168
7.5 Single-wall CNT high-field resistance model
and current density ............................... 171
7.6 Multi-wall CNT resistance model ................... 174
7.7 Transmission line interconnect model .............. 176
7.8 Lossless CNT transmission line model .............. 182
7.9 Lossy CNT transmission line model ................. 183
7.10 Performance comparison of CNTs and copper
interconnects ..................................... 184
7.11 Summary ........................................... 186
7.12 Problem set ....................................... 188
8 Carbon nanotube field-effect transistors ............... 191
8.1 Introduction ...................................... 191
8.2 Survey of CNFET device geometries ................. 192
8.3 Surface potential ................................. 195
8.4 Ballistic theory of ohmic-contact CNFETs .......... 200
8.5 Ballistic theory of CNFETs including drain
optical phonon scattering ......................... 206
8.6 Ballistic CNFET performance parameters ............ 209
8.7 Quantum CNFETs .................................... 212
8.8 Schottky-barrier ballistic CNFETs ................. 213
8.9 Unipolar CNFETs ................................... 223
8.10 Paradigm difference between conventional 2D
MOSFETs and ballistic ID FETs ..................... 225
8.11 Summary ........................................... 227
8.12 Problem set ....................................... 228
9 Applications of carbon nanotubes ....................... 233
9.1 Introduction ...................................... 233
9.2 Chemical sensors and biosensors ................... 234
9.3 Probe tips for scanning probe microscopy .......... 236
9.4 Nano-electromechanical systems (NEMS) ............. 237
9.5 Field emission of electrons ....................... 238
9.6 Integrated electronics on flexible substrates ..... 240
9.7 Hydrogen storage .................................. 242
9.8 Composites ........................................ 244
9.9 References ........................................ 245
Index ..................................................... 249
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