1 Introduction ............................................... 1
1.1 Moore's law ................................................ 2
1.2 The MOS transistor ......................................... 4
1.3 Classical scaling laws ..................................... 8
1.4 Short-channel effects ...................................... 8
1.5 Technology boosters ........................................ 9
1.5.1 New materials ...................................... 10
1.5.2 Strain ............................................. 11
1.5.3 Electrostatic control of the channel ............... 11
1.6 Ballistic transport in nanotransistors .................... 12
1.6.1 Top-of-the-barrier model ........................... 12
1.6.2 Ballistic scaling laws ............................. 14
1.7 Summary ................................................... 15
References ..................................................... 16
2 Multigate and nanowire transistors ........................ 18
2.1 Introduction .............................................. 18
2.2 The multigate architecture ................................ 19
2.3 Reduction of short-channel effects using multigate
architectures ............................................. 20
2.3.1 Single-gate MOSFET ................................. 22
2.3.2 Double-gate MOSFET ................................. 23
2.3.3 Triple-and quadruple-gate MOSFETs .................. 24
2.3.4 Cylindrical gate-all-around MOSFET ................. 25
2.4 Quantum confinement effects in nanoscale multigate
transistors ............................................... 29
2.4.1 Energy subbands .................................... 29
2.4.2 Increase of band gap energy ........................ 36
2.4.3 Quantum capacitance ................................ 37
2.4.4 Valley occupancy and transport effective mass ...... 38
2.4.5 Semimetal-semiconductor nanowire transitions ....... 40
2.4.6 Topological insulator nanowire transistor .......... 43
2.4.7 Nanowire-SET transition ............................ 43
2.5 Other multigate field-effect devices ...................... 44
2.5.1 Junctionless transistor ............................ 44
2.5.2 Tunnel field-effect transistor ..................... 45
2.6 Summary ............................................... 46
Further reading ........................................... 47
References ................................................ 47
3 Synthesis and fabrication of semiconductor nanowires ...... 54
3.1 Top-down fabrication techniques ........................... 54
3.1.1 Horizontal nanowires ............................... 54
3.1.2 Vertical nanowires ................................. 57
3.2 Bottom-up fabrication techniques .......................... 58
3.2.1 Vapor-liquid-solid growth technique ................ 59
3.2.2 Growth without catalytic particles ................. 63
3.2.3 Heterojunctions and core-shell nanowires ........... 64
3.3 Silicon nanowire thinning ................................. 66
3.3.1 Hydrogen annealing ................................. 66
3.3.2 Oxidation .......................................... 67
3.3.3 Mechanical properties of silicon nanowires ......... 69
3.4 Carrier mobility in strained nanowires .................... 72
3.5 Summary ................................................... 73
References ................................................ 74
4 Quantum mechanics in one dimension ........................ 81
4.1 Overview .................................................. 81
4.2 Survey of quantum mechanics in ID ......................... 81
4.2.1 Schrцdinger wave equation in one spatial
dimension .......................................... 82
4.2.2 Electron current in quantum mechanics .............. 83
4.2.3 Quantum mechanics in momentum space ................ 84
4.3 Momentum eigenstates ...................................... 85
4.4 Electron incident on a potential energy barrier ........... 88
4.5 Electronic band structure ................................. 92
4.5.1 Brillouin zone ..................................... 93
4.5.2 Bloch wave functions ............................... 94
4.6 LCAO and tight binding approximation ...................... 95
4.6.1 Linear combination of atomic orbitals (LCAO) ....... 95
4.6.2 Tight binding approximation ........................ 97
4.7 Density of states and energy subbands .................... 100
4.7.1 Density of states in three spatial dimensions ..... 100
4.7.2 Density of states in two spatial dimensions ....... 102
4.7.3 Density of states in one spatial dimension ........ 104
4.7.4 Comparison of 3D, 2D, and ID density of states .... 104
4.8 Conclusions .............................................. 105
Further reading .......................................... 106
References ............................................... 106
5 Nanowire electronic structure ............................ 107
5.1 Overview ................................................. 107
5.2 Semiconductor crystal structures: group IV and III-V
materials ................................................ 107
5.2.1 Group IV bonding and the diamond crystal
structure ......................................... 107
5.2.2 III-V compounds and the zincblende structure ...... 110
5.2.3 Two-dimensional materials ......................... 113
5.3 Insulators, semiconductors, semimetals, and metals ....... 117
5.4 Experimental determination of electronic structure ....... 119
5.4.1 Temperature variation of electrical conductivity .. 119
5.4.2 Absorption spectroscopy ........................... 121
5.4.3 Scanning tunneling spectroscopy ................... 123
5.4.4 Angle resolved photo-emission spectroscopy ........ 127
5.5 Theoretical determination of electronic structure ........ 129
5.5.1 Quantum many-body Coulomb problems ................ 130
5.5.2 Self-consistent field theory ...................... 134
5.5.3 Optimized single determinant theories ............. 146
5.5.4 GW approximation .................................. 147
5.6 Bulk semiconductor band structures ....................... 149
5.7 Applications to semiconductor nanowires .................. 152
5.7.1 Nanowire crystal structures ....................... 152
5.7.2 Quantum confinement and band folding .............. 154
5.7.3 Semiconductor nanowire band structures ............ 157
5.8 Summary .................................................. 160
Further reading .......................................... 162
References ............................................... 162
6 Charge transport in quasi-1 D nanostructures ............. 167
6.1 Overview ................................................. 167
6.2 Voltage sources .......................................... 167
6.2.1 Semi-classical description ........................ 167
6.2.2 Electrode Fermi-Dirac distributions ............... 171
6.3 Conductance quantization ................................. 174
6.3.1 Subbands in a hard wall potential nanowire ........ 174
6.3.2 Conductance in a channel without scattering ....... 176
6.3.3 Time reversal symmetry and transmission ........... 179
6.3.4 Detailed balance at thermodynamic equilibrium ..... 182
6.3.5 Conductance with scattering ....................... 182
6.3.6 Landauer conductance formula: scattering at
non-zero temperature .............................. 186
6.4 Charge mobility .......................................... 188
6.5 Scattering mechanisms .................................... 191
6.5.1 Ionized impurity scattering ....................... 191
6.5.2 Resonant backscattering ........................... 193
6.5.3 Remote Coulomb scattering ......................... 194
6.5.4 Alloy scattering .................................. 194
6.5.5 Surface scattering ................................ 195
6.5.6 Surface roughness ................................. 195
6.5.7 Electron-phonon scattering ........................ 196
6.5.8 Carrier-carrier scattering ........................ 198
6.6 Scattering lengths ....................................... 200
6.6.1 Scattering lengths and conductance regimes ........ 200
6.6.2 Multiple scattering in a single channel ........... 201
6.7 Quasi-ballistic transport in nanowire transistors ........ 206
6.8 Green's function treatment of quantum transport .......... 210
6.8.1 Green's function for Poisson's equation ........... 210
6.8.2 Green's function for the Schrцdinger equation ..... 211
6.8.3 Application of Green's function to transport in
nanowires ......................................... 213
6.9 Summary .................................................. 217
Further reading .......................................... 217
References ............................................... 217
7 Nanowire transistor circuits ............................. 221
7.1 CMOS circuits ............................................ 221
7.1.1 CMOS logic ........................................ 221
7.1.2 SRAM cells ........................................ 224
7.1.3 Non-volatile memory devices ....................... 227
7.2 Analog and RF transistors ................................ 231
7.3 Crossbar nanowire circuits ............................... 234
7.4 Input/output protection devices .......................... 237
7.5 Chemical and biochemical sensors ......................... 238
7.6 Summary .................................................. 242
References ............................................... 242
Index ......................................................... 249
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