1 Introduction ................................................. 1
2 CNTFET fundamentals .......................................... 7
2.1 CNTFET technologies ..................................... 7
2.1.1 Fabrication of CNTs .............................. 8
2.1.2 Typical device structures ........................ 9
2.1.3 Doping of CNTs .................................. 11
2.2 CNT material properties ................................ 13
2.2.1 Crystal lattice ................................. 14
2.2.2 Band structure .................................. 16
2.2.3 Band gap ........................................ 20
2.2.4 Parabolic band approximation .................... 21
2.2.5 CNT types ....................................... 23
2.2.6 Semi-classical density of states ................ 24
2.2.7 Impact of non-idealities ........................ 27
2.3 CNT transport phenomena ................................ 27
2.4 Metal-CNT contacts ..................................... 34
2.4.1 Schottky-Mott contact model ..................... 38
2.4.2 Extended contact model .......................... 41
2.4.3 Contact resistance .............................. 48
2.5 CNTFET measurements .................................... 49
3 Models for ballistic transport .............................. 53
3.1 Fundamentals ........................................... 55
3.1.1 Ballistic transport ............................. 55
3.1.2 Charge calculation .............................. 61
3.1.3 Current calculation ............................. 65
3.1.4 Relation to the semi-classical charge
calculation ..................................... 69
3.2 Poisson equation ....................................... 75
3.3 Steady-state Schrödinger-Poisson solver ................ 78
3.3.1 Device model .................................... 79
3.3.2 Numerical solution .............................. 81
3.3.3 Adaptive integration ............................ 82
3.3.4 Example ......................................... 89
3.4 Time-dependent Schrödinger-Poisson solver .............. 93
3.4.1 Device model .................................... 93
3.4.2 Numerical solution .............................. 94
3.4.3 Example ......................................... 95
3.5 WKB-based Schrödinger-Poisson solver ................... 95
3.5.1 Transmission through a single barrier ........... 97
3.5.2 Transmission through multi-barrier structures ... 98
3.5.3 Relation to the carrier density ................. 99
3.5.4 Device model ................................... 101
3.6 Analytical ballistic model ............................ 103
3.6.1 Current control mechanisms ..................... 104
3.6.2 Simplification of Poisson equation ............. 109
3.6.3 Characteristic gate voltages ................... 115
3.6.4 Thermionic transport model ..................... 117
3.6.5 Current approximations ......................... 124
3.7 Compact modeling concepts ............................. 136
4 Aspects of device and circuit design ....................... 141
4.1 Device design aspects ................................. 142
4.1.1 Subthreshold slope ............................. 144
4.1.2 Ambipolarity ................................... 149
4.1.3 Ohmic region ................................... 151
4.2 Modeling layout parasitics ............................ 156
4.2.1 Gate impedance ................................. 158
4.2.2 Model limitations .............................. 162
4.2.3 Example ........................................ 163
4.3 Circuit design study .................................. 166
4.3.1 Power amplifier specifications ................. 167
4.3.2 Layout optimization ............................ 168
4.3.3 Conclusion ..................................... 172
4.4 Non-quasi-static effects .............................. 172
4.4.1 NQS modeling ................................... 173
4.4.2 Impact of layout parasitics .................... 176
4.4.3 Comparison to experimental results ............. 178
4.4.4 Conclusion ..................................... 180
5 Summary .................................................... 181
5.1 Conclusions ........................................... 181
5.2 Outlook ............................................... 185
A Review: Quantum states ..................................... 189
A.l Closed boundary conditions ............................ 191
A.2 Periodic boundary conditions .......................... 192
A.3 Open boundary conditions .............................. 192
A.4 Absorbing boundary conditions ......................... 196
В Current operator and transmission probability .............. 199
С Quantum reflections and resonances ......................... 207
D Discretized Schrödinger Equation ........................... 211
D.l Discretizing the Schrödinger equation ................. 211
D.2 Evaluation of bound states ............................ 214
D.3 Evaluation of scattering states ....................... 215
D.4 Evaluation of resonant states ......................... 221
E Model for metallic tubes ................................... 223
F Two-port chain ............................................. 229
G Z-Transform ................................................ 233
Bibliography .................................................. 235
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