Nanoelectronics : quantum engineering of low-dimensional nanoensembles

430 Pages·2013·13.11 MB·English

by  Vijay Kumar Arora

Nanoelectronics
Quantum Engineering of
Low-Dimensional Nanoensembles
© 2015 by Taylor & Francis Group, LLC
© 2015 by Taylor & Francis Group, LLC
Nanoelectronics
Quantum Engineering of
Low-Dimensional Nanoensembles
Vijay Kumar Arora

© 2015 by Taylor & Francis Group, LLC
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© 2015 by Taylor & Francis Group, LLC
© 2015 by Taylor & Francis Group, LLC
Contents
Preface ......................................................................................................................xi
1 Nanoengineering Overview .........................................................................1
1.1 Quantum Waves ....................................................................................1
1.2 Nanoengineering Circuits ...................................................................3
1.3 Bioapplications ......................................................................................9
1.4 Growth and Decay ..............................................................................12
1.5 Scope .....................................................................................................15
Examples .........................................................................................................16
Problems ..........................................................................................................19
CAD/CAE Projects ........................................................................................20
References .......................................................................................................21
2 Atoms, Bands, and Quantum Wells ..........................................................23
2.1 Birth of a Quantum Era ......................................................................23
2.2 Hydrogen-Like Atom .........................................................................25
2.3 Photon Emission and Absorption .....................................................29
2.4 Spherical Hydrogen-Like Atom ........................................................31
2.5 Atoms to Crystals—Bands and Bonds .............................................33
2.6 Thermal Band/Bond Tempering ......................................................38
2.7 Impurity Band/Bond Tempering .....................................................39
2.8 Compound Semiconductors ..............................................................41
2.9 Bands to Quantum Wells ...................................................................44
2.10 A Prototype Quantum Well ..............................................................48
2.11 3D (Bulk) Density of States ................................................................51
2.12 2D Quantum Well ...............................................................................53
2.13 1D Quantum Well ...............................................................................54
2.14 Quantum Dots: QOD Systems ..........................................................55
2.15 Generalized DOS ................................................................................56
2.16 Ellipsoidal Conduction Band Valleys ...............................................58
2.17 Heavy/Light Holes..............................................................................61
2.18 Electrons in a Magnetic Field ............................................................62
2.19 Triangular Quantum Well .................................................................64
2.20 Q2D Electrons in a MOSFET .............................................................67
2.21 Carbon Allotropes ..............................................................................70
2.22 Graphene to CNT ................................................................................73
2.23 Bandgap Engineering of Carbon Allotropes ..................................75
2.24 Tunneling through a Barrier .............................................................94
2.25 WKB Approximation ..........................................................................96
vii
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viii Contents
Examples .........................................................................................................98
Problems ........................................................................................................103
CAD/CAE Projects ......................................................................................108
Appendix 2A: Derivation of the Density of States Using δ-Function ......109
References .....................................................................................................114
3 Carrier Statistics .........................................................................................117
3.1 Fermi–Dirac Distribution Function ................................................117
3.2 Bulk (3D) Carrier Distribution ........................................................118
3.3 Bulk (3D) ND Approximation .........................................................122
3.4 Intrinsic Carrier Concentration .......................................................123
3.5 Charge Neutrality Compensation ..................................................126
3.6 Strong 3D (Bulk) Degenerate Limit ................................................128
3.7 Carrier Statistics in Low Dimensions ............................................129
3.8 The Velocity and the Energy Averages ..........................................132
3.9 Graphene/CNT Nanostructures .....................................................138
Examples .......................................................................................................144
Problems ........................................................................................................150
CAD/CAE Projects ......................................................................................153
Appendix 3A: Distribution Function ........................................................155
Appendix 3B: Electron Concentration for 2D and 1D Nanostructures .....157
Appendix 3C: Intrinsic Velocity .................................................................160
References .....................................................................................................161
4 Nonequilibrium Carrier Statistics and Transport ...............................163
4.1 Tilted Band Diagram in an Electric Field ......................................163
4.2 Velocity Response to an Electric Field ...........................................164
4.3 Ballistic Mobility ...............................................................................172
4.4 Quantum Emission ...........................................................................174
4.5 High-Field Distribution Function ...................................................176
4.6 ND Drift Response ...........................................................................179

4.7 Degenerate Drift Response ..............................................................181
4.8 Direct and Differential Mobility .....................................................187
4.9 Bandgap Narrowing and Carrier Multiplication .........................187
Examples .......................................................................................................191
Problems ........................................................................................................194
CAD/CAE Projects ......................................................................................196
Appendix 4A: Derivation of Velocity-Field Characteristics ..................197
References .....................................................................................................202
5 Charge Transport ........................................................................................203
5.1 Primer .................................................................................................203
5.2 Ohmic (Linear) Transport ................................................................204
5.3 Discovery of Sat Law ........................................................................206
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Contents ix
5.4 Charge Transport in 2D and 1D Resistors .....................................212
5.5 Charge Transport in a CNT .............................................................213
5.6 Power Consumption .........................................................................217
5.7 Transit Time Delay ............................................................................218
5.8 RC Time Delay ...................................................................................219
5.9 L/R Transient Delay ..........................................................................225
5.10 Voltage and Current Division ..........................................................228
Examples .......................................................................................................231
Problems ........................................................................................................233
CAD/CAE Projects ......................................................................................234
Appendix 5A: Derivation of the L/R Time Constant .............................236
References .....................................................................................................238
6 Nano-MOSFET and Nano-CMOS ..........................................................241
6.1 Primer .................................................................................................241
6.2 MOS Capacitor ...................................................................................242
6.3 I–V Characteristics of Nano-MOSFET ...........................................247
6.4 Long- (LC) and Short-Channel (SC) MOSFET ..............................253
6.5 Model Refinements for Nano-CMOS Application .......................255
6.6 CMOS Design ....................................................................................261
Examples .......................................................................................................268
Problems ........................................................................................................269
CAD/CAE Projects ......................................................................................272
Appendix 6A: Properties of Airy Function ..............................................272
References .....................................................................................................273
7 Nanowire Transport ...................................................................................277
7.1 Primer .................................................................................................277
7.2 Ballistic Quantum Conductance .....................................................280
7.3 Quantum Emission ...........................................................................283
7.4 Stochastic to Streamlined Unidirectional Velocity ......................285

7.5 NEADF Application to NW .............................................................289
7.6 NW Transistor ...................................................................................295
CAD/CAE Projects ......................................................................................299
References .....................................................................................................300
8 Quantum Transport in Carbon-Based Devices ....................................305
8.1 High-Field Graphene Transport ......................................................305
8.2 Application to Experimental Data for Graphene ..........................309
8.3 High-Field Transport in Metallic CNT ..........................................310
8.4 High-Field GNR Transport ..............................................................312
8.5 Ballistic Transport in Graphene, CNT, and GNR .........................314
CAD/CAE Projects ......................................................................................319
References .....................................................................................................321
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x Contents
9 Magneto- and Quantum-Confined Transport ......................................323
9.1 Classical Theory of MR ....................................................................323
9.2 Rationale for Density Matrix ...........................................................325
9.3 Density Matrix ...................................................................................327
9.4 Magnetoresistance ............................................................................331
9.5 An Application ..................................................................................336
9.6 Other Types of MR ............................................................................337
9.7 NW Effect in High Electric and Magnetic Fields .........................338
9.8 Quantum-Confined Transport ........................................................339
CAD/CAE Projects ......................................................................................341
References .....................................................................................................342
10 Drift-Diffusion and Multivalley Transport ..........................................345
10.1 Primer .................................................................................................345
10.2 Simplified Drift-Diffusion ...............................................................346
10.3 Einstein Ratio .....................................................................................350
10.4 A Refined Model ...............................................................................354
10.5 Multivalley Transport .......................................................................355
CAD/CAE Projects ......................................................................................360
References .....................................................................................................362
Appendix A: Physical Constants and Scales ................................................363
Appendix B: Silicon Parameters .....................................................................365
Appendix C: Gallium Arsenide Parameters ................................................367
Appendix D: Semiconductor Properties .......................................................369
Appendix E: Metal Properties .........................................................................373
Appendix F: Fermi–Dirac Integral .................................................................375
Appendix G: Table of Fermi–Dirac Integrals ..............................................377
Appendix H: Periodic Table .............................................................................381
Appendix I: General Comments on Project Execution ..............................383
Appendix J: Published Papers by the Author ..............................................387
Appendix K: Final Word ..................................................................................395
Index .....................................................................................................................401
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