Preface ....................................................... VII
1 Macroscopic Current Flow ..................................... 1
1.1 The Classical (Drude) Model of Electronic Conduction
and Ohm's Law ........................................... 2
1.2 The Quantum (Free-Electron) Model of Electronic
Conduction .............................................. 4
1.3 The Nearly-Free Electron Model of Electronic
Conduction and Band Structure .......................... 13
1.4 Effective Mass ......................................... 21
1.5 The Origins of Electrical Resistance ................... 24
1.6 Size Effects on Electrical Resistance .................. 31
1.7 Overview of Transistors ................................ 32
1.8 Surface Effects ........................................ 36
2 Quantum Current Flow ........................................ 41
2.1 Why Shrink Devices? .................................... 44
2.2 Point Contacts: From Mesoscopic to Atomic .............. 46
2.3 Conductance from Transmission .......................... 48
2.4 Calculation of Transmission Probability and Current
Flow in Quantum Systems ................................ 55
2.4.1 Introduction to the concept of transmission
probability ..................................... 55
2.4.2 Single potential step ........................... 57
2.4.3 Single potential barrier ........................ 61
2.4.3.1 Symmetric barrier: No applied voltage .. 61
2.4.3.2 Asymmetric barrier: Current flow due
to applied bias ........................ 66
2.4.4 Double potential barrier ........................ 69
2.4.4.1 Symmetric barriers: No applied
voltage ................................ 69
2.4.4.2 Tunnelling through multiple barriers
with no phase coherence ................ 74
2.4.4.3 Asymmetric barriers: Applied voltage ... 78
2.4.4.4 Resonant tunnelling devices: Further
details ................................ 82
2.4.5 A more realistic calculation for a single
potential barrier: The WKB approximation ........ 85
2.5 Techniques for the Fabrication of Quantum
Nanostructures ......................................... 92
3 Mesoscopic Transport: Between the Nanoscale and the
Macroscale .................................................. 99
3.1 Introduction ........................................... 99
3.2 Boltzmann Transport Equation .......................... 100
3.3 Resistivity of Thin Films and Wires: Surface
Scattering ............................................ 100
3.3.1 General principles ............................. 100
3.3.2 ID confinement: Thin film ...................... 103
3.3.3 2D confinement: Rectangular wire ............... 105
3.3.4 2D confinement: Cylindrical wires .............. 106
3.4 Resistivity of Thin Films and Wires: Grain-Boundary
Scattering ............................................ 107
3.5 Experimental Aspects: How to Measure the Resistance
of a Thin Film ........................................ 113
4 Scanning-Probe Multimeters ................................. 119
4.1 Scanning-Probe Microscopy: An Introduction ............ 119
4.2 Scanning Tunnelling Microscopy ........................ 121
4.2.1 Basic principles ............................... 121
4.2.2 Scanning tunnelling microscopy in practise ..... 126
4.3 Atomic Force Microscopy ............................... 134
4.3.1 Modes of operation of AFM ...................... 135
4.3.2 Kelvin-probe force microscopy .................. 140
4.3.3 Conducting mode AFM ............................ 143
5 Electromigration: How Currents Move Atoms, and
Implications for Nanoelectronics ........................... 155
5.1 Introduction to Electromigration, Wire Morphology ..... 155
5.2 Fundamentals of Electromigration — The Electron Wind .. 156
5.3 Electromigration-Induced Stress in a Nanowire Device .. 158
5.4 Current-Induced Heating in a Nanowire Device .......... 160
5.5 Diffusion of Material, Importance of Surfaces,
Failure of Wires ...................................... 167
5.6 Experimental Observations of Electromigration and
Heating in Nanowires .................................. 169
5.6.1 Failure as a function of wire length ........... 170
5.6.2 Failure as a function of wire width ............ 170
5.7 Experimental Observations of Electromigration in
Micron-Scale Wires .................................... 173
5.8 Wire Heating - Additional Considerations .............. 174
5.9 Consequences for Nanoelectronics ...................... 181
6 Elements of Single-Electron and Molecular Electronics ...... 185
6.1 Single-Electron Transport and Coulomb Blockade ........ 185
6.2 Molecular Electronics: Why Bother? .................... 188
6.3 Mechanisms of Electron Transport Through Molecules .... 190
6.4 Visualising Transport Through Molecules ............... 192
6.5 The Contact Resistance Problem ........................ 193
6.6 Contacting Molecules .................................. 194
6.1 Nanogaps formed by electron-beam lithography .......... 195
6.6.2 Nanogaps formed by electromigration ............ 195
6.6.3 Mechanically-controlled break junctions ........ 198
6.6.4 Molecular sandwiches ........................... 200
6.6.5 STM probing of molecules ....................... 201
6.7 The Future ............................................ 202
Solutions to Problems in Chapter 2 ............................ 207
Index ......................................................... 209
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