Fundamentals of Nanoelectronics

PREFACE xi

ACKNOWLEDGMENTS xiii

PHOTO CREDITS xv

 

PART I FUNDAMENTALS OF NANOSCOPIC PHYSICS 1

 

1 INTRODUCTION TO NANOELECTRONICS 3

1.1 The “Top-Down” Approach 61.1.1 Lithography, 8

1.2 The “Bottom-Up” Approach 12

1.3 Why Nanoelectronics? 12

1.4 Nanotechnology Potential 14

1.5 Main Points 15

1.6 Problems 16

 

2 CLASSICAL PARTICLES, CLASSICALWAVES, AND QUANTUM PARTICLES 17

2.1 Comparison of Classical and Quantum Systems 18

2.2 Origins of Quantum Mechanics 20

2.3 Light As a Wave, Light As a Particle 212.3.1 Light As a Particle, or Perhaps a Wave — The Early Years, 21

2.3.2 A Little Later — Light as a Wave, 21

2.3.3 Finally, Light As a Quantum Particle, 26

2.4 Electrons As Particles, Electrons As Waves 292.4.1 Electrons As Particles — The Early Years, 29

2.4.2 A Little Later — Electrons (and Everything Else) As Quantum Particles, 29

2.4.3 Further Development of Quantum Mechanics, 32

2.5 Wavepackets and Uncertainty 34

2.6 Main Points 41

2.7 Problems 42

 

3 QUANTUM MECHANICS OF ELECTRONS 44

3.1 General Postulates of Quantum Mechanics 463.1.1 Operators, 48

3.1.2 Eigenvalues and Eigenfunctions, 49

3.1.3 Hermitian Operators, 50

3.1.4 Operators for Quantum Mechanics, 53

3.1.5 Measurement Probability, 57

3.2 Time-Independent Schr¨odinger’s Equation 633.2.1 Boundary Conditions on the Wavefunction, 66

3.3 Analogies Between Quantum Mechanics and Classical Electromagnetics 71

3.4 Probabilistic Current Density 72

3.5 Multiple Particle Systems 76

3.6 Spin and Angular Momentum 80

3.7 Main Points 82

3.8 Problems 83

4 FREE AND CONFINED ELECTRONS 87

4.1 Free Electrons 874.1.1 One-Dimensional Space, 88

4.1.2 Three-Dimensional Space, 91

4.2 The Free Electron Gas Theory of Metals 92

4.3 Electrons Confined to a Bounded Region of Space, and Quantum Numbers 934.3.1 One-Dimensional Space, 93

4.3.2 Three-Dimensional Space, 99

4.3.3 Periodic Boundary Conditions, 100

4.4 Fermi Level and Chemical Potential 101

4.5 Partially Confined Electrons — Finite Potential Wells 1034.5.1 Finite Rectangular Well, 104

4.5.2 Parabolic Well — Harmonic Oscillator, 111

4.5.3 Triangular Well, 112

4.6 Electrons Confined to Atoms — The Hydrogen Atom and the Periodic Table 4.6 1134.6.1 The Hydrogen Atom and Quantum Numbers, 114

4.6.2 Beyond Hydrogen — Multiple Electron Atoms and the Periodic Table , 118

4.7 Quantum Dots, Wires, and Wells 1204.7.1 Quantum Wells, 124

4.7.2 Quantum Wires, 126

4.7.3 Quantum Dots, 128

4.8 Main Points 130

4.9 Problems 130

 

5 ELECTRONS SUBJECT TO A PERIODIC POTENTIAL — BAND THEORY OF SOLIDS 134

5.1 Crystalline Materials 135

5.2 Electrons in a Periodic Potential 139

5.3 Kronig—Penney Model of Band Structure 1405.3.1 Effective Mass, 144

5.4 Band Theory of Solids 1535.4.1 Doping in Semiconductors, 157

5.4.2 Interacting Systems Model, 160

5.4.3 The Effect of an Electric Field on Energy Bands, 163

5.4.4 Bandstructures of Some Semiconductors, 163

5.4.5 Electronic Band Transitions — Interaction of Electromagnetic Energy and Materials, 165

5.5 Graphene and Carbon Nanotubes 1735.5.1 Graphene, 173

5.5.2 Carbon Nanotubes, 175

5.6 Main Points 180

5.7 Problems 180

 

PART II SINGLE-ELECTRON AND FEW-ELECTRON PHENOMENA AND DEVICES 185

 

6 TUNNEL JUNCTIONS AND APPLICATIONS OF TUNNELING 187

6.1 Tunneling Through a Potential Barrier 188

6.2 Potential Energy Profiles for Material Interfaces 1946.2.1 Metal—Insulator, Metal-Semiconductor, and Metal—Insulator—Metal Junctions, 194

6.3 Applications of Tunneling 1996.3.1 Field Emission, 199

6.3.2 Gate—Oxide Tunneling and Hot Electron Effects in MOSFETs, 202

6.3.3 Scanning Tunneling Microscope, 206

6.3.4 Double Barrier Tunneling and the Resonant Tunneling Diode, 210

6.4 Main Points 214

6.5 Problems 214

 

7 COULOMB BLOCKADE AND THE SINGLE-ELECTRON TRANSISTOR 216

7.1 Coulomb Blockade 2167.1.1 Coulomb Blockade in a Nanocapacitor, 218

7.1.2 Tunnel Junctions, 223

7.1.3 Tunnel Junction Excited by a Current Source, 226

7.1.4 Coulomb Blockade in a Quantum Dot Circuit, 230

7.2 The Single-Electron Transistor 2407.2.1 Single-Electron Transistor Logic, 248

7.3 Other SET and FET Structures 2507.3.1 Carbon Nanotube Transistors (FETs and SETs), 250

7.3.2 Semiconductor Nanowire FETs and SETs, 255

7.3.3 Molecular SETs and Molecular Electronics, 257

7.4 Main Points 261

7.5 Problems 262

 

PART III MANY ELECTRON PHENOMENA 265

 

8 PARTICLE STATISTICS AND DENSITY OF STATES 267

8.1 Density of States 2688.1.1 Density of States in Lower Dimensions, 270

8.1.2 Density of States in a Semiconductor, 273

8.2 Classical and Quantum Statistics 273

8.2.1 Carrier Concentration in Materials, 276

8.2.2 The Importance of the Fermi Electrons, 280

8.2.3 Equilibrium Carrier Concentration and the Fermi Level in Semiconductors, 280

8.3 Main Points 283

8.4 Problems 283

9 MODELS OF SEMICONDUCTOR QUANTUM WELLS, QUANTUM WIRES, AND QUANTUM DOTS 286

9.1 Semiconductor Heterostructures and Quantum Wells 2889.1.1 Confinement Models and Two-Dimensional Electron Gas, 292

9.1.2 Energy Band Transitions in Quantum Wells, 295

9.2 Quantum Wires and Nanowires 301

9.3 Quantum Dots and Nanoparticles 3059.3.1 Applications of Semiconducting Quantum Dots, 306

9.3.2 Plasmon Resonance and Metallic Nanoparticles, 312

9.3.3 Functionalized Metallic Nanoparticles, 313

9.4 Fabrication Techniques for Nanostructures 3159.4.1 Lithography, 315

9.4.2 Nanoimprint Lithography, 317

9.4.3 Split-Gate Technology, 318

9.4.4 Self-Assembly, 318

9.5 Main Points 322

9.6 Problems 322

 

10 NANOWIRES, BALLISTIC TRANSPORT, AND SPIN TRANSPORT 326

    10.1 Classical and Semiclassical Transport 32710.1.1 Classical Theory of Conduction—Free Electron Gas Model, 327

    10.1.2 Semiclassical Theory of Electrical Conduction — Fermi Gas Model , 330

    10.1.3 Classical Resistance and Conductance, 333

    10.1.4 Conductivity of Metallic Nanowires — The Influence of Wire Radius, 335

    10.2 Ballistic Transport 33710.2.1 Electron Collisions and Length Scales, 338

    10.2.2 Ballistic Transport Model, 340

    10.2.3 Quantum Resistance and Conductance, 341

    10.2.4 Origin of the Quantum Resistance, 348

    10.3 Carbon Nanotubes and Nanowires 34910.3.1 The Effect of Nanoscale Wire Radius on Wave Velocity and Loss , 353

    10.4 Transport of Spin and Spintronics 35610.4.1 The Transport of Spin, 356

    10.4.2 Spintronic Devices and Applications, 361

    10.5 Main Points 362

    10.6 Problems 362

APPENDIX A SYMBOLS AND ACRONYMS 365

APPENDIX B PHYSICAL PROPERTIES OF MATERIALS 367

APPENDIX C CONVENTIONAL MOSFETS 372

APPENDIX D ANSWERS TO PROBLEMS 376

Problems Chapter 2: Classical Particles, Classical Waves, and Quantum Particles, 376

Problems Chapter 3: Quantum Mechanics of Electrons, 377

Problems Chapter 4: Free and Confined Electrons, 378

Problems Chapter 5: Electrons Subject to a Periodic Potential — Band Theory of Solids, 379

Problems Chapter 6: Tunnel Junctions and Applications of Tunneling, 380

Problems Chapter 7: Coulomb Blockade and the Single-Electron Transistor, 381

Problems Chapter 8: Particle Statistics and Density of States, 381

Problems Chapter 9: Models of Semiconductor Quantum Wells, Quantum Wires,

and Quantum Dots, 382

Problems Chapter 10: Nanowires, Ballistic Transport, and Spin Transport, 383

BIBLIOGRAPHY 383

INDEX 393