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Introductory Quantum Mechanics for Applied Nanotechnology

ISBN: 978-3-527-41245-7
392 pages
May 2015
Introductory Quantum Mechanics for Applied Nanotechnology (352741245X) cover image

Description

This introductory textbook covers fundamental quantum mechanics from an application perspective, considering optoelectronic devices, biological sensors and molecular imagers as well as solar cells and field effect transistors.

The book provides a brief review of classical and statistical mechanics and electromagnetism, and then turns to the quantum treatment of atoms, molecules, and chemical bonds.
Aiming at senior undergraduate and graduate students in nanotechnology related areas like physics, materials science, and engineering, the book could be used at schools that offer interdisciplinary but focused training for future workers in the semiconductor industry and for the increasing number of related nanotechnology firms, and even practicing people could use it when they need to learn related concepts.

The author is Professor Dae Mann Kim from the Korea Institute for Advanced Study who has been teaching Quantum Mechanics to engineering, material science and physics students for over 25 years in USA and Asia.
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Table of Contents

Preface XI

1 Review of Classical Theories 1

1.1 Harmonic Oscillator 1

1.2 Boltzmann Distribution Function 3

1.3 Maxwell’s Equations and EMWaves 6

Suggested Readings 11

2 Milestones Leading to Quantum Mechanics 13

2.1 Blackbody Radiation and Quantum of Energy 13

2.2 Photoelectric Effect and Photon 14

2.3 Compton Scattering 16

2.4 de BroglieWavelength and Duality of Matter 17

2.5 Hydrogen Atom and Spectroscopy 18

Suggested Readings 22

3 SchrödingerWave Equation 23

3.1 Operator Algebra and Basic Postulates 23

3.2 Eigenequation, Eigenfuntion and Eigenvalue 24

3.3 Properties of Eigenfunctions 25

3.4 Commutation Relation and Conjugate Variables 27

3.5 Uncertainty Relation 29

Suggested Readings 31

4 Bound States in QuantumWell and Wire 33

4.1 Electrons in Solids 33

4.2 1D, 2D, and 3D Densities of States 35

4.3 Particle in QuantumWell 38

4.4 QuantumWell andWire 40

Suggested Readings 43

5 Scattering and Tunneling of 1D Particle 45

5.1 Scattering at the Step Potential 45

5.2 Scattering from a QuantumWell 48

5.3 Tunneling 50

5.3.1 Direct and Fowler–Nordheim Tunneling 52

5.3.2 Resonant Tunneling 53

5.4 The Applications of Tunneling 56

5.4.1 Metrology and Display 57

5.4.2 Single-Electron Transistor 58

Suggested Readings 61

6 Energy Bands in Solids 63

6.1 BlochWavefunction in Kronig–Penney Potential 63

6.2 E–k Dispersion and Energy Bands 67

6.3 The Motion of Electrons in Energy Bands 70

6.4 Energy Bands and Resonant Tunneling 71

Suggested Readings 74

7 The Quantum Treatment of Harmonic Oscillator 75

7.1 Energy Eigenfunction and Energy Quantization 75

7.2 The Properties of Eigenfunctions 78

7.3 HO in Linearly Superposed State 81

7.4 The Operator Treatment of HO 83

7.4.1 Creation and Annihilation Operators and Phonons 84

Suggested Readings 86

8 Schrödinger Treatment of Hydrogen Atom 87

8.1 Angular Momentum Operators 87

8.2 Spherical Harmonics and Spatial Quantization 90

8.3 The H-Atom and Electron–Proton Interaction 93

8.3.1 Atomic Radius and the Energy Eigenfunction 97

8.3.2 Eigenfunction and Atomic Orbital 98

8.3.3 Doppler Shift 100

Suggested Readings 104

9 The Perturbation Theory 105

9.1 Time-Independent Perturbation Theory 105

9.1.1 Stark Effect in H-Atom 110

9.2 Time-Dependent Perturbation Theory 111

9.2.1 Fermi’s Golden Rule 113

Suggested Readings 116

10 System of Identical Particles and Electron Spin 117

10.1 Electron Spin 117

10.1.1 Pauli Spin Matrices 118

10.2 Two-Electron System 118

10.2.1 Helium Atom 120

10.2.2 Multi-Electron Atoms and Periodic Table 124

10.3 Interaction of Electron Spin with Magnetic Field 126

10.3.1 Spin–Orbit Coupling and Fine Structure 127

10.3.2 Zeeman Effect 129

10.4 Electron Paramagnetic Resonance 131

Suggested Readings 135

11 Molecules and Chemical Bonds 137

11.1 Ionized Hydrogen Molecule 137

11.2 H2 Molecule and Heitler-LondonTheory 141

11.3 Ionic Bond 144

11.4 van derWaals Attraction 146

11.5 Polyatomic Molecules and Hybridized Orbitals 148

Suggested Readings 150

12 Molecular Spectra 151

12.1 Theoretical Background 151

12.2 Rotational and Vibrational Spectra of Diatomic Molecule 154

12.3 Nuclear Spin and Hyperfine Interaction 158

12.4 Nuclear Magnetic Resonance (NMR) 161

12.4.1 Molecular Imaging 163

Suggested Readings 165

13 Atom–Field Interaction 167

13.1 Atom–Field Interaction: Semiclassical Treatment 167

13.2 Driven Two-Level Atom and Atom Dipole 169

13.3 Atom–Field Interaction: Quantum Treatment 171

13.3.1 Field Quantization 171

Suggested Readings 177

14 The Interaction of EMWaves with an Optical Media 179

14.1 Attenuation, Amplification, and Dispersion ofWaves 179

14.2 Atomic Susceptibility 181

14.3 Laser Device 185

14.3.1 Population Inversion 186

Suggested Readings 189

15 Semiconductor Statistics 191

15.1 Quantum Statistics 191

15.1.1 Bosons and Fermions 192

15.2 Carrier Concentration in Intrinsic Semiconductor 194

15.3 Carrier Densities in Extrinsic Semiconductors 197

15.3.1 Fermi Level in Extrinsic Semiconductors 199

Suggested Readings 201

16 Carrier Transport in Semiconductors 203

16.1 Quantum Description of Transport Coefficients 203

16.1.1 Mobility 204

16.1.2 Diffusion Coefficient 205

16.2 Equilibrium and Nonequilibrium 206

16.2.1 Nonequilibrium and Quasi-Fermi Level 208

16.3 Generation and Recombination Currents 209

16.3.1 Trap-Assisted Recombination and Generation 210

Suggested Readings 215

17 P–N Junction Diode: I–V Behavior and Device Physics 217

17.1 The p–n Junction in Equilibrium 217

17.2 The p–n Junction under Bias 220

17.3 Ideal Diode I–V Behavior 223

17.4 Nonideal I–V Behavior 226

Suggested Readings 229

18 P–N Junction Diode: Applications 231

18.1 Optical Absorption 231

18.2 Photodiode 233

18.3 Solar Cell 235

18.4 LED and LD 238

Suggested Readings 243

19 Field-Effect Transistors 245

19.1 The Modeling of MOSFET I–V 245

19.1.1 Channel Inversion in NMOS 246

19.1.2 Threshold Voltage and ON Current 250

19.1.3 Subthreshold Current ISUB 251

19.2 Silicon Nanowire Field-Effect Transistor 252

19.2.1 Short-Channel I–V Behavior in NWFET 256

19.2.2 Ballistic NWFET 257

19.3 Tunneling NWFET as Low-Power Device 259

Suggested Readings 262

20 The Application and Novel Kinds of FETs 263

20.1 Nonvolatile Flash EEPROM Cell 263

20.2 Semiconductor Solar Cells 266

20.3 Biosensor 268

20.4 Spin Field-Effect Transistor 271

20.5 Spin Qubits and Quantum Computing 273

Suggested Readings 278

Solutions 279

Index 369

Important Physical Numbers and Quantities 377

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Author Information

Dae Mann Kim is Professor of Computational Sciences, Korea Institute for Advanced Study. A physicist by training (PhD in physics, Yale University) but an engineer by profession, Kim started his teaching career at Rice University before moving to Oregon Graduate Institute of Science and Technology and later to POSTECH (S. Korea). He has over 25 years experience teaching quantum mechanics to senior students from engineering, materials science and physics departments. Collaborating extensively with industrial labs over the years, Kim offered short courses to working engineers at Samsung and LG.
Professor Kim has served as the chair of the curriculum committee of the Korean Nano Technology Research Society. Kim has over 100 publications on the quantum theory of lasers, quantum electronics and micro and nano electronics. He is a Fellow of the Korean Academy of Science and Technology and has also served as Associate Editor of IEEE Transactions on Circuits and Systems Video Technology.
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