Introductory Quantum Mechanics for Applied Nanotechnology

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.

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

About the Author :
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.