Introduction to Nanomaterials and Devices

Omar Manasreh , PhD, is a Full Professor of Electrical Engineering at the University of Arkansas. Dr. Manasreh has received several awards, including a Science and Technology Achievement Award presented by the Air Force Materiel Command at Wright-Patterson Air Force Base and the Aubrey E. Harvey Graduate Research Award presented by the University of Arkansas chapter of Sigma Xi. He has published more than 130 papers in technical journals, presented over fifty papers at national and international meetings, and has participated in over sixty invited talks. Dr. Manasreh is a member of the IEEE, American Physical Society, and the Materials Research Society.

Preface xiii Fundamental Constants xvii 1 Growth of Bulk, Thin Films, and Nanomaterials 1 1.1 Introduction, 1 1.2 Growth of Bulk Semiconductors, 5 1.2.1 Liquid-Encapsulated Czochralski (LEC) Method, 5 1.2.2 Horizontal Bridgman Method, 11 1.2.3 Float-Zone Growth Method, 14 1.2.4 Lely Growth Method, 16 1.3 Growth of Semiconductor Thin Films, 18 1.3.1 Liquid-Phase Epitaxy Method, 19 1.3.2 Vapor-Phase Epitaxy Method, 20 1.3.3 Hydride Vapor-Phase Epitaxial Growth of Thick GaN Layers, 22 1.3.4 Pulsed Laser Deposition Technique, 25 1.3.5 Molecular Beam Epitaxy Growth Technique, 27 1.4 Fabrication and Growth of Semiconductor Nanomaterials, 46 1.4.1 Nucleation, 47 1.4.2 Fabrications of Quantum Dots, 55 1.4.3 Epitaxial Growth of Self-Assembly Quantum Dots, 56 1.5 Colloidal Growth of Nanocrystals, 61 1.6 Summary, 63 Problems, 64 Bibliography, 67 2 Application of Quantum Mechanics to Nanomaterial Structures 68 2.1 Introduction, 68 2.2 The de Broglie Relation, 71 2.3 Wave Functions and Schr..odinger Equation, 72 2.4 Dirac Notation, 74 2.4.1 Action of a Linear Operator on a Bra , 77 2.4.2 Eigenvalues and Eigenfunctions of an Operator, 78 2.4.3 The Dirac delta -Function, 78 2.4.4 Fourier Series and Fourier Transform in Quantum Mechanics, 81 2.5 Variational Method, 82 2.6 Stationary States of a Particle in a Potential Step, 83 2.7 Potential Barrier with a Finite Height, 88 2.8 Potential Well with an Infinite Depth, 92 2.9 Finite Depth Potential Well, 94 2.10 Unbound Motion of a Particle (E > V 0 ) in a Potential Well With a Finite Depth, 98 2.11 Triangular Potential Well, 100 2.12 Delta Function Potentials, 103 2.13 Transmission in Finite Double Barrier Potential Wells, 108 2.14 Envelope Function Approximation, 112 2.15 Periodic Potential, 117 2.15.1 Bloch's Theorem, 119 2.15.2 The Kronig-Penney Model, 119 2.15.3 One-Electron Approximation in a Periodic Dirac delta -Function, 123 2.15.4 Superlattices, 126 2.16 Effective Mass, 130 2.17 Summary, 131 Problems, 132 Bibliography, 134 3 Density of States in Semiconductor Materials 135 3.1 Introduction, 135 3.2 Distribution Functions, 138 3.3 Maxwell-Boltzmann Statistic, 139 3.4 Fermi-Dirac Statistics, 142 3.5 Bose-Einstein Statistics, 145 3.6 Density of States, 146 3.7 Density of States of Quantum Wells, Wires, and Dots, 152 3.7.1 Quantum Wells, 152 3.7.2 Quantum Wires, 155 3.7.3 Quantum Dots, 158 3.8 Density of States of Other Systems, 159 3.8.1 Superlattices, 160 3.8.2 Density of States of Bulk Electrons in the Presence of a Magnetic Field, 161 3.8.3 Density of States in the Presence of an Electric Field, 163 3.9 Summary, 168 Problems, 168 Bibliography, 170 4 Optical Properties 171 4.1 Fundamentals, 172 4.2 Lorentz and Drude Models, 176 4.3 The Optical Absorption Coefficient of the Interband Transition in Direct Band Gap Semiconductors, 179 4.4 The Optical Absorption Coefficient of the Interband Transition in Indirect Band Gap Semiconductors, 185 4.5 The Optical Absorption Coefficient of the Interband Transition in Quantum Wells, 186 4.6 The Optical Absorption Coefficient of the Interband Transition in Type II Superlattices, 189 4.7 The Optical Absorption Coefficient of the Intersubband Transition in Multiple Quantum Wells, 191 4.8 The Optical Absorption Coefficient of the Intersubband Transition in GaN/AlGaN Multiple Quantum Wells, 196 4.9 Electronic Transitions in Multiple Quantum Dots, 197 4.10 Selection Rules, 201 4.10.1 Electron-Photon Coupling of Intersubband Transitions in Multiple Quantum Wells, 201 4.10.2 Intersubband Transition in Multiple Quantum Wells, 202 4.10.3 Interband Transition, 202 4.11 Excitons, 204 4.11.1 Excitons in Bulk Semiconductors, 205 4.11.2 Excitons in Quantum Wells, 211 4.11.3 Excitons in Quantum Dots, 213 4.12 Cyclotron Resonance, 214 4.13 Photoluminescence, 220 4.14 Basic Concepts of Photoconductivity, 225 4.15 Summary, 229 Problems, 230 Bibliography, 232 5 Electrical and Transport Properties 233 5.1 Introduction, 233 5.2 The Hall Effect, 237 5.3 Quantum Hall and Shubnikov-de Haas Effects, 241 5.3.1 Shubnikov-de Haas Effect, 243 5.3.2 Quantum Hall Effect, 246 5.4 Charge Carrier Transport in Bulk Semiconductors, 249 5.4.1 Drift Current Density, 249 5.4.2 Diffusion Current Density, 254 5.4.3 Generation and Recombination, 257 5.4.4 Continuity Equation, 259 5.5 Boltzmann Transport Equation, 264 5.6 Derivation of Transport Coefficients Using the Boltzmann Transport Equation, 268 5.6.1 Electrical Conductivity and Mobility in n-type Semiconductors, 270 5.6.2 Hall Coefficient, R H, 273 5.7 Scattering Mechanisms in Bulk Semiconductors, 274 5.7.1 Scattering from an Ionized Impurity, 276 5.7.2 Scattering from a Neutral Impurity, 277 5.7.3 Scattering from Acoustic Phonons: Deformation Potential, 277 5.7.4 Scattering from Acoustic Phonons: Piezoelectric Potential, 278 5.7.5 Optical Phonon Scattering: Polar and Nonpolar, 278 5.7.6 Scattering from Short-Range Potentials, 279 5.7.7 Scattering from Dipoles, 281 5.8 Scattering in a Two-Dimensional Electron Gas, 281 5.8.1 Scattering by Remote Ionized Impurities, 283 5.8.2 Scattering by Interface Roughness, 285 5.8.3 Electron-Electron Scattering, 286 5.9 Coherence and Mesoscopic Systems, 287 5.10 Summary, 293 Problems, 294 Bibliography, 297 6 Electronic Devices 298 6.1 Introduction, 298 6.2 Schottky Diode, 301 6.3 Metal-Semiconductor Field-Effect Transistors (MESFETs), 305 6.4 Junction Field-Effect Transistor (JFET), 314 6.5 Heterojunction Field-Effect Transistors (HFETs), 318 6.6 GaN/AlGaN Heterojunction Field-Effect Transistors (HFETs), 322 6.7 Heterojunction Bipolar Transistors (HBTs), 325 6.8 Tunneling Electron Transistors, 328 6.9 The p-n Junction Tunneling Diode, 329 6.10 Resonant Tunneling Diodes, 334 6.11 Coulomb Blockade, 338 6.12 Single-Electron Transistor, 340 6.13 Summary, 353 Problems, 354 Bibliography, 357 7 Optoelectronic Devices 359 7.1 Introduction, 359 7.2 Infrared Quantum Detectors, 361 7.2.1 Figures of Merit, 361 7.2.2 Noise in Photodetectors, 366 7.2.3 Multiple Quantum Well Infrared Photodetectors (QWIPs), 369 7.2.4 Infrared Photodetectors Based on Multiple Quantum Dots, 380 7.3 Light-Emitting Diodes, 387 7.4 Semiconductor Lasers, 392 7.4.1 Basic Principles, 392 7.4.2 Semiconductor Heterojunction Lasers, 399 7.4.3 Quantum Well Edge-Emitting Lasers, 403 7.4.4 Vertical Cavity Surface-Emitting Lasers, 406 7.4.5 Quantum Cascade Lasers, 409 7.4.6 Quantum Dots Lasers, 412 7.5 Summary, 416 Problems, 418 Bibliography, 419 Appendix A Derivation of Heisenberg Uncertainty Principle 420 Appendix B Perturbation 424 Bibliography, 428 Appendix C Angular Momentum 429 Appendix D Wentzel-Kramers-Brillouin (WKB) Approximation 431 Bibliography, 436 Appendix E Parabolic Potential Well 437 Bibliography, 441 Appendix F Transmission Coefficient in Superlattices 442 Appendix G Lattice Vibrations and Phonons 445 Bibliography, 455 Appendix H Tunneling Through Potential Barriers 456 Bibliography, 461 Index 463