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Fundamentals of Solid State Engineering

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Solid state Engineering is a multi-disciplinary field that combines disciplines such as physics, chemistry, electrical engineering, materials science and mechanical engineering. It provides the means to understand matter and to design and control its properties.
The 20th century has witnessed the phenomenal rise of natural science and technology into all aspects of human life. Three major sciences have emerged and marked this century. Physical science which has strived to understand the structure of atoms through quantum mechanics, Life Sciences which has attempted to understand the structure of cells and the mechanisms of life through biology and genetics, and Information Sciences which has symbiotically developed the communicative and computational means to advanced natural science.
Microelectronics has become one of today's principle enabling technologies supporting these three major sciences and touches every aspect of human life: food, energy, transportation, communication, entertainment, health/medicine and exploration. For example, microelectronic devices have now become building blocks of systems which are used to monitor food s energy more efficiently (LED), control electrical vehicles (automobiles), transmit information (optical fiber and wireless communications), entertain (virtual reality, video games, computers), help cure or enhance the human body (artificial senses, optically activated medicine) and support the exploration of new realms (space, underwater).
A different approach has been envisioned for future advances in semiconductor science and technology in the 21st century. This will consist of reaching closer to the structure of atoms by employing nanoscale electronics. Indeed, the history of microelectronics has been, itself, characterized by a constant drive to imitate natural objects (e.g. the brain cell) and thus move towards lower dimensions in order to increase integration density, system functionality and performance (e.g. speed and power consumption).
Fundamentals of Solid State Engineering is structured in two major parts. It first addresses the basic physics concepts, which are at the base of solid state matter in general and semiconductors in particular. The second part reviews the technology for modern Solid State Engineering. This includes a review of compound semiconductor bulk and epitaxial thin films growth techniques, followed by a description of current semiconductor device processing and nano-fabrication technologies. A few examples of semiconductor devices and a description of their theory of operational are then discussed, including transistors, semiconductor lasers, and photodetectors.

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List of Symbols
Foreword
Preface
1.
Contents
Crystalline Properties of Solids 1.1.Introduction 1.2. Crystal lattices and the seven crystal systems 1.3.The unit cell concept 1.4.Bravais lattices 1.5.Point groups 1.5.1. group (plane reflection) 1.5.2. groups (rotation) 1.5.3. and groups 1.5.4. groups 1.5.5. and groups 1.5.6.group 1.5.7. and groups 1.5.8. T group 1.5.9. group 1.5.10.O group 1.5.11.group 1.5.12. List of crystallographic point groups 1.6. Space groups 1.7. Directions and planes in crystals: Miller indices 1.8.Real crystal structures 1.8.1. Diamond structure 1.8.2. Zinc blende structure 1.8.3.Sodium chloride structure 1.8.4. Cesium chloride structure 1.8.5. Hexagonal closepacked structure 1.8.6.Wurtzite structure 1.8.7. Packing factor
xv
xix
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1 2 5 8 11 13 13 14 15 16 17 18 18 19 20 21 21 21 23 23 28 28 30 31 31 32 34 35
vi
2.
3.
4.
1.9.Summary Further reading Problems
Fundamentals of Solid State Engineering
Electronic Structure of Atoms 2.1.Introduction 2.2. Spectroscopic emission lines and atomic structure of hydrogen 2.3. Atomic orbitals 2.4. Structures of atoms with many electrons 2.5. Bonds in solids 2.5.1. General principles 2.5.2. Ionic bonds 2.5.3.Covalent bonds 2.5.4.Mixed bonds 2.5.5.Metallic bonds 2.5.6. Secondary bonds 2.6. Introduction to energy bands 2.7.Summary Further reading Problems
37 37 39
41 41
42 48 50 54 54 56 58 60 61 61 64 66 67 68
Introduction to Quantum Mechanics71 3.1.The quantum concepts71 3.1.1. Blackbody radiation72 3.1.2. The photoelectric effect74 3.1.3. Waveparticle duality77 3.1.4. The DavissonGermer experiment77 3.2. Elements of quantum mechanics79 3.2.1. Basic formalism79 3.2.2.General properties of wavefunctions and the Schrödinger equation82 3.3. Simple quantum mechanical systems82 3.3.1. Free particle82 3.3.2.Particle in a 1D box84 3.3.3.Particle in a finite potential well87 3.4. Reciprocal lattice93 3.5.Summary96 Further reading96 Problems97
Electrons and Energy Band Structures in Crystals 4.1.Introduction 4.2.Electrons in a crystal
99 99 100
Contents
5.
6.
4.2.1. Bloch theorem 4.2.2. Onedimensional KronigPenney model 4.2.3. Energy bands 4.2.4. Nearlyfree electron approximation 4.2.5.Tight binding approximation 4.2.6.Heisenberg uncertainty principle 4.2.7. Dynamics of electrons in a crystal 4.2.8. Fermi energy 4.2.9.Electron distribution function 4.2.10.Electrons and holes 4.3. Band structures in real semiconductors 4.3.1. First Brillouin zone of an fcc lattice 4.3.2. First Brillouin zone of a bcc lattice 4.3.3.First Brillouin zones of a few semiconductors 4.4. Band structures in metals 4.5.Summary References Further reading Problems
Low Dimensional Quantum Structures 5.1.Introduction 5.2. Density of states (3D) 5.2.1. Direct calculation 5.2.2. Other approach 5.3. Twodimensional structures: quantum wells 5.3.1. Energy spectrum 5.3.2.Density of states 5.3.3.Effect of effective mass 5.4. Onedimensional structures: quantum wires 5.5. Zerodimensional structures: quantum dots 5.6. Optical properties of 3D and 2D structures 5.6.1.Absorption coefficient 5.6.2. Excitonic effects 5.7. Examples of low dimensional structures 5.7.1. Quantum wires 5.7.2. Quantum dots 5.8.Summary References Further reading Problems
Phonons 6.1. Introduction
vii 100 102 106 109 111 113 115 118 119 122 124 125 127 128 130 132 133 133 134
135 135 136 136 141 143 143 148 152 152 155 157 157 158 161 163 167 167 168 168 169
171 171
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7.
8.
Fundamentals of Solid State Engineering
6.2.atoms in crystals: origin and formalismInteraction of 6.3.Onedimensional monoatomic harmonic crystal 6.3.1. Traveling wave formalism 6.3.2.Boundary conditions 6.3.3.Phonon dispersion relation 6.4.Sound velocity 6.5.Onedimensional diatomic harmonic crystal 6.5.1.Formalism 6.5.2. Phonon dispersion relation 6.5.3. Extension to threedimensional case 6.6.Phonons 6.7.Summary Further reading Problems
171 174 174 176 177 179 182 182 183 189 191 193 194 195
Thermal Properties of Crystals197 7.1.Introduction197 7.2.Phonon density of states (Debye model)197 7.2.1. Debye model197 7.2.2. Phonon density of states200 7.3.Heat capacity203 7.3.1. Lattice contribution to the heat capacity (Debye model) 203 7.3.2. Electronic contribution to the heat capacity210 7.4.Thermal expansion213 7.5.Thermal conductivity215 7.6.Summary219 References219 Further reading219 Problems220
Equilibrium Charge Carrier Statistics in Semiconductors 8.1.Introduction 8.2.Density of states 8.3.states (conduction band)Effective density of 8.4.Effective density of states (valence band) 8.5.Mass action law 8.6.Doping: intrinsic vs. extrinsic semiconductor 8.7.Charge neutrality 8.8.Fermi energy as a function of temperature 8.9.Carrier concentration in a semiconductor 8.10.Summary Further reading Problems
221 221 222 225 228 231 233 237 238 242 246 246 247
Contents 9.
10.
NonEquilibrium Electrical Properties of Semiconductors 9.1. Introduction 9.2. Electrical conductivity 9.2.1. Ohm’s law in solids 9.2.2.Case of semiconductors 9.3. Hall effect 9.3.1.Ptype semiconductor 9.3.2.Ntype semiconductor 9.3.3.Compensated semiconductor 9.4. Charge carrier diffusion 9.4.1.Diffusion currents 9.4.2.Einstein relations 9.4.3.Diffusion lengths 9.5. QuasiFermi energy 9.6. Carrier generation and recombination mechanisms 9.6.1.Carrier generation 9.6.2.Direct bandtoband recombination 9.6.3. SchokleyReadHall recombination 9.6.4. Auger bandtoband recombination 9.6.5.Surface recombination 9.7.Summary Further reading Problems
ix 249 249 250 250 255 256 257 259 261 261 262 263 265 270 272 273 273 278 287 290 291 291 293
Semiconductor Junctions297 10.1.Introduction297 10.2. Ideal pn junction at equilibrium298 10.2.1. Ideal pn junction298 10.2.2. Depletion approximation299 10.2.3. Builtin electric field304 10.2.4. Builtin potential306 10.2.5. Depletion width309 10.2.6. Energy band profile and Fermi energy311 10.3. Nonequilibrium properties of pn junctions313 10.3.1. Forward bias: a qualitative description314 10.3.2. Reverse bias: a qualitative description317 10.3.3.A quantitative description319 10.3.4. Ideal pn junction diode equation323 10.3.5. Minority and majority carrier currents in neutral regions 331 10.4.Deviations from the ideal pn diode case333 10.4.1.Avalanche breakdown334 10.4.2. Zener breakdown337 10.5.Metalsemiconductor junctions338
x
11.
12.
Fundamentals of Solid State Engineering
10.5.1. Formalism 10.5.2.Schottky and ohmic contacts 10.6.Summary Further reading Problems
Compound Semiconductors and Crystal Growth Techniques 11.1. Introduction 11.2.IIIV semiconductor alloys 11.2.1. IIIV binary compounds 11.2.2. IIIV ternary compounds 11.2.3.IIIV quaternary compounds 11.3. Bulk single crystal growth techniques 11.3.1. Czochralski growth method 11.3.2. Bridgman growth method 11.3.3.Floatzone crystal growth method 11.3.4. Crystal wafer fabrication 11.4.Epitaxial growth techniques 11.4.1. Liquid phase epitaxy 11.4.2. Vapor phase epitaxy 11.4.3. Metalorganic chemical vapor deposition 11.4.4.Molecular beam epitaxy 11.4.5. Exsitu characterization of epitaxial thin films 11.5.Summary References Further reading Problems
Semiconductor Device Technology 12.1.Introduction 12.2.Oxidation 12.2.1. Oxidation process 12.2.2. Modeling of oxidation 12.2.3. Factors influencing oxidation rate 12.2.4. Oxide thickness characterization 12.3.Diffusion of dopants 12.3.1.Diffusion process 12.3.2. Constantsource diffusion: predeposition 12.3.3. Limitedsource diffusion: drivein 12.3.4. Junction formation 12.4.dopantsIon implantation of 12.4.1.Ion generation 12.4.2. Parameters of ion implantation 12.4.3. Ion range distribution
338 340 344 344 346
349 349 350 350 352 353 357 357 361 362 365 366 366 367 371 378 383 384 384 385 386
387 387 388 388 390 395 397 400 401 403 404 405 408 408 409 410
Contents
13.
14.
12.5. Characterization of diffused and implanted layers 12.5.1. Sheet resistivity 12.5.2. Junction depth 12.6.Summary References Further reading Problems
Semiconductor Device Processing 13.1. Introduction 13.2. Photolithography 13.2.1.Mask fabrication 13.2.2. Positive and negative resists 13.2.3. Exposure and developing 13.2.4. Direct patterning and liftoff techniques 13.3. Electronbeam lithography 13.3.1. Electronbeam lithography system 13.3.2. Electronbeam lithography process 13.3.3.electronbeam lithographyParameters of 13.3.4. Multilayer resist systems 13.3.5. Examples of structures 13.4. Etching 13.4.1.Wet chemical etching 13.4.2. Plasma etching 13.4.3. Reactive ion etching 13.4.4. Sputter etching 13.4.5. Ion milling 13.5.Metallization 13.5.1.Metal interconnections 13.5.2. Vacuum evaporation 13.5.3. Sputtering deposition 13.6. Packaging of devices 13.6.1. Dicing 13.6.2. Wire bonding 13.6.3. Packaging 13.7.Summary References Further reading Problems
Transistors 14.1. Introduction 14.2.Overview of amplification and switching 14.3. Bipolar junction transistors
xi
411 412 414 416 416 417 418
419 419 420 421 423 427 428 430 431 433 434 437 438 440 440 442 446 447 447 449 449 450 453 454 454 456 458 459 460 460 461
463 463 464 466
xii
15.
Fundamentals of Solid State Engineering
14.3.1. Principles of operation for bipolar junction transistors 466 14.3.2. Amplification process using BJTs467 14.3.3. Electrical charge distribution and transport in BJTs.471 14.3.4. Current transfer ratio474 14.4.transistorsHeterojunction bipolar 475 14.4.1.AlGaAs/GaAs HBT476 14.4.2. GaInP/GaAs HBT478 14.5.Field effect transistors481 14.5.1. Gate control482 14.5.2.Currentvoltage characteristics483 14.6.Summary485 References485 Problems487
Semiconductor Lasers 15.1.Introduction 15.2.Types of lasers 15.3.General laser theory 15.3.1. Stimulated emission 15.3.2. Resonant cavity 15.3.3. Waveguides 15.3.4. Laser propagation and beam divergence 15.3.5. Waveguide design considerations 15.4.Ruby laser 15.5.Semiconductor lasers 15.5.1.Population inversion 15.5.2.Threshold condition and output power 15.5.3. Homojunction Laser 15.5.4. Heterojunction lasers 15.5.5.Device Fabrication 15.5.6. Separate confinement and quantum well lasers 15.5.7.Laser packaging 15.5.8. Distributed feedback lasers 15.5.9. Material choices for common interband lasers 15.5.10.Quantum cascade lasers 15.5.11.Type II lasers 15.5.12. Vertical cavity surface emitting lasers 15.5.13. Low dimensional lasers 15.6.Summary References Further reading Problems
489 489 490 491 492 494 496 504 507 507 511 512 513 517 517 520 524 527 528 529 530 533 536 538 540 540 542 543
Contents 16.
Photodetectors 16.1.Introduction 16.2.Electromagnetic radiation 16.3. Photodetector parameters 16.3.1.Responsivity 16.3.2.Noise in photodetectors 16.3.3. Noise mechanisms 16.3.4.Detectivity 16.3.5.Frequency response 16.4. Thermal detectors 16.5.Photon detectors 16.5.1.Photoconductive detectors 16.5.2.Photovoltaic detectors 16.5.3. Detectivity in photovoltaic detectors 16.6. Examples of photon detectors 16.6.1.Pin photodiodes 16.6.2. Avalanche photodiodes 16.6.3.Schottky barrier photodiodes 16.6.4. Metalsemiconductormetal photodiodes 16.6.5. Type II superlattice photodetectors 16.6.6. Quantum well intersubband photodetectors 16.6.7. Photoelectromagnetic detectors 16.7.Summary References Further reading Problems
Appendix
Index
xiii 545 545 548 549 549 550 552 555 556 557 560 561 564 567 568 568 570 572 573 574 576 577 578 578 578 580
583
625