fundamental of solid state engineering

FUNDAMENTALS OF SOLID STATE ENGINEERING This Page Intentionally Left Blank FUNDAMENTALS OF SOLID STATE ENGINEERING by Manijeh Razeghi Northwestern University, U.S.A KLUWER ACADEMIC PUBLISHERS NEW YORK, BOSTON, DORDRECHT, LONDON, MOSCOW eBook ISBN: Print ISBN: 0-306-47567-7 0-7923-7629-3 ©2002 Kluwer Academic Publishers New York, Boston, Dordrecht, London, Moscow Print ©2002 Kluwer Academic Publishers Dordrecht All rights reserved No part of this eBook may be reproduced or transmitted in any form or by any means, electronic, mechanical, recording, or otherwise, without written consent from the Publisher Created in the United States of America Visit Kluwer Online at: and Kluwer's eBookstore at: http://kluweronline.com http://ebooks.kluweronline.com Contents List of Symbols xv Foreword xix Preface xxi 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 groups 1.5.4 and groups 1.5.5 1.5.6 group and groups 1.5.7 1.5.8 T group group 1.5.9 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 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 Fundamentals of Solid State Engineering 1.9 Summary Further reading Problems 37 37 39 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 41 41 42 48 50 54 54 56 58 60 61 61 64 66 67 68 71 Introduction to Quantum Mechanics 3.1 The quantum concepts 71 72 3.1.1 Blackbody radiation 3.1.2 The photoelectric effect 74 77 3.1.3 Wave-particle duality 3.1.4 The Davisson-Germer experiment 77 3.2 Elements of quantum mechanics 79 3.2.1 Basic formalism 79 3.2.2 General properties of wavefunctions and the Schrödinger equation 82 3.3 Simple quantum mechanical systems 82 3.3.1 Free particle 82 3.3.2 Particle in a 1-D box 84 3.3.3 Particle in a finite potential well 87 3.4 Reciprocal lattice 93 3.5 Summary 96 Further reading 96 Problems 97 Electrons and Energy Band Structures in Crystals 4.1 Introduction 4.2 Electrons in a crystal 99 99 100 Contents vii 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 100 102 106 109 111 113 115 118 119 122 124 125 127 128 130 132 133 133 134 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 135 135 136 136 141 143 143 148 152 152 155 157 157 158 161 163 167 167 168 168 169 Phonons 6.1 Introduction 171 171 viii Fundamentals of Solid State Engineering 6.2 Interaction of atoms in crystals: origin and formalism 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 Crystals 197 7.1 Introduction 197 7.2 Phonon density of states (Debye model) 197 7.2.1 Debye model 197 7.2.2 Phonon density of states 200 7.3 Heat capacity 203 7.3.1 Lattice contribution to the heat capacity (Debye model) 203 7.3.2 Electronic contribution to the heat capacity 210 7.4 Thermal expansion 213 7.5 Thermal conductivity 215 7.6 Summary 219 References 219 Further reading 219 Problems 220 Equilibrium Charge Carrier Statistics in Semiconductors 8.1 Introduction 8.2 Density of states 8.3 Effective density of states (conduction band) 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 ix Contents 249 249 250 250 255 256 257 259 261 261 262 263 265 270 272 273 273 278 287 290 291 291 293 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 10 297 Semiconductor Junctions 10.1 Introduction 297 298 10.2 Ideal p-n junction at equilibrium 298 10.2.1 Ideal p-n junction 299 10.2.2 Depletion approximation 304 10.2.3 Built-in electric field 10.2.4 Built-in potential 306 309 10.2.5 Depletion width 311 10.2.6 Energy band profile and Fermi energy 10.3 Non-equilibrium properties of p-n junctions 313 314 10.3.1 Forward bias: a qualitative description 317 10.3.2 Reverse bias: a qualitative description 319 10.3.3 A quantitative description 10.3.4 Ideal p-n junction diode equation 323 10.3.5 Minority and majority carrier currents in neutral regions 331 10.4 Deviations from the ideal p-n diode case 333 10.4.1 Avalanche breakdown 334 10.4.2 Zener breakdown 337 10.5 Metal-semiconductor junctions 338 616 Fundamentals of Solid State Engineering This expression shows that the thermionic emission current resembles the diode equation obtained in Eq ( 10.46 ) The difference lies in the saturation current density which is now given by: References H.A Bethe, “Theory of the boundary layer of crystal rectifiers,” MIT Radiation Laboratory Report 43-12, 1042 Sze, S.M., Physics of Semiconductor Devices, John Wiley & Sons, New York, 1981 Appendix A.8 Physical properties and safety information of metalorganics Fig A.16 and Fig A.17 summarize some of the basic physical properties of metalorganic sources commonly used in MOCVD, including their chemical formula and abbreviation, boiling point, melting point, and the expression of their vapor pressure as a function of temperature Additional information, including safety data, is also provided for a number of important metalorganic sources, including diethylzinc (Table A.2), trimethylindium (Table A.3), triethylindium (Table A.4), trimethylgallium (Table A.5), and triethylgallium (Table A.6) 618 Fundamentals of Solid State Engineering Appendix 619 620 Fundamentals of Solid State Engineering Appendix 621 622 Fundamentals of Solid State Engineering Appendix 623 624 Fundamentals of Solid State Engineering References Ludowise, M., “Metalorganic chemical vapor deposition of III-V semiconductors,” Journal of Applied Physics 58, R31-R55, 1985 Razeghi, M., The MOCVD Challenge Volume 1: A Survey of GalnAsP-InP for Photonic and Electronic Applications, Adam Hilger, Bristol, UK, 1989 Sze, S.M., Physics of Semiconductor Devices, John Wiley & Sons, New York, 1981 Index Index 1/f noise 554 abrupt junction 298 absorption 492 absorption coefficient 158 acceptor 236 acoustic phonon 186 503 active region 372 alkyls alloying 450 amorphous amplification 465 angle-lap method 414 angular frequency 175 anharmonic vibrations 193 anharmonicity 215 Arrhenius 377, 395 atomic vibrations 172 Auger electron 287 Auger hole 287 Auger recombination 287 Auger recombination lifetime 289 avalanche breakdown 334 570 avalanche photodiode background carrier concentration 403 569 back-side illumination 43 Balmer series band diagram 107 band structure 107 bandgap 65, 119 base transport factor 469 base-to-collector current amplification factor 470 bcc lattice 127 Bernard-Durafforg condition 513 binding energy 160 bipolar transistors 463 BJT 464 blackbody 72 Bohr orbit 48 Bohr radius 49, 159 bolometer 558 bond energy bond length Born-von Karman Bose-Einstein boule boundary conditions boundary layer bowing parameter Bragg’s law Bravais lattice breakdown voltage Bridgman Brillouin zone broad area laser bubbler built-in electric field built-in potential buried-heterostructure laser calorie capture cross-section cesium chloride channel charge control approximation charge neutrality chemical potential cladding layers cleavage planes collector compensation complementary error function compound semiconductors conduction band conduction band offset conduction bands conductivity confinement factor constant-source diffusion contrast covalent bonds critical electric field critical thickness 55 55 136, 176 192 358 136, 176 369, 376 352 528 11 333 361 108 520 373 300 306 523 203 280 31 481 329 237 120 498 511 467 237 403 349 119 144 65 253 503 403 434 58 333 526 626 crucible 452 crystal momentum 108 crystallography current density 251 current responsivity 549 current transfer ratio 469 502 cutoff frequency 560 cut-off wavelength Czochralski 357 dark current 565 de Broglie 77 198 Debye frequency 198 Debye temperature degeneracy 222 degenerate semiconductor 228 density of states 120, 136, 200 depletion approximation 303 depletion width 301 detectivity 555, 556 DFB 528 diamond 28 die chip 454 differential quantum efficiency 516 differential resistance 551,567 diffusion 261, 400, 401 diffusion coefficient 262, 370, 402 diffusion current 263,316 diffusion length 269 diffusivity 262 diode equation 323, 328 dipole 62 Dirac function 142 direct patterning 428 direct-gap 130 distributed feedback 528 donor 234 dopants 234 doping 234 dose 404, 409 double-heterojunction laser 518 double-heterostructure laser 518 drain 482 drift current 250, 317 drift velocity 252 drive-in 403, 404 Drude model 250 dry etching 442 dual line package 458 Dulong and Petit 206 Fundamentals of Solid State Engineering 52 effective charge effective conduction band density of 227 states 364 effective distribution coefficient 116, 144 effective mass effective Richardson constant 572, 614 effective valence band density of states 230 379 effusion cells 80 eigenvalues 493 Einstein coefficients Einstein relations 265 electric displacement 497 497 electrical field 122 electron electron density function 48 120 electron gas 147 electron lifetime 266 electron recombination lifetime 280 electron thermal velocity 563 electron transit time 452 electron-beam evaporation 420, 430 electron-beam lithography 42 electronic structure 281 emission probability emitter 466 469 emitter injection efficiency energy bands 64 107, 143 energy spectrum 366 epitaxy 273 excess generation rate 158 exciton 80 expectation value extended-zone representation 107, 110 221, 560 extrinsic 234 extrinsic semiconductor 505 far-field pattern 10, 125 fcc lattice 119 Fermi level 211 Fermi temperature 119, 122, 225 Fermi-Dirac 464, 481 FET 262, 390 Fick’s first law 481 field effect transistor 463 field effect transistors 452 filament evaporation 27 flat 362 float-zone 314 forward bias Index 432 forward scattering 412 four point probe 609 Fourier coefficients 609 Fourier series Fourier transform 610 525 free-carrier absorption 513 gain 495 gain curve gain-guided laser 523 gas Gauss’s law 304 Gaussian 404 generalized Ohm’s law 253 Generation-recombination noise 554 414 groove and stain method group velocity 115, 180, 192 growth rate 376 Hall constant 259 256 Hall effect 259 Hall factor Hall mobility 259 harmonic crystal 173 HBT 475 heat capacity 203 heat sink 520, 522 heavy-hole 129 heavy-hole effective mass 225 Heisenberg uncertainty principle 113 Henry’s law 391 heterojunction bipolar transistor 475 heterojunction laser 517 hexagonal close-packed 32 hole recombination lifetime 269 holes 122 homojunction laser 517 Hund’s rule 50 hydrogen bond 63 ideal gas law 452 ideal p-n junction diode 298 ideality factor 344 impact ionization 334, 570 implantation 400 indirect-gap 130 infrared 546 interstitial diffusion 401 intersubband 531 intrinsic 221, 560 intrinsic carrier concentration 232 intrinsic semiconductor 232, 233 627 447 ion milling 421 ion-beam lithography 56 ionic bonds 571 ionization coefficients 235, 236 ionization energy 236 ionized acceptor 234 ionized donor 234 isoelectronic 481 JFET 552 Johnson noise 158 joint density of states 404, 414 junction depth 216, 250, 451 kinetic theory of gases 81 Laplacian 489 laser lattice 191 lattice wave 520 lattice-matched 428 lift-off technique 129 light-hole 225 light-hole effective mass 403 limited-source diffusion liquid 361 Liquid Encapsulated Czochralski 366 liquid phase epitaxy 465 load line 190 longitudinal longitudinal electron effective mass 223 495 longitudinal optical modes 257, 359 Lorentz force 514 loss 366 LPE 43 Lyman series 497 magnetic field strength 256, 497 magnetic induction 316 majority carriers 373 manifold 420, 422 mask 231 mass action law 373 mass flow controllers 370, 390 mass transfer coefficient 496 Maxwell equations 214 Maxwell-Boltzmann 366 MBE 217, 218, 379, 451 mean free path 481 MESFET 338 metal contact 449 metal interconnection 61 metallic bond 628 metallization 449 338 metallurgic junction metalorganic 373 metalorganic chemical vapor deposition 366, 371 metal-semiconductor junction 298, 338 metal-semiconductor-metal (MSM) 573 metastable state 509 Miller indices 23 534 minibands minority carrier extraction 323 minority carrier injection 323 minority carriers 316, 317 MISFET 481 mixed bonds 60 mobility 252 MOCVD 366, 371 modal threshold gain 526 mode 191 molecular beam epitaxy 366 momentum space 93 MOSFET 481 MQW 525 multiplication factor 335 multi-quantum well 525 nearly-free electron approximation 109 n-fold symmetry 14 noise 550 noise equivalent circuit 551 noise spectral density 551 noise-equivalent-power 555 nominal dose 434 non-degenerate semiconductor 227, 230 non-radiative recombination 278 normal processes 217 normalization 79 n-type doping 234 Ohm’s law 253 ohmic contact 341 operator 80 optical phonon 186 optoelectronic 350 organometallic 373 packing factor 35 particle momentum 83 Paschen series 43 50, 119 Pauli exclusion principle 102 periodic boundary conditions periodic potential 109 Fundamentals of Solid State Engineering 497 permeability 497 permittivity 354 phase diagram 180 phase velocity 178, 191 phonon 178, 185 phonon dispersion relation 186 phonon spectrum 561 photoconductive detector 563 photoconductive gain 562 photoconductivity 561 photoconductor 549, 562, 565 photocurrent 546 photodetectors 564 photodiode 75 photoelectric effect photoelectromagnetic (PEM) effect 577 420, 421 photolithography 76 photon 560 photon detectors 555 photon noise 423 photoresist 560, 564 photoresponse 549 photovoltage 564 photovoltaic detector p-i-n 568 481, 482 pinch-off 442 plasma etching 433 PMMA 297 p-n junctions 13 point group 13 point symmetry 60 polar bond 532 polarization polycrystalline 494 population inversion 491 power conversion efficiency 403 predeposition primitive unit cell 410 projected range 236 p-type doping 558 pyroelectric 373 pyrometers 510 Q-switching 155 quantum box 530 quantum cascade laser 136 quantum dot 515, 558 quantum efficiency 135, 525 quantum well Index quantum well intersubband photodetector 576 135 quantum wire quasi-equilibrium 512 quasi-Fermi energies 513 quasi-Fermi energy 271 quasi-momentum 108 525 QW QWIP 576 radiative recombination 273 492 radiative recombination lifetime range distribution 410 73 Rayleigh-Jeans law reactive ion etching 446 93 reciprocal lattice 110 reciprocal lattice vector recombination 266 recombination center 278 274 recombination coefficient recombination lifetime 277 rectifying contact 340 reduced effective mass 158 reduced Planck’s constant 73 reduced-zone representation 107, 111 reflection high-energy electron diffraction 381 refractive index 495 relaxation process 275, 289 relaxation time 252 resist 420 resistance 255 549, 563 responsivity 317 reverse bias reverse breakdown 333 381 RHEED RHEED pattern 381 Richardson constant 614 159 Rydberg energy saturation current 329, 554, 616 scattering 216 SCH 524 Schockley-Read-Hall recombination lifetime 286 Schokley-Read-Hall recombinations 278 Schottky barrier photodiodes 572 Schottky contact 340 Schottky potential barrier height 344, 572 Schrödinger equation 81, 82 357 seed 629 360 segregation constant 491 semiconductor laser 434 sensitivity separate confinement heterostructure 524 516 series resistance 412 sheet receptivity 566 short-circuit current 553 shot noise 550, 555 signal-to-noise ratio single crystal 516 slope efficiency 31 sodium chloride solid 403 solid solubility 179, 180 sound velocity 482 source 301 space charge region 556 specific detectivity 203 specific heat 138 spin degeneracy 129 split-off 492 spontaneous emission 447 sputter etching 453 sputtering deposition 81 stationary states 149 step function 298 step junction 492 stimulated emission 410 straggle 167 Stranski-Krastanow 234 substitutional 401 substitutional diffusion 357 substrate 534 superlattice 290 surface recombination 291 surface recombination velocity 536 surface-emitting lasers 372 susceptor 465 switching 125 symmetry directions 125 symmetry points 172, 607 Taylor expansion 499 TE polarization 555 temperature noise 465 terminals 558 thermal conductance 215 thermal conductivity 215 thermal conductivity coefficient 216 thermal current density 630 558 thermal detector thermal expansion 213 thermal expansion coefficient 213 273 thermal generation rate 388 thermal oxidation 559 thermal response time 572 thermionic emission thermocouple 558 373 thermocouples thermoelectric cooler 527 thermopile 558 threshold current density 515 tight-binding approximation 111 TM polarization 499 TO-style package 458 translation 13 transparency gain 525 transparency point 513 transversal 190 transverse electron effective mass 223 transverse modes 496 traveling wave 175 tunneling 91 turn-on voltage 516 two-dimensional electrons 148 type I 533 type II 533, 574 type II misaligned 533 type II staggered 533 Fundamentals of Solid State Engineering ultraviolet umklapp processes unit cell vacuum deposition valence band valence electrons Van der Pauw’s Van der Pauw’s method van der Waals vapor phase epitaxy vapor pressure Vegard’s law voltage responsivity VPE wave equation waveguide wavenumber wave-particle duality wavevector wet chemical etching white noise Wigner-Seitz cell wire bonding work function wurtzite x-ray lithography Young’s modulus Zener breakdown zinc blende 546 217 8,9 450 65, 119 53 413 413 62 366 361 353 549 366 81, 498 496, 498 83, 175 77 100, 500 440 552 456 75 34 420 195 337 30 [...]... to a book on the Fundamentals of Solid State Engineering by Professor Manijeh Razeghi Professor Razeghi is one of the world’s foremost experts in the field of electronic materials crystal growth, bandgap engineering and device physics The text combines her unique expertise in the field, both as a researcher and as a teacher The book is all-encompassing and spans fundamental solid state physics, quantum... for students of solid state devices in electrical engineering and materials science The book has learning aids through exceptional illustrations and end of chapter summaries and problems Recent publications are often cited The text is a wonderful introduction to the field of solid state engineering The breadth of subjects covered serves a very useful integrative function in combining fundamental science... 1.8.7 Packing factor Summary 2 Fundamentals of Solid State Engineering 1.1 Introduction This Chapter gives a brief introduction to crystallography, which is the science that studies the structure and properties of the crystalline state of matter We will first discuss the arrangements of atoms in various solids, distinguishing between single crystals and other forms of solids We will then describe the... container, a liquid has constant volume but adopts the shape of its container, while a solid retains both its shape and volume independently of its container This is illustrated in Fig 1.3 The natural forms of each element in the periodic table are given in Fig A 1 in Appendix A 1 Crystalline Properties of Solids 3 4 Fundamentals of Solid State Engineering Gases Molecules or atoms in a gas move rapidly... prompted me to write this book, entitled Fundamentals of Solid State Engineering This book is primarily aimed at the undergraduate level but graduate students and researchers in the field will also find useful material in the appendix and references After studying it, the student will be well versed in a variety of fundamental scientific concepts essential to Solid State Engineering, as well as the latest... xxiv Fundamentals of Solid State Engineering The scientific and technological accomplishments of earlier centuries represent the first stage in the development of Natural Science and Technology, that of understanding (Fig E) As the century begins, we are entering the creation stage where promising opportunities lie ahead for creative minds to enhance the quality of human life through the advancement of. .. the future of Solid State Engineering, this course will be able to provide some of the basis necessary for this endeavor, inspire the creativity of the reader and lead them to further explorative study Since 1992 when I joined Northwestern University as a faculty member and started to teach, I have established the Solid State Engineering (SSE) research group in the Electrical and Computer Engineering. .. dimensions may be formed The distribution of molecules or atoms, when a liquid or a gas cools to the solid state, determines the type of solid Depending on how the solid is formed, a compound can exist in any of the three forms in Fig 1.4 The ordered crystalline phase is the stable state with the lowest internal energy (absolute thermal equilibrium) The solid in this state is called the single crystal form... single atom, group of atoms or other compounds The periodic arrangement of such patterns in a crystal is represented by a lattice A lattice is a mathematical object which consists of a periodic arrangement of points in 6 Fundamentals of Solid State Engineering all directions of space One pattern is located at each lattice point An example of a two-dimensional lattice is shown in Fig 1.5(a) With the pattern... building blocks of modern electronics In these Chapters, the derivation of the mathematical relations has been spelled out in thorough detail so that the reader can understand the limits of applicability of these expressions and adapt them to his or her particular situations The second part of this book reviews the technology for modern Solid State Engineering This includes a review of compound semiconductor