FUNDAMENTALS OF SOLID STATE ENGINEERING, Pd Edition FUNDAMENTALS OF SOLID STATE ENGINEERING, PdEdition Manijeh Razeghi Northwestern University Evanston, IL, USA Q - Springer Manijeh Razeghi Northwestern University Evanston, IL, USA Fundamentals of Solid State Engineering, 2ndEdition Library of Congress Control Number: 2005937004 ISBN 10: 0-387-28152-5 ISBN 13: 978-0-387-28152-0 EISBN: 0-387-2875 1-5 (ebook) Printed on acid-free paper O 2006 Springer Science+BusinessMedia, Inc All rights reserved This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, Inc., 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden The use in this publication of trade names, trademarks, service marks and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights Printed in the United States of America SPIN 11530428 Contents List of Symbols xix Foreword xxm Preface xxv Crystalline Properties of Solids 1.1 Introduction 1.2 Crystal lattices and the seven crystal systems 1.3 The unit cell concept 1.4 The Wigner-Seitz cell 10 1.5 Bravais lattices 11 1.6 Point groups 13 1.6.1 C, group (plane reflection) 13 1.6.2 C,,groups (rotation) 14 1.6.3 Cnhand C,, groups 15 1.6.4 D, groups 16 1.6.5 Dnhand Dndgroups 1.6.6 Ci group 18 1.6.7 C3iand S4groups 18 1.6.8 T group 19 1.6.9 Td group 1.6.10 group 21 1.6.11 Ohgroup 21 1.6.12 List of crystallographic point groups 21 1.7 Space groups .23 1.8 Directions and planes in crystals: Miller indices 23 1.9 Real crystal structures 28 1.9.1 Diamond structure 28 1.9.2 Zinc blende structure 30 1.9.3 Sodium chloride structure 31 1.9.4 Cesium chloride structure 1.9.5 Hexagonal close-packed structure 32 1.9.6 Wurtzite structure Fundamentals of Solid State Engineering vi 1.9.7 Packing factor 35 1.10 The reciprocal lattice 1.11 The Brillouin zone -40 1.12 Summary 40 Further reading 41 Problems 42 Electronic Structure of Atoms 45 2.1 Introduction 45 2.2 Spectroscopic emission lines and atomic structure of hydrogen 46 2.3 Atomic orbitals 2.4 Structures of atoms with many electrons 55 2.5 Bonds in solids 59 2.5.1 General principles 59 2.5.2 Ionic bonds 61 2.5.3 Covalent bonds 2.5.4 Mixed bonds 65 2.5.5 Metallic bonds 66 2.5.6 Secondary bonds 70 2.6 Atomic property trends in the periodic table 2.6.1 The periodic table .7 2.6.2 Atomic and ionic radii 2.6.3 Ionization energy 2.6.4 Electron affinity 2.6.5 Electronegativity 73 2.6.6 Summary of trends .7 2.7 Introduction to energy bands 73 2.8 Summary 75 Further reading 76 Problems 77 Introduction to Quantum Mechanics 81 3.1 The quantum concepts 3.1.1 Blackbody radiation 3.1.2 The photoelectric effect 84 3.1.3 Wave-particle duality 87 3.1.4 The Davisson-Germer experiment 88 3.2 Elements of quantum mechanics 89 3.2.1 Basic formalism 89 3.2.2 The time independent Schrodinger equation 93 3.2.3 The Heisenberg uncertainty principle 95 3.2.4 First summary 96 Contents vii 3.2.5 General properties of wavefunctions and the Schrodinger equation 3.3 Simple quantum mechanical systems 97 3.3.1 Free particle 3.3.2 Particle in a 1D box 99 3.3.3 Particle in a finite potential well 102 3.4 Summary 108 Further reading Problems 10 Electrons and Energy Band Structures in Crystals 115 4.1 Introduction 115 4.2 Electrons in a crystal 116 4.2.1 Bloch theorem 116 4.2.2 One-dimensional Kronig-Penney model 118 4.2.3 Energy bands 122 4.2.4 Nearly free electron approximation 126 4.2.5 Tight binding approximation 127 4.2.6 Dynamics of electrons in a crystal 130 4.2.7 Fermi energy 3 4.2.8 Electron distribution function 135 4.3 Density of states (3D) 136 4.3.1 Direct calculation 137 4.3.2 Other approach 142 4.3.3 Electrons and holes 146 4.4 Band structures in real semiconductors 148 4.4.1 First Brillouin zone of an fcc lattice 148 4.4.2 First Brillouin zone of a bcc lattice 150 4.4.3 First Brillouin zones of a few semiconductors 151 4.5 Band structures in metals 154 4.6 Summary 156 References 157 Further reading 157 Problems 158 Phonons 5.1 Introduction 161 5.2 Interaction of atoms in crystals: origin and formalism 162 5.3 One-dimensional monoatomic harmonic crystal 165 5.3.1 Traveling wave formalism 165 5.3.2 Boundary conditions 167 5.3.3 Phonon dispersion relation 5.4 One-dimensional diatomic harmonic crystal 170 5.4.1 Formalism 170 Fundamentals of Solid State Engineering vlu 5.4.2 Phonon dispersion relation 172 5.5 Extension to three-dimensional case 179 5.5.1 Formalism 179 5.5.2 Silicon 182 5.5.3 Gallium arsenide 5.6 Phonons 183 5.7 Sound velocity 186 5.8 Summary References 189 Further reading 189 Problems 191 Thermal Properties of Crystals 193 6.1 Introduction 193 6.2 Phonon density of states (Debye model) 193 6.2.1 Debye model .1 6.2.2 Phonon density of states 196 6.3 Heat capacity 199 6.3.1 Lattice contribution to the heat capacity (Debye model) 199 6.3.2 Electronic contribution to the heat capacity 207 6.4 Thermal expansion 209 6.5 Thermal conductivity 214 6.6 Summary 219 References 219 Further reading 220 Problems 2 Equilibrium Charge Carrier Statistics in Semiconductors .223 7.1 Introduction 223 7.2 Density of states 224 7.3 Effective density of states (conduction band) .227 7.4 Effective density of states (valence band) 232 7.5 Mass action law .2 7.6 Doping: intrinsic vs extrinsic semiconductor 236 7.7 Charge neutrality 7.8 Fermi energy as a function of temperature 243 7.9 Carrier concentration in an n-type semiconductor 247 7.10 Summary 251 References 251 Further reading 251 Problems Non-Equilibrium Electrical Properties of Semiconductors .255 Contents 8.1 Introduction -255 8.2 Electrical conductivity 8.2.1 Ohm's law in solids 256 8.2.2 Case of semiconductors 8.3 Carrier mobility in solids 262 8.4 Hall effect 264 8.4.1 p-type semiconductor 265 8.4.2 n-type semiconductor 267 8.4.3 Compensated semiconductor 269 8.4.4 Hall effect with both types of charge carriers 269 8.5 Charge carrier diffusion 270 8.5.1 Diffusion currents -271 8.5.2 Einstein relations 8.5.3 Diffusion lengths 274 8.6 Carrier generation and recombination mechanisms 279 8.6.1 Carrier generation 280 8.6.2 Direct band-to-band recombination 280 8.6.3 Shockley-Read-Hallrecombination 285 8.6.4 Auger band-to-band recombination 294 8.6.5 Surface recombination -297 8.7 Quasi-Fermi energy 8.8 Summary 300 Further reading 300 Problems 302 Semiconductor p-n and Metal-Semiconductor Junctions 305 9.1 Introduction 305 9.2 Ideal p-n junction at equilibrium 306 9.2.1 Ideal p-n junction 306 9.2.2 Depletion approximation 9.2.3 Built-in electric field 312 9.2.4 Built-in potential 314 9.2.5 Depletion width 9.2.6 Energy band profile and Fermi energy 319 9.3 Non-equilibrium properties of p-n junctions 321 9.3.1 Forward bias: a qualitative description 322 9.3.2 Reverse bias: a qualitative description 325 9.3.3 A quantitative description 327 9.3.4 Depletion layer capacitance 330 9.3.5 Ideal p-n junction diode equation 332 9.3.6 Minority and majority carrier currents in neutral regions 341 9.4 Deviations from the ideal p-n diode case 343 9.4.1 Reverse bias deviations from the ideal case 344 Fundamentals of Solid State Engineering x 9.4.2 Forward bias deviations from the ideal case .345 9.4.3 Reverse breakdown 9.4.4 Avalanche breakdown 348 9.4.5 Zener breakdown 9.5 Metal-semiconductorjunctions 352 9.5.1 Formalism 352 9.5.2 Schottky and ohmic contacts 354 9.6 Summary 358 Further reading 358 Problems 10 Optical Properties of Semiconductors .363 10.1 Introduction 364 10.2 The complex refractive index of a solid 365 10.2.1 Maxwell's equations 365 10.2.2 Reflectivity 368 10.2.3 Transmission through a thin slab 370 10.3 The free carrier contribution to the complex refractive index 10.3.1 The Drude theory of conductivity .372 10.3.2 The classical and quantum conductivity 375 10.4 The bound and valence electron contributions to the permittivity 7 10.4.1 Time dependent perturbation theory 377 10.4.2 Real transitions and absorption of light 381 10.4.3 The permittivity of a semiconductor 383 10.4.4 The effect of bound electrons on the low frequency optical properties 385 10.5 The optical absorption in semiconductors 386 10.5.1 Absorption coefficient 10.5.2 Excitonic effects .3 8 10.5.3 Direct and indirect bandgap absorption 391 10.6 The effect of phonons on the permittivity 393 10.6.1 Photon polar mode coupling 393 10.6.2 Application to ionic insulators 396 10.6.3 The phonon-polariton 10.7 Free electrons in static electric fields: the FranzKeldysh effect 399 10.8 Nearly free electrons in a magnetic field 403 10.9 Nonlinear optical susceptibility 410 10.10 Summary 412 References 413 Further reading 414 Contents xi Problems 415 11 Semiconductor Heterostructures and Low-Dimensional Quantum Structures 417 11.1 Introduction 417 11.2 Energy band offsets 419 11.2.1 Type I alignment 419 11.2.2 Type I1 alignments 420 11.3 Application of model solid theory 420 11.4 Anderson model for heterojunctions 422 11.5 Multiple quantum wells and superlattices 425 11.6 Two-dimensional structures: quantum wells 427 11.6.1 Energy spectrum 427 11.6.2 Density of states 11.6.3 The influence of an effective mass 435 11.7 One-dimensional structures: quantum wires 436 11.7.1 Density of states 436 11.7.2 Infinitely deep rectangular wires 439 11.8 Zero-dimensional structures: quantum dots 441 11.8.1 Density of states 441 11.8.2 Infinite spherical quantum dot 442 11.9 Optical properties of low-dimensional structures 444 11.9.1 Interband absorption coefficients of quantum welk.445 11.9.2 Absorption coefficient of quantum wires 448 11.9.3 Absorption coefficient of quantum dots 449 11.10 Examples of low-dimensional structures 450 11.10 Quantum wires 452 11.10.2 Quantum dots 455 11.lo.3 Effect of electric and magnetic fields 456 11.1 Summary .462 References 462 Further reading 463 Problems 465 Compound Semiconductors and Crystal Growth Techniques 469 12.1 Introduction 469 12.2 111-V semiconductor alloys 470 12.2.1 111-V binary compounds -470 12.2.2 111-V ternary compounds -472 12.2.3 111-V quaternary compounds 473 12.3 11-VI compound semiconductors 477 12.4 Bulk single crystal growth techniques 478 12.4.1 Czochralski growth method 479 12.4.2 Bridgman growth method 482 Formula Abbreviation Melting point Boiling point Lo ,,,.- m P(mmHd T, Tanperature Range Table A.2 Physical properties of some organometallics used in MOCVD [Ludowise 1985, and http://electronicmaterials.rohmhaas.com] Triethylindium Trimethylindium Ethyldimethylindium Triethylgdium Trimethylgallium Triethylaluminum Trimethylaluminum Group III snurces Dimethylcadmium Diethylzinc Dimethylzinc Group IIB sources Eiscyclopentadienyl m a p esium Diethylberyllium Dimethylb eryllium Group II sources Camp ound TBAs TEP TMP TEP TMAs TEAS TMSb TESb Tertiarybutylarsine Tertiarybutylphosphine Trimethylphosphorus Triethylphosphorus Trimethylarsenic Triethylarsenic Trimethylantimony Triethylantimony DMTe DETe (CH&Te (C&)zTe Dimethyltellurium Diethyltellunum 7.97 - l8651T 7.99 - 20931T 137-138 108 82 e T anp erature Range c) Table A.3 Physical properties of some organometallics used in MOCVD [Ludowise 1985, and http://electronicmaterials.rohmhaas.com] DESe (C2&)*Se Diethylselmide Group VI sources DEAs Diethylarsine Hydride 10 TESn Tetraethyltin Group V saurces 7.495 - 1620fT 78 181 -53 -112 TMSh (CH3)rSn (C*&)dGe Tetramethyltin P(mmHg) (T in K) I39 L-o 43.6 Boiling point PC) -88 eo Melting point TMGe Abbrwiatian (CH3)rGe Formula Tetramethylgermmiurn Group IV sources Compound Appendix Acronym DEZn Formula Formula weight Metallic purity 99.9999 wt% (min) zinc Appearance Clear, colorless liquid Density Melting point Vapor pressure 3.6 mmHg at OC 16 mmHg at 25 OC 760 mmHg at 117.6 "C Behavior towards organic solvents Completely miscible, without reaction, with aromatic and saturated aliphatic and alicyclic hydrocarbons Forms relatively unstable complexes with simple ethers, thioethers, phosphines and arsines, but more stable complexes with tertiary amines and cyclic ethers Stability in air Ignites on exposure (pyrophoric) Stability in water Reacts violently, evolving gaseous hydrocarbons, carbon dioxide and water Storage stability Stable indefinitely at ambient temperatures when stored in an inert atmosphere Table A.4 Chemical properties of diethylzinc [Razeghi 19891 Fundamentals of Solid State Engineering Acronym TMIn Formula (CH3)3In Formula weight 159.85 Metallic purity 99.999 wt% (min) indium Appearance White, crystalline solid Density 1S86 g.ml-' at 19 "C Melting point 89 "C Boiling point 135.8 "C at 760 rnmHg 67 "C at 12 mmHg Vapor pressure 15 mmHg at 41.7 "C Stability in air Pyrophoric, ignites spontaneously in air Solubility Completely miscible with most common solvents Storage stability Stable indefinitely when stored in an inert atmosphere - - Table A.5 Chemical properties of trimethylindium [Razeghi 19891 Acronym Formula Formula weight Metallic purity 99.9999 wt% (min) indium Appearance Clear, colorless liquid Density Melting point Vapor pressure 1.18 mmHg at 40 OC 4.05 mmHg at 60 OC 12.0 mmHg at 80 OC Behavior towards organic solvents Completely miscible, without reaction, with aromatic and saturated aliphatic and alicyclic hydrocarbons Forms complexes with ethers, thioethers, tertiary amines, phosphines, arsines and other Lewis bases Stability in air Ignites on exposure (pyrophoric) Stability in water Partially hydrolyzed; loses one ethyl group with cold water Storage stability Stable indefinitely at ambient temperatures when stored in an inert atmosphere Table A.6 Chemical properties of triethylindium [Razeghi 19891 Fundamentals of Solid State Engineering Acronym TMGa Formula Formula weight Metallic purity 99.9999 wt% (min) gallium Appearance Clear, colorless liquid Density Melting point Vapor pressure Behavior towards organic solvents Completely miscible, without reaction, with aromatic and saturated aliphatic and alicyclic hydrocarbons Forms complexes with ethers, thioethers, tertiary amines, tertiary phosphines, tertiary arsines, and other Lewis bases Stability in air Ignites on exposure (pyrophoric) Stability in water Reacts violently, forming methane and Me2GaOHor [(Me2Ga)20], Storage stability Stable indefinitely at ambient temperatures when stored in an inert atmosphere Table A Chemical properties of trimethylgallium [Razeghi 19891 Appendix 873 Acronym TEGa Formula Formula weight Metallic purity 99.9999 wt% (min) gallium Appearance Clear, colorless liquid Density Melting point Vapor pressure Behavior towards organic solvents Completely miscible, without reaction, with aromatic and saturated aliphatic and alicyclic hydrocarbons Forms complexes with ethers, thioethers, tertiary amines, tertiary phosphines, tertiary arsines and other Lewis bases Stability in air Ignites on exposure (pyrophoric) Stability in water Reacts vigorously, forming ethane and Et2GaOH or [(Et,Ga),O], Storage stability Stable indefinitely at room temperatures in an inert atmosphere Table A.8 Chemical properties of triethylgallium [Razeghi 19891 References Ludowise, M., "Metalorganic chemical vapor deposition of 111-Vsemiconductors," Journal of Applied Physics 58, R3 1-R55, 1985 Mudry, W.L., Burleson, D.C., Malpass, D.B., and Watson, S.C., Journal of Fire Flammability 6, p 478, 1975 Razeghi, M., The MOCVD Challenge Volume I : A Survey of GaInAsP-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 Ilfnoise 774 abrupt junction 306 absorbance 537 704 absorption absorption coefficient 368.387.445.448 537 acceptor 240 acoustic phonon 175 715 active region 400 Airy functions alkyl 495 alloying 650 amorphous amplification 667 Anderson model 422 angle-lap method 609 angular frequency 166 anharmonic vibrations 185 anharmonicity 214 anti-site defect 556 anti-Stokes scattering 539 Arrhenius 582 atomic force microscopy 533 506 atomic layer epitaxy atomic radius 71 atomic vibrations 163 Auger electron 294 Auger electron spectroscopy 529 294 Auger hole Auger recombination 294 426 Auger recombination lifetime 296 348 avalanche breakdown avalanche photodiode 797 background carrier concentration .595 back-side illumination 797 47 Balmer series band alignment I9 band diagram 123 123 band structure band-bending 419 bandgap 134 base transport factor 675 base-to-collector current amplification factor 676 bcc lattice 150 Beer Lambert law .368 Bernard-Durafforg condition 725 390 binding energy bipolar transistors 665 666 BJT 82 blackbody 116 118 Bloch theorem Bohr magneton 404 Bohr orbit 52 Bohr radius 53 54 389 bolometer 780 Boltzmann distribution 96 Boltzmann equation 853 60 bond energy bond length 60 Born-von Karman 137 167 194 Bose-Einstein 185 189 bosons 217 bode 479 482 boundary conditions 137 167 boundary layer 492 498 bowing parameter .472 Bragg's law 523 741 Bravais lattice 11 breakdown voltage .347 Bremsstrahlung effect 522 482 Bridgman Brillouin zone 40 124 150 broad area laser 733 bubbler 496 built-in electric field 308 314 built-in potential bulk modulus 188 Burger's vector 560 buried-heterostructure laser 736 calorie 199 capacitance techniques 543 Fundamentals of Solid State Engineering capacitance-voltagemeasurements 543 capture cross-section 287 capture rate 287 cathode ray tube 525 cathodoluminescence 537 ceramics 66 cesium chloride channel 688 charge control approximation 339 charge neutrality 242 25 chemical diffusion 555 chemical potential 135 cladding layers 71 cleavage planes 724 coherent interphase boundary 565 cohesive energy 62 collector 669 compensation 240 complementary error function 594 470 compound semiconductors conduction band 74 134 conduction band offset 427 conductivity 259 confinement factor 15 constant-source diffusion 593 634 contrast Coulomb blockage 454 covalent bonds 63 critical electric field 347 critical thickness .739 crucible 652 crystal momentum 125 crystallography .2 current density 257 770 current responsivity 676 current transfer ratio cutoff frequency 15 cut-off wavelength .788 cyclotron frequency 405 cyclotron resonance 409 Czochralski 479, 48 dark current 793 de Broglie 87 Debye frequency 195 Debye model 193 197 Debye temperature 195 207 Debye wavenumber 195 deep-level transient spectroscopy .544 defect characterization 568 defects 551 degeneracy 2 degenerate semiconductor 230 234 density of states 136 196 depletion approximation 11 332 depletion layer 330 345 depletion layer width depletion width 309 330 detectivity 776 777 DFB 741 diamond 28 die chip .655 differential quantum efficiency 729 differential resistance 772 794 diffusion 589 diffusion coefficient 272 493 591 diffusion current 272 324 diffusion currents 336 diffusion length 278 diffusivity 272 diode equation 332 338 dipole 68 dip-pen lithography 629 Dirac delta function 142 382 Dirac notation 379 direct bandgap 391 625 direct patterning direct-gap 154 484 558 dislocation 174 dispersion relation displacement 365 741 distributed feedback 544 DLTS donor 237 dopants 237 doping 156 237 dose 596 602 double-heterojunction laser 731 double-heterostructure laser .731 drain 688 drift current 256 325 327 drift velocity .258 drive-in 594, 596 Drude model .256 372 Drude theory 372 376 383 642 dry etching dry oxidation method 575 658 dual line package Dulong and Petit 202 Index Early effect 677 680 edge dislocation 558 EDX 529 effective charge 58 effective conduction band density of states 229 effective distribution coefficient .485 effective mass 132 146 427 effective Richardson constant 800 860 effective valence band density of states .233 effusion cells 500 eigenfunction 91 91 eigenstate eigenvalues I Einstein coefficients 705 Einstein relations 273 274 elastic scattering 262 263 709 electric displacement 709 electric field electrochemical capacitance-voltage 544 profiling electron .146 electron affinity 72 electron density function 53 electron gas 135 43 I electron lifetime electron microscopy 524 electron recombination lifetime 275 electron thermal velocity 287 electron transit time 79 electron-beam evaporation 652 electron-beam lithography 627 630 electronegativity 73 electronic structure .46 electron-phonon interaction 262 electro-optic 41 ellipsometry 585 emission probability 288 emitter 669 emitter injection efficiency 675 energy bands 74 energy dispersive analysis using x-rays .529 energy spectrum 123 132 427 enthalpy 508 entropy 508 epitaxy 489 equilibrium state 280 excess generation rate 280 exciton 391 expectation value 92 extended-zone representation 123 126 external planar defect 566 external planar defects 562 extrinsic 223 787 extrinsic point defects 556 extrinsic semiconductor .237 far-field pattern 717 fcc lattice 148 Fermi golden rule .382 392 Fermi level 134 208 Fermi temperature Fermi-Dirac 135 145 228 FET 688 271 576 Fick's first law field effect transistor 665 688 652 filament evaporation flat 27 float-zone 484 focal plane array 660 803 807 forward bias 322 632 forward scattering Fourier coefficients 839 Fourier series 839 Fourier transform 840 Fourier transform spectroscopy 540 542 607 four-point probe Frank-van der Menve 513 Franz-Keldysh effect 399 Franz-Keldysh oscillations 402 free-carrier absorption 738 Frenkel defect 554 frequency dependent conductivity 365 366 FTIR 541 Full Width at Half Maximum .524 gain 725 gain curve 707 gain-guided laser 735 gas Gauss's law 312 Gaussian 596 Gaussian distribution 449 259 generalized Ohm's law generation rate 28 344 generation-recombinationnoise 775 Gibbs free-energy .507 Fundamentals of Solid State Engineering Gibbs Phase Rule 10 grain boundary 562 563 groove and stain method 609 group velocity 130 184 187 growth rate 498 Hall constant 267 Hall effect 543 267 Hall factor Hall mobility 267 Hall resistance 460 Hall voltage 461 Hamiltonian 90, 95 harmonic crystal 164 Hartree-Fock 843 Hartree-Fock self consistent field .844 HBT 682 heat capacity 199 205 heat sink .7 3 734 heavy-hole I53 heavy-hole effective mass 227 Heisenberg uncertainty principle 95 382 HEMT 696 Henry's law 577 Hermite polynomials 405 hermitian 93 heterojunction 41 422 hetcrojunction bipolar transistor.418, 682 heterojunction laser 730 heterostructure I8 hexagonal close.packed 32 Hilbert space 91 hole effective mass 227 hole recombination lifetime 279 holes 146 730 homojunction laser Hund's rule 57 hybridization 65 69 hydrogen bond ideal gas law 652 ideal p-n junction diode 306 ideality factor 346 358 impact ionization 348 798 implantation 589 601 incoherent interphase boundary 566 indirect bandgap 39 I indirect-gap 154 262 inelastic scattering infrared 765 infrared photodetectors 477 internal planar defects 562 interphase boundary 562 interstitial 554 interstitial defect 553 interstitial diffusion 591 interstitial impurity 556 intersubband .747 intrinsic 223, 787 intrinsic carrier concentration 235 248 intrinsic contribution intrinsic point defects 554 intrinsic semiconductor 235.236 245 inversion symmetry 18 ion implantation 601 647 ion milling ion-beam lithography 628 ionic bonds GI ionic radii 71 ionization coefficients 798 ionization energy 72 238 240 557 ionized acceptor 240 ionized donor 238 isoelectronic 237 JFET 688 Johnson noise 773 joint density of states 388 junction depth 595 609 Kane parameter 385 Kane theory 385 kinetic theory of gases 216.256 65 Landau gauge 404 Landau level 405 409 460 404 Lande factor Laplacian 93 701 laser lattice lattice constant 524 183 lattice wave lattice-matched 732 Lely method 486 LIDAR 799 lifetime 382 lift-off technique 625 light-hole 153 light-hole effective mass 227 limited-source diffusion 594 line defect 558 linear response 410 liquid Index Liquid Encapsulated Czochralski .482 liquid phase epitaxy 489 load line 667 local density of states 402 longitudinal 180 194 longitudinal electron effective mass 226 longitudinal optical modes 707 Lorentz force 265 408 46 48 loss 726 489 LPE Luttinger liquid 454 Lyman series 47 magnetic field 365 709 magnetic field strength magnetic flux 365 magnetic induction .264 709 41 I magneto-optic majority carriers 324 manifold .496 621 mask mass action law 235 mass flow controller 496 mass transfer coefficient 493 577 Maxwell's equations 365 709 Maxwell-Boltzmann 213 MBE 489 mean free path 217 219 501 651 MESFET 688 metal contact 352 metal interconnection 649 metallic bond 66 metallization 649 metallurgic junction 352 metalorganic 496 metalorganic chemical vapor deposition 489, 494 metal-oxide-semiconductor 574 586 metal-semiconductorjunction 306 352 metal-semiconductor-metal (MSM) 80 metastable state 721 Michelson interferometer 540 migration enhanced epitaxy 506 Miller indices 23 24 25 miniband 426, 75 minority carrier extraction 334 minority carrier injection 333 minority carriers 324 325 MISFET 688 mixed bonds 65 mixed dislocation 560 258 mobility MOCVD 494 modal threshold gain 739 model solid theory 420 modified Lely method 486 molecular beam epitaxy .489 momentum space 41 Monte-Carlo simulation 855 MOSFET 688, 692 Moss-Burstein shift 466 MQW 426, 738 multiplication factor 348 multi-quantum well 738 nano-imprint lithography 629 nanopillar 456 near-field scanning optical microscopy nearly free electron approximation 126 n-fold symmetry 14 noise 770 noise equivalent circuit 772 771 noise spectral density noise-equivalent-power 776 nominal dose 634 non-degenerate semiconductor 229 233 nonlinear optical susceptibility 410 non-radiative recombination 285 normal processes 217 normalization 90 n-type doping 237 Ohm's law 259 ohmic contact 355 operator 91 optical phonon 175 optoelectronic 470 organometallic 496 oscillator strength 379 384 oxidation 582 35 packing factor particle momentum .98 Paschen series 47 Pauli exclusion principle 55 134 periodic boundary conditions 118 periodic potential 126 permeability 365 709 permittivity 365, 709 perturbation theory 377 456 phase diagram 474 10 Fundamentals of Solid State Engineering phase velocity 186 phonon 168 169 184 phonon dispersion relation 169 phonon polariton 399 174 phonon spectrum phonons 162 16 789 photoconductive detector photoconductive gain 79 photoconductivity 789 photoconductor 789 photocurrent .770 790 793 photodetectors 766 photodiode 792 photoelectric effect .85 photoelectromagnetic (PEM) effecL.804 photolithography 16 621 photoluminescence 535 photomultiplier tube 525 photon 86 photon detectors 787 photon noise .775 photon-phonon coupling 394 photoresist 585 17 photoresponse 79 photovoltage .770 photovoltaic detector 792 534 piezoelectric tube p-i-n 796 pinch-off 689 690 562 planar defect Planck's law .769 plasma etching 642 plasma frequency 373 375 PMMA 632 306 p-n junctions point defect .553 point group 13 point symmetry 13 polar bond 66 polarizability 373 379 polarization vector 365 polycrystalline population inversion 706 power conversion efficiency 703 Poynting vector 368 precipitates 567 predeposition 593 594 preferential etching 568 primitive unit cell projected range 603 pseudopotential method .843 p-type doping 239 pyroelectric 780 pyrometer 496 722 Q-switching quantum box 441 747 quantum cascade laser quantum dot .418 442 455 535 727 780 quantum efficiency Quantum Hall effect 461 quantum we11 406.418.425.427.433 738 quantum well intersubband photodetector 805 quantum wire .418 437 454 724 quasi-equilibrium quasi-Fermi energy 298 299 724 quasi.momentum 125 184 quasi-particle quaternary compounds .473 475 QW 738 QWIP 805 radiative recombination 280 radiative recombination lifetime 704 Raman 757 539 Raman scattering Raman spectroscopy 539 539 Rayleigh scattering 83 Rayleigh-Jeans law 646 reactive ion etching reciprocal lattice 37 reciprocal lattice vector 39 127 recombination .275 279 685 recombination center 285 recombination coefficient 28 I 283 recombination current 346 recombination lifetime .284 rectifying contact 354 reduced effective mass 388 reduced Planck's constant 83 reduced-zone representation .123 127 reflectance 537 reflection 538 reflection high-energy electron diffraction 503 reflectivity 370, 371 refractive index 366 368 385 707 relaxation process .282 296 Index relaxation time 258 resist I6 resistance 26 I responsivity 770 79 reverse bias 327 reverse breakdown .347 RHEED 503 RHEED pattern 503 Richardson constant 358 860 Riemann zeta function 204 Rutherford backscattering 533 Rydberg 46 Rydberg constant 47 50 389 Rydberg energy saturation current 339 774 862 scanning electron microscope 524 scanning probe microscopy 533 scanning tunneling microscopy 534 scattering I6 737 SCH Schottky barrier photodiodes 799 Schottky contact 354 355 357 Schottky defect 554 Schottky potential barrier height 358 800 Schrodinger equation 89 93 94 97 screw dislocation 559 Second Law of thermodynamics 508 secondary bond 67 secondary ion mass spectroscopy 53 610 seed 479 segregation constant 48 self-interstitial 554 SEM 524 semi-coherent interphase boundary 565 semiconductor heterostructures 589 semiconductor laser 703 sensitivity 634 separate confinement heterostructure.737 series resistance 728 sheet resistivity 542, 606 Shockley-Read-Hall recombination 285 297 Shockley-Read-Hallrecombination lifetime 293 short-circuit current 793 shot noise 774 Shubnikov de-Haas effect 407 signal-to-noise ratio 771 776 SIMS 531 610 single crystal Slater determinant 844 slope efficiency 728 sodium chloride 31 solid solid solubility 594 sound velocity 186 source 8 space charge region 309 specific detectivity 776 specific heat .200 spherical Bessel functions 443 spherical harmonics 443 spin degeneracy 138 420 spin-orbit splitting split-off 153 spontaneous emission 704 sputter etching 647 653 sputtering deposition stacking fault 562 Stark shift 458 stationary states 94 steady state 280 step function 433 306 step junction stimulated emission 704 Stokes scattering 539 straggle 604 Stranski-Krastanow 455 13 553 substitutional 237 substitutional defect 553 substitutional diffusion 591 substitutional impurity 556 478 substrate 426 75 superlattice surface leakage 343 345 surface plasmon 375 surface recombination 297 surface recombination velocity 298 surface-emitting lasers 753 susceptibility tensor 411 susceptor 495 switching 667 symmetry directions 148 symmetry operations 13 symmetry points 148 Taylor expansion 163 837 711 TE polarization Fundamentals of Solid State Engineering TE propagation mode 82 temperature noise .775 terminals 667 thermal conductance 780 thermal conductivity 214 thermal conductivity coefficient .2 14 thermal current density 215 thermal detector 780 thermal expansion 209 thermal expansion coefficient 209 thermal generation rate .280 thermal oxidation 574 78 thermal response time thermionic emission 800 thermocouple 496, 780 thermoelectric cooler 740 thermopile 780 threshold current 45 threshold current density 727 tight-binding approximation .127 TM polarization 71 1, 748 TM propagation mode 82 658 TO-style package translation 13 transmission 538 transmission electron microscopy 526 transmissivity .370 transparency gain 738 transparency point 725 180 194 transversal transverse electron effective mass 226 transverse modes 708 traveling wave 166 tunneling 107 turn-on voltage 728 twin boundary 563 two-dimensional electrons 43 419, 750 type I type I1 750, 802 750 type I1 misaligned type I1 staggered 420 750 ultraviolet 766 umklapp processes .2 17 unit cell vacancy 553 554 555 650 vacuum deposition valence band 74 134 valence electrons 58 van der Pauw 542 607 van der Waals 67 68 vapor phase epitaxy 489 576 vapor pressure 482 403 vector potential Vegard's law 473 vertical cavity surface-emitting lasers 753 vibrational mode 184 567 voids Volmer-Weber 513 770 voltage responsivity volume defect .553 567 VPE 489 710 wave equation wavefunction 89 waveguide 708 710 wavenumber 97 166 wave-particle duality 87 wavevector 116 712 wet chemical etching 640 wet oxidation method 575 white noise 772 Wien's law 769 10 Wigner-Seitz cell wire bonding 656 work function 85 wurtzite 34 x-ray diffraction 522 x-ray lithography 627 x-ray photoelectron spectroscopy 530 Young's modulus .192 Zeeman energy 406 Zeeman splitting .404 Zener breakdown 350 682 Zener tunneling 351 zero point energy 162 zero point motion 162 zinc blende 30 ... Mass of a particle mo Electron rest mass m *, m , Electron effective mass Effective mass of holes, of heavy-holes, of light holes mh, mhh, mlh * m Reduced effective mass MV Solid. .. to the second edition of 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... the necessary material in the same volume, and this prompted me to write the first edition of a textbook on the Fundamentals of Solid State Engineering The book was primarily aimed at the undergraduate