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This page intentionally left blank Electronic and Optoelectronic Properties of Semiconductor Structures presents the underlying physics behind devices that drive today’s technologies The book covers important details of structural properties, bandstructure, transport, optical and magnetic properties of semiconductor structures Effects of low-dimensional physics and strain – two important driving forces in modern device technology – are also discussed In addition to conventional semiconductor physics the book discusses self-assembled structures, mesoscopic structures and the developing field of spintronics The book utilizes carefully chosen solved examples to convey important concepts and has over 250 figures and 200 homework exercises Real-world applications are highlighted throughout the book, stressing the links between physical principles and actual devices Electronic and Optoelectronic Properties of Semiconductor Structures provides engineering and physics students and practitioners with complete and coherent coverage of key modern semiconductor concepts A solutions manual and set of viewgraphs for use in lectures is available for instructors received his Ph.D from the University of Chicago and is Professor of Electrical Engineering and Computer Science at the University of Michigan, Ann Arbor He has held visiting positions at the University of California, Santa Barbara and the University of Tokyo He is the author of over 250 technical papers and of seven previous textbooks on semiconductor technology and applied physics Electronic and Optoelectronic Properties of Semiconductor Structures Jasprit Singh University of Michigan, Ann Arbor Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo Cambridge University Press The Edinburgh Building, Cambridge , United Kingdom Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridge.org/9780521823791 © Cambridge University Press 2003 This book is in copyright Subject to statutory exception and to the provision of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press First published in print format 2003 - - ---- eBook (NetLibrary) --- eBook (NetLibrary) - - ---- hardback --- hardback Cambridge University Press has no responsibility for the persistence or accuracy of s for external or third-party internet websites referred to in this book, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate CONTENTS PREFACE xiii INTRODUCTION xiv I.1 SURVEY OF ADVANCES IN SEMICONDUCTOR PHYSICS I.2 PHYSICS BEHIND SEMICONDUCTORS xvi I.3 xiv ROLE OF THIS BOOK xviii STRUCTURAL PROPERTIES OF SEMICONDUCTORS 1.1 INTRODUCTION 1.2 CRYSTAL GROWTH 1.2.1 Bulk Crystal Growth 1.2.2 Epitaxial Crystal Growth 1.2.3 Epitaxial Regrowth 2 1.3 CRYSTAL STRUCTURE 1.3.1 Basic Lattice Types 1.3.2 Basic Crystal Structures 1.3.3 Notation to Denote Planes and Points in a Lattice: Miller Indices 1.3.4 Artificial Structures: Superlattices and Quantum Wells 1.3.5 Surfaces: Ideal Versus Real 1.3.6 Interfaces 1.3.7 Defects in Semiconductors 10 12 15 16 21 22 23 24 vi Contents 1.4 26 1.5 STRAINED TENSOR IN LATTICE MISMATCHED EPITAXY 32 1.6 POLAR MATERIALS AND POLARIZATION CHARGE 35 1.7 TECHNOLOGY CHALLENGES 41 1.8 PROBLEMS 41 1.9 STRAINED HETEROSTRUCTURES REFERENCES 44 SEMICONDUCTOR BANDSTRUCTURE 46 2.1 INTRODUCTION 46 2.2 BLOCH THEOREM AND CRYSTAL MOMENTUM 2.2.1 Significance of the k-vector 47 49 2.3 METALS, INSULATORS, AND SEMICONDUCTORS 51 2.4 TIGHT BINDING METHOD 2.4.1 Bandstructure Arising From a Single Atomic s-Level 2.4.2 Bandstructure of Semiconductors 54 57 60 2.5 SPIN-ORBIT COUPLING 2.5.1 Symmetry of Bandedge States 62 68 2.6 ORTHOGONALIZED PLANE WAVE METHOD 70 2.7 PSEUDOPOTENTIAL METHOD 71 2.8 k • p METHOD 74 2.9 SELECTED BANDSTRUCTURES 80 2.10 MOBILE CARRIERS: INTRINSIC CARRIERS 84 2.11 DOPING: DONORS AND ACCEPTORS 2.11.1 Carriers in Doped Semiconductors 2.11.2 Mobile Carrier Density and Carrier Freezeout 2.11.3 Equilibrium Density of Carriers in Doped Semiconductors 2.11.4 Heavily Doped Semiconductors 92 95 96 97 99 2.12 TECHNOLOGY CHALLENGES 102 2.13 PROBLEMS 104 2.14 REFERENCES 107 vii Contents 109 3.1 BANDSTRUCTURE OF SEMICONDUCTOR ALLOYS 3.1.1 GaAs/AlAs Alloy 3.1.2 InAs/GaAs Alloy 3.1.3 HgTe/CdTe Alloy 3.1.4 Si/Ge Alloy 3.1.5 InN, GaN, AlN System 109 113 113 116 117 117 3.2 BANDSTRUCTURE MODIFICATIONS BY HETEROSTRUCTURES 3.2.1 Bandstructure in Quantum Wells 3.2.2 Valence Bandstructure in Quantum Wells 118 119 123 3.3 SUB-2-DIMENSIONAL SYSTEMS 124 3.4 STRAIN AND DEFORMATION POTENTIAL THEORY 3.4.1 Strained Quantum Wells 3.4.2 Self-Assembled Quantum Dots 129 137 140 3.5 POLAR HETEROSTRUCTURES 142 3.6 TECHNOLOGY ISSUES 145 3.7 PROBLEMS 145 3.8 BANDSTRUCTURE MODIFICATIONS REFERENCES 149 TRANSPORT: GENERAL FORMALISM 152 4.1 INTRODUCTION 152 4.2 BOLTZMANN TRANSPORT EQUATION 4.2.1 Diffusion-Induced Evolution of fk(r) 4.2.2 External Field-Induced Evolution of fk(r) 4.2.3 Scattering-Induced Evolution of fk(r) 153 155 156 156 4.3 AVERAGING PROCEDURES 163 4.4 TRANSPORT IN A WEAK MAGNETIC FIELD: HALL MOBILITY 165 4.5 SOLUTION OF THE BOLTZMANN TRANSPORT EQUATION 4.5.1 Iterative Approach 168 168 4.6 BALANCE EQUATION: TRANSPORT PARAMETERS 169 4.7 TECHNOLOGY ISSUES 175 4.8 PROBLEMS 176 4.9 REFERENCES 177 viii Contents DEFECT AND CARRIER–CARRIER SCATTERING 179 5.1 IONIZED IMPURITY SCATTERING 181 5.2 ALLOY SCATTERING 191 5.3 NEUTRAL IMPURITY SCATTERING 194 5.4 INTERFACE ROUGHNESS SCATTERING 196 5.5 CARRIER–CARRIER SCATTERING 5.5.1 Electron–Hole Scattering 5.5.2 Electron–Electron Scattering: Scattering of Identical Particles 198 198 201 5.6 205 5.7 PROBLEMS 213 5.8 AUGER PROCESSES AND IMPACT IONIZATION REFERENCES 214 LATTICE VIBRATIONS: PHONON SCATTERING 217 6.1 LATTICE VIBRATIONS 217 6.2 PHONON STATISTICS 6.2.1 Conservation Laws in Scattering of Particles Involving Phonons 223 6.3 POLAR OPTICAL PHONONS 225 6.4 PHONONS IN HETEROSTRUCTURES 230 6.5 PHONON SCATTERING: GENERAL FORMALISM 231 6.6 LIMITS ON PHONON WAVEVECTORS 6.6.1 Intravalley Acoustic Phonon Scattering 6.6.2 Intravalley Optical Phonon Scattering 6.6.3 Intervalley Phonon Scattering 237 238 239 240 6.7 ACOUSTIC PHONON SCATTERING 241 6.8 OPTICAL PHONONS: DEFORMATION POTENTIAL SCATTERING 243 6.9 OPTICAL PHONONS: POLAR SCATTERING 246 6.10 INTERVALLEY SCATTERING 251 224 Appendix D: Important Properties of Semiconductors 521 108 CARRIER DRIFT VELOCITY (cm/s) Ga0.47In0.53As InP GaAs 107 Ge Ge Ga0.47In0.53As 106 Si Electrons Holes 105 102 103 104 105 ELECTRIC FIELD (V/cm) Figure D.3: Velocity-Field relations for several semiconductors at 300 K 106 522 Appendix D: Important Properties of Semiconductors BREAKDOWN ELECTRIC FIELDS IN SEMICONDUCTORS MATERIAL BANDGAP (eV) BREAKDOWN ELECTRIC FIELD(V/cm) GaAs 1.43 x 105 Ge 0.664 105 InP 1.34 Si 1.1 x 105 In0.53Ga0.47As 0.8 x 105 C 5.5 107 SiC 2.9 SiO2 107 Si3N4 107 − x 10 Table D.5: Breakdown electric fields in some semiconductors Appendix D: Important Properties of Semiconductors 523 F (105 V/cm) 10 106 2.5 10 300 K Electrons αimp Holes βimp InP (Eg = 1.35 eV) IONIZATION (cm− 1) 105 IMPACT 2.5 GaAs (1.42 eV) Ge (Eg = 0.66 eV) 104 In0.53Ga0.47As (0.75 eV) 103 Si (1.12 eV) 102 101 8 1/F (10− cm/V) (a) (b) Figure D.4: Ionization rates for electrons and holes at 300 K versus reciprocal electric field for Ge, Si, GaAs, In0.53 Ga0.47 and InP (Si, Ge results are after S.M Sze, Physics of Semiconductor Devices, John Wiley and Sons (1981); InP, GaAs, InGaAs results are after G Stillman, Properties of Lattice Matched and Strained Indium Gallium Arsenide, ed P Bhattacharya, INSPEC, London (1993) 524 Appendix D: Important Properties of Semiconductors PHOTON ENERGY 1.5 (eV) 0.7 106 Ge ABSORPTION COEFFICIENT (cm− 1) 105 Ga0.3In0.7As0.64P0.36 InGaAs GaAs 104 InP Si 103 GaP 102 Amorphous Si 10 0.2 0.6 1.4 1.8 WAVELENGTH (µm) Figure D.5: Absorption coefficient as a function of wavelength for several semiconductors Appendix D: Important Properties of Semiconductors MATERIAL b d (eV) (eV) (10 − 12 525 dEg/dp Ξu eV cm 2/dyne) (eV) Si − 1.50 300 K − 3.40 300 K Ge − 2.20 300 K − 4.40 300 K AlSb − 1.35 77 K − 4.30 77 K − 3.50 77 K 6.2 300 K GaP − 1.30 80 K − 4.00 80 K − 1.11 300 K 6.2 80 K GaAs − 2.00 300 K − 6.00 300 K 11.70 300 K GaSb − 3.30 77 K − 8.35 77 K 14.00 300 K InP − 1.55 77 K − 4.40 77 K 4.70 300 K InAs InSb − 1.41 300 K 9.2 295 K 5.00 300 K 15.9 297 K 10.00 300 K − 2.05 80 K − 5.80 80 K − 16.00 300 K Table D.6: Strain parameters of some semiconductors The temperature is specified 526 Appendix D: Important Properties of Semiconductors Material Auger Coefficient (cm6s − 1) Comments In0.53Ga0.47As ~10− 28 at 300 K For a compilation of results in the literature, see J Shah in "Indium Gallium Arsenide," ed P Bhattacharya, INSPEC, London (1992) GaInAsP ~6 x 10− 28 at Eg = 0.8 eV at 300 K Based on work of A Sugimura, Quantum Electronics, QE-18, 352 (1982) ~1.2 x 10− 27 at Eg = 0.7 eV at 300 K GaInAsSb ~6 x 10 − 27 at Eg = 0.4 eV at 300 K Table D.7: Auger coefficients of some semiconductors Considerable uncertainty still exists in the Auger coefficients The values given are only rough estimates Index Absorption coefficient, 360 Absorption coefficient, in indirect semiconductors, 364 Acceptor level, 94 Acoustic phonon, mobility, 262 Acoustic waves, 221 Affinity rule, 118 Aharonov–Bohm effect, 457 Alloy scattering, 243 Alloy, GaAs/AlAs, 113 Alloy, HgTe/CdTe, 116 Alloy, InAs/GaAs, 113 Alloy, InN/GaN,AlN, 114 Alloy, phase separated, 110 Alloy, random, 110 Alloy, scattering rate, 193 Alloy, Si/Ge, 117 Alloy, superlattice, 110 Auger coefficient, 210 Auger processes, 205, 382 Averaging procedures for scattering time, 163 Balance equation, 174, 292 Ballistic transport, 290 Band, tailing, 101 Band lineups in heterostructures, 118 Bandedge, strain splitting of in SiGe alloys, 138 Bandedge states, 68 Bandgap, narrowing, 101, 395 Bandgap, optical, 101 Bandgap, strain effects, 137 Bandgap, temperature dependence of, 86 Bandstructure, effects on devices, 103 Bandstructure, in quantum wells, 119 Bandstructure, of AlAs, 83 of GaAs, 62, 67, 82 of Ge, 83 of nitrides, 84 Bandstructure, Kohn–Luttinger formalism, 77 Bandstructure, k · p method for, 74 Bandstructure, of Si, 80 Bandstructure, of alloys, 111 Bandstructure, orthogonalized plane wave (OPW) method for, 70 Bandstructure, pseudopotential method for, 71 Bandstructure, self–assembled structures, 140 Bandstructure, Slater–Koster method for, 61 Bandstructure, spin–orbit effect, 62 Bandstructure in strained structures, 129 Bandstructure, strained SiGe, 138 Bandstructure, tight–binding method, 54 Bandstructure, valence band, in strained quantum wells, 138 Bandstructure, valence, in quantum wells, 123, 138 Bandtail states, 101 Basis, 11 Binding energy of crystals, 218 Bloch function, 49 Bloch oscillations, 313 Bloch theorem, 47 Body centered cubic (bcc) lattice, 14 Boltzmann, transport equation, 153 Boltzmann, transport equation, numerical techniques, 168 Bound state problem, 511 Bowing effect in alloys, 112 528 Bragg’s law, 484 Breakdown, in devices, 296 Bridgeman technique, Brillouin zone, 59 Bulk crystal growth, Carrier, extrinsic, 95 Carrier, freezeout, 96 Carrier temperature, 174 Clebsch–Gordan coefficients, 65 Coherent structures, 27 Conduction bandedge states, 64 Conduction, hopping, 334 Critical thickness, 28 Crystal, binding, 218 Crystal growth, bulk, epitaxial, Crystal, restoring force, 219 Crystal structure, 10 Curie temperature, 40 Cutoff wavelength, 116 Cyclotron frequency, 443 Cyclotron mass, 445 Czochralski technique, Defect, cross–section, 381 Defect, interstitial, 26 Defect, substitutional, 26 Defects, 24 Deformation potential theory, 129 Density of states, 84, 127 Density of states, effective, 86 Density of states, in 2D systems, 121, 127, 502 Density of states, in one dimension, 127, 502 Density of states, in semiconductors, 499 Density of states, in three dimensions, 84, 500 Diamond lattice, 15 Dielectric response, 182 Diffusion, coefficient, 172, 488 Diffusion processes, 155 Dislocation generation, 28 Dislocation content, 486 Index Disordered semiconductors, 324 extended states, 326 localized states, 326 Disordered system, transport, 329 Donor, energy levels, 92, 100 Doping, 92 Doping, heavy, 99 Effective charge, 227, 247 Effective mass, 76 Effective mass, conductivity, 94 Effective mass, equation, 77 Effective mass, in k · p method, 76 Effective mass, strain effects, 139 Elastic collisions, 160 Elastic constants, 480 Elastic strain, 478 Electric fields, built-in, from strained epitaxy, 36, 143 Electro-optic effect, 421 Electron–electron scattering, 205 Electron–hole scattering, 198 Electrons, in a magnetic field, quantum theory, 451 Electrons, in a magnetic field, semiclassical dynamics, 441 Energy, elastic strain, 481 Epitaxial crystal growth, Epitaxial regrowth, Epitaxy, coherent, 27 Epitaxy, incoherent, 27 Epitaxy, lattice matched and dislocations, 28 Equation of motion, for k, 50 Exciton, 403 Exciton, absorption in quantum wells, 415 Exciton, absorption spectra, 408 Exciton, absorption spectra, in GaAs, 413 Exciton, binding energy, 405 Exciton, broadening effects, 416 homogeneous, 416 inhomogeneous, 416 Exciton, Frenkel, 404 Index Exciton, in magnetic field, 467 Exciton, in quantum wells, 413 Exciton, Mott, 404 Exciton, quenching, 432 Exciton, temperature dependence, 417 Extrinsic carriers, 95 Face centered cubic (fcc) lattice, 14 Fermi energy, 86 Fermi, Golden Rule, 509 Fermi–Dirac distribution, 86, 95 Ferroelectric materials, 39 Flux for crystal growth, Free carriers, 95 Freezeout, carrier, 96 Gain in a semiconductor, 378 Group velocity, for lattice vibrations, 220 Hall, coefficient, 449 Hall, effect, 166, 460, 490 Hall, factor, 167, 447 Hall, mobility, 167, 447, 487 Haynes–Shockley experiment, 488 Heavy hole states, 69 Heterointerface polar charge, 35 Heterostructures, bandlineup, 118 Hexagonal close packed (hcp) structure, 15 High symmetry points in k-space, 59 Holes, 53 Hole, effective mass, 53 Hole, energy, 53 Hole, equation of motion, 53 Hole, momentum, 53 Hopping conductivity, 334 Hysterisis loop for ferroelectrics, 39 Ideal surfaces, 22 Identical particle scattering, 201 Impact ionization, 212, 295 Impact ionization, coefficient, 296 Impact ionization, threshold, 212 Impurity, scattering, 194 InAs/GaAs dots, 31 Inelastic collisions, 162 529 Insulators, simple description, 51 Interband transitions, bulk semiconductors, 359 Interband transitions, quantum wells, 361 Interface roughness, 23 Interface roughness, scattering, 196 Interfaces, 23 Interference, quantum, 323 Intervalley scattering, 251 Intraband transitions, in quantum wells, 370 Intraband transitions, 370 Intrinsic carriers, 85, 89 Ionized impurity scattering, 181, 187 Joyce–Dixon approximation, 95 k-vector, significance of, 49 k · p method for bandstructure, 74 Kohn–Luttinger Hamiltonian, 77, 123 Kramers–Kronig relation, 350 Kubo formalism for transport, 330 Landau levels, density of states, 455 Landau levels, 454 Landau levels, magneto-optics, 465 Laser diode, 387 Laser, optical confinement, 389 Laser, threshold, 390 Lattice, 11 Lattice constant, for selected semiconductors, 18 Lattice types, 11 Lattice vibrations, 219 Law of mass action, 88 Light emitting diode, 386 Light hole states, 69 Liquid phase epitaxy, Localized states, 326, 464 Longitudinal optical phonons, 227 Lorentz gauge, 347 Magnetic semiconductors, 469 Magnetoresistance, 449 Magnetotransport, semiclassical theory, 447 530 Mass action, law of, 88 Material parameters, for transport in Si and GaAs, 278 Maxwell equations, 346 Mesoscopic structures, 334 Metal-organic chemical vapor deposition (MOCVD), Metals, simple description, 51 Miller indices, 16 Mobility, 159 Mobility, edge, 326 Mobility, Hall, 166 Mobility, in GaAs, 189, 190, 262 Mobility, in Si, 190, 262 Mobility, in modulation doped structures, 189 Mobility, in selected semiconductors, 264 Molecular beam epitaxy (MBE), Monte Carlo method, 264 Monte Carlo, injection of carriers, 266 Monte Carlo, scattering times, 269 Monte Carlo, transport simulation, 264 Mott conductivity model, 332 Negative resistance, 318 in resonant tunneling, 318 in GaAs, 289 Newton’s equation of motion, 50 Nitrides, spontaneous polarization, 36 bandstructure, 84 optical properties, 431 piezoelectric effect, 37 Non–parabolic band, 212 Non–radiative processes, 381 Optical confinement, 389 Optical interband transitions, 358 Optical lattice vibrations, 221 Optical phonon, scattering, 245 Optical polarization, selection rules, 358 Optical processes, selection rules, 358 Orthogonalized plane wave method, 70 Perturbation theory, 504 Phonons, 223 Phonon, acoustic scattering, 243 Index Phonon, conservation laws for scattering, 224 Phonon, dispersion, 222 Phonon, in heterostructures, 230 Phonon, interface, 230 Phonon, intervalley scattering rate, 251 Phonon, optical mode, 221 Phonon, optical scattering, 245 Phonon, polar optical, 225 Phonon, polar optical scattering, 246 Phonon scattering, 237 Phonon, scattering, intervalley, 251 Phonon, scattering, limits on wavevectors, 238 Phonon, statistics, 223 Photon, absorption rate, 360 Photoluminescence, 490 Piezoelectric effect, 36, 144 Plasma, frequency, 253 Plasmon, scattering, 252 Polar charge at interfaces, 35, 144 Polar materials, 35, 431 Polar heterostructures, band profile, 143 Potential, screened Coulomb, 181 Poynting vector, 348 Pseudopotential method, 71 Quantum confined Stark effect, 426 Quantum dots, 126 optical transitions, 374 transport, 304 Quantum Hall effect, 460 Quantum interference, 323, 458 Quantum wells, 121, 123 bandstructure, 121, 123 optical transitions, 363 structure, 21 transport, 299 Quantum wire, 126 transport, 303 Radiative lifetime, 379 Radiative transitions, recombination time, 376 Refractive index, 349 Index Regrowth of crystals, Relaxation time, alloy scattering, 193 approximation, 158 averaging procedure, 163 ionized impurity, 187 Resonant tunneling, 316 Resonant tunneling, current in an RTD, 322 Restoring force, crystal, 219 Scattering, acoustic phonon, 243 Scattering, alloy, 193 Scattering, electron–electron, 205 Scattering, electron–hole, 198 Scattering, f and g in Si, 240 Scattering, identical particle, 201 Scattering, interface roughness, 196 Scattering, intervalley in GaAs, 251 Scattering, intervalley phonon, 251 Scattering, ionized impurity, 187 Scattering, phonon, 237 Scattering, plasmon, 252 Scattering, polar optical phonon, 246 Scattering, rate, acoustic phonon, 280 Scattering, rate, alloy, 277 Scattering, rate, intervalley, 280 Scattering, rate, ionized impurity, 187, 274 Scattering, rate, polar optical phonon, 277 Scattering, time, 158 Schockley, Read, Hall recombination, 381 Screened Coulomb potential, 181 Screening, length, 183 Screening, of impurity level, 99 Second quantization, phonons, 233 photons, 353 Selection rules, 358 Self-assembled structures, 30 bandstructure, 140 Self-scattering, 271 Semiconductor material properties, 514 Semiconductors, simple description, 51 Simple cubic lattice, 14 Soret, coefficient, 172 531 Spin–orbit coupling, 62 Spin–orbit splitting, 66 Spin selection, optical, 470 electrical, 471 Spintronics, 469 Split gate transistor, 325 Spontaneous emission rate, 355, 376 Spontaneous polarization, 37 Statistics, phonon, 223 Stimulated emission, 355 Strain, Hamiltonian, 129 Strain splitting of bandedge, in SiGe alloys, 138 Strain tensor, for self-assembled dots, 33 Strain tensor, in epitaxy, 32 Strained heterostructures, 26, 138 Stranski Krastanow growth, 31 Superlattice structure, 21 Surfaces, ideal and real, 22 Surface reconstruction, 22 Temperature, electron in transport, 293 Tight binding matrix elements, 56 Tight binding method (TBM), 54 Tight binding method, for the s-band, 57 Time of flight measurement, 488 Topics for a couse, xix Transport, averaging procedures, 163 Transport, in GaAs and Si, 190 Transport, Hall, 165 Transport, high field, in GaAs, 288 Transport, high field in Si, 291 Transport, overview, 180 Transport, in quantum dots, 304 Transport, in quantum wells, 298 Transport, in quantum wires, 303 Transport, simulation by Monte Carlo, 264 Transport, transient, electron in GaAs, 290 Trapping, by deep levels, 381 Tunneling, in heterostructures, 320 Variable range hopping, 334 532 Vector potential, 346 Vegard’s law, 111 Velocity overshoot, 290 Vertical transitions, 357 Vibration, crystal with diatomic basis, 219 Virtual crystal approximation, 111 Volmer Weber growth, 31 X-ray diffraction, 484 Zener–Bloch oscillations, 313 Zinc–blende structure, 15 Index Golden Land Travel - Photo Gallery Myanmar Cities Guide Historical Information Facts and Figures Must Know Ya n gon Photo Gallery Embassy Shwedagon Novitation Ceremony Karaweik Royal Barge Myanmar Traditonal Regatta Thingyan Festival Memorial Cemetry Young 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Electronic and Optoelectronic Properties of Semiconductor Structures provides engineering and physics students and practitioners with complete and coherent coverage of key modern semiconductor. .. seven previous textbooks on semiconductor technology and applied physics Electronic and Optoelectronic Properties of Semiconductor Structures Jasprit Singh University of Michigan, Ann Arbor ... transport and optical properties of semiconductors and their heterostructures; and iv) behavior of electrons in small and disordered structures As much as possible I have attempted to relate semiconductor