Marius Grundmann The Physics of Semiconductors Marius Grundmann The Physics of Semiconductors An Introduction Including Devices and Nanophysics With 587 Figures, 6 in Color, and 36 Tables 123 Marius Grundmann Institut für Experimentelle Physik II Universität Leipzig Linnéstraße 5 04103 Leipzig e-mail: grundma nn@physik.uni-leipzig.de Library of Congress Control Number: 2006923434 ISBN-10 3-540-25370-X Springer Berlin Heidelberg New York ISBN-13 978-3-540-25370-9 Springer Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. 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Steinen-Broo, Pau/Girona, Spain Printed on acid-free paper 57/3100/YL 543210 To Michelle, Sophia Charlotte and Isabella Rose Preface Semiconductor devices are nowadays commonplace in every household. In the late 1940s the invention of the transistor was the start of a rapid development towards ever faster and smaller electronic components. Complex systems are built with these components. The main driver of this development was the economical benefit from packing more and more wiring, transistors and func- tionality on a single chip. Now every human is left with about 100 million transistors (on average). Semiconductor devices have also enabled economi- cally reasonable fiber-based optical communication, optical storage and high- frequency amplification and have only recently revolutionized photography, display technology and lighting. Along with these tremendous technological developments, semiconductors have changed the way we work, communicate, entertain and think. The technological sophistication of semiconductor ma- terials and devices is progressing continuously with a large worldwide effort in human and monetary capital, partly evolutionary, partly revolutionary embracing the possibilities of nanotechnology. For students, semiconductors offer a rich, diverse and exciting field with a great tradition and a bright future. This book is based on the two semester semiconductor physics course taught at Universit¨at Leipzig. The material gives the students an overview of the subject as a whole and brings them to the point where they can specialize and enter supervised laboratory research. For the interested reader some ad- ditional topics are included in the book that are taught in subsequent, more specialized courses. The first semester contains the fundamentals of semiconductor physics (Part I – Chaps. 1–17). Besides important aspects of solid-state physics such as crystal structure, lattice vibrations and band structure, semiconductor specifics such as technologically relevant materials and their properties, elec- tronic defects, recombination, hetero- and nanostructures are discussed. Semi- conductors with electric polarization and magnetization are introduced. The emphasis is put on inorganic semiconductors, but a brief introduction to or- ganic semiconductors is given in Chap. 16. In Chap. 17 dielectric structures are treated. Such structures can serve as mirrors, cavities and microcavities and are a vital part of many semiconductor devices. The second part (Part II – Chaps. 18–21) is dedicated to semiconduc- tor applications and devices that are taught in the second semester of the VIII Preface course. After a general and detailed discussion of various diode types, their applications in electrical circuits, photodetectors, solar cells, light-emitting diodes and lasers are treated. Finally, bipolar and field-effect transistors are discussed. The course is designed to provide a balance between aspects of solid-state and semiconductor physics and the concepts of various semiconductor devices and their applications in electronic and photonic devices. The book can be followed with little or no pre-existing knowledge in solid-state physics. I would like to thank several colleagues for their various contributions to this book, in alphabetical order (if no affiliation is given, from Universit¨at Leipzig): Klaus Bente, Rolf B¨ottcher, Volker Gottschalch, Axel Hoffmann (Technische Universit¨at Berlin), Alois Krost (Otto-von-Guericke Univer- sit¨at Magdeburg), Michael Lorenz, Thomas Nobis, Rainer Pickenhain, Hans- Joachim Queisser (Max-Planck-Institut f¨ur Festk¨orperforschung, Stuttgart), Bernd Rauschenbach (Leibniz-Institut f¨ur Oberfl¨achenmodifizierung, Leipzig), Bernd Rheinl¨ander, Heidemarie Schmidt, R¨udiger Schmidt-Grund, Mathias Schubert, Gerald Wagner, Holger von Wenckstern, Michael Ziese, and Gregor Zimmermann. Their comments, proof reading and graphic mate- rial improved this work. Also, numerous helpful comments from my students on my lectures and on preliminary versions of the present text are gratefully acknowledged. I am also indebted to many other colleagues, in particular to (in alphabetical order) Gerhard Abstreiter, Zhores Alferov, Levon Asryan, G¨unther Bauer, Manfred Bayer, Immanuel Broser, J¨urgen Christen, Laurence Eaves, Ulrich G¨osele, Alfred Forchel, Manus Hayne, Frank Heinrichsdorff, Fritz Henneberger, Detlev Heitmann, Robert Heitz † , Nils Kirstaedter, Fred Koch, Nikolai Ledentsov, Evgeni Kaidashev, Eli Kapon, Claus Klingshirn, J¨org Kotthaus, Axel Lorke, Anupam Madhukar, Bruno Meyer, David Mow- bray, Hisao Nakashima, Mats-Erik Pistol, Fred Pollak, Volker Riede, Hiroyuki Sakaki, Lars Samuelson, Vitali Shchukin, Maurice Skolnick, Oliver Stier, Robert Suris, Volker T¨urck, Konrad Unger, Victor Ustinov, Leonid Vorob’jev, Richard Warburton, Alexander Weber, Eicke Weber, Peter Werner, Ulrike Woggon, Roland Zimmermann and Alex Zunger, with whom I have worked closely, had enjoyable discussions with and who have posed questions that stimulated me. I reserve special thanks for Dieter Bimberg, who supported me throughout my career. I leave an extra niche – as the Romans did, in or- der not to provoke the anger of a God missed in a row of statues – for those who had an impact on my scientific life and that I have omitted to mention. Leipzig, January 2006 Marius Grundmann Contents Abbreviations XXI Symbols XXVII Physical Constants XXXI 1 Introduction 1 1.1 Timetable 1 1.2 NobelPrizeWinners 7 1.3 GeneralInformation 9 Part I Fundamentals 2 Bonds 15 2.1 Introduction 15 2.2 CovalentBonds 15 2.2.1 Electron-PairBond 15 2.2.2 sp 3 Bond 15 2.2.3 sp 2 Bond 19 2.3 Ionic Bonds 21 2.4 Mixed Bond 23 2.5 Metallic Bond 25 2.6 van-der-WaalsBond 26 2.7 Hamilton Operator oftheSolid 27 3 Crystals 29 3.1 Introduction 29 3.2 CrystalStructure 29 3.3 Lattice 30 3.3.1 UnitCell 30 3.3.2 Point Group 31 3.3.3 Space Group 33 3.3.4 2DBravaisLattices 34 3.3.5 3DBravaisLattices 34 3.3.6 Polycrystalline Semiconductors 39 XContents 3.3.7 Amorphous Semiconductors 39 3.4 ImportantCrystalStructures 40 3.4.1 Rocksalt Structure 41 3.4.2 CsClStructure 41 3.4.3 DiamondStructure 41 3.4.4 ZincblendeStructure 42 3.4.5 WurtziteStructure 43 3.4.6 ChalcopyriteStructure 45 3.4.7 DelafossiteStructure 46 3.4.8 Perovskite Structure 48 3.4.9 NiAsStructure 48 3.5 Polytypism 48 3.6 ReciprocalLattice 50 3.6.1 ReciprocalLatticeVectors 51 3.6.2 Miller Indices 52 3.6.3 Brillouin Zone 54 3.7 Alloys 54 3.7.1 RandomAlloys 55 3.7.2 Phase Diagram 57 3.7.3 VirtualCrystalApproximation 59 3.7.4 LatticeParameter 59 3.7.5 Ordering 61 4 Defects 63 4.1 Introduction 63 4.2 Point Defects 63 4.3 ThermodynamicsofDefects 65 4.4 Dislocations 67 4.5 StackingFaults 71 4.6 Grain Boundaries 72 4.7 Antiphase andInversionDomains 73 4.8 Disorder 76 5 Mechanical Properties 77 5.1 Introduction 77 5.2 LatticeVibrations 77 5.2.1 MonoatomicLinear Chain 77 5.2.2 Diatomic LinearChain 80 5.2.3 Lattice Vibrations of a Three-Dimensional Crystal . 84 5.2.4 Phonons 86 5.2.5 Localized VibrationalModes 87 5.2.6 PhononsinAlloys 89 5.2.7 Electric FieldCreatedby OpticalPhonons 91 5.3 Elasticity 94 5.3.1 Stress–Strain Relation 94 Contents XI 5.3.2 BiaxialStrain 99 5.3.3 Three-DimensionalStrain 100 5.3.4 Substrate Bending 102 5.3.5 Scrolling 103 5.3.6 Critical Thickness 105 5.4 Cleaving 109 6 Band Structure 111 6.1 Introduction 111 6.2 Bloch’sTheorem 111 6.3 Free-ElectronDispersion 112 6.4 Kronig–PenneyModel 114 6.5 ElectronsinaPeriodicPotential 116 6.5.1 Approximate Solution at the Zone Boundary 117 6.5.2 Solution in the Vicinity of the Zone Boundary 118 6.5.3 Kramer’s degeneracy 119 6.6 Band Structure of Selected Semiconductors 119 6.6.1 Silicon 119 6.6.2 Germanium 119 6.6.3 GaAs 119 6.6.4 GaP 120 6.6.5 GaN 120 6.6.6 LeadSalts 121 6.6.7 Chalcopyrites 122 6.6.8 Delafossites 123 6.6.9 Perovskites 123 6.7 Alloy Semiconductors 124 6.8 Amorphous Semiconductors 125 6.9 Systematics of Semiconductor Bandgaps 125 6.10 TemperatureDependence oftheBandgap 129 6.11 Equation ofElectronMotion 131 6.12 Electron Mass 132 6.12.1 EffectiveMass 132 6.12.2 PolaronMass 135 6.12.3 Nonparabolicity ofElectronMass 136 6.13 Holes 136 6.13.1 HoleConcept 136 6.13.2 HoleDispersionRelation 138 6.13.3 Valence-Band Fine Structure 140 6.14 StrainEffectonthe Band Structure 142 6.14.1 StraineffectonBandEdges 143 6.14.2 Strain Effect on Effective Masses 144 6.15 DensityofStates 144 6.15.1 GeneralBandStructure 144 6.15.2 Free-ElectronGas 145 XII Contents 7 Electronic Defect States 149 7.1 Introduction 149 7.2 FermiDistribution 149 7.3 CarrierConcentration 151 7.4 Intrinsic Conduction 153 7.5 ShallowImpurities,Doping 156 7.5.1 Donors 157 7.5.2 Acceptors 164 7.5.3 Compensation 167 7.5.4 AmphotericImpurities 170 7.5.5 HighDoping 171 7.6 Quasi-FermiLevels 174 7.7 DeepLevels 175 7.7.1 ChargeStates 176 7.7.2 Jahn–TellerEffect 177 7.7.3 Negative-U Center 178 7.7.4 DXCenter 180 7.7.5 EL2Defect 182 7.7.6 Semi-insulating Semiconductors 183 7.7.7 SurfaceStates 184 7.8 Hydrogen in Semiconductors 185 8 Transport 189 8.1 Introduction 189 8.2 Conductivity 190 8.3 Low-Field Transport 191 8.3.1 Mobility 191 8.3.2 Microscopic Scattering Processes 192 8.3.3 IonizedImpurityScattering 193 8.3.4 DeformationPotential Scattering 193 8.3.5 PiezoelectricPotentialScattering 194 8.3.6 PolarOpticalScattering 194 8.3.7 TemperatureDependence 194 8.4 HallEffect 197 8.5 High-FieldTransport 200 8.5.1 Drift-SaturationVelocity 200 8.5.2 VelocityOvershoot 201 8.5.3 ImpactIonization 202 8.6 High-FrequencyTransport 205 8.7 Diffusion 205 8.8 ContinuityEquation 206 8.9 Heat Conduction 207 8.10 CoupledHeatand ChargeTransport 209 8.10.1 SeebeckEffect 209 8.10.2 PeltierEffect 210 [...]... bipolar transistors and five resistors Initially, the invention of the integrated circuit5 met scepticism because of concerns regarding yield and the achievable quality of the transistors and the other components (such as resistors and capacitors) 1959 J Hoerni and R Noyce – first realization of a planar transistor (Fig 1.6) [29] 1960 D Kahng and M.M Atalla – first realization of a MOSFET [30] 1962 The first... m 1 Introduction The proper conduct of science lies in the pursuit of Nature’s puzzles, wherever they may lead J.M Bishop [1] The historic development of semiconductor physics and technology began in the second half of the 19th century In 1947, the realization of the transistor was the impetus to a fast-paced development that created the electronics and photonics industries Products founded on the. .. discoveries and inventions in the field of semiconductor physics (Fig 1.2) 1909 Karl Ferdinand Braun ‘in recognition of his contributions to the development of wireless telegraphy’ 1914 Max von Laue ‘for his discovery of the diffraction of X-rays by crystals’ 1915 Sir William Henry Bragg William Lawrence Bragg ‘for their services in the analysis of crystal structure by means of X-rays’ 6 www.nobel.se 8 1 Introduction. .. Davydov – theoretical prediction of rectification in Cu2 O [17] W Schottky – theory of the boundary layer in metal–semiconductor contacts [18], being the basis for Schottky contacts and field-effect transistors (FETs) 2 After obtaining his PhD in 1905 from the Friedrich-Wilhelms-Universit¨t a Berlin, J.E Lilienfeld joined the Physics Department of University of Leipzig and worked on gas liquification and with... nppnand pnnp-transistors (US patent 1,877,140, 1932) Fig 1.2 Sketch of a field-effect transistor, 1926 From [12] 1927 A Schleede and Baggisch – impurities are of decisive importance for conductivity 1931 R de L Kronig and W.G Penney – properties of periodic potentials in solids [13] A.H Wilson – development of band-structure theory [14] C Zener – Zener tunneling [15] 1936 J Frenkel – description of excitons... gold contact For the first time, amplification was observed [22] More details about the history and development of the semiconductor transistor can be found in [23], written on the occasion of the 50th anniversary of its invention Fig 1.4 The first transistor, 1947 (length of side of wedge: 32 mm) 1952 H Welker – fabrication of compound semiconductors [24] (Verfahren zur Herstellung eines Halbleiterkristalls... germanium (Fig 1.4) The one 3 Subsequently, AT&T, under pressure from the US Justice Department’s antitrust division, licensed the transistor for $25,000 This action initiated the rise of companies like Texas Instruments, Sony and Fairchild 1.1 Timetable 5 gold contact controls via the field effect (depletion of a surface layer) the current from Ge to the other gold contact For the first time, amplification... collector Fig 1.6 Planar pnp silicon transistor, 1959 The contacts are Al surfaces (not bonded) 1966 Zh.I Alferov – report of the first DH laser on the basis of GaInP at 77 K [34] C.A Mead – proposal of the MESFET (‘Schottky Barrier Gate FET’) [35] 1967 W.W Hooper and W.I Lehrer – first realization of a MESFET [36] 1968 DH laser on the basis of GaAs/AlGaAs at room temperature by Zh.I Alferov [37] and I Hayashi... the basis of semiconductor devices such as computers (CPUs, memories), optical-storage media (CD, DVD), communication infrastructure (optical-fiber technology, mobile communication) and lighting (LEDs) are commonplace Thus, fundamental research on semiconductors and semiconductor physics and its offspring in the form of devices has contributed largely to the development of modern civilization and culture... QW QWIP QWR quantum cascade laser quantum confined Stark effect quantum dot quantum Hall effect quantum well quantum-well intersubband photodetector quantum wire Abbreviations RAM RAS REI RF RGB RHEED RKKY rms ROM random access memory reflection anisotropy spectroscopy random element isodisplacement radio frequency red-green-blue (color system) reflection high-energy electron diffraction Ruderman–Kittel–Kasuya–Yoshida . Marius Grundmann The Physics of Semiconductors Marius Grundmann The Physics of Semiconductors An Introduction Including Devices and Nanophysics With 587 Figures, 6 in Color, and 36 Tables 123 Marius. are discussed. The course is designed to provide a balance between aspects of solid-state and semiconductor physics and the concepts of various semiconductor devices and their applications in electronic and. Universit¨at Leipzig. The material gives the students an overview of the subject as a whole and brings them to the point where they can specialize and enter supervised laboratory research. For the interested