Graduate Texts in Physics

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1 Graduate Texts in Physics

2 Graduate Texts in Physics Graduate Texts in Physics publishes core learning/teaching material for graduate- and advanced-level undergraduate courses on topics of current and emerging fields within physics, both pure and applied. These textbooks serve students at the MS- or PhD-level and their instructors as comprehensive sources of principles, definitions, derivations, experiments and applications (as relevant) for their mastery and teaching, respectively. International in scope and relevance, the textbooks correspond to course syllabi sufficiently to serve as required reading. Their didactic style, comprehensiveness and coverage of fundamental material also make them suitable as introductions or references for scientists entering, or requiring timely knowledge of, a research field. Series Editors Professor William T. Rhodes Florida Atlantic University Department of Computer and Electrical Engineering and Computer Science Imaging Science and Technology Center 777 Glades Road SE, Room 456 Boca Raton, FL33431, USA wrhodes@fau.edu Professor H. Eugene Stanley Boston University Center for Polymer Studies Department of Physics 590 Commonwealth Avenue, Room 204B Boston, MA 02215, USA hes@bu.edu Professor Richard Needs Cavendish Laboratory JJ Thomson Avenue Cambridge CB3 ohe, UK rn11@cam.ac.uk For further volumes:

3 Marius Grundmann The Physics of Semiconductors An Introduction Including Nanophysics and Applications Second Edition With 247 Figures 123

4 Prof. Dr. Marius Grundmann Universität Leipzig Inst.f.ExperimentellePhysikII AG Halbleiterphysik Linnéstr Leipzig Germany grundmann@physik.uni-leipzig.de ISSN e-issn ISBN e-isbn DOI / Springer Heidelberg Dordrecht London New York Library of Congress Control Number: c Springer-Verlag Berlin Heidelberg 2010 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. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: estudio Calamar S.L., Heidelberg Printed on acid-free paper Springer is part of Springer Science+Business Media (

5 To Michelle, Sophia Charlotte and Isabella Rose

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7 Preface Semiconductor electronics is commonplace in every household. Semiconductor devices have also enabled economically reasonable fiber-based optical communication, optical storage and high-frequency amplification and have 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 progress of semiconductor materials and devices is evolving continuously with a large worldwide effort in human and monetary capital. For students, semiconductors offer a rich, diverse and exciting field with a great tradition and a bright future. This book introduces students to semiconductor physics and semiconductor devices. It brings them to the point where they can specialize and enter supervised laboratory research. It is based on the two semester semiconductor physics course taught at Universität Leipzig in its Master of Science physics curriculum. Since the book can be followed with little or no pre-existing knowledge in solid-state physics and quantum mechanics, it is also suitable for undergraduate students. For the interested reader some additional topics are included in the book that can be covered in subsequent, more specialized courses. The material is selected to provide a balance between aspects of solid-state and semiconductor physics, the concepts of various semiconductor devices and modern applications in electronics and photonics. The first semester contains the fundamentals of semiconductor physics (Part I, Sects. 1 10) and selected topics from Part II (Sects ). 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, electronic defects, recombination, hetero- and nanostructures are discussed. Semiconductors with electric polarization and magnetization are introduced. The emphasis is put on inorganic semiconductors, but a brief introduction to organic semiconductors is given in Sect. 16. Dielectric structures (Sect. 18) serve as mirrors, cavities and microcavities and are a vital part of many semiconductor devices. Other sections give introductions to carbon-based nanostructures and transparent conductive oxides (TCOs). The third part (Part III Sects ) is dedicated to semiconductor applications and devices that are taught in the second semester of the course. After a general and detailed discussion of VII

8 VIII Preface various diode types, their applications in electrical circuits, photodetectors, solar cells, light-emitting diodes and lasers are treated. Finally, bipolar and field-effect transistors including thin film transistors are discussed. In the present text of the second edition a few errors and misprints of the first edition have been corrected. Many topics have been extended and are treated in more depth, e.g. dopant diffusion, partial dislocations, etching of semiconductors, double donors/acceptors, excess charge carrier profiles, direct transitions in germanium, alloy broadening, nanowires, recombination in organic semiconductors, depletion layers beyond the abrupt approximation, Schottky diodes with inhomogeneous barrier, multi-junction solar cells, quantum dot and organic LEDs, LED degradation, strained channel transistors, MOSFET scaling, memory concepts and thin film transistors. The two chapters on carbon-based nanostructures and transparent conductive oxides have been added. The number of references has been doubled with respect to the first edition. The references have been selected to (i) cover important historical and milestone papers, (ii) direct to reviews and topical books for further reading and (iii) give access to current literature and up-to-date research. In Fig. 1, the almost 1500 references in this book are shown by year. Roughly three phases of semiconductor physics and technology can be seen. Before the realization of the first transistor in 1947, only a few publications are noteworthy. Then an intense phase of understanding the physics of semiconductors and developing semiconductor technology and devices based on bulk semiconductors (mostly Ge, Si, GaAs) followed. At the end of the 1970s, a new era began with the advent of quantum wells and heterostructures, and later nanostructures (nanotubes, nanowires and quantum dots) and new materials (e.g. organic semiconductors, nitrides or graphene). Fig. 1. Histogram of references in this book

9 Preface IX I would like to thank several colleagues for their various contributions to this book, in alphabetical order (if no affiliation is given, from Universität Leipzig): Gabriele Benndorf, Klaus Bente, Rolf Böttcher, Matthias Brandt, Christian Czekalla, Christof Peter Dietrich, Pablo Esquinazi, Heiko Frenzel, Volker Gottschalch, Helena Hilmer, Axel Hoffmann (TU Berlin), Alois Krost (Otto-von-Guericke Universität Magdeburg), Alexander Lajn, Michael Lorenz, Thomas Nobis, Rainer Pickenhain, Hans-Joachim Queisser (Max- Planck-Institut für Festkörperforschung, Stuttgart), Bernd Rauschenbach (Leibniz-Institut für Oberflächenmodifizierung, Leipzig), Bernd Rheinländer, Heidemarie Schmidt, Mathias Schmidt, Rüdiger Schmidt-Grund, Matthias Schubert, Jan Sellmann, Oliver Stier (TU Berlin), Chris Sturm, Gerald Wagner, Holger von Wenckstern, Michael Ziese, and Gregor Zimmermann. Their comments, proof reading, experimental data and graphic material improved this work. Also, numerous helpful comments from my students on my lectures and the first edition of this book are gratefully acknowledged. I am also indebted to many other colleagues, in particular to (in alphabetical order) Gerhard Abstreiter, Zhores Alferov, Levon Asryan, Günther Bauer, Manfred Bayer, Friedhelm Bechstedt, Dieter Bimberg, Fernando Briones, Immanuel Broser, Jürgen Christen, Laurence Eaves, Ulrich Gösele, Alfred Forchel, Manus Hayne, Frank Heinrichsdorff, Fritz Henneberger, Detlev Heitmann, Robert Heitz, Evamarie Hey-Hawkins, Evgeni Kaidashev, Eli Kapon, Nils Kirstaedter, Claus Klingshirn, Fred Koch, Jörg Kotthaus, Nikolai Ledentsov, Axel Lorke, Anupam Madhukar, Ingrid Mertig, Bruno Meyer, David Mowbray, Hisao Nakashima, Jörg Neugebauer, Mats-Erik Pistol, Fred Pollak, Volker Riede, Hiroyuki Sakaki, Lars Samuelson, Vitali Shchukin, Maurice Skolnick, Robert Suris, Volker Türck, Konrad Unger, Victor Ustinov, Leonid Vorob jev, Richard Warburton, Alexander Weber, Eicke Weber, Peter Werner, Ulrike Woggon, Roland Zimmermann, Alex Zunger and Jesus Zúñiga-Pérez with whom I have worked closely, had enjoyable discussions with and who have posed questions that stimulated me. Leipzig, April 2010 Marius Grundmann

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11 Contents 1 Introduction Timetable Nobel Prize Winners General Information Part I Fundamentals 2 Bonds Introduction Covalent Bonds Electron-Pair Bond sp 3 Bonds sp 2 Bonds Ionic Bonds Mixed Bonds Metallic Bonding van-der-waals Bonds Hamilton Operator of the Solid Crystals Introduction Crystal Structure Lattice Unit Cell Point Group Space Group D Bravais Lattices D Bravais Lattices Polycrystalline Semiconductors Amorphous Semiconductors Important Crystal Structures Rocksalt Structure CsCl Structure Diamond Structure XI

12 XII Contents Zincblende Structure Wurtzite Structure Chalcopyrite Structure Fluorite Structure Delafossite Structure Perovskite Structure NiAs Structure Further Structures Polytypism Reciprocal Lattice Reciprocal Lattice Vectors Miller Indices Brillouin Zone Alloys Random Alloys Phase Diagram Virtual Crystal Approximation Lattice Parameter Ordering Defects Introduction Point Defects Point Defect Types Thermodynamics Diffusion Dopant Distribution Large Concentration Effects Dislocations Dislocation Types Visualization of Dislocations by Etching Impurity Hardening Extended Defects Micro-cracks Stacking Faults Grain Boundaries Antiphase and Inversion Domains Disorder Mechanical Properties Introduction Lattice Vibrations Monoatomic Linear Chain Diatomic Linear Chain Lattice Vibrations of a Three-Dimensional Crystal. 110

13 Contents XIII Density of States Phonons Localized Vibrational Modes Phonons in Alloys Electric Field Created by Optical Phonons Elasticity Thermal Expansion Stress Strain Relation Biaxial Strain Three-Dimensional Strain Substrate Bending Scrolling Critical Thickness Cleaving Band Structure Introduction Electrons in a Periodic Potential Bloch s Theorem Free-Electron Dispersion Kronig Penney Model Lattice Vector Expansion Kramer s degeneracy Band Structure of Selected Semiconductors Silicon Germanium GaAs GaP GaN Lead Salts Chalcopyrites Delafossites Perovskites Alloy Semiconductors Amorphous Semiconductors Systematics of Semiconductor Band Gaps Temperature Dependence of the Band Gap Electron Dispersion Equation of Electron Motion Effective Mass of Electrons Polaron Mass Nonparabolicity of Electron Mass Holes Hole Concept Hole Dispersion Relation Valence-Band Fine Structure

14 XIV Contents 6.10 Strain Effect on the Band Structure Strain Effect on Band Edges Strain Effect on Effective Masses Interaction with a Localized Level Density of States General Band Structure Free-Electron Gas Electronic Defect States Introduction Fermi Distribution Carrier Concentration Intrinsic Conduction Shallow Defects Donors Acceptors Compensation Multiple Impurities Amphoteric Impurities High Doping Quasi-Fermi Levels Deep Levels Charge States Double Donors Double Acceptors Jahn Teller Effect Negative-U Center DX Center EL2 Defect Semi-insulating Semiconductors Isoelectronic Impurities Surface States Hydrogen in Semiconductors Transport Introduction Conductivity Low-Field Transport Mobility Microscopic Scattering Processes Ionized Impurity Scattering Deformation Potential Scattering Piezoelectric Potential Scattering Polar Optical Scattering Dislocation Scattering

15 Contents XV Grain Boundary Scattering Temperature Dependence Doping Dependence Piezoresistivity Hall Effect High-Field Transport Drift-Saturation Velocity Negative Differential Resistivity Velocity Overshoot Impact Ionization High-Frequency Transport Diffusion Continuity Equation Heat Conduction Coupled Heat and Charge Transport Seebeck Effect Peltier Effect Optical Properties Spectral Regions and Overview Reflection and Diffraction Absorption Electron Photon Interaction Band Band Transitions Joint Density of States Direct Transitions Indirect Transitions Urbach Tail Intravalence-Band Absorption Amorphous Semiconductors Excitons Phonon Broadening Exciton Polariton Bound-Exciton Absorption Biexcitons Trions Burstein Moss Shift Band Gap Renormalization Electron Hole Droplets Two-Photon Absorption Impurity Absorption Free-Carrier Absorption Lattice Absorption Dielectric Constant Reststrahlenbande

16 XVI Contents Polaritons Phonon Plasmon Coupling Recombination Introduction Band Band Recombination Spontaneous Emission Absorption Stimulated Emission Net Recombination Rate Recombination Dynamics Lasing Exciton Recombination Free Excitons Bound Excitons Alloy Broadening Phonon Replica Self-absorption Donor Acceptor Pair Transitions Inner-Impurity Recombination Auger Recombination Band Impurity Recombination Shockley-Read-Hall Kinetics Multilevel Traps Field Effect Thermally Activated Emission Direct Tunneling Assisted Tunneling Recombination at Extended Defects Surfaces Grain Boundaries Dislocations Excess-Carrier Profiles Generation at Surface Generation in the Bulk Part II Selected Topics 11 Heterostructures Introduction Heteroepitaxy Growth Methods Substrates Growth Modes

17 Contents XVII Heterosubstrates Pseudomorphic Structures Plastic Relaxation Surfactants Energy Levels in Heterostructures Band Lineup in Heterostructures Quantum Wells Superlattices Single Heterointerface Between Doped Materials Recombination in Quantum Wells Thickness Dependence Broadening Effects Quantum Confined Stark Effect Isotope Superlattices Wafer Bonding External Fields Electric Fields Bulk Material Quantum Wells Magnetic Fields Free-Carrier Absorption Energy Levels in Bulk Crystals Energy Levels in a 2DEG Shubnikov de Haas Oscillations Quantum Hall Effect Integral QHE Fractional QHE Weiss Oscillations Nanostructures Introduction Quantum Wires V-Groove Quantum Wires Cleaved-Edge Overgrowth Quantum Wires Nanowhiskers Nanobelts Quantization in Two-Dimensional Potential Wells Quantum Dots Quantization in Three-Dimensional Potential Wells Electrical and Transport Properties Self-assembled Preparation Optical Properties

18 XVIII Contents 14 Polarized Semiconductors Introduction Spontaneous Polarization Ferroelectricity Materials Soft Phonon Mode Phase Transition Domains Optical Properties Piezoelectricity Piezoelectric Effect Zincblende Crystals Wurtzite Crystals Piezoelectric Effects in Nanostructures Magnetic Semiconductors Introduction Magnetic Semiconductors Diluted Magnetic Semiconductors Spintronics Spin Transistor Spin LED Organic Semiconductors Materials Small Organic Molecules, Polymers Organic Semiconductor Crystals Electronic Structure Doping Transport Properties Optical Properties Graphene and Carbon Nanotubes Graphene Structure Band Structure Electrical Properties Other Two-Dimensional Crystals Carbon Nanotubes Structure Band Structure Optical Properties Other Anorganic Nanotubes

19 Contents XIX 18 Dielectric Structures Photonic Band Gap Materials Introduction General 1D Scattering Theory Transmission of an N-Period Potential The Quarter-Wave Stack Formation of a 3D Band Structure Disorder Defect Modes Coupling to an Electronic Resonance Microscopic Resonators Microdiscs Purcell Effect Deformed Resonators Hexagonal Cavities Transparent Conductive Oxide Semiconductors Materials Properties Part III Applications 20 Diodes Introduction Metal Semiconductor Contacts Band Diagram in Equilibrium Space-Charge Region Schottky Effect Capacitance Current Voltage Characteristic Ohmic Contacts Metal Contacts to Organic Semiconductors Metal Insulator Semiconductor Diodes Band Diagram for Ideal MIS Diode Space-Charge Region Capacitance Nonideal MIS Diode Bipolar Diodes Band Diagram Space-Charge Region Capacitance Current Voltage Characteristics Breakdown Organic Semiconductor Diodes

20 XX Contents 20.5 Applications and Special Diode Devices Rectification Frequency Mixing Voltage Regulator Zener Diodes Varactors Fast-Recovery Diodes Step-Recovery Diodes pin-diodes Tunneling Diodes Backward Diodes Gunn Diodes Heterostructure Diodes Light-to-Electricity Conversion Photocatalysis Photoconductors Introduction Photoconductivity Detectors Electrophotography QWIPs Blocked Impurity-Band Detectors Photodiodes Introduction pn Photodiodes pin Photodiodes Position-Sensing Detector MSM Photodiodes Avalanche Photodiodes Traveling-Wave Photodetectors Charge Coupled Devices Photodiode Arrays Solar Cells Solar Radiation Ideal Solar Cells Real Solar Cells Design Refinements Modules Solar-Cell Types Commercial Issues Electricity-to-Light Conversion Radiometric and Photometric Quantities Radiometric Quantities Photometric Quantities

21 Contents XXI 22.2 Scintillators CIE Chromaticity Diagram Display Applications Radiation Detection Luminescence Mechanisms Light-Emitting Diodes Introduction Spectral Ranges Quantum Efficiency Device Design White LEDs Quantum Dot LED Organic LED Lasers Introduction Applications Gain Optical Mode Loss Mechanisms Threshold Spontaneous Emission Factor Output Power Temperature Dependence Mode Spectrum Longitudinal Single-Mode Lasers Tunability Modulation Surface-Emitting Lasers Optically Pumped Semiconductor Lasers Quantum Cascade Lasers Hot-Hole Lasers Semiconductor Optical Amplifiers Transistors Introduction Bipolar Transistors Carrier Density and Currents Current Amplification Ebers Moll Model Current Voltage Characteristics Basic Circuits High-Frequency Properties Heterobipolar Transistors Light-Emitting Transistors Field-Effect Transistors

22 XXII Contents 23.4 JFET and MESFET General Principle Static Characteristics Normally On and Normally Off FETs Field-Dependent Mobility High-Frequency Properties MOSFETs Operation Principle Current Voltage Characteristics MOSFET Types Complementary MOS Large-Scale Integration Tunneling FETs Nonvolatile Memories Heterojunction FETs Thin-Film Transistors Annealing of Amorphous Silicon TFT Devices OFETs Part IV Appendices A Tensors B Space Groups C Kramers Kronig Relations D Oscillator Strength E Quantum Statistics F Thek p Perturbation Theory G Effective-Mass Theory References Index

23 Abbreviations 2DEG two-dimensional electron gas A atomic mass (A =12for 12 C) AAAS American Association for the Advancement of Science AB antibonding (position) ac alternating current ACS American Chemical Society AFM atomic force microscopy AIP American Institute of Physics AM air mass APD antiphase domain APD avalanche photodiode APS American Physical Society AR antireflection ARPES angle-resolved photoemission spectroscopy ASE amplified spontaneous emission AVS American Vacuum Society (The Science & Technology Society) BC bc bcc BD BEC BGR CAS CCD CD CEO CIE CIGS CIS CL bond center (position) body-centered body-centered cubic Blu-ray TM disc Bose Einstein condensation band gap renormalization calorimetric absorption spectroscopy charge coupled device compact disc cleaved-edge overgrowth Commission Internationale de l Éclairage Cu(In,Ga)Se 2 material CuInSe 2 material cathodoluminescence XXIII

24 XXIV CMOS CMY CNT COD CPU CRT CSL CVD cw CZ DAP DBR dc DFB DH(S) DLTS DMS DOS DPSS DRAM DVD Abbreviations complementary metal oxide semiconductor cyan-magenta-yellow (color system) carbon nanotube catastrophical optical damage central processing unit cathode ray tube coincident site lattice chemical vapor deposition continuous wave Czochralski (growth) donor acceptor pair distributed Bragg reflector direct current distributed feedback double heterostructure deep level transient spectroscopy diluted magnetic semiconductor density of states diode-pumped solid-state (laser) dynamic random access memory digital versatile disc EBL EEPROM EHL EIL EL ELO EMA EML ELA EPR ESR EPROM ESF ETL EXAFS F 4 -TCNQ fc fcc FeRAM FET FIR electron blocking layer electrically erasable programmable read-only memory electron hole liquid electron injection layer electroluminescence epitaxial lateral overgrowth effective mass approximation emission layer excimer laser annealing electron paramagnetic resonance electron spin resonance erasable programmable read-only memory extrinsic stacking fault electron transport layer extended X-ray absorption fine structure 2,3,5,6-tetrafluoro-7,7,8,8-tetracyano-quinodimethane face-centered face-centered cubic ferroelectric random access memory field-effect transistor far infrared

25 Abbreviations XXV FKO FLG FPA FQHE FWHM FZ Franz Keldysh oscillation few layer graphene focal plane array fractional quantum Hall effect full width at half-maximum float-zone (growth) Gb Gigabit GIZO GaInZnO GLAD glancing-angle deposition GRINSCH graded-index separate confinement heterostructure GSMBE gas-source molecular beam epitaxy GST Ge 2 Sb 2 Te 5 HBL hole blocking layer HBT heterobipolar transistor hcp hexagonally close packed HCSEL horizontal cavity surface-emitting laser HEMT high electron mobility transistor HIGFET heterojunction insulating gate FET HIL hole injection layer HJFET heterojunction FET hh heavy hole HOPG highly ordered pyrolithic graphite HOMO highest occupied molecular orbital HR high reflection HRTEM high-resolution transmission electron microscopy HTL hole transport layer HWHM half-width at half-maximum IC integrated circuit IDB inversion domain boundary IEEE Institute of Electrical and Electronics Engineers 1 IF intermediate frequency IPAP Institute of Pure and Applied Physics, Tokyo IQHE integral quantum Hall effect IR infrared ISF intrinsic stacking fault ITO indium tin oxide JDOS JFET KKR joint density of states junction field-effect transistor Kramers Kronig relation 1 Pronounced Eye-triple-E

26 XXVI KOH KTP LA LCD LDA LEC LED lh LO LPE LPCVD LPP LST LT LUMO LVM Abbreviations potassium hydroxide KTiOPO 4 material longitudinal acoustic (phonon) liquid crystal display local density approximation liquid encapsulated Czochralski (growth) light-emitting diode light hole longitudinal optical (phonon), local oscillator liquid phase epitaxy low-pressure chemical vapor deposition longitudinal phonon plasmon (mode) Lyddane Sachs Teller (relation) low temperature lowest unoccupied molecular orbital local vibrational mode MBE MEMS MESFET MIGS MILC MIOS MIR MIS MHEMT ML MLC MMIC MO MODFET MOMBE MOPA MOS MOSFET MOVPE MQW MRAM MRS MS MSA MSM MTJ MWNT molecular beam epitaxy micro-electro-mechanical system metal semiconductor field-effect transistor midgap (surface) states metal-induced lateral crystallization metal insulator oxide semiconductor mid-infrared metal insulator semiconductor metamorphic HEMT monolayer multi-level cell millimeter-wave integrated circuit master oscillator modulation-doped FET metalorganic molecular beam epitaxy master oscillator power amplifier metal oxide semiconductor metal oxide semiconductor field-effect transistor metalorganic chemical vapor deposition multiple quantum well magnetic random access memory Materials Research Society metal semiconductor (diode) mobility spectral analysis metal semiconductor metal (diode) magneto-tunneling junction multi-walled (carbon) nanotube

27 Abbreviations XXVII NDR NEP NIR NMOS NTSC OLED OMC ONO OPSL PA PBG pc PCM PFM PHEMT PL PLD PLE PMC PMMA PMOS PPC PPLN PV PWM PZT QCL QCSE QD QHE QW QWIP QWR negative differential resistance noise equivalent power near infrared n-channel metal oxide semiconductor (transistor) national television standard colors organic light emitting diode organic molecular crystals oxide/nitride/oxide optically pumped semiconductor laser power amplifier photonic band gap primitive cubic phase change memory piezoresponse force microscopy pseudomorphic HEMT photoluminescence pulsed laser deposition photoluminescence excitation (spectroscopy) programmable metallization cell poly-methyl methacrylate p-channel metal oxide semiconductor (transistor) persistent photoconductivity periodically poled lithium niobate photovoltaic pulsewidth modulation PbTi x Zr 1 x O 3 material quantum cascade laser quantum confined Stark effect quantum dot quantum Hall effect quantum well quantum-well intersubband photodetector quantum wire RAM RAS RF RFID RGB RHEED RIE random access memory reflection anisotropy spectroscopy radio frequency radio frequency identification red-green-blue (color system) reflection high-energy electron diffraction reactive ion etching

28 XXVIII RKKY rms ROM RRAM SAGB SAM sc SCH SdH SEL SEM SET SGDBR SHG si SIA SIMS SL SLC SLG s-o SOA SPD SPIE SPS srgb SRH SSR STM SWNT Abbreviations Ruderman Kittel Kasuya Yoshida (interaction) root mean square read-only memory resistance random access memory small-angle grain boundary separate absorption and amplification (structure) simple cubic separate confinement heterostructure Shubnikov-de Haas (oscillation) surface-emitting laser scanning electron microscopy single-electron transistor, single electron tunneling sampled grating distributed Bragg reflector second-harmonic generation semi-insulating Semiconductor Industry Association secondary ion mass spectrometry superlattice single-level cell single layer graphene spin-orbit (or split-off) semiconductor optical amplifier spectral power distribution International Society for Optical Engineering short-period superlattice standard RGB Shockley Read Hall (kinetics) side-mode suppression ratio scanning tunneling microscopy single-walled (carbon) nanotube TA TAS TCO TE TED TFET TFT TEGFET TEM TES TF TFT TM transverse acoustic (phonon) thermal admittance spectroscopy transparent conductive oxide transverse electric (polarization) transferred electron device transparent FET, tunneling FET thin film transistor two-dimensional electron gas FET transmission electron microscopy two-electron satellite thermionic field emission thin-film transistor transverse magnetic (polarization)

29 Abbreviations XXIX TMAH TMR TO TOD TPA TSO UHV UV VCA VCO VCSEL VFF VGF VIS VLSI WGM WKB WS tetramethyl-ammonium-hydroxide tunnel-magnetoresistance transverse optical (phonon) turn-on delay (time) two-photon absorption transparent semiconducting oxide ultrahigh vacuum ultraviolet virtual crystal approximation voltage-controlled oscillator vertical-cavity surface-emitting laser valence force field vertical gradient freeze (growth) visible very large scale integration whispering gallery mode Wentzel Kramer Brillouin (approximation or method) Wigner Seitz (cell) YSZ Yttria-stabilized zirconia (ZrO 2 ) X XX XSTM Z ZnPc exciton biexciton cross-sectional STM atomic number (Z = 2 for helium) zinc-phthalocyanine

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31 Symbols α Madelung constant, disorder parameter, linewidth enhancement factor α(ω) absorption coefficient α m mirror loss α n electron ionization coefficient α p hole ionization coefficient β used as abbreviation for e/(k B T ), spontaneous emission coefficient γ broadening parameter, Grüneisen parameter Γ broadening parameter γ 1, γ 2, γ 3 Luttinger parameters δ ij Kronecker symbol Δ 0 spin-orbit splitting ɛ(ω) dielectric function ɛ 0 permittivity of vacuum ɛ i dielectric constant of insulator ɛ r relative dielectric function ɛ s dielectric function of semiconductor (= ɛ r ɛ 0 ) ɛ xy components of strain tensor η quantum efficiency η d differential quantum efficiency η ext external quantum efficiency η int internal quantum efficiency η w wall-plug efficiency θ angle Θ D Debye temperature Θ B typical phonon energy parameter κ imaginary part of index of refraction, heat conductivity λ wavelength λ p plasma wavelength μ mobility μ 0 magnetic susceptibility of vacuum μ h hole mobility electron mobility μ n XXXI

32 XXXII Symbols ν Π π xy ρ ρ xy σ Σn σ n σ p σ P σ xy τ Θ D φ χ χ ex χ sc χ(r) ψ Ψ(r) ω Ω frequency Peltier coefficient components of piezoresistivity tensor mass density, charge density, resistivity components of resistivity tensor standard deviation, conductivity, stress, effective mass ratio grain boundary type electron capture cross section hole capture cross section polarization charge components of stress tensor, components of conductivity tensor lifetime, time constant Debye temperature phase electron affinity, electric susceptibility light extraction efficiency electron affinity (of semiconductor) envelope wavefunction angle wavefunction angular frequency interaction parameter a hydrostatic deformation potential a acceleration A area A, A vector potential A Richardson constant a 0 (cubic) lattice constant b bowing parameter, deformation potential b Burger s vector B bimolecular recombination coefficient, bandwidth B, B magnetic field c velocity of light in vacuum, lattice constant (along c-axis) C capacitance, spring constant C n, C p Auger recombination coefficient C ij elastic constants d distance, shear deformation potential d i insulator thickness D density of states, diffusion coefficient D, D displacement field D e (E) electron density of states D h (E) hole density of states electron diffusion coefficient D n

33 Symbols XXXIII D p hole diffusion coefficient e elementary charge E energy, electric field E, E electric field E A energy of acceptor level EA b acceptor ionization energy E C energy of conduction-band edge E D energy of donor level, Dirac energy (in graphene) ED b donor ionization energy E F Fermi energy E Fn electron quasi-fermi energy E Fp hole quasi-fermi energy E g band gap E m maximum electric field E P energy parameter E V energy of valence-band edge E vac energy of vacuum level E X exciton energy EX b exciton binding energy f oscillator strength F free energy F, F force F (M) excess noise factor F B Schottky barrier height f e Fermi Dirac distribution function f i ionicity F n electron quasi-fermi energy f p hole population F p hole quasi-fermi energy F P Purcell factor g degeneracy, g-factor, gain G free enthalpy, generation rate G vector of reciprocal lattice g m transconductance G th thermal generation rate h Planck constant H enthalpy H, H magnetic field H Hamiltonian h/(2π) i imaginary number I current I s saturation current I thr threshold current j current density, orbital momentum

34 XXXIV Symbols j s j thr saturation current density threshold current density k wavenumber, Boltzmann constant k wavevector k B Boltzmann constant k F Fermi wavevector l angular orbital momentum L length of line element L line vector (of dislocation) L D diffusion length L z quantum-well thickness m mass m 0 free electron mass m effective mass m c cyclotron mass M mass, multiplication factor M, M magnetization m e effective electron mass m h effective hole mass m j magnetic quantum number m r reduced mass n electron concentration (in conduction band), ideality factor n normal vector N(E) number of states n complex index of refraction (= n r +iκ) N A acceptor concentration N c critical doping concentration N C conduction-band edge density of states N D donor concentration n i intrinsic electron concentration n if ideality factor due to image force effect n r index of refraction (real part) n s sheet electron density N t trap concentration n tr transparency electron concentration n thr threshold electron concentration N V valence-band edge density of states p pressure, free hole density p, p momentum P power P, P electric polarization p cv momentum matrix element p i intrinsic hole concentration q charge

35 Symbols XXXV q, q heat flow Q charge, quality factor, impurity-bound exciton localization energy r radius r spatial coordinate R resistance, radius, recombination rate R λ responsivity R vector of direct lattice r H Hall factor R H Hall coefficient s spin S entropy, Seebeck coefficient, total spin, surface index, surface recombination velocity S ij stiffness coefficients t time t ox (gate) oxide thickness T temperature u displacement, cell-internal parameter u nk Bloch function U energy v, v velocity V volume, voltage, potential V (λ) (standardized) sensitivity of human eye V a unit-cell volume V bi built-in voltage v g group velocity v s velocity of sound, drift-saturation velocity v th thermal velocity w depletion-layer width W m work function X electronegativity Y Young s module, CIE brightness parameter Z partition sum, atomic order number

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37 Physical Constants constant symbol numerical value unit speed of light in vacuum c ms 1 permeability of vacuum μ 0 4π 10 7 NA 2 permittivity of vacuum ɛ 0 =(μ 0 c 2 0) Fm 1 elementary charge e C electron mass m e kg Planck constant h Js = h/(2π) Js ev s Boltzmann constant k B JK mev K 1 von-klitzing constant R H Ω Rydberg constant ev Bohr radius a B m XXXVII