Understanding solid state physics

Sharon Ann Holgate Boca Raton London New York CRC Press is an imprint of the Taylor & Francis Group, an informa business A TA Y L O R & F R A N C I S B O O K This book contains activities that may be dangerous if you not follow suitable safety procedures These activities should be carried out under the supervision of a qualified instructor and using suitable safety precautions and equipment The authors and publishers exclude all liability associated with this book to the extent permitted by law CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2010 by Sharon Ann Holgate CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S Government works Version Date: 20110725 International Standard Book Number-13: 978-1-4200-1232-3 (eBook - PDF) This book contains information obtained from authentic and highly regarded sources Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint Except as permitted under U.S Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers For permission to photocopy or use material electronically from this work, please access www.copyright com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400 CCC is a not-for-profit organization that provides licenses and registration for a variety of users For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com Dedication In memory of my grandmother Louisa Edmondson, and my friend John Wilson Contents Preface xiii Author xv Further Acknowledgments xvii Chapter Introduction Chapter Crystal Clear: Bonding and Crystal Structures 2.1 Bonding in Solids 2.1.1 Electrons in Atoms 2.1.2 Ionic Bonding 2.1.3 Covalent Bonding 12 2.1.4 Metallic Bonding 13 2.1.5 van der Waals Bonding 15 2.1.6 Hydrogen Bonding 16 2.1.7 Mixed Bonding 20 2.2 Crystalline Solids 21 2.2.1 Describing Crystal Structures 22 2.2.2 Crystalline Structures 29 2.2.3 Quasicrystals 48 2.2.4 Liquid Crystals 49 2.2.5 Allotropes and Polymorphs 49 2.2.6 Single Crystals and Polycrystals 51 2.2.7 Directions, Planes, and Atomic Coordinates 52 Further Reading 57 Selected Questions From Questions and Answers Manual 58 Chapter The Rejection of Perfection: Defects, Amorphous Materials, and Polymers 61 3.1 Defects 62 3.1.1 Point Defects 62 3.1.2 Dislocations 68 3.2 Amorphous Materials 73 3.2.1 Structure of Amorphous Materials 73 3.2.2 Models of Amorphous Structures 75 3.2.3 Glasses 77 3.2.4 Preparation of Amorphous Materials 80 3.3 Polymers 85 3.3.1 Structure of Polymers 86 vii viii Contents 3.3.2 Thermoplastics 88 3.3.3 Thermosets 90 3.3.4 Elastomers 90 3.3.5 Additives 92 Further Reading 93 Selected Questions From Questions and Answers Manual 93 Chapter Stressed Out: The Mechanical Properties of Solids 95 4.1 Introduction to Mechanical Properties of Solids 95 4.1.1 Stress and Strain 96 4.1.2 Plastic Deformation 102 4.1.3 Testing, Testing 106 4.1.4 Elasticity 111 4.1.5 Hardness 115 4.2 The Right Material for the Job 118 4.2.1 Alloys and Composites 118 4.2.2 Altering the Mechanical Properties of a Solid 119 4.2.3 Recycling 121 Further Reading 123 Selected Questions From Questions and Answers Manual 123 Chapter In, Out, Shake It All About: Diffraction, Phonons, and Thermal Properties of Solids 125 5.1 Diffraction 126 5.1.1 Propagation of Electromagnetic Radiation 126 5.1.2 How Waves Interact with Crystalline Solids 127 5.1.3 Obtaining X-Ray Diffraction Patterns 132 5.1.4 Electron and Neutron Diffraction 135 5.2 Lattice Vibrations and Phonons 139 5.2.1 Atomic Vibrations in Crystalline Solids 141 5.2.2 Phonons 143 5.3 Thermal Properties 144 5.3.1 Specific Heat 144 5.3.2 Thermal Conductivity 149 5.3.3 Thermal Expansion 150 Further Reading 154 Selected Questions From Questions and Answers Manual 154 Chapter Unable to Resist: Metals, Semiconductors, and Superconductors 157 6.1 Free Electron Models of Electrical Conduction 158 6.1.1 Overview of Electrical Conduction 158 6.1.2 Drude’s Classical Free Electron Model 164 6.1.3 Pauli’s Quantum Free Electron Model 165 Contents ix 6.2 Energy Band Formation 174 6.2.1 Nearly Free Electron Model 175 6.2.2 Tight-Binding Model 177 6.3 Simple Band Theory 180 6.3.1 Application of Band Theory to Real Solids 180 6.3.2 Density of States in Energy Bands 184 6.4 Elemental and Compound Semiconductors 185 6.4.1 Intrinsic and Extrinsic Semiconductors 185 6.4.2 Motion of Charge Carriers in Semiconductors 197 6.5 Superconductivity 201 6.5.1 Introduction to Superconductivity 201 6.5.2 Superconductor Technology 211 Further Reading 213 Selected Questions From Questions and Answers Manual 213 Chapter Chips with Everything: Semiconductor Devices and Dielectrics 215 7.1 Introduction to Semiconductor Devices 216 7.1.1 p-n Junctions 216 7.1.2 Bipolar Junction Transistors 223 7.1.3 Field-Effect Transistors 225 7.2 Optoelectronic Devices 230 7.2.1 Interaction Between Light and Semiconductors 230 7.2.2 LEDs 235 7.2.3 Semiconductor Lasers 238 7.2.4 Solar Cells 240 7.2.5 MOS Capacitor 242 7.3 Device Manufacture 243 7.3.1 Crystal Growth 244 7.3.2 Epitaxial Growth Methods 247 7.3.3 Deposition 249 7.3.4 Doping Semiconductors 252 7.3.5 MEMS 254 7.4 Dielectrics 254 7.4.1 Introduction to Dielectrics 254 7.4.2 Ferroelectricity 259 7.4.3 Piezoelectricity 262 Further Reading 264 Selected Questions From Questions and Answers Manual 264 Chapter Living in a Magnetic World: Magnetism and Its Applications 267 8.1 Introduction to Magnetism 268 8.1.1 The Origins of Magnetism 268 8.1.2 Magnetic Properties and Quantities 269 Appendix F: Glossary of Terms acceptor:  A dopant atom that has fewer valence electrons than needed to bond with the atoms of the semiconductor it is placed into See also p-type allotrope:  One of the possible crystal structures of an allotropic element See also allotropic allotropic: A description of an element that has more than one possible crystal structure Compare with polymorphic alloy:  A mixture of two or more metals that can include nonmetallic elements amorphous:  A description of a noncrystalline material in which the arrangement of atoms lacks long-range order annealing:  A heat treatment that involves heating a solid to a high temperature (below its melting point) and holding the solid at that temperature for a period of time before slowly cooling it atomic coordinates:  A set of three numbers used to indicate the position of atoms with respect to a unit cell atomic density:  The number of atoms per unit volume in a solid bandgap:  In general, a range of energy states between the allowed energy bands of a solid, but often used to mean the difference in energy between the top of the valence band and the bottom of the conduction band in an insulator or semiconductor basis:  A single atom (or ion) or group of atoms (or ions) with a fixed spacing and orientation to each other and of a specific composition An identical basis must be added to every point of a lattice in order to represent a crystal structure brittle:  A material which tends to show little or no plastic deformation before it breaks, so is likely to shatter if hit with a hammer Compare with ductile bulk modulus:  The ratio of the pressure applied to a material (solid or fluid) as it is compressed to the fractional change in volume the material experiences as a result of this pressure ceramic:  A compound such as zinc sulphide, silicon carbide, or calcium fluoride that contains either a metallic or semiconducting element as well as a nonmetallic element Many ceramics have a mixture of ionic and covalent bonding chip: A thin layer of high-purity single crystal When an integrated circuit is mounted on a single silicon crystal like this, the whole structure is commonly referred to as a “silicon chip” cohesive energy:  The energy per atom that would be needed to separate out a solid into the individual atoms (or ions) that it is made from colour centre:  A type of point defect that can form in ionic crystals and which changes their colour composite: A combination of two or more different materials that have different properties compressive stress:  The force per unit cross-sectional area squeezing a solid object along its longitudinal axis Compare with tensile stress 337 338 Appendix F: Glossary of Terms conduction band:  The highest energy band in a metal that contains electrons, and the first unoccupied or partially occupied band directly above the valence band in semiconductors and insulators conductivity (electrical):  A measure of the ability of a material to conduct electricity The greater the value of the conductivity, the better a conductor the material is continuous random network (CRN) model:  A model that can be used to describe the structure of amorphous materials in which the atoms are held together by covalent bonds coordination number:  The number of nearest neighbours that an atom in a solid has covalent bond:  A type of chemical bond in which valence electrons are shared between atoms It is found in both elements and compounds, including the important semiconducting materials silicon and gallium arsenide critical field:  The value of magnetic field above which a superconducting m ­ aterial loses its superconductivity crystalline:  A description of a solid composed of a regularly repeating pattern of atoms crystal structure:  The spatial arrangement of atoms inside a crystal Compare with lattice deformation:  A change in the shape or size of a solid material produced by the application of a force delocalized:  A description of an electron in a solid that does not remain in the local environment of either a single bond or of its parent atom dense random packing (DRP) model:  A model that can be used to describe the structure of amorphous materials in which the atoms are held together by metallic, ionic, or molecular bonds diamagnetism:  A weak form of magnetism that only exists in the presence of an applied magnetic field, and opposes the applied field dielectric:  An insulator that becomes polarised in the presence of an electric field diffusion: In solid state physics, this usually refers to the movement of charge ­carriers away from a region where their concentration is high diode:  An electronic device with two electrodes direct-gap semiconductor: A semiconductor in which the maximum energy of the valence band occurs at the same value of wave vector, k, as the minimum energy level of the conduction band Compare with indirect-gap semiconductor dislocation:  A defect involving a whole line of atoms which can allow planes of atoms to slip over one another with a much lower value of applied stress than would be required to produce slip in a perfect crystal Compare with point defect dislocation density:  The number of dislocations intersecting a randomly chosen unit area of a crystal dislocation line:  The line which for edge dislocations runs along parallel to the end of the extra part-plane of atoms, and in screw dislocations is the line which the planes of atoms spiral around Appendix F: Glossary of Terms 339 domain:  In magnetism, it is an area in a ferromagnetic material within which all the magnetic moments point in the same direction In ferroelectricity, it is a region containing unit cells polarised in the same direction donor:  A dopant atom that has more valence electrons than needed to bond with the atoms of the semiconductor it is placed into See n-type drift current:  The movement of charge carriers in a solid under the influence of an electric field drift velocity:  The average velocity of the carriers in a drift current ductile: A material which tends to show a large amount of plastic deformation before it breaks, so it is likely to be flattened if hit with a hammer and can be drawn out into a wire Compare with brittle effective mass:  The ratio of force to acceleration that an electron has when it is moving under the influence of an electric field in a crystal (It is not a true mass, but enables equations that describe electrons moving in a vacuum to still be used for electrons in crystals.) elastic deformation:  A deformation of a solid in which the solid returns to its original shape and size when the deforming stress on it is removed Compare with plastic deformation elastic limit:  The point that divides elastic and plastic behaviour Below the elastic limit, only elastic deformation takes place, and materials that are under stress return to their original shape and size when the stress is removed Above the elastic limit, stress will cause a permanent change in the shape of a material elastomer:  An elastic polymer electric dipole moment:  The product of the distance between a slightly separated pair of equal and opposite electric charges and either one of the charges electromagnet:  A soft ferromagnetic material surrounded by a current-carrying coil electronegative (atom):  An atom able to accept more electrons relatively easily or to share valence electrons, becoming a negative ion in the process electronegativity:  A measure of an element’s ability to accept an additional electron into its outermost atomic shell electropositive (atom):  An atom which can lose its valence electron(s) relatively easily, becoming both a positive ion and more stable in the process energy band:  A range of allowed energies for electrons in a solid epitaxy:  A method of manufacturing semiconductor devices in which layers are grown with the same crystal orientation as that of the substrate extrinsic semiconductor:  A semiconductor that has had the atoms of another semiconductor added to it (doping) to alter its properties Compare with intrinsic semiconductor Fermi energy: At T = 0K, the energy of the highest filled energy level in a solid More generally, the energy for which the probability of occupation is one half ferroelectrics: Materials that acquire a spontaneous electric dipole moment below a critical temperature ferromagnetic Curie temperature: The temperature at which the spontaneous magnetisation in a ferromagnet becomes zero Above this temperature, the material behaves like a paramagnetic material 340 Appendix F: Glossary of Terms ferromagnetic materials:  Materials that have spontaneous atomic magnetic moments in the absence of any external field They can be permanently magnetised by weak magnetic fields, and are attracted to magnets and magnetic fields filler:  A material that can be added to a polymer to enhance its properties Frenkel defect:  A point defect consisting of an interstitial atom and the vacancy it has left behind after moving from its normal position in the lattice glass transition temperature:  A range of temperatures, rather than a single temperature, over which a supercooled liquid gradually changes into a glass Despite not being a single temperature, a rapidly cooling amorphous material is considered to be a glass below its glass transition temperature but a supercooled liquid above it grain boundaries:  Boundaries separating the individual grains (little crystals) of a polycrystalline solid hardness:  The resistance of a material to being dented or scratched heat treatment:  Any of a number of processes involving heating and cooling a solid to change its properties hole:  An unoccupied state in the valence band that has a charge of exactly +1e and that behaves like a positive charge carrier in a solid hydrogen bond:  A type of chemical bond which occurs when a hydrogen atom covalently bonds to an atom of either oxygen, fluorine, or nitrogen The single valence electron from the hydrogen atom spends more time nearer the atom of the other element than near its own nucleus As a consequence, the hydrogen atom is left with a positive charge and can then attract a negatively charged part of either another molecule or its own molecule and form a hydrogen bond indirect-gap semiconductor: A semiconductor in which the maximum energy of the valence band occurs at a different value of wave vector, k, to the minimum energy level of the conduction band Compare with direct-gap semiconductor integrated circuit:  A complete circuit of electronic devices and their connections which is made on a single substrate interstitial:  An atom (which can be either an impurity or a host atom) that sits in between the normal lattice sites of a crystal intrinsic semiconductor:  A pure semiconductor that has not had impurities added Compare with extrinsic semiconductor ionic bond:  A type of chemical bond in which an electron is transferred from an electropositive atom to an electronegative atom The resulting ions have opposite electrostatic charges, and their attraction to one another forms the bond Ionic bonding is found in solids like NaCl which are composed of two elements, one of which is metallic lattice:  An infinite array of points arranged in such a way that if you were able to stand on one of these points, no matter which of the points you chose to step onto, your surroundings would look exactly the same Crystal structures can be represented by a lattice together with a basis lattice parameters:  The lengths of the sides of any given unit cell, and the angles between them Appendix F: Glossary of Terms 341 liquid crystal:  A state of matter with a structure between that of a solid and a liquid in which there is long-range order of the molecules mean free path:  The average distance a phonon or free electron travels before being scattered mean free time:  The average time for which a charge carrier travels through a metal or semiconductor before having its path altered by a collision melt quenching:  A method of forming amorphous materials by cooling them ­rapidly from their liquid state metallic bond:  A type of chemical bond found in metals in which the atoms exist as positive ions surrounded by a “sea” of electrons The attraction between the ions and the electrons forms the bond Miller indices:  A set of three (or—for hexagonal crystals—four) numbers used to describe planes within a crystal monomer:  A small molecule that can join with many other monomers to form a polymer nearest neighbours:  The atoms closest to any given atom within a solid nonprimitive unit cell: Any unit cell containing more than one lattice point Compare with primitive unit cell n-type: An extrinsic semiconductor that has had donor impurities added and so has electrons as its majority charge carriers Compare with p-type packing fraction:  The ratio of the volume of the atoms within a unit cell to the total volume of the cell (which is taken to be 1) paramagnetism:  A type of magnetism that causes a weak attraction to an applied magnetic field Pauli exclusion principle:  The principle proposed by Austrian physicist Wolfgang Pauli in 1925 which states that no two identical fermions (elementary particles with half-integer spin) in any system can exist in the same quantum state This means that, within the same atom, no electron can have a set of quantum numbers exactly the same as that of another electron phonons:  Particles of vibratory energy in solids, in the same way that photons are particles of electromagnetic energy piezoelectrics:  Materials in which the surfaces acquire an electric dipole moment when they are under stress plastic deformation:  The permanent deformation of a solid subjected to a deforming stress Compare with elastic deformation plasticiser:  A substance that can be added to polymers to increase their flexibility p-n junction:  A layer of p-type semiconductor back to back with a layer of n-type semiconductor point defect:  A defect—such as an impurity atom—involving one or, in some cases, a small number of atomic sites in a crystal polycrystalline:  A crystalline solid consisting of lots of little crystals known as grains rather than being one single crystal polymer:  A huge molecule made up from lots of small molecules (called m ­ onomers) joined together polymerization: Any of a number of processes in which monomers are joined together to form artificial polymers 342 Appendix F: Glossary of Terms polymorph:  One of the possible crystal structures of a polymorphic compound polymorphic:  A description of a compound that has more than one possible crystal structure Compare with allotropic population inversion:  A nonequilibrium state essential for laser operation in which more electrons are in a higher energy level than in a lower level primitive unit cell:  Any unit cell containing only one single lattice point p-type: An extrinsic semiconductor that has had acceptor impurities added and so has holes as its majority charge carriers Compare with n-type quasicrystal:  A solid which produces a sharp X-ray diffraction pattern like a ­crystal but does not have the symmetry characteristics of a crystal quenching: A heat treatment in which a solid is heated and then cooled very rapidly recombination:  An electron and hole “joining together” and cancelling each other out (One way of thinking about recombination is to imagine an electron disappearing into a hole.) resistance:  A measure of how much a piece of material or electrical component resists the flow of an electric current resistivity:  The reciprocal of the electrical conductivity, which is therefore a measure of the ability of a material to resist the flow of electricity through it saturation magnetisation:  The maximum value of the magnetisation in a ferromagnetic material, above which it cannot be magnetised any further by an increase in applied magnetic field Schottky defect:  A point defect, commonly known as a vacancy, which consists of a vacant lattice site single crystal: A crystalline solid made from a perfect continuous pattern of atoms slip:  The sliding of one plane of atoms in a solid over another plane solenoid:  A coil of conducting wire wound into a cylindrical shape so that the length of the wire is much greater than the diameter of the coil specific heat capacity:  The amount of heat required to raise the temperature of 1 kg of a substance by 1K stabiliser: A substance added to a polymer to reduce the damage caused by its working environment stiffness:  A measure of how much a material resists elastic deformation when it is under stress strain:  The change in volume or shape that the stress acting on an object produces, defined as the change in length or volume divided by the original length or volume, respectively strength: The maximum amount of stress a material can withstand without fracturing stress:  A force acting on an object, defined as the force per unit cross-sectional area substitutional (impurity):  An impurity atom that replaces one of the host atoms at a normal lattice site substrate:  A solid layer that acts as a base for the growth of other materials Appendix F: Glossary of Terms 343 superconducting transition temperature (Tc): The temperature separating the superconducting state from the normal state of a solid Below Tc the solid becomes superconducting superconductor:  A material that loses all its resistance to an electric current below a temperature called the superconducting transition temperature supercooled liquid:  A liquid which has been cooled so quickly that it could not crystallise into a solid at its normal freezing point and is therefore still liquid below it tensile strength:  The maximum tensile stress a solid object can withstand without breaking tensile stress:  The force per unit cross-sectional area pulling on a solid object and stretching it along its longitudinal axis Compare with compressive stress tetrahedral angle:  The angle (109°28′) between covalent bonds in a covalent solid in which every atom can be considered to be at the centre of symmetry of a tetrahedron, and is bonded to four other atoms positioned at the corners of this tetrahedron thermal conduction:  The transfer of heat from hot regions of a substance to cooler regions thermal conductivity:  A measure of the ability of a material to conduct heat The higher the value, the better a material is at conducting heat thermoplastic:  A polymer that becomes soft when heated and hardens when cooled It can be softened and reshaped several times and so can be recycled thermoset:  A polymer that chars and begins to decompose when heated and so ­cannot be recycled like a thermoplastic unit cell:  A building block for a crystal lattice, containing enough lattice points that repeating it over and over again with the relevant basis of atoms placed at each lattice point allows the entire structure of a given crystal to be represented valence band:  The energy band containing the valence electrons of a solid Compare with conduction band valence electrons:  Electrons in the outermost occupied shell of an atom that take part in bonding processes between atoms van der Waals forces: Weak intermolecular or interatomic electrostatic forces (due to the formation of dipoles) that cause molecules and atoms to become attracted to one another when they are very close together vulcanisation:  The process of adding sulphur to natural rubber Small quantities of sulphur make it more elastic and less sticky, while larger quantities harden the rubber work hardening:  Hardening a crystalline material by applying a stress greater than its elastic limit X-ray diffraction:  A widely used technique for determining the positions of atoms inside crystals Young’s modulus:  The ratio of stress over strain for materials under tensile stress and beneath their elastic limit zero-point motion:  The movement of atoms in a crystal at absolute zero Index A Absorption, 232–233 Acceptor impurities, 189–192 Acoustic waves in solids, 142–143 Additives, 92–93 Allotropes, 49–51 Alloys, 118–119 Altering mechanical properties of solid, 119–121 Amorphous materials, 73–85, 106 Annealing, 120–121 Antiferromagnetism, 282–285 Atom, properties, 309–310 Atomic coordinates, 56–57 Atomic density, 31–33, 35 Atomic electron configuration, 314 Atomic mass units, 310 Atomic movement, 115 Atomic number, 309 Atomic paramagnetism, 276–277 Atomic physics, revision, 309–319 Atomic radius, 30, 34–35 Atomic scattering factor, 129–130 Atomic shells, 310–312 Atomic structure, 309–310 Atomic vibrations, 141–142 Atomic weight, 145, 310, 319 Attraction, 10–11 Avalanche multiplication, 221–223 B Band formation, 157, 180–181, 309 Band structure, 178–179, 182, 191, 234 Band theory, 180–184 Bandgap, 182–183, 186–187, 191–192 Basis, 24 BCS theory, 201–211 Bend test, 106 Bias, 219–221 Biomaterials, 82 Bipolar junction transistors, 223–225 Boltzmann occupation factor, 332 Boltzmann’s distribution law, 332 Bonding in polymers, 86 Bonding in solids, 6–21 Bose-Einstein statistics, 335–336 Bosons, 324 Bragg diffraction, 134, 140, 155 Bragg law, 127–132 Branched polymer, 87–88 Bravais lattices, 28–29 Bridgeman technique, 246 Bulk modulus, 98, 111, 114, 337 C Caesium chloride structure, 40 Capacitors, 261–262 Carrier concentrations, 185–196 Cartesian coordinates, 296–298 Chemical vapour deposition, 85, 242–252 Classical statistical mechanics, 330–333 CMOS, 230 Coefficients of expansion, 151–152 Cohesive energy, 11–12 Colour centres, 65–66 Composites, 118–119 Compound semiconductors, 185–201 Compressibility, 114, 123 Compressive stress, 96–97, 114, 337, 343 Computer disk drives, 291–292 Conduction band, 182–184, 186–189 Conduction in polymers, 180–184 Conductivity, 149–150, 159–160, 186–189, 197–201 Conductor, energy band formation, 180–182 Configurations, 331–332 Continuous random network model, 76–77 Cooper pair, 210–211 Coordination number, 29–30, 33, 40–42, 44 Covalent bonding, 12–13 CRN model, 75, 77, 338 Cross-linked polymer, 87 Crystal growth, 70, 244–247 Crystal planes, 128–129, 134, 238 Crystal structures, 24–27, 40, 42–43, 48–50 Crystal systems, 28–29 Crystalline solids, 21–59, 127–132, 141–143 Curie temperature, 259–260, 282–283, 290, 339 Cystallinity, 86–88 Czocchralski technique, 244–246 D Debye temperature, 145, 148 Defects, 62–73 Definition of specific heat, 144 Deformation, 95–99, 102 Dense random packing, 75–76 Density of states in energy bands, 184–185 345 346 Index Depletion mode MOSFETs, 227–230 Deposition, 249–252 Device manufacture, 243–254 Diamagnetism, 272–273 Diamond structure, 42 Dielectrics, 215–265 Diffraction, 126–139, 305–307 Diffraction gratings, 127 Diffraction of electromagnetic waves, 126–127 Diffraction patterns, x-ray, 132–135 Diffusion, 197–201, 253 Direct gap semiconductors, 234–235 Dislocation density, 70–72 Dislocation line, 68, 70, 104, 338 Domain structure, 280 Donor impurities, 189, 341 Dopants, 191, 200–201, 248, 253 Doping semiconductors, 185–196, 252–254 Drift current, 197, 218, 220–221, 339 Drift velocity, 197 DRP model, 75–76, 338 Drude’s classical free electron model, 164–165 E E-k relationship, 165–180 Edge dislocation, 68–69, 74, 104 Effective mass, 169–170 Elastic waves, 301–302 Elasticity, 111–115 Elastomers, 90–92 Electric dipoles, 15, 255–256, 259, 339, 341 Electrical conduction, 158–164 Electrical conductivity, 159–160, 163–164 Electromagnetic radiation, 126–127 Electromagnetic wave diffraction, 126–127 Electromagnetic waves, 126–127, 301–302 Electromagnets, 286–287 Electron configuration of atom, 314 Electron diffraction, 135 –139 Electron mean free path, 158–164 Electron shell notation, 310–315 Electronic contribution to specific heat, 165–180 Electronic polarization, 260 Electrons in atoms, 6–8 Elemental semiconductors, 185–201 Emission, 232–234 Energy band formation, 174–182 Energy bands, 174, 176–179, 181–185 Enhancement mode MOSFETs, 225–227 Epitaxial growth methods, 247–249 Equipartition of energy, 332–333 Exclusion principle, 324 Expansion, 150–153 Expansion coefficients, 151–152 Extrinsic semiconductors, 185–196, 300 F Fermi-Dirac statistics, 333–335 Fermi energy, 165–180 Fermi gas, 165, 167, 173–174, 213 Fermi level, 185–196 Fermi surfaces, 165–180 Fermions, 324 Ferrimagnetism, 284–285 Ferroelectric domains, 260 Ferroelectricity, 259–262 Ferromagnetism, 267, 272, 278, 282–283 Field-effect transistors, 225–230 Fillers, 92 Floating zone method, 246–247 Formation of domains, 278–280 Forward bias, 220–221 Free electron models, 158–174 Frenkel defects, 62–65 G Gas model, 330–331 Giant magnetoresistance, 292 Glass transition temperature, 77, 80, 340 Glasses, 77–80 Glow-discharge decomposition, 84–85 Grain boundaries, 52, 67, 161, 218, 340 Graphite, 20–21 Gratings, diffraction, 307–308 H Hard magnetic materials, 287 Hardness, 115–117 Heat, specific, 144–149 Heat treatment, 66, 110, 119, 337, 340, 342 Heisenberg’s uncertainty principle, 323–324 Hexagonal close-packed structure, 42–44 High-temperature superconductors, 201–211 Hooke’s law, 97–98, 116 Hydrogen bonding, 16–20 Hysteresis, 261, 281–282 I Impact ionization, 222–223 Impact tests, 110 Impurities, 62–65 Indirect gap semiconductors, 234–235 Indistinguishable particles, configurations of, 333 Insulators, energy bands for, 180–184 Interference, 305 Intrinsic carrier concentrations, 185–196 Intrinsic semiconductors, 185–196, 300 Ion implantation, 253–254 347 Index Ionic bonding, 10–11 Isotopes, 309–310 K Kepler conjecture, 38–39 L Lattice, 24, 139–141 Lattice vibrations, 139–141 Laue diffraction, 132–135 LEDS, 235–238 LEED, 125, 139, 322 Light, semiconductors, 230–235 Light-emitting diodes, 180, 235 Linear polymer, 86–89 Liquid crystals, 49 Liquid phase epitaxy, 248 Long-range order, 75–77, 106, 177, 337, 341 Longitudinal waves, 302 M Maglev trains, 211–213 Magnet susceptibility, 271–172 Magnetic field changes, 280 Magnetic flux density, 269–270 Magnetic permeability, 287 Magnetic properties, 269–272 Magnetic quantities, 269–272 Magnetic quantum number, 313 Magnetic recording, 289–292 Magnetic resonance, 211, 288–289, 292 Magnetic susceptibility, 203, 267, 271–273, 283, 293 Magnetisation, 271 Magnetism, 267–293 Magnetism types, 272–285 Magnetoresistance, 267, 292 Magnets, 211–212, 285–292 Majority carriers, 192 Mass density, 33 Mass number, 309–310 Maxwell-Boltzmann distribution, 165 Mechanical properties of solids, 95–123 Mechanics, statistical, 329–336 Meissner effect, 201–211 Melt quenching, 80, 82, 341 MEMS, 254 Metallic bonding, 5, 13–14, 20, 30, 159, 164 Metals, 157–213 Miller indices, 54–56, 132, 341 MiniDisc, 290–292 Minority carriers, 192 Mixed bonding, 20–21 Moduli of elasticity, 111, 114 Molecular beam epitaxy, 248–249 Monoclinic structures, 45–48 Monomer, 85–86, 341 MOS capacitor, 242–243 MOSFETs, 225–230 Motion of charge carriers, semiconductors, 197–201 MRI, 211, 288–289 N N-type semiconductors, doping to produce, 185–196 Nanotubes, 108, 110, 179–180, 213 Nearest neighbours, 22, 29–31, 33, 37, 40–44 Nearly free electron model, 175–177 Neutron diffraction, 135–139 Nonstoichiometry, 62–68 O Optical absorption, 232–234 Optical waves in solids, 142–143 Optoelectronic devices, 230–243 Orbital quantum number, 312–313 Origins of magnetism, 268–269 Origins of resistivity, 158–164 Orthorhombic structure, 45 Overall magnetism, 278 Overall motion, 197–201 P P-n junctions, 216–223 P-type semiconductors, doping to produce, 189–192 Packing fraction, 36–37, 42, 44, 76, 341 Paramagnetic region, 282 Paramagnetism, 273–278 Particle in a box, 324–327 Pauli exclusion principle, 324 Pauli paramagnetism, 277–278 Pauli’s quantum free electron model, 165–180 Periodic table, 315–319 Permanent magnets, 287–288 Permeability, 270–272 Phonons, 139–141, 143–144 Photoconductivity, 231 Physics, atomic, revision, 309–319 Piezoelectricity, 262–264 Plastic deformation, 102–106 Plasticiser, 88–90, 341 Point defects, 62–68 colour centres, 65–66 Frenkel defects, 62–65 impurities, 62–65 Schottky defects, 62–65 vacancies, 62–67 Poisson’s ratio, 114–115 Polarisation, 256–259 348 Index Polycrystals, 51–52 Polymerization, 86 Polymers, 85–93, 106 Polymorphs, 49–51 Polythene, 78–79, 85–89, 94 Population inversion, 233–234, 239, 342 Powder diffraction, 132–135 Primitive cell, 26–27, 32, 35–36 Principal quantum number, 312 Probability, 329–330 Propagation of electromagnetic radiation, 126–127 Propagation velocity, 305 PVC, 85, 87–90 Q Quantisation, 323 Quantum behaviour, particles, 324–327 Quantum dot, 4, 112–113, 249 Quantum mechanics, revision of, 321–324 Quantum number, 312–314 Quantum statistics, 333–336 Quantum theory, 321–324 Quasicrystals, 48–49 Quenching, 80, 82, 120, 341–342 R Real solids, application of band theory to, 180–184 Rectification, 221 Recycling, 121–122 Repulsion, 10–11 Resistance, 118–120, 158, 160–161, 165 Resistivity, 159–162 Reverse bias, 219–220 Revision of atomic physics, 309–319 Revision of quantum mechanics, 321–324 Revision of statistical mechanics, 329–336 RHEED, 125, 139 Right material for job, 118–122 Robots, 86, 229 Rotating crystal diffraction, 132–135 S Scalar, vs vector, 295 Schottky defect, 61–64, 183 Schrödinger equation, 311, 326, 329 Screw dislocation, 69–70, 104 Semiconductor devices, 216–230 Semiconductor lasers, 238–240 Semiconductors, 157–213 Shear stress, 96–97, 103–106, 114 Short-range order, 76 Simple band theory, 180–185 Simple cubic structures, 29–32 Simple probability calculations, 330 Single crystals, 51–52 Slip, 102–105 Sodium chloride structure, 40–41 Solar cells, 240–242 Solenoids, 285–286 Solid state physics, statistics, 329 Solids acoustic waves in, 142–143 mechanical properties of, 95–123 optical waves in, 142–143 thermal properties of, 144 Specific heat, 144–149, 174 Spin quantum number, 313–314 Spontaneous emission, 232–234 Sputtering, 84 Stabiliser, 92, 342 Stacking faults, 72–73 States of free electron model, 165–166 Statistical mechanics, 329–336 Statistics, solid state physics, 329 Stiffness, 92, 98, 102, 342 Stimulated emission, 232–234 Stress-strain curves, 97–100 Structure factor (geometrical), 130–132 Subshells, filling of, 314–315 Substitutional impurities, 65 Superconducting magnets, 211–212 Superconducting transition temperature, 202–203, 206–207, 213, 343 Superconductivity, 201–213 Superconductor technology, 211–213 Superconductors, 157–213 Supercooled liquid, 79–80, 93, 340, 343 T Tape recording, 289–290 Tensile strength, 92, 97–98, 108, 110, 118–119, 343 Tensile stress, 96–99, 114, 116, 123, 337, 343 Tensile testing, 106–110 Testing, 106–111 Tetragonal structure, 44 Thermal conductivity, 149–150 Thermal equilibrium, unbiased junction in, 218–219 Thermal evaporation, 61, 80–81, 84 Thermal expansion, 150–153 Thermal properties of solids, 144 Thermal stresses, 150–154 Thermal velocity, 197–201 Thermoplastics, 88–90 Thermosets, 90 Thin-film transistors, 230 Tight-binding model, 177–180 Transverse waves, 302 Triclinic structures, 45–48 Trigonal structures, 45–48 349 Index Type I superconductor, 204–205 Type II superconductors, 204–205 Types of magnetism, 272–285 U Ultrasound, 263–264 Unbiased junction in thermal equilibrium, 218–219 Uncertainty principle, Heisenberg, 323–324 Unit cells, 26–28 Unit vectors, 295 V Vacancies, 62–67 Valence band, 182–183, 185–189, 191–192, 194–195 van der Waals forces, 15–21, 86, 101, 106, 343 Vapour phase epitaxy, 248 Vector vs scalar, 295 Vectors, 24–25, 27, 52, 57, 176, 270, 295–297, 304, 313 addition, 296 unit, 295 Velocity, 197–198 Velocity drift, 197 Velocity of propagation, 305 Vibrations, 301–308 lattice, 139–141 Virtual testing, 111 Vulcanisation, 92, 343 W Wave behaviour, 305–308 Wave functions, 322 Wave number, 173, 304 Wave-particle duality, 321–322 Waves, 301–308 Wiedemann-Franz law, 158–164 Work hardening, 121, 343 X X-ray diffraction patterns, 132–135 Y Yield stress, 97–98 Young’s modulus, 97–99, 101–102, 104, 111, 114, 116, 123, 343 Z Zero-point energy, 141, 326 Zero-point motion, 141, 343 Zinchlende structure, 41–42 Physics and Materials Science “The book is written in a very user-friendly and engaging style, as one might expect from a science writer/journalist This way, the author succeeds in making the material approachable and interesting The presentation is not as formal as most treatments The emphasis is less on the theoretical and mathematical basis of the subject and more on the intuitive understanding of ideas and concepts, but the approach is fresh and the explanations are clear What I like most of all is that it brings solid-state physics up-to-date, introducing modern topics and showing how the core ideas in condensed matter physics underpin so much of the technology we use today.” —Professor Andrew Boothroyd, Oxford University, UK Keeping the mathematics to a minimum yet losing none of the required rigor, Understanding Solid State Physics clearly explains basic physics principles to provide a firm grounding in the subject The text provides a useful introduction to readers who feel daunted by a highly mathematical approach By relating the theories and concepts to practical applications, it shows how physics is used in the real world Features • Highlights various technological applications of physics, from locomotive lights to medical implants to hard drives • Provides captivating images of real-life applications that demonstrate the multidisciplinary nature of scientific research • Uses an accessible writing style and format, offering journalistic accounts of interesting research • Contains worked examples, self-test questions, and a helpful glossary of frequently used terms • Includes derivations of key equations and reviews of essential physics in the appendices • Offers ancillary resources on www.crcpress.com IP662 an informa business w w w c r c p r e s s c o m 6000 Broken Sound Parkway, NW Suite 300, Boca Raton, FL 33487 270 Madison Avenue New York, NY 10016 Park Square, Milton Park Abingdon, Oxon OX14 4RN, UK ISBN: 978-0-7503-0972-1 90000 780750 309721 ... laboratory-based devices 4 Understanding Solid State Physics laboratories The next generation of so-called “quantum dot” lasers should be even smaller than solid- state lasers, which could lead... while as Chapter will reveal, amorphous solids have structures in which the arrangement of atoms is much more random The physics 22 Understanding Solid State Physics EXAMPLE QUESTION 2.3  BONDING... in Solid State Physics, International Edition, Neil W Ashcroft and N David Mermin, p 388, copyright Elsevier [W B Saunders Company], 1976 Reproduced with permission.) 24 Understanding Solid State