Lecture 1 - Introduction to Solid State Physics - University of Surrey

Solid State PhysicsProfessor Stephen SweeneyAdvanced Technology Institute and Department of PhysicsUniversity of Surrey, Guildford, GU2 7XH, UKs.sweeney@surrey.ac.ukOffice: 12ATI01 (book appointments by email)Solid State Physics - Lecture 1

Where does this fit in?Nuclear physics: fundamental particles,radioactivity, fission, nuclear reactionsetc.Atomic physics: energy levels,chemistry, spin-effects,spectroscopy etc.Solid-state physics: crystal structures, conductors,insulators, semiconductors, thermal properties,strength of materials etc.Solid State Physics - Lecture 1

Solid-State Physics• Solid-state physics provides a description of how atoms bond to form solids• It shows how microscopic effects give rise to macroscopic behaviour:• Thermal conductivity• Electrical conductivitySource: PRB Germany• Semiconductors and optical propertiesSolid State Physics - Lecture 1

Course structure• Delivery :• Assessment:39 hours of lectures and tutorial periods& laboratory based activities within level 2 lab. classesCoursework test (week 15, Jan/Feb 2011) [13% of mm]Examination (two papers in May/June 2011) [23% of mm]• Suggested reading (the course will not follow any particular book):Rosenberg, The Solid State, OxfordRudden & Wilson, Elements of Solid State Physics, WileyKittel, Introduction to Solid-State Physics, WileyBlakemore, Solid State Physics, Cambridge Univ. PressAshcroft & Mermin, Solid State Physics, WileySolid State Physics - Lecture 1

Course Aims• Learn about basic concepts in Solid State Physics:- Crystal structure (types, terminology, real and reciprocal lattices,diffraction)- Lattice Dynamics (phonons, thermal conduction, heat capacity)- Thermal statistics, i.e. how to describe the energy of electrons in solids(Fermi-Dirac distributions, Fermi energy, density of states)- Free electron theory (electrical conduction)- Band structure theory (collective behaviour of atoms in a crystal, bandgaps, metals, insulators, semiconductors)- Low dimensional systems (quantum wells, quantum dots, application insemiconductor devices such as light emitting diodes and lasers)Solid State Physics - Lecture 1

Why is this important?SiliconSilicon waferSand (mainly SiO 2 )iPhoneLaptopSat NavToasteretc…Processor chipSolid State Physics - Lecture 1

Progress1cm30nmFirst transistor (1947)Intel transistor (2009)Solid State Physics - Lecture 1

States of MatterSolid: atoms are packed together in a rigid structure with shortorlong-range order (more later).As the solid is heated up, the atoms oscillate around theirequilibrium positions but retain a rigid structure.Liquid: atoms are closely packed but do not form a rigidstructure. As the liquid is heated up the atoms move aroundbut without clear relation to one another.Gas: atoms are located far away from each other (a muchlower density than for a liquid or gas) with little interactionwith each other. As the gas is heated up the atoms becomemore energetic, increasing the probability of collision.(also plasmas, but we won’t worry about those here…)Solid State Physics - Lecture 1

What is a Solid?Could be a bulk composite with weakly bondedconstituents. The atomic arrangement is completelyrandom. Such materials are relatively weak, and are poorthermal and electrical conductors (e.g. wood).In amorphous solids there may be shortrange order between atoms but the atomsdo not overall form a periodic structure.The atoms themselves are at equilibriumspacing (e.g. glasses)In crystalline solids the atoms form a periodicstructure and there is long range order in the positionof the atoms (e.g. metals, diamond, silicon etc.).More than 90% of solids form crystalline structures.Solid State Physics - Lecture 1

Crystal StructuresAn ideal crystal is constructed from an infinite repetition of identical groups of atoms• The group is known as the basis (this will contain one or more atoms)• The set of points on which the basis sits is called the lattice(a mathematical construction)Solid State Physics - Lecture 1

Lattices & lattice translation vectorsLattice translation vectors describe how to move around a crystal1 dimensional (1D) casear r’r'r uaa 1a 22 dimensional (2D) case(where u is an integer)r' r u a ua1 1 2 2Solid State Physics - Lecture 1

Lattices & lattice translation vectors3 dimensional (3D) casea 1a 2r' r ua ua u21123a3a 3More generally, for n dimensions:r' rnu annAll possible combinations of u n define the latticeLattice translation vectors a n are primitive if there is no other cell ofvolume

Primitive cell & uniqueness (2D)a 1a 2a 1a 2 a 1 a2In 2D case primitive basis set whenA primitive cell contains 1 lattice point!a1 a2is minimisedA primitive cell can be defined in more than one waySolid State Physics - Lecture 1

Wigner-Seitz Primitive Cell (2D)Define a primitive cell by bisecting lines connecting lattice points…2D latticeSolid State Physics - Lecture 1

Wigner-Seitz Primitive Cell (2D)Define a primitive cell by bisecting lines connecting lattice points…2D latticeSolid State Physics - Lecture 1

Wigner-Seitz Primitive Cell (2D)Define a primitive cell by bisecting lines connecting lattice points…2D latticeSolid State Physics - Lecture 1

Wigner-Seitz Primitive Cell (2D)Define a primitive cell by bisecting lines connecting lattice points…2D latticeSolid State Physics - Lecture 1

Wigner-Seitz Primitive Cell (2D)Define a primitive cell by bisecting lines connecting lattice points…2D latticeSolid State Physics - Lecture 1

Wigner and SeitzEugene Wigner (1902-1995)• American-Hungarianphysicist based in Princeton• Nobel Prize in Physics(1963) for theory of atomicnucleusFrederick Seitz (1911-2008)• American physicist studied PhDunder Wigner• Former President of US NationalAcademy of Sciences• National Medal of Science (1973)for work on solid state physicsSolid State Physics - Lecture 1

Crystal structure = lattice + basis2D latticeSolid State Physics - Lecture 1

Crystal structure = lattice + basisBasisElement AElement BThe position of the centre of an atom/ion j relative to the lattice point is:latticepointa 1a 2r jr x a1For blue atom/ion:r j 0For red atom/ion:rj xja1a 2 z aIn 3D: j j j j 3yyja 2LatticetranslationvectorsSolid State Physics - Lecture 10 x , y , z 1(Usual to define )jjj

Crystal structure = lattice + basis2D Crystal structureSolid State Physics - Lecture 1

Bravais lattices• There are 14 possibletypes of lattice in 3Dspace based around7 groups• We will mainlyconsider cubicsystemsSolid State Physics - Lecture 1

Auguste Bravais (1811-1863)• French physicist renowned for hiswork on crystallography• Chair of Physics at EcolePolytechnique, Paris• Proved the existence of 14 uniquelattices in 3D crystallographicsystemsSolid State Physics - Lecture 1

Cubic systems – unit cellsSimple cubic(sc)Body-centred cubic(bcc)Face-centred cubic(fcc)NB:Only sc is primitive since it contains one lattice pointQ. How many lattice points are contained in a bcc and fcc unit cell?Q. What are basis vectors for each structure?Solid State Physics - Lecture 1

Cubic systems – unit cellsSimple cubic(sc)Body-centred cubic(bcc)Face-centred cubic(fcc)NB:Only sc is primitive since it contains one lattice pointQ. How many lattice points are contained in a bcc (2) and fcc unit cell? (4)Q. What are basis vectors for each structure?Solid State Physics - Lecture 1

Examples – simple cubic (sc)The simple cubic structure is notcommon in nature.Why?Simple cubicExample – Polonium (alpha form)Q. If the length of one side of theunit cell is 335.2pm. What isdensity of alpha polonium?(9200kg/m 3 )Solid State Physics - Lecture 1

Examples – body centred cubic (bcc)Iron is a common bccstructure.Q. If the density of iron is7800kg/m 3 what is thelength of each side of theunit cell?(280pm)Body-centred cubicAnimation at:http://stokes.byu.edu/bcc.htmSolid State Physics - Lecture 1

Examples – face-centred cubicQ. Copper is known tocrystallise in cubic form. If thedensity of copper is 8900kg/m 3and the length of each side ofthe unit cell is 360pm, showthat copper must have a fccstructure.Face-centred cubicAnimation at:http://stokes.byu.edu/fcc.htmSolid State Physics - Lecture 1

Packing factorssc bcc fccQ. Assuming a lattice of identical atoms, calculate the volume packingfactor for each of the cubic structures above.Solid State Physics - Lecture 1

Packing factorssc (52%) bcc (68%) fcc (74%)Q. Assuming a lattice of identical atoms, calculate the volume packingfactor for each of the cubic structures above.Solid State Physics - Lecture 1

Key:bccfccscSolid State Physics - Lecture 1

Crystal basis with >1 atomBasis can in practice contain many atoms:Silicon is fcc with 2 atom basisTwo interpenetrating fcc structuresis called the diamond structureDiamond structure:Co-ordinates of atoms in basis areThis is often called a tetrahedral structure000and1 1 14 4 4Q. Calculate the bond angle.(109.5 o )Solid State Physics - Lecture 1

Crystal basis with >1 atomIonic structure (more on bonding later in the course):NaCl – based on fcc structure ofNa + and Cl - ionsQ. What is the density of salt if thecrystal has a lattice constant,a, of 563pm? (~2200kgm -3 )Virus (e.g. flu) ~ basis contains ~10 7 -10 9 atoms !aSolid State Physics - Lecture 1