Download Basic aproximations in the band theory of solid state

SYLLABUS
COURSE TITLE
FACULTY/INSTITUTE
SOLID STATE PHYSICS
FACULTY OF MATHEMATICS AND NATURAL
SCIENCES / DEPARTMENT OF THEORETICAL
PHYSICS
COURSE CODE
DEGREE PROGRAMME
FIELD OF STUDY
DEGREE LEVEL
FORMA
MODE
PHYSICS
MASTER
STATIONARY
COURSE FORMAT
YEAR AND SEMESTER
NAME OF THE TEACHER
STUDIÓW/STUDY
2015/2016 SUMMER SEMESTER
MALGORZATA SZNAJDER
COURSE OBJECTIVES
THE AIM OF THE LECTURE IS TO PRESENT A BASIC KNOWLEDGE ABOUT CRYSTALLOGRAPHY,
BONDING, THERMAL PROPERTIES OF CRYSTAL LATTICE, WAVE DIFFRACTION, AS WELL AS
ITS DYNAMICAL, STATISTICAL, KINETIC, MAGNETIC AND OPTICAL PROPERTIES. AN
UDERGRADUATE STUDENT GAINS KNOWLEDGE ON QUANTUM STATISTICS OF CHARGE
CARRIERS AND THE THEORY OF TRANSPORT PHENOMENA IN SOLIDS BEING THE
BACGROUND OF ELECTRONICS AND SEMICONDUCTOR MICROELECTRONICS. ADDITIONALLY,
IN THE COURSE BASIC PROPERTIES OF METALS, SEMICONDUCTORS, SUPERCONDUCTORS,
DIELECTRICS, MAGNETS, AND LOW-DIMENSIONAL STRUCTURES ARE PRESENTED. BASED ON
THEM, A STUDENT SHOULD DEVELOP ABILITY TO UNDERSTAND INTUITIVELY THE
DISCUSSED PHYSICAL PHENOMENA AND TO USE A CORRECT PHYSICAL TERMINOLOGY.
PREREQUISITES
KNOWLEDGE ABOUT FUNDAMENTALS OF PHYSICS
(KINEMATICS, ELECTROMAGNETISM, OPTICS, STRUCTURE OF
ATOMS), MATHEMATICAL ANALYSIS (DIFFERENTATIONS,
INTEGRATIONS), AND QUANTUM MECHANICS (TIME
INDEPENDENT SCHRODINGER’S EQUATION, PERTURBATION
THEORY).
KNOWLEDGE:
LEARNING OUTCOMES
K_W01 STUDENT HAS EXTENDED KNOWLEDGE IN PHYSICS,
ITS DEVELOPEMENT AND IMPORTANCE FOR PROGRESS IN
NATURAL SCIENCES AND HUMAN DEVELOPEMENT,
K_W06 HAS GENERAL KONWLEDGE ABOUT TRENDS,
DEVELOPEMENT AND DISCOVERIES IN PHYSICS
SKILLS:
K_U01 CAN PLAN, DO BASIC RESEARCH AND OBSERVATIONS
CONCERGING EDUCATION IN BASIC PHYSICS
K_U02 CAN ESTIMATE RESULTS OF EXPERIMENTS,
OBSERVATIONS AND THEORETICAL CALCULATIONS, AS WELL
AS DISCUSS MEASUREMENT UNCERTAINTIES
K_U05 CAN PRESENT RESULTS OF INVESTIGATIONS IN FORM
OF A REPORT
K_U06 CAN PRESENT IN AN ACCESSIBLE WAY RESULTS OF
DISCOVERIES IN PHYSICS, MATERIAL ENGINEERING AND
CHEMISTRY
K_U07 IS ABLE TO SELF-EDUCATE
K_U09 IS ABLE TO PREPARE AN ORAL PRESENTATION ABOUT
PROBLEMS IN PHYSICS OR IN THE FIELD ON THE BORDER OF
MATERIAL ENGINEERING AND CHEMISTRY
FINAL COURSE OUTPUT - SOCIAL COMPETENCES
K_K05 UNDERSTANDS A NECESSITY TO READ SCIENTIFIC AND
POPULAR SCIENCES JOURNALS IN PHYSICS IN ORDER TO BROADEN
KNOWLEDGE
COURSE ORGANISATION –LEARNING FORMAT AND NUMBER OF HOURS
45 HOURS OF LECTCURES AND 45 HOURS OF CLASS EXERCISES
COURSE DESCRIPTION
1. INTRODUCTION. SOLIDS: CRYSTALS, AMORPHOUS MATERIALS,
POLYCRYSTALS, LIQUID CRYSTALS, GLASSES. APPLICATION OF LIQUID CRYSTALS
– DISPLAYS.
2. BASIC CRYSTALLOGRAPHY: STRUCTURE AND SYMMETRY OF CRYSTALS
PRIMITIVE AND COMPLEX LATTICES, THE BRAVAIS LATTICE, TRANSLATION
SYMMETRY, POINT SYMMETRY, CRYSTALLOGRAPHIC SYSTEMS, SIMPLE
CRYSTAL STRUCTURES (FCC, BCC, SODIUM CHLORIDE, DIAMOND, ZINCBLENDE, HCP, WURTZITE STRUCTURE), PACKING, DIRECT IMAGING OF ATOMIC
STRUCTURE: STM.
3. CHEMICAL BONDING IN SOLIDS: IONIC, COVALENT, METALIC, HYDROGEN,
AND VAN DER WAALS BONDING.
4. WAVE DIFFRACTION AND THE RECIPROCAL LATTICE: X-RAY DIFFRACTION IN
PERIODIC STRUCTURES, BRAGG LAW, RECIPROCAL LATTICE VECTORS.
DIFFRACTION CONDITIONS, LAUE EQUATIONS. THE STRUCTURE FACTOR,
ATOMIC FORM FACTOR. EVALD’S CONSTRUCTION. EXPERIMENTAL METHODS
TO STUDY SCATTERING: DEBYE-SCHERRER METHOD, ROTATING CRYSTAL
METHOD.
5. DYNAMICS AND THERMAL PROPERTIES OF CRYSTAL LATTICE:
VIBRATIONS OF ONE DIMENSIONAL CRYSTAL LATTICE WITH MONO- AND
DIATOMIC BASIS. DISPERSION RELATIONS: ACOUSTIC AND OPTICAL
BRANCHES. GROUP VELOCITY, PHASE VELOCITY, LONG WAVELENGTH LIMIT.
NORMAL VIBRATION MODES IN ONE DIMENSIONAL LATTICE, QUANTISATION,
PHONOS. VIBRATIONS IN THREE-DIMENSIONAL COMPLEX CRYSTAL LATTICE.
PHONON HEAT CAPACITY, DENSITY OF STATES FUNCTION. DEBYE T3 LAW.
THERMAL EXPANSION. THERMAL RESISITIVITY OF PHONON GAS, UMKLAPP
PROCESSES.
6. BASIC APROXIMATIONS IN THE BAND THEORY OF SOLID STATE: ADIABATIC
APPROXIMATION, ONE-ELECTRON APPROXIMATION.
7. ELECTRON STATES IN A PERFECT CRYSTAL: ELECTRON MOTION IN A
PERIODIC POTENTIAL FIELD. BLOCH THEOREM. K VECTOR AS A QUANTUM
NUMBER. EMPTY LATTICE APPROXIMATION, NEARLY-FREE ELECTRON
APPROXIMATION. FIRST BRILLOUIN ZONE, ENERGY BAND GAPS. DIVISION OF
SOLIDS: METALS, SEMIMETALS, DIELECTRICS, SEMICONDUCTORS. THE E(K)
DEPENDENCE OF AN ELECTRON NEAR A ZONE BOUNDARY. ELECTRON MOTION
UNDER INFLUENCE OF EXTERNAL ELECTRIC FIELD, EFFECTIVE MASS.
8. FREE ELECTRON FERMI GAS IN METALS: FERMI GAS OF ELECTRONS AT
T=0K. FERMI ENERGY. FERMI-DIRAC DISTRIBUTION FUNCTION AT T=0K AND
T>0K. DENSITY OF STATES FUNCTION. CONCENTRATION, DEGENERATE
ELECTRON GAS. FERMI SURFACES FOR METALS. FREE ELECTRON IN MAGNETIC
FIELD. LANDAU LEVELS. HEAT CAPACITY OF THE ELECTRON GAS.
9. PHYSICAL PROPERTIES OF SEMICONDUCTORS: EQUATION OF MOTION OF
AN ELECTRON IN A BAND. HOLES. PHYSICAL INTERPRETATION OF THE
EFFECTIVE MASS. EFFECTIVE MASSES IN SEMICONDUCTORS. THE BAND
STRUCTURES OF BASIC SEMICONDUCTORS. ELECTRON MOTION IN MAGNETIC
FIELD, CYCLOTRON RESONANCE. CONCENTRATION OF FREE CHARGE CARRIERS
IN INTRINSIC SEMICONDUCTORS. INFLUENCE OF TEMPERATURE ON
CONCENTRATION OF CHARGE CARRIERS. DOPANTS IN SEMICONDUCTORS,
DONOR AND ACCEPTOR LEVELS. P-N JUNCTION AND ITS APPLICATION IN
SEMICONDUCTORS. THE PHOTOVOLTAIC EFFECT, PHOTO-ELECTROMOTORIC
FORCE. SILICON-BASED SOLAR CELLS. HETEROSTRUCTURES AND
SEMICONDUCTOR LASERS, LIGHT-EMITTING DIODES, ORGANIC LED.
9. TRANSPORT PHENOMENA IN METALS AND SEMICONDUCTORS: THE
DRUDE THEORY OF CONDUCTIVITY IN METALS. HALL EFFECT IN METALS.
BOLTZMANN TRANSPORT EQUATION, RELAXATION TIME APPROXIMATION.
ELECTRIC CONDUCTIVITY. ELECTRIC CONDUCTIVITY OF NONDEGENERATE
SEMICONDUCTORS WITH SIMPLE BAND STRUCTURE. MECHANISMS OF
SCATTERING OF CHARGE CARRIERS AND THEIR INFLUENCE ON THE
RELAXATION TIME. THE HALL EFFECT IN SEMICONDUCTORS. HALL CONSTANT,
MAGNETORESISTANCE. THERMOELECTRIC EFFECT, THE PELTIER EFFECT.
10. MAGNETIC PROPERTIES OF SOLIDS: INFLUENCE OF THE MAGNETIC FIELD
ON ANGULAR MOTION OF ELECTRON. DIAMAGNETISM. PARAMAGNETISM.
LANGEVIN EQUATION, THE CURIE LAW. MAGNETIC PROPERTIES OF
CONDUCTION ELECTRONS. FERROMAGNETISM, EXCHANGE INTERACTION
BETWEEN LOCALISED ELECTRONS. THE HEISENBERG MODEL OF SPIN
ORDERING. DOMAINS. FERRI- AND ANTIFERROMAGNETISM.
11. PHYSICAL PROPERTIES OF DIELECTRICS: INDUCED AND ORIENTATION
POLARISATION OF DIELECTRICS, ION POLARISATION. THE CLAUSIUS-MOSSOTTI
RELATION, LORENTZ LOCAL FIELD. DIELECTRIC LOSES, DIPOLE RELAXATION,
RESONANT ABSORPTION, LO-TO SPLITING. PYROELECTRIC EFFECT,
PIEZOEFFECT.
12. PHASE TRANSITIONS: CLASSIFICATION OF PHASE TRANSITIONS, 1ST AND
2ND ORDER PHASE TRANSITIONS. THE LANDAU THEORY OF 2ND ORDER PHASE
TRANSITION. SOFT MODE. FERROELECTRICS.
13. SUPERCONDUCTIVITY: BASIC PROPERTIES OF SUPERCONDUCTING STATE,
1ST AND 2ND KIND SUPERCONDUCTORS. PHENOMENOLOGICAL DESCRIPTION
OF SUPERCONDUCTIVITY. ELEMENTS OF THE MICROSCOPIC BCS THEORY.
SUPERFLUIDITY OF LIQUID HELLIUM. THE CONSTANT CURRENT JOSEPHSON
EFFECT.
14. SURFACE PHYSICS: REFLECTION DIFFRACTION OF HIGH ENERGY
ELECTRONS (RHEED). ELECTRON STRUCTURE OF SURFACE, WORK FUNCTION,
THERMAL EMISSION, SURFACE STATES, CHARGE TRANSPORT IN TWODIMENSIONAL STRUCTURES. MAGNETORESISTANCE IN TWO-DIMENSIONAL
ELECTRON GAS, THE SCHUBNIKOV - DE HAAS OSCILATIONS, QUANTUM HALL
EFFECT.
METHODS OF INSTRUCTION
REQUIREMENTS AND ASSESSMENTS
GRADING SYSTEM
TOTAL STUDENT WORKLOAD
NEEDED TO ACHIEVE EXPECTED
LEARNING OUTCOMES EXPRESSED
IN TIME AND ECTS CREDIT POINTS
LANGUAGE OF INSTRUCTION
INTERNSHIP
MATERIALS
LECTURE, CLASS EXERCISES
CONTINUOUS ASSESSMENTS
TUTORIAL WORK AND ATTENDANCE (5%)
EXAM (95%)
Lectures
45 hr
Class exercises
45 hr
Preparation for classes
35 hr
Tutorials
6 hr
Preparation for exam
40 hr
Exam
4 hr
Total number of hours
175 hr
ECTS
7
ENGLISH
PRIMARY OR REQUIRED BOOKS/READINGS:
CH.KITTEL, INTRODUCTION TO SOLID STATE PHYSICS,
JOHN WILEY & SONS, LTD, 2005
H. IBACH, H. LUTH, SOLID-STATE PHYSICS, SPRINGER
2003
O. MADELUNG INTRODUCTION TO SOLID-STATE
THEORY, SPRINGER, 1996
SUPPLEMENTAL OR OPTIONAL BOOKS/READINGS:
MICHAEL C. PETTY “MOLECULAR ELECTRONICS FROM
PRINCIPLES TO PRACTICE”, JOHN WILEY & SONS, LTD,
2008
O.
MADELUNG,
“SEMICONDUCTORS:
DATA
HANDBOOK”, 3RD ED. EDITED BY O. MADELUNG,
SPRINGER, BERLIN 2004