PHY2024 2013-2014 - Module Description

PHY2024	Condensed Matter I	2013-14
	Dr V.V. Kruglyak

Delivery Weeks:	T2:01-11
Level:	5 (NQF)
Credits:	15 NICATS / 7.5 ECTS
Enrolment:	71 students (approx)

Description

This module will explain how electrons, and other waves, propagate within crystalline materials and affect their properties. The properties of periodic structures are discussed, particularly the relationship between real space and reciprocal space and the representation of elastic and inelastic scattering in both spaces. Both phonons and electrons are profoundly influenced by the crystal structure in which they propagate. The last section of this module considers the transport of electrons in the free-electron and nearly-free-electron approximations, which give a good description of the behaviour of electrons in metals and semiconductors. The vibrational excitations of the crystal lattice (phonons) are of particular importance to the properties of insulators.

Module Aims

Condensed matter physics, particularly in the solid-state, underpins modern technology and is also important because it provides the physical realisation of much fundamental physics. This module aims to give the student a firm grounding in the traditional areas of the subject but also to introduce some of the latest developments in one- and two-dimensional systems that are being studied in the research groups at Exeter.

Intended Learning Outcomes (ILOs)

A student who has passed this module should be able to:

Module Specific Skills and Knowledge:
1. explain how elastic scattering by a crystal is treated using the concept of the reciprocal lattice and how calculations separate factors which depend on the lattice and on the basis and solve problems relating to representative solid state materials;
2. describe the features of the vibrations of monatomic and of diatomic linear chains and explain the significance of dispersion curves in three dimensions;
3. discuss the scattering of phonons, and in particular the occurrence of Umklapp scattering of phonons near the Brillouin zone edge;
4. describe the free electron model and apply it in calculations;
5. use the nearly free electron model to account for the occurrence of energy gaps at the Brillouin zone edges, and the consequent behaviour of the group velocity and effective mass of the electrons;
6. explain qualitatively band theory and the concepts of Brillouin zone, density of states, Fermi energy, effective mass and holes;
7. state Bloch's theorem, and sketch E-k diagrams;
8. describe acceptors, donors and the basic optical transitions in semiconductors;
9. distinguish between extrinsic and intrinsic properties of semiconductors;
10. define drift, diffusion and thermal conduction and the relations between them for metals, semiconductors and degenerate semiconductors;
11. explain how to construct a Fermi surface;
Discipline Specific Skills and Knowledge:
1. apply thermodynamics, electromagnetism and quantum mechanics to the sold-state;
2. use mathematical abstraction to represent and solve problems involving periodic structures;
Personal and Key Transferable / Employment Skills and Knowledge:
1. solve problems requiring spatial reasoning;
2. use a range of resources to develop an understanding of topics through independent study;
3. meet deadlines for completion of work for problems classes and develop appropriate time-management strategies.

Syllabus Plan

Introduction
Brief historical survey.
Bragg scattering
1. Crystal Sructures (Revision)
2. General features of scattering by solids
3. Scattered-wave amplitude
4. Laue conditions for diffraction
5. Reciprocal lattice and Brillouin zones
6. Structure factor
7. Examples: X-ray diffractometer; transmission electron microscope
Free-electron model
1. Free-electron Fermi gas
2. Energy dispersion in k-space
3. Reduced and extended zones
4. Effective mass
5. Density of states
6. Electron-distribution function; Fermi level
7. Heat capacity
Nearly-Free-Electron Model
1. Effect of crystal potential on the free-electron picture
2. Bloch electron
3. Origin of energy-band gaps
4. Holes
Band Picture for Classification of Solids
1. Formation of energy bands in solids
2. Band picture for insulators, semiconductors and metals
Fermi surfaces
1. Fermi surfaces in metals
2. Harrison's construction of the Fermi sphere
Intrinsic and Extrinsic Semiconductors
1. Donor and acceptor levels in semiconductors; ionization energy of a donor electron, and the Bohr radius
2. Free-charge-carrier concentration and the Fermi level at different temperatures
3. The significance of the Fermi level; band structure of a p-n junction
4. Elementary Optical Properties of Semiconductors: Fundamental absorption; direct and indirect transitions; absorption coefficient; recombination
Phonons
1. Lattice vibrations of the monatomic linear chain
2. Diatomic linear chain.
3. Lattice vibrations of three-dimensional crystals
  1. Longitudinal and transverse phonons;
  2. Plotting of dispersion relations
4. Heat Capacity
Transport Properties (Electrical and Thermal)
1. Relaxation times: phonon/lattice; electronic
2. Drift and diffusion in semiconductors; the Einstein relation
3. Thermal conduction in semiconductors and insulators
4. Drift and thermal conduction in metals
5. The Wiedemann-Franz law
Introduction to Nanostructures and Nanomaterials
1. Quantum Wells, Wires and Dots
2. Carbon nanotubes
3. Graphene

Learning and Teaching

Learning Activities and Teaching Methods

Description	Study time	KIS type
22×1-hour lectures	22 hours	SLT
5×6-hour self-study packages	30 hours	GIS
8×2-hour problems sets	16 hours	GIS
Problems class support	8 hours	SLT
Tutorial support	3 hours	SLT
Reading, private study and revision	71 hours	GIS

Assessment

Weight	Form	Size	When	ILOS assessed	Feedback
0%	Exercises set by tutor	3×1-hour sets (typical)	Scheduled by tutor	1-16	Discussion in tutorials
0%	Guided self-study	5×6-hour packages	Fortnightly	1-16	Discussion in tutorials
10%	8 × Problems sets	2 hours per set	Weekly	1-16	Marked in problems class, then discussed in tutorials
15%	Mid-term test	30 minutes	Weeks T2:06	1-15	Marked, then discussed in tutorials
75%	Examination	120 minutes	May/June assessment period	1-15	Mark via MyExeter, collective feedback via ELE and solutions.

Resources

The following list is offered as an indication of the type & level of information that students are expected to consult. Further guidance will be provided by the Module Instructor(s).

Core text:

Kittel C. (2005), Introduction to Solid State Physics (8^th edition), Wiley, ISBN 978-0-471-41526-8 (UL: 530.41 KIT)

Supplementary texts:

Christman J.R. (1988), Fundamentals of Solid State Physics, Wiley, ISBN 0-471-81095-9 (UL: 530.41 CHR)
Hook J.R. and Hall H.E. (1991), Solid State Physics (2^nd edition), Wiley, ISBN 0-471-928054 (UL: 530.41 HOO)

ELE:

http://newton.ex.ac.uk/redirects/ELE/phy2024

Further Information

Prior Knowledge Requirements

Pre-requisite Modules	Properties of Matter (PHY1024)
Co-requisite Modules	none

Re-assessment

Re-assessment is not available except when required by referral or deferral.

Original form of assessment	Form of re-assessment	ILOs re-assessed	Time scale for re-assessment
Whole module	Written examination (100%)	1-15	August/September assessment period

Notes: See Physics Assessment Conventions.

KIS Data Summary

Learning activities and teaching methods
SLT - scheduled learning & teaching activities	33 hrs
GIS - guided independent study	117 hrs
PLS - placement/study abroad	0 hrs
Total	150 hrs

Summative assessment
Coursework	10%
Written exams	90%
Practical exams	0%
Total	100%

Miscellaneous

IoP Accreditation Checklist	SS-03 Phonons and heat capacity SS-04 Crystal structure and Bragg scattering SS-05 Electron theory of solids to the level of simple band structure SS-06 Semiconductors and doping
Availability	unrestricted
Distance learning	NO
Keywords	Physics; Electronic; Semiconductor; Fermi; Phonons; Lattices; Energy; Properties; Crystal; Bands; State.
Created	01-Oct-10
Revised	01-Oct-11