Study information

Condensed Matter I - 2023 entry

MODULE TITLECondensed Matter I CREDIT VALUE15
MODULE CODEPHY2024 MODULE CONVENERDr Steven Hepplestone (Coordinator)
DURATION: TERM 1 2 3
DURATION: WEEKS 11
Number of Students Taking Module (anticipated) 146
DESCRIPTION - summary of the module content

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.

AIMS - intentions of the module

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) (see assessment section below for how ILOs will be assessed)
 
A student who has passed this module should be able to:
 
Module Specific Skills and Knowledge:
1. describe the features of the vibrations of monatomic and of diatomic linear chains and explain the significance of dispersion curves in three dimensions;
2. discuss the scattering of phonons, and in particular the occurrence of Umklapp scattering of phonons near the Brillouin zone edge;
3. describe the free electron model and apply it in calculations;
4. 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;
5. explain qualitatively band theory and the concepts of Brillouin zone, density of states, Fermi energy, effective mass and holes;
6. state Bloch's theorem, and sketch E-k diagrams;
7. describe acceptors, donors and the basic optical transitions in semiconductors;
8. distinguish between extrinsic and intrinsic properties of semiconductors;
9. define drift, diffusion and thermal conduction and the relations between them for metals, semiconductors and degenerate semiconductors;
10. explain how to construct a Fermi surface;
 
Discipline Specific Skills and Knowledge:
11. apply thermodynamics, electromagnetism and quantum mechanics to the sold-state;
12. use mathematical abstraction to represent and solve problems involving periodic structures;
 
Personal and Key Transferable / Employment Skills and Knowledge:
13. solve problems requiring spatial reasoning;
14. use a range of resources to develop an understanding of topics through independent study;
15. meet deadlines for completion of work for problems classes and develop appropriate time-management strategies.
SYLLABUS PLAN - summary of the structure and academic content of the module
I. Introduction
  1. Brief historical survey.
II. Crystal Structures
  1. Direct and reciprocal lattices (Revision)
  2. General features of scattering by solids (Revision)
  3. Scattered-wave amplitude, structure factor, form factor
  4. Brillouin zones
III. 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
IV. 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
V. Band Picture for Classification of Solids
  1. Formation of energy bands in solids
  2. Band picture for insulators, semiconductors and metals
VI. Fermi surfaces
  1. Fermi surfaces in metals
  2. Harrison's construction of the Fermi sphere
VII. 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
VIII. Phonons
  1. Lattice vibrations of the monatomic linear chain
  2. Diatomic linear chain.
  3. Lattice vibrations of three-dimensional crystals
    • Longitudinal and transverse phonons;
    • Plotting of dispersion relations
  4. Heat Capacity
IX. 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
X. Introduction to Nanostructures and Nanomaterials
  1. Quantum Wells, Wires and Dots
  2. Carbon nanotubes
  3. Graphene
LEARNING AND TEACHING
LEARNING ACTIVITIES AND TEACHING METHODS (given in hours of study time)
Scheduled Learning & Teaching Activities 33 Guided Independent Study 117 Placement / Study Abroad
DETAILS OF LEARNING ACTIVITIES AND TEACHING METHODS
Category Hours of study time Description
Scheduled learning & teaching activities 22 hours 22×1-hour lectures
Guided independent study 30 hours 5×6-hour self-study packages
Guided independent study 16 hours 8×2-hour problems sets
Scheduled learning & teaching activities 8 hours Problems class support
Scheduled learning & teaching activities 3 hours Tutorial support
Guided independent study 71 hours Reading, private study and revision

 

ASSESSMENT
FORMATIVE ASSESSMENT - for feedback and development purposes; does not count towards module grade
Form of Assessment Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
Exercises set by tutor (0%) 3×1-hour sets (typical) (Scheduled by tutor) 1-16 Discussion in tutorials
Guided self-study (0%) 5×6-hour packages (Fortnightly) 1-16 Discussion in tutorials
       
       
       

 

SUMMATIVE ASSESSMENT (% of credit)
Coursework 10 Written Exams 90 Practical Exams
DETAILS OF SUMMATIVE ASSESSMENT
Form of Assessment % of Credit Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
8 × Problems sets 10% 2 hours per set (weekly) 1-16 Marked in problems class, then discussed in tutorials
Mid-term Test 15% 30 minutes (Term 2, Week 6) 1-15 Marked, then discussed in tutorials
Examination 75% 120 minutes (May/June assessment period) 1-15 Mark via MyExeter, collective feedback via ELE and solutions.
         
         

 

DETAILS OF RE-ASSESSMENT (where 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

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

RE-ASSESSMENT NOTES
An original assessment that is based on both examination and coursework, tests, etc., is considered as a single element for the purpose of referral; i.e., the referred mark is based on the referred examination only, discounting all previous marks. In the event that the mark for a referred assessment is lower than that of the original assessment, the original higher mark will be retained.
 
Physics Modules with PHY Codes
Referred examinations will only be available in PHY3064, PHYM004 and those other modules for which the original assessment includes an examination component - this information is given in individual module descriptors.
RESOURCES
INDICATIVE LEARNING RESOURCES - The following list is offered as an indication of the type & level of
information that you are expected to consult. Further guidance will be provided by the Module Convener
ELE:
 

Reading list for this module:

Type Author Title Edition Publisher Year ISBN
Set Kittel, C. Introduction to Solid State Physics 8th edition Wiley 2005 978-0-471-41526-8
Extended Christman, J.R. Fundamentals of Solid State Physics Wiley 1988 0-471-81095-9
Extended Hook, J.R. and H. E. Hall Solid State Physics 2nd edition Wiley 1991 0-471-928054
CREDIT VALUE 15 ECTS VALUE 7.5
PRE-REQUISITE MODULES PHY1024, PHY2022
CO-REQUISITE MODULES
NQF LEVEL (FHEQ) 5 AVAILABLE AS DISTANCE LEARNING No
ORIGIN DATE Thursday 15th December 2011 LAST REVISION DATE Thursday 26th January 2023
KEY WORDS SEARCH Physics; Electronic; Semiconductor; Fermi; Phonons; Lattices; Energy; Properties; Crystal; Bands; State.

Please note that all modules are subject to change, please get in touch if you have any questions about this module.