PHY2024 Condensed Matter I 2017-18
Dr S. Hepplestone
 
Delivery Weeks: T2:01-11
Level: 5 (NQF)
Credits: 15 NICATS / 7.5 ECTS
Enrolment: 127 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:

Syllabus Plan

  1. Introduction
    Brief historical survey.
  2. 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
  3. 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
  4. 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
  5. Band Picture for Classification of Solids
    1. Formation of energy bands in solids
    2. Band picture for insulators, semiconductors and metals
  6. Fermi surfaces
    1. Fermi surfaces in metals
    2. Harrison's construction of the Fermi sphere
  7. 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
  8. 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
  9. 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
  10. 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:

Supplementary texts:

ELE:

Further Information

Prior Knowledge Requirements

Pre-requisite Modules Properties of Matter (PHY1024) and Quantum Mechanics I (PHY2022)
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-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