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. 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

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

Assessment

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

Supplementary texts:

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

ELE:

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

Further Information

Prior Knowledge Requirements

Re-assessment

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

Notes: See Physics Assessment Conventions.

KIS Data Summary

Miscellaneous