Module Description

PHY2024 Condensed Matter I

2011-2012

Code: PHY2024
Level: 2
Title: Condensed Matter I
Instructors: Dr J. Martin
CATS Credit Value: 15
ECTS Credit Value: 7.5
Pre-requisites: N/A
Co-requisites: N/A
Duration: T2:01-11
Availability: unrestricted
Background Assumed: -

Total Student Study Time

150 hours, to include: 22×1-hour lectures; 44 hours directed self-study; 10 hours of problems class support; 3 hours of tutorial support; 72 hours private study.

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. In this module, the student will discover 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. The module concludes with a brief introduction to some of the latest developments in one- and two-dimensional systems that are being studied in the research groups at Exeter.

Intended Learning Outcomes

Students will be able to:

  1. Module Specific Skills:
    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.
  2. Discipline Specific Skills:
    1. apply thermodynamics, electromagnetism and quantum mechanics to the sold-state;
    2. use mathematical abstraction to represent and solve problems involving periodic structures.
  3. Personal Transferable Skills:
    1. solve problems requiring spatial reasoning;
    2. use a range of resources to develop an understanding of topics through independent study.

Learning / Teaching Methods

Lectures, e-Learning resources (ELE PHY2024), and problems classes.

Assessment and Assignments

ContributionAssessment/AssignmentSize (duration/length)When
10%Problem Sets8×2hrsWeekly
15%Mid-term Test30 minutesWeek T2:06
75%Final examination120 minutesTerm 3
FormativeGuided self-study5×6-hour packagesFortnightly

Syllabus Plan and Content

  1. Introduction
    Brief historical survey.
  2. 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
  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

Core Text

Kittel C. , Introduction to Solid State Physics, Wiley (UL: 530.41 KIT)

Supplementary Text(s)

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 (2nd edition), Wiley, ISBN 0-471-928054 (UL: 530.41 HOO)

IOP Accreditation Compliance Checklist

Formative Mechanisms

The problems that students are set on this module are marked and discussed in detail in the problems classes and in tutorials. Students monitor their own progress by attempting the problems set. Students who need additional guidance are encouraged to discuss the matter with their tutor or the lecturer.

Evaluation Mechanisms

The module will be evaluated using information gathered via the student representation mechanisms, the staff peer appraisal scheme, and measures of student attainment based on summative assessment.

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