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(NS) Solid State II - PHY00060H

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  • Department: Physics
  • Module co-ordinator: Dr. Stuart Cavill
  • Credit value: 10 credits
  • Credit level: H
  • Academic year of delivery: 2022-23
    • See module specification for other years: 2021-22

Module summary

Related modules

Pre-requisite modules

  • None

Co-requisite modules

  • None

Prohibited combinations


Module will run

Occurrence Teaching period
A Spring Term 2022-23

Module aims

If we want to understand physical properties such as electrical and thermal conductivity, magnetism or reflectivity and absorption, it is necessary to study the electronic structure and transport properties of electrons in solids. Starting with the classical free electron gas approximation we will develop the concepts of the Fermi gas and nearly free electron theory making use of the quantum mechanical description of electrons in a periodic potential. This leads to the band structure model, which will allow us to describe material systems such as semiconductors and metals. These concepts will then be used to obtain insight into the origin of magnetism and optical properties of materials.

Module learning outcomes

Learning outcomes: at the end of this module successful students will be able to:

  • Understand the different models involved describing the interaction between electrons and electrons as well between electrons and crystal lattice and the underlying physical principles.

  • Explain the concept of the free electron approximation in metals.

  • Describe the interaction of free electrons with a constant electric and a constant magnetic field.

  • Calculate the density of states based on the Fermi statistics.

  • Determine the electronic contribution to the heat capacity.

  • Distinguish direct and indirect band gap semiconductors.

  • Describe the different mechanisms of conductivity in semiconductors.

  • Explain the principles of semiconductor devices such as diodes and transistors.

  • Distinguish the different types of magnetic properties in solids.

  • Understand the principles of superconductivity

Module content

Syllabus

Recap of the Fermi-gas model

  • Free electron gas approximation (Drude – d.c. and a.c. response)
  • Fermi-Dirac statistics, Fermi-sphere, Fermi-distribution, density of electronic states, Energy dispersion
  • Heat capacity and electrical conductivity of the Fermi-gas
  • Interactions with constant electric/magnetic fields.

Nearly Free electron model

  • Perturbation Theory
  • Electrons in a periodic potential
  • Reduced Zone scheme, Extended Zone scheme
  • Tight Binding Model
  • Band structure and band gaps
  • Fermi surfaces and Brilliouin zones
  • Effective electron mass approximation
  • Measuring the Fermi surface. de-Haas van Alphen effect and ARPES
  • Failures of the Band-theory of Metals and Insulators

Semiconductors

  • Direct and indirect band gaps
  • Intrinsic and doped semiconductors
  • Cyclotron Resonance
  • Impact of temperature on charge density and conductivity
  • The p-n junction

Dielectric and optical properties

  • Optical transitions in direct and indirect semiconductors
  • Plasma Frequency
  • Reflectivity and absorption of metals

Magnetic properties

  • Para-, dia-, ferro- and antiferromagnetism
  • Ising Model of Ferromagnetism
  • Hubbard Model of Itinerant Magnetism and the Stoner Criteria

Superconductivity

  • London Equations
  • Meissner effect
  • BCS-theory

Assessment

Task Length % of module mark
Essay/coursework
Solid State II Assignment 1		 N/A 40
Essay/coursework
Solid State II Assignment 2		 N/A 60

Special assessment rules

None

Reassessment

Task Length % of module mark
Essay/coursework
Solid State II Assignment 1		 N/A 40
Essay/coursework
Solid State II Assignment 2		 N/A 60

Module feedback

Our policy on how you receive feedback for formative and summative purposes is contained in our Department Handbook.

Indicative reading

C. Kittel: Introduction to Solid State Physics (Wiley and Sons)

N.W. Ashcroft and N.D. Mermin: Solid State Physics (Saunders College Publishing)

H. Ibach and H. Lüth: Solid-State Physics – An Introduction to Principles of Materials Science (Springer-Verlag)


The information on this page is indicative of the module that is currently on offer. The University is constantly exploring ways to enhance and improve its degree programmes and therefore reserves the right to make variations to the content and method of delivery of modules, and to discontinue modules, if such action is reasonably considered to be necessary by the University. Where appropriate, the University will notify and consult with affected students in advance about any changes that are required in line with the University's policy on the Approval of Modifications to Existing Taught Programmes of Study.