# MPhys Physics / Course details

Year of entry: 2022

## Course unit details:Fundamentals of Solid State Physics

Unit code PHYS20252 10 Level 2 Semester 2 Department of Physics & Astronomy No

### Overview

Fundamentals of Solid State Physics

### Pre/co-requisites

Unit title Unit code Requirement type Description
Vibrations & Waves PHYS10302 Pre-Requisite Compulsory
Properties of Matter PHYS10352 Pre-Requisite Compulsory
Mathematics 2 PHYS10372 Pre-Requisite Compulsory
Introduction to Quantum Mechanics PHYS20101 Pre-Requisite Compulsory

### Aims

To introduce the fundamental principles of solid state physics, taking wave motion in a crystal as the unifying concept; the waves include X rays, lattice vibrations and de Broglie waves of electrons. To show how the form of the electron wave functions, their energies, and their occupation by electrons help us to understand the differences between metals, insulators and semiconductors.

### Learning outcomes

‘This course unit detail provides the framework for delivery in 21/22 and may be subject to change due to any additional Covid-19 impact.  Please see Blackboard / course unit related emails for any further updates.’

On completion, successful students will be able to:

1. Describe how wave motion in periodic structures leads to an understanding of the temperature dependence of specific heat, and calculate the phonon dispersin relation for a chain of atoms.
2. Explain how electron wave functions and energies are changed by the presence of the periodic crystal potential.
3. Demonstrate how the electrical properties of metals, insulators and semiconductors are related to their electronic structure.
4. Explain how simple semiconductor devices (such as the p-n junction) work.

### Syllabus

Syllabus

1 Molecules (2 lectures)

Molecular orbital theory applied to covalent bonding. H2+ion. Hydrogen molecule.

2 Cyrstal Bonding & Structure (3 lectures)

Van der Waals, ionic, covalent and metallic bonding and their relation to crystal structure. Lattice, basis and unit cell. Some common 2D and 3D crystal structures. Diffraction of waves by a crystal, Bragg’s Law.

3 Lattice vibrations (4 lectures)

Einstein model of specific heat. Vibrations of a one-dimensional chain of atoms. Diatomic chain; optical and acoustic modes. Extension to three dimensions; the [first] Brillouin zone; transverse and longitudinal modes. Quantized lattice vibrations [phonons]; crystal momentum of phonons. Debye model of specific heat.

4 Electrons in solids (5 lectures)

Effects of exchange antisymmetry for electrons in solids at zero temperature and low temperatures. Free-electron model of a metal; states of free electrons; density of states and Fermi surface; the metallic bond. The Fermi-Dirac distribution function. Weidemann-Franz Law. Electrical and thermal conductivity: scattering of electrons from crystal defects and phonons. Quantum description of electronic heat capacity.

5 Interaction of electrons with the crystal lattice (3 lectures)

Wave functions of electrons in a one-dimensional crystal; crystal momentum. Modification of free-electron dispersion relation; energy bands and band gaps. Classification of solids by their electrical properties at zero temperature: metals and insulators. Semi-classical dynamics of electrons; effective mass; holes. Hall effect.

6 Semiconductors (4 lectures)

Intrinsic and extrinsic semiconductors, donors and acceptors, p-n junction, light emitting diode, solar cell, quantum dots.

7 Graphene (1 lecture)

Introduction to the band structure and physical properties of graphene.

Method Weight
Other 10%
Written exam 90%

### Feedback methods

Feedback will be offered by tutors on students’ written solutions to weekly examples sheets, and model answers will be issued.

Eisberg, R.M. & Resnick, R. Quantum Physics of Atoms, Molecules, Solids, Nuclei and Particles (Wiley)
De Podesta, M. Understanding the Properties of Matter, 2nd ed (Taylor & Francis)
Hook, J.R. & Hall, H.E. Solid State Physics, 2/e (Wiley)

### Study hours

Scheduled activity hours
Assessment written exam 1.5
Lectures 24
Tutorials 4
Independent study hours
Independent study 70.5

### Teaching staff

Staff member Role
Yang Xian Unit coordinator