# MPhys Physics with Theoretical Physics

Year of entry: 2024

## Course unit details:Fundamentals of Solid State Physics

Unit code PHYS20252 10 Level 2 Semester 2 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

On completion, successful students will be able to:

1. On completion, successful students will be able to:

2. Understand how atoms form molecules and solids.

3. Describe how wave motion in periodic structures leads to an understanding of the temperature dependence of specific heat and calculate the phonon dispersion relation for a chain of atoms.

4. Explain how electron wave functions and energies are changed by the presence of the periodic crystal potential.

5. Demonstrate how the electrical properties of metals, insulators and semiconductors are related to their electronic structure.

6. Explain how simple semiconductor devices (such as the p-n junction) work.

### Syllabus

1. From molecular to crystal bonding (5 lectures)

Molecular orbital theory applied to covalent bonding. H2+ ion. Hydrogen molecule. Molecular excitations. Van der Waals, ionic, covalent and metallic bonding and their relation to crystal structure.

2. Crystal structure (3 lectures)

Lattice, basis, and unit cell. Some common 2D and 3D crystal structures. Miler index.   Diffraction of waves by a crystal, Bragg's Law.

3. Lattice vibrations (2 lectures)

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.

4. Interaction of electrons with the crystal lattice (6 lectures)

Free electron model of a metal; states of free electrons; density of states and Fermi surface. Nearly free electron model; wave function electrons in 1D crystal; modification of free-electron dispersion relation; energy bands and band gaps. Classification of solids by their electric properties at zero temperature: metals and insulators. Tight-binding model. Sp-hybridizations. Graphene.

5. Nonzero-temperature properties of solids (4 lectures)

Einstein model of specific heat of lattice vibrations. Correction to Einstein model: Debye model. Effects of exchange antisymmetry for electrons in solids at zero temperature and low temperatures. The Fermi-Dirac distribution function. Quantum description of electronic heat capacity. Weidemann- Franz Law. Electrical and thermal conductivity: scattering of electrons from crystal defects and phonons.

6. Semiconductors (3 lectures)

Semiclassical dynamics of electrons; effective mass; holes; Hall effect. Intrinsic and extrinsic semiconductors, donors and acceptors, p-n junction. Semiconductor devices.

### Assessment methods

Method Weight
Other 10%
Written exam 90%

* Other 10% Tutorial Work/attendance

### 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