Course Contents
This course is an introduction to the quantum mechanics of functional materials. We will cover fundamental concepts such as phonons, crystal electrons and other quasi particles which are used to model functional properties of materials such as metals, semi-conductors, magnets, superconductors etc. A profound knowledge of these concepts is essential to pass most compulsory modules of our master's programme.
The lecture starts with the basics such as the PSE and lattices in the first two weeks to get everybody on board. Then we will move on the the quantum mechanical description of lattice vibration, the quantum mechanics of electrons in metals, semiconductors and other quantum related phenomena.
A word of caution: To our experience, the difficulty to understand quantum mechanics and to apply it to solid state phenomena is often underestimated. If you are not yet fluent with Hamilton operators, second quantization or other concepts you will need your time to digest the topic. We thus strongly recommend that you attend the lecture, tutorials and excercises in person.
[b]Content[/b]
• Properties of crystalline solids: orientation dependence, lattice and reciprocal lattice, semiconductors, metals and isolators.
• Lattice dynamics: lattice with monatomic and diatomic basis, dispersion relation, Brillouin zones, acoustic and optical modes, phonons, density of states, specific heat, thermal transport, thermal expansion.
• Metals: electronic structure, band model, free electron gas, density of states, Fermi-Dirac statistics, Bloch functions
• Electronic transport: Drude model, Drude-Sommerfeld model, thermal properties of the electron gas.
• Semiconductors: synthesis (examples), doping, electronic transport, effective mass, chemical potential, optical properties, density of states, diodes.
• Solid state ionics: ionic and mixed transport.
• Dielectric properties: polarisation and polarizability, electronic and ionic polarization, optical properties, electro-elastic properties
• Magnetism: para, dia- and ferromagnetism, magnetism of solids.
Literature
Online @ ULB:
[list]
[*]Hofmann, Philip; Solid state physics : an Introduction
[*]John J. Quinn, Kyung-Soo Yi Solid State Physics : Principles and Modern Applications
[*]Harald Ibach, Hans LüthSolid-State, Physics : An Introduction to Principles of Materials Science
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The books of C. Kittel und Ashcroft/Mermin are available in print.
At https://libretexts.org you find a collection of open textbooks. Hava a look at the chemistry section.
Preconditions
The module exam is an individual obligation (admission letter) or requires individual permission by the examination board.
This module cannot be selected by graduates holding a Bachelor’s degree in Materials Science from TU Darmstadt.
Official Course Description
[b]Learning Outcomes[/b]
On successful completion of the module, students are able to:
[list=1]
[*]describe crystals as the combination of a lattice with a pattern and can explain interference phenomena using the concept of the reciprocal lattice;
[*]explain diffraction of electromagnetic waves, electron waves or collective excitations in a lattice;
[*]critically discuss electrical and thermal transport properties based on crystal structure, phononic and/or electronic structure;
[*]explain fundamental material properties in appropriate pictures of quasi-particles and collective excitations based on a quantum mechanical approach;
[*]explain ionic transport in solid;
[*]explain the interaction of electromagnetic fields and waves with materials;
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- Lecturer: Franziska Scheibel
- Lecturer: Robert Stark
