Solids and Surfaces

Course goals

Content

This course deals with a physical understanding of the electronic properties of solids.
Part I presents an elementary explanation of the band theory for three-dimensional crystals, with the distinction between metals, insulators and semiconductors. The models are simple and based on the free electron model with planar waves, and nearly free electrons represented by Bloch-type wavefunctions. We will discuss:

• Free electron Fermi gas: properties of metals, the model of planar waves with periodic boundary conditions, Fermi-Dirac statistics, specific heat, electronic conduction, the Hall effect.
• Electronic band theory: empirical distinction between insulators and metals, an intuitive model based on Bragg scattering of planar waves, the LCAO theory, solution of the Schrödinger equation with planar waves, Bloch-type wave functions, filling of the bands with electrons.
• Semiconductors: empirical properties and societal impact, optical transitions, electrons and holes, response of electrons and holes to external fields: group velocity and effective mass, variation of the electron and hole concentration in semiconductors.

Part 2 presents how electrons behave when confined into two dimensions, with electrons in surfaces, graphene and topological insulators as examples. Part 2 also introduces tight-binding models. We will discuss:

• Geometric structure of surfaces and materials in real and reciprocal space (Bravais lattices, Quasicrystals, Miller indices, diffraction, workfunction).
• Electronic structure of 2D (and 3D) materials based on tight-binding.
• Graphene and topological insulators.

The course builds on the leerlijnen “Fysische Chemie” and “Quantum Chemie en Anorganische Chemie”. Subsequently, the course Quantum Chemistry 2 (SK-B2QC2) is closely connected to the present course.