6: The Electronic Structure of Materials — Read

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The particle in the box approximation completely ignores the internal structure of conductors. For example, it treats an insulator such as diamond the same as a conductor such as gold. Despite this it can be surprisingly useful, as we have seen in the discussion of ballistic transistors. We are concerned now with more accurate calculations of electronic structure. Unfortunately, exact solutions are not usually possible. Determining the energies and wavefunctions of multiple electrons in a solid is a classic "many body problem". For example, to solve for the electrons, we must know the exact position of each atom in the solid, and also calculate all interactions between multiple electrons. Nevertheless, there is much to be learnt from a first principles analysis of electronic structure. We‟ll begin at the bottom, with the hydrogen atom.

6.1: The hydrogen atom
6.2: Atoms to Molecules
6.3: Molecular orbitals
6.4: Linear combination of atomic orbitals (LCAO)
6.5: The Tight Binding Approximation
6.6: Solving for the energy
6.7: Examples of tight binding calculations
6.8: Polyacetylene
6.9: Crystals and periodic molecules
6.10: Polyacetylene (average bond model)
6.11: Polyacetylene (alternating bond model)
6.12: Graphene
6.13: Simple cubic, face centered cubic and diamond lattices
6.14: Bloch functions- wavefunctions in periodic molecules
6.15: The first Brillouin zone
6.16: 2-d and 3-d periodic materials
6.17: Tight Binding Calculations in Periodic molecules and crystals
We now repeat the polyacetylene calculation, but this time we impose periodic boundary conditions and assume molecular wavefunctions of the Bloch form. The solutions are almost identical to the previous calculation in the absence of periodic boundary conditions, but there are some subtle yet important differences in the dispersion relation.
6.18: Bandstructure of Bulk Semiconductors
6.19: Band Gaps and Conduction and Valence bands
6.20: Analytic approximations for the bandstructure of graphene and carbon nanotubes
6.21: Band diagrams
6.22: Semiconductors and Insulators
6.23: Problems

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