Quick and Dirty Preview of Solid State Physics
JHU Seal Quick and Dirty Preview of Solid State Physics

Jeffrey Wasserman
Second Year Seminar
Presented April 9, 2002
Johns Hopkins University

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Table of Contents

  1. Presentation Title
  2. What is Solid State Physics?
  3. What does Solid State Physics entail?
  4. Relative Importance of Solid State Physics
  5. Why is there interest in Solid State Physics?
  6. Historical Approach Part I - The Drude Model
  7. Successes of the Drude Model
  8. Historical Approach Part II - The Sommerfeld Model
  9. Inadequacies of the Drude and Sommerfeld Models
  10. Crystals and Lattices
  11. More About Lattices
  12. Reciprocal Lattice
  13. X-Ray Diffraction and Scattering from Lattices
  14. Effects of the Periodicity of the Lattice
  15. Bloch Waves and Brillouin Zones
  16. Brillouin Zones in Three Dimensions
  17. The Fermi Energy and the Fermi Surface
  18. The Nearly-Free Electron Gas
  19. Illustration of Nearly-Free Electron Gas in 1 Dimension
  20. Nearly-Free Electron Gas and Conductivity
  21. Nearly-Free Electron Gas in Aluminum
  22. Tightly-Bound Electrons - Overview
  23. Tightly-Bound Electrons and Band Structure
  24. Further Topics and Applications
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Aluminum is a metal with an FCC lattice. Aluminum is a good conductor, and the electrons can be thought of as nearly-free. Because of the three-dimensional aspects of the lattice, there are different energy levels for different directions. The letters on the figure to the right represent different crystal indices often reported.

For the free electron gas, the energy goes as the square of the distance to the origin. The left plot represents the free electron gas for a number of crystal indices. The right plot represents a detailed calculation of the energy structure for aluminum, along the same index vectors. Note the similarity between the two plots. Also note the creation of the bandgap in the detailed calculation.