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
Previous Slide Next Slide
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Above are a number of views demonstrating the lifting of the degeneracy on the Bragg plane, and the creation of the energy gap.

The upper left picture represents the parabolic energy due to a perfectly-free electron around the k-space origin.

The next picture to the right shows two intersecting parabolae about two subsequent atoms in k-space. Notice the parabolae intersect halfway between the two atoms.

The degeneracy at the Bragg plane halfway-point is lifted because the electrons are MOSTLY free but not ALL free.

Redrawn to the right, getting rid of the duplicate information, the original parabola, as shown in the left half, gets a discontinuity on the right half at the Bragg plane. note that nearby the plane the energy curves into the Bragg plane. This is similar to the Fermi Surface from Slide #17.

The bottom three pictures show three ways of presenting the same information. The Extended-Zone Scheme shows the parabolic shape of electron states extending out over many one-dimensional Brillouin Zones, with the appropriate gaps at the Bragg planes.

The Reduced-Zone Scheme gives the same information, but with all the higher-order Brillouin zones folded over into the first zone. This portrayal of the band structure is usually the one most often used.

Finally, the Repeated-Zone Scheme shows the same information of the Reduced-Zone Scheme repeated over several Brillouin zones.

It is important to note that these three views all display the same information equally, they are just useful in different circumstances for presenting the band structure of the material.