Key Points
- Kronig-Penny model is a infinite array of finite wells.
- Solution produces a "quantization equation" that
produces band gaps in the E(k) relationship.
- Transistion from:
- Isolated well -- descrete energy values, wave
functions are standing waves.
- A few wells -- energy values split, tunneling between
wells.
- Periodic wells - energy bands, plane wave "like"
solution due to tunneling, weak potential produces almost parabolic
E(k), but multivalued and repeated in k space.
- Free electrons -- continueous E(k), parabolic, plane
wave solution.
Questions
- What are energy bands?
- Explain the E(k) relationship
for an isolated well, a few wells and periodic wells.