Experiment 5
Electronic Band Structure: Metals, Semiconductors, Insulators
Observe how a periodic lattice potential opens band gaps in the free-electron dispersion.
Model Parameters
Classification
Semiconductor (Small Gap)
Key Equations
Kronig-Penney Condition:
cos(ka) = P sin(αa)/(αa) + cos(αa)
When |val| > 1, no solution for real k exists, leading to forbidden band gaps.
E-k Dispersion Relation
Dispersion Fermi Level Gap (White Space)
Task: Potential Strength
Set P = 0 and observe the free-electron parabola. Slowly increase P and watch the gaps open at the zone boundaries (k = 1.0). How does gap width change with P?
Teaching Connection
Band theory is the foundation of modern electronics. The visual of "EF lying inside a band = conductor" vs "EF inside a gap = insulator" is the most useful mental model for students.
Reflection Questions
- Why does the group velocity (dE/dk) go to zero at the zone boundaries?
- What is the difference between an insulator and a semiconductor in terms of band structure?
- Explain why sodium is a metal even though it has a partially filled band.