Introduction: Band Theory in Action
The distinction between conductors, insulators, and semiconductors comes from how electrons fill the energy bands. This is quantum mechanics determining everyday material properties.
The Fermi Level
Electrons fill bands from lowest energy up (Pauli exclusion). The highest occupied level at T = 0 is the Fermi level \(E_F\).
Three Types of Materials
Conductor (Metal):
- Fermi level in the middle of a band
- Empty states available just above \(E_F\)
- Electrons can easily gain energy and move → conducts
Insulator:
- Fermi level in a large band gap (\(> 3\) eV)
- No accessible empty states
- Electrons can't move → insulates
Semiconductor:
- Fermi level in a small band gap (\(\approx 1\) eV)
- Thermal excitation can promote electrons across gap
- Conductivity controllable → basis of electronics
The Quantum Connection
Transistors, solar cells, LEDs—all rely on band structure. Doping adds electrons to the conduction band (n-type) or creates holes in the valence band (p-type). Modern electronics is applied quantum mechanics of periodic potentials.