Solid State Physics
Electrons in Periodic Potentials
Bloch's Theorem and Band Structure
In a periodic lattice with potential , Bloch's theorem states that electron wavefunctions take the form: where has the lattice periodicity. This leads to energy bands separated by band gaps.
Band Theory of Solids
- Conductors: Partially filled valence band — electrons free to move.
- Insulators: Large band gap ( eV) — valence band full, conduction band empty at .
- Semiconductors: Small gap ( eV for Si) — thermal promotion of electrons into conduction band. Holes carry current in valence band.
Doping: donor atoms add electrons (n-type); acceptor atoms add holes (p-type).
Effective Mass
In a band, electrons behave as free particles but with an effective mass . Near a band minimum (maximum), is positive (negative).
Why is silicon a semiconductor and not a metal?
Small band gap means some thermal excitation at room temperature, giving finite but low conductivity.
Correct answer: Its band gap ~1.1 eV allows thermal excitation of carriers
An n-type semiconductor is created by:
Donors (e.g., phosphorus in silicon) have one extra electron that goes into the conduction band.
Correct answer: Doping with donor atoms that add extra electrons to the conduction band
Explain the concept of a 'hole' in semiconductor physics.
Holes are quasi-particles representing missing electrons in the valence band.
Correct answer: When an electron is excited from the valence band, it leaves behind a vacant state (hole). This hole behaves as a positive charge carrier with its own effective mass, moving in the opposite direction to electrons.