From energy levels to energy bands
In an isolated atom, electrons occupy sharp energy levels. In a solid, atoms are packed so closely that their outer electrons interact, and each level spreads into a band of very closely spaced levels. Two bands matter most:
- The valence band, holding the valence electrons.
- The conduction band, above it. Electrons in this band are free to move and carry current.
The energy difference between the top of the valence band and the bottom of the conduction band is the band gap, E_g.
Conductors, insulators and semiconductors
- Conductors (metals): the conduction band is partly filled or overlaps the valence band (E_g = 0), so many free electrons are always available. Resistivity is very low (about 10⁻² to 10⁻⁸ Ω m).
- Insulators: E_g is large (more than about 3 eV; diamond has about 5.4 eV). Ordinary thermal energy cannot lift electrons across the gap. Resistivity is very high (about 10¹¹ to 10¹⁹ Ω m).
- Semiconductors: E_g is small (less than about 3 eV; Si about 1.1 eV, Ge about 0.7 eV). Resistivity lies in between (about 10⁻⁵ to 10⁶ Ω m).
Effect of temperature
At 0 K, the valence band of a semiconductor is full and the conduction band empty, so it behaves as an insulator. As temperature rises, some electrons gain enough thermal energy to cross the gap, leaving holes behind, and conductivity increases. Thus a semiconductor's resistance decreases with increasing temperature (negative temperature coefficient), unlike a metal.
Light and band gap
A photon can lift an electron across the gap only if hν ≥ E_g. The longest wavelength that can do this is λ = hc/E_g. For silicon, λ ≈ 1240/1.1 ≈ 1130 nm (about 1.13 μm, in the infrared).
Key points
- E_g = 0 (overlap) for conductors.
- E_g > 3 eV for insulators; < 3 eV for semiconductors.
- Si ≈ 1.1 eV, Ge ≈ 0.7 eV.
- Semiconductors are insulators at 0 K; their resistance falls as temperature rises.
Common mistakes
- Saying metals have a large band gap.
- Thinking semiconductor resistance rises with temperature like a metal.