Energy Bands in Solids: Conductors and Semiconductors

In a solid, atoms are packed so close that their energy levels merge into broad bands of allowed energies. The way electrons fill these bands decides whether the solid behaves as a conductor, an insulator or a semiconductor. This simple idea explains why copper carries current easily, rubber blocks it, and silicon can be controlled.

Energy bands are important because all modern electronics, from wires to computer chips, depends on choosing the right material. By understanding the valence band, conduction band and the gap between them, we can predict electrical behaviour without memorising each material separately.

Key Concepts

• Valence band: The highest band that is filled or partly filled by valence electrons at low temperature.
• Conduction band: The next higher band. Electrons here are free to move and carry current.
• Forbidden gap (Eg): Energy region between valence and conduction bands where no electron states exist. Measured in electron volt (eV).
• Fermi level: The energy level with 50 percent probability of being occupied at a given temperature.
• Conductor: Valence and conduction bands overlap, Eg is zero. Example: copper, aluminium.
• Insulator: Large gap, about 5 eV or more. Example: diamond about 5.5 eV, rubber.
• Semiconductor: Small gap, about 1 eV. Silicon Eg is 1.1 eV, germanium is 0.67 eV at room temperature.

How It Works

1. At absolute zero, semiconductors and insulators have a full valence band and empty conduction band, so they do not conduct.
2. When heated, some electrons gain thermal energy, jump across the gap and leave holes behind in the valence band.
3. Both the free electrons and the holes carry current when a voltage is applied.
4. In metals, the conduction band is already partly filled, so current flows even at very low temperature.
5. Conductivity increases with temperature for semiconductors, but decreases for metals due to more lattice vibrations.

Worked Example

Find the wavelength of light that can just excite an electron across silicon gap of 1.1 eV. Photon energy E = hc / λ. Using hc = 1240 eV nm, λ = 1240 / 1.1 = 1127 nm. This is in the infrared region. So silicon absorbs visible light of shorter wavelength and is used in solar cells and photodiodes.

Common Misconceptions

• Semiconductors are medium conductors like a weak wire: Wrong. Their conductivity can be changed enormously by temperature, light and doping.
• Holes are real particles inside the solid: A hole is the absence of an electron, but it moves like a positive charge carrier.
• Insulators never conduct: At very high voltage they break down and conduct suddenly.

Real-World Applications

• Copper and aluminium wires for power transmission as conductors.
• Silicon and gallium arsenide for diodes, transistors and solar cells.
• Glass, ceramic and plastic insulators for safe electrical fittings.
• LEDs use band gap engineering to produce different colours of light.

Energy bands give one clear picture for all solids: overlapping bands make conductors, a large gap makes insulators, and a small gap makes useful semiconductors whose conduction can be controlled.