8.1 Energy band theory

Energy band theory explains why some solids conduct electricity well, some hardly at all, and some, the semiconductors, conduct moderately in a way that can be controlled. In a single isolated atom, electrons occupy sharp energy levels. When billions of atoms are packed together in a solid, the levels of neighbouring atoms overlap and spread out into continuous bands of allowed energies, separated by forbidden gaps where no electron can exist. Whether a solid conducts depends on how these bands are filled and how wide the gap between them is. Example: an electronics assembly plant in Kiamariga that builds solar charge controllers trains its technicians in band theory so that they understand why silicon devices behave differently when hot.

The bands

• Valence band: The highest band that is normally filled with the outer (valence) electrons that bind the atoms together. Electrons in a full band cannot carry current, because there are no empty states for them to move into.
• Conduction band: The band above the valence band. Electrons that reach it are free to move through the solid and carry current.
• Forbidden gap (band gap, Eg): The energy gap between the top of the valence band and the bottom of the conduction band, measured in electronvolts (1 eV = 1.6 × 10⁻¹⁹ J). An electron must gain at least Eg to jump into the conduction band.

Conductors, insulators and semiconductors

Intrinsic semiconductors

A pure (intrinsic) semiconductor such as silicon has four valence electrons per atom, each shared in a covalent bond with a neighbour. At absolute zero all the electrons are in bonds and it is an insulator. At room temperature, thermal energy breaks a few bonds, lifting electrons into the conduction band. Each freed electron leaves behind a vacancy in the valence band called a hole, which behaves as a positive charge carrier because a neighbouring electron can move into it, so the hole moves. In an intrinsic semiconductor the number of free electrons equals the number of holes.

• Effect of temperature: More bonds break as temperature rises, so the number of carriers increases and the resistance falls. This is the opposite of a metal and is the basis of thermistors.
• Effect of light: Photons with energy greater than Eg free electrons, so conductivity increases in light, the basis of light dependent resistors and photodiodes.

Extrinsic (doped) semiconductors

Adding a tiny, controlled amount of impurity (doping, about one atom in a million) greatly increases conductivity and decides which carrier dominates.

• n-type: Silicon doped with a pentavalent element (five valence electrons) such as phosphorus, arsenic or antimony. Four electrons bond; the fifth is only loosely held and is easily freed into the conduction band. Electrons are the majority carriers and holes the minority carriers. The impurity is called a donor.
• p-type: Silicon doped with a trivalent element (three valence electrons) such as boron, aluminium or gallium. One bond is left incomplete, creating a hole. Holes are the majority carriers and electrons the minority carriers. The impurity is called an acceptor.
• Still neutral: Both n-type and p-type materials are electrically neutral overall, because each impurity atom brings equal numbers of protons and electrons.

Band gap and light

The band gap sets the wavelength of light a semiconductor absorbs or emits, through E = hf = hc ÷ λ. A photon must have at least Eg of energy to free an electron. For silicon, λ = hc ÷ Eg = (6.626 × 10⁻³⁴ × 3.0 × 10⁸) ÷ (1.12 × 1.6 × 10⁻¹⁹) ≈ 1,110 nm, so silicon detectors respond to all visible light and the near infrared, which is why they are used as detectors in spectrophotometers and cameras.

Why band theory matters in the laboratory

• Detectors: Silicon photodiodes and diode arrays in UV-visible spectrophotometers, and cooled germanium or silicon detectors in X-ray and gamma spectrometers, all rely on photons lifting electrons across the band gap.
• Temperature sensors: Thermistors and silicon sensors measure temperature through the change in carrier numbers.
• Instrument drift: Semiconductor circuits change with temperature, so instruments need warm-up time and stable room temperatures.