Insulators
An electrical insulator is a material whose electrical resistivity is extremely high (typically above about 1010 Ω·m); in band-theory terms, its highest occupied band is completely full and is separated from the next empty band by a wide band gap (typically more than about 4 eV), so thermally excited carriers are vanishingly rare. Other mechanisms, such as strong electron correlation (Mott insulators) or disorder (Anderson insulators), can also produce insulating behaviour.
Curious
Glass, rubber, plastic, porcelain and diamond are insulators: they barely conduct electricity at all. The reason is quantum mechanical. Electrons in a solid occupy energy bands. In an insulator the lower band is completely full, so electrons cannot move within it, and the next band is separated by a wide gap. At room temperature, heat cannot provide enough energy to push electrons across.
The difference between an insulator and a semiconductor is one of degree: the gap is larger. Insulators are essential to all electrical technology: they confine current to wires, separate the plates of capacitors, and form the gate oxide in every transistor.
Exploring
| Material | Approx. resistivity at room temperature (Ω·m) | Band gap (eV) |
|---|---|---|
| Copper (metal) | 1.7×10−8 | none |
| Silicon (pure) | ~2×103 | 1.12 |
| Glass | 1010–1014 | ~9 (SiO2) |
| Diamond | 1011–1018 | 5.47 |
| PTFE | 1022–1024 | wide |
Deep Dive
Band insulators. Alan Wilson (1931) explained the metal–insulator distinction with band theory: a filled band carries no net current because for every electron with crystal momentum k there is one with −k. A band insulator needs an even number of electrons per primitive cell. Real insulators conduct slightly through impurities, ions or surface leakage, so measured resistivities vary by orders of magnitude with purity and humidity.
Beyond band theory. Nevill Mott showed that materials such as NiO, which band theory predicts to be metals, are insulating because electron–electron repulsion prevents electrons from hopping between sites (Mott insulators); Philip Anderson showed that strong disorder can localise electron waves (Anderson localisation). Mott and Anderson shared the 1977 Nobel Prize in Physics with John van Vleck. The high-temperature cuprate superconductors are doped Mott insulators, and their mechanism is still debated (see Superconductivity).
Topological insulators and breakdown. Topological insulators are insulating in the bulk but have protected conducting surface states, a distinction based on the global topology of their bands (see Brillouin Zone). Every insulator fails at a high enough field (dielectric breakdown, about 109 V/m in high-quality SiO2 and roughly 3×106 V/m in dry air), with values that depend on purity, thickness and test conditions.
Concept Relationship Map
Requires: energy bands, band theory
Enables: dielectrics, gate oxides, topological insulators
Commonly confused with: thermal insulators
Sources
- Wilson, A.H. (1931). Proceedings of the Royal Society A, 133, 458–491.
- Mott, N.F. (1949). “The Basis of the Electron Theory of Metals, with Special Reference to the Transition Metals.” Proceedings of the Physical Society A, 62, 416–422.
- Kittel, C. (2004). Introduction to Solid State Physics (8th ed.). Wiley.