Editing Semiconductor (section)

=== Energy bands and electrical conduction ===
{{Main article|Electronic band structure|Electrical resistivity and conductivity}}
{{Band structure filling diagram}}

Semiconductors are defined by their unique electric conductive behavior, somewhere between that of a conductor and an insulator.<ref>{{cite book |title=Fundamentals of Semiconductors |last=Yu |first=Peter |publisher=Springer-Verlag |year=2010 |isbn=978-3-642-00709-5 |location=Berlin}}</ref> The differences between these materials can be understood in terms of the [[quantum state]]s for electrons, each of which may contain zero or one electron (by the [[Pauli exclusion principle]]). These states are associated with the [[electronic band structure]] of the material. [[Electrical conductivity]] arises due to the presence of electrons in states that are [[delocalized electron|delocalized]] (extending through the material), however in order to transport electrons a state must be ''partially filled'', containing an electron only part of the time.<ref>As in the Mott formula for conductivity, see {{cite journal |last1=Cutler |first1=M. |last2=Mott |first2=N. |doi=10.1103/PhysRev.181.1336 |title=Observation of Anderson Localization in an Electron Gas |journal=Physical Review |volume=181 |issue=3 |pages=1336 |year=1969 |bibcode=1969PhRv..181.1336C}}</ref> If the state is always occupied with an electron, then it is inert, blocking the passage of other electrons via that state. The energies of these quantum states are critical since a state is partially filled only if its energy is near the [[Fermi level]]{{cn|date=January 2025}} (see [[Fermi–Dirac statistics]]).

High conductivity in material comes from it having many partially filled states and much state delocalization.
Metals are good [[electrical conductor]]s and have many partially filled states with energies near their Fermi level.
[[Insulator (electricity)|Insulators]], by contrast, have few partially filled states, their Fermi levels sit within [[band gap]]s with few energy states to occupy. Importantly, an insulator can be made to conduct by increasing its temperature: heating provides energy to promote some electrons across the band gap, inducing partially filled states in both the band of states beneath the band gap ([[valence band]]) and the band of states above the band gap ([[conduction band]]). An (intrinsic) semiconductor has a band gap that is smaller than that of an insulator and at room temperature, significant numbers of electrons can be excited to cross the band gap.<ref name="Kittel">[[Charles Kittel]] (1995) ''[[Introduction to Solid State Physics]]'', 7th ed. Wiley, {{ISBN|0-471-11181-3}}.</ref>

A pure semiconductor, however, is not very useful, as it is neither a very good insulator nor a very good conductor.
However, one important feature of semiconductors (and some insulators, known as ''semi-insulators'') is that their conductivity can be increased and controlled by [[doping (semiconductor)|doping]] with impurities and [[field effect (semiconductor)|gating]] with electric fields. Doping and gating move either the conduction or valence band much closer to the Fermi level and greatly increase the number of partially filled states.{{cn|date=January 2025}}

Some [[wide-bandgap semiconductor|wider-bandgap semiconductor]] materials are sometimes referred to as '''semi-insulators'''. When undoped, these have electrical conductivity nearer to that of electrical insulators, however they can be doped (making them as useful as semiconductors). Semi-insulators find niche applications in micro-electronics, such as substrates for [[high-electron-mobility transistor|HEMT]]. An example of a common semi-insulator is [[gallium arsenide]].<ref>{{cite journal |author=J. W. Allen |title=Gallium Arsenide as a semi-insulator |journal=Nature |volume=187 |pages=403–05 |year=1960 |doi=10.1038/187403b0 |bibcode=1960Natur.187..403A |issue=4735 |s2cid=4183332}}</ref> Some materials, such as [[titanium dioxide]], can even be used as insulating materials for some applications, while being treated as wide-gap semiconductors for other applications.{{cn|date=January 2025}}