Editing Semiconductor (section)

== Physics of semiconductors ==

=== 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}}

=== Charge carriers (electrons and holes) ===
{{Main article|Electron hole}}

The partial filling of the states at the bottom of the conduction band can be understood as adding electrons to that band. The electrons do not stay indefinitely (due to the natural thermal [[recombination (physics)|recombination]]) but they can move around for some time. The actual concentration of electrons is typically very dilute, and so (unlike in metals) it is possible to think of the electrons in the conduction band of a semiconductor as a sort of classical [[ideal gas]], where the electrons fly around freely without being subject to the [[Pauli exclusion principle]]. In most semiconductors, the conduction bands have a parabolic [[dispersion relation]], and so these electrons respond to forces (electric field, magnetic field, etc.) much as they would in a vacuum, though with a different [[effective mass (solid-state physics)|effective mass]].<ref name="Kittel"/> Because the electrons behave like an ideal gas, one may also think about conduction in very simplistic terms such as the [[Drude model]], and introduce concepts such as [[electron mobility]].

For partial filling at the top of the valence band, it is helpful to introduce the concept of an [[electron hole]]. Although the electrons in the valence band are always moving around, a completely full valence band is inert, not conducting any current. If an electron is taken out of the valence band, then the trajectory that the electron would normally have taken is now missing its charge. For the purposes of electric current, this combination of the full valence band, minus the electron, can be converted into a picture of a completely empty band containing a positively charged particle that moves in the same way as the electron. Combined with the ''negative'' effective mass of the electrons at the top of the valence band, we arrive at a picture of a positively charged particle that responds to electric and magnetic fields just as a normal positively charged particle would do in a vacuum, again with some positive effective mass.<ref name=" Kittel"/> This particle is called a hole, and the collection of holes in the valence band can again be understood in simple classical terms (as with the electrons in the conduction band).

==== Carrier generation and recombination ====
{{Main article|Carrier generation and recombination}}

When [[ionizing radiation]] strikes a semiconductor, it may excite an electron out of its energy level and consequently leave a hole. This process is known as [[carrier generation and recombination|''electron-hole pair generation'']]. Electron-hole pairs are constantly generated from [[thermal energy]] as well, in the absence of any external energy source.

Electron-hole pairs are also apt to recombine. [[Conservation of energy]] demands that these recombination events, in which an electron loses an amount of [[energy]] larger than the [[band gap]], be accompanied by the emission of thermal energy (in the form of [[phonon]]s) or radiation (in the form of [[photon]]s).

In some states, the generation and recombination of electron–hole pairs are in equipoise. The number of electron-hole pairs in the [[steady state]] at a given temperature is determined by [[quantum statistical mechanics]]. The precise [[quantum mechanics|quantum mechanical]] mechanisms of generation and recombination are governed by the [[conservation of energy]] and [[conservation of momentum]].

As the probability that electrons and holes meet together is proportional to the product of their numbers, the product is in the steady-state nearly constant at a given temperature, providing that there is no significant electric field (which might "flush" carriers of both types, or move them from neighbor regions containing more of them to meet together) or externally driven pair generation. The product is a function of the temperature, as the probability of getting enough thermal energy to produce a pair increases with temperature, being approximately {{nowrap|exp(−''E''<sub>G</sub>/''kT'')}}, where ''k'' is the [[Boltzmann constant]], ''T'' is the absolute temperature and ''E''<sub>G</sub> is bandgap.

The probability of meeting is increased by carrier traps&nbsp;– impurities or dislocations which can trap an electron or hole and hold it until a pair is completed. Such carrier traps are sometimes purposely added to reduce the time needed to reach the steady-state.<ref>{{cite book |last1=Louis Nashelsky |first1=Robert L.Boylestad |title=Electronic Devices and Circuit Theory |year=2006 |publisher=Prentice-Hall of India Private Limited |location=India |isbn=978-81-203-2967-6 |pages=7–10 |edition=9th}}</ref>

=== Doping ===
{{Main article|Doping (semiconductor)}}
[[Image:Silicon doping - Type P and N.svg|thumb|400px|Doping of a pure [[silicon]] array. Silicon based intrinsic semiconductor becomes extrinsic when impurities such as [[Boron]] and [[Antimony]] are introduced.]]
The conductivity of semiconductors may easily be modified by introducing impurities into their [[crystal lattice]]. The process of adding controlled impurities to a semiconductor is known as '''doping'''. The amount of impurity, or dopant, added to an ''[[intrinsic semiconductor|intrinsic]]'' (pure) semiconductor varies its level of conductivity.<ref>{{cite web |url=http://hyperphysics.phy-astr.gsu.edu/hbase/Solids/dope.html |title=Doped Semiconductors |access-date=May 3, 2021 |first=R. |last=Nave}}</ref> Doped semiconductors are referred to as [[extrinsic semiconductor|''extrinsic'']].<ref>{{cite web |url=https://electronicsdesk.com/difference-between-intrinsic-and-extrinsic-semiconductor.html |title=Difference Between Intrinsic and Extrinsic Semiconductors |first=Roshni |last=Y. |date=5 February 2019 |access-date=May 3, 2021}}</ref> By adding impurity to the pure semiconductors, the electrical conductivity may be varied by factors of thousands or millions.<ref>{{cite web |title=Lesson 6: Extrinsic semiconductors |url=https://archive.nptel.ac.in/content/storage2/courses/113106065/Week%203/Lesson6.pdf |archive-url=https://web.archive.org/web/20230128211456/https://archive.nptel.ac.in/content/storage2/courses/113106065/Week%203/Lesson6.pdf |archive-date=January 28, 2023 |access-date=January 28, 2023}}</ref>

A 1&nbsp;cm<sup>3</sup> specimen of a metal or semiconductor has the order of 10<sup>22</sup> atoms.<ref>{{cite web |url=https://www.chemteam.info/Liquids&Solids/WS-unit-cell-AP.html |title=General unit cell problems |access-date=May 3, 2021}}</ref> In a metal, every atom donates at least one free electron for conduction, thus 1&nbsp;cm<sup>3</sup> of metal contains on the order of 10<sup>22</sup> free electrons,<ref>{{cite web |url=http://hydrogen.physik.uni-wuppertal.de/hyperphysics/hyperphysics/hbase/electric/ohmmic.html |title=Ohm's Law, Microscopic View |access-date=May 3, 2021 |first=R. |last=Nave |archive-date=May 3, 2021 |archive-url=https://web.archive.org/web/20210503095813/http://hydrogen.physik.uni-wuppertal.de/hyperphysics/hyperphysics/hbase/electric/ohmmic.html |url-status=dead }}</ref> whereas a 1&nbsp;cm<sup>3</sup> sample of pure germanium at 20{{nbsp}}°C contains about {{val|4.2|e=22}} atoms, but only {{val|2.5|e=13}} free electrons and {{val|2.5|e=13}} holes. The addition of 0.001% of [[arsenic]] (an impurity) donates an extra 10<sup>17</sup> free electrons in the same volume and the electrical conductivity is increased by a factor of 10,000.<ref>{{cite web |url=https://ecee.colorado.edu/~bart/ecen3320/newbook/chapter2/ch2_6.htm |title=Carrier densities |date=2000 |access-date=May 3, 2021 |first=Bart |last=Van Zeghbroeck |archive-date=May 3, 2021 |archive-url=https://web.archive.org/web/20210503141622/https://ecee.colorado.edu/~bart/ecen3320/newbook/chapter2/ch2_6.htm |url-status=dead }}</ref><ref>{{cite web |url=http://www.ioffe.ru/SVA/NSM/Semicond/Ge/bandstr.html |title=Band strcutre and carrier concentration (Ge) |access-date=May 3, 2021}}</ref>

The materials chosen as suitable dopants depend on the atomic properties of both the dopant and the material to be doped. In general, dopants that produce the desired controlled changes are classified as either electron [[acceptor (semiconductors)|acceptors]] or [[donor (semiconductors)|donors]]. Semiconductors doped with ''donor'' impurities are called ''n-type'', while those doped with ''acceptor'' impurities are known as ''p-type''. The n and p type designations indicate which charge carrier acts as the material's [[majority carrier]]. The opposite carrier is called the [[minority carrier]], which exists due to thermal excitation at a much lower concentration compared to the majority carrier.<ref>{{cite web |url=https://www.halbleiter.org/en/fundamentals/doping/ |title=Doping: n- and p-semiconductors |access-date=May 3, 2021}}</ref>

For example, the pure semiconductor [[silicon]] has four valence electrons that bond each silicon atom to its neighbors.<ref>{{cite web |url=http://hyperphysics.phy-astr.gsu.edu/hbase/Solids/sili.html |title=Silicon and Germanium |access-date=May 3, 2021 |first=R. |last=Nave}}</ref> In silicon, the most common dopants are [[Boron group|group III]] and [[group V]] elements. Group III elements all contain three valence electrons, causing them to function as acceptors when used to dope silicon. When an acceptor atom replaces a silicon atom in the crystal, a vacant state (an electron "hole") is created, which can move around the lattice and function as a charge carrier. Group V elements have five valence electrons, which allows them to act as a donor; substitution of these atoms for silicon creates an extra free electron. Therefore, a silicon crystal doped with [[boron]] creates a p-type semiconductor whereas one doped with [[phosphorus]] results in an n-type material.<ref>{{cite web |url=https://www.pveducation.org/pvcdrom/pn-junctions/semiconductor-materials |title=Semiconductor Materials |first1=Christiana |last1=Honsberg |first2=Stuart |last2=Bowden |access-date=May 3, 2021}}</ref>

During [[semiconductor device fabrication|manufacture]], dopants can be diffused into the semiconductor body by contact with gaseous compounds of the desired element, or [[ion implantation]] can be used to accurately position the doped regions.

=== Amorphous semiconductors ===
Some materials, when rapidly cooled to a glassy amorphous state, have semiconducting properties. These include B, [[amorphous silicon|Si]], Ge, Se, and Te, and there are multiple theories to explain them.<ref>{{cite web| url = https://www.jhuapl.edu/Content/techdigest/pdf/APL-V07-N03/APL-07-03-Feldman.pdf| title = ''Amorphous semiconductors'' 1968}}</ref><ref>{{cite journal |title=Amorphous semiconductors: a review of current theories |first1=K. |last1=Hulls |first2=P. W. |last2=McMillan |date=May 22, 1972 |journal=Journal of Physics D: Applied Physics |volume=5 |issue=5 |pages=865–82 |doi=10.1088/0022-3727/5/5/205|s2cid=250874071 }}</ref>