Editing Semiconductor

{{Short description|Material that has electrical conductivity intermediate to that of a conductor and an insulator}}
{{For-multi|devices using semiconductors and their history|Semiconductor device|other uses}}
[[File:Monokristalines Silizium für die Waferherstellung.jpg|thumb|upright=0.8|An [[boule (crystal)|ingot]] of [[monocrystalline silicon]]]]
{{Semiconductor manufacturing processes}}

A '''semiconductor''' is a material with [[electrical conductivity]] between that of a [[Electrical conductor|conductor]] and an [[Insulator (electricity)|insulator]].<ref>{{cite web |last=Tatum |first=Jeremy |date=13 December 2016 |title=Resistance and Temperature |url=https://phys.libretexts.org/Bookshelves/Electricity_and_Magnetism/Electricity_and_Magnetism_(Tatum)/04%3A_Batteries_Resistors_and_Ohm's_Law/4.03%3A_Resistance_and_Temperature |access-date=2023-12-22 |website=LibreTexts}}</ref> Its conductivity can be modified by adding impurities ("[[doping (semiconductor)|doping]]") to its [[crystal structure]]. When two regions with different doping levels are present in the same crystal, they form a [[semiconductor junction]]. 

The behavior of [[charge carrier]]s, which include [[electron]]s, [[ion]]s, and [[electron hole]]s, at these junctions is the basis of [[diode]]s, [[transistor]]s, and most modern [[electronics]]. Some examples of semiconductors are [[silicon]], [[germanium]], [[gallium arsenide]], and elements near the so-called "[[metalloid staircase]]" on the [[periodic table]]. After silicon, gallium arsenide is the second-most common semiconductor and is used in [[laser diode]]s, [[solar cell]]s, microwave-frequency [[integrated circuit]]s, and others. Silicon is a critical element for fabricating most [[electronic circuit]]s.

[[Semiconductor device]]s can display a range of different useful properties, such as passing current more easily in one direction than the other, showing variable resistance, and having sensitivity to light or heat. Because the electrical properties of a semiconductor material can be modified by doping and by the application of electrical fields or light, devices made from semiconductors can be used for amplification, switching, and [[energy conversion]]. The term semiconductor is also used to describe materials used in high capacity, medium- to [[high-voltage cable]]s as part of their insulation, and these materials are often plastic XLPE ([[cross-linked polyethylene]]) with carbon black.<ref>{{cite book | url=https://books.google.com/books?id=X8QfRT_SYDgC&dq=carbon+black+cable&pg=PA20 | title=Submarine Power Cables: Design, Installation, Repair, Environmental Aspects | isbn=978-3-642-01270-9 | last1=Worzyk | first1=Thomas | date=11 August 2009 | publisher=Springer }}</ref>

The conductivity of silicon is increased by adding a small amount (of the order of 1 in 10<sup>8</sup>) of pentavalent ([[antimony]], [[phosphorus]], or [[arsenic]]) or trivalent ([[boron]], [[gallium]], [[indium]]) atoms.<ref>{{Cite web |title=Electrical Conduction in Semiconductors |url=https://www.mks.com/n/electrical-conduction-semiconductors |access-date=2024-04-01 |website=www.mks.com}}</ref> This process is known as doping, and the resulting semiconductors are known as doped or [[extrinsic semiconductor]]s. Apart from doping, the conductivity of a semiconductor can be improved by increasing its temperature. This is contrary to the behavior of a metal, in which conductivity decreases with an increase in temperature.<ref>{{Cite web |date=2015-01-12 |title=Joshua Halpern |url=https://chem.libretexts.org/Courses/Howard_University/General_Chemistry%3A_An_Atoms_First_Approach/Unit_5%3A_States_of_Matter/Chapter_12%3A_Solids/Chapter_12.06%3A_Metals_and_Semiconductors |access-date=2024-04-01 |website=Chemistry 003 |language=en}}</ref>

The modern understanding of the properties of a semiconductor relies on [[quantum physics]] to explain the movement of charge carriers in a [[crystal structure|crystal lattice]].<ref name=Feynman>{{cite book |last1=Feynman |first1=Richard |title=Feynman Lectures on Physics |url=https://feynmanlectures.caltech.edu}}</ref> Doping greatly increases the number of charge carriers within the crystal. When a semiconductor is doped by Group V elements, they will behave like [[Donor (semiconductors)|donors]] creating free [[electron]]s, known as "[[extrinsic semiconductor#N-type semiconductors|n-type]]" doping. When a semiconductor is doped by Group III elements, they will behave like [[acceptor (semiconductors)|acceptors]] creating free holes, known as "[[extrinsic semiconductor#P-type semiconductors|p-type]]" doping. The semiconductor materials used in electronic devices are doped under precise conditions to control the concentration and regions of p- and n-type dopants. A single semiconductor device [[crystal]] can have many p- and n-type regions; the [[p–n junction]]s between these regions are responsible for the useful electronic behavior. Using a [[hot-point probe]], one can determine quickly whether a semiconductor sample is p- or n-type.<ref>{{cite web |title=2.4.7.9 The "hot-probe" experiment |url=https://ecee.colorado.edu/~bart/book/hotprobe.htm |website=ecee.colorado.edu |access-date=27 November 2020 |archive-date=6 March 2021 |archive-url=https://web.archive.org/web/20210306224540/https://ecee.colorado.edu/~bart/book/hotprobe.htm |url-status=dead }}</ref>

A few of the properties of semiconductor materials were observed throughout the mid-19th and first decades of the 20th century. The first practical application of semiconductors in electronics was the 1904 development of the [[cat's-whisker detector]], a primitive semiconductor diode used in early [[wireless telegraphy|radio]] receivers. Developments in quantum physics led in turn to the invention of the [[transistor]] in 1947<ref>{{cite book |last1=Shockley |first1=William |title=Electrons and holes in semiconductors: with applications to transistor electronics |date=1950 |publisher=R. E. Krieger Pub. Co |isbn=978-0-88275-382-9}}</ref> and the [[integrated circuit]] in 1958.

== Properties ==

=== Variable electrical conductivity ===
Semiconductors in their natural state are poor conductors because a [[electric current|current]] requires the flow of electrons, and semiconductors have their [[valence band]]s filled, preventing the entire flow of new electrons. Several developed techniques allow semiconducting materials to behave like conducting materials, such as [[doping (semiconductor)|doping]] or [[field effect (semiconductor)|gating]]. These modifications have two outcomes: '''n-type''' and '''p-type'''. These refer to the excess or shortage of electrons, respectively. A balanced number of electrons would cause a current to flow throughout the material.<ref name="Neamen">{{cite book |last1=Neamen |first1=Donald A.|title=Semiconductor Physics and Devices |url=http://www.fulviofrisone.com/attachments/article/403/Semiconductor%20Physics%20And%20Devices%20-%20Donald%20Neamen.pdf|archive-url=https://web.archive.org/web/20221027123709/http://www.fulviofrisone.com/attachments/article/403/Semiconductor%20Physics%20And%20Devices%20-%20Donald%20Neamen.pdf|year=2003|archive-date=October 27, 2022 |publisher=Elizabeth A. Jones}}</ref>

=== Homojunctions ===
'''[[Homojunction]]s''' occur when two differently doped semiconducting materials are joined. For example, a configuration could consist of p-doped and n-doped [[germanium]]. This results in an exchange of electrons and holes between the differently doped semiconducting materials. The n-doped germanium would have an excess of electrons, and the p-doped germanium would have an excess of holes. The transfer occurs until an equilibrium is reached by a process called [[recombination (physics)|recombination]], which causes the migrating electrons from the n-type to come in contact with the migrating holes from the p-type.<ref>{{Cite web |date=2016-07-28 |title=Electron-Hole Recombination |url=https://eng.libretexts.org/Bookshelves/Materials_Science/Supplemental_Modules_(Materials_Science)/Electronic_Properties/Electron-Hole_Recombination |access-date=2024-04-01 |website=Engineering LibreTexts |language=en}}</ref> The result of this process is a narrow strip of immobile [[ion]]s, which causes an [[electric field]] across the junction.<ref name="Feynman" /><ref name="Neamen"
 />

=== Excited electrons ===
A difference in electric potential on a semiconducting material would cause it to leave thermal equilibrium and create a non-equilibrium situation. This introduces electrons and holes to the system, which interact via a process called [[ambipolar diffusion]]. Whenever thermal equilibrium is disturbed in a semiconducting material, the number of holes and electrons changes. Such disruptions can occur as a result of a temperature difference or [[photon]]s, which can enter the system and create electrons and holes. The processes that create or annihilate electrons and holes are called [[carrier generation and recombination|generation]] and recombination, respectively.<ref name="Neamen" />

=== Light emission ===
In certain semiconductors, excited electrons can relax by emitting light instead of producing heat.<ref>By Abdul Al-Azzawi. "[https://books.google.com/books?id=Iw7NBQAAQBAJ&dq=In+certain+semiconductors,+excited+electrons+can+relax+by+emitting+light+instead+of+producing+heat.%5C&pg=PA54 Light and Optics: Principles and Practices]." 2007. March 4, 2016.</ref> Controlling the semiconductor composition and [[Electric current|electrical current]] allows for the manipulation of the emitted light's properties.<ref>{{Cite web |title=Electrical Property of Semiconductor - an overview {{!}} ScienceDirect Topics |url=https://www.sciencedirect.com/topics/engineering/electrical-property-of-semiconductor |access-date=2023-12-14 |website=www.sciencedirect.com}}</ref> These semiconductors are used in the construction of [[light-emitting diode]]s and fluorescent [[quantum dot]]s.

===High thermal conductivity===
Semiconductors with high thermal conductivity can be used for heat dissipation and improving [[Thermal management (electronics)|thermal management]] of electronics. They play a crucial role in [[electric vehicle]]s, high-brightness [[Light-emitting diode|LEDs]] and [[power module]]s, among other applications.<ref>{{Citation |last1=Wang |first1=Yangang |title=Status and Trend of Power Semiconductor Module Packaging for Electric Vehicles |date=2016-10-05 |work=Modeling and Simulation for Electric Vehicle Applications |url=https://www.intechopen.com/chapters/51578 |access-date=2024-01-24 |publisher=IntechOpen |language=en |isbn=978-953-51-2637-9 |last2=Dai |first2=Xiaoping |last3=Liu |first3=Guoyou |last4=Wu |first4=Yibo |last5=Jones |first5=Yun Li and Steve}}</ref><ref>Arik, Mehmet, and Stanton Weaver. "Chip-scale thermal management of high-brightness LED packages." ''Fourth International Conference on Solid State Lighting''. Vol. 5530. SPIE, 2004.</ref><ref>{{Cite book |last1=Boteler |first1=L. |last2=Lelis |first2=A. |last3=Berman |first3=M. |last4=Fish |first4=M. |chapter=Thermal Conductivity of Power Semiconductors—When Does It Matter? |date=2019 |title=2019 IEEE 7th Workshop on Wide Bandgap Power Devices and Applications (WiPDA) |chapter-url=https://ieeexplore.ieee.org/document/8998802 |publisher=IEEE |pages=265–271 |doi=10.1109/WiPDA46397.2019.8998802 |isbn=978-1-7281-3761-2|s2cid=211227341 }}</ref>

=== Thermal energy conversion ===
Semiconductors have large [[thermoelectric power factor]]s making them useful in [[thermoelectric generator]]s, as well as high [[thermoelectric figure of merit|thermoelectric figures of merit]] making them useful in [[thermoelectric cooler]]s.<ref>{{cite web |url=https://ii-vi.com/how_do_thermoelectric_coolers_tec_work/ |title=How do thermoelectric coolers (TECs) work? |website=ii-vi.com |access-date=2021-11-08}}</ref>

== Materials ==
{{Main article|List of semiconductor materials}}

[[File:Silicon.jpg|thumb|[[Silicon]] crystals are the most common semiconducting materials used in [[microelectronics]] and [[photovoltaics]].]]

A large number of elements and compounds have semiconducting properties, including:<ref name=Yacobi03>B. G. Yacobi, ''Semiconductor Materials: An Introduction to Basic Principles'', Springer 2003 {{ISBN|0-306-47361-5}}, pp. 1–3.</ref>
* Certain pure elements are found in [[Group 14 elements|group&nbsp;14]] of the [[periodic table]]; the most commercially important of these elements are [[silicon]] and [[germanium]]. Silicon and germanium are used here effectively because they have 4 valence electrons in their outermost shell, which gives them the ability to gain or lose electrons equally at the same time.
* [[Binary compound]]s, particularly between elements in groups&nbsp;13 and 15, such as [[gallium arsenide]], groups&nbsp;12 and 16, groups&nbsp;14 and 16, and between different group-14 elements, e.g. [[silicon carbide]].
* Certain ternary compounds, oxides, and alloys.
* [[Organic semiconductor]]s, made of [[organic compound]]s.
* Semiconducting [[metal–organic framework]]s.<ref>{{cite journal |last1=Dong |first1=Renhao |last2=Han |first2=Peng |last3=Arora |first3=Himani |last4=Ballabio |first4=Marco |last5=Karakus |first5=Melike |last6=Zhang |first6=Zhe |last7=Shekhar |first7=Chandra |last8=Adler |first8=Peter |last9=Petkov |first9=Petko St. |last10=Erbe |first10=Artur |last11=Mannsfeld |first11=Stefan C. B. |date=2018 |title=High-mobility band-like charge transport in a semiconducting two-dimensional metal–organic framework |url=https://www.nature.com/articles/s41563-018-0189-z |journal=Nature Materials |language=en |volume=17 |issue=11 |pages=1027–1032 |doi=10.1038/s41563-018-0189-z |pmid=30323335 |bibcode=2018NatMa..17.1027D |s2cid=53027396 |issn=1476-4660}}</ref><ref>{{cite book |last=Arora |first=Himani |url=https://himani-arora-ha.github.io/pdf/Dissertation.pdf |title=Charge transport in two-dimensional materials and their electronic applications |publisher=Qucosa |year=2020 |location=Dresden}}</ref>

The most common semiconducting materials are crystalline solids, but [[amorphous silicon|amorphous]] and liquid semiconductors are also known. These include [[hydrogenated amorphous silicon]] and mixtures of [[arsenic]], [[selenium]], and [[tellurium]] in a variety of proportions. These compounds share with better-known semiconductors the properties of intermediate conductivity and a rapid variation of conductivity with temperature, as well as occasional [[negative resistance]]. Such disordered materials lack the rigid crystalline structure of conventional semiconductors such as silicon. They are generally used in [[thin film]] structures, which do not require material of higher electronic quality, being relatively insensitive to impurities and radiation damage.

=== Preparation of semiconductor materials ===
Almost all of today's electronic technology involves the use of semiconductors, with the most important aspect being the [[integrated circuit]] (IC), which are found in [[desktop computer|desktops]], [[laptop computer|laptops]], scanners, [[cell-phone]]s, and other electronic devices. Semiconductors for ICs are mass-produced. To create an ideal semiconducting material, chemical purity is paramount. Any small imperfection can have a drastic effect on how the semiconducting material behaves due to the scale at which the materials are used.<ref name=Neamen />

A high degree of crystalline perfection is also required, since faults in the crystal structure (such as [[dislocation]]s, [[crystal twinning|twins]], and [[stacking fault]]s) interfere with the semiconducting properties of the material. Crystalline faults are a major cause of defective semiconductor devices. The larger the crystal, the more difficult it is to achieve the necessary perfection. Current mass production processes use crystal [[ingot]]s between {{convert|100|and|300|mm|in|abbr=on}} in diameter, grown as cylinders and sliced into [[wafer (electronics)|wafers]]. The round shape characteristic of these wafers comes from [[Boule (crystal)|single-crystal ingots]] usually produced using the [[Czochralski method]]. Silicon wafers were first introduced in the 1940s.<ref>{{cite journal |author=Reinhard Voelkel | title=Wafer-scale micro-optics fabrication | journal=Advanced Optical Technologies | year=2012 | volume=1 | issue=3 | page=135 | doi=10.1515/aot-2012-0013| bibcode=2012AdOT....1..135V | s2cid=137606531 | doi-access=free }}</ref><ref>{{cite book |author1=T. Doi |author2=I.D. Marinescu |author3=Syuhei Kurokawa | title=Advances in CMP Polishing Technologies, Chapter 6 – Progress of the Semiconductor and Silicon Industries – Growing Semiconductor Markets and Production Areas | pages=297–304 | publisher=Elsevier | year=2012 | doi=10.1016/B978-1-4377-7859-5.00006-5}}</ref>

There is a combination of processes that are used to prepare semiconducting materials for ICs. One process is called [[thermal oxidation]], which forms [[silicon dioxide]] on the surface of the [[silicon]]. This is used as a [[gate dielectric|gate insulator]] and [[LOCOS|field oxide]]. Other processes are called [[photomask]]s and [[photolithography]]. This process is what creates the patterns on the circuit in the integrated circuit. [[Ultraviolet light]] is used along with a [[photoresist]] layer to create a chemical change that generates the patterns for the circuit.<ref name=Neamen />

The etching is the next process that is required. The part of the silicon that was not covered by the [[photoresist]] layer from the previous step can now be etched. The main process typically used today is called [[plasma etching]]. Plasma etching usually involves an [[plasma etching|etch gas]] pumped in a low-pressure chamber to create [[plasma (physics)|plasma]]. A common etch gas is [[chlorofluorocarbon]], or more commonly known [[Freon]]. A high [[radio-frequency]] [[voltage]] between the [[cathode]] and [[anode]] is what creates the plasma in the chamber. The [[wafer (electronics)|silicon wafer]] is located on the cathode, which causes it to be hit by the positively charged ions that are released from the plasma. The result is silicon that is etched [[anisotropy|anisotropically]].<ref name=Feynman /><ref name=Neamen />

The last process is called [[doping (semiconductor)|diffusion]]. This is the process that gives the semiconducting material its desired semiconducting properties. It is also known as [[doping (semiconductor)|doping]]. The process introduces an impure atom to the system, which creates the [[p–n junction]]. To get the impure atoms embedded in the silicon wafer, the wafer is first put in a 1,100 degree Celsius chamber. The atoms are injected in and eventually diffuse with the silicon. After the process is completed and the silicon has reached room temperature, the doping process is done and the semiconducting [[Wafer (electronics)|wafer]] is almost prepared.<ref name=Feynman /><ref name=Neamen />

== Metrology in Semiconductor Manufacturing ==

As semiconductor devices grow in complexity, ensuring dimensional accuracy and surface quality has become increasingly critical throughout the entire manufacturing process. Metrology plays a pivotal role in monitoring and controlling fabrication steps, from wafer preparation to final testing, without disrupting production.

Traditional 2D vision systems are effective for fast inspection, but lack depth resolution. As a result, 3D optical metrology has become essential for high-resolution, non-contact surface characterization. Techniques such as white-light interferometry, confocal microscopy, focus variation, and spectroscopic reflectometry are used to measure film thickness, step height, surface roughness, and defects with sub-nanometer precision.

These technologies are applied across both front-end and back-end semiconductor processes:

* In wafer fabrication, profilometry is used to evaluate raw materials such as silicon carbide (SiC), diamond, and perovskites. Accurate surface and flatness measurements ensure quality in crystal growth, slicing, and polishing stages.
* During front-end processing, 3D optical profilers are used to measure oxidation and deposition film thicknesses, etch profiles, photolithographic mask structures, and planarization pad wear.
* In back-end processes, metrology verifies bump dimensions, die bonding layers, laser engraving depth, and pin coplanarity—ensuring reliable electrical and mechanical performance in advanced packaging.

By enabling precise, repeatable, and fast surface metrology, these tools support semiconductor manufacturers in improving process yield, reducing costs, and meeting the demands of emerging technologies like AI, IoT, and heterogeneous integration.
<ref name="IRDS2015">International Roadmap for Devices and Systems (IRDS), 2015 Edition.</ref>
<ref name="Sensofar2025">Sensofar Metrology, "White Paper: Semiconductor Manufacturing", 2025. [https://www.sensofar.com/metrology/applications/semiconductors/]</ref>

== 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>

== Early history of semiconductors ==
{{See also|Semiconductor device#History of semiconductor device development|Timeline of electrical and electronic engineering}}

The history of the understanding of semiconductors begins with experiments on the electrical properties of materials. The properties of the time-temperature coefficient of resistance, rectification, and light-sensitivity were observed starting in the early 19th century.

[[File:Ferdinand Braun.jpg|thumb|218x218px|[[Karl Ferdinand Braun]] developed the [[crystal detector]], the first [[semiconductor device]], in 1874.]]

[[Thomas Johann Seebeck]] was the first to notice that semiconductors exhibit special feature such that experiment concerning an [[thermoelectric effect#Seebeck effect|Seebeck effect]] emerged with much stronger result when applying semiconductors, in 1821.<ref>{{cite web |url=https://www.kirj.ee/public/Engineering/2007/issue_4/eng-2007-4-2.pdf |title=Kirj.ee}}</ref> In 1833, [[Michael Faraday]] reported that the resistance of specimens of [[silver sulfide]] decreases when they are heated. This is contrary to the behavior of metallic substances such as copper. In 1839, [[Alexandre Edmond Becquerel]] reported observation of a voltage between a solid and a liquid electrolyte, when struck by light, the [[photovoltaic effect]]. In 1873, [[Willoughby Smith]] observed that [[selenium]] [[resistor]]s exhibit decreasing resistance when light falls on them. In 1874, [[Karl Ferdinand Braun]] observed conduction and [[rectifier|rectification]] in metallic [[sulfide]]s, although this effect had been discovered earlier by Peter Munck af Rosenschöld ([[:sv:Peter Munck af Rosenschöld|sv]]) writing for the ''Annalen der Physik und Chemie'' in 1835; Rosenschöld's findings were ignored.<ref name=":0">{{cite book |url=https://books.google.com/books?id=rslXJmYPjGIC&q=Semiconductor+Rectifier+Rosenschold&pg=PA24 |title=A History of the World Semiconductor Industry |first=Peter Robin |last=Morris |date=July 22, 1990 |publisher=IET |via=Google Books |isbn=9780863412271}}</ref> [[Simon Sze]] stated that Braun's research was the earliest systematic study of semiconductor devices.<ref>{{Cite book |last=Sze |first=Simon |author-link=Simon Sze |title=Semiconductor Devices: Physics and Technology |publisher=Wiley |year=2002 |isbn=9789971513955 |edition=2nd |pages=3}}</ref> Also in 1874, [[Arthur Schuster]] found that a copper oxide layer on wires had rectification properties that ceased when the wires are cleaned. [[William Grylls Adams]] and Richard Evans Day observed the photovoltaic effect in selenium in 1876.<ref name=JTIT10>{{cite journal |author1=Lidia Łukasiak |author2=Andrzej Jakubowski |name-list-style=amp |date=January 2010 |url=http://www.nit.eu/czasopisma/JTIT/2010/1/3.pdf |title=History of Semiconductors |journal=Journal of Telecommunication and Information Technology |page=3 |access-date=2012-08-03 |archive-date=2013-06-22 |archive-url=https://web.archive.org/web/20130622045329/http://www.nit.eu/czasopisma/JTIT/2010/1/3.pdf |url-status=dead }}</ref>

A unified explanation of these phenomena required a theory of [[solid-state physics]], which developed greatly in the first half of the 20th century. In 1878 [[Edwin Herbert Hall]] demonstrated the deflection of flowing charge carriers by an applied magnetic field, the [[Hall effect]]. The discovery of the [[electron]] by [[J.J. Thomson]] in 1897 prompted theories of electron-based conduction in solids. [[Karl Baedeker (scientist)|Karl Baedeker]], by observing a Hall effect with the reverse sign to that in metals, theorized that copper iodide had positive charge carriers. {{ill|Johan Koenigsberger|de|Johann Koenigsberger}} classified solid materials like metals, insulators, and "variable conductors" in 1914 although his student Josef Weiss already introduced the term '''''Halbleiter''''' (a semiconductor in modern meaning) in his Ph.D. thesis in 1910.<ref>{{cite journal |doi=10.1088/0143-0807/10/4/002 |volume=10 |issue=4 |title=Early history of the physics and chemistry of semiconductors-from doubts to fact in a hundred years |journal=European Journal of Physics |pages=254–64 |bibcode=1989EJPh...10..254B |year=1989 |last1=Busch |first1=G|s2cid=250888128 }}</ref><ref>{{cite web |url=https://books.google.com/books?id=oVBNQwAACAAJ |title=Experimentelle Beiträge Zur Elektronentheorie Aus dem Gebiet der Thermoelektrizität, Inaugural-Dissertation ... von J. Weiss, ... |first=Josef Weiss (de |last=Überlingen.) |date=July 22, 1910 |publisher=Druck- und Verlags-Gesellschaft |via=Google Books}}</ref> [[Felix Bloch]] published a theory of the movement of electrons through atomic lattices in 1928. In 1930, {{ill|B. Gudden|de|Bernhard Gudden}} stated that conductivity in semiconductors was due to minor concentrations of impurities. By 1931, the band theory of conduction had been established by [[Alan Herries Wilson]] and the concept of band gaps had been developed. [[Walter H. Schottky]] and [[Nevill Francis Mott]] developed models of the potential barrier and of the characteristics of a [[metal–semiconductor junction]]. By 1938, Boris Davydov had developed a theory of the copper-oxide rectifier, identifying the effect of the [[p–n junction]] and the importance of minority carriers and surface states.<ref name=":0" />

Agreement between theoretical predictions (based on developing quantum mechanics) and experimental results was sometimes poor. This was later explained by [[John Bardeen]] as due to the extreme "structure sensitive" behavior of semiconductors, whose properties change dramatically based on tiny amounts of impurities.<ref name=":0" /> Commercially pure materials of the 1920s containing varying proportions of trace contaminants produced differing experimental results. This spurred the development of improved material refining techniques, culminating in modern semiconductor refineries producing materials with parts-per-trillion purity.

Devices using semiconductors were at first constructed based on empirical knowledge before semiconductor theory provided a guide to the construction of more capable and reliable devices.

[[Alexander Graham Bell]] used the light-sensitive property of selenium to [[photophone|transmit sound]] over a beam of light in 1880. A working solar cell, of low efficiency, was constructed by [[Charles Fritts]] in 1883, using a metal plate coated with selenium and a thin layer of gold; the device became commercially useful in photographic light meters in the 1930s.<ref name=":0" /> Point-contact microwave detector rectifiers made of lead sulfide were used by [[Jagadish Chandra Bose]] in 1904; the [[cat's-whisker detector]] using natural galena or other materials became a common device in the [[history of radio|development of radio]]. However, it was somewhat unpredictable in operation and required manual adjustment for best performance. In 1906, [[H.J. Round]] observed light emission when electric current passed through [[silicon carbide]] crystals, the principle behind the [[light-emitting diode]]. [[Oleg Losev]] observed similar light emission in 1922, but at the time the effect had no practical use. Power rectifiers, using copper oxide and selenium, were developed in the 1920s and became commercially important as an alternative to [[vacuum tube]] rectifiers.<ref name=JTIT10/><ref name=":0" />

The first [[semiconductor device]]s used [[galena]], including German [[physicist]] Ferdinand Braun's [[crystal detector]] in 1874 and Indian physicist Jagadish Chandra Bose's [[radio]] crystal detector in 1901.<ref name="computerhistory-timeline">{{cite web |title=Timeline |url=https://www.computerhistory.org/siliconengine/timeline/ |website=The Silicon Engine |publisher=[[Computer History Museum]] |access-date=22 August 2019}}</ref><ref name="computerhistory-1901">{{cite web |title=1901: Semiconductor Rectifiers Patented as "Cat's Whisker" Detectors |url=https://www.computerhistory.org/siliconengine/semiconductor-rectifiers-patented-as-cats-whisker-detectors/ |website=The Silicon Engine |publisher=[[Computer History Museum]] |access-date=23 August 2019}}</ref>

In the years preceding World War II, infrared detection and communications devices prompted research into lead-sulfide and lead-selenide materials. These devices were used for detecting ships and aircraft, for infrared rangefinders, and for voice communication systems. The point-contact crystal detector became vital for microwave radio systems since available vacuum tube devices could not serve as detectors above about 4000&nbsp;MHz; advanced radar systems relied on the fast response of crystal detectors. Considerable research and development of [[silicon]] materials occurred during the war to develop detectors of consistent quality.<ref name=":0" />

=== Early transistors ===
{{Main article|History of the transistor}}
[[File:Bardeen Shockley Brattain 1948.JPG|thumb|[[John Bardeen]], [[William Shockley]] and [[Walter Brattain]] developed the bipolar [[point-contact transistor]] in 1947.]]

Detector and power rectifiers could not amplify a signal. Many efforts were made to develop a solid-state amplifier and were successful in developing a device called the [[point contact transistor]] which could amplify 20&nbsp;dB or more.<ref name="Morris90">Peter Robin Morris (1990) ''A History of the World Semiconductor Industry'', IET, {{ISBN|0-86341-227-0}}, pp. 11–25</ref> In 1922, [[Oleg Losev]] developed two-terminal, [[negative resistance]] amplifiers for radio, but he died in the [[Siege of Leningrad]] after successful completion. In 1926, [[Julius Edgar Lilienfeld]] patented a device resembling a [[field-effect transistor]], but it was not practical. {{ill|R. Hilsch|de|Rudolf Hilsch}} and {{ill|R. W. Pohl|de|Robert Wichard Pohl}} in 1938 demonstrated a solid-state amplifier using a structure resembling the control grid of a vacuum tube; although the device displayed power gain, it had a [[cut-off frequency]] of one cycle per second, too low for any practical applications, but an effective application of the available theory.<ref name=":0" /> At [[Bell Labs]], [[William Shockley]] and A. Holden started investigating solid-state amplifiers in 1938. The first p–n junction in silicon was observed by [[Russell Ohl]] about 1941 when a specimen was found to be light-sensitive, with a sharp boundary between p-type impurity at one end and n-type at the other. A slice cut from the specimen at the p–n boundary developed a voltage when exposed to light.

The first working [[transistor]] was a [[point-contact transistor]] invented by [[John Bardeen]], [[Walter Houser Brattain]], and [[William Shockley]] at Bell Labs in 1947. Shockley had earlier theorized a [[field-effect transistor|field-effect amplifier]] made from germanium and silicon, but he failed to build such a working device, before eventually using germanium to invent the point-contact transistor.<ref>{{cite web |title=1947: Invention of the Point-Contact Transistor |url=https://www.computerhistory.org/siliconengine/invention-of-the-point-contact-transistor/ |website=The Silicon Engine |publisher=Computer History Museum |access-date=23 August 2019}}</ref> In France, during the war, [[Herbert Mataré]] had observed amplification between adjacent point contacts on a germanium base. After the war, Mataré's group announced their "[[Transistron]]" amplifier only shortly after Bell Labs announced the "[[transistor]]".

In 1954, [[physical chemist]] [[Morris Tanenbaum]] fabricated the first silicon [[junction transistor]] at [[Bell Labs]].<ref>{{cite web |title=1954: Morris Tanenbaum fabricates the first silicon transistor at Bell Labs |url=https://www.computerhistory.org/siliconengine/silicon-transistors-offer-superior-operating-characteristics/ |website=The Silicon Engine |publisher=Computer History Museum |access-date=23 August 2019}}</ref> However, early [[junction transistor]]s were relatively bulky devices that were difficult to manufacture on a [[mass-production]] basis, which limited them to a number of specialised applications.<ref name="Moskowitz">{{cite book |last1=Moskowitz |first1=Sanford L. |title=Advanced Materials Innovation: Managing Global Technology in the 21st century |date=2016 |publisher=[[John Wiley & Sons]] |isbn=9780470508923 |page=168 |url=https://books.google.com/books?id=2STRDAAAQBAJ&pg=PA168}}</ref>
== See also ==
{{Portal|Electronics}}
* [[Deathnium]]
* [[Semiconductor device fabrication]]
* [[Semiconductor industry]]
* [[Semiconductor characterization techniques]]
* [[Transistor count]]

== References ==
{{reflist}}

== Further reading ==
* {{cite book |author1=A. A. Balandin |author2=K. L. Wang |name-list-style=amp |year=2006 |title=Handbook of Semiconductor Nanostructures and Nanodevices (5-Volume Set) |publisher=American Scientific Publishers |isbn=978-1-58883-073-9}}
* {{cite book |author=Sze, Simon M. |title=Physics of Semiconductor Devices (2nd ed.) |publisher=John Wiley and Sons (WIE) |year=1981 |isbn=978-0-471-05661-4 |author-link=Simon Sze |url-access=registration |url=https://archive.org/details/physicsofsemicon00szes}}
* {{cite book |author=Turley, Jim |title=The Essential Guide to Semiconductors |publisher=Prentice Hall PTR |year=2002 |isbn=978-0-13-046404-0 |url-access=registration |url=https://archive.org/details/essentialguideto00turl_0}}
* {{cite book |author1=Yu, Peter Y. |author2=Cardona, Manuel |title=Fundamentals of Semiconductors: Physics and Materials Properties |publisher=Springer |year=2004 |isbn=978-3-540-41323-3}}
* {{cite book |author=Sadao Adachi |year=2012 |title=The Handbook on Optical Constants of Semiconductors: In Tables and Figures |publisher=World Scientific Publishing |isbn=978-981-4405-97-3}}
* G. B. Abdullayev, T. D. Dzhafarov, S. Torstveit (Translator), ''Atomic Diffusion in Semiconductor Structures,'' Gordon & Breach Science Pub., 1987 {{ISBN|978-2-88124-152-9}}
* [https://feynmanlectures.caltech.edu/III_14.html Feynman's lecture on Semiconductors]

== External links ==
{{Commons category|Semiconductors|lcfirst=yes}}
{{Wikiquote}}

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[[Category:Semiconductors|Semiconductors]]