View source for Physics:Metal–semiconductor junction

{{Short description|Type of electrical junction}}
In [[Physics:Solid-state physics|solid-state physics]], a '''metal–semiconductor (M–S) junction''' is a type of electrical junction in which a [[Chemistry:Metal|metal]] comes in close contact with a [[Physics:Semiconductor|semiconductor]] material.  It is the oldest practical [[Physics:Semiconductor device|semiconductor device]].  M–S junctions can either be rectifying or non-rectifying.  The rectifying metal–semiconductor junction forms a [[Physics:Schottky barrier|Schottky barrier]], making a device known as a [[Engineering:Schottky diode|Schottky diode]], while the non-rectifying junction is called an [[Physics:Ohmic contact|ohmic contact]].<ref>''Semiconductor Devices: Modelling and Technology'', Nandita Dasgupta, Amitava Dasgupta.(2004) {{ISBN|81-203-2398-X}}.</ref>  (In contrast, a rectifying semiconductor–semiconductor junction, the most common semiconductor device today, is known as a [[Physics:P–n junction|p–n junction]].)

Metal–semiconductor junctions are crucial to the operation of all semiconductor devices. Usually an [[Physics:Ohmic contact|ohmic contact]] is desired, so that electrical charge can be conducted easily between the active region of a [[Engineering:Transistor|transistor]] and the external circuitry.
Occasionally however a [[Physics:Schottky barrier|Schottky barrier]] is useful, as in [[Engineering:Schottky diode|Schottky diode]]s, [[Engineering:Schottky transistor|Schottky transistor]]s, and metal–semiconductor field effect transistors.

== The critical parameter: Schottky barrier height ==

[[File:Schottky barrier zero bias.svg|thumb|Band diagram for metal-semiconductor junction at zero bias (equilibrium). Shown is the graphical definition of the '''Schottky barrier height''', Φ<sub>B</sub>, for an ''n''-type semiconductor as the difference between the interfacial conduction band edge ''E''<sub>C</sub> and Fermi level ''E''<sub>F</sub>.]]

Whether a given metal-semiconductor junction is an ohmic contact or a Schottky barrier depends on the Schottky barrier height, Φ<sub>B</sub>, of the junction.
For a sufficiently large Schottky barrier height, that is, Φ<sub>B</sub> is significantly higher than the thermal energy ''kT'', the semiconductor is [[Physics:Depletion region|depleted]] near the metal and behaves as a [[Physics:Schottky barrier|Schottky barrier]]. For lower Schottky barrier heights, the semiconductor is not depleted and instead forms an [[Physics:Ohmic contact|ohmic contact]] to the metal.

The Schottky barrier height is defined differently for n-type and p-type semiconductors (being measured from the conduction band edge and valence band edge, respectively). The alignment of the semiconductor's bands near the junction is typically independent of the semiconductor's doping level, so the ''n''-type and ''p''-type Schottky barrier heights are ideally related to each other by:
:<math>\Phi_{\rm B}^{(n)} + \Phi_{\rm B}^{(p)} = E_{\rm g}</math>
where ''E''<sub>g</sub> is the semiconductor's [[Physics:Band gap|band gap]].

In practice, the Schottky barrier height is not precisely constant across the interface, and varies over the interfacial surface.<ref>{{Cite web|url=http://academic.brooklyn.cuny.edu/physics/tung/Schottky/inhomo.htm|title=Inhomogeneous Schottky Barrier}}</ref>

== Schottky–Mott rule and Fermi level pinning ==
{{anchor|Schottky–Mott rule}}

{{multiple image
|image1   = Metal semiconductor junction Schottky approximation.svg
|caption1 = '''Schottky–Mott rule''': As the materials are brought together, the bands in the silicon bend such that the silicon's [[Physics:Work function|work function]] Φ matches the silver's. The bands retain their bending upon contact. This model predicts silver to have a very low Schottky barrier to ''n''-doped silicon, making an excellent ohmic contact.
|image2   = Metal semiconductor junction Bardeen picture.svg
|caption2 = Picture showing '''Fermi level pinning''' effect from [[Physics:Metal-induced gap states|metal-induced gap states]]: The bands in the silicon already start out bent due to [[Physics:Surface states|surface states]]. They are bent again just before contact (to match work functions). Upon contact however, the band bending changes completely, in a way that depends on the chemistry of the Ag-Si bonding.<ref>{{Cite journal | last1 = Tung | first1 = R. | doi = 10.1103/PhysRevB.64.205310 | title = Formation of an electric dipole at metal-semiconductor interfaces | journal = Physical Review B | volume = 64 | issue = 20 | pages = 205310 | year = 2001 |bibcode = 2001PhRvB..64t5310T }}</ref>
|footer=[[Physics:Band diagram|Band diagram]]s for models of formation of junction between silver and ''n''-doped silicon.<ref name="bardeen">{{Cite journal | last1 = Bardeen | first1 = J. | title = Surface States and Rectification at a Metal Semi-Conductor Contact | doi = 10.1103/PhysRev.71.717 | journal = Physical Review | volume = 71 | issue = 10 | pages = 717–727 | year = 1947 |bibcode = 1947PhRv...71..717B }}</ref> In practice this Schottky barrier is approximately Φ<sub>B</sub>&nbsp;=&nbsp;0.8&nbsp;eV.
}}


The '''[[Biography:Walter H. Schottky|Schottky]]–Mott rule''' of Schottky barrier formation predicts the Schottky barrier height based on the vacuum [[Physics:Work function|work function]] of the metal relative to the vacuum [[Physics:Electron affinity|electron affinity]] (or vacuum [[Physics:Ionization energy|ionization energy]]) of the semiconductor:
:<math>\Phi_{\rm B}^{(n)} \approx \Phi_{\rm metal} - \chi_{\rm semi}</math>
This model is derived based on the thought experiment of bringing together the two materials in vacuum, and is closely related in logic to [[Physics:Anderson's rule|Anderson's rule]] for semiconductor-semiconductor junctions. Different semiconductors respect the Schottky–Mott rule to varying degrees.<ref name="tungsys"/>

Although the Schottky–Mott model correctly predicted the existence of [[Physics:Band bending|band bending]] in the semiconductor, it was found experimentally that it would give grossly incorrect predictions for the height of the Schottky barrier. A phenomenon referred to as "Fermi level pinning" caused some point of the band gap, at which finite [[Physics:Density of states|DOS]] exists, to be locked (pinned) to the Fermi level. This made the Schottky barrier height almost completely insensitive to the metal's work function:<ref name="tungsys">{{Cite web|url=http://academic.brooklyn.cuny.edu/physics/tung/Schottky/systematics.htm|title = Barrier Height Correlations and Systematics}}</ref>
:<math>\Phi_{\rm B} \approx \frac{1}{2} E_{\rm bandgap}</math>
where ''E''<sub>bandgap</sub> is the size of [[Physics:Band gap|band gap]] in the semiconductor.

In fact, empirically, it is found that neither of the above extremes is quite correct. The choice of metal does have some effect, and there appears to be a weak correlation between the metal work function and the barrier height, however the influence of the work function is only a fraction of that predicted by the Schottky-Mott rule.<ref>{{Cite book|last=Sze, S. M. Ng, Kwok K.|url=http://worldcat.org/oclc/488586029|title=Physics of semiconductor devices.|date=2007|publisher=John Wiley & Sons|isbn=978-0-471-14323-9|oclc=488586029}}</ref>{{rp|143}}

It was noted in 1947 by [[Biography:John Bardeen|John Bardeen]] that the Fermi level pinning phenomenon would naturally arise if there were chargeable states in the semiconductor right at the interface, with energies inside the semiconductor's gap. These would either be induced during the direct chemical bonding of the metal and semiconductor ([[Physics:Metal-induced gap states|metal-induced gap states]]) or be already present in the semiconductor–vacuum surface (surface states). These highly dense surface states would be able to absorb a large quantity of charge donated from the metal, effectively shielding the semiconductor from the details of the metal. As a result, the semiconductor's bands would necessarily align to a location relative to the surface states which are in turn pinned to the Fermi level (due to their high density), all without influence from the metal.<ref name="bardeen"/>

The Fermi level pinning effect is strong in many commercially important semiconductors (Si, Ge, GaAs),<ref name="tungsys"/> and thus can be problematic for the design of semiconductor devices. For example, nearly all metals form a significant Schottky barrier to ''n''-type [[Chemistry:Germanium|germanium]] and an ohmic contact to ''p''-type germanium, since the valence band edge is strongly pinned to the metal's Fermi level.<ref>{{Cite journal | last1 = Nishimura | first1 = T. | last2 = Kita | first2 = K. | last3 = Toriumi | first3 = A. | doi = 10.1063/1.2789701 | title = Evidence for strong Fermi-level pinning due to metal-induced gap states at metal/germanium interface | journal = Applied Physics Letters | volume = 91 | issue = 12 | pages = 123123 | year = 2007 |bibcode = 2007ApPhL..91l3123N }}</ref> The solution to this inflexibility requires additional processing steps such as adding an intermediate insulating layer to unpin the bands. (In the case of germanium, [[Chemistry:Germanium nitride|germanium nitride]] has been used<ref>{{Cite journal | last1 = Lieten | first1 = R. R. | last2 = Degroote | first2 = S. | last3 = Kuijk | first3 = M. | last4 = Borghs | first4 = G. | title = Ohmic contact formation on n-type Ge | doi = 10.1063/1.2831918 | url =https://zenodo.org/record/897811 | journal = Applied Physics Letters | volume = 92 | issue = 2 | pages = 022106 | year = 2008 |bibcode = 2008ApPhL..92b2106L }}</ref>)

== History ==

The rectification property of metal–semiconductor contacts was discovered by Ferdinand Braun in 1874 using [[Chemistry:Mercury (element)|mercury]] metal contacted with [[Chemistry:Copper sulfide|copper sulfide]] and [[Chemistry:Iron sulfide|iron sulfide]] semiconductors.<ref>{{Citation |last=Braun |first=F. |year=1874 |url=https://books.google.com/books?id=YBJbAAAAYAAJ&pg=PA556 |title=Ueber die Stromleitung durch Schwefelmetalle |trans-title=On current conduction through metal sulfides |language=de |journal=Annalen der Physik und Chemie |volume=153 |issue=4 |pages=556–563 |doi=10.1002/andp.18752291207|bibcode=1875AnP...229..556B }}</ref> Sir Jagadish Chandra Bose applied for  a US patent for a metal-semiconductor diode in 1901.  This patent  was awarded in 1904.{{Wikisource |1=Page:US_Patent_755840_(Bose's_Microwave_Apparatus).djvu/2|2=JC Bose patent}} [[Biography:Greenleaf Whittier Pickard|G.W. Pickard]] received a [[Social:Patent|patent]] in 1906 on a point-contact rectifier using [[Chemistry:Silicon|silicon]]. In 1907, George W. Pierce published a paper in [[Physics:Physical Review|Physical Review]] showing rectification properties of [[Engineering:Diode|diode]]s made by [[Physics:Sputtering|sputtering]] many metals on many semiconductors.<ref>{{Cite journal | last1 = Pierce | first1 = G. W. | doi = 10.1103/PhysRevSeriesI.25.31 | title = Crystal Rectifiers for Electric Currents and Electric Oscillations. Part I. Carborundum | journal = Physical Review |series=Series I | volume = 25 | issue = 1 | pages = 31–60 | year = 1907 |bibcode = 1907PhRvI..25...31P | url = https://zenodo.org/record/1644567 }}</ref> The use of the metal–semiconductor diode rectifier was proposed by [[Biography:Julius Edgar Lilienfeld|Lilienfeld]] in 1926 in the first of his three transistor patents as the gate of the metal–semiconductor field effect transistors.<ref>{{patent|US|1745175|"Method and apparatus for controlling electric current" first filed in Canada on 22.10.1925.}}</ref> The theory of the [[Engineering:Field-effect transistor|field-effect transistor]] using a metal/semiconductor gate was advanced by [[Biography:William Shockley|William Shockley]] in 1939.

The earliest metal–semiconductor diodes in [[Engineering:Electronics|electronics]] application occurred around 1900, when the cat's whisker rectifiers were used in receivers.<ref>{{cite patent |inventor-first=Jagadis Chunder |inventor-last=Bose |inventorlink=Jagadish Chandra Bose |country-code=US |patent-number=755840 |title=Detector for electrical disturbances |publication-date=September 30, 1901 |issue-date=March 29, 1904}}</ref> They consisted of pointed tungsten wire (in the shape of a cat's whisker) whose tip or point was pressed against the surface of a [[Chemistry:Galena|galena]] (lead sulfide) crystal. The first large area rectifier appeared around 1926 which consisted of a [[Chemistry:Copper(I) oxide|copper(I) oxide]] semiconductor thermally grown on a copper [[Physics:Substrate (materials science)|substrate]]. Subsequently, [[Chemistry:Selenium|selenium]] films were [[Physics:Evaporation (deposition)|evaporated]] onto large metal substrates to form the rectifying diodes. These selenium rectifiers were used (and are still used) to convert alternating current to direct current in electrical power applications. During 1925–1940, diodes consisting of a pointed [[Chemistry:Tungsten|tungsten]] metal wire in contact with a [[Chemistry:Silicon|silicon]] crystal base, were fabricated in laboratories to detect microwaves in the UHF range. A World War II program to manufacture high-purity silicon as the crystal base for the point-contact rectifier was suggested by [[Biography:Frederick Seitz|Frederick Seitz]] in 1942 and successfully undertaken by the Experimental Station of the E. I du Pont de Nemours Company.

The first theory that predicted the correct direction of rectification of the metal–semiconductor junction was given by [[Biography:Nevill Francis Mott|Nevill Mott]] in 1939. He found the solution for both the [[Physics:Diffusion|diffusion]] and [[Drift (telecommunication)|drift]] currents of the majority carriers through the semiconductor surface space charge layer which has been known since about 1948 as the Mott barrier. [[Biography:Walter H. Schottky|Walter H. Schottky]] and Spenke extended Mott's theory by including a donor [[Physics:Ion|ion]] whose [[Physics:Density|density]] is spatially constant through the semiconductor surface layer. This changed the constant [[Physics:Electric field|electric field]] assumed by Mott to a linearly decaying electric field. This semiconductor space-charge layer under the metal is known as the [[Physics:Schottky barrier|Schottky barrier]]. A similar theory was also proposed by Davydov in 1939. Although it gives the correct direction of rectification, it has also been proven that the Mott theory and its Schottky-Davydov extension  gives the wrong current limiting mechanism and wrong current-voltage formulae in silicon metal/semiconductor diode rectifiers. The correct theory was developed by [[Biography:Hans Bethe|Hans Bethe]] and reported by him in a M.I.T. Radiation Laboratory Report dated November 23, 1942. In Bethe's theory, the current is limited by [[Physics:Thermionic emission|thermionic emission]] of electrons over the metal–semiconductor potential barrier. Thus, the appropriate name for the metal–semiconductor diode should be the Bethe diode, instead of the [[Engineering:Schottky diode|Schottky diode]], since the Schottky theory does not predict the modern metal–semiconductor diode characteristics correctly.<ref>{{cite book |title=Fundamentals of Solid-State Electronics |last1=Sah |first1=Chih-Tang |year=1991 |publisher=World Scientific |isbn=9810206372 }}</ref>

If a metal-semiconductor junction is formed by placing a [[Physics:Drop (liquid)|droplet]] of [[Chemistry:Mercury (element)|mercury]], as [[Biography:Karl Ferdinand Braun|Braun]] did, onto a semiconductor, e.g.[[Chemistry:Silicon|silicon]], to form a [[Physics:Schottky barrier|Schottky barrier]] in a [[Engineering:Schottky diode|Schottky diode]] electrical setup – [[Engineering:Electrowetting|electrowetting]] can be observed, where the droplet spreads out with increasing voltage. Depending on the [[Physics:Doping (semiconductor)|doping]] type and density in the semiconductor, the droplet spreading depends on the magnitude and sign of the voltage applied to the mercury droplet.<ref>S. Arscott and M. Gaudet "Electrowetting at a liquid metal-semiconductor junction" Appl. Phys. Lett. '''103''', 074104 (2013). {{doi|10.1063/1.4818715}}</ref> This effect has been termed ‘Schottky electrowetting’, effectively linking electrowetting and semiconductor effects.<ref>S. Arscott "Electrowetting and semiconductors" RSC Advances '''4''', 29223 (2014). {{doi|10.1039/C4RA04187A}}</ref>

The [[Engineering:MOSFET|MOSFET]] (metal–oxide–semiconductor field-effect transistor) was  invented by Mohamed Atalla and [[Biography:Dawon Kahng|Dawon Kahng]] at [[Organization:Bell Labs|Bell Labs]] in 1959, and presented in 1960. They extended their work on MOS technology to do pioneering work on hot carrier devices, which used what would later be called a Schottky barrier.<ref name="Bassett">{{cite book |last1=Bassett |first1=Ross Knox |title=To the Digital Age: Research Labs, Start-up Companies, and the Rise of MOS Technology |date=2007 |publisher=Johns Hopkins University Press |isbn=9780801886393 |page=328 |url=https://books.google.com/books?id=UUbB3d2UnaAC&pg=PA328}}</ref> The Schottky diode, also known as the Schottky-barrier diode, was theorized for years, but was first practically realized as a result of the work of Atalla and Kahng during 1960{{ndash}}1961.<ref name="government">{{cite book |title=The Industrial Reorganization Act: The communications industry |date=1973 |publisher=U.S. Government Printing Office |page=1475 |url=https://books.google.com/books?id=EUTQAAAAMAAJ&pg=PA1475}}</ref> They published their results in 1962 and called their device the "hot electron" triode structure with semiconductor-metal emitter.<ref>{{cite journal |last1=Atalla |first1=M. |last2=Kahng |first2=D. |title=A new "Hot electron" triode structure with semiconductor-metal emitter |journal=IRE Transactions on Electron Devices |date=November 1962 |volume=9 |issue=6 |pages=507–508 |doi=10.1109/T-ED.1962.15048 |bibcode=1962ITED....9..507A |s2cid=51637380 |issn=0096-2430}}</ref> It was one of the first metal-base transistors.<ref>{{cite book |last1=Kasper |first1=E. |title=Silicon-Molecular Beam Epitaxy |date=2018 |publisher=CRC Press |isbn=9781351093514 |url=https://books.google.com/books?id=MUtaDwAAQBAJ&pg=PA37-IA4}}</ref> Atalla continued research on Schottky diodes with Robert J. Archer at [[Company:Hewlett-Packard|HP Associates]]. They developed high [[Physics:Vacuum deposition|vacuum]] metal film [[Chemistry:Chemical vapor deposition|deposition]] technology,<ref name="Siegel">{{cite book |last1=Siegel |first1=Peter H. |last2=Kerr |first2=Anthony R. |last3=Hwang |first3=Wei |title=NASA Technical Paper 2287: Topics in the Optimization of Millimeter-Wave Mixers |date=March 1984 |publisher=[[Organization:NASA|NASA]] |pages=12–13 |url=https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19840012690.pdf}}</ref> and fabricated stable evaporated/sputtered [[Engineering:Electrical contacts|contacts]],<ref name="Button">{{cite book |last1=Button |first1=Kenneth J. |title=Infrared and Millimeter Waves V6: Systems and Components |date=1982 |publisher=[[Company:Elsevier|Elsevier]] |isbn=9780323150590 |page=214 |url=https://books.google.com/books?id=DZ2xbIAxRRIC&pg=PA214}}</ref><ref>{{cite book |last1=Anand |first1=Y. |chapter=Microwave Schottky Barrier Diodes |title=Metal-Semiconductor Schottky Barrier Junctions and Their Applications |date=2013 |publisher=Springer Science & Business Media |isbn=9781468446555 |page=220 |chapter-url=https://books.google.com/books?id=Bk3jBwAAQBAJ&pg=PA220}}</ref> publishing their results in January 1963.<ref>{{cite journal |last1=Archer |first1=R. J. |last2=Atalla |first2=M. M. |title=Metals Contacts on Cleaved Silicon Surfaces |journal=Annals of the New York Academy of Sciences |date=January 1963 |volume=101 |issue=3 |pages=697–708 |doi=10.1111/j.1749-6632.1963.tb54926.x |bibcode=1963NYASA.101..697A |s2cid=84306885 |issn=1749-6632}}</ref> Their work was a breakthrough in metal–semiconductor junction<ref name="Button"/> and Schottky barrier research, as it overcame most of the [[Engineering:Semiconductor device fabrication|fabrication]] problems inherent in point-contact diodes and made it possible to build practical Schottky diodes.<ref name="Siegel"/>

==See also==
* [[Physics:Schottky barrier|Schottky barrier]]

==References==
{{reflist}}

==Further reading==
* {{cite book |last1=Streetman | first1=Ben G. |last2=Banerjee |first2=Sanjay Kumar | title=Solid state electronic devices | publisher=Pearson | location=Boston | year=2016 | isbn=978-1-292-06055-2 | oclc=908999844 | page=251-257}}


{{DEFAULTSORT:Metal-semiconductor junction}}
[[Category:Semiconductor structures]]

{{Sourceattribution|Metal–semiconductor junction}}