Editing Epitaxy

{{Short description|Crystal growth process relative to the substrate}}
{{Redirect-distinguish|Epitaxis|Epistaxis}}
{{Use dmy dates|date=April 2024}}

{{Crystallization}}
'''Epitaxy''' (prefix ''epi-'' means "on top of”) is a type of crystal growth or material deposition in which new [[crystal]]line layers are formed with one or more well-defined orientations with respect to the crystalline seed layer. The deposited crystalline film is called an epitaxial film or epitaxial layer.  The relative orientation(s) of the epitaxial layer to the seed layer is defined in terms of the orientation of the crystal lattice of each material. For most epitaxial growths, the new layer is usually crystalline and each crystallographic domain of the overlayer must have a well-defined orientation relative to the substrate crystal structure. Epitaxy can involve single-crystal structures, although grain-to-grain epitaxy has been observed in granular films.<ref name="Prab">{{cite journal |last1=K |first1=Prabahar |title=Grain to Grain Epitaxy-Like Nano Structures of (Ba,Ca)(ZrTi)O3/ CoFe2O4 for Magneto–Electric Based Devices |journal=ACS Appl. Nano Mater. |date=26 October 2020 |volume=3 |issue=11 |pages=11098–11106 |doi=10.1021/acsanm.0c02265|s2cid=228995039 }}</ref><ref name="Hwang">{{cite journal |last1=Hwang |first1=Cherngye |title=Imaging of the grain-to-grain epitaxy in NiFe/FeMn thin-film couples |journal=Journal of Applied Physics |date=30 September 1998 |volume=64 |issue=6115 |pages=6115–6117 |doi=10.1063/1.342110}}</ref> For most technological applications, single-domain epitaxy, which is the growth of an overlayer crystal with one well-defined orientation with respect to the substrate crystal, is preferred. Epitaxy can also play an important role in the growth of superlattice structures.<ref>{{cite book |last1=Christensen |first1=Morten Jagd |title=Epitaxy, Thin films and Superlattices |date=April 1997 |publisher=Risø National Laboratory |isbn=8755022987}}</ref>

The term ''epitaxy'' comes from the [[Greek language|Greek]] roots ''epi'' (ἐπί), meaning "above", and ''taxis'' (τάξις), meaning "an ordered manner".

One of the main commercial applications of epitaxial growth is in the semiconductor industry, where semiconductor films are grown epitaxially on semiconductor substrate wafers.<ref name="Pohl2013">{{cite book|author=[[Udo W. Pohl]]|title=Epitaxy of Semiconductors: Introduction to Physical Principles|url=https://books.google.com/books?id=DShEAAAAQBAJ|date=11 January 2013|publisher=Springer Science & Business Media|isbn=978-3-642-32970-8|pages=4–6}}</ref>  For the case of epitaxial growth of a planar film atop a substrate wafer, the epitaxial film's lattice will have a specific orientation relative to the substrate wafer's crystalline lattice, such as the [001] [[Miller index]] of the film aligning with the [001] index of the substrate. In the simplest case, the epitaxial layer can be a continuation of the same semiconductor compound as the substrate; this is referred to as homoepitaxy.  Otherwise, the epitaxial layer will be composed of a different compound; this is referred to as heteroepitaxy.

==Types==
'''Homoepitaxy''' is a kind of epitaxy performed with only one material, in which a crystalline film is grown on a substrate or film of the same material. This technology is often used to grow a more pure film than the substrate and to fabricate layers with different [[doping (semiconductors)|doping]] levels. In academic literature, homoepitaxy is often abbreviated to "homoepi".

'''Homotopotaxy''' is a process similar to homoepitaxy except that the thin-film growth is not limited to two-dimensional growth. Here the substrate is the thin-film material.

'''Heteroepitaxy''' is a kind of epitaxy performed with materials that are different from each other. In heteroepitaxy, a crystalline film grows on a crystalline substrate or film of a different material. This technology is often used to grow crystalline films of materials for which crystals cannot otherwise be obtained and to fabricate integrated crystalline layers of different materials. Examples include [[silicon on sapphire]], [[gallium nitride]] (GaN) on [[sapphire]], [[aluminium gallium indium phosphide]] (AlGaInP) on [[gallium arsenide]] (GaAs) or diamond or [[iridium]],<ref>M. Schreck et al., Appl. Phys. Lett. 78, 192 (2001); {{doi|10.1063/1.1337648}}</ref> and [[graphene]] on [[hexagonal boron nitride]] (hBN).<ref>{{cite journal |title=Silane-catalysed fast growth of large single-crystalline graphene on hexagonal boron nitride |journal=Nature Communications |volume=6 |issue=6499 |year=2015|page=6499|doi=10.1038/ncomms7499 |pmid=25757864 |pmc=4382696 |last1=Tang |first1=Shujie |last2=Wang |first2=Haomin|last3=Wang |first3=Huishan |arxiv=1503.02806|bibcode=2015NatCo...6.6499T}}</ref>

Heteroepitaxy occurs when a film of different composition and/or crystalline films grown on a substrate. In this case, the amount of strain in the film is determined by the ''lattice mismatch'' Ԑ:

<math>\varepsilon=\frac{a_f-a_s}{a_f}</math>

Where <math>a_f</math> and  <math>a_s</math> are the [[lattice constant]]s of the film and the substrate. The film and substrate could have similar lattice spacings but also different thermal expansion coefficients. If a film is grown at a high temperature, it can experience large strains upon cooling to room temperature. In reality, <math>\varepsilon<9\%</math> is necessary for obtaining epitaxy. If <math>\varepsilon</math> is larger than that, the film experiences a volumetric strain that builds with each layer until a critical thickness. With increased thickness, the elastic strain in the film is relieved by the formation of dislocations, which can become scattering centers that damage the quality of the structure. Heteroepitaxy is commonly used to create so-called [[Band-gap engineering|bandgap]] systems thanks to the additional energy caused by de deformation. [[Silicon-germanium]] epitaxial layers are heavily used in [[CMOS]] [[microelectronics]] and [[silicon photonics]].<ref>{{cite journal |last=Paul|first=Douglas J.|year= 2004|title= Si/SiGe heterostructures: from material and physics to devices and circuits
|journal=Semicond. Sci. Technol. |volume=19 |issue= 10|pages= R75–R108|doi=10.1088/0268-1242/19/10/R02|url=http://www.iop.org/EJ/abstract/0268-1242/19/10/R02|access-date=2007-02-18|format= abstract|bibcode = 2004SeScT..19R..75P |s2cid=250846255 }}</ref>

'''Heterotopotaxy''' is a process similar to heteroepitaxy except that thin-film growth is not limited to two-dimensional growth; the substrate is similar only in structure to the thin-film material.

'''Pendeo-epitaxy''' is a process in which the heteroepitaxial film is growing vertically and laterally simultaneously.
In 2D crystal heterostructure, graphene nanoribbons embedded in hexagonal boron nitride<ref>{{cite journal |title=Oriented graphene nanoribbons embedded in hexagonal boron nitride trenches |journal=Nature Communications |volume=8 |issue=2017 |year=2017|page=14703|doi=10.1038/ncomms14703 |pmid=28276532 |pmc=5347129 |last1=Chen |first1=Lingxiu |last2=He |first2=Li|last3=Wang |first3=Huishan |arxiv=1703.03145|bibcode=2017NatCo...814703C}}</ref><ref>{{cite journal |title=Edge control of graphene domains grown on hexagonal boron nitride |journal=Nanoscale |volume=9 |issue=32 |year=2017|pages=1–6|doi=10.1039/C7NR02578E |pmid=28580985 |last1=Chen |first1=Lingxiu |last2=Wang |first2=Haomin|last3=Tang |first3=Shujie|arxiv=1706.01655 |bibcode=2017arXiv170601655C |s2cid=11602229 }}</ref> give an example of pendeo-epitaxy.

'''Grain-to-grain epitaxy''' involves epitaxial growth between the grains of a multicrystalline epitaxial and seed layer.<ref name="Prab" /><ref name="Hwang" /> This can usually occur when the seed layer only has an out-of-plane texture but no in-plane texture. In such a case, the seed layer consists of grains with different in-plane textures. The epitaxial overlayer then creates specific textures along each grain of the seed layer, due to lattice matching. This kind of epitaxial growth doesn't involve single-crystal films.

Epitaxy is used in [[silicon]]-based manufacturing processes for [[bipolar junction transistor]]s (BJTs) and modern [[CMOS|complementary metal–oxide–semiconductors]] (CMOS), but it is particularly important for [[compound semiconductor]]s such as [[gallium arsenide]]. Manufacturing issues include control of the amount and uniformity of the deposition's resistivity and thickness, the cleanliness and purity of the surface and the chamber atmosphere, the prevention of the typically much more highly doped substrate wafer's diffusion of dopant to the new layers, imperfections of the growth process, and protecting the surfaces during manufacture and handling.

==Mechanism==
[[Image:GrowthModes.png|thumb|450px|'''Figure 1'''. Cross-section views of the three primary modes of thin-film growth including (a) Volmer–Weber (VW: island formation), (b) Frank–van der Merwe (FM: layer-by-layer), and (c) Stranski–Krastanov (SK: layer-plus-island). Each mode is shown for several different amounts of surface coverage, Θ.]]

Heteroepitaxial growth is classified into three primary growth modes-- '''Volmer–Weber''' (VW), [[Frank–Van der Merwe growth|'''Frank–van der Merwe''']] (FM) and [[Stranski–Krastanov growth|'''Stranski–Krastanov''']] (SK).<ref name="Bauer pp. 372–394">{{cite journal |last=Bauer |first=Ernst |title=Phänomenologische Theorie der Kristallabscheidung an Oberflächen. I |url=https://ui.adsabs.harvard.edu/abs/1958ZK....110..372B/abstract |journal=Zeitschrift für Kristallographie |year=1958 |volume=110 |issue=1–6 |pages=372–394 |doi=10.1524/zkri.1958.110.1-6.372 |bibcode=1958ZK....110..372B |access-date=2022-05-03}}</ref><ref name="Brune 2009 p.">{{cite journal |last=Brune |first=H. |date=2009-04-14 |title=Growth Modes |url=https://infoscience.epfl.ch/record/135795 |journal=Encyclopedia of Materials: Science and Technology, Sect. 1.9, Physical Properties of Thin Films and Artificial Multilayers |page= |access-date=2022-05-03}}</ref>

In the VW growth regime, the epitaxial film grows out of 3D nuclei on the growth surface. In this mode, the adsorbate-adsorbate interactions are stronger than adsorbate-surface interactions, leading to island formation by local nucleation and the epitaxial layer is formed when the islands join.

In the FM growth mode, adsorbate-surface and adsorbate-adsorbate interactions are balanced, which promotes 2D layer-by-layer or step-flow epitaxial growth.

The SK mode is a combination of VW and FM modes. In this mechanism, the growth initiates in the FM mode, forming 2D layers, but after reaching a critical thickness, enters a VW-like 3D island growth regime.

Practical epitaxial growth, however, takes place in a high supersaturation regime, away from thermodynamic equilibrium. In that case, the epitaxial growth is governed by adatom kinetics rather than thermodynamics, and 2D step-flow growth becomes dominant.<ref name="Brune 2009 p." />

==Methods==
{{See also|Epitaxial wafer}}

===Vapor-phase===
[[Image:CBE im1.png|right|500px|thumb|Figure 1: Basic processes inside the growth chambers of a) MOVPE, b) MBE, and c) CBE.]]
Homoepitaxial growth of semiconductor thin films are generally done by [[Chemical vapor deposition|chemical]] or [[physical vapor deposition]] methods that deliver the precursors to the substrate in gaseous state. For example, '''silicon''' is most commonly deposited from [[silicon tetrachloride]] (or [[germanium tetrachloride]]) and [[hydrogen]] at approximately 1200 to 1250&nbsp;°C:<ref name="Morgan&Board">{{cite book|last1=Morgan|first1=D. V.|last2=Board|first2=K.|title=An Introduction To Semiconductor Microtechnology|url={{google books |plainurl=y|id=yQ5TAAAAMAAJ|page=23}} |date=1991|publisher=John Wiley & Sons|location=Chichester, West Sussex, England|isbn=978-0471924784|page=23|edition=2nd}}</ref>
:SiCl<sub>4(g)</sub> + 2H<sub>2(g)</sub> ↔ Si<sub>(s)</sub> + 4HCl<sub>(g)</sub>

where (g) and (s) represent gas and solid phases, respectively. This reaction is reversible, and the growth rate depends strongly upon the proportion of the two source gases. Growth rates above 2 micrometres per minute produce polycrystalline silicon, and negative growth rates ([[etching (microfabrication)|etching]]) may occur if too much [[hydrogen chloride]] byproduct is present. (Hydrogen chloride may be intentionally added to etch the wafer.){{Cn|date=April 2023}} An additional etching reaction competes with the deposition reaction:
:SiCl<sub>4(g)</sub> + Si<sub>(s)</sub> ↔ 2SiCl<sub>2(g)</sub>

Silicon VPE may also use [[silane]], [[dichlorosilane]], and [[trichlorosilane]] source gases. For instance, the silane reaction occurs at 650&nbsp;°C in this way:
:SiH<sub>4</sub> → Si + 2H<sub>2</sub>

VPE is sometimes classified by the chemistry of the source gases, such as [[hydride VPE]] (HVPE) and [[MOVPE|metalorganic VPE]] (MOVPE or MOCVD).

The reaction chamber where this process takes place may be heated by lamps located outside the chamber.<ref>{{cite web | url=https://www.chiphistory.org/89-applied-materials-series-7600-epitaxial-reactor-system | title=Applied Materials Series 7600 Epitaxial Reactor System - the Chip History }}</ref> A common technique used in [[compound semiconductor]] growth is [[Molecular-beam epitaxy|molecular beam epitaxy]] (MBE). In this method, a source material is heated to produce an [[evaporate]]d beam of particles, which travel through a very high [[vacuum]] (10<sup>−8</sup> [[pascal (unit)|Pa]]; practically free space) to the substrate and start epitaxial growth.<ref>A. Y. Cho, "Growth of III\–V semiconductors by molecular beam epitaxy and their properties," Thin Solid Films, vol. 100, pp. 291–317, 1983.</ref><ref>{{Cite journal |last=Cheng |first=K. Y. |date=November 1997 |title=Molecular beam epitaxy technology of III-V compound semiconductors for optoelectronic applications |journal=Proceedings of the IEEE |volume=85 |issue=11 |pages=1694–1714 |doi=10.1109/5.649646 |issn=0018-9219}}</ref> [[Chemical beam epitaxy]], on the other hand, is an ultra-high vacuum process that uses gas phase precursors to generate the molecular beam.<ref name=Tsang1989>{{cite journal | last=Tsang | first=W.T. | title=From chemical vapor epitaxy to chemical beam epitaxy | journal=Journal of Crystal Growth | publisher=Elsevier BV | volume=95 | issue=1–4 | year=1989 | issn=0022-0248 | doi=10.1016/0022-0248(89)90364-3 | pages=121–131| bibcode=1989JCrGr..95..121T }}</ref>

Another widely used technique in microelectronics and nanotechnology is [[atomic layer epitaxy]], in which precursor gases are alternatively pulsed into a chamber, leading to atomic monolayer growth by surface saturation and [[chemisorption]].

===Liquid-phase===
Liquid-phase epitaxy (LPE) is a method to grow semiconductor crystal layers from the melt on solid substrates. This happens at temperatures well below the melting point of the deposited semiconductor. The semiconductor is dissolved in the melt of another material. At conditions that are close to the equilibrium between dissolution and deposition, the deposition of the semiconductor crystal on the substrate is relatively fast and uniform. The most used substrate is indium phosphide (InP). Other substrates like glass or ceramic can be applied for special applications. To facilitate nucleation, and to avoid tension in the grown layer the thermal expansion coefficient of substrate and grown layer should be similar.

Centrifugal liquid-phase epitaxy is used commercially to make thin layers of [[silicon]], [[germanium]], and [[gallium arsenide]].<ref name="Capper2007">{{cite book|last1=Capper|first1=Peter|last2=Mauk|first2=Michael|title=Liquid Phase Epitaxy of Electronic, Optical and Optoelectronic Materials|date=2007|publisher=John Wiley & Sons|isbn=9780470319499|pages=134–135|url={{google books |plainurl=y |id=e5mM5INQK9IC|page=135}}|access-date=3 October 2017|language=en}}</ref><ref name="Farrow2013">{{cite book|author1-link=Robin F. C. Farrow|last1=Farrow|first1=R. F. C.|last2=Parkin|first2=S. S. P.|last3=Dobson|first3=P. J.|last4=Neave|first4=J. H.|last5=Arrott|first5=A. S.|title=Thin Film Growth Techniques for Low-Dimensional Structures|date=2013|publisher=Springer Science & Business Media|isbn=9781468491456|pages=174–176|url={{google books |plainurl=y |id=WM7kBwAAQBAJ|page=192}}|access-date=3 October 2017|language=en}}</ref> Centrifugally formed film growth is a process used to form thin layers of materials by using a [[centrifuge]]. The process has been used to create silicon for thin-film solar cells<ref name="Christensen2015">{{cite web|last1=Christensen|first1=Arnfinn|title=Speedy production of silicon for solar cells|url=http://sciencenordic.com/alternative-energy-environmental-technology-forskningno/speedy-production-of-silicon-for-solar-cells/1419392|website=sciencenordic.com|date=29 July 2015 |publisher=ScienceNordic|access-date=3 October 2017|language=en}}</ref><ref name="Luque2012">{{cite book|last1=Luque|first1=A.|last2=Sala|first2=G.|last3=Palz|first3=Willeke|last4=Santos|first4=G. dos|last5=Helm|first5=P.|title=Tenth E.C. Photovoltaic Solar Energy Conference: Proceedings of the International Conference, held at Lisbon, Portugal, 8–12 April 1991|date=2012|publisher=Springer|isbn=9789401136228|page=694|url={{google books |plainurl=y |id=CKfnCAAAQBAJ|page=694}}|access-date=3 October 2017|language=en}}</ref> and far-infrared photodetectors.<ref name="Katterloher2002">{{cite journal|last1=Katterloher|first1=Reinhard O.|last2=Jakob|first2=Gerd|last3=Konuma|first3=Mitsuharu|last4=Krabbe|first4=Alfred|last5=Haegel|first5=Nancy M.|author5-link=Nancy Haegel|last6=Samperi|first6=S. A.|last7=Beeman|first7=Jeffrey W.|last8=Haller|first8=Eugene E.|editor-first1=Marija |editor-first2=Bjorn F. |editor-last1=Strojnik |editor-last2=Andresen |title=Liquid phase epitaxy centrifuge for growth of ultrapure gallium arsenide for far-infrared photoconductors|journal=Infrared Spaceborne Remote Sensing IX|date=8 February 2002|volume=4486|pages=200–209|doi=10.1117/12.455132|bibcode=2002SPIE.4486..200K|s2cid=137003113}}</ref> Temperature and centrifuge spin rate are used to control layer growth.<ref name="Farrow2013" /> Centrifugal LPE has the capability to create dopant concentration gradients while the solution is held at constant temperature.<ref name="Pauleau2012">{{cite book|last1=Pauleau|first1=Y.|title=Chemical Physics of Thin Film Deposition Processes for Micro- and Nano-Technologies|date=2012|publisher=Springer Science & Business Media|isbn=9789401003537|page=45|url={{google books |plainurl=y |id=fsXoCAAAQBAJ|page=67}}|access-date=3 October 2017|language=en}}</ref>

===Solid-phase===
Solid-phase epitaxy (SPE) is a transition between the amorphous and crystalline phases of a material. It is usually produced by depositing a film of amorphous material on a crystalline substrate, then heating it to crystallize the film. The single-crystal substrate serves as a template for crystal growth. The annealing step used to recrystallize or heal silicon layers amorphized during ion implantation is also considered to be a type of solid phase epitaxy. The impurity segregation and redistribution at the growing crystal-amorphous layer interface during this process is used to incorporate low-solubility dopants in metals and silicon.<ref>{{cite journal |first1=J.S. |last1=Custer |first2=A. |last2=Polman |first3=H. M. |last3=Pinxteren| journal=Journal of Applied Physics |volume= 75 |issue= 6 |pages=2809 |date=15 March 1994 |title=Erbium in crystal silicon: Segregation and trapping during solid phase epitaxy of amorphous silicon|bibcode=1994JAP....75.2809C |doi=10.1063/1.356173 }}</ref>

==[[Doping (semiconductor)|Doping]]==
An epitaxial layer can be [[Doping (semiconductor)|doped]] during deposition by adding impurities to the source gas, such as [[arsine]], [[phosphine]], or [[diborane]]. [[Dopant|Dopants]] in the source gas, liberated by evaporation or wet etching of the surface, may also diffuse into the epitaxial layer and cause ''autodoping''. The concentration of impurity in the gas phase determines its concentration in the deposited film. Doping can also be achieved by a site-competition technique, where the growth precursor ratios are tuned to enhance the incorporation of vacancies, specific dopant species or vacant-dopant clusters into the lattice.<ref name="Larkin Neudeck Powell Matus pp. 1659–1661">{{cite journal |last1=Larkin |first1=David J. |last2=Neudeck |first2=Philip G. |last3=Powell |first3=J. Anthony |last4=Matus |first4=Lawrence G. |date=1994-09-26 |title=Site-competition epitaxy for superior silicon carbide electronics |journal=Applied Physics Letters |publisher=AIP Publishing |volume=65 |issue=13 |pages=1659–1661 |doi=10.1063/1.112947 |bibcode=1994ApPhL..65.1659L |issn=0003-6951}}</ref><ref name="Zhang Gao Yu Liao pp. 655–668">{{cite journal |last1=Zhang |first1=Xiankun |last2=Gao |first2=Li |last3=Yu |first3=Huihui |last4=Liao |first4=Qingliang |last5=Kang |first5=Zhuo |last6=Zhang |first6=Zheng |last7=Zhang |first7=Yue |date=2021-07-20 |title=Single-Atom Vacancy Doping in Two-Dimensional Transition Metal Dichalcogenides |journal=Accounts of Materials Research |publisher=American Chemical Society (ACS) |volume=2 |issue=8 |pages=655–668 |doi=10.1021/accountsmr.1c00097 |s2cid=237642245 |issn=2643-6728}}</ref><ref name="Holmes-Hewett p.">{{cite journal |last=Holmes-Hewett |first=W. F. |date=2021-08-16 |title=Electronic structure of nitrogen-vacancy doped SmN: Intermediate valence and 4f transport in a ferromagnetic semiconductor |journal=Physical Review B |publisher=American Physical Society (APS) |volume=104 |issue=7 |page= 075124|doi=10.1103/physrevb.104.075124 |bibcode=2021PhRvB.104g5124H |s2cid=238671328 |issn=2469-9950}}</ref>  Additionally, the high temperatures at which epitaxy is performed may allow dopants to [[diffusion|diffuse]] into the growing layer from other layers in the wafer (''out-diffusion'').

==Minerals==
[[File:Rutile-Hematite-171993.jpg|thumb|alt=text|Rutile epitaxial on hematite nearly 6 cm long. [[Bahia]], Brazil]]

In mineralogy, epitaxy is the overgrowth of one mineral on another in an orderly way, such that certain [[crystal structure#Planes and directions|crystal directions]] of the two minerals are aligned. This occurs when some planes in the [[crystal structure#Planes and directions|lattices]] of the overgrowth and the substrate have similar spacings between [[atoms]].<ref name="JR" />

If the crystals of both minerals are well formed so that the directions of the [[crystal structure#Planes and directions|crystallographic axes]] are clear then the epitaxic relationship can be deduced just by a visual inspection.<ref name="JR" />

Sometimes many separate crystals form the overgrowth on a single substrate, and then if there is epitaxy all the overgrowth crystals will have a similar orientation. The reverse, however, is not necessarily true. If the overgrowth crystals have a similar orientation there is probably an epitaxic relationship, but it is not certain.<ref name="JR">{{cite journal | last=Rakovan | first=John | title=Epitaxy | journal=Rocks & Minerals | publisher=Informa UK Limited | volume=81 | issue=4 | year=2006 | issn=0035-7529 | doi=10.3200/rmin.81.4.317-320 | pages=317–320| bibcode=2006RoMin..81..317R | s2cid=219714821 }}</ref>

Some authors<ref name="PR">{{cite journal | last1=White | first1=John S. | last2=Richards | first2=R. Peter | title=Let's Get It Right: Epitaxy—A Simple Concept? | journal=Rocks & Minerals | publisher=Informa UK Limited | volume=85 | issue=2 | date=2010-02-17 | issn=0035-7529 | doi=10.1080/00357521003591165 | pages=173–176| bibcode=2010RoMin..85..173W | s2cid=128758902 }}</ref> consider that overgrowths of a second generation of the same mineral species should also be considered as epitaxy, and this is common terminology for [[semiconductor]] scientists who induce epitaxic growth of a film with a different [[doping (semiconductor)|doping]] level on a semiconductor substrate of the same material. For naturally produced minerals, however, the [[International Mineralogical Association]] (IMA) definition requires that the two minerals be of different species.<ref name="AC">Acta Crystallographica Section A Crystal Physics, Diffraction, Theoretical and General Crystallography Volume 33, Part 4 (July 1977)</ref>

Another man-made application of epitaxy is the making of artificial snow using [[silver iodide]], which is possible because [[hexagonal crystal system|hexagonal]] silver iodide and ice have similar cell dimensions.<ref name="PR" />

===Isomorphic minerals===
Minerals that have the same structure ([[isomorphism (crystallography)|isomorphic minerals]]) may have epitaxic relations. An example is [[albite]] {{chem|NaAlSi|3|O|8}} on [[microcline]] {{chem|KAlSi|3|O|8}}. Both these minerals are [[triclinic crystal system|triclinic]], with [[space group]] {{overline|1}}, and with similar [[unit cell]] parameters, a = 8.16 Å, b = 12.87 Å, c = 7.11 Å, α = 93.45°, β = 116.4°, γ = 90.28° for albite and a = 8.5784 Å, b = 12.96 Å, c = 7.2112 Å, α = 90.3°, β = 116.05°, γ = 89° for microcline.

===Polymorphic minerals===
[[File:Rutile-Hematite-113489.jpg|thumb|alt=text|Rutile on hematite, from Novo Horizonte, Bahia, Northeast Region, Brazil]]
[[File:Hematite-Magnetite-180698.jpg|thumb|alt=text|Hematite [[pseudomorph]] after magnetite, with terraced epitaxial faces. [[La Rioja Province, Argentina|La Rioja]], Argentina]]
Minerals that have the same composition but different structures ([[polymorphism (materials science)|polymorphic minerals]]) may also have epitaxic relations. Examples are [[pyrite]] and [[marcasite]], both FeS<sub>2</sub>, and [[sphalerite]] and [[wurtzite]], both ZnS.<ref name="JR" />

===Rutile on hematite===
Some pairs of minerals that are not related structurally or compositionally may also exhibit epitaxy. A common example is [[rutile]] TiO<sub>2</sub> on [[hematite]] Fe<sub>2</sub>O<sub>3</sub>.<ref name="JR" /><ref name="MF">{{cite web|title=FMF - Friends of Minerals Forum, discussion and message board :: Index|url=http://www.mineral-forum.com/message-board/|website=www.mineral-forum.com/message-board/}}</ref> Rutile is [[tetragonal crystal system|tetragonal]] and hematite is [[trigonal crystal system|trigonal]], but there are directions of similar spacing between the atoms in the [[Miller index|(100)]] plane of rutile (perpendicular to the a [[crystal structure#Lattice systems|axis]]) and the [[Miller index|(001)]] plane of hematite (perpendicular to the c axis). In epitaxy these directions tend to line up with each other, resulting in the axis of the rutile overgrowth being parallel to the c axis of hematite, and the c axis of rutile being parallel to one of the axes of hematite.<ref name="JR" />

===Hematite on magnetite===
Another example is [[hematite]] {{chem|Fe|3+|2|O|3}} on [[magnetite]] {{chem|Fe|2+|Fe|3+|2|O|4}}. The magnetite structure is based on close-packed [[oxygen]] [[ion#Anions and cations|anions]] stacked in an ABC-ABC sequence. In this packing the close-packed layers are parallel to [[Miller index|(111)]] (a plane that symmetrically "cuts off" a corner of a cube). The hematite structure is based on close-packed oxygen anions stacked in an AB-AB sequence, which results in a crystal with hexagonal symmetry.<ref name="WN">Nesse, William (2000). Introduction to Mineralogy. Oxford University Press. Page 79</ref>

If the [[cations]] were small enough to fit into a truly close-packed structure of oxygen anions then the spacing between the nearest neighbour oxygen sites would be the same for both species. The radius of the oxygen ion, however, is only 1.36 Å<ref name="MOM">{{cite book|last1=Klein|first1=Cornelis|last2=Hurlbut|first2=Cornelius Searle|last3=Dana|first3=James Dwight|title=Manual of mineralogy|url={{google books |plainurl=y |id=8ybwAAAAMAAJ}}|year=1993|publisher=Wiley|isbn=978-0-471-57452-1}}</ref> and the Fe cations are big enough to cause some variations. The Fe radii vary from 0.49 Å to 0.92 Å,<ref name="IC">{{Cite web|url=http://abulafia.mt.ic.ac.uk/shannon/ptable.php|title=Shannon Radii|website=abulafia.mt.ic.ac.uk}}</ref> depending on the [[Ion#Denoting the charged state|charge]] (2+ or 3+) and the [[coordination number]] (4 or 8). Nevertheless, the O spacings are similar for the two minerals hence hematite can readily grow on the [[Miller index|(111)]] faces of magnetite, with hematite [[Miller index|(001)]] parallel to magnetite [[Miller index|(111)]].<ref name="WN" />

==Applications==
Epitaxy is used in [[nanotechnology]] and in [[semiconductor fabrication]]. Indeed, epitaxy is the only affordable method of high quality crystal growth for many semiconductor materials. In [[surface science]], epitaxy is used to create and study [[monolayer]] and multilayer films of [[adsorption|adsorbed]] [[organic molecule]]s on [[single crystal]]line surfaces via [[scanning tunnelling microscopy]].<ref>{{cite journal |last1=Waldmann |first1=T. |year=2011 |title=Growth of an oligopyridine adlayer on Ag(100) – A scanning tunnelling microscopy study |journal=Physical Chemistry Chemical Physics |volume=13 |issue=46 |pages=20724–8 |bibcode=2011PCCP...1320724W |doi=10.1039/C1CP22546D |pmid=21952443}}</ref><ref>{{cite journal |last1=Waldmann |first1=T. |year=2012 |title=The role of surface defects in large organic molecule adsorption: substrate configuration effects |journal=Physical Chemistry Chemical Physics |volume=14 |issue=30 |pages=10726–31 |bibcode=2012PCCP...1410726W |doi=10.1039/C2CP40800G |pmid=22751288}}</ref>

==See also==
*[[Heterojunction]]
*[[Island growth]]
*[[Nano-RAM]]
*[[Quantum cascade laser]]
*[[Selective area epitaxy]]
*[[Silicon on sapphire]]
*[[Single event upset]]
*[[Thermal laser epitaxy]]
*[[Thin film]]
*[[Vertical-cavity surface-emitting laser]]
*[[Wake Shield Facility]]
*[[Zhores Alferov]]

==References==
{{Reflist|30em}}

== Bibliography ==
*{{cite book |last=Jaeger |first=Richard C. |title=Introduction to Microelectronic Fabrication |chapter-url={{google books |plainurl=y |id=yqi3QgAACAAJ}}|edition=2nd |year=2002 |publisher=Prentice Hall |location=Upper Saddle River |isbn=978-0-201-44494-0 |chapter=Film Deposition}}

==External links==
{{Commons category multi |Semiconductor devices fabrication|Semiconductors}}
*[http://www.epitaxy.net/ epitaxy.net] {{Webarchive|url=https://web.archive.org/web/20130309052505/http://www.epitaxy.net/ |date=9 March 2013 }}: a central forum for the epitaxy-communities
*[http://www.memsnet.org/mems/processes/deposition.html Deposition processes]
*[http://www.crystalxe.com/ CrystalXE.com]: a specialized software in epitaxy

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[[Category:Thin film deposition]]
[[Category:Semiconductor device fabrication]]
[[Category:Crystallography]]
[[Category:Methods of crystal growth]]