Two-dimensional semiconductor

{{Short description|Type of natural semiconductor with thicknesses on the atomic scale}} A '''two-dimensional semiconductor''' (also known as '''2D semiconductor''') is a type of natural [[semiconductor]] with thicknesses on the atomic scale. Geim and Novoselov et al. initiated the field in 2004 when they reported a new semiconducting material [[graphene]], a flat monolayer of carbon atoms arranged in a [[2D materials|2D honeycomb lattice]].<ref name="Novoselov2004">{{cite journal|last1=Novoselov|first1=K. S.|title=Electric Field Effect in Atomically Thin Carbon Films|journal=Science|volume=306|issue=5696|year=2004|pages=666–669|issn=0036-8075|doi=10.1126/science.1102896|arxiv = cond-mat/0410550 |bibcode = 2004Sci...306..666N|pmid=15499015|s2cid=5729649 }}</ref> A 2D monolayer semiconductor is significant because it exhibits stronger [[Piezoelectricity|piezoelectric]] coupling than traditionally employed bulk forms. This coupling could enable applications.<ref name=song13>{{cite journal|last1=Song|first1=Xiufeng|last2=Hu|first2=Jinlian|last3=Zeng|first3=Haibo|title=Two-dimensional semiconductors: recent progress and future perspectives|journal=Journal of Materials Chemistry C|date=2013|volume=1|issue=17|page=2952|doi=10.1039/C3TC00710C|url=https://www.researchgate.net/publication/236747849}}</ref> One research focus is on designing [[nanoelectronic]] components by the use of graphene as [[electrical conductor]], [[Boron nitride|hexagonal boron nitride]] as [[electrical insulator]], and a transition metal [[Chalcogenide|dichalcogenide]] as [[semiconductor]].<ref name="Radisavljevic">{{cite journal|last1=Radisavljevic|first1=B.|last2=Radenovic|first2=A.|last3=Brivio|first3=J.|last4=Giacometti|first4=V.|last5=Kis|first5=A.|year=2011| title=Single-layer MoS₂ transistors| journal=Nature Nanotechnology| volume=6| issue=3| pages=147–150|doi=10.1038/nnano.2010.279| pmid=21278752|bibcode=2011NatNa...6..147R|url=http://infoscience.epfl.ch/record/164049}}</ref><ref name="GeimGrigorieva2013">{{cite journal|last1=Geim|first1=A. K.|last2=Grigorieva|first2=I. V.|title=Van der Waals heterostructures|journal=Nature|volume=499|issue=7459|year=2013|pages=419–425|issn=0028-0836|doi=10.1038/nature12385|pmid=23887427|arxiv=1307.6718|s2cid=205234832 }}</ref>

==Materials== [[File:Graphen.jpg|thumb|right|200px|Monolayer graphene]]

===Graphene=== {{Main|Graphene}} Graphene, consisting of single sheets of carbon atoms, has high [[electron mobility]] and high [[thermal conductivity]]. One issue regarding graphene is its lack of a [[band gap]], which poses a problem in particular with [[digital electronics]] because it is unable to switch off [[field-effect transistor]]s (FETs).<ref name="Radisavljevic"/>

[[File:Boron-nitride-(hexagonal)-side-3D-balls.png|thumb|right|200px|Layered structure of h-BN]]

===Hexagonal boron nitride=== Monolayer hexagonal [[boron nitride]] (h-BN) is an insulator with a high [[energy gap]] (5.97 eV).<ref name="DeanYoung2010">{{cite journal|last1=Dean|first1=C. R.|last2=Young|first2=A. F.|last3=Meric|first3=I.|last4=Lee|first4=C.|last5=Wang|first5=L.|last6=Sorgenfrei|first6=S.|last7=Watanabe|first7=K.|last8=Taniguchi|first8=T.|last9=Kim|first9=P.|last10=Shepard|first10=K. L.|last11=Hone|first11=J.|title=Boron nitride substrates for high-quality graphene electronics|journal=Nature Nanotechnology|volume=5|issue=10|year=2010|pages=722–726|issn=1748-3387|doi=10.1038/nnano.2010.172|arxiv = 1005.4917 |bibcode = 2010NatNa...5..722D|pmid=20729834|s2cid=1493242 }}</ref> However, it can also function as a semiconductor with enhanced conductivity due to its zigzag sharp edges and vacancies. h-BN is often used as substrate and barrier due to its insulating property. h-BN also has a large thermal conductivity.<ref>{{Cite web |title=Boron Nitride (BN) Materials: Properties, Types & Applications |url=https://www.samaterials.com/204-boron-nitride.html |access-date=2025-12-19 |website=www.samaterials.com |language=en}}</ref> [[File:Molybdenite-3D-balls.png|thumb|right|200px|Layered structure of MoS₂, Mo in green, S in yellow]]

===Transition-metal dichalcogenides=== {{Main|Transition metal dichalcogenide monolayers}} Stacks of two-dimensional materials held together by [[Van der Waals force|van der Waals forces]] can form van der Waals heterostructures, in which each atomic sheet simultaneously serves as the bulk and the interface. Interlayer charge transfer, proximity coupling, and moiré superlattice reconstruction lead to emergent properties such as secondary [[Dirac cone|Dirac points]] in graphene/hBN and enhanced [[spin–orbit interaction]] in graphene adjacent to [[Transition metal|Transition-metal]] dichalcogenides.<ref>{{Cite journal |last=Novoselov |first=K. |title=2D materials and van der Waals heterostructures |journal=Science |year=2016 |volume=353 |issue=6298 |doi=10.1126/science.aac9439|arxiv=1608.03059 }}</ref>

Transition-metal dichalcogenide monolayers (TMDs or TMDCs) are a class of two-dimensional materials that have the chemical formula MX₂, where M represents [[transition metals]] from group IV, V and VI, and X represents a [[chalcogen]] such as [[sulfur]], [[selenium]] or [[tellurium]].<ref name="WangKalantar-Zadeh2012">{{cite journal|last1=Wang|first1=Qing Hua|last2=Kalantar-Zadeh|first2=Kourosh|last3=Kis|first3=Andras|last4=Coleman|first4=Jonathan N.|last5=Strano|first5=Michael S.|author-link5=Michael Strano|title=Electronics and optoelectronics of two-dimensional transition metal dichalcogenides|journal=Nature Nanotechnology|volume=7|issue=11|year=2012|pages=699–712|issn=1748-3387|doi=10.1038/nnano.2012.193|bibcode = 2012NatNa...7..699W|pmid=23132225|s2cid=6261931 |url=http://infoscience.epfl.ch/record/182177}}</ref> [[Molybdenum disulfide|MoS₂]], [[Molybdenum diselenide|MoSe₂]], [[Molybdenum ditelluride|MoTe₂]], [[Tungsten(IV) sulfide|WS₂]] and [[Tungsten(IV) selenide|WSe₂]] are TMDCs. TMDCs have layered structure with a plane of metal atoms in between two planes of chalcogen atoms as shown in Figure 1. Each layer is bonded strongly in plane, but weakly in interlayers. Therefore, TMDCs can be easily exfoliated into atomically thin layers through various methods. TMDCs show layer-dependent optical and electrical properties. When exfoliated into monolayers, the band gaps of several TMDCs change from indirect to direct,<ref name="KucZibouche2011">{{cite journal |last1=Kuc |first1=A. |last2=Zibouche |first2=N. |last3=Heine |first3=T. |title=Influence of quantum confinement on the electronic structure of the transition metal sulfideTS2 |journal=Physical Review B |volume=83 |issue=24 |article-number=245213 |year=2011 |issn=1098-0121|doi=10.1103/PhysRevB.83.245213 |arxiv=1104.3670 |bibcode=2011PhRvB..83x5213K|s2cid=119112827 }}</ref> which lead to broad applications in nanoelectronics,<ref name="Radisavljevic"/> [[optoelectronics]],<ref name="WilsonYoffe1969">{{cite journal|last1=Wilson|first1=J. A.|last2=Yoffe|first2=A. D.|title=The transition metal dichalcogenides discussion and interpretation of the observed optical, electrical and structural properties|journal=Advances in Physics|volume=18|issue=73|year=1969|pages=193–335|issn=0001-8732|doi=10.1080/00018736900101307|bibcode = 1969AdPhy..18..193W}}</ref><ref name="Yoffe1973">{{cite journal|last1=Yoffe|first1=A D|title=Layer Compounds|journal=[[Annual Review of Materials Science]]|volume=3|issue=1|year=1973|pages=147–170|issn=0084-6600|doi=10.1146/annurev.ms.03.080173.001051|bibcode = 1973AnRMS...3..147Y}}</ref> and [[quantum computing]].<ref name="Lucatto2019"> {{cite journal |title = Charge qubit in van der Waals heterostructures |author = B. Lucatto |journal = Physical Review B |volume = 100 |issue = 12 |article-number = 121406 |year = 2019 |doi = 10.1103/PhysRevB.100.121406 |url = https://link.aps.org/doi/10.1103/PhysRevB.100.121406 |display-authors=etal|arxiv = 1904.10785 |bibcode = 2019PhRvB.100l1406L |s2cid = 129945636 }}</ref> While exfoliated TMDC monolayers exhibit promising optoelectronic properties, they are often limited by intrinsic and extrinsic defects,<ref>{{Cite journal |last1=Rhodes |first1=Daniel |last2=Chae |first2=Sang Hoon |last3=Ribeiro-Palau |first3=Rebeca |last4=Hone |first4=James |date=2019-05-21 |title=Disorder in van der Waals heterostructures of 2D materials |journal=Nature Materials |volume=18 |issue=6 |pages=541–549 |doi=10.1038/s41563-019-0366-8 |pmid=31114069 |bibcode=2019NatMa..18..541R |issn=1476-1122}}</ref> such as sulfur vacancies and grain boundaries, which can negatively affect their performance. To address these issues, various chemical passivation techniques, including the use of superacids and [[thiol]] molecules,<ref>{{Cite journal |last1=Li |first1=Zhaojun |last2=Bretscher |first2=Hope |last3=Zhang |first3=Yunwei |last4=Delport |first4=Géraud |last5=Xiao |first5=James |last6=Lee |first6=Alpha |last7=Stranks |first7=Samuel D. |last8=Rao |first8=Akshay |date=2021-10-18 |title=Mechanistic insight into the chemical treatments of monolayer transition metal disulfides for photoluminescence enhancement |journal=Nature Communications |volume=12 |issue=1 |page=6044 |doi=10.1038/s41467-021-26340-6 |pmid=34663820 |issn=2041-1723|pmc=8523741 |arxiv=2009.11123 |bibcode=2021NatCo..12.6044L }}</ref> have been developed to enhance their photoluminescence and charge transport properties. Additionally, phase<ref>{{Cite journal |last1=Huang |first1=H. H. |last2=Fan |first2=Xiaofeng |last3=Singh |first3=David J. |last4=Zheng |first4=W. T. |date=2020 |title=Recent progress of TMD nanomaterials: phase transitions and applications |journal=Nanoscale |volume=12 |issue=3 |pages=1247–1268 |doi=10.1039/c9nr08313h |pmid=31912836 |issn=2040-3364}}</ref> and strain engineering<ref>{{Cite journal |last1=Liu |first1=Zheng |last2=Amani |first2=Matin |last3=Najmaei |first3=Sina |last4=Xu |first4=Quan |last5=Zou |first5=Xiaolong |last6=Zhou |first6=Wu |last7=Yu |first7=Ting |last8=Qiu |first8=Caiyu |last9=Birdwell |first9=A. Glen |last10=Crowne |first10=Frank J. |last11=Vajtai |first11=Robert |last12=Yakobson |first12=Boris I. |last13=Xia |first13=Zhenhai |last14=Dubey |first14=Madan |last15=Ajayan |first15=Pulickel M. |date=2014-11-18 |title=Strain and structure heterogeneity in MoS2 atomic layers grown by chemical vapour deposition |journal=Nature Communications |volume=5 |issue=1 |page=5246 |doi=10.1038/ncomms6246 |pmid=25404060 |issn=2041-1723}}</ref> have emerged as powerful strategies to further optimize the electronic characteristics of TMDCs, making them more suitable for advanced applications in nanoelectronics and quantum computing.

=== III-VI chalcogenides === Another class of 2D semiconductors are III–VI chalcogenides. These materials have the chemical formula MX, where M is a metal from group 13 ([[Gallium|Ga]], [[Indium|In]]) and X is a chalcogen atom ([[Sulfur|S]], [[Selenide|Se]], [[Tellurium|Te]]). Typical members of this group are [[Indium(II) selenide|InSe]] and [[Gallium selenide|GaSe]], both of which have shown high electronic mobilities and [[Band gap|band gaps]] suitable for a wide range of electronic applications.<ref>{{Cite journal |last1=Arora |first1=Himani |last2=Jung |first2=Younghun |last3=Venanzi |first3=Tommaso |last4=Watanabe |first4=Kenji |last5=Taniguchi |first5=Takashi |last6=Hübner |first6=René |last7=Schneider |first7=Harald |last8=Helm |first8=Manfred |last9=Hone |first9=James C. |last10=Erbe |first10=Artur |date=2019-11-20 |title=Effective Hexagonal Boron Nitride Passivation of Few-Layered InSe and GaSe to Enhance Their Electronic and Optical Properties |url=https://pubs.acs.org/doi/10.1021/acsami.9b13442 |journal=ACS Applied Materials & Interfaces |language=en |volume=11 |issue=46 |pages=43480–43487 |doi=10.1021/acsami.9b13442 |pmid=31651146 |bibcode=2019AAMI...1143480A |hdl=11573/1555190 |s2cid=204884014 |issn=1944-8244|hdl-access=free }}</ref><ref>{{Cite journal |last1=Arora |first1=Himani |last2=Erbe |first2=Artur |date=2021 |title=Recent progress in contact, mobility, and encapsulation engineering of InSe and GaSe |journal=InfoMat |language=en |volume=3 |issue=6 |pages=662–693 |doi=10.1002/inf2.12160 |s2cid=228902032 |issn=2567-3165|doi-access=free }}</ref>

==Synthesis== [[File:CVD setup.PNG|thumb|upright=1.6|CVD setup for MoS₂ synthesis]] 2D semiconductor materials are often synthesized using a [[chemical vapor deposition]] (CVD) method. Because CVD can provide large-area, high-quality, and well-controlled layered growth of 2D semiconductor materials, it also allows synthesis of two-dimensional [[heterojunction]]s.<ref name="DuanWang2014">{{cite journal|last1=Duan|first1=Xidong|last2=Wang|first2=Chen|last3=Shaw|first3=Jonathan C.|last4=Cheng|first4=Rui|last5=Chen|first5=Yu|last6=Li|first6=Honglai|last7=Wu|first7=Xueping|last8=Tang|first8=Ying|last9=Zhang|first9=Qinling|last10=Pan|first10=Anlian|last11=Jiang|first11=Jianhui|last12=Yu|first12=Ruqing|last13=Huang|first13=Yu|last14=Duan|first14=Xiangfeng|title=Lateral epitaxial growth of two-dimensional layered semiconductor heterojunctions|journal=Nature Nanotechnology|volume=9|issue=12|year=2014|pages=1024–1030|issn=1748-3387|doi=10.1038/nnano.2014.222 |pmid=25262331 |bibcode=2014NatNa...9.1024D|pmc=12049235}}</ref> When building devices by stacking different 2D materials, [[Graphene#Exfoliation|mechanical exfoliation]] followed by transferring is often used.<ref name="GeimGrigorieva2013" /><ref name="WangKalantar-Zadeh2012" /> Other possible synthesis methods include [[Electroplating|electrochemical deposition]],<ref>{{Cite journal |last1=Noori |first1=Yasir J. |last2=Thomas |first2=Shibin |last3=Ramadan |first3=Sami |last4=Smith |first4=Danielle E. |last5=Greenacre |first5=Vicki K. |last6=Abdelazim |first6=Nema |last7=Han |first7=Yisong |last8=Beanland |first8=Richard |last9=Hector |first9=Andrew L. |last10=Klein |first10=Norbert |last11=Reid |first11=Gillian |last12=Bartlett |first12=Philip N. |last13=Kees de Groot |first13=C. H. |date=2020-11-04 |title=Large-Area Electrodeposition of Few-Layer MoS 2 on Graphene for 2D Material Heterostructures |url=https://pubs.acs.org/doi/10.1021/acsami.0c14777 |journal=ACS Applied Materials & Interfaces |language=en |volume=12 |issue=44 |pages=49786–49794 |doi=10.1021/acsami.0c14777 |pmid=33079533 |s2cid=224828493 |issn=1944-8244|arxiv=2005.08616 |bibcode=2020AAMI...1249786N }}</ref><ref>{{Cite journal |last1=Noori |first1=Y. J. |last2=Thomas |first2=S. |last3=Ramadan |first3=S. |last4=Greenacre |first4=V. K. |last5=Abdelazim |first5=N. M. |last6=Han |first6=Y. |last7=Zhang |first7=J. |last8=Beanland |first8=R. |last9=Hector |first9=A. L. |last10=Klein |first10=N. |last11=Reid |first11=G. |last12=Bartlett |first12=P. N. |last13=de Groot |first13=C. H. |date=2022-01-01 |title=Electrodeposited WS 2 monolayers on patterned graphene |url=https://iopscience.iop.org/article/10.1088/2053-1583/ac3dd6 |journal=2D Materials |volume=9 |issue=1 |page=015025 |doi=10.1088/2053-1583/ac3dd6 |arxiv=2109.00083 |bibcode=2022TDM.....9a5025N |s2cid=244693600 |issn=2053-1583}}</ref> chemical exfoliation, [[hydrothermal synthesis]], and [[thermal oxidation|thermal decomposition]]. In 2008 [[cadmium selenide]] CdSe quasi 2D platelets were first synthesized by colloidal method with thicknesses of several atomic layers and lateral sizes up to dozens of nanometers.<ref>{{Cite journal |last1=Ithurria |first1=Sandrine |last2=Dubertret |first2=Benoit |date=2008-12-10 |title=Quasi 2D Colloidal CdSe Platelets with Thicknesses Controlled at the Atomic Level |journal=Journal of the American Chemical Society |volume=130 |issue=49 |pages=16504–16505 |doi=10.1021/ja807724e |pmid=19554725 |bibcode=2008JAChS.13016504I |issn=0002-7863}}</ref> Modification of the procedure allowed to obtain other nanoparticles with different compositions (like CdTe,<ref>{{Cite journal |last1=Pedetti |first1=Silvia |last2=Nadal |first2=Brice |last3=Lhuillier |first3=Emmanuel |last4=Mahler |first4=Benoit |last5=Bouet |first5=Cécile |last6=Abécassis |first6=Benjamin |last7=Xu |first7=Xiangzhen |last8=Dubertret |first8=Benoit |date=2013-06-25 |title=Optimized Synthesis of CdTe Nanoplatelets and Photoresponse of CdTe Nanoplatelets Films |journal=Chemistry of Materials |volume=25 |issue=12 |pages=2455–2462 |doi=10.1021/cm4006844 |s2cid=101411815 |issn=0897-4756}}</ref> HgSe,<ref>{{Cite journal |last1=Izquierdo |first1=Eva |last2=Dufour |first2=Marion |last3=Chu |first3=Audrey |last4=Livache |first4=Clément |last5=Martinez |first5=Bertille |last6=Amelot |first6=Dylan |last7=Patriarche |first7=Gilles |last8=Lequeux |first8=Nicolas |last9=Lhuillier |first9=Emmanuel |last10=Ithurria |first10=Sandrine |date=2018-06-26 |title=Coupled HgSe Colloidal Quantum Wells through a Tunable Barrier: A Strategy To Uncouple Optical and Transport Band Gap |journal=Chemistry of Materials |volume=30 |issue=12 |pages=4065–4072 |doi=10.1021/acs.chemmater.8b01028 |s2cid=103490948 |issn=0897-4756}}</ref> CdSe_xS_1−x alloys,<ref>{{Cite journal |last1=Fan |first1=Fengjia |last2=Kanjanaboos |first2=Pongsakorn |last3=Saravanapavanantham |first3=Mayuran |last4=Beauregard |first4=Eric |last5=Ingram |first5=Grayson |last6=Yassitepe |first6=Emre |last7=Adachi |first7=Michael M. |last8=Voznyy |first8=Oleksandr |last9=Johnston |first9=Andrew K. |last10=Walters |first10=Grant |last11=Kim |first11=Gi-Hwan |date=2015-07-08 |title=Colloidal CdSe1–xSx Nanoplatelets with Narrow and Continuously-Tunable Electroluminescence |journal=Nano Letters |volume=15 |issue=7 |pages=4611–4615 |doi=10.1021/acs.nanolett.5b01233 |pmid=26031416 |bibcode=2015NanoL..15.4611F |issn=1530-6984}}</ref> core/shell<ref>{{Cite journal |last1=Mahler |first1=Benoit |last2=Nadal |first2=Brice |last3=Bouet |first3=Cecile |last4=Patriarche |first4=Gilles |last5=Dubertret |first5=Benoit |date=2012-11-14 |title=Core/Shell Colloidal Semiconductor Nanoplatelets |journal=Journal of the American Chemical Society |volume=134 |issue=45 |pages=18591–18598 |doi=10.1021/ja307944d |pmid=23057684 |bibcode=2012JAChS.13418591M |issn=0002-7863}}</ref> and core/crown<ref>{{Cite journal |last1=Kelestemur |first1=Yusuf |last2=Olutas |first2=Murat |last3=Delikanli |first3=Savas |last4=Guzelturk |first4=Burak |last5=Akgul |first5=Mehmet Zafer |last6=Demir |first6=Hilmi Volkan |date=2015-01-29 |title=Type-II Colloidal Quantum Wells: CdSe/CdTe Core/Crown Heteronanoplatelets |journal=The Journal of Physical Chemistry C |volume=119 |issue=4 |pages=2177–2185 |doi=10.1021/jp510466k |hdl=11693/23136 |issn=1932-7447|hdl-access=free }}</ref> heterostructures) and shapes (as scrolls,<ref>{{Cite journal |last1=Vasiliev |first1=Roman B. |last2=Lazareva |first2=Elizabeth P. |last3=Karlova |first3=Daria A. |last4=Garshev |first4=Alexey V. |last5=Yao |first5=Yuanzhao |last6=Kuroda |first6=Takashi |last7=Gaskov |first7=Alexander M. |last8=Sakoda |first8=Kazuaki |date=2018-03-13 |title=Spontaneous Folding of CdTe Nanosheets Induced by Ligand Exchange |journal=Chemistry of Materials |volume=30 |issue=5 |pages=1710–1717 |doi=10.1021/acs.chemmater.7b05324 |issn=0897-4756}}</ref> nanoribbons,<ref>{{Cite journal |last1=Deng |first1=Zhengtao |last2=Cao |first2=Di |last3=He |first3=Jin |last4=Lin |first4=Su |last5=Lindsay |first5=Stuart M. |last6=Liu |first6=Yan |date=2012-07-24 |title=Solution Synthesis of Ultrathin Single-Crystalline SnS Nanoribbons for Photodetectors via Phase Transition and Surface Processing |journal=ACS Nano |volume=6 |issue=7 |pages=6197–6207 |doi=10.1021/nn302504p |pmid=22738287 |bibcode=2012ACSNa...6.6197D |issn=1936-0851}}</ref> etc.).

== Mechanical behavior == 2D semiconductor materials unique crystal structures often yield unique mechanical properties, especially in the monolayer limit, such as high stiffness and strength in the 2D atomic plane, but low flexural rigidity.<ref>Akinwande, D.; Brennan, C. J.; Bunch, J. S.; Egberts, P.; Felts, J. R.; Gao, H.; Huang, R.; Kim, J.-S.; Li, T.; Li, Y.; Liechti, K. M.; Lu, N.; Park, H. S.; Reed, E. J.; Wang, P.; Yakobson, B. I.; Zhang, T.; Zhang, Y.-W.; Zhou, Y.; Zhu, Y. A Review on Mechanics and Mechanical Properties of 2D Materials—Graphene and Beyond. ''Extreme Mech. Lett.'' '''2017''', ''13'', 42–77. <nowiki>https://doi.org/10.1016/j.eml.2017.01.008</nowiki>.</ref> Testing these materials is more challenging than their bulk counterparts, with methods employing the use of scanning probe techniques such as [[atomic force microscopy]] (AFM). These experimental methods are typically performed on 2D materials suspended over holes in a substrate. The tip of the AFM is then used to press into the flake and measure the response of the material. From this mechanical properties such as Young modulus, yield strain, and [[flexural strength]].

=== Graphene === With a Youngs modulus of almost 1 TPa,<ref>Lee, C.; Wei, X.; Kysar, J. W.; Hone, J. Measurement of the Elastic Properties and Intrinsic Strength of Monolayer Graphene. ''Science'' '''2008''', ''321'' (5887), 385–388. <nowiki>https://doi.org/10.1126/science.1157996</nowiki>.</ref> graphene boasts incredible toughness due to the strength of the carbon-carbon bonding. Graphene however, has a [[fracture toughness]] of about 4 MPa/m, making it brittle and easy to crack .<ref>Zhang, P.; Ma, L.; Fan, F.; Zeng, Z.; Peng, C.; Loya, P. E.; Liu, Z.; Gong, Y.; Zhang, J.; Zhang, X.; Ajayan, P. M.; Zhu, T.; Lou, J. Fracture Toughness of Graphene. ''Nat. Commun.'' '''2014''', ''5'' (1), 3782. <nowiki>https://doi.org/10.1038/ncomms4782</nowiki>.</ref> Graphene was later shown by the same group that discovered its fracture toughness, to have incredible force distribution abilities, with about ten times the ability of steel.<ref>Dorrieron, Jason (4 December 2014). "Graphene Armor Would Be Light, Flexible and Far Stronger Than Steel". ''Singularity Hub''. Retrieved 6 October 2016.</ref>

=== Atomically thin boron nitride === Monolayer boron nitride has fracture strength and Youngs modulus of 70.5 GPa and 0.865 TPa, respectively. Boron nitride also maintains its high Youngs modulus and fracture strengths with increasing thickness.<ref>Falin, A.; Cai, Q.; Santos, E. J. G.; Scullion, D.; Qian, D.; Zhang, R.; Yang, Z.; Huang, S.; Watanabe, K.; Taniguchi, T.; Barnett, M. R.; Chen, Y.; Ruoff, R. S.; Li, L. H. Mechanical Properties of Atomically Thin Boron Nitride and the Role of Interlayer Interactions. ''Nat. Commun.'' '''2017''', ''8'', 15815. <nowiki>https://doi.org/10.1038/ncomms15815</nowiki>.</ref>

=== Transition metal dichalcogenides === 2D transition metal dichalcogenides are often used in applications such as flexible and stretchable electronics, where an understanding of their mechanical properties and the operational impact of mechanical changes to the materials is paramount for device performance. Under strain TMDs change their electronic bandgap structure of both the direct gap monolayer and the indirect gap few layer cases indicating applied strain as a tunable parameter.<ref>Conley, H. J.; Wang, B.; Ziegler, J. I.; Haglund Jr., R. F.; Pantelides, S. T.; Bolotin, K. I. Bandgap Engineering of Strained Monolayer and Bilayer MoS2. ''Nano Lett.'' '''2013''', ''13'' (8), 3626–3630. <nowiki>https://doi.org/10.1021/nl4014748</nowiki>.</ref> Monolayer MoS₂ has a Youngs modulus of 270 GPA and with a maximum strain of 10% before yield.<ref name=":0">Bertolazzi, S.; Brivio, J.; Kis, A. Stretching and Breaking of Ultrathin MoS2. ''ACS Nano'' '''2011''', ''5'' (12), 9703–9709. <nowiki>https://doi.org/10.1021/nn203879f</nowiki>.</ref> In comparison, bilayer MoS2 has a Youngs modulus of 200 GPa attributed to interlayer slip.<ref name=":0" /> As layer number is increased further the interlayer slip is overshadowed by the bending rigidity with a Youngs modulus of 330 GPa.<ref>Castellanos-Gomez, A.; Poot, M.; Steele, G. A.; van der Zant, H. S. J.; Agraït, N.; Rubio-Bollinger, G. Elastic Properties of Freely Suspended MoS2 Nanosheets. ''Adv. Mater.'' '''2012''', ''24'' (6), 772–775. <nowiki>https://doi.org/10.1002/adma.201103965</nowiki>.</ref>

[[File:VdW qubit.png|thumb|upright=1.6|Proposed vdW qubit composed of ZrSe₂/SnSe₂. The electrode V_G applies the vertical electric field, changing the state of the electron in the conduction band, represented by the green [[Bloch sphere]]. Zr, Sn, and Se in red, blue, and gray, respectively.<ref name="Lucatto2019" />]]

==Proposed applications== Some applications include electronic devices,<ref>{{Cite web|url=http://2d.stanford.edu/2D_Trends|title=Stanford 2D Device Trends|date=|website=|last1=McClellan |first1=Connor }}</ref> photonic and energy harvesting devices, and flexible and transparent substrates.<ref name="Radisavljevic"/> Other applications include on [[quantum computing]] [[qubit]] devices,<ref name="Lucatto2019" /> [[Solar cell|solar cells]],<ref name="ShanmugamJacobs-Gedrim2014">{{cite journal|last1=Shanmugam|first1=Mariyappan|last2=Jacobs-Gedrim|first2=Robin|last3=Song|first3=Eui Sang|last4=Yu|first4=Bin|title=Two-dimensional layered semiconductor/graphene heterostructures for solar photovoltaic applications|journal=Nanoscale|volume=6|issue=21|year=2014|pages=12682–12689|issn=2040-3364|doi=10.1039/C4NR03334E|pmid=25210837|bibcode = 2014Nanos...612682S}}</ref> and [[flexible electronics]].<ref name="WangKalantar-Zadeh2012" />

===Quantum computing=== Theoretical work has predicted the control of the band edges hybridization on some van der Waals heterostructures via electric fields and proposed its usage in quantum bit devices, considering the ZrSe₂/SnSe₂ heterobilayer as an example.<ref name="Lucatto2019" /> Further experimental work has confirmed these predictions for the case of the MoS₂/WS₂ heterobilayer.<ref name="Kiemle2020">{{cite journal|last1=Kiemle|first1=Jonas|year=2020|title=Control of the orbital character of indirect excitons in MoS₂/WS₂ heterobilayers| journal=Phys. Rev. B| volume=101| issue=12| display-authors=etal| article-number=121404|doi=10.1103/PhysRevB.101.121404|url=https://link.aps.org/doi/10.1103/PhysRevB.101.121404|arxiv=1912.02479|bibcode=2020PhRvB.101l1404K |s2cid=208637170 }}</ref>[[File:2D device.PNG|thumb|upright=1.5|Proposed TMDC-based [[high-electron-mobility transistor]] device with top-gated [[Schottky barrier|Schottky contact]] and TMDC layers with different doping levels.<ref>{{cite journal|last1=Ong|first1=Zhun-Yong|last2=Bae|first2=Myung-Ho|title=Energy dissipation in van der Waals 2D devices|journal=2D Materials|date=2019|volume=6|issue=3|page= 032005|doi=10.1088/2053-1583/ab20ea|arxiv=1904.09752|bibcode=2019TDM.....6c2005O |s2cid=128345575 }}</ref>]]

===Magnetic NEMS=== 2D layered magnetic materials are attractive building blocks for [[nanoelectromechanical systems]] (NEMS): while they share high stiffness and strength and low mass with other 2D materials, they are magnetically active. Among the large class of newly emerged 2D layered magnetic materials, of particular interest is few-layer CrI3, whose magnetic ground state consists of antiferromagnetically coupled ferromagnetic (FM) monolayers with out-of-plane easy axis. The interlayer exchange interaction is relatively weak, a magnetic field on the order of 0.5 T in the out-of-plane (𝒛) direction can induce spin-flip transition in bilayer CrI3. Remarkable phenomena and device concepts based on detecting and controlling the interlayer magnetic state have been recently demonstrated, including spin-filter giant [[magnetoresistance]], magnetic switching by electric field or electrostatic [[Doping (semiconductor)|doping]], and spin transistors. The coupling between the magnetic and mechanical properties in atomically thin materials, the basis for 2D magnetic NEMS, however, remains elusive although NEMS made of thicker magnetic materials or coated with FM metals have been studied.

==References== {{reflist|30em}}

[[Category:Semiconductors]] [[Category:Two-dimensional nanomaterials]] [[Category:Condensed matter physics]]