Editing Quantum tunnelling (section)

== Applications ==
Tunnelling is the cause of some important macroscopic physical phenomena.

=== Solid-state physics ===

==== Electronics ====
Tunnelling is a source of current leakage in [[very-large-scale integration]] (VLSI) electronics and results in a substantial power drain and heating effects that plague such devices. It is considered the lower limit on how microelectronic device elements can be made.<ref>{{Cite web |title=Applications of ''tunneling'' |url=http://psi.phys.wits.ac.za/teaching/Connell/phys284/2005/lecture-02/lecture_02/node13.html |access-date=2023-04-30 |website=psi.phys.wits.ac.za}}</ref> Tunnelling is a fundamental technique used to program the floating gates of [[flash memory]].

==== Cold emission ====
{{Main|Field electron emission}}

Cold emission of [[electrons]] is relevant to [[semiconductor]]s and [[superconductor]] physics. It is similar to [[thermionic emission]], where electrons randomly jump from the surface of a metal to follow a voltage bias because they statistically end up with more energy than the barrier, through random collisions with other particles. When the electric field is very large, the barrier becomes thin enough for electrons to tunnel out of the atomic state, leading to a current that varies approximately exponentially with the electric field.<ref name="Taylor">{{cite book|last=Taylor|first=J.|title=Modern Physics for Scientists and Engineers|publisher=Prentice Hall|year=2004|isbn=978-0-13-805715-2|page=479}}</ref> These materials are important for flash memory, vacuum tubes, and some electron microscopes.

==== Tunnel junction ====
{{Main|Tunnel junction}}

A simple barrier can be created by separating two conductors with a very thin [[Insulator (electricity)|insulator]]. These are tunnel junctions, the study of which requires understanding quantum tunnelling.<ref>{{cite book|last1=Lerner|url=https://archive.org/details/encyclopediaofph00lern/page/1308|title=Encyclopedia of Physics|last2=Trigg|publisher=VCH|year=1991|isbn=978-0-89573-752-6|edition=2nd|location=New York|pages=[https://archive.org/details/encyclopediaofph00lern/page/1308 1308–1309]}}</ref> [[Josephson junction]]s take advantage of quantum tunnelling and superconductivity to create the [[Josephson effect]]. This has applications in precision measurements of voltages and [[magnetic fields]],<ref name="Taylor" /> as well as the [[multijunction solar cell]].

==== Tunnel diode ====
{{Main|Tunnel diode}}

[[File:Rtd seq v3.gif|thumb|upright=1.6|right|A working mechanism of a [[resonant tunnelling diode]] device, based on the phenomenon of quantum tunnelling through the potential barriers]]

[[Diode]]s are electrical [[semiconductor device]]s that allow [[electric current]] flow in one direction more than the other. The device depends on a [[depletion layer]] between [[N-type semiconductor|N-type]] and [[P-type semiconductor]]s to serve its purpose. When these are heavily doped the depletion layer can be thin enough for tunnelling. When a small forward bias is applied, the current due to tunnelling is significant. This has a maximum at the point where the [[voltage bias]] is such that the energy level of the p and n [[conduction band]]s are the same. As the voltage bias is increased, the two conduction bands no longer line up and the diode acts typically.<ref name="Krane">{{cite book|last=Krane|first=Kenneth|url=https://archive.org/details/modernphysics00kran/page/423|title=Modern Physics|publisher=John Wiley and Sons|year=1983|isbn=978-0-471-07963-7|location=New York|page=[https://archive.org/details/modernphysics00kran/page/423 423]}}</ref>

Because the tunnelling current drops off rapidly, tunnel diodes can be created that have a range of voltages for which current decreases as voltage increases. This peculiar property is used in some applications, such as high speed devices where the characteristic tunnelling probability changes as rapidly as the bias voltage.<ref name="Krane" />

The [[resonant tunnelling diode]] makes use of quantum tunnelling in a very different manner to achieve a similar result. This diode has a resonant voltage for which a current favors a particular voltage, achieved by placing two thin layers with a high energy conductance band near each other. This creates a quantum [[potential well]] that has a discrete lowest [[energy level]]. When this energy level is higher than that of the electrons, no tunnelling occurs and the diode is in reverse bias. Once the two voltage energies align, the electrons flow like an open wire. As the voltage further increases, tunnelling becomes improbable and the diode acts like a normal diode again before a second energy level becomes noticeable.<ref name="Knight">{{cite book|last=Knight|first=R. D.|title=Physics for Scientists and Engineers: With Modern Physics|publisher=Pearson Education|year=2004|isbn=978-0-321-22369-2|page=1311}}</ref>

==== Tunnel field-effect transistors ====
{{Main|Tunnel field-effect transistor}}

A European research project demonstrated [[field effect transistors]] in which the gate (channel) is controlled via quantum tunnelling rather than by thermal injection, reducing gate voltage from ≈1 volt to 0.2 volts and reducing power consumption by up to 100×. If these transistors can be scaled up into [[Vlsi|VLSI chips]], they would improve the performance per power of [[integrated circuit]]s.<ref>{{cite journal|last1=Ionescu|first1=Adrian M.|last2=Riel|first2=Heike|author2-link=Heike Riel|year=2011|title=Tunnel field-effect transistors as energy-efficient electronic switches |journal=[[Nature (journal)|Nature]]|volume=479|issue=7373|pages=329–337|bibcode=2011Natur.479..329I|doi=10.1038/nature10679|pmid=22094693|s2cid=4322368}}</ref><ref>{{Cite journal|last1=Vyas|first1=P. B. |last2=Naquin |first2=C. |last3=Edwards |first3=H. |last4=Lee |first4=M. |last5=Vandenberghe |first5=W. G.|last6=Fischetti|first6=M. V.|date=2017-01-23|title=Theoretical simulation of negative differential transconductance in lateral quantum well nMOS devices|url=https://aip.scitation.org/doi/10.1063/1.4974469 |journal=Journal of Applied Physics |volume=121 |issue=4 |pages=044501 |doi=10.1063/1.4974469|bibcode=2017JAP...121d4501V|issn=0021-8979}}</ref>

==== Conductivity of crystalline solids ====
While the [[Drude-Lorentz model]] of [[electrical conductivity]] makes excellent predictions about the nature of electrons conducting in metals, it can be furthered by using quantum tunnelling to explain the nature of the electron's collisions.<ref name="Taylor" /> When a free electron wave packet encounters a long array of uniformly spaced [[potential barrier|barriers]], the reflected part of the wave packet interferes uniformly with the transmitted one between all barriers so that 100% transmission becomes possible. The theory predicts that if positively charged nuclei form a perfectly rectangular array, electrons will tunnel through the metal as free electrons, leading to extremely high [[Electrical conductance|conductance]], and that impurities in the metal will disrupt it.<ref name="Taylor" />

==== Scanning tunneling microscope ====
{{Main|Scanning tunnelling microscope}}

The scanning tunnelling microscope (STM), invented by [[Gerd Binnig]] and [[Heinrich Rohrer]], may allow imaging of individual atoms on the surface of a material.<ref name="Taylor" /> It operates by taking advantage of the relationship between quantum tunnelling with distance. When the tip of the STM's needle is brought close to a conduction surface that has a voltage bias, measuring the current of electrons that are tunnelling between the needle and the surface reveals the distance between the needle and the surface. By using [[Piezoelectric sensor|piezoelectric rods]] that change in size when voltage is applied, the height of the tip can be adjusted to keep the tunnelling current constant. The time-varying voltages that are applied to these rods can be recorded and used to image the surface of the conductor.<ref name="Taylor" /> STMs are accurate to 0.001&nbsp;nm, or about 1% of atomic diameter.<ref name="Knight" />

=== Nuclear physics ===
==== Nuclear fusion ====
{{Main|Nuclear fusion}}

Quantum tunnelling is an essential phenomenon for nuclear fusion. The temperature in [[stellar core]]s is generally insufficient to allow atomic nuclei to overcome the [[Coulomb barrier]] and achieve [[thermonuclear fusion]]. Quantum tunnelling increases the probability of penetrating this barrier. Though this probability is still low, the extremely large number of nuclei in the core of a star is sufficient to sustain a steady fusion reaction.<ref name="Trixler2013">{{cite journal |last=Trixler |first=F. |date=2013 |title=Quantum tunnelling to the origin and evolution of life |journal=Current Organic Chemistry |volume=17 |pages=1758–1770 |doi=10.2174/13852728113179990083 |pmc=3768233 |pmid=24039543 |number=16}}</ref>

==== Radioactive decay ====
{{Main|Radioactive decay}}

Radioactive decay is the process of emission of particles and energy from the unstable nucleus of an atom to form a stable product. This is done via the tunnelling of a particle out of the nucleus (an electron tunneling into the nucleus is [[electron capture]]). This was the first application of quantum tunnelling. Radioactive decay is a relevant issue for [[astrobiology]] as this consequence of quantum tunnelling creates a constant energy source over a large time interval for environments outside the [[circumstellar habitable zone]] where insolation would not be possible ([[Planetary oceanography#Extraterrestrial water oceans|subsurface oceans]]) or effective.<ref name="Trixler2013" />

Quantum tunnelling may be one of the mechanisms of hypothetical [[proton decay]].<ref name="url[nucl-th/9809006] Time-dependent properties of proton decay from crossing single-particle metastable states in deformed nuclei">{{cite journal |title=Time-dependent properties of proton decay from crossing single-particle metastable states in deformed nuclei |year=1998 |doi=10.1103/PhysRevC.58.3280 |arxiv=nucl-th/9809006 |last1=Talou |first1=P. |last2=Carjan |first2=N. |last3=Strottman |first3=D. |journal=Physical Review C |volume=58 |issue=6 |pages=3280–3285 |bibcode=1998PhRvC..58.3280T |s2cid=119075457 }}</ref><ref name="urladsabs.harvard.edu">{{cite web |url=http://adsabs.harvard.edu/pdf/1982ApJ...252....1D |title=adsabs.harvard.edu |format= |accessdate=}}</ref>

=== Chemistry ===

==== Energetically forbidden reactions ====
Chemical reactions in the [[interstellar medium]] occur at extremely low energies. Probably the most fundamental ion-molecule reaction involves hydrogen ions with hydrogen molecules.  
The quantum mechanical tunnelling rate for the same reaction using the [[hydrogen]] isotope [[deuterium]], D<sup>−</sup> + H<sub>2</sub> → H<sup>−</sup> + HD, has been measured experimentally in an ion trap.
The deuterium was placed in an [[ion trap]] and cooled. The trap was then filled with hydrogen. At the temperatures used in the experiment, the energy barrier for reaction would not allow the reaction to succeed with classical dynamics alone. Quantum tunneling allowed reactions to happen in rare collisions. It was calculated from the experimental data that collisions happened one in every hundred billion.<ref>{{Cite journal |last1=Wild |first1=Robert |last2=Nötzold |first2=Markus |last3=Simpson |first3=Malcolm |last4=Tran |first4=Thuy Dung |last5=Wester |first5=Roland |date=2023-03-16 |title=Tunnelling measured in a very slow ion–molecule reaction |url=https://www.nature.com/articles/s41586-023-05727-z |journal=Nature |language=en |volume=615 |issue=7952 |pages=425–429 |doi=10.1038/s41586-023-05727-z |pmid=36859549 |bibcode=2023Natur.615..425W |issn=0028-0836|arxiv=2303.14948 }}</ref>

==== Kinetic isotope effect ====
{{Main|Kinetic isotope effect}}

In [[chemical kinetics]], the substitution of a light [[isotope]] of an element with a heavier one typically results in a slower reaction rate. This is generally attributed to differences in the zero-point vibrational energies for chemical bonds containing the lighter and heavier isotopes and is generally modeled using [[transition state theory]]. However, in certain cases, large isotopic effects are observed that cannot be accounted for by a semi-classical treatment, and quantum tunnelling is required. [[Ronnie Bell (chemist)|R. P. Bell]] developed a modified treatment of Arrhenius kinetics that is commonly used to model this phenomenon.<ref>{{Cite book |last=Bell |first=Ronald Percy |title=The tunnel effect in chemistry |date=1980 |publisher=Chapman and Hall |isbn=0412213400 |location=London |oclc=6854792}}</ref>

==== Astrochemistry in interstellar clouds ====
By including quantum tunnelling, the [[Astrochemistry|astrochemical]] syntheses of various molecules in [[interstellar cloud]]s can be explained, such as the synthesis of [[Hydrogen#Spin isomers|molecular hydrogen]], [[water]] ([[ice]]) and the [[Abiogenesis|prebiotic]] important [[formaldehyde]].<ref name="Trixler2013" /> Tunnelling of molecular hydrogen has been observed in the lab.<ref>{{Cite journal |last1=Wild |first1=Robert |last2=Nötzold |first2=Markus |last3=Simpson |first3=Malcolm |last4=Tran |first4=Thuy Dung |last5=Wester |first5=Roland |date=2023-03-01 |title=Tunnelling measured in a very slow ion–molecule reaction |url=https://www.nature.com/articles/s41586-023-05727-z |journal=Nature |volume=615 |issue=7952 |language=en |pages=425–429 |doi=10.1038/s41586-023-05727-z |pmid=36859549 |arxiv=2303.14948 |bibcode=2023Natur.615..425W |s2cid=257282176 |issn=1476-4687}}</ref>

==== Quantum biology ====
Quantum tunnelling is among the central non-trivial quantum effects in [[quantum biology]].<ref name="life">{{cite journal |title=Quantum Tunnelling to the Origin and Evolution of Life |year=2013 |pmc=3768233 |last1=Trixler |first1=F. |journal=Current Organic Chemistry |volume=17 |issue=16 |pages=1758–1770 |doi=10.2174/13852728113179990083 |pmid=24039543 }}</ref> Here it is important both as electron tunnelling and [[proton tunneling|proton tunnelling]]. Electron tunnelling is a key factor in many biochemical [[redox reactions]] ([[photosynthesis]], [[cellular respiration]]) as well as enzymatic catalysis. Proton tunnelling is a key factor in spontaneous [[DNA]] mutation.<ref name="Trixler2013" />

Spontaneous mutation occurs when normal DNA replication takes place after a particularly significant proton has tunnelled.<ref>{{cite book |last=Matta |first=Cherif F. |title=Quantum Biochemistry: Electronic Structure and Biological Activity |location=Weinheim |publisher=Wiley-VCH |year=2014 |url=https://books.google.com/books?id=a4JhVFaUOjgC |isbn=978-3-527-62922-0 }}</ref> A hydrogen bond joins DNA base pairs. A double well potential along a hydrogen bond separates a potential energy barrier. It is believed that the double well potential is asymmetric, with one well deeper than the other such that the proton normally rests in the deeper well. For a mutation to occur, the proton must have tunnelled into the shallower well. The proton's movement from its regular position is called a [[Tautomer|tautomeric transition]]. If DNA replication takes place in this state, the base pairing rule for DNA may be jeopardised, causing a mutation.<ref>{{cite book |last=Majumdar |first=Rabi |title=Quantum Mechanics: In Physics and Chemistry with Applications to Bioloty |location=Newi |publisher=PHI Learning |year=2011 |url=https://books.google.com/books?id=IJDvyNVeBiYC |isbn=9788120343047 }}</ref> [[Per-Olov Lowdin]] was the first to develop this theory of spontaneous mutation within the [[Nucleic acid double helix|double helix]]. Other instances of quantum tunnelling-induced mutations in biology are believed to be a cause of ageing and cancer.<ref>{{cite journal |last=Cooper |first=W. G. |date=June 1993 |title=Roles of Evolution, Quantum Mechanics and Point Mutations in Origins of Cancer |journal=Cancer Biochemistry Biophysics |volume=13 |issue=3 |pages=147–170 |pmid=8111728}}</ref>