22:
485:
473:
79:
497:
933:
Ionic
Coulomb blockade (ICB) is the special case of CB, appearing in the electro-diffusive transport of charged ions through sub-nanometer artificial nanopores or biological ion channels. ICB is widely similar to its electronic counterpart in quantum dots, but presents some specific features defined
545:
When a positive voltage is applied to the gate electrode the energy levels of the island electrode are lowered. The electron (green 1.) can tunnel onto the island (2.), occupying a previously vacant energy level. From there it can tunnel onto the drain electrode (3.) where it inelastically scatters
410:
In order for the
Coulomb blockade to be observable, the temperature has to be low enough so that the characteristic charging energy (the energy that is required to charge the junction with one elementary charge) is larger than the thermal energy of the charge carriers. In the past, for capacitances
1556:
Prati, E.; De
Michielis, M.; Belli, M.; Cocco, S.; Fanciulli, M.; Kotekar-Patil, D.; Ruoff, M.; Kern, D. P.; Wharam, D. A.; Verduijn, J.; Tettamanzi, G. C.; Rogge, S.; Roche, B.; Wacquez, R.; Jehl, X.; Vinet, M.; Sanquer, M. (2012). "Few electron limit of n-type metal oxide semiconductor single
880:
A typical
Coulomb blockade thermometer (CBT) is made from an array of metallic islands, connected to each other through a thin insulating layer. A tunnel junction forms between the islands, and as voltage is applied, electrons may tunnel across this junction. The tunneling rates and hence the
397:
is the capacitance of the junction. If the capacitance is very small, the voltage build up can be large enough to prevent another electron from tunnelling. The electric current is then suppressed at low bias voltages and the resistance of the device is no longer constant. The increase of the
458:. The integration of quantum dot fabrication with standard industrial technology has been achieved for silicon. CMOS process for obtaining massive production of single electron quantum dot transistors with channel size down to 20 nm x 20 nm has been implemented.
300:
is applied, this means that there will be a current, and, neglecting additional effects, the tunnelling current will be proportional to the bias voltage. In electrical terms, the tunnel junction behaves as a
339:) through the tunnel barrier (we neglect cotunneling, in which two electrons tunnel simultaneously). The tunnel junction capacitor is charged with one elementary charge by the tunnelling electron, causing a
1495:
Shin, S. J.; Lee, J. J.; Kang, H. J.; Choi, J. B.; Yang, S. -R. E.; Takahashi, Y.; Hasko, D. G. (2011). "Room-Temperature Charge
Stability Modulated by Quantum Effects in a Nanoscale Silicon Island".
542:
In the blocking state no accessible energy levels are within tunneling range of an electron (in red) on the source contact. All energy levels on the island electrode with lower energies are occupied.
793:
1022:
695:
644:
1096:
865:
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refrigerators. Thanks to small sized quantum dots of only few nanometers, Coulomb blockade has been observed next above liquid helium temperature, up to room temperature.
1253:
573:
962:
1122:
125:. Because of the CB, the conductance of a device may not be constant at low bias voltages, but disappear for biases under a certain threshold, i.e. no current flows.
1045:
375:
224:
263:
593:
395:
1825:
Kaufman, Igor Kh.; Fedorenko, Olena A.; Luchinsky, Dmitri G.; Gibby, William A.T.; Roberts, Stephen K.; McClintock, Peter V.E.; Eisenberg, Robert S. (2017).
938:
of charge carriers (permeating ions vs electrons) and by the different origin of transport engine (classical electrodiffusion vs quantum tunnelling).
442:, one has to create electrodes with dimensions of approximately 100 by 100 nanometers. This range of dimensions is routinely reached for example by
1294:
Averin, D. V.; Likharev, K. K. (1986-02-01). "Coulomb blockade of single-electron tunneling, and coherent oscillations in small tunnel junctions".
164:
273:
The following section is for the case of tunnel junctions with an insulating barrier between two normal conducting electrodes (NIN junctions).
335:
Due to the discreteness of electrical charge, current through a tunnel junction is a series of events in which exactly one electron passes (
967:
1827:"Ionic Coulomb blockade and anomalous mole fraction effect in the NaChBac bacterial ion channel and its charge-varied mutants"
111:
738:
660:
399:
65:
43:
36:
601:
320:
An arrangement of two conductors with an insulating layer in between not only has a resistance, but also a finite
1442:
Couto, ODD; Puebla, J (2011). "Charge control in InP/(Ga,In)P single quantum dots embedded in
Schottky diodes".
280:
is, in its simplest form, a thin insulating barrier between two conducting electrodes. According to the laws of
1883:
Fulton, T.A.; Dolan, G.J. (1987). "Observation of single-electron charging effects in small tunnel junctions".
881:
conductance vary according to the charging energy of the islands as well as the thermal energy of the system.
1054:
1951:
455:
451:
1956:
833:
103:
1389:
Crippa A; et al. (2015). "Valley blockade and multielectron spin-valley Kondo effect in silicon".
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500:
489:
477:
467:
1197:
443:
281:
176:
1375:
1946:
1194:
In biological ion channels ICB typically manifests itself in such valence selectivity phenomena as
703:
30:
1127:
801:
1714:
Feng, Jiandong; Liu, Ke; Graf, Michael; Dumcenco, Dumitru; Kis, Andras; Di Ventra, Massimiliano;
1229:
1162:
1269:
1264:
928:
911:, the full width at half minimum of the measured differential conductance dip over an array of
552:
47:
944:
431:
1362:
1101:
868:
515:
The simplest device in which the effect of
Coulomb blockade can be observed is the so-called
313:
on the barrier thickness. Typically, the barrier thickness is on the order of one to several
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8:
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535:. The electrical potential of the island can be tuned by a third electrode, known as the
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based on electric conductance characteristics of tunnel junction arrays. The parameter
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The thermal energy in the source contact plus the thermal energy in the island, i.e.
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geometry with a capacitance of 1 femtofarad, using an oxide layer of electric
194:
137:
107:
1926:
1778:"Coulomb blockade model of permeation and selectivity in biological ion channels"
549:
The energy levels of the island electrode are evenly spaced with a separation of
277:
144:
and the current-voltage relation of the
Coulomb blockade looks like a staircase.
122:
1904:
1473:
1420:
172:
160:
284:, no current can flow through an insulating barrier. According to the laws of
1940:
1852:
1843:
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1811:
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1323:
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is defined by dielectric self-energy of incoming ion inside the pore/channel
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235:
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1346:
795:
or else the electron will be able to pass the QD via thermal excitation; and
1912:
1759:
1719:
1697:
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1534:
435:
306:
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141:
140:
preventing other electrons to flow. Thus, the device will no longer follow
115:
83:
1879:, eds. B.L. Altshuler, P.A. Lee, and R.A. Webb (Elsevier, Amsterdam, 1991)
885:
321:
289:
190:
129:
119:
527:, connected through tunnel junctions to one common electrode with a low
492:
for the blocking state (upper part) and transmitting state (lower part).
292:
for an electron on one side of the barrier to reach the other side (see
1315:
412:
325:
128:
Coulomb blockade can be observed by making a device very small, like a
1526:
1354:
1931:
1870:
Single Charge
Tunneling: Coulomb Blockade Phenomena in Nanostructures
1743:
508:
439:
329:
314:
226:) carry the current. In the case that the electrodes are metallic or
186:
1403:
1255:) and concentration-dependent divalent blockade of sodium current.
424:
302:
239:
133:
1872:, eds. H. Grabert and M. H. Devoret (Plenum Press, New York, 1992)
1662:
1571:
1509:
1456:
419:), this implied that the temperature has to be below about 1
159:. However, when few electrons are involved and an external static
504:
340:
1345:
Wang, Xufeng; Muralidharan, Bhaskaran; Klimeck, Gerhard (2006).
649:
To achieve the
Coulomb blockade, three criteria have to be met:
472:
147:
Even though the Coulomb blockade can be used to demonstrate the
1776:
Kaufman, I. Kh; McClintock, P. V. E.; Eisenberg, R. S. (2015).
1159:
ICB has been recently experimentally observed in sub-nanometer
420:
78:
1824:
488:
Left to right: energy levels of source, island and drain in a
496:
423:. This temperature range is routinely reached for example by
416:
1620:"2.5 Minimum Tunnel Resistance for Single Electron Charging"
1555:
1775:
1177:
118:
of a small electronic device comprising at least one low-
1344:
163:
is applied, Coulomb blockade provides the ground for a
1347:"nanoHUB.org - Resources: Coulomb Blockade Simulation"
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288:, however, there is a nonvanishing (larger than zero)
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206:
1720:"Observation of ionic Coulomb blockade in nanopores"
788:{\displaystyle k_{\rm {B}}T<{\frac {e^{2}}{2C}},}
1713:
1644:Krems, Matt; Di Ventra, Massimiliano (2013-01-10).
171:, which include quantum mechanical effects due to
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546:and reaches the drain electrode Fermi level (4.).
389:
369:
328:in this context, the tunnel junction behaves as a
257:
218:
1017:{\displaystyle \Delta E={\frac {z^{2}e^{2}}{2C}}}
690:{\displaystyle V_{\text{bias}}<{\frac {e}{C}}}
402:around zero bias is called the Coulomb blockade.
155:effect and its main description does not require
1938:
539:, which is capacitively coupled to the island.
1494:
875:
657:divided by the self-capacitance of the island:
1643:
1293:
1098:, even at the room temperature, for ions with
519:. It consists of two electrodes known as the
461:
305:with a constant resistance, also known as an
86:) of an electron tunnelling through a barrier
639:{\displaystyle C={\frac {e^{2}}{\Delta E}}.}
182:The devices can comprise either metallic or
1882:
1441:
1624:About Single-Electron Devices and Circuits
884:Coulomb blockade thermometer is a primary
1842:
1801:
1687:
1661:
1617:
1570:
1508:
1455:
1402:
922:
189:. If the electrodes are superconducting,
66:Learn how and when to remove this message
1626:(Ph.D.). Vienna University of Technology
1388:
653:The bias voltage must be lower than the
495:
483:
471:
77:
29:This article includes a list of general
1091:{\textstyle (\Delta E\gg k_{\rm {B}}T)}
268:
136:inside the device will create a strong
1939:
575:This gives rise to a self-capacitance
1927:Computational Single-Electronics book
1771:
1769:
1646:"Ionic Coulomb blockade in nanopores"
82:Schematic representation (similar to
1709:
1707:
1650:Journal of Physics: Condensed Matter
179:respectively between the electrons.
15:
867:which is derived from Heisenberg's
860:{\displaystyle {\frac {h}{e^{2}}},}
735:must be below the charging energy:
149:quantization of the electric charge
132:. When the device is small enough,
13:
1766:
1296:Journal of Low Temperature Physics
1239:
1226:conduction bands (vs fixed charge
1076:
1061:
1031:
971:
948:
919:provide the absolute temperature.
811:
748:
713:
624:
556:
35:it lacks sufficient corresponding
14:
1968:
1920:
1875:D.V. Averin and K.K Likharev, in
1704:
1287:
1831:EPJ Nonlinear Biomedical Physics
1219:{\displaystyle {\text{Ca}}^{2+}}
941:In the case of ICB, Coulomb gap
20:
1932:Coulomb blockade online lecture
1818:
324:. The insulator is also called
167:(like Pauli spin blockade) and
1877:Mesoscopic Phenomena in Solids
1637:
1611:
1589:10.1088/0957-4484/23/21/215204
1549:
1488:
1435:
1382:
1338:
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934:by possibly different valence
405:
1:
1803:10.1088/1367-2630/17/8/083021
1680:10.1088/0953-8984/25/6/065101
1618:Wasshuber, Christoph (1997).
1280:
1149:{\displaystyle {\ce {Ca^2+}}}
728:{\displaystyle k_{\rm {B}}T,}
430:To make a tunnel junction in
1184:{\displaystyle {\ce {MoS2}}}
915:junctions together with the
876:Coulomb blockade thermometer
823:{\displaystyle R_{\rm {t}},}
456:shadow evaporation technique
7:
1258:
1248:{\displaystyle Q_{\rm {f}}}
104:Charles-Augustin de Coulomb
10:
1973:
1905:10.1103/PhysRevLett.59.109
1474:10.1103/PhysRevB.84.125301
1421:10.1103/PhysRevB.92.035424
926:
798:The tunneling resistance,
595:of the island, defined as
517:single-electron transistor
501:Single-electron transistor
490:single-electron transistor
478:single-electron transistor
468:Single-electron transistor
465:
462:Single-electron transistor
568:{\displaystyle \Delta E.}
444:electron beam lithography
309:. The resistance depends
282:classical electrodynamics
957:{\displaystyle \Delta E}
452:Niemeyer–Dolan technique
1557:electron transistors".
1117:{\displaystyle z>=2}
1047:depends on ion valence
830:should be greater than
450:technologies, like the
400:differential resistance
50:more precise citations.
1844:10.1051/epjnbp/2017003
1782:New Journal of Physics
1370:Cite journal requires
1270:Quantisation of charge
1265:Ionic Coulomb blockade
1249:
1220:
1185:
1150:
1118:
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1041:
1018:
958:
929:Ionic Coulomb blockade
923:Ionic Coulomb blockade
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112:electrical conductance
87:
1716:Radenovic, Aleksandra
1250:
1221:
1186:
1151:
1119:
1093:
1051:. ICB appears strong
1042:
1040:{\textstyle \Delta E}
1019:
959:
869:uncertainty principle
862:
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790:
730:
692:
641:
590:
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487:
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438:10 and thickness one
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372:
370:{\displaystyle U=e/C}
265:) carry the current.
260:
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110:, is the decrease in
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739:
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602:
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269:In a tunnel junction
246:
204:
177:orbital interactions
1952:Quantum electronics
1897:1987PhRvL..59..109F
1794:2015NJPh...17h3021K
1736:2016NatMa..15..850F
1672:2013JPCM...25f5101K
1581:2012Nanot..23u5204P
1519:2011NanoL..11.1591S
1466:2011PhRvB..84l5301C
1413:2015PhRvB..92c5424C
1308:1986JLTP...62..345A
1179:
219:{\displaystyle -2e}
1957:Mesoscopic physics
1316:10.1007/BF00683469
1245:
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917:physical constants
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294:quantum tunnelling
258:{\displaystyle -e}
255:
242:(with a charge of
216:
199:elementary charges
92:mesoscopic physics
88:
1527:10.1021/nl1044692
1444:Physical Review B
1391:Physical Review B
1355:10.4231/d3c24qp1w
1275:Elementary charge
1205:
1170:
1135:
1012:
852:
780:
685:
671:
655:elementary charge
631:
588:{\displaystyle C}
390:{\displaystyle C}
286:quantum mechanics
228:normal-conducting
157:quantum mechanics
138:Coulomb repulsion
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529:self-capacitance
454:, also known as
448:pattern transfer
446:and appropriate
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232:superconducting
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184:superconducting
169:valley blockade
151:, it remains a
123:tunnel junction
102:), named after
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42:Please help to
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1497:Nano Letters
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191:Cooper pairs
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1349:. nanoHUB.
1124:, e.g. for
886:thermometer
406:Observation
322:capacitance
290:probability
130:quantum dot
120:capacitance
48:introducing
1941:Categories
1630:2012-01-01
1404:1501.02665
1281:References
1024:and hence
507:leads and
413:femtofarad
326:dielectric
315:nanometers
296:). When a
187:electrodes
31:references
1853:2195-0008
1812:1367-2630
1752:1476-4660
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625:Δ
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509:aluminium
440:nanometer
415:(10
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330:capacitor
250:−
240:electrons
208:−
153:classical
142:Ohm's law
134:electrons
114:at small
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1259:See also
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425:Helium-3
377:, where
303:resistor
193:(with a
56:May 2012
1893:Bibcode
1864:General
1790:Bibcode
1732:Bibcode
1689:4324628
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