33:
496:
484:
90:
508:
944:
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
556:
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
421:
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
1567:
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
891:
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
408:
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
469:. 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.
311:
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
350:) 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
1506:
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".
553:
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.
804:
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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.
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584:
973:
1133:
136:. 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.
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386:
235:
274:
604:
406:
1836:
Kaufman, Igor Kh.; Fedorenko, Olena A.; Luchinsky, Dmitri G.; Gibby, William A.T.; Roberts, Stephen K.; McClintock, Peter V.E.; Eisenberg, Robert S. (2017).
949:
of charge carriers (permeating ions vs electrons) and by the different origin of transport engine (classical electrodiffusion vs quantum tunnelling).
453:, one has to create electrodes with dimensions of approximately 100 by 100 nanometers. This range of dimensions is routinely reached for example by
1305:
Averin, D. V.; Likharev, K. K. (1986-02-01). "Coulomb blockade of single-electron tunneling, and coherent oscillations in small tunnel junctions".
284:
The following section is for the case of tunnel junctions with an insulating barrier between two normal conducting electrodes (NIN junctions).
122:
346:
Due to the discreteness of electrical charge, current through a tunnel junction is a series of events in which exactly one electron passes (
54:
978:
76:
1838:"Ionic Coulomb blockade and anomalous mole fraction effect in the NaChBac bacterial ion channel and its charge-varied mutants"
749:
466:
462:
1962:
671:
1967:
114:
47:
41:
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511:
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An arrangement of two conductors with an insulating layer in between not only has a resistance, but also a finite
454:
292:
187:
1453:
Couto, ODD; Puebla, J (2011). "Charge control in InP/(Ga,In)P single quantum dots embedded in
Schottky diodes".
291:
is, in its simplest form, a thin insulating barrier between two conducting electrodes. According to the laws of
58:
1957:
1894:
Fulton, T.A.; Dolan, G.J. (1987). "Observation of single-electron charging effects in small tunnel junctions".
892:
conductance vary according to the charging energy of the islands as well as the thermal energy of the system.
1065:
1280:
1275:
939:
844:
1373:
879:
410:
1400:
Crippa A; et al. (2015). "Valley blockade and multielectron spin-valley Kondo effect in silicon".
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1903:
1800:
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1726:
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In biological ion channels ICB typically manifests itself in such valence selectivity phenomena as
714:
175:
163:
1138:
812:
1725:
Feng, Jiandong; Liu, Ke; Graf, Michael; Dumcenco, Dumitru; Kis, Andras; Di Ventra, Massimiliano;
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1515:
1488:
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1435:
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1338:
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927:
304:
102:
922:, the full width at half minimum of the measured differential conductance dip over an array of
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1919:
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1112:
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The simplest device in which the effect of
Coulomb blockade can be observed is the so-called
324:
on the barrier thickness. Typically, the barrier thickness is on the order of one to several
1911:
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546:. 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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179:
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446:
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geometry with a capacitance of 1 femtofarad, using an oxide layer of electric
308:
126:
94:
317:
152:
1937:
1789:"Coulomb blockade model of permeation and selectivity in biological ion channels"
560:
The energy levels of the island electrode are evenly spaced with a separation of
155:
and the current-voltage relation of the
Coulomb blockade looks like a staircase.
896:
539:
332:
300:
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140:
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1915:
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295:, no current can flow through an insulating barrier. According to the laws of
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1334:
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is defined by dielectric self-energy of incoming ion inside the pore/channel
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or else the electron will be able to pass the QD via thermal excitation; and
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450:
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197:
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preventing other electrons to flow. Thus, the device will no longer follow
1890:, eds. B.L. Altshuler, P.A. Lee, and R.A. Webb (Elsevier, Amsterdam, 1991)
89:
435:
313:
250:
144:
538:, connected through tunnel junctions to one common electrode with a low
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for the blocking state (upper part) and transmitting state (lower part).
303:
for an electron on one side of the barrier to reach the other side (see
1326:
515:
507:
351:
139:
Coulomb blockade can be observed by making a device very small, like a
1537:
1365:
1942:
1881:
Single Charge
Tunneling: Coulomb Blockade Phenomena in Nanostructures
1754:
431:
237:) carry the current. In the case that the electrodes are metallic or
1414:
1266:) and concentration-dependent divalent blockade of sodium current.
1883:, eds. H. Grabert and M. H. Devoret (Plenum Press, New York, 1992)
1673:
1582:
1520:
1467:
506:
494:
482:
430:), this implied that the temperature has to be below about 1
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170:. However, when few electrons are involved and an external static
88:
1356:
Wang, Xufeng; Muralidharan, Bhaskaran; Klimeck, Gerhard (2006).
660:
To achieve the
Coulomb blockade, three criteria have to be met:
158:
Even though the Coulomb blockade can be used to demonstrate the
1787:
Kaufman, I. Kh; McClintock, P. V. E.; Eisenberg, R. S. (2015).
1170:
ICB has been recently experimentally observed in sub-nanometer
499:
Left to right: energy levels of source, island and drain in a
26:
434:. This temperature range is routinely reached for example by
1631:"2.5 Minimum Tunnel Resistance for Single Electron Charging"
1188:
129:
of a small electronic device comprising at least one low-
174:
is applied, Coulomb blockade provides the ground for a
1358:"nanoHUB.org - Resources: Coulomb Blockade Simulation"
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1041:
299:, however, there is a nonvanishing (larger than zero)
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217:
1731:"Observation of ionic Coulomb blockade in nanopores"
799:{\displaystyle k_{\rm {B}}T<{\frac {e^{2}}{2C}},}
1655:Krems, Matt; Di Ventra, Massimiliano (2013-01-10).
182:, which include quantum mechanical effects due to
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557:and reaches the drain electrode Fermi level (4.).
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380:
339:in this context, the tunnel junction behaves as a
268:
229:
1028:{\displaystyle \Delta E={\frac {z^{2}e^{2}}{2C}}}
701:{\displaystyle V_{\text{bias}}<{\frac {e}{C}}}
413:around zero bias is called the Coulomb blockade.
166:effect and its main description does not require
550:, which is capacitively coupled to the island.
668:divided by the self-capacitance of the island:
1109:, even at the room temperature, for ions with
530:. It consists of two electrodes known as the
316:with a constant resistance, also known as an
97:) of an electron tunnelling through a barrier
8:
650:{\displaystyle C={\frac {e^{2}}{\Delta E}}.}
193:The devices can comprise either metallic or
1635:About Single-Electron Devices and Circuits
895:Coulomb blockade thermometer is a primary
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216:
200:. If the electrodes are superconducting,
77:Learn how and when to remove this message
1637:(Ph.D.). Vienna University of Technology
664:The bias voltage must be lower than the
40:This article includes a list of general
1297:
1102:{\textstyle (\Delta E\gg k_{\rm {B}}T)}
147:inside the device will create a strong
1382:
1371:
586:This gives rise to a self-capacitance
1938:Computational Single-Electronics book
1782:
1780:
1657:"Ionic Coulomb blockade in nanopores"
93:Schematic representation (similar to
7:
1720:
1718:
1661:Journal of Physics: Condensed Matter
190:respectively between the electrons.
878:which is derived from Heisenberg's
871:{\displaystyle {\frac {h}{e^{2}}},}
746:must be below the charging energy:
160:quantization of the electric charge
143:. When the device is small enough,
1307:Journal of Low Temperature Physics
1250:
1237:conduction bands (vs fixed charge
1087:
1072:
1042:
982:
959:
930:provide the absolute temperature.
822:
759:
724:
635:
567:
46:it lacks sufficient corresponding
25:
1886:D.V. Averin and K.K Likharev, in
1842:EPJ Nonlinear Biomedical Physics
1230:{\displaystyle {\text{Ca}}^{2+}}
952:In the case of ICB, Coulomb gap
31:
1943:Coulomb blockade online lecture
335:. The insulator is also called
178:(like Pauli spin blockade) and
1888:Mesoscopic Phenomena in Solids
1600:10.1088/0957-4484/23/21/215204
1096:
1069:
945:by possibly different valence
1:
1814:10.1088/1367-2630/17/8/083021
1691:10.1088/0953-8984/25/6/065101
1629:Wasshuber, Christoph (1997).
1160:{\displaystyle {\ce {Ca^2+}}}
739:{\displaystyle k_{\rm {B}}T,}
441:To make a tunnel junction in
1195:{\displaystyle {\ce {MoS2}}}
926:junctions together with the
887:Coulomb blockade thermometer
834:{\displaystyle R_{\rm {t}},}
467:shadow evaporation technique
1259:{\displaystyle Q_{\rm {f}}}
115:Charles-Augustin de Coulomb
18:Single electron transistors
1984:
1916:10.1103/PhysRevLett.59.109
1485:10.1103/PhysRevB.84.125301
1432:10.1103/PhysRevB.92.035424
937:
809:The tunneling resistance,
606:of the island, defined as
528:single-electron transistor
512:Single-electron transistor
501:single-electron transistor
489:single-electron transistor
479:Single-electron transistor
476:
473:Single-electron transistor
579:{\displaystyle \Delta E.}
455:electron beam lithography
320:. The resistance depends
293:classical electrodynamics
968:{\displaystyle \Delta E}
463:Niemeyer–Dolan technique
1568:electron transistors".
1128:{\displaystyle z>=2}
1058:depends on ion valence
841:should be greater than
461:technologies, like the
411:differential resistance
61:more precise citations.
1855:10.1051/epjnbp/2017003
1793:New Journal of Physics
1381:Cite journal requires
1281:Quantisation of charge
1276:Ionic Coulomb blockade
1260:
1231:
1196:
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1103:
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1029:
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940:Ionic Coulomb blockade
934:Ionic Coulomb blockade
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835:
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123:electrical conductance
98:
1727:Radenovic, Aleksandra
1261:
1232:
1197:
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1130:
1104:
1062:. ICB appears strong
1053:
1051:{\textstyle \Delta E}
1030:
970:
880:uncertainty principle
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741:
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652:
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449:10 and thickness one
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383:
381:{\displaystyle U=e/C}
276:) carry the current.
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121:, is the decrease in
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280:In a tunnel junction
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188:orbital interactions
1963:Quantum electronics
1908:1987PhRvL..59..109F
1805:2015NJPh...17h3021K
1747:2016NatMa..15..850F
1683:2013JPCM...25f5101K
1592:2012Nanot..23u5204P
1530:2011NanoL..11.1591S
1477:2011PhRvB..84l5301C
1424:2015PhRvB..92c5424C
1319:1986JLTP...62..345A
1190:
230:{\displaystyle -2e}
1968:Mesoscopic physics
1327:10.1007/BF00683469
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928:physical constants
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305:quantum tunnelling
269:{\displaystyle -e}
266:
253:(with a charge of
227:
210:elementary charges
103:mesoscopic physics
99:
1538:10.1021/nl1044692
1455:Physical Review B
1402:Physical Review B
1366:10.4231/d3c24qp1w
1286:Elementary charge
1216:
1181:
1146:
1023:
863:
791:
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666:elementary charge
642:
599:{\displaystyle C}
401:{\displaystyle C}
297:quantum mechanics
239:normal-conducting
168:quantum mechanics
149:Coulomb repulsion
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540:self-capacitance
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457:and appropriate
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57:this article by
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289:tunnel junction
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243:superconducting
241:, i.e. neither
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195:superconducting
180:valley blockade
162:, it remains a
134:tunnel junction
113:), named after
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53:Please help to
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301:probability
141:quantum dot
131:capacitance
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1952:Categories
1641:2012-01-01
1415:1501.02665
1292:References
1035:and hence
518:leads and
424:femtofarad
337:dielectric
326:nanometers
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198:electrodes
42:references
1864:2195-0008
1823:1367-2630
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451:nanometer
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145:electrons
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67:May 2012
1904:Bibcode
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