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| [[Image:TyTunnelling.png|thumb|right|Schematic representation (similar to [[band diagram]]) of an electron tunnelling through a barrier]]In physics, a '''Coulomb blockade''' (abbreviated CB), named after [[Charles-Augustin de Coulomb]]'s electrical force, is the increased [[electrical resistance|resistance]] at small [[voltage bias|bias voltage]]s of an electronic device comprising at least one low-[[capacitance]] [[tunnel junction]]. Because of the CB, the resistances of devices are not constant at low bias voltages, but increase to infinity for biases under a certain threshold (i.e. no current flows). When few electrons are involved and an external static magnetic field is applied, Coulomb blockade provides the ground for [[spin blockade]] (also called Pauli blockade) which includes quantum mechanical effects due to spin interactions between the electrons.
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| ==Coulomb blockade in a tunnel junction==
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| A tunnel junction is, in its simplest form, a thin insulating barrier between two conducting [[electrode]]s. If the electrodes are [[Superconductivity|superconducting]], [[Cooper pair]]s (with a [[charge (physics)|charge]] of two [[elementary charge]]s) carry the current. In the case that the electrodes are ''normalconducting'', i.e. neither [[Superconductivity|superconducting]] nor [[Semiconductor|semiconducting]], [[electron]]s (with a charge of one [[elementary charge]]) carry the current. The following reasoning is for the case of tunnel junctions with an insulating barrier between two
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| normal conducting electrodes (NIN junctions).
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| According to the laws of [[classical electrodynamics]], no current can flow through an insulating barrier. According to the laws of [[quantum mechanics]], however, there is a nonvanishing (larger than zero)
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| [[probability]] for an electron on one side of the barrier to reach the other side (see [[quantum tunnelling]]). When a [[bias voltage]] 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 [[resistor]] with a constant resistance, also known as an [[Ohm's law|ohmic resistor]]. The resistance depends [[exponential function|exponentially]] on the barrier thickness. Typical barrier thicknesses are on the order of one to several [[nanometer]]s.
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| An arrangement of two conductors with an insulating layer in between not only has a resistance, but also a finite [[capacitance]]. The insulator is also called [[dielectric]] in this context, the tunnel junction behaves as a [[capacitor]].
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| Due to the discreteness of electrical charge, current through a tunnel junction is a series of events in which exactly one electron passes (''tunnels'') 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 [[voltage]] buildup <math>U=e/C</math>, where <math>e</math> is the [[elementary charge]] of 1.6×10<sup>−19</sup> [[coulomb]] and <math>C</math> the capacitance of the junction. If the capacitance is very small, the voltage buildup can be large enough to prevent another electron from tunnelling. The electrical current is then suppressed at low bias voltages and the resistance of the device is no longer constant. The increase of the [[Electrical resistance#Differential resistance|differential resistance]] around zero bias is called the Coulomb blockade.
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| ==Observing the Coulomb blockade ==
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| 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 above 1 [[femtofarad]] (10<sup>−15</sup> [[farad]]), this implied that the temperature has to be below about 1 [[kelvin]]. This temperature range is routinely reached for example by 3He 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. <ref>{{cite doi|10.1021/nl1044692}}</ref>
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| To make a tunnel junction in [[plate condenser]] geometry with a capacitance of 1 femtofarad, using an oxide layer of electric [[permittivity]] 10 and thickness one [[nanometer]], one has to create electrodes with dimensions of approximately 100 by 100 nanometers. This range of dimensions is routinely reached for example by [[electron beam lithography]] and appropriate [[pattern transfer]] technologies, like the [[Niemeyer-Dolan technique]], also known as [[Niemeyer-Dolan technique|shadow evaporation technique]]. 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. <ref>{{cite doi|10.1088/0957-4484/23/21/215204|url=http://arxiv.org/pdf/1203.4811.pdf|format=pdf}}</ref>
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| ==Single electron transistor==
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| [[Image:Set schematic.svg|thumb|right|Schematic of a single electron transistor]]
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| [[Image:Single electron transistor.svg|thumb|right|Energylevels of source, island and drain (from left to right) in a single electron transistor for both the blocking state (upper part) and the transmitting state (lower part).]]
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| [[Image:TySETimage.png|thumb|right|Single electron transistor with [[niobium]] leads and [[aluminium]] island]]
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| The simplest device in which the effect of Coulomb blockade can be observed is the so-called '''single electron transistor'''. It consists of two electrodes known as the ''drain'' and the ''source'', connected through tunnel junctions to one common electrode with a low [[Capacitance#Self-capacitance|self-capacitance]], known as the ''island''. The electrical potential of the island can be tuned by a third electrode, known as the ''gate'', capacitively coupled to the island. <!--The current-voltage characteristics are modulated between maximum and minimum Coulomb blockade, with a periodicity of one elementary charge in the charge induced on the island.-->
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| In the blocking state no accessible energy levels are within tunneling range of the electron (red) on the source contact. All energy levels on the island electrode with lower energies are occupied.
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| 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 and reaches the drain electrode Fermi level (4.).
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| The energy levels of the island electrode are evenly spaced with a separation of <math>\Delta E.</math> This gives rise to a self-capacitance <math>C</math> of the island, defined as
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| :<math>C=\frac{e^2}{\Delta E}.</math>
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| To achieve the Coulomb blockade, three criteria have to be met:
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| # The bias voltage must be lower than the [[elementary charge]] divided by the self-capacitance of the island: <math>V_\text{bias} < \frac{e}{C}</math> ;
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| # The thermal energy in the source contact plus the thermal energy in the island, i.e. <math>k_BT,</math> must be below the charging energy: <math>k_BT < \frac{e^2}{C},</math> or else the electron will be able to pass the QD via thermal excitation; and
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| # The tunneling resistance, <math>R_t,</math> should be greater than <math>\frac{h}{e^2},</math> which is derived from Heisenberg's [[uncertainty principle]]. <ref>{{Cite thesis |type=Ph.D. |chapter=2.5 Minimum Tunnel Resistance for Single Electron Charging |title=About Single-Electron Devices and Circuits |url=http://www.iue.tuwien.ac.at/phd/wasshuber/node20.html |last=Wasshuber |first= Christoph|year= 1997|publisher= Vienna University of Technology |accessdate= 12/5/2012}}</ref>
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| ==Coulomb blockade thermometer==
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| 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 conductance vary according to the charging energy of the islands as well as the thermal energy of the system.
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| Coulomb blockade thermometer is a primary [[thermometer]] based on electric conductance characteristics of tunnel junction arrays. The parameter V<sub>½</sub>=5.439Nk<sub>B</sub>T/e, the full width at half
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| minimum of the measured differential conductance dip over an array of N junctions together with the [[physical constants]] provide the absolute temperature.
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| ==References==
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| {{reflist}}
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| * ''Single Charge Tunneling: Coulomb Blockade Phenomena in Nanostructures'', eds. H. Grabert and M. H. Devoret (Plenum Press, New York, 1992)
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| * D.V. Averin and K.K Likharev, in ''Mesoscopic Phenomena in Solids'', eds. B.L. Altshuler, P.A. Lee, and R.A. Webb (Elsevier, Amsterdam, 1991)
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| * Fulton, T.A. & Dolan, G.J. "Observation of single-electron charging effects in small tunnel junctions" ''Phys. Rev. Lett.'' '''59''', 109-112 (1987), {{doi|10.1103/PhysRevLett.59.109}}
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| ==External links==
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| * [http://books.google.com/books?id=TNZyxqXGFY8C Computational Single-Electronics book]
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| * [http://nanohub.org/resources/756 Online lecture on Coulomb Blockade] by S. Datta (2004)
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| {{DEFAULTSORT:Coulomb Blockade}}
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| [[Category:Nanoelectronics]]
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| [[Category:Quantum electronics]]
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| [[Category:Mesoscopic physics]]
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Hello and welcome. My name is Ling. One of the issues I adore most is greeting card collecting but I don't have the time lately. Managing people is how I make cash and it's some thing I truly enjoy. Her husband and her chose to reside in Delaware but she needs to transfer simply because of her family members.
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