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{{Short description|Electronic device}}
[[File:SET schematic2.jpg|thumb|Schematic of a basic SET and its internal electrical components]]
A '''single-electron transistor''' ('''SET''') is a sensitive electronic device based on the [[Coulomb blockade]] effect. In this device the electrons flow through a [[tunnel junction]] between source/drain to a [[quantum dot]] (conductive island). Moreover, the electrical potential of the island can be tuned by a third electrode, known as the gate, which is capacitively coupled to the island. The conductive island is sandwiched between two tunnel junctions<ref>{{cite journal|last1=Mahapatra|first1=S.|last2=Vaish|first2=V.|last3=Wasshuber|first3=C.|last4=Banerjee|first4=K.|last5=Ionescu|first5=A.M.|title=Analytical Modeling of Single Electron Transistor for Hybrid CMOS-SET Analog IC Design|journal=IEEE Transactions on Electron Devices|volume=51|issue=11|year=2004|pages=1772–1782|issn=0018-9383|doi=10.1109/TED.2004.837369|bibcode=2004ITED...51.1772M|s2cid=15373278}}</ref> modeled by capacitors, <math>C_{\rm D}</math> and <math>C_{\rm S}</math>, and resistors, <math>R_{\rm D}</math> and <math>R_{\rm S}</math>, in parallel.
== History ==
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A new subfield of condensed matter physics began in 1977 when [[David Thouless]] pointed out that, when made small enough, the size of a conductor affects its electronic properties.<ref>{{cite journal |last1=Thouless |first1=David J. |author-link=David J. Thouless| title=Maximum Metallic Resistance in Thin Wires |journal=Phys. Rev. Lett. |volume=39 |issue=18 |pages=1167–1169 |year=1977 |doi=10.1103/PhysRevLett.39.1167|bibcode=1977PhRvL..39.1167T }}</ref> This was followed by mesoscopic physics research in the 1980s based on the submicron-size of systems investigated.<ref>{{cite journal|last1=Al'Tshuler|first1=Boris L.|last2=Lee|first2=Patrick A.|title=Disordered electronic systems|journal=Physics Today|volume=41|issue=12|year=1988|pages=36–44|doi=10.1063/1.881139|bibcode=1988PhT....41l..36A}}</ref> Thus began research related to the single-electron transistor.
The
== Relevance ==
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[[File:Single electron transistor.svg|thumb|right|Left to right: energy levels of source, island and drain in a single-electron transistor for the blocking state (upper part) and transmitting state (lower part).]]
The SET has, like the [[field-effect transistor|FET]], three electrodes: source, drain, and a gate. The main technological difference between the transistor types is in the channel concept. While the channel changes from insulated to conductive with applied gate voltage in the FET, the SET is always insulated. The source and drain are coupled through two
The current, <math>I,</math> from source to drain follows [[Ohm's law]] when <math>V_{\rm SD}</math> is applied, and it equals <math>\tfrac{V_{\rm SD}}{R},</math> where the main contribution of the resistance, <math>R,</math> comes from the tunnelling effects when electrons move from source to QD, and from QD to drain. <math>V_{\rm G}</math> regulates the resistance of the QD, which regulates the current. This is the exact same behaviour as in regular FETs. However, when moving away from the macroscopic scale, the quantum effects will affect the current, <math>I.</math>
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At zero temperatures, only transitions with negative free energy are allowed: <math>\Delta F_{\rm S} < 0</math> or <math>\Delta F_{\rm D} < 0</math>. These conditions can be used to find areas of stability in the plane <math>V_{\rm bias} - V_{\rm G}.</math>
With increasing voltage at the gate electrode, when the supply voltage is
=== Temperature dependence ===
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The level of the electrical current of the SET can be amplified enough to work with available [[CMOS]] technology by generating a hybrid SET–[[field-effect transistor|FET]] device.<ref name="IonescuMahapatra2004">{{cite journal|last1=Ionescu|first1=A.M.|last2=Mahapatra|first2=S.|last3=Pott|first3=V.|title=Hybrid SETMOS Architecture With Coulomb Blockade Oscillations and High Current Drive|journal=IEEE Electron Device Letters|volume=25|issue=6|year=2004|pages=411–413|issn=0741-3106|doi=10.1109/LED.2004.828558|bibcode=2004IEDL...25..411I|s2cid=42715316}}</ref><ref name="AmatBausells2017">{{cite journal|last1=Amat|first1=Esteve|last2=Bausells|first2=Joan|last3=Perez-Murano|first3=Francesc|title=Exploring the Influence of Variability on Single-Electron Transistors Into SET-Based Circuits|journal=IEEE Transactions on Electron Devices|volume=64|issue=12|year=2017|pages=5172–5180|issn=0018-9383|doi=10.1109/TED.2017.2765003|bibcode=2017ITED...64.5172A|s2cid=22082690}}</ref>
The EU funded, in 2016, project IONS4SET (#688072)<ref>{{cite web|url=http://www.ions4set.eu|title=IONS4SET Website|access-date=2019-09-17}}</ref> looks for the manufacturability of SET–FET circuits operative at room temperature. The main goal of this project is to design a SET-manufacturability process-flow for large-scale operations seeking to extend the use of the hybrid SET–CMOS architectures. To assure room temperature operation, single dots of diameters below 5 nm have to be fabricated and located between source and drain with tunnel distances of a few nanometers.<ref name="KlupfelBurenkov2016">{{cite book|last1=Klupfel|first1=F. J.|title=2016 International Conference on Simulation of Semiconductor Processes and Devices (SISPAD)|last2=Burenkov|first2=A.|last3=Lorenz|first3=J.|chapter=Simulation of silicon-dot-based single-electron memory devices|year=2016|pages=237–240|doi=10.1109/SISPAD.2016.7605191|isbn=978-1-5090-0818-6|s2cid=15721282}}</ref> Up to now there is no reliable process-flow to manufacture a hybrid SET–FET circuit operative at room temperature. In this context, this EU project explores a more feasible way to manufacture the SET–FET circuit by using pillar dimensions of approximately 10 nm.<ref name="Xu2019">{{cite
== See also ==
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