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A diagram demonstrating that acarbon nanotube is essentially rolledup graphene

Carbon nanotube field-effect transistorFrom Wikipedia, the free encyclopedia

A carbon nanotube field-effect transistor (CNTFET) refers to a field-effect transistor that utilizes a singlecarbon nanotube or an array of carbon nanotubes as the channel material instead of bulk silicon in the traditional

MOSFET structure. First demonstrated in 1998, there have been major developments in CNTFETs.[1][2]

Contents

1 Introduction and background2 Electronic structure of carbon nanotubes3 Motivations for transistor applications4 Device fabrication

4.1 Back-gated CNTFETs

4.2 Top-gated CNTFETs4.3 Wrap-around gate CNTFETs4.4 Suspended CNTFETs4.5 CNTFET material considerations

5 I –V characteristics5.1 Theoretical derivation of drain current

6 Key advantages7 Comparison to MOSFETs8 Heat dissipation

9 Disadvantages9.1 Lifetime (degradation)9.2 Reliability9.3 Difficulties in mass production, production cost

10 Future work 11 References12 External links

Introduction and backgroundAccording to Moore's law, the dimensions of individual devices in anintegrated circuit have been decreased by a factor of approximatelytwo every two years. This scaling down of devices has been thedriving force in technological advances since late 20th century.However, as noted by ITRS 2009 edition, further scaling down hasfaced serious limits related to fabrication technology and device performances as the critical dimension shrunk down to sub-22 nm

range.[3] The limits involve electron tunneling through short channelsand thin insulator films, the associated leakage currents, passive power dissipation, short channel effects, and variations in device structure and doping.[4] These limits can be

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Graphene atomic structure with atranslational vector T and a chiralvector Ĉh of a CNT

One-dimensional energy dispersionrelations for (a) (n,m)=(5,5) metallictube, (b) (n,m)=(10,0)semiconducting tube.

overcome to some extent and facilitate further scaling down of device dimensions by modifying the channelmaterial in the traditional bulk MOSFET structure with a single carbon nanotube or an array of carbonnanotubes.

Electronic structure of carbon nanotubes

The exceptional electrical properties of carbon nanotubes arise from

the unique electronic structure of graphene itself that can roll up andform a hollow cylinder. The circumference of such carbon nanotubecan be expressed in terms of a chiral vector: Ĉh=nâ1+mâ2 which

connects two crystallographically equivalent sites of the two-dimensional graphene sheet. Here n and m are integers and â1 and â2

are the unit vectors of the hexagonal honeycomb lattice. Therefore,the structure of any carbon nanotube can be described by an indexwith a pair of integers (n,m) that define its chiral vector.

In terms of the integers (n,m), the nanotube diameter dt and the chiralangle θ  are given by:

.[5]

The differences in the chiral angle and the diameter cause the

differences in the properties of the various carbon nanotubes. For example, it can be shown that an (n,m) carbon nanotube is metallicwhen n = m, has a small gap (i.e. semi-metallic) when n – m = 3i,

where i is an integer, and is semiconducting when n – m ≠ 3i.[6] Thisis due to the fact that the periodic boundary conditions for the one-dimensional carbon nanotubes permit only a few wave vectors to existaround the circumference of carbon nanotubes. Metallic conductionoccurs when one of these wave vectors passes through the K-point of 

graphene’s 2D hexagonal Brillouin zone, where the valence and conduction bands are degenerate. [5] For the

semiconducting carbon nanotubes, there is a diameter dependency on bandgap. For example, according to asingle-particle tight-binding description of the electronic structure, where γ is the hopping

matrix element, and a is the carbon–carbon bond distance.[7]

Motivations for transistor applications

A carbon nanotube’s bandgap is directly affected by its chirality and diameter. If those properties can becontrolled, CNTs would be a promising candidate for future nano-scale transistor devices. Moreover, because

of the lack of boundaries in the perfect and hollow cylinder structure of CNTs, there is no boundary scattering.CNTs are also quasi-1D materials in which only forward scattering and back scattering are allowed, and elasticscattering mean free paths in carbon nanotubes are long, typically on the order of micrometers. As a result,

quasi-ballistic transport can be observed in nanotubes at relatively long lengths and low fields.[8] Because of the

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Top view Side view

Top and side view of carbon nanotubes deposited on a siliconoxide substrate pre-patterned with source and drain contacts.

strong covalent carbon–carbon bonding in the sp2 configuration, carbon nanotubes are chemically inert and areable to transport large amounts of electric current. In theory, carbon nanotubes are also able to conduct heatnearly as well as diamond or sapphire, and because of their miniaturized dimensions, the CNTFET should

switch reliably using much less power than a silicon-based device.[9]

Device fabrication

There are many types of CNTFET devices; a general survey of the most common geometries are covered below.

Back-gated CNTFETs

The earliest techniques for fabricatingcarbon nanotube (CNT) field-effecttransistors involved pre-patterning parallelstrips of metal across a silicon dioxide

substrate, and then depositing the CNTson top in a random pattern.[1][2] Thesemiconducting CNTs that happened tofall across two metal strips meet all therequirements necessary for a rudimentaryfield-effect transistor. One metal strip is the"source" contact while the other is the"drain" contact. The silicon oxide substratecan be used as the gate oxide and adding a

metal contact on the back makes the semiconducting CNT gateable.This technique suffered from several drawbacks, which made for non-optimized transistors. The first was themetal contact, which actually had very little contact to the CNT, since the nanotube just lay on top of it and thecontact area was therefore very small. Also, due to the semiconducting nature of the CNT, a Schottky barrier 

forms at the metal-semiconductor interface,[10] increasing the contact resistance. The second drawback was dueto the back-gate device geometry. Its thickness made it difficult to switch the devices on and off using low

voltages, and the fabrication process led to poor contact between the gate dielectric and CNT. [11]

Top-gated CNTFETs

Eventually, researchers migrated from the back-gate approach to a more advanced top-gate fabrication

 process.[11] In the first step, single-walled carbon nanotubes are solution deposited onto a silicon oxidesubstrate. Individual nanotubes are then located via atomic force microscope or scanning electron microscope.After an individual tube is isolated, source and drain contacts are defined and patterned using high resolutionelectron beam lithography. A high temperature anneal step reduces the contact resistance by improving adhesion

 between the contacts and CNT.[citation needed ] A thin top-gate dielectric is then deposited on top of thenanotube, either via evaporation or atomic layer deposition. Finally, the top gate contact is deposited on the gatedielectric, completing the process.

Arrays of top-gated CNTFETs can be fabricated on the same wafer, since the gate contacts are electricallyisolated from each other, unlike in the back-gated case. Also, due to the thinness of the gate dielectric, a larger electric field can be generated with respect to the nanotube using a lower gate voltage. These advantages mean

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Field effect mobility of a back-gatedCNTFET device with varying channel

lengths. SiO2 is used as the gatedielectric. Tool: 'CNT Mobility' at

nanoHUB.org[18]

Structure of a top-gate CNTtransistor 

There are general decisions one must make when considering what materials to use when fabricating aCNTFET. Semiconducting single-walled carbon nanotubes are preferred over metallic single-walled andmetallic multi-walled tubes since they are able to be fully switched off, at least for low source/drain biases. A lotof work has been put into finding a suitable contact material for semiconducting CNTs; the best material to dateis Pd, because its work function matches closely with that of nanotubes and it adheres to the CNTs quite

well.[17]

I–V characteristics

In CNT–metal contacts, the different work functions of the metal andthe CNT result in the Schottky barrier at the source and drain, which

are made of metals like Au, Ti, Pd and Al.[19] Even though likeSchottky barrier diodes, the barriers would have made this FET totransport only one type of carrier, the carrier transport through themetal-CNT interface is dominated by quantum mechanical tunnelingthrough the Schottky barrier. CNTFETs can easily be thinned by the

gate field such that tunneling through them results in a substantialcurrent contribution. CNTFETs are ambipolar; either electrons or 

holes, or both electrons and holes can be injected simultaneously.[19]

This makes the thickness of the Schottky barrier a critical factor.

CNTFETs conduct electrons when a positive bias is applied to thegate and holes when a negative bias is applied, and drain current

increases with increasing a magnitude of an applied gate voltage.[20]

Around Vg = Vds/2, the current gets the minimum due to the same

amount of the electron and hole contributions to the current.Like other FETs, the drain current increases with an increasing drain bias unless the applied gate voltage is below the threshold voltage.For planar CNTFETs with different design parameters, the FET witha shorter channel length produces a higher saturation current, and the saturation drain current also becomeshigher for the FET consisting of smaller diameter keeping the length constant. For cylindrical CNTFETs, it isclear that a higher drain current is driven than that of planar CNTFETs since a CNT is surrounded by an oxide

layer which is finally surrounded by a metal contact serving as the gate terminal.[21]

Theoretical derivation of drain current

Theoretical investigation on drain current of the top-gate CNT

transistor has been done by T.Kazierski et al..[22] When an electricfield is applied to a CNT transistor, a mobile charge is induced in thetube from the source and drain. These charges are from the density of  positive velocity states filled by the source NS and that of negative

velocity states filled by the drain ND,[22] and these densities are

determined by the Fermi-Dirac probability distributions.

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and the equilibrium electron density is

.

where the density of states at the channel D(E), USF, and UDF are defined as

The term, is 1 when the value inside the bracket is positive and 0 when negative. VSC is the

self-consistent voltage that illustrates that the CNT energy is affected by external terminal voltages and isimplicitly related to the device terminal voltages and charges at terminal capacitances by the following nonlinear equation:

where Qt represents the charge stored in terminal capacitances, and the total terminal capacitance C Σ is the sum

of the gate, drain, source, and substrate capacitances shown in the figure above. The standard approach to thesolution to the self-consistent voltage equation is to use the Newton-Raphson iterative method. According to theCNT ballistic transport theory, the drain current caused by the transport of the nonequilibrium charge across thenanotube can be calculated using the Fermi–Dirac statistics.

Here F 0 represents the Fermi–Dirac integral of order 0, k  is the Boltzmann’s constant, T  is the temperature, and

ℏ the reduced Planck’s constant. This equation can be solved easily as long as the self-consistent voltage isknown. However the calculation could be time-consuming when it needs to solve the self-consistent voltage withthe iterative method, and this is the main drawback of this calculation.

Key advantages

Better control over channel formationBetter threshold voltageBetter subthreshold slope

High electron mobilityHigh current densityHigh transconductance

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Comparison to MOSFETs

CNTFETs show different characteristics compared to MOSFETs in their performances. In a planar gatestructure, the p-CNTFET produces ~1500 A/m of the on-current per unit width at a gate overdrive of 0.6 V

while p-MOSFET produces ~500 A/m at the same gate voltage.[23] This on-current advantage comes from thehigh gate capacitance and improved channel transport. Since an effective gate capacitance per unit width of CNTFET is about double that of p-MOSFET, the compatibility with high- k gate dielectrics becomes a definite

advantage for CNTFETs.[21] About twice higher carrier velocity of CNTFETs than MOSFETs comes from theincreased mobility and the band structure. CNTFETs, in addition, have about four times higher 

transconductance.[citation needed ]

Heat dissipation

The decrease of the current and burning of the CNT can occur due to the temperature raised by severalhundreds of kelvins. Generally, the self-heating effect is much less severe in a semiconducting CNTFET than in a

metallic one due to different heat dissipation mechanisms. A small fraction of the heat generated in the CNTFETis dissipated through the channel. The heat is non-uniformly distributed, and the highest values appear at the

source and drain sides of the channel.[24] Therefore, the temperature significantly gets lowered near the sourceand drain regions. For semiconducting CNT, the temperature rise has a relatively small effect on the I-Vcharacteristics compared to silicon.

Disadvantages

Lifetime (degradation)

The carbon nanotube degrades in a few days when exposed to oxygen. There have been several works done on

 passivating the nanotubes with different polymers and increasing their lifetime.[25]

Reliability

Carbon nanotubes have shown reliability issues when operated under high electric field or temperature gradients.Avalanche breakdown occurs in semiconducting CNT and joule breakdown in metallic CNT. Unlike avalanche behavior in silicon, avalanche in CNTs is negligibly temperature-dependent. Applying high voltages beyond

avalanche point results in Joule heating and eventual breakdown in CNTs.[26]

 This reliability issue has beenstudied, and it is noticed that the multi-channeld structure can improve the reliability of the CNTFET. The multi-channeled CNTFETs can keep a stable performance after several months, while the single-channeled

CNTFETs are usually out of work after a few weeks in the ambient atmosphere. [27] The multi-channeledCNTFETs keep operating when some channels break down, this won’t happen in the single-channeled ones.

Difficulties in mass production, production cost

Although CNTs have unique properties such as stiffness, strength, and tenacity compared to other materialsespecially to silicon, There is currently no technology for their mass production and high production cost. Toovercome the fabrication difficulties, several methods have been studied such as direct growth, solution

dropping, and various transfer printing techniques.[28]

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Future work 

The most desirable future work involved in CNTFETs will be the transistor with higher reliability, cheap production cost, or the one with more enhanced performances. For example, such efforts could be made:adding eff ects external to the inner CNT transistor like the Schottky barrier between the CNT and metal

contacts, multiple CNTs at a single gate,[22] channel fringe capacitances, parasitic source/drain resistance, andseries resistance due to the scattering effects.

References

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4/17/2014 Carbon nanotube field-effect transistor - Wikipedia, the free encyclopedia

27. ^ C.Changxin and Z.Yafei, "Nanowelded Carbon Nanotubes: From Field-Effect Transistor to Solar Microcells"(htt p://books.google.com/books?id=GX8fyYtq44cC&pg=PA63&lpg=PA63) Nano Science and Technologyseries (2009), pp. 63 ff ISBN 3-642-01498-4

28. ^ Chang-Jian, Shiang-Kuo; Ho, Jeng-Rong; John Cheng, J.-W. (2010). "Characterization of developingsour ce/drain current of carbon nanotube field-effect transistors with n-doping by polyethylene imine". Micr oelectronic Engineering  87 (10): 1973. doi:10.1016/j.mee.2009.12.019(htt p://dx.doi.org/10.1016%2Fj.mee.2009.12.019).

External links

 Nano Hub (http://nanohub.org/)CNT Mobility (https://nanohub.org/tools/cntmob/)Cylindrical CNT MOSFET Simulator (https://nanohub.org/resources/moscntr/)

Retrieved f rom "http://en.wikipedia.org/w/index.php?title=Carbon_nanotube_field-effect_transistor&oldid=594838927"Categories:  Carbon nanotubes

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