Carbon Nanotube Field

8/6/2019 Carbon Nanotube Field

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Carbon Nanotube Field-Effect Transistor

Contents:

1 Abstract 2 Introduction 3 Electronic structure of carbon nanotubes 4 Motivations for transistor applications 5 Device fabrication

o 5 .1 Back-gated CNTFETso 5 .2 Top-gated CNTFETso 5 .3 Wrap-around gate CNTFETso 5 .4 Suspended CNTFETso 5 .5 CNTFET material considerations

6 I-V characteristicso 6 .1 Theoretical derivation of drain current

7 Comparison to MOSFETs 8 Heat dissipation 9 Disadvantages

o

9 .1 Lifetime (degradation)o 9 .2 Reliabilityo 9 .3 Difficulties in mass production, production cost

10 Future work 11 References

.
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Abstract

A simple model for ballistic nanotransistors, which extends previous work by treatingboth the charge control and the quantum capacitance limits of MOSFET-like transistors,is presented. . The limits involve electron tunneling through short channels and thininsulator films, the associated leakage currents, passive power dissipation, short channeleffects, and variations in device structure and doping. We apply this new model toMOSFET-like carbon nanotube FETs (CNTFETs) and to MOSFETs at the scaling limit.The device physics for operation at ballistic and quantum capacitance limits are explored.

Based on the analysis of recently reported CNTFETs, we compare CNTFETs toMOSFETs. The potential performance advantages over Si that might be achieved at thescaling limit are established by using the new model

Introduction

A Carbon Nano Tube Field Effect Transistor (CNTFET) refers to Field Effect Transistorthat utilizes a single carbon nano tube or an array of carbon nano tubes as the channelmaterial instead of bulk silicon in the traditional MOSFET structure .According toMoore's law, the dimensions of individual devices in an integrated circuit have beendecreased by a factor of approximately two every two years. This scaling down of

devices has been the driving force in technological advances since late 20th century.However, as noted by ITRS 2009 edition, further scaling down has faced serious limitsrelated to fabrication technology and device performances as the critical dimensionshrunk down to sub-22 nm range. The limits involve electron tunneling through shortchannels and thin insulator films, the associated leakage currents, passive powerdissipation, short channel effects, and variations in device structure and doping. Theselimits can be overcome to some extent and facilitate further scaling down of devicedimensions by modifying the channel material in the traditional bulk MOSFET structurewith a single carbon nanotube or an array of carbon nanotubes.

Carbon nanotubes (CNTs) are allotropes of carbon with a cylindrical nanostructure.

Nanotubes have been constructed with length-to-diameter ratio of up to 132,000,000:1, [1]significantly larger than for any other material. These cylindrical carbonmolecules haveunusual properties, which are valuable fornanotechnology,electronics, optics and otherfields of materials science and technology. In particular, owing to their extraordinarythermal conductivity and mechanical and electricalproperties, carbon nanotubes mayfind applications as additives to various structural materials. Nanotubes are categorized assingle-walled nanotubes(SWNTs) and multi-walled nanotubes(MWNTs).
http://en.wikipedia.org/wiki/Moore's_lawhttp://en.wikipedia.org/wiki/Allotropes_of_carbonhttp://en.wikipedia.org/wiki/Allotropes_of_carbonhttp://en.wikipedia.org/wiki/Carbon_nanotube#cite_note-Longest-0http://en.wikipedia.org/wiki/Carbonhttp://en.wikipedia.org/wiki/Carbonhttp://en.wikipedia.org/wiki/Moleculehttp://en.wikipedia.org/wiki/Nanotechnologyhttp://en.wikipedia.org/wiki/Electronicshttp://en.wikipedia.org/wiki/Electronicshttp://en.wikipedia.org/wiki/Opticshttp://en.wikipedia.org/wiki/Materials_sciencehttp://en.wikipedia.org/wiki/Thermal_conductivityhttp://en.wikipedia.org/wiki/Electricityhttp://en.wikipedia.org/wiki/Electricityhttp://en.wikipedia.org/wiki/Carbon_nanotube#Single-walledhttp://en.wikipedia.org/wiki/Carbon_nanotube#Single-walledhttp://en.wikipedia.org/wiki/Carbon_nanotube#Multi-walledhttp://en.wikipedia.org/wiki/Carbon_nanotube#Multi-walledhttp://en.wikipedia.org/wiki/Moore's_lawhttp://en.wikipedia.org/wiki/Allotropes_of_carbonhttp://en.wikipedia.org/wiki/Carbon_nanotube#cite_note-Longest-0http://en.wikipedia.org/wiki/Carbonhttp://en.wikipedia.org/wiki/Moleculehttp://en.wikipedia.org/wiki/Nanotechnologyhttp://en.wikipedia.org/wiki/Electronicshttp://en.wikipedia.org/wiki/Opticshttp://en.wikipedia.org/wiki/Materials_sciencehttp://en.wikipedia.org/wiki/Thermal_conductivityhttp://en.wikipedia.org/wiki/Electricityhttp://en.wikipedia.org/wiki/Carbon_nanotube#Single-walledhttp://en.wikipedia.org/wiki/Carbon_nanotube#Multi-walled


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Electronic structure of carbon nanotubes

Fig1.Graphene atomic structure with a translational vector T and a chiral vector h of aCNT

One-dimensional energy dispersion relations for (a) (n,m)=(5,5) metallic tube, (b)(n,m)=(10,0) semiconducting tube.

The exceptional electrical properties of carbon nanotubes arise from the unique electronicstructure of graphene itself that can roll up and form a hollow cylinder. Thecircumference of such carbon nanotube can be expressed in terms of a chiral vector:h=n1+m2 which connects two crystallographically equivalent sites of the two-dimensional graphene sheet. Here n and m are integers and 1 and 2 are the unit vectorsof the hexagonal honeycomb lattice. Therefore, the structure of any carbon nanotube canbe described by an index with a pair of integers (n,m) that define its chiral vector.

In terms of the integers (n,m), the nanotube diameter dt is given by:

and the chiral angle is given by:
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.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 metallic when n = m, has a small gap when n m = 3i, where i is aninteger, and is semiconducting when n m 3i. This is due to the fact that the periodicboundary conditions for the one-dimensinal carbon nanotubes permit only a few wavevectors to exist around the circumference of carbon nanotubes. Metallic conductionoccurs when one of these wave vectors passes through the K-point of graphenes 2Dhexagonal Brillouin zone, where the valence and conduction bands are degenerate. Forthe semiconducting carbon nanotubes, there is a diameter dependency on bangap. Forexample, according to a single-particle tight-binding description of the electronic

structure, where is the hopping matrix element, and a is the carbon-carbonbond distance.

Motivations for transistor applications

A carbon nanotubes bandgap is directly affected by its chirality and diameter. If thoseproperties can be controlled, CNTs would be a promising candidate for future nano-scaletransistor devices. Moreover, because of the lack of boundaries in the perfect and hollowcylinder structure of CNTs, there is no boundary scattering. CNTs are also quasi-1Dmaterials in which only forward scattering and back scattering are allowed, and elasticscattering mean free paths in carbon nanotubes are long, typically on the order ofmicrometers. As a result, quasi-ballistic transport can be observed in nanotubes atrelatively long lengths and low fields. Because of the strong covalent carbon-carbon

bonding in the sp2 configuration, carbon nanotubes are chemically inert and are able totransport large amounts of electric current. In theory, carbon nanotubes are also able toconduct heat nearly as well as diamond or sapphire, and because of their miniaturizeddimensions, the CNTFET should switch reliably using much less power than a silicon-based device.

Device fabrication

There are many types of CNTFET devices; a general survey of the most commongeometries are covered below.
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Back-gated CNTFETs

Top view Side viewTop and side view of carbon nanotubes deposited on a silicon oxide substrate pre-patterned with source and drain contacts.

The earliest techniques for fabricating carbon nanotube (CNT) field-effect transistorsinvolved pre-patterning parallel strips of metal across a silicon dioxide substrate, and thendepositing the CNTs on top in a random pattern.The semiconducting CNTs that happenedto fall across two metal strips meet all the requirements necessary for a rudimentary field-effect transistor. One metal strip is the source contact while the other is the draincontact. The silicon oxide substrate can be used as the gate oxide and adding a metalcontact on the back makes the semiconducting CNT gateable.

This technique suffered from several drawbacks, which made for non-optimizedtransistors. The first was the metal contact, which actually had very little contact to theCNT, since the nanotube just lay on top of it and the contact area was therefore verysmall. Also, due to the semiconducting nature of the CNT, a Schottkey Barrier forms atthe metal-semiconductor interface, increasing the contact resistance. The seconddrawback was due to the back-gate device geometry. Its thickness made it difficult toswitch the devices on and off using low voltages, and the fabrication process led to poorcontact between the gate dielectric and CNT.
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Top-gated CNTFETs

The process for fabricating a top-gated CNTFET.

Eventually, researchers migrated from the back-gate approach to a more advanced top-gate fabrication process. In the first step, single-walled carbon nanotubes are solutiondeposited onto a silicon oxide substrate. Individual nanotubes are then located via atomicforce microscope or scanning electron microscope. After an individual tube is isolated,source and drain contacts are defined and patterned using high resolution electron beamlithography. A high temperature anneal step reduces the contact resistance by improvingadhesion between the contacts and CNT. A thin top-gate dielectric is then deposited on

top of the nanotube, either via evaporation or atomic layer deposition. Finally, the topgate contact is deposited on the gate dielectric, completing the process.

Arrays of top-gated CNTFETs can be fabricated on the same wafer, since the gatecontacts are electrically isolated from each other, unlike in the back-gated case. Also, dueto the thinness of the gate dielectric, a larger electric field can be generated with respectto the nanotube using a lower gate voltage. These advantages mean top-gated devices aregenerally preferred over back-gated CNTFETs, despite their more complex fabricationprocess.
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Wrap-around gate CNTFETs

Sheathed CNT

Gate all-around CNT Device

Wrap-around gate CNTFETs, also known as gate-all-around CNTFETs were developedin 2008, and are a further improvement upon the top-gate device geometry. In this device,instead of gating just the part of the CNT that is closer to the metal gate contact, theentire circumference of the nanotube is gated. This should ideally improve the electricalperformance of the CNTFET, reducing leakage current and improving the device on/offratio.

Device fabrication begins by first wrapping CNTs in a gate dielectric and gate contact via

atomic layer deposition. These wrapped nanotubes are then solution-deposited on aninsulating substrate, where the wrappings are partially etched off, exposing the ends ofthe nanotube. The source, drain, and gate contacts are then deposited onto the CNT endsand the metallic outer gate wrapping.
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Suspended CNTFETs

A suspended CNTFET device.

Yet another CNTFET device geometry involves suspending the nanotube over a trench toreduce contact with the substrate and gate oxide. This technique has the advantage ofreduced scattering at the CNT-substrate interface, improving device performance. Thereare many methods used to fabricate suspended CNTFETs, ranging from growing themover trenches using catalyst particles, transferring them onto a substrate and then under-etching the dielectric beneath,] and transfer-printing onto a trenched substrate.

The main problem suffered by suspended CNTFETs is that they have very limitedmaterial options for use as a gate dielectric (generally air or vacuum), and applying a gate

bias has the effect of pulling the nanotube closer to the gate, which places an upper limiton how much the nanotube can be gated. This technique will also only work for shorternanotubes, as longer tubes will flex in the middle and droop towards the gate, possiblymaking touching the metal contact and shorting the device. In general, suspendedCNTFETs are not practical for commercial applications, but they can be useful forstudying the intrinsic properties of clean nanotubes.

CNTFET material considerations

There are general decisions one must make when considering what materials to use whenfabricating a CNTFET. Semiconducting single-walled carbon nanotubes are preferred

over metallic single-walled and metallic multi-walled tubes since they are able to be fullyswitched off, at least for low source/drain biases. A lot of work has been put into findinga suitable contact material for semiconducting CNTs; the best material to date is Pd, as itswork function matches closely with that of nanotubes and it adheres to the CNTs quitewell.
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I-V characteristics

Field effect mobility of a back-gated CNTFET device with varying channel lengths. SiO2is used as the gate dielectric. Tool: 'CNT Mobility' at nanoHUB.org

In CNT-metal contacts, the different work functions of the metal and the CNT result inthe Schottky barrierat the source and drain, which are made of metals like Au, Ti, Pd andAl. Even though like Schottky barrier diodes, the barriers would have made this FET totransport only one type of carrier, the carrier transport through the metal-CNT interface isdominated by quantum mechanical tunneling through the Schottky barrier. CNTFETs caneasily be thinned by the gate field such that tunneling through them results in asubstantial current contribution. CNTFETs are ambipolar; either electrons or holes, orboth electrons and holes can be injected simultaneously.This makes the thickness of theSchottky barrier a critical factor.

CNTFETs conduct electrons when a positive bias is applied to the gate and holes when anegative bias is applied, and drain current increases with increasing a magnitude of anapplied gate voltage. 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 theapplied gate voltage is below the threshold voltage. For planar CNTFETs with differentdesign parameters, the FET with a shorter channel length produces a higher saturationcurrent, and the saturation drain current becomes also higher for the one consisting ofsmaller diameter keeping the length constant. For cylindrical CNTFETs, it is clear that a
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higher drain current is driven than that of planar CNTFETs since a CNT is surrounded byan oxide layer which is finally surrounded by a metal contact serving as the gate terminal.

Theoretical derivation of drain current

Structure of a top-gate CNT transistor

Theoretical investigation on drain current of the top-gate CNT transistor has been doneby T.Kazierski et al.. When an electric field is applied to a CNT transistor, a mobilecharge is induced in the tube from the source and drain. These charges are from thedensity of positive velocity states filled by the source NS and that of negative velocitystates filled by the drain ND, and these densities are determined by the Fermi-Diracprobability distributions.

and the equilibrium electron density is

.

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

USF = EF qVSCUDF = EF qVSC qVDS.

The term, (E Eg / 2) is 1 when the value inside the bracket is positive and 0 whennegative. VSC is the self-consistent voltage that illustrates that the CNT energy is affected
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by external terminal voltages and is implicitly related to the device terminal voltages andcharges at terminal capacitances by the following nonlinear equation:

where Qt represents the charge stored in terminal capacitances, and the total terminalcapacitance C is the sum of the gate, drain, source, and substrate capacitances shown inthe figure above. The standard approach to the solution to the self-consistent voltageequation is to use the Newton-Raphson iterative method. According to the CNT ballistictransport theory, the drain current caused by the transport of the nonequilibrium chargeacross the nanotube can be calculated using the FermiDirac statistics.

Here F0 represents the FermiDirac integral of order 0, k is the Boltzmanns constant, Tis the temperature, and the reduced Plancks constant. This equation can be solvedeasily as long as the self-consistent voltage is known. However the calculation could betime-consuming when it needs to solve the self-consistent voltage with the iterativemethod, and this is the main drawback of this calculation.

Comparison to MOSFETs

CNTFETs show different characteristics compared toMOSFETs in their performances.In a planar gate structure, 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 gatevoltage.This on-current advantage comes from the high gate capacitance and improvedchannel transport. Since an effective gate capacitance per unit width of CNTFET is aboutdouble that of p-MOSFET, the compatibility with high- k gate dielectrics becomes adefinite advantage for CNTFETs.About twice higher carrier velocity of CNTFETs thanMOSFETs comes from the increased mobility and the band structure. CNTFETs, inaddition, have about four times higher transconductance.

Heat dissipation

The decrease of the current and burning of the CNT can occur due to the temperature

raised by several hundreds of kelvins. Generally, the self-heating effect is much lesssevere in a semiconducting CNTFET than in a metallic one due to different heatdissipation mechanisms. A small fraction of the heat generated in the CNTFET isdissipated through the channel. The heat is non-uniformly distributed, and the highestvalues appear at the source and drain sides of the channel. ] Therefore, the temperaturesignificantly gets lowered near the source and drain regions. For semiconducting CNT,the temperature rise has a relatively small effect on the I-V characteristics compared tosilicon.
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Disadvantages

Lifetime (degradation)

The carbon nanotube degrades in a few days when exposed to oxygen. There has been

several works done on passivating the nanotubes with different polymers and increasingtheir lifetime.

Reliability

Carbon nanotubes have shown reliability issues when operated under high electric fieldor temperature gradients. Avalanche breakdown occurs in semiconducting CNT and joulebreakdown in metallic CNT. Unlike avalanche behavior in silicon, avalanche in CNTs isnegligibly temperature-dependent. Applying high voltages beyond avalanche pointresults in Joule heating and eventual breakdown in CNTs. 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 severalmonths, while the single-channeled CNTFETs are usually out of work after a few weeksin the ambient atmosphere. The multi-channeled CNTFETs keep operating when somechannels break down, this wont happen in the single-channeled ones.

Difficulties in mass production, production cost

Although CNTs have unique properties such as stiffness, strength, and tenacity comparedto other materials especially to silicon, we are still experiencing lack of technology formass production and high production cost. To overcome the fabrication difficulties,several methods have been studied such as direct growth, solution dropping, and various

transfer printing techniques.

Future work

The most desirable future work involved in CNTFETs will be the transistor with higherreliability, cheap production cost, or the one with more enhanced performances. Forexample, such efforts could be made: adding effects external to the inner CNT transistorlike the Schottky barrier between the CNT and metal contacts, multiple CNTs at a singlegate, channel fringe capacitances, parasitic source/drain resistance, and series resistancedue to the scattering effects.

References

1. Dekker, Cees; Tans, Sander J.; Verschueren, Alwin R. M. (1998). Nature393 (6680): 49. Bibcode1998Natur.393...49T. doi:10.1038/29954.2. International Technology Roadmap for Semiconductors 2009 Edition3. Avouris, P; Chen, J (2006). "Nanotube electronics and optoelectronics".Materials Today 9 (10): 46. doi:10.1016/S1369-7021(06)71653-4.4. G. Timp,Nanotechnology Springer, 1999. ISBN 0387983341 p. 309
http://en.wikipedia.org/wiki/Bibcodehttp://adsabs.harvard.edu/abs/1998Natur.393...49Thttp://adsabs.harvard.edu/abs/1998Natur.393...49Thttp://en.wikipedia.org/wiki/Digital_object_identifierhttp://dx.doi.org/10.1038%2F29954http://public.itrs.net/http://en.wikipedia.org/wiki/Digital_object_identifierhttp://dx.doi.org/10.1016%2FS1369-7021(06)71653-4http://books.google.com/books?id=v0gMBF1EdGcC&pg=PA309http://en.wikipedia.org/wiki/Special:BookSources/0387983341http://en.wikipedia.org/wiki/Bibcodehttp://adsabs.harvard.edu/abs/1998Natur.393...49Thttp://en.wikipedia.org/wiki/Digital_object_identifierhttp://dx.doi.org/10.1038%2F29954http://public.itrs.net/http://en.wikipedia.org/wiki/Digital_object_identifierhttp://dx.doi.org/10.1016%2FS1369-7021(06)71653-4http://books.google.com/books?id=v0gMBF1EdGcC&pg=PA309http://en.wikipedia.org/wiki/Special:BookSources/0387983341

Carbon Nanotube Field

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