Carbon Nanotube Quantum Resistor Carbon Nanotube Quantum Resistor Lotti Christian Carezzano Linda Corso di Nanotecnologie 1 Prof. Di Zitti Anno accademico

Carbon Nanotube Quantum Carbon Nanotube Quantum ResistorResistor

Lotti ChristianLotti Christian

Carezzano LindaCarezzano Linda

Corso di Nanotecnologie 1 Prof. Di Zitti

Anno accademico 2002-2003

Corso di Nanotecnologie 1 Prof. Di Zitti

Anno accademico 2002-2003

SCIENCE,VOL.280,12 JUNE 1998

PHISICAL REVIEW LETTERS,VOL.84,NUM.9,28 FEBRUARY 2000

SCIENCE,VOL.280,12 JUNE 1998

PHISICAL REVIEW LETTERS,VOL.84,NUM.9,28 FEBRUARY 2000

Carbon NanotubeCarbon Nanotube

History and Definition:History and Definition:• Nanotube were discovered in 1991 by Sumio Nanotube were discovered in 1991 by Sumio

Iijima who produced them by vaporizing carbon Iijima who produced them by vaporizing carbon graphite with an electric arc under an inert graphite with an electric arc under an inert atmosphere.atmosphere.

• Nanotubes are long, cylindrical carbon Nanotubes are long, cylindrical carbon structures consisting of hexagonal graphite structures consisting of hexagonal graphite molecules attached at the edges.molecules attached at the edges.


Multiwall Nanotube Multiwall Nanotube (MWNT) 1991:(MWNT) 1991:

consist of several consist of several nested cylinders with nested cylinders with an interlayer spacing an interlayer spacing of 0.34 – 0.36 nm that of 0.34 – 0.36 nm that is close to the typical is close to the typical spacing of turbostratic spacing of turbostratic graphite.graphite.


Multi-wall Nanotubes by Tunneling Electron Multi-wall Nanotubes by Tunneling Electron MicroscopeMicroscope

Carbon Nanotube Carbon Nanotube

Singlewall Nanotube Singlewall Nanotube (SWNT) 1993:(SWNT) 1993:

in the ideal case, a in the ideal case, a carbon nanotube carbon nanotube consist of either one consist of either one cylindrical graphene cylindrical graphene sheet. sheet.


Carbon nanotubes are now considered to be the Carbon nanotubes are now considered to be the building blocks of future nanoscale electronic building blocks of future nanoscale electronic and mechanical devices. Hence the importance and mechanical devices. Hence the importance of studing their conducting behaviour. of studing their conducting behaviour.

Quantized ConductanceQuantized Conductance

Fundamental hypothesis:Fundamental hypothesis:

Considering MWNT as an extremely fine and Considering MWNT as an extremely fine and constricted wave guide with a length smaller than constricted wave guide with a length smaller than the electronic mean free path.the electronic mean free path.

Electronic transport is ballistic: every electron Electronic transport is ballistic: every electron injected into the nanotube at one end come out injected into the nanotube at one end come out the other end.the other end.


Ballistic Transport involved:Ballistic Transport involved:

• GG00 contribute to conductance of every contribute to conductance of every conducting channel.conducting channel.

• No energy dissipation along the nanotube No energy dissipation along the nanotube conductor.conductor.


GG00 is the fundamental quantum of conductance: is the fundamental quantum of conductance:

h

eG

2

0

2

• ee is the charge on the electron is the charge on the electron• hh is the Planck constant is the Planck constant

Multiwall Nanotube ConductanceMultiwall Nanotube Conductance

In order to verify the quantized conductingIn order to verify the quantized conducting

behaviour of nanotubes in 1998 Walt de Heer behaviour of nanotubes in 1998 Walt de Heer invented an ingenious way to measure the invented an ingenious way to measure the electrical conductance of MWNTs. electrical conductance of MWNTs.

Experimental SchemeExperimental SchemeUsing arc discharge process were produced Using arc discharge process were produced very fine and compact fibers composed of very fine and compact fibers composed of carbon nanotubes and graphitic particles.carbon nanotubes and graphitic particles.

Schematics of an arc dischargeSchematics of an arc discharge

Experimental SchemeExperimental Scheme

The nanotube fiber The nanotube fiber was attached to a was attached to a gold wire with gold wire with colloidal silver paint.colloidal silver paint.The fiber is a bundled The fiber is a bundled of nanotubes with of nanotubes with different lenghts and it different lenghts and it has been seen that has been seen that one MWNT protruding one MWNT protruding from the tip of the from the tip of the fiber.fiber.

Carbon fiber TEM micrograpyCarbon fiber TEM micrograpy


• nanotubes` length 1-10 nanotubes` length 1-10 µmµm• nanotubes` diameter 5-25 nmnanotubes` diameter 5-25 nm

Transmission electron micrograph of the end of a nanotube fibeTransmission electron micrograph of the end of a nanotube fibe

recovered from a nanotube arc depositrecovered from a nanotube arc deposit


• nanotubes` inner nanotubes` inner cavities 1-4 nmcavities 1-4 nm

• nanotubes` layers up nanotubes` layers up to 15to 15


The nanotube contact was installed in place of The nanotube contact was installed in place of the tip of a scanning probe microscope. Below the tip of a scanning probe microscope. Below the nanotube contact there was a heatable the nanotube contact there was a heatable copper reservoir containing mercury.copper reservoir containing mercury.


A macroscopic fiber of multiwall nanotubes was A macroscopic fiber of multiwall nanotubes was lowered into a drop of liquid metal.lowered into a drop of liquid metal.

Because individual nanotubes stick out from the Because individual nanotubes stick out from the fiber, by dipping the nanotubes to different fiber, by dipping the nanotubes to different depths is possible to determine the resistance of depths is possible to determine the resistance of individual nanotubes.individual nanotubes.

VVapap potential potential (10-50 mV) was applied to the (10-50 mV) was applied to the contact, the current through the circuit was contact, the current through the circuit was measured together with the piezo displacement.measured together with the piezo displacement.

ResultsResults

This figure shows conductance versus time; the This figure shows conductance versus time; the nanotube contact is moved at constant speed nanotube contact is moved at constant speed into and out of the liquid metal.into and out of the liquid metal.

ResultsResults

The period of motion is 2 s, the conductance The period of motion is 2 s, the conductance jumps to ~ 1Gjumps to ~ 1G00 and then remains constant and then remains constant

for ~ 2 for ~ 2 µm of its dipping depth.µm of its dipping depth.

Nanotube is a quantized conductorNanotube is a quantized conductor

ResultsResults

This figureThis figure presents a presents a sequence of steps at 1Gsequence of steps at 1G00 intervals, because other intervals, because other tubes come into contact tubes come into contact with the liquid metal.with the liquid metal.After a dipping distance After a dipping distance of 200 nm there is a of 200 nm there is a second step (the second second step (the second tube comes into contact tube comes into contact with the metal ~200nm with the metal ~200nm after the first). after the first).

ResultsResults

The conductance does not immediately The conductance does not immediately rise to Grise to G00 but is ~ 0,5 G but is ~ 0,5 G00 for the first 25nm for the first 25nm

This effect can be related to the tip structureThis effect can be related to the tip structure

of the nanotubes.of the nanotubes.

ResultsResults

The ~ 30% of the nanotubes have tapered tipsThe ~ 30% of the nanotubes have tapered tips

The conductance was reduced due to the presence of the tip-to-shaft The conductance was reduced due to the presence of the tip-to-shaft interfaceinterface

ResultsResults

This plot (GThis plot (G00 versus z- versus z-

position) is the tip position) is the tip effect; the scanning effect; the scanning range was reduced to range was reduced to 70 nm. 70 nm.

ResultsResults

The figure B is the histogram of the conductance The figure B is the histogram of the conductance data of all 250 traces in the sequence data of all 250 traces in the sequence represented in Fig. A.represented in Fig. A.

The plateus at 1GThe plateus at 1G00 and at 0 produce peaks in and at 0 produce peaks in the histogram.the histogram.

ResultsResults

Histogram of a Histogram of a nanotube with several nanotube with several liquid metal liquid metal (mercury,cerrolow,gall(mercury,cerrolow,gallium). The type of ium). The type of liquid metal used in liquid metal used in LMC does not effect LMC does not effect the properties the properties reported abovereported above

ConclusionConclusion

The nanotubes were not dameged even at high The nanotubes were not dameged even at high voltages (Vvoltages (Vapap=6V =6V J>10 J>1077AcmAcm-2-2) for extended ) for extended

times. times.

Power dissipated = 3 mWPower dissipated = 3 mW

Bulk thermal conductivity = 10 WcmBulk thermal conductivity = 10 Wcm-1-1KK-1-1

We would attain a temperature TWe would attain a temperature Tmaxmax=20000°K=20000°K

Impossible: nanotubes start to burn at~700°CImpossible: nanotubes start to burn at~700°C


Heat is dissipated in the leads to the Heat is dissipated in the leads to the ballistic element and not in the element ballistic element and not in the element itself. itself.


The conductance of MWNTs has been The conductance of MWNTs has been observed to be G~1Gobserved to be G~1G0 0 and it’s and it’s

independent of the number of layers independent of the number of layers because by geometrical and energetical because by geometrical and energetical evidence only one layer can conduct.evidence only one layer can conduct.

Unsolved problemUnsolved problem

As shown the conductance of nanotubes As shown the conductance of nanotubes seems to have a behaviour in seems to have a behaviour in disagreement with theoretical prediction: disagreement with theoretical prediction: the conductance in MWNTs was observed the conductance in MWNTs was observed to be 1Gto be 1G00 instead of 2G instead of 2G0.0.

MTWNs’ Fractional Quantum MTWNs’ Fractional Quantum ConductanceConductance

Using a scattering tecnique based on a Using a scattering tecnique based on a parametrized linear combination of atomic parametrized linear combination of atomic orbitals Hamiltonian, Sanvito, Kwon, Tomanek orbitals Hamiltonian, Sanvito, Kwon, Tomanek and Lambert calculate the conductance and find and Lambert calculate the conductance and find the reason of the phenomena observed in Walt the reason of the phenomena observed in Walt de Heer’s experiment. de Heer’s experiment.


The work is based on the consideration that The work is based on the consideration that MWNTs have a finite lenght and a MWNTs have a finite lenght and a

non-homogeneous structure.non-homogeneous structure.

This leads to strong interwall interactions that blocked This leads to strong interwall interactions that blocked some of the conduction channels and are responsible of some of the conduction channels and are responsible of a non-uniform redistribution of the total current density a non-uniform redistribution of the total current density over the individual tube walls.over the individual tube walls.


The key problem in explaining de Heer’s The key problem in explaining de Heer’s experimental data was that nothing was experimental data was that nothing was known about the MWNTs’ internal known about the MWNTs’ internal structure and about the nature of the structure and about the nature of the contact between nanotubes and Au and contact between nanotubes and Au and Hg electrodes. Tomanek and his group Hg electrodes. Tomanek and his group start their calculation assuming the start their calculation assuming the following scenario. following scenario.


Hypotesis:Hypotesis:• Current injection from the gold electrode Current injection from the gold electrode

occurs only into the outermost tube wall.occurs only into the outermost tube wall.• Chemical potential equals that of mercury, Chemical potential equals that of mercury,

shifted by a contact potential, only within shifted by a contact potential, only within the submersed portion of the tube.the submersed portion of the tube.


This is the scheme of the This is the scheme of the inhomogenous structure of the inhomogenous structure of the MWNT. It’s to note that even if MWNT. It’s to note that even if only the outer layer is in direct only the outer layer is in direct contact with Hg electrode, we can contact with Hg electrode, we can consider equipotential with consider equipotential with mercury all the layers immersed mercury all the layers immersed into Hg. into Hg. Hg(#1) – single-wall MWNT’s Hg(#1) – single-wall MWNT’s portion eq. with Hg.portion eq. with Hg.

Hg(#2) – double-wall MWNT’s Hg(#2) – double-wall MWNT’s portion eq with Hg.portion eq with Hg.

Hg(#3) – triple-wall MWNT’s Hg(#3) – triple-wall MWNT’s portion eq with Hg.portion eq with Hg.


(b) the calculation for (b) the calculation for submersion depth Hg(#1) submersion depth Hg(#1) consider a scattering consider a scattering region consisting in a region consisting in a finite length triple-wall finite length triple-wall nanotube connected to nanotube connected to another finite double-wall another finite double-wall nanotube region; this is nanotube region; this is then connected to an then connected to an external semi-infinite external semi-infinite single-wall SWNT.single-wall SWNT.


(c) calculation for (c) calculation for depth Hg(#2) depth Hg(#2) consider a scattering consider a scattering region made up of a region made up of a finite-length triple-wall finite-length triple-wall nanotube segment nanotube segment attached a SWNT on attached a SWNT on one end and to a one end and to a double-wall nanotube double-wall nanotube on the other one.on the other one.


(d) calculation for (d) calculation for depth Hg(#3) depth Hg(#3) consider a triple-wall consider a triple-wall nanotube in contact nanotube in contact with a SWNT lead.with a SWNT lead.


The calculated conductance depend also The calculated conductance depend also on the Fermi level that lies within the on the Fermi level that lies within the narrow energy window indicated by the narrow energy window indicated by the grey region in the previous pictures.grey region in the previous pictures.


The results of the calculation show that The results of the calculation show that also in theoretical predictions conductance also in theoretical predictions conductance increase in discrete step of 0.5Gincrease in discrete step of 0.5G0 0 until the until the

value of 1Gvalue of 1G00.. G does not exceed this value G does not exceed this value

because only the single-wall portion of the because only the single-wall portion of the MWNT is in direct contact with the gold MWNT is in direct contact with the gold electrode. electrode.


In summary it has been shown that In summary it has been shown that fractional quantum conductance may fractional quantum conductance may occur in multiwall nanotubes due to occur in multiwall nanotubes due to interwall interaction that modify the density interwall interaction that modify the density of state near the Fermi level, and due to of state near the Fermi level, and due to tube inhomogeneities, such as a varying tube inhomogeneities, such as a varying number of walls along the tube.number of walls along the tube.

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Carbon Nanotube Quantum Resistor Carbon Nanotube Quantum Resistor Lotti Christian Carezzano Linda Corso di Nanotecnologie 1 Prof. Di Zitti Anno accademico