Carbon Nanotube Quantum Resistor Carbon Nanotube Quantum Resistor Lotti Christian Carezzano Linda Corso di Nanotecnologie 1 Prof. Di Zitti Anno accademico Corso di Nanotecnologie 1 Prof. Di Zitti Anno accademico 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 Nanotube History and Definition: Nanotube were discovered in 1991 by Sumio Iijima who produced them by vaporizing carbon graphite with an electric arc under an inert atmosphere. Nanotube were discovered in 1991 by Sumio Iijima who produced them by vaporizing carbon graphite with an electric arc under an inert atmosphere. Nanotubes are long, cylindrical carbon structures consisting of hexagonal graphite molecules attached at the edges. Nanotubes are long, cylindrical carbon structures consisting of hexagonal graphite molecules attached at the edges.

Carbon Nanotube Multiwall Nanotube (MWNT) 1991: consist of several nested cylinders with an interlayer spacing of 0.34 – 0.36 nm that is close to the typical spacing of turbostratic graphite.

Carbon Nanotube Multi-wall Nanotubes by Tunneling Electron Microscope

Carbon Nanotube Singlewall Nanotube (SWNT) 1993: in the ideal case, a carbon nanotube consist of either one cylindrical graphene sheet.

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

Quantized Conductance Fundamental hypothesis: Considering MWNT as an extremely fine and constricted wave guide with a length smaller than the electronic mean free path. Electronic transport is ballistic: every electron injected into the nanotube at one end come out the other end.

Quantized Conductance Ballistic Transport involved: G 0 contribute to conductance of every conducting channel. G 0 contribute to conductance of every conducting channel. No energy dissipation along the nanotube conductor. No energy dissipation along the nanotube conductor.

Quantized Conductance G 0 is the fundamental quantum of conductance: e is the charge on the electron e is the charge on the electron h is the Planck constant h is the Planck constant

Multiwall Nanotube Conductance In order to verify the quantized conducting behaviour of nanotubes in 1998 Walt de Heer invented an ingenious way to measure the electrical conductance of MWNTs.

Experimental Scheme Using arc discharge process were produced very fine and compact fibers composed of carbon nanotubes and graphitic particles. Schematics of an arc discharge

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

Experimental Scheme nanotubes` length 1-10 µm nanotubes` length 1-10 µm nanotubes` diameter 5-25 nm nanotubes` diameter 5-25 nm Transmission electron micrograph of the end of a nanotube fibe recovered from a nanotube arc deposit

Experimental Scheme nanotubes` inner cavities 1-4 nm nanotubes` inner cavities 1-4 nm nanotubes` layers up to 15 nanotubes` layers up to 15

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

Experimental Scheme A macroscopic fiber of multiwall nanotubes was lowered into a drop of liquid metal. Because individual nanotubes stick out from the fiber, by dipping the nanotubes to different depths is possible to determine the resistance of individual nanotubes. Because individual nanotubes stick out from the fiber, by dipping the nanotubes to different depths is possible to determine the resistance of individual nanotubes. V ap potential (10-50 mV) was applied to the contact, the current through the circuit was measured together with the piezo displacement. V ap potential (10-50 mV) was applied to the contact, the current through the circuit was measured together with the piezo displacement.

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

Results The period of motion is 2 s, the conductance jumps to ~ 1G 0 and then remains constant for ~ 2 µm of its dipping depth. Nanotube is a quantized conductor

Results This figure presents a sequence of steps at 1G 0 intervals, because other tubes come into contact with the liquid metal. After a dipping distance of 200 nm there is a second step (the second tube comes into contact with the metal ~200nm after the first).

Results The conductance does not immediately rise to G 0 but is ~ 0,5 G 0 for the first 25nm This effect can be related to the tip structure of the nanotubes. of the nanotubes.

Results The ~ 30% of the nanotubes have tapered tips The conductance was reduced due to the presence of the tip-to-shaft interface

Results This plot (G 0 versus z-position) is the tip effect; the scanning range was reduced to 70 nm.

Results The figure B is the histogram of the conductance data of all 250 traces in the sequence represented in Fig. A. The plateus at 1G 0 and at 0 produce peaks in the histogram.

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

Conclusion The nanotubes were not dameged even at high voltages (V ap =6V  J>10 7 Acm -2 ) for extended times. Power dissipated = 3 mW Bulk thermal conductivity = 10 Wcm -1 K -1 We would attain a temperature T max =20000°K We would attain a temperature T max =20000°K Impossible: nanotubes start to burn at~700°C

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

Conclusion The conductance of MWNTs has been observed to be G~1G 0 and it’s independent of the number of layers because by geometrical and energetical evidence only one layer can conduct.

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

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

MTWNs’ Fractional Quantum Conductance The work is based on the consideration that MWNTs have a finite lenght and a non-homogeneous structure. non-homogeneous structure. This leads to strong interwall interactions that blocked some of the conduction channels and are responsible of a non-uniform redistribution of the total current density over the individual tube walls.

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

MTWNs’ Fractional Quantum Conductance Hypotesis: Current injection from the gold electrode occurs only into the outermost tube wall. Current injection from the gold electrode occurs only into the outermost tube wall. Chemical potential equals that of mercury, shifted by a contact potential, only within the submersed portion of the tube. Chemical potential equals that of mercury, shifted by a contact potential, only within the submersed portion of the tube.

MTWNs’ Fractional Quantum Conductance This is the scheme of the inhomogenous structure of the MWNT. It’s to note that even if only the outer layer is in direct contact with Hg electrode, we can consider equipotential with mercury all the layers immersed into Hg. Hg(#1) – single-wall MWNT’s portion eq. with Hg. Hg(#2) – double-wall MWNT’s portion eq with Hg. Hg(#2) – double-wall MWNT’s portion eq with Hg. Hg(#3) – triple-wall MWNT’s portion eq with Hg. Hg(#3) – triple-wall MWNT’s portion eq with Hg.

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

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

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

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

MTWNs’ Fractional Quantum Conductance The results of the calculation show that also in theoretical predictions conductance increase in discrete step of 0.5G 0 until the value of 1G 0. G does not exceed this value because only the single-wall portion of the MWNT is in direct contact with the gold electrode.

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