properties of carbon nanotubes krisztian kordas [email protected]

YKSIKKÖ, MATTI MEIKÄLÄINEN, x.x.2006

Properties of carbon nanotubes

Krisztian [email protected]

Microelectronics and Materials Physics Laboratories

Department of Electrical and Information Engineering

P.O. Box 4500, FIN-90014 University of Oulu

Understanding carbon nanotubesOulu, 1-2 October 2008


Outline


−Polymorphism of carbon

−Electrical properties−Thermal transport−Optical properties−Mechanical behavior


Allotropic forms of carbon: Diamond, graphite …

C-C: 1.54 Å

sp3 – diamond

sp2 – graphite

C-C: 1.42 Å

www.wikipedia.org

www.wikipedia.org

−Polymorphism of carbon−Electrical properties−Thermal transport−Optical properties−Mechanical behavior



Allotropic forms of carbon: Defects in graphitic carbon

fullerenesC60 = 12 pentagons + 20 hexagons

Eulers polyhedron formula|V|-|E|+|F| = 2, where |V|, |E|, |F| indicate the number of vertices,

edges, and faces Understanding carbon nanotubesOulu, 1-2 October 2008

Krishnan, A., Dujardin, E., Treacy, M.M.J., Hugdahl, J., Lynum, S., Ebbesen, T.W. Nature, 1997, 388, 451-454.

cones



The rolled graphene layers (up to 50) are in co-axial arrangement. The typical diameter is 1-5 nm (SWCNTs) and 5-100 nm (MWCNTs) with lengths up to a few cm!

Bundles of SWCNTs

MWCNT

Carbon nanotubes


M. Monthioux, et al., Carbon 39 (2001) 1261–1272

Bundles of MWCNTs



Other forms of carbon


Bamboo-type CNTs

Carbon onions

J. Miyawaki, et al., Adv. Mater. 2006, 18, 1010

Carbon nanohorns

F. Banhart, T. Füller, Ph. Redlich and P.M. Ajayan, Chem. Phys. Lett. 269, 349 (1997)

Ph. Redlich, F. Banhart, Y. Lyutovich and P.M. Ajayan, Carbon 36, 561 (1998)

F. Banhart and P.M. Ajayan, Nature 382, 433-435 (1996)

Carbon onions and diamonds



Chirality of CNTs




Chirality of CNTs


Ph. Lambin et al., Carbon 40 (2002) 1635



DOS vs. structure: Nanotubes


The product of the DOS g(E) and the probability distribution function f(E) is the number of occupied states per unit volume at a given energy for a system in thermal equilibrium.

number of states per unit sample volume at an energy E inside an interval [E,E + dE]

probability that a fermion occupies a specific quantum state in a system at thermal equilibrium



2D energy dispersion relations for bands of graphite, with overlap integral:

R. Saito, M. Fujita, G. Dresselhaus, M. S Dresselhaus, APL 60 (1992) 2204.


Periodic boundary condition for k.

Condition for having metallic nanotube:




V0 is the hopping matrix element for adjacent 2p orbitals of C atoms having distance of d0

CT White, et al., PRB, 47 (1993) 5485.





J.W.G. Wildöer, et al., Nature, 391 (1998) 59.T.W. Odom, et al., Nature 391 (1998) 62.


tunnelling spectroscopy




Uniaxial stress

Twist

A. Kleiner and S. Eggert, PRB, 63 (2001) 73408.

Primary metallic or small-gap semiconducting nanotubes are tubes with band gaps that arise solely from breaking the bond symmetry due to curvature. The unified gap equation as a function of chirality and deformations:



DOS vs. structure: Penta-Hexa-Heptites

P.M. Ajayan, Nanotube course, Oulu, 2005.


•453



FETs with individual CNTs


Back-side gated structures on over-doped Si wafers


R. Martel, T. Schmidt, H. R. Shea, T. Hertel, and Ph. Avouris, APL 73 (1998) 2447.IBM group

IW

LC V V VDS n O GS T DS ( )

IW

LC V V

VV

W

LC V V V

V

DS n O G TDS

DS

n O G T DSDS

2

2

2

( )

Q C VV

V WLn O GDS

T ( )2

Q CV

C V V WLn

O GS T

( )

I satW

LC V V

V V

W

LC V V

DS n O GS TGS DS

nO GS T

( ) ( )( )

22

2

2

2

constant

A

B

C

www.plato.ul.ie/academic/Vincent.Casey/PH4608SS2/MOSFET.ppt


FETs with individual CNTs


Back-side gated structures on over-doped Si wafers

SWCNTs acting as p-type channels


R. Martel, T. Schmidt, H. R. Shea, T. Hertel, and Ph. Avouris, APL 73 (1998) 2447.IBM group

Deformed MWCNTs acting as gate controlled channels


Doping of CNTs

V. Derycke, R.Martel, J.Appenzeller, P.Avouris, Nano. Lett. 1 (2001) 453.IBM group


Changing the p-type character to n-type by annealing and/or K-doping



Transistors, logic circuits, memory, oscillator

A. Bachtold, P. Hadley, T. Nakanishi, C.Dekker, Science 294 (2001) 1317.Delft group


http://home.tudelft.nl/en/


Doping of CNTs and logic gates

A. Javey, Q. Wang, A. Urai, Y. Li, H.Dai, Nano. Lett. 2 (2002) 929.Stanford group


G: -40 V; SD: 20 V anneals to desorb oxygen


R ~1nm!

Field-emission from CNTs


Philip G. Collins and A. Zettl, PRB 55 (1997) 9391.



E-J characteristic curve measured using an 0.25 cm2 anode in 2×10-7 mbar pressure. ITO glass is used as anode, which is separated 0.5 mm from the sample. Turn-on and threshold fields are 3.2 V/μm and 4.4 V/μm. The inset shows the corresponding fairly linear Fowler-Nordheim plot.

S. Hofmann, C. Ducati, B. Kleinsorge, J. Robertson, Appl. Phys. Lett 83 (2003) 4661.

Field-emitter nanofibers




Ballistic transport: standing waves and resonance scattering in SWCNTs

200 mV periods: quantized energies of electron standing waves

1.5 V periods are due to localized states

J. Kong, et al., PRL 87 (2001) 106801.



Quantum conductance

Experiments in gated 2D electron (Fermi) gas e.g. GaAs/AlGaAs heterostructures with point type contacts. (Any point contact between metals is also good).

Tn(Ef) is the transmission probability of different sub-bands at the Fermi level.

At finite temperatures:



Conductance at a given gate at 0 K

http://arxiv.org/PS_cache/cond-mat/pdf/0512/0512609v1.pdf


Quantum conductancein nanotubes

MWCNTs - single channel is present.


S. Frank, P. Poncharal, Z. L. Wang, W. A. de Heer, Science, 280 (1998) 1744.

Ballistic transport:- No heat dissipation in the wire but

at the contacts (elastic scattering is allowed)

- Quantized conductance (elastic scattering ruins it)



Only tunneling between adjacent shells!

B. Bourlon et al., PRL 93 (2004) 176806.

Inter-shell transport




Dependence of the phase of the electron wave on the magnetic field (vector potential).

A. Bachtold, Nature 397 (1999) 673.

Aharonov-Bohm oscillations



YKSIKKÖ, MATTI MEIKÄLÄINEN, x.x.2006K. Tsukagosh, Nature 401 (1999) 572.

Magnetoresistance




Ballistic electrical and thermal transportin carbon nanotubes


E. Brown et al., APL 87 (2005) 23107.

10,10 CNT d ~1.4 nm 120 phonon channels200,200 CNT d ~27.5 nm 2400 phonon channels.

2N is the number of channels


264 K

114 K


Extremely high current carrying capability.

Large current carrying capabilityBallistic carriers

A SWNT bulb made from SWNT filament compared with a tungsten bulb operated at same voltage (20 V). The nanotube bulb shows a high brightness and reliability.

J Wei, H Zhou, D Wu, BQ Wei, Carbon nanotube filaments in household light bulbs, Appl. Phys. Lett. 84 (2004) 4869.

BQ Wei, R Vajtai, PM Ajayan, Appl. Phys. Lett. 71 (2001) 1172.



The thermal conductance of an individual MWCNT. Inset: Solid line represents κ(T) of an individual MWCNT, broken and dotted lines are 80 nm and 200 nm) bundles, respectively. The positive thermoelectric power suggests hole-type major carriers taking part in the conductivity. The high Lorentz-ratio κ/σT~2-6×10-6 WΩ/K2 suggests phonon transport.

P. Kim et al., Phys. Rev. Lett. 87 (2001) 215502.J. Hone et al., Synth. Metals 103 (1999) 2498.

Thermal management of epoxy-CNT composites.

M.J. Biercuk et al., Appl. Phys. Lett. 80 (2002) 2767.

Nanotubes as perfect crystalsThermal transport




Zhuangchun Wu, et al. Science 305, 1273 (2004)

Optical properties



Optical properties


K. Kordás, T. Mustonen, G. Tóth, H. Jantunen, M. Lajunen, C. Soldano, S. Talapatra, S. Kar, R. Vajtai, P.M. Ajayan, Small 2 (2006) 1021.


J. Maultzsch, et al., PRB 72, 205438 2005


Zhuangchun Wu, et al. Science 305, 1273 (2004)J. Maultzsch, et al., PRB 72, 205438 2005.H. Kataura et al., Synth. Met. 103, 2555 (1999).

Optical properties



Mechanical properties


SWCNT bundles on alumina membrane support

J.P. Salvetat, et al., PRL 82 (1999) 944.





Good fit is obtained with SWCNTs E ~1TPaMWCNTs E ~0.3 TPa

D. Garcia-Sanchez, et al., PRL 99 (2007) 085501



•Young’s modulus ~ 1TPa•Tensile strength 4-22 GPa

•Low density

MWCNT (5 wt%) - Polystyrene composite

ET Thostenson et al., J. Phys. D 35 (2002) L77.

Young’s moduli of single- and multi-walled CNTs T Natsuki et al., Appl. Phys. A 79 (2004) 117.

J-P Salvetat et al., Phys. Rev. Lett. 82 (1999) 944.

A. Krishnan et al., Phys. Rev. B 58 (1998) 14013.

F. Li et al., Appl. Phys. Lett. 77 (2000) 3161.


Improved reinforcement:•Oxidation in acids followed by amino functionalization using triethylenetetramine•Embedding in epoxy resin

F.H. Gojny et al., Chem. Phys. Lett. 370 (2003) 820.




Properties of CNTs: Summary

MaterialYoung’s modulus

(GPa)Thermal conductivity

(W/mK)

Electrical resistivity

(cm)Density (g/cm3)

nanotubes 1200 3000 10-4 2.6

steel 208 52 7.2 10-5 7.8

epoxy 3.5 0.43 insulate 1.25

wood 16 0.1 insulate 0.6

SWCNTsChirality dependent band gap up to ~1 eVTunable conduction by external field (gate) or by chemicals (sensors)Large specific surface

MWCNTsStructural integrityEasy applicability: handling and assembly

http://www.nec.co.jp/press/en/0309/1701.html

http://www.samsung.coml

http://www.montreal.fi



References

Papers cited in the presentation

Springer Handbook of Nanotechnology, Bhushan, (Ed.) Springer, Heidelberg 2004.

Lecture Notes in Physics, Understanding Carbon Nanotubes, Loiseau, Lanunois, Petit, Roche, Salvetat (Eds.) Springer, Heidelberg, 2006.


properties of carbon nanotubes krisztian kordas [email protected]

Documents