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Properties of carbon nanotubes Krisztian Kordas lapy@ee.oulu.fi

Microelectronics and Materials Physics Laboratories Department of Electrical and Information Engineering P.O. Box 4500, FIN-90014 University of Oulu. Properties of carbon nanotubes Krisztian Kordas lapy@ee.oulu.fi. Understanding carbon nanotubes Oulu, 1-2 October 2008. Outline.

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Properties of carbon nanotubes Krisztian Kordas lapy@ee.oulu.fi

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  1. Microelectronics and Materials Physics Laboratories Department of Electrical and Information Engineering P.O. Box 4500, FIN-90014 University of Oulu Properties of carbon nanotubesKrisztian Kordaslapy@ee.oulu.fi Understanding carbon nanotubes Oulu, 1-2 October 2008

  2. Outline • Polymorphism of carbon • Electrical properties • Thermal transport • Optical properties • Mechanical behavior Understanding carbon nanotubes Oulu, 1-2 October 2008

  3. Polymorphism of carbon • Electrical properties • Thermal transport • Optical properties • Mechanical behavior Allotropic forms of carbon: Diamond, graphite … sp3 – diamond C-C: 1.54 Å www.wikipedia.org sp2 – graphite C-C: 1.42 Å www.wikipedia.org Understanding carbon nanotubes Oulu, 1-2 October 2008

  4. Polymorphism of carbon • Electrical properties • Thermal transport • Optical properties • Mechanical behavior Allotropic forms of carbon: Defects in graphitic carbon fullerenes C60 = 12 pentagons + 20 hexagons Eulers polyhedron formula |V|-|E|+|F| = 2, where |V|, |E|, |F| indicate the number of vertices, edges, and faces cones Krishnan, A., Dujardin, E., Treacy, M.M.J., Hugdahl, J., Lynum, S., Ebbesen, T.W. Nature, 1997, 388, 451-454. Understanding carbon nanotubes Oulu, 1-2 October 2008

  5. Polymorphism of carbon • Electrical properties • Thermal transport • Optical properties • Mechanical behavior Carbon nanotubes Bundles of SWCNTs MWCNT Bundles of MWCNTs 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! M. Monthioux, et al., Carbon 39 (2001) 1261–1272 Understanding carbon nanotubes Oulu, 1-2 October 2008

  6. Polymorphism of carbon • Electrical properties • Thermal transport • Optical properties • Mechanical behavior Other forms of carbon Bamboo-type CNTs Carbon onions and diamonds Carbon onions Carbon nanohorns J. Miyawaki, et al., Adv. Mater.2006, 18, 1010 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) Understanding carbon nanotubes Oulu, 1-2 October 2008

  7. Polymorphism of carbon • Electrical properties • Thermal transport • Optical properties • Mechanical behavior Chirality of CNTs Understanding carbon nanotubes Oulu, 1-2 October 2008

  8. Polymorphism of carbon • Electrical properties • Thermal transport • Optical properties • Mechanical behavior Chirality of CNTs Ph. Lambin et al., Carbon 40 (2002) 1635 Understanding carbon nanotubes Oulu, 1-2 October 2008

  9. Polymorphism of carbon • Electrical properties • Thermal transport • Optical properties • Mechanical behavior DOS vs. structure: Nanotubes 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 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.

  10. Polymorphism of carbon • Electrical properties • Thermal transport • Optical properties • Mechanical behavior DOS vs. structure: Nanotubes R. Saito, M. Fujita, G. Dresselhaus, M. S Dresselhaus, APL 60 (1992) 2204. 2D energy dispersion relations for p bands of graphite, withgoverlap integral: Periodic boundary condition for k. Condition for having metallic nanotube: Understanding carbon nanotubes Oulu, 1-2 October 2008

  11. Polymorphism of carbon • Electrical properties • Thermal transport • Optical properties • Mechanical behavior DOS vs. structure: Nanotubes CT White, et al., PRB, 47 (1993) 5485. V0 is the hopping matrix element for adjacent 2p orbitals of C atoms having distance of d0 Understanding carbon nanotubes Oulu, 1-2 October 2008

  12. Polymorphism of carbon • Electrical properties • Thermal transport • Optical properties • Mechanical behavior DOS vs. structure: Nanotubes tunnelling spectroscopy J.W.G. Wildöer, et al., Nature, 391 (1998) 59. T.W. Odom, et al., Nature 391 (1998) 62.

  13. Polymorphism of carbon • Electrical properties • Thermal transport • Optical properties • Mechanical behavior DOS vs. structure: Nanotubes 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: Uniaxial stress Twist A. Kleiner and S. Eggert, PRB, 63 (2001) 73408. Understanding carbon nanotubes Oulu, 1-2 October 2008

  14. Polymorphism of carbon • Electrical properties • Thermal transport • Optical properties • Mechanical behavior DOS vs. structure: Penta-Hexa-Heptites • 453 P.M. Ajayan, Nanotube course, Oulu, 2005. Understanding carbon nanotubes Oulu, 1-2 October 2008

  15. Polymorphism of carbon • Electrical properties • Thermal transport • Optical properties • Mechanical behavior FETs with individual CNTs A B C 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 Understanding carbon nanotubes Oulu, 1-2 October 2008 www.plato.ul.ie/academic/Vincent.Casey/PH4608SS2/MOSFET.ppt

  16. Polymorphism of carbon • Electrical properties • Thermal transport • Optical properties • Mechanical behavior FETs with individual CNTs Back-side gated structures on over-doped Si wafers SWCNTs acting as p-type channels Deformed MWCNTs acting as gate controlled channels R. Martel, T. Schmidt, H. R. Shea, T. Hertel, and Ph. Avouris, APL 73 (1998) 2447. IBM group Understanding carbon nanotubes Oulu, 1-2 October 2008

  17. Polymorphism of carbon • Electrical properties • Thermal transport • Optical properties • Mechanical behavior Doping of CNTs Changing the p-type character to n-type by annealing and/or K-doping V. Derycke, R.Martel, J.Appenzeller, P.Avouris, Nano. Lett. 1 (2001) 453. IBM group Understanding carbon nanotubes Oulu, 1-2 October 2008

  18. http://home.tudelft.nl/en/ • Polymorphism of carbon • Electrical properties • Thermal transport • Optical properties • Mechanical behavior Transistors, logic circuits, memory, oscillator A. Bachtold, P. Hadley, T. Nakanishi, C.Dekker, Science 294 (2001) 1317. Delft group

  19. Polymorphism of carbon • Electrical properties • Thermal transport • Optical properties • Mechanical behavior Doping of CNTs and logic gates G: -40 V; SD: 20 V  anneals to desorb oxygen A. Javey, Q. Wang, A. Urai, Y. Li, H.Dai, Nano. Lett. 2 (2002) 929. Stanford group

  20. Polymorphism of carbon • Electrical properties • Thermal transport • Optical properties • Mechanical behavior Field-emission from CNTs R ~1nm! Philip G. Collins and A. Zettl, PRB 55 (1997) 9391. Understanding carbon nanotubes Oulu, 1-2 October 2008

  21. Polymorphism of carbon • Electrical properties • Thermal transport • Optical properties • Mechanical behavior Field-emitter nanofibers 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. Understanding carbon nanotubes Oulu, 1-2 October 2008

  22. Polymorphism of carbon • Electrical properties • Thermal transport • Optical properties • Mechanical behavior 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.

  23. Polymorphism of carbon • Electrical properties • Thermal transport • Optical properties • Mechanical behavior 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). Conductance at a given gate at 0 K Tn(Ef) is the transmission probability of different sub-bands at the Fermi level. At finite temperatures: Understanding carbon nanotubes Oulu, 1-2 October 2008 http://arxiv.org/PS_cache/cond-mat/pdf/0512/0512609v1.pdf

  24. Polymorphism of carbon • Electrical properties • Thermal transport • Optical properties • Mechanical behavior Quantum conductancein nanotubes MWCNTs - single channel is present. Ballistic transport: • No heat dissipation in the wire but at the contacts (elastic scattering is allowed) • Quantized conductance (elastic scattering ruins it) S. Frank, P. Poncharal, Z. L. Wang, W. A. de Heer, Science, 280 (1998) 1744. Understanding carbon nanotubes Oulu, 1-2 October 2008

  25. Polymorphism of carbon • Electrical properties • Thermal transport • Optical properties • Mechanical behavior Inter-shell transport Only tunneling between adjacent shells! B. Bourlon et al., PRL 93 (2004) 176806. Understanding carbon nanotubes Oulu, 1-2 October 2008

  26. Polymorphism of carbon • Electrical properties • Thermal transport • Optical properties • Mechanical behavior Aharonov-Bohm oscillations Dependence of the phase of the electron wave on the magnetic field (vector potential). A. Bachtold, Nature 397 (1999) 673. Understanding carbon nanotubes Oulu, 1-2 October 2008

  27. Polymorphism of carbon • Electrical properties • Thermal transport • Optical properties • Mechanical behavior Magnetoresistance Understanding carbon nanotubes Oulu, 1-2 October 2008 K. Tsukagosh, Nature 401 (1999) 572.

  28. Polymorphism of carbon • Electrical properties • Thermal transport • Optical properties • Mechanical behavior Ballistic electrical and thermal transportin carbon nanotubes 264 K 2N is the number of channels 114 K 10,10 CNT d ~1.4 nm  120 phonon channels 200,200 CNT d ~27.5 nm  2400 phonon channels. E. Brown et al., APL 87 (2005) 23107. Understanding carbon nanotubes Oulu, 1-2 October 2008

  29. Polymorphism of carbon • Electrical properties • Thermal transport • Optical properties • Mechanical behavior Large current carrying capabilityBallistic carriers Extremely high current carrying capability. BQ Wei, R Vajtai, PM Ajayan, Appl. Phys. Lett. 71 (2001) 1172. 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.

  30. Polymorphism of carbon • Electrical properties • Thermal transport • Optical properties • Mechanical behavior Nanotubes as perfect crystalsThermal transport 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. Understanding carbon nanotubes Oulu, 1-2 October 2008

  31. Polymorphism of carbon • Electrical properties • Thermal transport • Optical properties • Mechanical behavior Optical properties Zhuangchun Wu, et al. Science 305, 1273 (2004)

  32. Polymorphism of carbon • Electrical properties • Thermal transport • Optical properties • Mechanical behavior Optical properties J. Maultzsch, et al., PRB 72, 205438 2005 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. Understanding carbon nanotubes Oulu, 1-2 October 2008

  33. Polymorphism of carbon • Electrical properties • Thermal transport • Optical properties • Mechanical behavior Optical properties 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).

  34. Polymorphism of carbon • Electrical properties • Thermal transport • Optical properties • Mechanical behavior Mechanical properties SWCNT bundles on alumina membrane support Understanding carbon nanotubes Oulu, 1-2 October 2008 J.P. Salvetat, et al., PRL 82 (1999) 944.

  35. Polymorphism of carbon • Electrical properties • Thermal transport • Optical properties • Mechanical behavior Mechanical properties Good fit is obtained with SWCNTs  E ~1TPa MWCNTs  E ~0.3 TPa Understanding carbon nanotubes Oulu, 1-2 October 2008 D. Garcia-Sanchez, et al., PRL 99 (2007) 085501

  36. Polymorphism of carbon • Electrical properties • Thermal transport • Optical properties • Mechanical behavior Mechanical properties 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. • Young’s modulus ~ 1TPa • Tensile strength 4-22 GPa • Low density 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. 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. Understanding carbon nanotubes Oulu, 1-2 October 2008

  37. Properties of CNTs: Summary SWCNTs Chirality dependent band gap up to ~1 eV Tunable conduction by external field (gate) or by chemicals (sensors) Large specific surface MWCNTs Structural integrity Easy applicability: handling and assembly http://www.samsung.coml http://www.montreal.fi http://www.nec.co.jp/press/en/0309/1701.html Understanding carbon nanotubes Oulu, 1-2 October 2008

  38. 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. Understanding carbon nanotubes Oulu, 1-2 October 2008

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