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Phonon populations and electrical power dissipation in carbon nanotube transistors

Nature Nanotechnology volume 4, pages 320–324 (2009)Cite this article

Abstract

Carbon nanotubes and graphene are candidate materials for nanoscale electronic devices1,2. Both materials show weak acoustic phonon scattering and long mean free paths for low-energy charge carriers. However, high-energy carriers couple strongly to optical phonons1,3, which leads to current saturation4,5,6 and the generation of hot phonons7. A non-equilibrium phonon distribution has been invoked to explain the negative differential conductance observed in suspended metallic nanotubes8, while Raman studies have shown the electrical generation of hot G-phonons in metallic nanotubes9,10. Here, we present a complete picture of the phonon distribution in a functioning nanotube transistor including the G and the radial breathing modes, the Raman-inactive zone boundary K mode and the intermediate-frequency mode populated by anharmonic decay. The effective temperatures of the high- and intermediate-frequency phonons are considerably higher than those of acoustic phonons, indicating a phonon-decay bottleneck. Most importantly, inclusion of scattering by substrate polar phonons is needed to fully account for the observed electronic transport behaviour.

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Figure 1: Non-equilibrium temperature of G, RBM and K phonons in a carbon nanotube as a function of electrical power.
Figure 2: Raman shifts and spectral widths of carbon nanotube G-band phonons reveal the phonon temperatures of their decay products.
Figure 3: Decay pathways of electrically excited phonon populations and electronic transport characteristics of a carbon nanotube on a substrate.

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References

  1. Avouris, P., Chen, Z. & Perebeinos, V. Carbon-based electronics. Nature Nanotech. 2, 605–615 (2007).

    Article  CAS  Google Scholar 

  2. Geim, A. K. & Novoselov, K. S. The rise of graphene. Nature Mater. 6, 183–191 (2007).

    Article  CAS  Google Scholar 

  3. Avouris, P., Freitag, M. & Perebeinos, V. Carbon-nanotube photonics and optoelectronics. Nature Photon. 2, 341–350 (2008).

    Article  CAS  Google Scholar 

  4. Yao, Z., Kane, C. L. & Dekker, C. High-field electrical transport in single-wall carbon nanotubes. Phys. Rev. Lett. 84, 2941–2944 (2000).

    Article  CAS  Google Scholar 

  5. Javey, A. et al. High-field quasiballistic transport in short carbon nanotubes. Phys. Rev. Lett. 92, 106804 (2004).

    Article  Google Scholar 

  6. Park, J. Y. et al. Electron–phonon scattering in metallic single-walled carbon nanotubes. Nano Lett. 4, 517–520 (2004).

    Article  CAS  Google Scholar 

  7. Lazzeri, M., Piscanec, S., Mauri, F., Ferrari, A. C. & Robertson, J. Electron transport and hot phonons in carbon nanotubes. Phys. Rev. Lett. 95, 236802 (2005).

    Article  Google Scholar 

  8. Pop, E. et al. Negative differential conductance and hot phonons in suspended nanotube molecular wires. Phys. Rev. Lett. 95, 155505 (2005).

    Article  Google Scholar 

  9. Bushmaker, A. W., Deshpande, V. V., Bockrath, M. W. & Cronin, S. B. Direct observation of mode selective electron–phonon coupling in suspended carbon nanotubes. Nano Lett. 7, 3618–3622 (2007).

    Article  CAS  Google Scholar 

  10. Oron-Carl, M. & Krupke, R. Raman spectroscopic evidence for hot-phonon generation in electrically biased carbon nanotubes. Phys. Rev. Lett. 100, 127401 (2008).

    Article  CAS  Google Scholar 

  11. Reich, S., Thomsen, C. & Maultzsch, J., eds, Carbon Nanotubes: Basic Concepts and Physical Properties (Wiley, 2004).

    Google Scholar 

  12. Dresselhaus, M. S., Dresselhaus, G., Saito, R. & Jorio, A. Raman spectroscopy of carbon nanotubes. Phys. Rep. 409, 47–99 (2005).

    Article  Google Scholar 

  13. Jorio, A., Dresselhaus, M. S. & Dresselhaus, G., eds, Carbon Nanotubes: Advanced Topics in Synthesis, Structure, Properties and Applications (Springer, 2008).

    Book  Google Scholar 

  14. Jorio, A. et al. Structural (n, m) determination of isolated single-wall carbon nanotubes by resonant Raman scattering. Phys. Rev. Lett. 86, 1118–1121 (2001).

    Article  CAS  Google Scholar 

  15. Jorio, A. et al. Joint density of electronic states for one isolated single-wall carbon nanotube studied by resonant Raman scattering. Phys. Rev. B 63, 245416 (2001).

    Article  Google Scholar 

  16. Fantini, C. et al. Optical transition energies for carbon nanotubes from resonant Raman spectroscopy: Environment and temperature effects. Phys. Rev. Lett. 93, 147406 (2004).

    Article  CAS  Google Scholar 

  17. Perebeinos, V., Tersoff, J. & Avouris, P. Effect of exciton–phonon coupling in the calculated optical absorption of carbon nanotubes. Phys. Rev. Lett. 94, 27402 (2005).

    Article  Google Scholar 

  18. Hertel, T., Perebeinos, V., Crochet, J., Arnold, K., Kappes, M. & Avouris, Ph. Intersubband decay of 1-d exciton resonances in carbon nanotubes. Nano Lett. 8, 87–91 (2008).

    Article  CAS  Google Scholar 

  19. Bonini, N., Lazzeri, M., Marzari, N. & Mauri, F. Phonon anharmonicities in graphite and graphene. Phys. Rev. Lett. 99, 176802 (2007).

    Article  Google Scholar 

  20. Compaan, A. & Trodahl, H. J. Resonance Raman scattering in Si at elevated temperatures. Phys. Rev. B 29, 793–801 (1984).

    Article  CAS  Google Scholar 

  21. Capaz, R. B., Spataru, C. D., Tangney, P., Cohen, M. L. & Louie, S. G. Temperature dependence of the band gap of semiconducting carbon nanotubes. Phys. Rev. Lett. 94, 036801 (2005).

    Article  Google Scholar 

  22. Cronin, S. B. et al. Temperature dependence of the optical transition energies of carbon nanotubes: The role of electron–phonon coupling and thermal expansion. Phys. Rev. Lett. 96, 127403 (2006).

    Article  CAS  Google Scholar 

  23. Perebeinos, V., Tersoff, J. & Avouris, P. Scaling of excitons in carbon nanotubes. Phys. Rev. Lett. 92, 257402 (2004).

    Article  Google Scholar 

  24. Zhang, Y., Xie, L., Zhang, J., Wu, Z. & Liu, Z. Temperature coefficients of Raman frequency of individual single-walled carbon nanotubes. J. Phys. Chem. C 111, 14031–14034 (2007).

    Article  CAS  Google Scholar 

  25. Pop, E., Mann, D. A., Goodson, K. E. & Dai, H. Electrical and thermal transport in metallic single-wall carbon nanotubes on insulating substrates. J. Appl. Phys. 101, 093710 (2007).

    Article  Google Scholar 

  26. Wang, S. Q. & Mahan, G. D. Electron scattering from surface excitations. Phys. Rev. B 6, 4517–4524 (1972).

    Article  CAS  Google Scholar 

  27. Perebeinos, V., Tersoff, J. & Avouris, P. Electron–phonon interaction and transport in semiconducting carbon nanotubes. Phys. Rev. Lett. 94, 086802 (2005).

    Google Scholar 

  28. Fischetti, M. V., Neumayer, D. A. & Cartier, E. A. Effective electron mobility in Si inversion layers in metal-oxide–semiconductor systems with a high-kappa insulator: The role of remote phonon scattering. J. Appl. Phys. 90, 4587–4608 (2001).

    Article  CAS  Google Scholar 

  29. Petrov, A. G. & Rotkin, S. V. Energy relaxation of hot carriers in single-wall carbon nanotubes by surface optical phonons of the substrate. JETP Lett. 84, 156–160 (2006).

    Article  CAS  Google Scholar 

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Authors and Affiliations

  1. IBM Thomas J. Watson Research Center, Yorktown Heights, New York, 10598, USA

    Mathias Steiner, Marcus Freitag, Vasili Perebeinos, James C. Tsang, Joshua P. Small, Megumi Kinoshita & Phaedon Avouris

  2. Department of Chemistry, Duke University, North Carolina, 27708, USA

    Dongning Yuan & Jie Liu

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Correspondence to Phaedon Avouris.

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Steiner, M., Freitag, M., Perebeinos, V. et al. Phonon populations and electrical power dissipation in carbon nanotube transistors. Nature Nanotech 4, 320–324 (2009). https://doi.org/10.1038/nnano.2009.22

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