Journal of Applied Physics
Feedback | Help | Exit
Journal of Applied Physics
Search:
   
 
 
 
Previous Article
Brightness of carbon nanotube electron sources
The virtual source sizes of individual multiwalled carbon nanotube electron emitters were investigated with a point projection microscope. The average radius of the virtual source size was found to be...
Next Article
Theoretical study of electrical transport in a fullerene-doped semiconducting carbon nanotubes
Using a tight-binding model and the Landauer–Büttiker formalism, we have calculated the current–voltage characteristics of a semiconducting single-walled carbon nanotube and that of a f...

Theoretical phonon thermal conductivity of Si/Ge superlattice nanowires

J. Appl. Phys. 95, 682 (2004); doi:10.1063/1.1631734

Issue Date: 15 January 2004

You are not logged in to this journal. Log in

C. Dames and G. Chen
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
An incoherent particle model has been developed to calculate the phonon thermal conductivity of superlattice nanowires. This is an extension of the photon net-radiation method and Schuster–Schwarzschild approximation to dispersive acoustic phonons in a gray medium. By comparing the roughness and geometric variations of typical nanowires to the characteristic phonon wavelength (~1 nm at 300 K), diffuse scattering and incoherent three-dimensional dispersion are justified. An isotropic sine-type (Born–von Karman) dispersion is used, which requires only the sound velocity, atomic number density, and bulk conductivity to fully describe a material. A simple picture is also given in terms of Matthiessen's rule and three effective mean free paths. Agreement with available experimental data is poor at the smallest diameters, but good above 30 nm diameter. Compared to a conventional superlattice, calculations show that the additional sidewall scattering in a superlattice nanowire can reduce the thermal conductivity by a factor of 2 or more. ©2004 American Institute of Physics.
History: Received 24 February 2003; accepted 19 October 2003
Permalink: http://link.aip.org/link/?JAPIAU/95/682/1
BUY THIS ARTICLE   (US$24)
Download HTML Download Sectioned HTML Download PDF (191 kB) View Cart

KEYWORDS and PACS

Keywords
PACS
  • 66.70.+f
    Nonelectronic thermal conduction and heat-pulse propagation in solids including thermal waves
  • 63.22.+m
    Phonons or vibrational states in low-dimensional structures and nanoscale materials
  • 68.65.Cd
    Superlattices (structure and nonelectronic properties)
  • 68.65.La
    Quantum wires (structure and nonelectronic properties)
  • 81.05.Cy
    Elemental semiconductors: fabrication, treatment, testing and analysis
  • YEAR: 2004

RELATED DATABASES


To view database links for this article,
you need to log in.
To view database links for this article,
you need to log in.

PUBLICATION DATA

ISSN:
0021-8979 (print)   1089-7550 (online)
Publisher:
AIP is a member of CrossRef AIP

REFERENCES (47)
View in Separate Window/Tab
For access to fully linked references, you need to log in. For access to fully linked references, you need to Log in.
  1. Y. Wu, R. Fan, and P. Yang, Nano Lett. 2, 83 (2002).
  2. M. S. Gudiksen, L. J. Lauhon, J. Wang, D. C. Smith, and C. M. Lieber, Nature (London) 415, 617 (2002).
  3. M. T. Bjork et al., Nano Lett. 2, 87 (2002).
  4. Y. M. Lin and M. S. Dresselhaus, Phys. Rev. B 68, 075304 (2003).
  5. L. D. Hicks and M. S. Dresselhaus, Phys. Rev. B 47, 16631 (1993).
  6. L. D. Hicks, T. C. Harman, X. Sun, and M. S. Dresselhaus, Phys. Rev. B 53, 10493 (1996).
  7. R. Venkatasubramanian, E. Siivola, T. Colpitts, and B. O'Quinn, Nature (London) 413, 597 (2001).
  8. K. Schwab, E. A. Henriksen, J. M. Worlock, and M. L. Roukes, Nature (London) 404, 974 (2000).
  9. M. V. Simkin and G. D. Mahan, Phys. Rev. Lett. 85, 927 (2000).
  10. B. Yang and G. Chen, Phys. Rev. B 67, 195311 (2003).
  11. S. G. Volz and G. Chen, Appl. Phys. Lett. 75, 2056 (1999).
  12. J. Zou and A. Balandin, J. Appl. Phys. 89, 2932 (2001).
  13. S. Volz and D. Lemonnier, Phys. Low-Dimens. Semicond. Struct. 5/6, 91 (2000).
  14. X. Lu, W. Z. Shen, and J. H. Chu, J. Appl. Phys. 91, 1542 (2002).
  15. S. G. Walkauskas, D. A. Broido, K. Kempa, and T. L. Reinecke, J. Appl. Phys. 85, 2579 (1999).
  16. N. Mingo, Phys. Rev. B 68, 113308 (2003).
  17. D. Li, Y. Wu, P. Kim, L. Shi, P. Yang, and A. Majumdar, Appl. Phys. Lett. 83, 2934 (2003).
  18. D. Li, Y. Wu, R. Fan, P. Yang, and A. Majumdar, Appl. Phys. Lett. 83, 3188 (2003).
  19. L. J. Lauhon, M. S. Gudiksen, D. Wang, and C. M. Lieber, Nature (London) 420, 57 (2002).
  20. J. M. Ziman, Electrons and Phonons (Oxford University Press, New York, 1960).
  21. T. S. Tighe, J. M. Worlock, and M. L. Roukes, Appl. Phys. Lett. 70, 2687 (1997).
  22. W. Fon, W. C. Schwab, J. M. Worlock, and M. L. Roukes, Phys. Rev. B 66, 045302 (2002).
  23. M. G. Holland, Phys. Rev. 132, 2461 (1963).
  24. M. F. Modest, Radiative Heat Transfer (McGraw-Hill, New York, 1993).
  25. T. Klitsner et al., Phys. Rev. B 38, 7576 (1988).
  26. This is because we have defined the effective temperature using G. The temperature has also [G. Chen, Phys. Rev. B 57, 14958 (1998)] been defined using H. In that approach, G becomes a function of both T and q, while H only depends on T, and the correct form of Eq. (10) uses H rather than G.
  27. N. S. Snyder, Cryogenics 10, 89 (1970).
  28. R. J. Stoner and H. J. Maris, Phys. Rev. B 48, 16373 (1993).
  29. E. T. Swartz and R. O. Pohl, Rev. Mod. Phys. 61, 605 (1989).
  30. G. Chen, Phys. Rev. B 57, 14958 (1998).
  31. H. C. Hottel and J. D. Keller, Trans. ASME 55, 39 (1933).
  32. J. R. Howell, A Catalog of Radiation Heat Transfer Configuration Factors, 2nd ed., 2001, http://www.me.utexas.edu/howell/.
  33. J. B. Casimir, Physica (Amsterdam) 5, 495 (1938).
  34. Y.-M. Lin (private communication).
  35. CRC Handbook of Thermoelectrics, edited by D. M. Rowe (CRC Press, Cleveland, 1995).
  36. H. Bilz and W. Kress, Phonon Dispersion Relations in Insulators (Springer, New York, 1979).
  37. J. A. Carruthers, T. H. Geballe, H. M. Rosenberg, and J. M. Ziman, Proc. R. Soc. London, Ser. A 238, 502 (1957), some data available online at http://www.ioffe.rssi.ru/SVA/NSM/Semicond/Ge/thermal.html.
  38. C. J. Glassbrenner and G. A. Slack, Phys. Rev. 134, A1059 (1964), some data available online at http://www.ioffe.rssi.ru/SVA/NSM/Semicond/Si/thermal.html.
  39. B. Abeles, Phys. Rev. 131, 1906 (1963).
  40. G. Chen, J. Heat Transfer 121, 945 (1999).
  41. D. Cahill, W. K. Ford, K. E. Goodson, G. D. Mahan, A. Majumdar, H. J. Maris, R. Merlin, and S. R. Phillpot, J. Appl. Phys. 93, 793 (2003).
  42. R. Berman, E. L. Foster, and J. M. Ziman, Proc. R. Soc. London 231, 130 (1955).
  43. D. Li, Ph.D. thesis, U. Calif. Berkeley, 2002.
  44. P. G. Klemens, Phys. Rev. 119, 507 (1960).
  45. N. W. Ashcroft and N. D. Mermin, Solid State Physics (<<saunders College, Philadelphia, 1976).
  46. N. Savvides and H. J. Goldsmid, J. Phys. C 6, 1701 (1973).
  47. The exact value is (6/pi)–(48/pi3)[approximate]0.3618. If instead of the mean free path the relaxation time is assumed frequency-independent then the reduction is sqrt((1/2) - (3/pi[sup 2]))[approximate]0.4428.

CITING ARTICLES
For access to citing articles, you need to log in.
For access to citing articles, you need to Log in.


Copyright © American Institute of Physics