Journal of Electronic Materials

, Volume 48, Issue 4, pp 1909–1916 | Cite as

Enhanced Phonon Boundary Scattering at High Temperatures in Hierarchically Disordered Nanostructures

  • Dhritiman ChakrabortyEmail author
  • Laura de Sousa Oliveira
  • Neophytos Neophytou
Open Access
Topical Collection: International Conference on Thermoelectrics 2018
Part of the following topical collections:
  1. International Conference on Thermoelectrics 2018


Boundary scattering in hierarchically disordered nanomaterials is an effective way to reduce the thermal conductivity of thermoelectric materials and increase their performance. In this work, we investigate thermal transport in silicon-based nanostructured materials in the presence of nanocrystallinity and nanopores at the range of 300–900 K using a Monte Carlo simulation approach. The thermal conductivity in the presence of nanocrystallinity follows the same reduction trend as in the pristine material. We show, however, that the relative reduction is stronger with temperature in the presence of nanocrystallinity, a consequence of the wavevector-dependent (q-dependent) nature of phonon scattering on the domain boundaries. In particular, as the temperature is raised, the proportion of large wavevector phonons increases. Since these phonons are more susceptible to boundary scattering, we show that this q-dependent surface scattering could account for as much as a ∼ 40% reduction in the thermal conductivity of nanocrystalline Si. The introduction of nanopores with randomized positions magnifies this effect, which suggests that hierarchical nanostructuring is actually more effective at high temperatures than previously thought.


Thermal conductivity phonon transport boundary scattering thermoelectrics nanotechnology nanocrystalline silicon Monte Carlo simulations 



This work has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 Research and Innovation Programme (Grant Agreement No. 678763). The authors would also like to thank Dr. Patrizio Graziosi at the University of Warwick for useful discussions.


  1. 1.
    K. Biswas, J. He, Q. Zhang, G. Wang, C. Uher, V.P. Dravid, and M.G. Kanatzidis, Nat. Chem. 3, 160 (2011).CrossRefGoogle Scholar
  2. 2.
    K. Biswas, J. He, I.D. Blum, C.-I. Wu, T.P. Hogan, D.N. Seidman, V.P. Dravid, and M.G. Kanatzidis, Nature 489, 414 (2012).CrossRefGoogle Scholar
  3. 3.
    B.T. Kearney, B. Jugdersuren, D.R. Queen, T.H. Metcalf, J.C. Culbertson, P.A. Desario, R.M. Stroud, W. Nemeth, Q. Wang, and X. Liu, J. Phys.: Condens. Matter 30, 085301 (2018).Google Scholar
  4. 4.
    Z. Wang, J.E. Alaniz, W. Jang, J.E. Garay, and C. Dames, Nano Lett. 11, 2206 (2011).CrossRefGoogle Scholar
  5. 5.
    M.T. Dunham, B. Lorenzi, S.C. Andrews, A. Sood, M. Asheghi, D. Narducci, and K.E. Goodson, Appl. Phys. Lett. 109, 253104 (2016).CrossRefGoogle Scholar
  6. 6.
    S. Basu and M. Francoeur, Appl. Phys. Lett. 98, 113106 (2011).CrossRefGoogle Scholar
  7. 7.
    J.A.P. Taborda, M.M. Rojo, J. Maiz, N. Neophytou, and M.M. González, Nat. Sci. Rep. 6, 32778 (2016).CrossRefGoogle Scholar
  8. 8.
    G. Tan, F. Shi, S. Hao, L.D. Zhao, H. Chi, X. Zhang, C. Uher, C. Wolverton, V.P. Dravid, and M.G. Kanatzidis, Nat. Commun. 7, 12167 (2016).CrossRefGoogle Scholar
  9. 9.
    N. Neophytou, X. Zianni, H. Kosina, S. Frabboni, B. Lorenzi, and D. Narducci, Nanotechnology 24, 205402 (2013).CrossRefGoogle Scholar
  10. 10.
    N. Neophytou, X. Zianni, H. Kosina, S. Frabboni, B. Lorenzi, and D. Narducci, J. Electron. Mater. 43, 1896 (2014).CrossRefGoogle Scholar
  11. 11.
    B. Lorenzi, D. Narducci, R. Tonini, S. Frabboni, G.C. Gazzadi, G. Ottaviani, N. Neophytou, and X. Zianni, J. Electron. Mater. 43, 3812 (2014).CrossRefGoogle Scholar
  12. 12.
    S. Foster, M. Thesberg, and N. Neophytou, Phys. Rev. B 96, 195425 (2017).CrossRefGoogle Scholar
  13. 13.
    V. Vargiamidis, S. Foster, and N. Neophytou, Phys. Status Solidi A 215, 1700997 (2018).CrossRefGoogle Scholar
  14. 14.
    E. Pop, S. Sinha, and K.E. Goodson, J. Electron. Packag. 128, 102 (2006).CrossRefGoogle Scholar
  15. 15.
    D. Lacroix, K. Joulain, and D. Lemonnier, Phys. Rev. B 72, 064305 (2005).CrossRefGoogle Scholar
  16. 16.
    K. Kukita and Y. Kamakura, J. Appl. Phys. 114, 154312 (2013).CrossRefGoogle Scholar
  17. 17.
    E. Pop, R.W. Dutton, and K.E. Goodson, J. Appl. Phys. 96, 4998 (2004).CrossRefGoogle Scholar
  18. 18.
    S. Mazumdar and A. Majumdar, J. Heat Transfer 123, 749 (2001).CrossRefGoogle Scholar
  19. 19.
    S. Wolf, N. Neophytou, and H. Kosina, J. Appl. Phys. 115, 1 (2014).CrossRefGoogle Scholar
  20. 20.
    S. Wolf, N. Neophytou, Z. Stanojevic, and H. Kosina, J. Electron. Mater. 43, 3870 (2014).CrossRefGoogle Scholar
  21. 21.
    L.N. Maurer, Z. Aksamija, E.B. Ramayya, A.H. Davoody, and I. Knezevic, Appl. Phys. Lett. 106, 133108 (2015).CrossRefGoogle Scholar
  22. 22.
    D. Chakraborty, S. Foster, and N. Neophytou, Phys. Rev. B 98, 115435 (2018).CrossRefGoogle Scholar
  23. 23.
    Q. Hao, G. Chen, and M.S. Jeng, J. Appl. Phys. 106, 114321 (2009).Google Scholar
  24. 24.
    L. Weber and E. Gmelin, Appl. Phys. A 53, 136 (1991).CrossRefGoogle Scholar
  25. 25.
    S. Ju and X. Liang, J. Appl. Phys. 112, 064305 (2012).CrossRefGoogle Scholar
  26. 26.
    M.G. Holland, Phys. Rev. 132, 2461 (1963).CrossRefGoogle Scholar
  27. 27.
    C. Jeong, S. Datta, and M. Lundstrom, J. Appl. Phys. 111, 093708 (2012).CrossRefGoogle Scholar
  28. 28.
    R. Dettori, C. Melis, X. Cartoixà, R. Rurali, and L. Colombo, Phys. Rev. B 91, 054305 (2015).CrossRefGoogle Scholar
  29. 29.
    Z. Aksamija and I. Knezevic, Phys. Rev. B 90, 035419 (2014).CrossRefGoogle Scholar
  30. 30.
    H. Karamitaheri, N. Neophytou, and H. Kosina, J. Appl. Phys. 115, 024302 (2014).CrossRefGoogle Scholar
  31. 31.
    D.G. 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).CrossRefGoogle Scholar
  32. 32.
    K. Goodson, D.G. Cahill, and A. Majumdar, J. Heat Trans. 124, 223 (2002).CrossRefGoogle Scholar
  33. 33.
    M. Verdier, K. Termentzidis, and D. Lacroix, J. Phys.: IOP Conf. Ser. 785, 012009 (2017).Google Scholar
  34. 34.
    M. Maldovan, J. Appl. Phys. 110, 114310 (2011).CrossRefGoogle Scholar
  35. 35.
    M. Maldovan, Nature 503, 209 (2013).CrossRefGoogle Scholar
  36. 36.
    S. Uma, A.D. McConnell, M. Asheghi, K. Kurabayashi, and K.E. Goodson, Int. J. Thermophys. 22, 605 (2001).CrossRefGoogle Scholar

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© The Author(s) 2019

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.School of EngineeringUniversity of WarwickCoventryUK

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