Skip to main content
SpringerLink
Log in

Phonon considerations in the reduction of thermal conductivity in phononic crystals

  • Published:
Applied Physics A Aims and scope Submit manuscript

Abstract

Periodic porous structures offer unique material solutions to thermoelectric applications. With recent interest in phonon band gap engineering, these periodic structures can result in reduction of the phonon thermal conductivity due to coherent destruction of phonon modes characteristic in phononic crystals. In this paper, we numerically study phonon transport in periodic porous silicon phononic crystal structures. We develop a model for the thermal conductivity of phononic crystal that accounts for both coherent and incoherent phonon effects, and show that the phonon thermal conductivity is reduced to less than 4% of the bulk value for Si at room temperature. This has substantial impact on thermoelectric applications, where the efficiency of thermoelectric materials is inversely proportional to the thermal conductivity.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. D.G. Cahill, W.K. Ford, K.E. Goodson, G.D. Mahan, A. Majumdar, H.J. Maris, R. Merlin, S.R. Phillpot, Nanoscale thermal transport. J. Appl. Phys. 93, 793–818 (2003)

    Article  ADS  Google Scholar 

  2. A.I. Boukai, Y. Bunimovich, J. Tahir-Kheli, J.-K. Yu, W.A. Goddard, J.R. Heath, Silicon nanowires as efficient thermoelectric materials. Nature 451, 168–171 (2008)

    Article  ADS  Google Scholar 

  3. G. Chen, Size and interface effects on thermal conductivity of superlattices and periodic thin-film structures. J. Heat Transf. 119, 220–229 (1997)

    Article  Google Scholar 

  4. M.S. Dresselhaus, G. Dresselhaus, X. Sun, Z. Zhang, S.B. Cronin, T. Koga, J.Y. Ying, G. Chen, The promise of low-dimensional thermoelectric materials. Microscale Thermophys. Eng. 3, 89–100 (1999)

    Article  Google Scholar 

  5. S. Riffat, X. Ma, Thermoelectrics: A review of present and potential applications. Appl. Therm. Eng. 23, 913–935 (2003)

    Article  Google Scholar 

  6. G. Benedetto, L. Boarino, R. Spangnolo, Evaluation of thermal conductivity of porous silicon layers by a photoacoustic method. Appl. Phys. A, Mater. Sci. Process., 64, 155–159 (1997)

    Article  ADS  Google Scholar 

  7. U. Bernini, R. Bernini, P. Maddalena, E. Massera, P. Rucco, Determination of thermal diffusivity of suspended porous silicon films by thermal lens techniques. Appl. Phys. A, Mater. Sci. Process., 81, 399–404 (2005)

    Article  ADS  Google Scholar 

  8. D. Song, G. Chen, Thermal conductivity of periodic microporous silicon films. Appl. Phys. Lett. 84, 687–689 (2004)

    Article  ADS  Google Scholar 

  9. P.E. Hopkins, P.M. Norris, L.M. Phinney, S.A. Policastro, R.G. Kelly, Thermal conductivity in nanoporous gold films during electron–phonon nonequilibrium. J. Nanomater. 2008, 418050 (2008). doi:10.1155/2008/418050

    Article  Google Scholar 

  10. R.H. Olsson III, I. El-Kady, Microfabricated phononic crystals devices and applications. Meas. Sci. Technol. 20, 012002 (2009)

    Article  ADS  Google Scholar 

  11. M.G. Holland, Analysis of lattice thermal conductivity. Phys. Rev. 132, 2461–2471 (1963)

    Article  ADS  Google Scholar 

  12. P.E. Hopkins, P.T. Rakich, R.H. Olsson III, I. El-Kady, L.M. Phinney, Origin of reduction in phonon thermal conductivity of microporous solids. Appl. Phys. Lett. 95, 161902 (2009)

    Article  ADS  Google Scholar 

  13. G. Nilsson, G. Nelin, Study of the homology between silicon and germanium by thermal-neutron spectrometry. Phys. Rev. B, Condens. Matter Mater. Phys. 6, 3777–3786 (1972)

    Article  ADS  Google Scholar 

  14. B.N. Brockhouse, Lattice vibrations in silicon and germanium. Phys. Rev. Lett. 2, 256–258 (1959)

    Article  ADS  Google Scholar 

  15. G. Chen, Nanoscale Energy Transport and Conversion: A Parallel Treatment of Electrons, Molecules, Phonons, and Photons (Oxford University Press, New York, 2005)

    Google Scholar 

  16. C.Y. Ho, R.W. Powell, P.E. Liley, Thermal conductivity of the elements. J. Phys. Chem. Ref. Data 1, 279–422 (1972)

    Article  Google Scholar 

  17. A.S. Henry, G. Chen, Spectral phonon transport properties of silicon based on molecular dynamics simulations and lattice dynamics. J. Comput. Theor. Nanosci. 5, 1–12 (2008)

    Article  Google Scholar 

  18. A.D. Mcconnell, K.E. Goodson, Thermal conduction in silicon micro- and nanostructures. Annu. Rev. Heat Transf. 14, 129–168 (2005)

    Google Scholar 

  19. A.D. Mcconnell, S. Uma, K.E. Goodson, Thermal conductivity of doped polysilicon layers. J. Microelectromech. Syst. 10, 360–369 (2001)

    Article  Google Scholar 

  20. D.E. Gray, American Institute of Physics Handbook (McGraw-Hill, New York, 1972)

    Google Scholar 

  21. A. Eucken, Die warmeleitfahigkeit keramischer feuerfester stoffe: Ihre berechnung aus der warmeleitfahigkeit der bestandteile (Thermal conductivity of ceramic refractory materials: calculations from thermal conductivity of constituents). Forsch. Geb. Ing.wes. (Ausg. B) 3/4, 353 (1932)

    Google Scholar 

  22. N. Mingo, Calculation of Si nanowire thermal conductivity using complete phonon dispersion relation. Phys. Rev. B, Condens. Matter Mater. Phys. 68, 113308 (2003)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Sandia National Laboratories, Albuquerque, NM, 87185-0346, USA

    P. E. Hopkins, L. M. Phinney, P. T. Rakich, R. H. Olsson III & I. El-Kady

  2. Electrical and Computer Engineering, University of New Mexico, Albuquerque, NM, 87131-0001, USA

    I. El-Kady

Authors
  1. P. E. Hopkins
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. L. M. Phinney
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. P. T. Rakich
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. R. H. Olsson III
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. I. El-Kady
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to P. E. Hopkins.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hopkins, P.E., Phinney, L.M., Rakich, P.T. et al. Phonon considerations in the reduction of thermal conductivity in phononic crystals. Appl. Phys. A 103, 575–579 (2011). https://doi.org/10.1007/s00339-010-6189-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00339-010-6189-8

Keywords

Search

Navigation