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Journal of Applied Physics / Volume 107 / Issue 8 / ARTICLES / Structural, Mechanical, Thermodynamic, and Optical Properties of Condensed Matter

J. Appl. Phys. 107, 083503 (2010); doi:10.1063/1.3340973 (14 pages)

Thermal conductivity of silicon bulk and nanowires: Effects of isotopic composition, phonon confinement, and surface roughness

M. Kazan1, G. Guisbiers2, S. Pereira2, M. R. Correia3, P. Masri4, A. Bruyant1, S. Volz5, and P. Royer1

1Laboratoire de Nanotechnologie et d’Instrumentation Optique, ICD, CNRS (FRE2848), Université de Technologie de Troyes, 10010 Troyes, France
2Department of Physics, CICECO, University of Aveiro, Aveiro 3810-193, Portugal
3Department of Physics, I3N, University of Aveiro, Aveiro 3810-193, Portugal
4Groupe d’Etude des Semiconducteurs, CNRS-UMR 5650, University of Montpellier II, Montpellier 34095, France
5Laboratoire d’Energie Moléculaire et Macroscopique, Combustion CNRS UPR 288, Ecole Centrale Paris, Grande Voie des Vignes, F-92295 Châtenay-Malabry Cedex, France

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(Received 24 March 2009; accepted 30 January 2010; published online 21 April 2010)

We present a rigorous analysis of the thermal conductivity of bulk silicon (Si) and Si nanowires (Si NWs) which takes into account the exact physical nature of the various acoustic and optical phonon mechanisms. Following the Callaway solution for the Boltzmann equation, where resistive and nonresistive phonon mechanisms are discriminated, we derived formalism for the lattice thermal conductivity that takes into account the phonon incidence angles. The phonon scattering processes are represented by frequency-dependent relaxation time. In addition to the commonly considered acoustic three-phonon processes, a detailed analysis of the role of the optical phonon decay into acoustic phonons is performed. This optical phonon decay mechanism is considered to act as acoustic phonon generation rate partially counteracting the acoustic phonon scattering rates. We have derived the analytical expression describing this physical mechanism which should be included in the general formalism as a correction to the resistive phonon-point-defects and phonon-boundary scattering expressions. The phonon-boundary scattering mechanism is taken as a function of the phonon frequency, incidence angles, and surface roughness. The importance of all the mechanisms we have involved in the model is demonstrated clearly with reference to reported data regarding the isotopic composition effect in bulk Si and Si NW samples. Namely, our model accounts for previously unexplained experimental results regarding (i) the isotope composition effect on the thermal conductivity of bulk silicon reported by Ruf et al. [Solid State Commun. 115, 243 (2000)] , (ii) the size effect on κ(T) of individual Si NWs reported by Li et al. [Appl. Phys. Lett. 83, 2934 (2003)] , and (iii) the dramatic decrease in the thermal conductivity for rough Si NWs reported by Hochbaum et al. [Nature (London) 451, 163 (2008)] .

© 2010 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. THEORIES
    1. General formalism for the lattice thermal conductivity
    2. Expressions for the various phonon relaxation times
  3. PHONON-POINT-DEFECTS SCATTERING
  4. PHONON-BOUNDARY SCATTERING
  5. NORMAL THREE-PHONON SCATTERING
  6. UMKLAPP THREE-PHONON SCATTERING
  7. DECAY OF OPTICAL PHONONS INTO ACOUSTIC PHONONS
  8. COMPARISION WITH EXPERIMENTS
    1. Isotopic composition effect on the thermal conductivity of bulk Si
    2. Thermal conductivity of individual silicon NWs
  9. SIZE EFFECT ON THE THERMAL CONDUCTIVITY OF Si NWs
  10. SURFACE ROUGHNESS EFFECT ON THE THERMAL CONDUCTIVITY OF Si NWs
  11. CONCLUSION

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KEYWORDS and PACS

Keywords

Boltzmann equation, elemental semiconductors, multiphoton processes, nanowires, phonon-defect interactions, silicon, surface roughness, thermal conductivity

PACS

  • 66.70.-f

    Nonelectronic thermal conduction and heat-pulse propagation in solids; thermal waves

  • 68.35.B-

    Structure of clean surfaces (and surface reconstruction)

  • 71.55.Cn

    Elemental semiconductors

  • 63.20.kp

    Phonon-defect interactions

ARTICLE DATA

Permalink
http://link.aip.org/link/doi/10.1063/1.3340973

PUBLICATION DATA

ISSN:

0021-8979 (print)  
1089-7550 (online)

Publisher:

$abstract.society.value is a Member of CrossRef American Institute of Physics

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