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Theories of Phonon Transport in Bulk and Nanostructed Solids

  • G. P. SrivastavaEmail author
Chapter
Part of the Topics in Applied Physics book series (TAP, volume 128)

Abstract

In this chapter we outline the theories that are usually employed for phonon transport in solids. In particular, we provide a detailed description of the essential steps in deriving the lattice thermal conductivity expressions within the single-mode relaxation-time approximation. Explicit expression for various phonon scattering rates, in bulk and low-dimensional solids, have been provided. Numerical evaluation of scattering rates and the conductivity expressions is detailed using both Debye’s isotropic continuum scheme and a realistic Brillouin zone summation technique based upon the application of special phonon wavevectors scheme. Results of the conductivity are presented for selected bulk, superlattice, and nanostructed systems. Based on such results, we briefly discuss the concept of phonon engineering of high-efficiency thermoelectric materials.

Keywords

Phonon Mode Lattice Thermal Conductivity Phonon Dispersion Curve Phonon Transport Phonon Dispersion Relation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

I wish to thank my past and present Ph. D. students and postdoctoral fellows for their contribution towards the development of the subject matter presented here. Special thanks to Ceyda Yelgel for careful reading of the manuscript. This work has been supported by EPSRC (UK) through the grant number EP/H046690.

References

  1. 1.
    Kubo R (1957) J Phys Soc Jpn 12:570MathSciNetADSCrossRefGoogle Scholar
  2. 2.
    Ziman JM (1960) Electrons and phonons. Clarendon, OxfordzbMATHGoogle Scholar
  3. 3.
    Srivastava GP (1990) The physics of phonons. Adam Hilger, Bristol (now Taylor and Francis Group)Google Scholar
  4. 4.
    McGaughey AJH, Kaviany M (2004) Phys Rev B 69:094303ADSCrossRefGoogle Scholar
  5. 5.
    Kaburaki H, Yip S, Kimizuka H (2007) J Appl Phys 102:043514ADSCrossRefGoogle Scholar
  6. 6.
    Huang B-L, Kaviany M (2008) Phys Rev B 77:125209ADSCrossRefGoogle Scholar
  7. 7.
    Ziman JM (1969) Elements of advanced quantum thoery. Cambridge University Press, CambridgeGoogle Scholar
  8. 8.
    Guyer RA, Krumhansl JA (1966) Phys Rev 148:766ADSCrossRefGoogle Scholar
  9. 9.
    Benin D (1970) Phys Rev B 1:2777ADSCrossRefGoogle Scholar
  10. 10.
    Srivastava GP (1976) J Phys C Solid State Phys 9:3037ADSCrossRefGoogle Scholar
  11. 11.
    Srivastava GP (1976) J Phys C Solid State Phys 10:1843ADSCrossRefGoogle Scholar
  12. 12.
    Arthurs AM (1970) Complementary variational principles. Clarendon, OxfordzbMATHGoogle Scholar
  13. 13.
    Carruthers P (1961) Rev Mod Phys 33:92MathSciNetADSCrossRefzbMATHGoogle Scholar
  14. 14.
    Callaway J (1959) Phys Rev 113:1046ADSCrossRefzbMATHGoogle Scholar
  15. 15.
    Srivastava GP (1976) Phil Mag 34:795ADSCrossRefGoogle Scholar
  16. 16.
    Weber W (1977) Phys Rev B 15:4789ADSCrossRefGoogle Scholar
  17. 17.
    Tütüncü HM, Srivastava GP (1996) Phys Rev B 53:15675ADSCrossRefGoogle Scholar
  18. 18.
    Hepplestone SP, Srivastava GP (2008) Phys Rev Lett 101:105502ADSCrossRefGoogle Scholar
  19. 19.
    Baroni S, de Gironcoli S, Dal Corso A, Giannozzi P (2001) Rev Mod Phys 73:515ADSCrossRefGoogle Scholar
  20. 20.
    Dolling G (1963) Inelastic scattering of neutrons in solids and liquids, vol I. IAEA, Vienna, p 37Google Scholar
  21. 21.
    Nilsson G, Nelin G (1972) Phys Rev B 6:3777ADSCrossRefGoogle Scholar
  22. 22.
    Ezzahri Y, Grauby S, Rampnoux JM, Michel H, Pernot G, Claeys W, Dilhaire S, Rossignol C, Zeng G, Shakouri A (2007) Phys Rev B 75:195309ADSCrossRefGoogle Scholar
  23. 23.
    Hepplestone SP, Srivastava GP (2006) Nanotechnology 17:3288ADSCrossRefGoogle Scholar
  24. 24.
    Chadi DJ, Cohen ML (1973) Phys Rev B 8:5747MathSciNetADSCrossRefGoogle Scholar
  25. 25.
    Monkhorst HJ, Pack JD (1976) Phys Rev B 13:5189MathSciNetADSCrossRefGoogle Scholar
  26. 26.
    Holland MG (1964) Phys Rev 134:A471ADSCrossRefGoogle Scholar
  27. 27.
    Kim W, Majumdar A (2006) J Appl Phys 99:084306ADSCrossRefGoogle Scholar
  28. 28.
    Gillet J-N, Chalopin Y, Volz S (2009) J Heat Transfer 131:043206CrossRefGoogle Scholar
  29. 29.
    Hepplestone SP, Srivastava GP (2010) Phys Rev B 82:144303ADSCrossRefGoogle Scholar
  30. 30.
    Thomas IO, Srivastava GP (2012) Phys Rev B 86:045205ADSCrossRefGoogle Scholar
  31. 31.
    Parrott JE (1971) Phys Status Solid B 48:K159ADSCrossRefGoogle Scholar
  32. 32.
    Ren SY, Dow JD (1982) Phys Rev B 25:3750ADSCrossRefGoogle Scholar
  33. 33.
    Ziman JM (1956) Phil Mag 1:191ADSCrossRefGoogle Scholar
  34. 34.
    Ziman JM (1957) Phil Mag 2:292ADSCrossRefGoogle Scholar
  35. 35.
    Parrott JE (1979) Rev Int Hautes Tem Refract 16:393Google Scholar
  36. 36.
    Holland MG, Neuringer LJ (1962) In: Proc. Int. congr. on the physics of semiconductors, exeter, Institute of Physics, London, p 475Google Scholar
  37. 37.
    Geballle TH, Hull GW (1958) Phys Rev 110:773ADSCrossRefGoogle Scholar
  38. 38.
    Srivastava GP (1980) J Phys Chem Solid 41:357ADSCrossRefGoogle Scholar
  39. 39.
    Fon W, Schwab KC, Worlock JM, Roukes ML (2002) Phys Rev B 66:045302ADSCrossRefGoogle Scholar
  40. 40.
    Barman S, Srivastava GP (2006) Phys Rev B 73:205308ADSCrossRefGoogle Scholar
  41. 41.
    Walkauskas SG, Broido DA, Kempa K, Reinecke TL (1999) J Appl Phys 85:2579ADSCrossRefGoogle Scholar
  42. 42.
    Volz SG, Chen G (1999) Appl Phys Lett 75:2056ADSCrossRefGoogle Scholar
  43. 43.
    Murphy PG, Moore JE (2007) Phys Rev B 76:155313ADSCrossRefGoogle Scholar
  44. 44.
    Li D, Wu Y, Kim P, Shi L, Yang P, Majumdar A (2003) Appl Phys Lett 83:2934ADSCrossRefGoogle Scholar
  45. 45.
    Srivastava GP (2009) Mat Res Soc Symp Proc 1172:T08-07CrossRefGoogle Scholar
  46. 46.
    Lee SM, Cahill DG, Vekatasubramanian R (1997) Appl Phys Lett 70:2957ADSCrossRefGoogle Scholar
  47. 47.
    Cahill DG, Ford WK, Goodson KE, Mahan GD, Majumdar A, Maris HJ, Merlin R, Phillpot SR (2003) J Appl Phys 93:793ADSCrossRefGoogle Scholar
  48. 48.
    Capinski WS, Maris HJ, Ruf T, Cardona M, Ploog K, Katzer DS (1999) Phys Rev B 59:8105ADSCrossRefGoogle Scholar
  49. 49.
    Mo Y-W, Savage DE, Swartzentruber BS, Lagally MG (1990) Phys Rev Lett. 65:1020; Ma T, Tu H, Shao B, Liu A, Hu G (2006) Mater Sci Semicond Process 9:49Google Scholar
  50. 50.
    Dismukes JP, et al (1964) J Appl Phys 35:2899; Heddins HR, Parrott JE (1976) J Phys C Solid State Phys 9:1263Google Scholar
  51. 51.
    Goldsmid HJ (1964) Thermoelectric refrigeration. Plenum, New York; Goldsmid HJ (1986) Electronic refrigeration. Pion, LondonGoogle Scholar
  52. 52.
    Venkatasubramanium R, Siivola E, Colpitts T, O’Quinn B (2001) Nature 413:697CrossRefGoogle Scholar
  53. 53.
    Majumdar A (2004) Science 303:777CrossRefGoogle Scholar
  54. 54.
    Minnich AJ, Dresselhaus MS, Ren ZF, Chen G (2009) Energy Environ Sci 2:466CrossRefGoogle Scholar
  55. 55.
    Hsu KF, Loo S, Guo F, Chen W, Dyck JS, Uher C, Hogan T, Polychroniadis EK, Kanatzidis MG (2004) Science 303:818ADSCrossRefGoogle Scholar
  56. 56.
    McKilvey JP (1966) Solid state and semiconductor physics (International edition). Harper & Row, New York-Evanston-London, and John Weatherhill, TokyoGoogle Scholar
  57. 57.
    Drabble JR, Goldsmit HJ (1961) Thermal conduction in semiconductors. Pergamon Press, Oxford, pp 115–117zbMATHGoogle Scholar
  58. 58.
    Hicks LD, Dresselhaus MS (1993) Phys Rev B 47:12727ADSCrossRefGoogle Scholar
  59. 59.
    Price PJ (1955) Phil Mag 46:1252zbMATHGoogle Scholar
  60. 60.
    Vining CB (1991) J Appl Phys 69:331ADSCrossRefGoogle Scholar
  61. 61.
    Minnich AJ, Lee H, Wang XW, Joshi G, Dresselhaus MS, Ren ZF, Chen G, Vashaee D (2009) Phys Rev B 80:155327ADSCrossRefGoogle Scholar
  62. 62.
    Yelgel ŎC, Srivastava GP (2012) Phys Rev B 85:125207ADSCrossRefGoogle Scholar
  63. 63.
    Hochbaum A, Chen R, Deigado RD, Liang W, Garnett EC, Najarian M, Majumdar A, Yang P (2008) Nature 451:163ADSCrossRefGoogle Scholar
  64. 64.
    Goyal V, Teweldebrhan D, Balandin AA (2010) Appl Phys Lett 97:133117ADSCrossRefGoogle Scholar
  65. 65.
    Zahid F, Lake R (2010) Appl Phys Lett 97:212102ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.School of PhysicsUniversity of ExeterExeterUK

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