Elasticity and Phonons

  • Karl W. Böer
  • Udo W. PohlEmail author
Living reference work entry

Later version available View entry history



Springlike interatomic forces allow macroscopic elastic deformations of the semiconductor and coupled microscopic oscillations of each atom. The strain occurring as a response to external stress is conventionally described by elastic stiffness constants. When the strain exceeds the range in which the harmonic approximation of the interatomic potential is valid, higher-order stiffness constants are used. The symmetry of crystals strongly reduces the number of independent constants. Elastic properties can be measured by static deformations or kinetically by sound wave propagation.

Different modes of sound waves propagate with different velocities from which all stiffness constants can be determined. Each mode of such collective oscillations is equivalent to a harmonic oscillator which can be quantized as a phonon. Phonons are one of the most important quasiparticles in solids. They are responsible for all thermal properties and, when interacting with other quasiparticles, for the damping of their motion.


Bulk modulus Elastic compliance Elastic properties Elastic stiffness constants Elastic moduli Harmonic approximation Higher-order stiffness constants Hooke’s law Phonon Phonon density of states Phonon dispersion Shear modulus Sound wave propagation Strain Stress Stress-strain relation Young’s modulus 


  1. Adachi S (1985) GaAs, AlAs, and AlxGa1-xAs: material parameters for use in research and device applications. J Appl Phys 58:R1ADSCrossRefGoogle Scholar
  2. Adachi S (2005) Properties of group-IV, III-V and II-VI semiconductors. Wiley, ChichesterCrossRefGoogle Scholar
  3. Akhieser A (1939) On the absorption of sound in solids. J Phys (USSR) 1:277Google Scholar
  4. Anastassakis E, Cantarero A, Cardona M (1990) Piezo-Raman measurements and anharmonic parameters in silicon and diamond. Phys Rev B 41:7529ADSCrossRefGoogle Scholar
  5. Ayers JE (2007) Heteroepitaxy of semiconductors: theory, growth, and characterization. CRC, Boca RatonCrossRefGoogle Scholar
  6. Barker AS Jr, Sievers AJ (1975) Optical studies of the vibrational properties of disordered solids. Rev Mod Phys 47:S1CrossRefGoogle Scholar
  7. Bilz H, Kress W (1979) Phonon dispersion relations in insulators. Springer, BerlinCrossRefGoogle Scholar
  8. Brown FC (1967) The physics of solids. W.A. Benjamin, New YorkGoogle Scholar
  9. Brugger K (1964) Thermodynamic definition of higher order elastic coefficients. Phys Rev 133:1611ADSCrossRefGoogle Scholar
  10. Bruner LJ, Keyes RW (1961) Electronic effect in the elastic constants of Germanium. Phys Rev Lett 7:55ADSCrossRefGoogle Scholar
  11. Bührer W, Iqbal Z (1984) Neutron scattering studies of structural phase transitions. In: Iqbal Z, Owens FJ (eds) Vibrational spectroscopy of phase transitions. Academic Press, New YorkGoogle Scholar
  12. Cauchy A-L (1828) Lehrbuch der Algebraischen Analysis (trans: Huzler CLB, Textbook on algebraic analysis, in German). Bornträger, KönigsbergGoogle Scholar
  13. Colvard C (1987) Raman scattering characterization of quantum wells and superlattices. Proc SPIE 794:209Google Scholar
  14. Colvard C, Gant TA, Klein MV, Merlin R, Fisher R, Morkoç H, Gossard LA (1985) Folded acoustic and quantized optic phonons in (GaAl)As superlattices. Phys Rev B 31:2080ADSCrossRefGoogle Scholar
  15. Davydov AS (1964) The theory of molecular excitons. Sov Phys Usp (English trans) 7:145ADSCrossRefGoogle Scholar
  16. Davydov VY, Kitaev YE, Goncharuk IN, Smirnov AN, Graul J, Semchinova O, Uffmann D, Smirnov MB, Mirgorodsky AP, Evarestov RA (1998) Phonon dispersion and Raman scattering in hexagonal GaN and AlN. Phys Rev B 58:12899ADSCrossRefGoogle Scholar
  17. Deych LI, Yamilov A, Lisyansky AA (2000) Concept of local polaritons and optical properties of mixed polar crystals. Phys Rev B 62:6301ADSCrossRefGoogle Scholar
  18. Dolling G (1974) In: Norton GR, Maradudin AA (eds) Dynamic properties of solids. North Holland, AmsterdamGoogle Scholar
  19. Dorner B, Bokhenkov EL, Chaplot SL, Kalus J, Natkaniec I, Pawley GS, Schmelzer U, Sheka EF (1982) The 12 external and the 4 lowest internal phonon dispersion branches in d10-anthracene at 12 K. J Phys C Solid State Phys 15:2353ADSCrossRefGoogle Scholar
  20. Dunstan DJ (1997) Strain and strain relaxation in semiconductors. J Mater Sci Mater (in Electronics) 8:337Google Scholar
  21. Garber JA, Granato AV (1975) Theory of the temperature dependence of second-order elastic constants in cubic materials. Phys Rev B 11:3990; Fourth-order elastic constants and the temperature dependence of second-order elastic constants in cubic materials. Phys Rev B 11:3998ADSCrossRefGoogle Scholar
  22. Guyer RA (1966) Acoustic attenuation in dielectric solids. Phys Rev 148:789ADSCrossRefGoogle Scholar
  23. Hall JJ (1967) Electronic effects in the elastic constants of n-type silicon. Phys Rev 161:756ADSCrossRefGoogle Scholar
  24. Hiki Y (1981) Higher order elastic constants of solids. Ann Rev Mater Sci 11:51ADSCrossRefGoogle Scholar
  25. Hiki Y, Mukai K (1973) Ultrasonic three-phonon process in copper crystal. J Phys Soc Jpn 34:454ADSCrossRefGoogle Scholar
  26. Jasval SS (1975) Microscopic theory and deformation-dipole model of lattice dynamics. Phys Rev Lett 35:1600ADSCrossRefGoogle Scholar
  27. Jasval SS (1977) In: Balkanski M (ed) Lattice dynamics. Flammarion, ParisGoogle Scholar
  28. Joharapurkar D, Gerlich D, Breazealec MA (1992) Temperature dependence of elastic nonlinearities in single-crystal gallium arsenide. J Appl Phys 72:2202ADSCrossRefGoogle Scholar
  29. Joos G (1945) Lehrbuch der Theoretischen Physik (Textbook on theoretical physics, in German). Akademie Verlag Gesellschaft, LeipzigGoogle Scholar
  30. Keating PN (1966) Effect of invariance requirements on the elastic strain energy of crystals with application to the diamond structure. Phys Rev 145:637ADSCrossRefGoogle Scholar
  31. Klein MV (1986) Phonons in semiconductor superlattices. IEEE J Quantum Electron QE 22:1760ADSCrossRefGoogle Scholar
  32. Landau LD, Rumer G (1937) Absorption of sound in solids. Phys Z Sowjetunion 11:18zbMATHGoogle Scholar
  33. Lang JM Jr, Gupta YM (2011) Experimental determination of third-order elastic constants of diamond. Phys Rev Lett 106:125502ADSCrossRefGoogle Scholar
  34. Lucovsky G, Wong CK, Pollard WB (1983) Vibrational properties of glasses: intermediate range order. J Non Cryst Solid 59–60:839ADSCrossRefGoogle Scholar
  35. Ludwig WEW (1974) Theory of surface phonons in diamond- and zincblende-lattices. Jpn J Appl Phys 2(Supplement 2-2):879CrossRefGoogle Scholar
  36. Martienssen W, Warlimont H (2005) Handbook of condensed matter and materials data. Springer, Berlin/Heidelberg/New YorkCrossRefGoogle Scholar
  37. Martinez G (1980) Optical properties of semiconductors under pressure. In: Moss TS, Balkanski M (eds) Handbook on semiconductors, vol 2: Optical properties of solids. North Holland, AmsterdamGoogle Scholar
  38. Mason WP, Bateman TB (1964) Ultrasonic wave propagation in doped n-germanium and p-silicon. Phys Rev 134:A1387ADSCrossRefGoogle Scholar
  39. McSkimmin HJ, Andreatch P Jr (1964) Measurement of third-order moduli of silicon and germanium. J Appl Phys 35:3312ADSCrossRefGoogle Scholar
  40. McSkimmin HJ, Andreatch P Jr (1967) Third-order elastic moduli of gallium arsenide. J Appl Phys 38:2610ADSCrossRefGoogle Scholar
  41. Mitra SS, Massa ME (1982) Lattice vibrations in semiconductors. In: Moss TS, Paul W (eds) Handbook on semiconductors, vol 1: Band theory and transport properties. North Holland, AmsterdamGoogle Scholar
  42. Musgrave MJP (1970) Crystal acoustics. Holden-Day, San FranciscozbMATHGoogle Scholar
  43. Newman RC (1993) Vibrational mode spectroscopy of defects in III/V compounds. Semicond Semimet 38:117CrossRefGoogle Scholar
  44. Nye JF (1972) Physical properties of crystals – their representation by tensors and matrices. Oxford University Press, London. First published 1957, reprinted from corrected sheetszbMATHGoogle Scholar
  45. Patel C, Parker TJ, Jamshidi H, Sherman W (1984) Phonon frequencies in GaAs. Phys Stat Sol (B) 122:461ADSCrossRefGoogle Scholar
  46. Raja VS, Reddy PJ (1976) Measurement of third-order elastic constants of GaSb. Phys Lett A 56:215ADSCrossRefGoogle Scholar
  47. Rajagopal AK, Srinivasan R (1960) Lattice vibrations and specific heat of zinc blende. Z Phys 158:471ADSCrossRefGoogle Scholar
  48. Ruf T (1998) Phonon raman scattering in semiconductors, quantum wells and superlattices. Springer, BerlinzbMATHGoogle Scholar
  49. Ruf T, Serrano J, Cardona M, Pavone P, Pabst M, Krisch M, D’Astuto M, Suski T, Grzegory I, Leszczynski M (2001) Phonon dispersion curves in wurtzite-structure GaN determined by inelastic X-Ray scattering. Phys Rev Lett 86:906ADSCrossRefGoogle Scholar
  50. Truell R, Elbaum C, Crick BB (1969) Ultrasonic methods in solid state physics. Academic Press, New YorkGoogle Scholar
  51. Turbino R, Piseri L, Zerbi G (1972) Lattice dynamics and spectroscopic properties by a valence force potential of diamondlike crystals: Si, Ge, and Sn. J Chem Phys 56:1022ADSCrossRefGoogle Scholar
  52. Vurgaftman I, Meyer JR (2003) Band parameters for III-V nitrogen-containing semiconductors. J Appl Phys 94:3675ADSCrossRefGoogle Scholar
  53. Vurgaftman I, Meyer JR, Ram-Mohan LR (2001) Band parameters for III-V compound semiconductors and their alloys. J Appl Phys 89:5815ADSCrossRefGoogle Scholar
  54. Wallis RF (1994) Surface phonons: theoretical developments. Surf Sci 299/300:612ADSCrossRefGoogle Scholar
  55. Weber W (1977) Adiabatic bond charge model for the phonons in diamond, Si, Ge, and α-Sn. Phys Rev B 15:4789ADSCrossRefGoogle Scholar
  56. Weißmantel C, Hamann C (1979) Grundlagen der Festkörperphysik. Springer, Berlin/Heidelberg/New YorkCrossRefGoogle Scholar
  57. Woodruff TO, Ehrenreich H (1961) Absorption of sound in insulators. Phys Rev 123:1553ADSCrossRefGoogle Scholar
  58. Yoğurtçu YK, Miller AJ, Saunders GA (1981) Pressure dependence of elastic behaviour and force constants of GaP. J Phys Chem Sol 42:49ADSCrossRefGoogle Scholar
  59. Zener C (1947) A defense of the cauchy relations. Phys Rev 71:323ADSCrossRefGoogle Scholar

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Authors and Affiliations

  1. 1.NaplesUSA
  2. 2.Institut für Festkörperphysik, EW5-1Technische Universität BerlinBerlinGermany

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