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Vibrational Properties of Semiconductors, and Electron-Phonon Interactions

  • Peter Y. Yu
  • Manuel Cardona
Part of the Graduate Texts in Physics book series (GTP)

Summary

Although the atoms in semiconductors are not stationary, their motion is so slow compared to that of electrons that they were regarded as static in Chap. 2. In this chapter we have analyzed the motion of atoms in semiconductors in terms of simple harmonic oscillations. Instead of calculating from first principles the force constants for these quantized oscillators or phonons, we have studied models based on which these force constants can be deduced from experimental results. The usefulness of these models is judged by the minimum number of parameters they require to describe experimental phonon dispersion curves. The more successful models typically treat the interaction between the electrons and ions in a realistic manner. The shell model assumes that the valence electrons are localized in deformable shells surrounding the ions. Bond models regard the solid as a very large molecule in which atoms are connected by bonds. Interactions between atoms are expressed in terms of bond stretching and bond bending force constants. In covalent semiconductors charges are known to pile up in regions between adjacent atoms, giving rise to bond charges. So far, models based on bond charges have been most successful in fitting experimental results.

In this chapter we have also studied the different ways electrons can be affected by phonons, i. e., electron-phonon interactions. These interactions have a significant effect on the optical and transport properties of electrons in semiconductors. We showed how long-wavelength acoustic phonons can change the energy of electrons via their strain field. These interactions can be described in terms of deformation potentials. Optical phonons can be regarded as giving rise to “internal strain” and their interactions with electrons can likewise be described by optical-phonon deformation potentials. In polar semiconductors both long-wavelength acoustic and optical phonons can generate electric fields through the charges associated with the moving ions. These fields can interact very strongly with electrons, giving rise to piezoelectric electron-phonon interactions for acoustic phonons and the Fröhlich interaction for optical phonons. Electrons located at band extrema near or at zone boundaries can be scattered from one valley to another equivalent valley via intervalley electron-phonon interactions.

Keywords

Optical Phonon Acoustic Phonon Vibrational Property Deformation Potential Phonon Dispersion Curve 
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.

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Chapter 3

  1. 3.1
    D.N. Talwar, M. Vandevyver, K. Kunc, M. Zigone: Lattice dynamics of zinc chalcogenides under compression: Phonon dispersion, mode Grüneisen, and thermal expansion. Phys. Rev. B 24, 741–753 (1981) A. Debernardi, M. Cardona: Isotope effects on the lattice constant by perturbation theory: an ab initio calculation, Phys. Rev. B 54, 11305–11310 (1996)CrossRefGoogle Scholar
  2. 3.2
    H. Goldstein: Classical Mechanics (Addison-Wesley, Reading 1950) p. 329Google Scholar
  3. 3.3
    A. Debernardi: Phonon Linewidth in III–V semiconductors from density functional perturbation theory. Phys. Rev. B 57, 12847–12858 (1998)CrossRefGoogle Scholar
  4. 3.4
    G. Nilsson, G. Nelin: Study of the homology between silicon and germanium by thermal-neutron spectroscopy. Phys. Rev. B 6, 3777–3786 (1972)CrossRefGoogle Scholar
  5. 3.5
    W. Weber: Adiabatic bond charge model for the phonons in diamond, Si, Ge, and α-Sn. Phys. Rev. B 15, 4789–4803 (1977)CrossRefGoogle Scholar
  6. 3.6
    D. Strauch, B. Dorner: Phonon dispersion in GaAs. J. Phys.: Condens. Matter 2, 1457–1474 (1990)Google Scholar
  7. 3.7
    T. Ruf, J. Serrano, M. Cardona, P. Pavone, M. Pabst, M. Krisch, M. D'Astuto, T. Suski, I. Grzegory and M. Leszczynski: Phonon Dispersion curves in wurtzite-structure GaN determined by inelastic x-ray scattering. Phys. Rev. Lett. 86, 906–909 (2001)CrossRefGoogle Scholar
  8. 3.8
    R. Zallen, R.M. Martin, V. Natoli: Infrared Activity in Elemental Crystals. Phys. Rev. B49, 7032 (1994)CrossRefGoogle Scholar
  9. 3.9
    M. Born, K. Huang: Dynamical Theory of Crystal Lattices (Oxford Univ. Press, Oxford 1988, reprint of the original 1954 edition)Google Scholar
  10. 3.10
    M. Born: The space lattice theory of diamond. Ann. Physik 44, 605–642 (1914) in GermanCrossRefGoogle Scholar
  11. 3.11
    Y.C. Hsieh: The vibrational spectrum and the specific heat of germanium and silicon. J. Chem. Phys. 22, 306–311 (1954)CrossRefGoogle Scholar
  12. 3.12
    F. Herman: Lattice vibrational spectrum of germanium. J. Phys. Chem. Solids 8, 405–418 (1959)CrossRefGoogle Scholar
  13. 3.13
    W. Cochran: Theory of the lattice vibrations of germanium. Proc. R. Soc. (London) Ser.A 253, 260–276 (1959)CrossRefGoogle Scholar
  14. 3.14
    G. Dolling, R.A. Cowley: The thermodynamics and optical properties of germanium, silicon, diamond, and gallium arsenide, Proc. Phys. Soc. 88, 463–494 (1966)CrossRefGoogle Scholar
  15. 3.15
    J.C. Phillips: Covalent bonds in crystals. I. Elements of a structural theory. Phys. Rev. 166, 832–838 (1968); II. Partially ionic bonding. ibid. 168, 905–911 (1968)CrossRefGoogle Scholar
  16. 3.16
    M.J.P. Musgrave, J.A. Pople: A general valence force field for diamond. Proc. R. Soc. (London) Ser.A 268, 474–484 (1962)CrossRefGoogle Scholar
  17. 3.17
    M.A. Nusimovici, J.L. Birman: Lattice dynamics of Wurtzite: CdS. Phys. Rev. 156, 925–938 (1967)CrossRefGoogle Scholar
  18. 3.18
    A. Debernardi, N.M. Pyka, A. Göbel, T. Ruf, R. Lauck, S. Kramp, M. Cardona: Lattice Dynamics of Wurtzite CdS, Solid State Commun. 103, 297–301 (1997)CrossRefGoogle Scholar
  19. 3.19
    J.M. Rowe, R.M. Nicklow, D.L. Price, K. Zanio: Lattice dynamics of cadmium telluride. Phys. Rev. B 10, 671–675 (1974)CrossRefGoogle Scholar
  20. 3.20
    F. Widulle, S. Kramp, N.M. Pyka, A. Göbel, T. Ruf, A. Debernardi, R. Lauck, M. Cardona: The phonon dispersion of wurtzite CdSe. Physica B263–264, 448–451 (1998)Google Scholar
  21. 3.21
    G. Lang, K. Karch, M. Schmitt, P. Pavone, A.P. Mayer, R.K. Wehner, D. Strauch: Anharmonic lineshift and linewidth of the Raman mode in Ge and Si. Phys. Rev. B59, 6182 (1999); S. Shobhana, D. Vanderbilt: Anharmonic self-energies of phonons in silicon. Phys. Rev. B43, 4541 (1991)CrossRefGoogle Scholar
  22. 3.22
    P.N. Keating: Effect of invariance requirements on the elastic strain energy of crystals with application to the diamond structure. Phys. Rev. 145, 637–645 (1966)CrossRefGoogle Scholar
  23. 3.23
    R.M. Martin: Elastic properties of ZnS structure semiconductors. Phys. Rev. B 1, 4005–4011 (1970) R.M. Martin: Dielectric screening model for lattice vibrations of diamondstructure crystals. Phys. Rev. 186, 871 (1969)CrossRefGoogle Scholar
  24. 3.24
    J. Noolandi: Theory of crystal distortions in AIIBIVC2 V and A1BIIIC2 VI chalcopyrite semiconductors. Phys. Rev. B 10, 2490–2494 (1974)CrossRefGoogle Scholar
  25. 3.25
    S. Göttlicher, E. Wolfel: X-ray determination of the electron distribution in crystals (in German). Z. Elektrochem. 63, 891–901 (1959)Google Scholar
  26. 3.26
    L.W. Yang, P. Coppens: On the experimental electron distribution in silicon. Solid State Commun. 15, 1555–1559 (1974)CrossRefGoogle Scholar
  27. 3.27
    J. Chelikowsky, M.L. Cohen: Nonlocal pseudopotential calculations for the electronic structure of eleven diamond and zincblende semiconductors. Phys. Rev. B 14, 556–582 (1976)CrossRefGoogle Scholar
  28. 3.28
    P. Pavone, K. Karch, O. Schütt, W. Windl, D. Strauch, P. Gianozzi, S. Baroni: Ab initio lattice dynamics of diamond. Phys. Rev. B 48, 3156–3163 (1993) M. Schwoerer-Bohning, A.T. Macrauder, D.A. Arms: Phonon Dispersion in Diamond measured by inelastic X-ray scattering. Phys. Rev. Lett. 80, 5572–5575 (1998)CrossRefGoogle Scholar
  29. 3.29
    G.P. Srivastava: The Physics of Phonons (Hilger, Bristol 1990)Google Scholar
  30. 3.30
    A. Blacha, H. Presting, M. Cardona: Deformation potentials of k=0 states of tetrahedral semiconductors. Phys. Stat. Solidi b 126, 11–36 (1984)CrossRefGoogle Scholar
  31. 3.31
    D.D. Nolte, W. Walukiewicz, E.E. Haller: Critical criterion for axial modes of defects in as-grown n-type GaAs. Phys. Rev. B 36, 9374–9377 (1987)CrossRefGoogle Scholar
  32. 3.32
    M. Cardona, N.E. Christensen: Acoustic deformation potentials and heterostructure band offsets in semiconductors. Phys. Rev. B 35, 6182–6194 (1987)CrossRefGoogle Scholar
  33. 3.33
    E.O. Kane: Strain effects on optical critical-point structure in diamond-type crystals. Phys. Rev. 178, 1368–1398 (1969)CrossRefGoogle Scholar
  34. 3.34
    G.E. Pikus, G.L. Bir: Effect of deformation on the hole energy spectrum of germanium and silicon. Sov. Phys. — Solid State 1, 1502–1517 (1960)Google Scholar
  35. 3.35
    G.E. Pikus, G.L. Bir: Symmetry and Strain Induced Effects in Semiconductors (Wiley, New York 1974)Google Scholar
  36. 3.36
    E.L. Ivchenko and G.E. Pikus: Superlattices and other Heterostructures, (Springer, Heidelberg, 1997), p. 71CrossRefGoogle Scholar
  37. 3.37
    C. Herring, E. Vogt: Transport and deformation-potential theory for manyvalley semiconductors with anisotropic scattering. Phys. Rev. 101, 944–961 (1956)CrossRefGoogle Scholar
  38. 3.38
    H. Brooks: Theory of the electrical properties of germanium and silicon. Advances in Electronics and Electron Physics 7, 85–182 (Academic, New York 1955)Google Scholar
  39. 3.39
    J.F. Nye: Physical Properties of Crystals (Oxford Univ. Press, Oxford 1969)Google Scholar
  40. 3.40
    G.D. Mahan, J.J. Hopfield: Piezoelectric polaron effects in CdS. Phys. Rev. Lett. 12, 241–243 (1964)CrossRefGoogle Scholar
  41. 3.41
    K. Hübner: Piezoelectricity in zincblende-and wurtzite-type crystals. Phys. Stat. Solidi B 57, 627–634 (1973)CrossRefGoogle Scholar
  42. 3.42
    W.A. Harrison: Electronic Structure and the Properties of Solids: The Physics of the Chemical Bond (Dover, New York 1989) p. 224Google Scholar
  43. 3.43
    O. Madelung, M. Schulz, H. Weiss (eds.): Landolt-Börnstein, Series III, Vol. 22 (Semiconductors), Subvolume a. Intrinsic Properties of Group IV Elements, III–V, II–VI and I–VII Compounds (Springer, Berlin, Heidelberg 1987)Google Scholar
  44. 3.44
    S. Adachi: GaAs, AlAs, and AlxGa1−xAs: Materials parameters for use in research and device applications. J. Appl. Phys. 58, R1–29 (1985)CrossRefGoogle Scholar
  45. 3.45
    L. Kleinmann: Deformation potentials in Si: I. Uniaxial strain. Phys. Rev. 128, 2614–2621 (1962)CrossRefGoogle Scholar
  46. 3.46
    E. Anastassakis, M. Cardona: Internal strains and Raman-active optical phonons. Phys. Stat. Solidi B 104, 589–600 (1981)CrossRefGoogle Scholar
  47. 3.47
    W. Plötz, P. Vogl: Theory of optical-phonon deformation potentials in tetrahedral semiconductors. Phys. Rev. B 24, 2025–2037 (1981)CrossRefGoogle Scholar
  48. 3.48
    M. Cardona, M. Grimsditch, D. Olego: Theoretical and experimental determinations of Raman scattering cross sections in simple solids, in Light Scattering in Solids, ed. by J.L. Birman, H.Z. Cummins, K.K. Rebane (Plenum, New York 1979) pp. 249–256CrossRefGoogle Scholar
  49. 3.49
    S. Zollner, S. Gopalan, M. Cardona: Intervalley deformation potentials and scattering rates in zincblende semiconductors. Appl. Phys. Lett. 54, 614–616 (1989)CrossRefGoogle Scholar
  50. 3.50
    C. Carabatos, B. Prevot: Rigid ion model lattice dynamics of cuprite (Cu2O). Phys. Status Solid B 44, 701–712 (1971)CrossRefGoogle Scholar
  51. 3.51
    P. Molinàs-Mata, M. Cardona: Planar force-constant models and internal strain parameter of Ge and Si. Phys. Rev. B 43, 9799–9809 (1991)CrossRefGoogle Scholar
  52. 3.52
    P. Molinàs-Mata, A.J. Shields, M. Cardona: Phonons and internal stresses in IV–VI and III–V semiconductors: The planar bond-charge model. Phys. Rev. B 47, 1866–1875 (1993)CrossRefGoogle Scholar
  53. 3.53
    C.H. Xu, C.Z. Wang, C.T. Chan, K.M. Ho: Theory of the thermal expansion of Si and Diamond. Phys. Rev. B43, 5024–5027 (1991)CrossRefGoogle Scholar
  54. 3.54
    A. Debernardi and M. Cardona: Isotopic effects on the lattice constant in compound semiconductors by perturbation theory: an ab initio calculation. Phys. Rev. B54, 11305–11310 (1996)CrossRefGoogle Scholar

Lattice Dynamics

  1. Bilz, H., W. Kress: Phonon Dispersion Relations in Insulators, Springer Ser. Solid-State Sci., Vol. 10 (Springer, Berlin, Heidelberg 1979). This is touted as a “phonon atlas” by its authors. It presents a collection of phonon dispersion curves and densities of states for more than a hundred insulators, including all the well-known semiconductors.Google Scholar
  2. Born, M., K. Huang: Dynamical Theory of Crystal Lattices (Oxford Univ. Press, Oxford 1988), reprint of the original 1954 editionGoogle Scholar
  3. Horton G.K., Maradudin, A.A. (eds.): Dynamical Properties of Solids, Vols. 1–5 (North-Holland, Amsterdam 1974)Google Scholar
  4. Sinha S.K.: Phonons in semiconductors. CRC Critical Reviews in Solid State Sciences 3, 273–334 (1973)CrossRefGoogle Scholar
  5. Srivastava G.P.: The Physics of Phonons (Hilger, Bristol 1990)Google Scholar

Properties Related to Phonons

  1. Harrison W.A.: Electronic Structure and the Properties of Solids: The Physical of the Chemical Bond (Dover, New York, 1989)Google Scholar
  2. Kittel C.: Introduction to Solid State Physics, 7th edn. (Wiley, New York 1995) Chap. 4Google Scholar
  3. Madelung O.: Introduction to Solid-State Theory, Springer Ser. Solid-State Sci., Vol. 2 (Springer, Berlin, Heidelberg 1978)Google Scholar
  4. Madelung O., Schulz, M., Weiss, H. (eds.): Landolt-Börnstein, Series III, Vol. 22 (Semiconductors), Subvolume a) Intrinsic Properties of Group IV Elements, III–V, II–VI and I–VII Compounds (Springer, Berlin, Heidelberg 1987)Google Scholar
  5. Nye J.F.: Physical Properties of Crystals (Oxford Univ. Press, Oxford 1969)Google Scholar
  6. Pikus G.E., Bir, G.L.: Symmetry and Strain Induced Effects in Semiconductors (Wiley, New York 1974)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Peter Y. Yu
    • 1
  • Manuel Cardona
    • 2
  1. 1.Department of PhysicsUniversity of CaliforniaBerkeleyUSA
  2. 2.Max-Planck-Institut für FestkörperforschungStuttgartGermany

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