Skip to main content
SpringerLink
Log in

Charge Transport and Scattering Processes in the Many-Valley Model

  • Chapter
Semiconductor Physics

Part of the book series: Springer Study Edition ((SSE))

  • 452 Accesses

Abstract

In Chap.2d, Figs.2.25 and 2.26, we have seen that the conduction bands of silicon and germanium near the band edges have constant energy surfaces which are either 8 half-ellipsoids or 6 ellipsoids of revolution; these correspond to 4 and 6 energy valleys, respectively. In these and many other semiconductors the “many-valley-model” of the energy bands has proved to be a fruitful concept for a description of the observed anisotropy of electrical and optical phenomena. Cyclotron resonance (Chap.11 k) provides a direct experimental determination of the effective masses in each valley for any crystallographic direction.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 29.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. See e.g. C. Kittel: Introduction to Solid State Physics, chap. 4. New York: J. Wiley and Sons. 1965.

    Google Scholar 

  2. C. Herring, Bell Syst. Tech. J. 34 (1955) 237.

    Article  Google Scholar 

  3. C. Herring and E. Vogt, Phys. Rev. 101 (1956) 944. Err.: ibid.105 (1957) 1933.

    Google Scholar 

  4. C. Herring and E. Vogt, Phys. Rev. 101 (1956) 944. Err.: ibid.105 (1957) 1933.

    Google Scholar 

  5. S. H. Koenig: Proc. Int. School of Physics Vol.XXII, p. 515. New York: Acad. Press. 1961.

    Google Scholar 

  6. J. E. Smith,Jr., Appl. Phys. Lett. 12 (1968) 233.

    Google Scholar 

  7. E. G. S. Paige, Proc. in Semicond. 8 (1960) 158, Fig. 36.

    Google Scholar 

  8. H. Heinrich and M. Kriechbaum, J. Phys. Chem. Solids 31 (1970) 927; K. Bulthuis, Philips Res. Repts. 23 (1968) 25.

    Google Scholar 

  9. C. Herring and E. Vogt, Phys. Rev. 101 (1956) 944. Err.: ibid.105 (1957) 1933.

    Google Scholar 

  10. M. Shibuya, Phys. Rev. 95 (1954) 1385; Physica 20 (1954) 971. A. C. Beer: Solid State Physics, Suppl. 4, p. 228. (F. Seitz and D. Turnbull, eds.). New York: Acad. Press. 1963.

    Google Scholar 

  11. E. G. S. Paige: Progress in Semiconductors, Vol.8, p. 22. (A. F. Gibson and R. E. Burgess, eds.). London: Temple Press. 1960.

    Google Scholar 

  12. E. G. S. Paige: Progress in Semiconductors, Vol.8, p. 22. (A. F. Gibson and R. E. Burgess, eds.). London: Temple Press. 1960.

    Google Scholar 

  13. G. L. Pearson and H. Suhl, Phys. Rev. 83 (1951) 768.

    Article  ADS  Google Scholar 

  14. G. L. Pearson and C. Herring, Physica 20 (1954) 975.

    Article  ADS  Google Scholar 

  15. A. C. Beer: Solid State Physics (F. Seitz and D. Turnbull, eds.) Suppl. 4, Table VII, p. 228. New York: Acad. Press. 1963.

    Google Scholar 

  16. F. Seitz, Phys. Rev. 79 (1950) 372.

    Article  ADS  MATH  Google Scholar 

  17. H. Miyazawa, Proc. Int. Conf. Phys. Semic. Exeter (1962) p. 636. London: The Institute of Physics and The Physical Society. 1962.

    Google Scholar 

  18. A. C. Beer: Solid State Physics (F. Seitz and D. Turnbull, eds.) Suppl. 4, Table VII, p. 228. New York: Acad. Press. 1963.

    Google Scholar 

  19. F. Seitz, Phys. Rev. 79 (1950) 372.

    Article  ADS  MATH  Google Scholar 

  20. H. Miyazawa, Proc. Int. Conf. Phys. Semic. Exeter (1962) p. 636. London: The Institute of Physics and The Physical Society. 1962.

    Google Scholar 

  21. R. J. Stirn and W. M. Becker, Phys. Rev. 141 (1966) 621.

    Article  ADS  Google Scholar 

  22. C. Herring, T. H. Geballe, and J. E. Kunzler, Bell Syst. Tech. J. 38 (1959) 657.

    Google Scholar 

  23. C. Herring and E. Vogt, Phys. Rev. 101 (1956) 944. Err.: ibid. 105 (1957) 1933.

    Google Scholar 

  24. P. M. Eagles and D. M. Edwards, Phys. Rev. 138 (1965) A 1706.

    Google Scholar 

  25. D. Long, Phys. Rev. 120 (1960) 2024.

    Google Scholar 

  26. R. A. Laff and H. Y. Fan, Phys. Rev. 112 (1958) 317.

    Article  ADS  Google Scholar 

  27. H. O. Haller, thesis, Univ. Wien, Austria. 1972.

    Google Scholar 

  28. C. Herring, T. H. Geballe, and J. E. Kunzler, Bell Syst. Tech. J. 38 (1959) 657.

    Google Scholar 

  29. C. Herring and E. Vogt, Phys. Rev. 101 (1956) 944. Err.: ibid. 105 (1957) 1933.

    Google Scholar 

  30. P. M. Eagles and D. M. Edwards, Phys. Rev. 138 (1965) A 1706.

    Google Scholar 

  31. D. Long, Phys. Rev. 120 (1960) 2024.

    Google Scholar 

  32. R. A. Laff and H. Y. Fan, Phys. Rev. 112 (1958) 317.

    Article  ADS  Google Scholar 

  33. H. O. Haller, thesis, Univ. Wien, Austria. 1972.

    Google Scholar 

  34. C. Herring, Bell Syst. Tech. J. 34 (1955) 237.

    Article  Google Scholar 

  35. H. W. Streitwolf, phys. stat. sol. 37 (1970) K 47, and references therein.

    Google Scholar 

  36. D. Long, Phys. Rev. 120 (1960) 2024; M. Asche, B. L. Boichenko, V. M. Bondar and O. G. Sarbej, Proc. Int. Conf. Semic. Physics Moscow 1968, p. 793. Leningrad: Nauka 1968; W. A. Harrison, Phys. Rev. 104 (1956) 1281, has shown that optical intervalley scattering in n-Si is negligible.

    Google Scholar 

  37. H. W. Streitwolf, phys. stat. sol. 37 (1970) K 47, and references therein.

    Google Scholar 

  38. D. Long, Phys. Rev. 120 (1960) 2024; M. Asche, B. L. Boichenko, V. M. Bondar and O. G. Sarbej, Proc. Int. Conf. Semic. Physics Moscow 1968, p. 793. Leningrad: Nauka 1968; W. A. Harrison, Phys. Rev. 104 (1956) 1281, has shown that optical intervalley scattering in n-Si is negligible.

    Google Scholar 

  39. E. M. Conwell: High Field Effects in Semiconductors, Solid State Physics, Suppl. 9, p.154 (F. Seitz, D. Turnbull, and H. Ehrenreich, eds.). New York: Acad. Press. 1967.

    Google Scholar 

  40. E. M. Conwell: High Field Effects in Semiconductors, Solid State Physics, Suppl. 9, p.154 (F. Seitz, D. Turnbull, and H. Ehrenreich, eds.). New York: Acad. Press. 1967.

    Google Scholar 

  41. Ref.4,p.115 and p.124 for acoustic and p.152 and p.155 for optical scattering.

    Google Scholar 

  42. W. Sasaki, M. Shibuya, and K. Mizuguchi, J. Phys. Soc. Japan 13 (1958) 456; W. Sasaki, M. Shibuya, K. Mizuguchi, and G. Hatoyama, J. Phys. Chem. Solids 8 (1959) 250.

    Article  Google Scholar 

  43. M. Shibuya, Phys. Rev. 99 (1955) 1189.

    Google Scholar 

  44. H. G. Reik and H. Risken, Phys. Rev. 126 (1962) 1737.

    Google Scholar 

  45. D. Schweitzer and K. Seeger, Zeitschr. f. Physik 183 (1965) 207.

    Article  ADS  Google Scholar 

  46. K. J. Schmidt-Tiedemann, Philips Res. Repts. 18 (1963) 338.

    Google Scholar 

  47. D. Schweitzer and K. Seeger, Zeitschr. f. Physik 183 (1965) 207.

    Article  ADS  Google Scholar 

  48. K. J. Schmidt-Tiedemann, Philips Res. Repts. 18 (1963) 338.

    Google Scholar 

  49. R. J. Sladek, Phys. Rev. 120 (1960) 1589.

    Google Scholar 

  50. H. F. Budd, Phys. Rev. 140 (1965) A 2170.

    Google Scholar 

  51. H. Heinrich and M. Kriechbaum, J. Phys. Chem. Solids 31 (1970) 927; M. Asche, V. M. Bondar, and O. G. Sarbej, phys. stat. sol. 31 (1969) K 143.

    Google Scholar 

  52. E. A. Movchan and E. G. Miselyuk, Sov. Phys. Semicond. 3 (1969) 571.

    Google Scholar 

  53. M. I. Nathan, Phys. Rev. 130 (1963) 2201.

    Google Scholar 

  54. H. Heinrich and M. Kriechbaum, J. Phys. Chem. Solids 31 (1970) 927; M. Asche, V. M. Bondar, and O. G. Sarbej, phys. stat. sol. 31 (1969) K 143.

    Google Scholar 

  55. E. A. Movchan and E. G. Miselyuk, Sov. Phys. Semicond. 3 (1969) 571.

    Google Scholar 

  56. M. I. Nathan, Phys. Rev. 130 (1963) 2201.

    Google Scholar 

  57. M. I. Nathan, Phys. Rev. 130 (1963) 2201.M. Asche, Yu. G. Zav’yalov, and O. G. Sarbej, Pisma v JETP 13 (1971) 401 [Engl.: JETP Letters 13 (1971) 285] and private communication M. Asche.

    Google Scholar 

  58. M. Asche, A. G. Maksimchuk, and O. G. Sarbej, phys. stat. sol. (b) 47 (1971) K 45.

    Google Scholar 

  59. H. Heinrich and M. Kriechbaum, phys. stat. sol. (b) 50 (1972) K 45.

    Google Scholar 

  60. M. Kriechbaum, H. Heinrich, and J. Wajda, J. Phys. Chem. Solids 33 (1972) 829.

    Article  ADS  Google Scholar 

  61. M. Asche, Yu. G. Zav’yalov, and O. G. Sarbej, Pisma v JETP 13 (1971) 401 [Engl.: JETP Letters 13 (1971) 285] and private communication M. Asche.

    Google Scholar 

  62. M. Asche, A. G. Maksimchuk, and O. G. Sarbej, phys. stat. sol. (b) 47 (1971) K 45.

    Google Scholar 

  63. H. Heinrich and M. Kriechbaum, phys. stat. sol. (b) 50 (1972) K 45.

    Google Scholar 

  64. M. Kriechbaum, H. Heinrich, and J. Wajda, J. Phys. Chem. Solids 33 (1972) 829.

    Article  ADS  Google Scholar 

  65. J. E. Smith, M. I. Nathan, J. C. McGroddy, S. A. Porowski, and W. Paul, Appl. Phys. Lett. 15 (1969) 242.

    Article  ADS  Google Scholar 

  66. B. K. Ridley and T. B. Watkins, Proc. Phys. Soc. 78 (1961) 293; B. K. Ridley, Proc. Phys. Soc. 82 (1963) 954.

    Article  Google Scholar 

  67. C. Hilsum, Proc. IRE 50 (1962) 185.

    Article  Google Scholar 

  68. J. B. Gunn, Solid State Comm. 1 (1963) 88; J. B. Gunn: Plasma Effects in Solids (J. Bok, ed.), p. 199. Paris: Dunod. 1964.

    Google Scholar 

  69. For a historical review see J. B. Gunn, Int. J. Sci. Technol. 46 (1965) 43.

    Google Scholar 

  70. See e.g. E. M. Conwell: Solid State Physics (F. Seitz and D. Turnbull, eds.) Suppl. 9, p. 254. New York: Acad. Press. 1967.

    Google Scholar 

  71. For a historical review see J. B. Gunn, Int. J. Sci. Technol. 46 (1965) 43.

    Google Scholar 

  72. See e.g. E. M. Conwell: Solid State Physics (F. Seitz and D. Turnbull, eds.) Suppl. 9, p. 254. New York: Acad. Press. 1967.

    Google Scholar 

  73. J. E. Carroll: Hot Electron Microwave Generators, p. 105 ff. London: Arnold. 1970.

    Google Scholar 

  74. P. N. Butcher and W. Fawcett, Brit. J. Appl. Phys. 17 (1966) 1425.

    Google Scholar 

  75. J. B. Gunn, J. Phys. Soc. Japan, Suppl. 21 (1966) 505.

    Google Scholar 

  76. B. K. Ridley, Phys. Lett. 16 (1965) 105.

    Article  ADS  Google Scholar 

  77. A. R. Hutson, A. Jayaraman, A. G. Chynoweth, A. S. Corriel, and A. L. Feldman, Phys. Rev. Lett. 14 (1965) 639.

    Article  ADS  Google Scholar 

  78. J. W. Allen, M. Shyam, Y. S. Chen, and G. L. Pearson, Appl. Phys. Lett. 7 (1965) 78.

    Article  ADS  Google Scholar 

  79. M. Shyam, J. W. Allen, and G. L. Pearson, IEEE-Trans. ED-13 (1966) 63.

    Google Scholar 

  80. P. N. Butcher and W. Fawcett, Brit. J. Appl. Phys. 17 (1966) 1425.

    Google Scholar 

  81. J. B. Gunn, J. Phys. Soc. Japan, Suppl. 21 (1966) 505.

    Google Scholar 

  82. B. K. Ridley, Phys. Lett. 16 (1965) 105.

    Article  ADS  Google Scholar 

  83. A. R. Hutson, A. Jayaraman, A. G. Chynoweth, A. S. Corriel, and A. L. Feldman, Phys. Rev. Lett. 14 (1965) 639.

    Article  ADS  Google Scholar 

  84. J. W. Allen, M. Shyam, Y. S. Chen, and G. L. Pearson, Appl. Phys. Lett. 7 (1965) 78.

    Article  ADS  Google Scholar 

  85. M. Shyam, J. W. Allen, and G. L. Pearson, IEEE-Trans. ED-13 (1966) 63.

    Google Scholar 

  86. R. W. Keyes: Solid State Physics (F. Seitz and D. Turnbull, eds.), Vol. 11, p. 149. New York: Acad Press. 1960.

    Google Scholar 

  87. C. Hilsum and H. D. Rees, Electr. Lett. 6 (1970) 277 and 310; H. C. Law and K. C. Kao, J. Appl. Phys. 41 (1970) 829; for energies in III-V compounds see C. Hilsum, Proc. Int. Conf. Semic. Phys. Paris (1964) p. 1127. Paris: Dunod. 1964.

    Google Scholar 

  88. H. W. Thim, M. R. Barber, B. W. Hakki, S. Knight, and M. Uenohara, Appl. Phys. Lett. 7 (1965) 167.

    Article  ADS  Google Scholar 

  89. J. A. Copeland, J. Appl. Phys. 38 (1967) 3096.

    Article  ADS  Google Scholar 

  90. I. B. Bott and C. Hilsum, IEEE-Trans. ED-14 (1967) 492.

    Google Scholar 

  91. S. Kataoka, H. Tateno, M. Kawashima, and Y. Komamiya, 7th Int. Conf. Microwave Optical Generation and Amplification, Hamburg/Germany, 1968. Berlin: VDE Verlag. 1968.

    Google Scholar 

  92. G. W. Ludwig, IEEE-Trans. ED-14 (1967) 547.

    Google Scholar 

  93. J. C. McGroddy, M. R. Lorenz, and T. S. Plaskett, Solid State Comm. 7 (1969) 901.

    Article  ADS  Google Scholar 

  94. J. W. Allen, M. Shyam, and G. L. Pearson, Appl. Phys. Lett. 11 (1967) 253.

    Article  Google Scholar 

  95. J. C. McGroddy, M. I. Nathan, and J. E. Smith, Jr., IBM-J. Res. Develop. 13 (1969) 543.

    Google Scholar 

  96. E. G. S. Paige, IBM-J. Res. Develop. 13 (1969) 562.

    Google Scholar 

  97. I. B. Bott and C. Hilsum, IEEE-Trans. ED-14 (1967) 492.

    Google Scholar 

  98. S. Kataoka, H. Tateno, M. Kawashima, and Y. Komamiya, 7th Int. Conf. Microwave Optical Generation and Amplification, Hamburg/Germany, 1968. Berlin: VDE Verlag. 1968.

    Google Scholar 

  99. G. W. Ludwig, IEEE-Trans. ED-14 (1967) 547.

    Google Scholar 

  100. J. C. McGroddy, M. R. Lorenz, and T. S. Plaskett, Solid State Comm. 7 (1969) 901.

    Article  ADS  Google Scholar 

  101. J. W. Allen, M. Shyam, and G. L. Pearson, Appl. Phys. Lett. 11 (1967) 253.

    Article  Google Scholar 

  102. J. C. McGroddy, M. I. Nathan, and J. E. Smith, Jr., IBM-J. Res. Develop. 13 (1969) 543.

    Google Scholar 

  103. E. G. S. Paige, IBM-J. Res. Develop. 13 (1969) 562.

    Google Scholar 

  104. J. E. Smith, Jr., Appl. Phys. Lett. 12 (1968) 233.

    Google Scholar 

  105. J. E. Smith, Jr., J. C. McGroddy, and M. I. Nathan, Proc. Int. Conf. Semic. Physics Moscow 1968, p. 950. Leningrad: Nauka. 1968.

    Google Scholar 

  106. T. K. Gaylord, P. L. Shah, and T. A. Rabson, IEEE-Trans. ED-15 (1968) 777, ED-16 (1969) 490.

    Google Scholar 

  107. J. E. Smith, Jr., Appl. Phys. Lett. 12 (1968) 233.

    Google Scholar 

  108. J. E. Smith, Jr., J. C. McGroddy, and M. I. Nathan, Proc. Int. Conf. Semic. Physics Moscow 1968, p. 950. Leningrad: Nauka. 1968.

    Google Scholar 

  109. T. K. Gaylord, P. L. Shah, and T. A. Rabson, IEEE-Trans. ED-15 (1968) 777, ED-16 (1969) 490.

    Google Scholar 

  110. Ref.7, p. 84–86.

    Google Scholar 

  111. A. M. Barnett, IBM-J. Res. Develop. 13 (1969) 522.

    Google Scholar 

  112. J. D. Maines and E. G. S. Paige, J. Phys. C 2 (1969) 175.

    Article  ADS  Google Scholar 

  113. G. Weinreich, T. M. Sanders, Jr., and H.G. White, Phys. Rev. 114 (1959) 33; this and more recent papers have been reviewed by N. G. Einspruch: Solid State Physics (F. Seitz and D. Turnbull, eds.), Vol. 17, p. 243. New York: Acad. Press. 1965; M. Pomerantz, Proc. IEEE 53 (1965) 1438.

    Google Scholar 

  114. J. D. Maines and E. G. S. Paige, J. Phys. C 2 (1969) 175.

    Article  ADS  Google Scholar 

  115. G. Weinreich, T. M. Sanders, Jr., and H.G. White, Phys. Rev. 114 (1959) 33; this and more recent papers have been reviewed by N. G. Einspruch: Solid State Physics (F. Seitz and D. Turnbull, eds.), Vol. 17, p. 243. New York: Acad. Press. 1965; M. Pomerantz, Proc. IEEE 53 (1965) 1438.

    Google Scholar 

  116. E. M. Conwell: Solid State Physics (F. Seitz and D. Turnbull, eds.), Suppl. 9, p. 142. New York: Acad. Press. 1967.

    Google Scholar 

  117. D. L. White, J. Appl. Phys. 33 (1962) 2547.

    Google Scholar 

  118. A. R. Hutson and D. L. White, J. Appl. Phys. 33 (1962) 40.

    Article  ADS  Google Scholar 

  119. N. I. Meyer and M. H. Jörgensen: Festkörperprobleme.Vol. X, p. 21. Oxford: Pergamon and Braunschweig: Vieweg. 1970.

    Google Scholar 

  120. D. L. White, E. T. Handelman, and J. T. Hanlon, Proc. IEEE 53 (1965) 2157.

    Google Scholar 

  121. J. H. McFee, J. Appl. Phys. 34 (1963) 1548.

    Google Scholar 

  122. W. Wettling: II-VI Semiconducting Compounds (D. G. Thomas, ed.), p. 928. New York: Benjamin. 1967; see also K. Hess and H. Kuzmany, Proc. Int. Conf. Phys. Semic. Warsaw 1972 (M.Miasek, ed.), p. 1233. Warsaw: PWN - Polish Scientific Publishers. 1972.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Ludwig Boltzmann-Institut für Festkörperphysik, Wien, Österreich

    Karlheinz Seeger

  2. Institut für Angewandte Physik, Universität Wien, Österreich

    Karlheinz Seeger

Authors
  1. Karlheinz Seeger
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 1973 Springer-Verlag Wien

About this chapter

Cite this chapter

Seeger, K. (1973). Charge Transport and Scattering Processes in the Many-Valley Model. In: Semiconductor Physics. Springer Study Edition. Springer, Vienna. https://doi.org/10.1007/978-3-7091-4111-3_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-7091-4111-3_7

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-211-81186-3

  • Online ISBN: 978-3-7091-4111-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation