Advertisement

Charge Transport and Scattering Processes in the Many-Valley Model

  • Karlheinz Seeger
Part of the Springer Study Edition book series (SSE)

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.

Keywords

Drift Velocity Charge Transport Threshold Field Central Valley Negative Differential Conductivity 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    See e.g. C. Kittel: Introduction to Solid State Physics, chap. 4. New York: J. Wiley and Sons. 1965.Google Scholar
  2. [2]
    C. Herring, Bell Syst. Tech. J. 34 (1955) 237.CrossRefGoogle Scholar
  3. [3]
    C. Herring and E. Vogt, Phys. Rev. 101 (1956) 944. Err.: ibid.105 (1957) 1933.Google Scholar
  4. [3]
    C. Herring and E. Vogt, Phys. Rev. 101 (1956) 944. Err.: ibid.105 (1957) 1933.Google Scholar
  5. [4]
    S. H. Koenig: Proc. Int. School of Physics Vol.XXII, p. 515. New York: Acad. Press. 1961.Google Scholar
  6. [5]
    J. E. Smith,Jr., Appl. Phys. Lett. 12 (1968) 233.Google Scholar
  7. [6]
    E. G. S. Paige, Proc. in Semicond. 8 (1960) 158, Fig. 36.Google Scholar
  8. [7]
    H. Heinrich and M. Kriechbaum, J. Phys. Chem. Solids 31 (1970) 927; K. Bulthuis, Philips Res. Repts. 23 (1968) 25.Google Scholar
  9. [1]
    C. Herring and E. Vogt, Phys. Rev. 101 (1956) 944. Err.: ibid.105 (1957) 1933.Google Scholar
  10. [2]
    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. [1]
    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. [1]
    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. [2]
    G. L. Pearson and H. Suhl, Phys. Rev. 83 (1951) 768.ADSCrossRefGoogle Scholar
  14. [3]
    G. L. Pearson and C. Herring, Physica 20 (1954) 975.ADSCrossRefGoogle Scholar
  15. [4]
    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. [5]
    F. Seitz, Phys. Rev. 79 (1950) 372.ADSCrossRefMATHGoogle Scholar
  17. [6]
    H. Miyazawa, Proc. Int. Conf. Phys. Semic. Exeter (1962) p. 636. London: The Institute of Physics and The Physical Society. 1962.Google Scholar
  18. [4]
    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. [5]
    F. Seitz, Phys. Rev. 79 (1950) 372.ADSCrossRefMATHGoogle Scholar
  20. [6]
    H. Miyazawa, Proc. Int. Conf. Phys. Semic. Exeter (1962) p. 636. London: The Institute of Physics and The Physical Society. 1962.Google Scholar
  21. [7]
    R. J. Stirn and W. M. Becker, Phys. Rev. 141 (1966) 621.ADSCrossRefGoogle Scholar
  22. [8]
    C. Herring, T. H. Geballe, and J. E. Kunzler, Bell Syst. Tech. J. 38 (1959) 657.Google Scholar
  23. [9]
    C. Herring and E. Vogt, Phys. Rev. 101 (1956) 944. Err.: ibid. 105 (1957) 1933.Google Scholar
  24. [10]
    P. M. Eagles and D. M. Edwards, Phys. Rev. 138 (1965) A 1706.Google Scholar
  25. [11]
    D. Long, Phys. Rev. 120 (1960) 2024.Google Scholar
  26. [12]
    R. A. Laff and H. Y. Fan, Phys. Rev. 112 (1958) 317.ADSCrossRefGoogle Scholar
  27. [13]
    H. O. Haller, thesis, Univ. Wien, Austria. 1972.Google Scholar
  28. [8]
    C. Herring, T. H. Geballe, and J. E. Kunzler, Bell Syst. Tech. J. 38 (1959) 657.Google Scholar
  29. [9]
    C. Herring and E. Vogt, Phys. Rev. 101 (1956) 944. Err.: ibid. 105 (1957) 1933.Google Scholar
  30. [10]
    P. M. Eagles and D. M. Edwards, Phys. Rev. 138 (1965) A 1706.Google Scholar
  31. [11]
    D. Long, Phys. Rev. 120 (1960) 2024.Google Scholar
  32. [12]
    R. A. Laff and H. Y. Fan, Phys. Rev. 112 (1958) 317.ADSCrossRefGoogle Scholar
  33. [13]
    H. O. Haller, thesis, Univ. Wien, Austria. 1972.Google Scholar
  34. [1]
    C. Herring, Bell Syst. Tech. J. 34 (1955) 237.CrossRefGoogle Scholar
  35. [2]
    H. W. Streitwolf, phys. stat. sol. 37 (1970) K 47, and references therein.Google Scholar
  36. [3]
    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. [2]
    H. W. Streitwolf, phys. stat. sol. 37 (1970) K 47, and references therein.Google Scholar
  38. [3]
    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. [4]
    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. [4]
    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. [5]
    Ref.4,p.115 and p.124 for acoustic and p.152 and p.155 for optical scattering.Google Scholar
  42. [6]
    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.CrossRefGoogle Scholar
  43. [7]
    M. Shibuya, Phys. Rev. 99 (1955) 1189.Google Scholar
  44. [8]
    H. G. Reik and H. Risken, Phys. Rev. 126 (1962) 1737.Google Scholar
  45. [9]
    D. Schweitzer and K. Seeger, Zeitschr. f. Physik 183 (1965) 207.ADSCrossRefGoogle Scholar
  46. [10]
    K. J. Schmidt-Tiedemann, Philips Res. Repts. 18 (1963) 338.Google Scholar
  47. [9]
    D. Schweitzer and K. Seeger, Zeitschr. f. Physik 183 (1965) 207.ADSCrossRefGoogle Scholar
  48. [10]
    K. J. Schmidt-Tiedemann, Philips Res. Repts. 18 (1963) 338.Google Scholar
  49. [1]
    R. J. Sladek, Phys. Rev. 120 (1960) 1589.Google Scholar
  50. [2]
    H. F. Budd, Phys. Rev. 140 (1965) A 2170.Google Scholar
  51. [3]
    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. [4]
    E. A. Movchan and E. G. Miselyuk, Sov. Phys. Semicond. 3 (1969) 571.Google Scholar
  53. [5]
    M. I. Nathan, Phys. Rev. 130 (1963) 2201.Google Scholar
  54. [3]
    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. [4]
    E. A. Movchan and E. G. Miselyuk, Sov. Phys. Semicond. 3 (1969) 571.Google Scholar
  56. [5]
    M. I. Nathan, Phys. Rev. 130 (1963) 2201.Google Scholar
  57. [6]
    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. [7]
    M. Asche, A. G. Maksimchuk, and O. G. Sarbej, phys. stat. sol. (b) 47 (1971) K 45.Google Scholar
  59. [8]
    H. Heinrich and M. Kriechbaum, phys. stat. sol. (b) 50 (1972) K 45.Google Scholar
  60. [9]
    M. Kriechbaum, H. Heinrich, and J. Wajda, J. Phys. Chem. Solids 33 (1972) 829.ADSCrossRefGoogle Scholar
  61. [6]
    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. [7]
    M. Asche, A. G. Maksimchuk, and O. G. Sarbej, phys. stat. sol. (b) 47 (1971) K 45.Google Scholar
  63. [8]
    H. Heinrich and M. Kriechbaum, phys. stat. sol. (b) 50 (1972) K 45.Google Scholar
  64. [9]
    M. Kriechbaum, H. Heinrich, and J. Wajda, J. Phys. Chem. Solids 33 (1972) 829.ADSCrossRefGoogle Scholar
  65. [2]
    J. E. Smith, M. I. Nathan, J. C. McGroddy, S. A. Porowski, and W. Paul, Appl. Phys. Lett. 15 (1969) 242.ADSCrossRefGoogle Scholar
  66. [3]
    B. K. Ridley and T. B. Watkins, Proc. Phys. Soc. 78 (1961) 293; B. K. Ridley, Proc. Phys. Soc. 82 (1963) 954.CrossRefGoogle Scholar
  67. [4]
    C. Hilsum, Proc. IRE 50 (1962) 185.CrossRefGoogle Scholar
  68. [5]
    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. [6]
    For a historical review see J. B. Gunn, Int. J. Sci. Technol. 46 (1965) 43.Google Scholar
  70. [7]
    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. [6]
    For a historical review see J. B. Gunn, Int. J. Sci. Technol. 46 (1965) 43.Google Scholar
  72. [7]
    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. [7]
    J. E. Carroll: Hot Electron Microwave Generators, p. 105 ff. London: Arnold. 1970.Google Scholar
  74. [9]
    P. N. Butcher and W. Fawcett, Brit. J. Appl. Phys. 17 (1966) 1425.Google Scholar
  75. [10]
    J. B. Gunn, J. Phys. Soc. Japan, Suppl. 21 (1966) 505.Google Scholar
  76. [11]
    B. K. Ridley, Phys. Lett. 16 (1965) 105.ADSCrossRefGoogle Scholar
  77. [12]
    A. R. Hutson, A. Jayaraman, A. G. Chynoweth, A. S. Corriel, and A. L. Feldman, Phys. Rev. Lett. 14 (1965) 639.ADSCrossRefGoogle Scholar
  78. [13]
    J. W. Allen, M. Shyam, Y. S. Chen, and G. L. Pearson, Appl. Phys. Lett. 7 (1965) 78.ADSCrossRefGoogle Scholar
  79. [14]
    M. Shyam, J. W. Allen, and G. L. Pearson, IEEE-Trans. ED-13 (1966) 63.Google Scholar
  80. [9]
    P. N. Butcher and W. Fawcett, Brit. J. Appl. Phys. 17 (1966) 1425.Google Scholar
  81. [10]
    J. B. Gunn, J. Phys. Soc. Japan, Suppl. 21 (1966) 505.Google Scholar
  82. [11]
    B. K. Ridley, Phys. Lett. 16 (1965) 105.ADSCrossRefGoogle Scholar
  83. [12]
    A. R. Hutson, A. Jayaraman, A. G. Chynoweth, A. S. Corriel, and A. L. Feldman, Phys. Rev. Lett. 14 (1965) 639.ADSCrossRefGoogle Scholar
  84. [13]
    J. W. Allen, M. Shyam, Y. S. Chen, and G. L. Pearson, Appl. Phys. Lett. 7 (1965) 78.ADSCrossRefGoogle Scholar
  85. [14]
    M. Shyam, J. W. Allen, and G. L. Pearson, IEEE-Trans. ED-13 (1966) 63.Google Scholar
  86. [15]
    R. W. Keyes: Solid State Physics (F. Seitz and D. Turnbull, eds.), Vol. 11, p. 149. New York: Acad Press. 1960.Google Scholar
  87. [16]
    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. [17]
    H. W. Thim, M. R. Barber, B. W. Hakki, S. Knight, and M. Uenohara, Appl. Phys. Lett. 7 (1965) 167.ADSCrossRefGoogle Scholar
  89. [18]
    J. A. Copeland, J. Appl. Phys. 38 (1967) 3096.ADSCrossRefGoogle Scholar
  90. [19]
    I. B. Bott and C. Hilsum, IEEE-Trans. ED-14 (1967) 492.Google Scholar
  91. [20]
    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. [21]
    G. W. Ludwig, IEEE-Trans. ED-14 (1967) 547.Google Scholar
  93. [22]
    J. C. McGroddy, M. R. Lorenz, and T. S. Plaskett, Solid State Comm. 7 (1969) 901.CrossRefADSGoogle Scholar
  94. [23]
    J. W. Allen, M. Shyam, and G. L. Pearson, Appl. Phys. Lett. 11 (1967) 253.CrossRefGoogle Scholar
  95. [24]
    J. C. McGroddy, M. I. Nathan, and J. E. Smith, Jr., IBM-J. Res. Develop. 13 (1969) 543.Google Scholar
  96. [25]
    E. G. S. Paige, IBM-J. Res. Develop. 13 (1969) 562.Google Scholar
  97. [19]
    I. B. Bott and C. Hilsum, IEEE-Trans. ED-14 (1967) 492.Google Scholar
  98. [20]
    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. [21]
    G. W. Ludwig, IEEE-Trans. ED-14 (1967) 547.Google Scholar
  100. [22]
    J. C. McGroddy, M. R. Lorenz, and T. S. Plaskett, Solid State Comm. 7 (1969) 901.CrossRefADSGoogle Scholar
  101. [23]
    J. W. Allen, M. Shyam, and G. L. Pearson, Appl. Phys. Lett. 11 (1967) 253.CrossRefGoogle Scholar
  102. [24]
    J. C. McGroddy, M. I. Nathan, and J. E. Smith, Jr., IBM-J. Res. Develop. 13 (1969) 543.Google Scholar
  103. [25]
    E. G. S. Paige, IBM-J. Res. Develop. 13 (1969) 562.Google Scholar
  104. [26]
    J. E. Smith, Jr., Appl. Phys. Lett. 12 (1968) 233.Google Scholar
  105. [27]
    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. [28]
    T. K. Gaylord, P. L. Shah, and T. A. Rabson, IEEE-Trans. ED-15 (1968) 777, ED-16 (1969) 490.Google Scholar
  107. [26]
    J. E. Smith, Jr., Appl. Phys. Lett. 12 (1968) 233.Google Scholar
  108. [27]
    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. [28]
    T. K. Gaylord, P. L. Shah, and T. A. Rabson, IEEE-Trans. ED-15 (1968) 777, ED-16 (1969) 490.Google Scholar
  110. [29]
    Ref.7, p. 84–86.Google Scholar
  111. [30]
    A. M. Barnett, IBM-J. Res. Develop. 13 (1969) 522.Google Scholar
  112. [1]
    J. D. Maines and E. G. S. Paige, J. Phys. C 2 (1969) 175.CrossRefADSGoogle Scholar
  113. [2]
    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. [1]
    J. D. Maines and E. G. S. Paige, J. Phys. C 2 (1969) 175.CrossRefADSGoogle Scholar
  115. [2]
    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. [3]
    E. M. Conwell: Solid State Physics (F. Seitz and D. Turnbull, eds.), Suppl. 9, p. 142. New York: Acad. Press. 1967.Google Scholar
  117. [4]
    D. L. White, J. Appl. Phys. 33 (1962) 2547.Google Scholar
  118. [5]
    A. R. Hutson and D. L. White, J. Appl. Phys. 33 (1962) 40.ADSCrossRefGoogle Scholar
  119. [6]
    N. I. Meyer and M. H. Jörgensen: Festkörperprobleme.Vol. X, p. 21. Oxford: Pergamon and Braunschweig: Vieweg. 1970.Google Scholar
  120. [7]
    D. L. White, E. T. Handelman, and J. T. Hanlon, Proc. IEEE 53 (1965) 2157.Google Scholar
  121. [8]
    J. H. McFee, J. Appl. Phys. 34 (1963) 1548.Google Scholar
  122. [9]
    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

Copyright information

© Springer-Verlag Wien 1973

Authors and Affiliations

  • Karlheinz Seeger
    • 1
    • 2
  1. 1.Ludwig Boltzmann-Institut für FestkörperphysikWienÖsterreich
  2. 2.Institut für Angewandte PhysikUniversität WienÖsterreich

Personalised recommendations