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Scattering Processes in a Spherical One-Valley Model

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

Abstract

In Chap.4 we frequently assumed an energy dependence of the momentum relaxation time, r m r, where r is a constant, for the calculation of the galvanomagnetic, thermoelectric, thermomagnetic etc. effects. We will now treat the important scattering mechanisms and find the energy dependence of r m. For those cases where a power law is found the magnitude of the exponent r will be determined.

Keywords

Drift Velocity Optical Phonon Phonon Spectrum Energy Loss Rate Ionize Impurity Scattering 
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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References

  1. [1]
    see e.g. L.I. Schiff: Quantum Mechanics, 3rd ed., p. 110. New York: McGraw-Hill. 1968.Google Scholar
  2. [1]
    see e.g. L. I. Schiff: Quantum Mechanics, 3rd ed., p. 110. New York: McGraw-Hill. 1968.Google Scholar
  3. [2]
    H. S. W. Massey and E. H. S. Burhop: Electronic and Ionic Impact Phenomena, vol. 1, chap. 6. 3. Oxford: Clarendon. 1969.Google Scholar
  4. [3]
    C. Ramsauer, Ann.der Phys. 64 (1921) 513; 66 (1921) 545.Google Scholar
  5. [4]
    C. Erginsoy, Phys. Rev. 79 (1950) 1013.Google Scholar
  6. [5]
    E.g. L. I. Schiff: Quantum Mechanics, chap. 5. New York: McGraw-Hill. 1968.Google Scholar
  7. [6]
    S. H. Koenig, R. D. Brown III, and W. Schillinger, Phys. Rev. 128 (1962) 1668.Google Scholar
  8. [7]
    E. Otsuka, K. Murase, and J. Iseki, J. Phys. Soc. Japan 21 (1966) 1104.Google Scholar
  9. [8]
    C. Schwartz, Phys. Rev. 124 (1961) 1468; M. Rotenberg, Ann. Phys. 19 (1962) 262.CrossRefGoogle Scholar
  10. [9]
    M. Pomerantz, Proc. IEEE 53 (1965) 1438. S. H. Koenig, R. D. Brown III, and W. Schillinger, Phys. Rev. 128 (1962) 1668.Google Scholar
  11. [10]
    E. Otsuka, K. Murase, and J. Iseki, J. Phys. Soc. Japan 21 (1966) 1104.Google Scholar
  12. [11]
    C. Schwartz, Phys. Rev. 124 (1961) 1468; M. Rotenberg, Ann. Phys. 19 (1962) 262.CrossRefGoogle Scholar
  13. [1]
    E. Fermi: Nuclear Physics, p.142. Chicago: Univ. Chicago Press. 1950; “Golden Rule No. 1”: l.c., p.148.Google Scholar
  14. [2]
    See e.g. R. B. Adler, A. C. Smith, and R. L. Longini: Introduction to Semiconductor Physics, Sec. 1.5.3 and 3. 3. New York: J. Wiley and Sons. 1964.Google Scholar
  15. [1]
    H. Brooks: Advances in Electronics and Electron Physics (L. Marton, ed.), Vol.7, p. 85. New York: Acad. Press Inc. 1955; H. Brooks, Phys. Rev. 83 (1951) 879.Google Scholar
  16. [2]
    E. Conwell and V. F. Weisskopf, Phys. Rev. 77 (1950) 388.ADSCrossRefMATHGoogle Scholar
  17. [3]
    L. I. Schiff: Quantum Mechanics, 3rd ed., p. 325. New York: McGraw-Hill. 1968.Google Scholar
  18. [4]
    F. J. Blatt, J. Phys. Chem. Solids 1 (1957) 262; F. J. Blatt: Solid State Physics (F. Seitz and D. Turnbull, eds.) Vol. 4, p. 199. New York: Acad. Press. 1957. See also D. Long, C. D. Motchenbacher, and J. Myers, J. Appl. Phys. 30 (1959) 353.Google Scholar
  19. [1]
    J. Bardeen and W. Shockley, Phys. Rev. 80 (1950) 72.MathSciNetADSCrossRefMATHGoogle Scholar
  20. [1]
    J. Bardeen and W. Shockley, Phys. Rev. 80 (1950) 72.MathSciNetADSCrossRefMATHGoogle Scholar
  21. [2]
    R. Peierls, Ann. Phys. (Leipzig) (5) 12 (1932) 154; see also A. H. Wilson: The Theory of Metals, p. 255 and 298. London: Cambridge Univ. Press. 1965.Google Scholar
  22. [1]
    R. F. Greene, J. Electronics and Control 3 (1957) 387.CrossRefGoogle Scholar
  23. [2]
    W. Shockley, Bell Syst. Tech. J. 30 (1951) 990.CrossRefGoogle Scholar
  24. [1]
    P. P. Debye and E. M. Conwell, Phys. Rev. 93 (1954) 693.ADSCrossRefGoogle Scholar
  25. [2]
    M. S. Sodha, Phys. Rev. 107 (1957)1266; K. Seeger, Zeitschr. f. Physik 156 (1959) 582.CrossRefGoogle Scholar
  26. [3]
    K. Seeger, Zeitschr. f. Physik 244 (1971) 439.ADSCrossRefGoogle Scholar
  27. [2]
    M. S. Sodha, Phys. Rev. 107 (1957)1266; K. Seeger, Zeitschr. f. Physik 156 (1959) 582.CrossRefGoogle Scholar
  28. [3]
    K. Seeger, Zeitschr. f. Physik 244 (1971) 439.ADSCrossRefGoogle Scholar
  29. [4]
    J. B. Gunn, J. Phys. Chem. Solids 8(1959) 239; see also Fig.4.35 and E. M. Conwell, Phys. Rev. 90 (1953) 769.CrossRefGoogle Scholar
  30. [5]
    G. Tschulena, Acta Phys. Austr. 33 (1971) 42.Google Scholar
  31. [6]
    For the case of a degenerate semiconductor see ref.5, chap. 61,and G. Tschulena and R. Keil, phys. stat. sol. (b) 49 (1972) 191.Google Scholar
  32. [7]
    H. Heinrich and W. Jantsch, Sol. State Comm. 7 (1969) 377.CrossRefADSGoogle Scholar
  33. [7]
    H. Heinrich and W. Jantsch, Sol. State Comm. 7 (1969) 377.CrossRefADSGoogle Scholar
  34. [8]
    W. W. Tyler and H. H. Woodbury, Phys. Rev. 102 (1956) 647.ADSCrossRefGoogle Scholar
  35. [9]
    D. Long, C. D. Motchenbacher, and J. Myers, J. Appl. Phys. 30 (1959) 353.ADSCrossRefGoogle Scholar
  36. [10]
    D. M. Brown and R. Bray, Phys. Rev. 127 (1962) 1593.Google Scholar
  37. [11]
    P. M. Eagles and D. M. Edwards, Phys. Rev. 138 (1965) A 1706.Google Scholar
  38. [12]
    C. Herring and E. Vogt, Phys. Rev. 101 (1956) 944. Chap.6g.Google Scholar
  39. [1]
    A. R. Hutson, J. Appl. Phys. 32 Suppl. (1961) 2287.Google Scholar
  40. [2]
    H. J. G. Meyer and D. Polder, Physica 19 (1953) 255.ADSCrossRefGoogle Scholar
  41. [3]
    C. Herring and E. Vogt, Phys. Rev. 101 (1956) 944. Chap.6g.Google Scholar
  42. [1]
    A. R. Hutson, J. Appl. Phys. 32 Suppl. (1961) 2287.Google Scholar
  43. [2]
    H. J. G. Meyer and D. Polder, Physica 19 (1953) 255.ADSCrossRefGoogle Scholar
  44. [3]
    Sh. M. Kogan, Fiz. Tverd. Tela 4(1962) 2474 (Engl. transi.: Soy. Phys.-Solid State 4 (1963) 1813 ).Google Scholar
  45. [3]
    Sh. M. Kogan, Fiz. Tverd. Tela 4(1962) 2474 (Engl. transl.: Soy. Phys.-Solid State 4 (1963) 1813 ).Google Scholar
  46. [1]
    R. A. Cowley: Modern Solid State Physics (R. H. Enns and R. R. Haering, eds.) Vol.2, p.43. New York: Gordon and Breach. 1969; L. S. Kothari and K. S. Singwi: Solid State Physics (F. Seitz and D. Turnbull, eds.) Vol.8, p. 108. New York: Academic Press. 1969.Google Scholar
  47. [2]
    I. Pelah, C. M. Eisenhauer, D. J. Hughes, and H. Palevsky, Phys. Rev. 108 (1957) 1091.Google Scholar
  48. [3]
    B. N. Brockhouse, H. Palevsky, D. J. Hughes, W. Kley, and E. Tunkelo, Phys. Rev. Lett. 2 (1959) 258.ADSCrossRefGoogle Scholar
  49. [1]
    R. A. Cowley: Modern Solid State Physics (R. H. Enns and R. R. Haering, eds.) Vol.2, p.43. New York: Gordon and Breach. 1969; L. S. Kothari and K. S. Singwi: Solid State Physics (F. Seitz and D. Turnbull, eds.) Vol.8, p. 108. New York: Academic Press. 1969.Google Scholar
  50. [2]
    I. Pelah, C. M. Eisenhauer, D. J. Hughes, and H. Palevsky, Phys. Rev. 108 (1957) 1091.Google Scholar
  51. [3]
    B. N. Brockhouse, H. Palevsky, D. J. Hughes, W. Kley, and E. Tunkelo, Phys. Rev. Lett. 2 (1959) 258.ADSCrossRefGoogle Scholar
  52. [4]
    R. H. Lyddane, R. G. Sachs, and E. Teller, Phys. Rev. 59 (1941) 673; the proof follows closely M. Born and K. Huang: Dynamical Theory of Crystal Lattices, p.82. Oxford: Clarendon Press. 1954.Google Scholar
  53. [4]
    R. H. Lyddane, R. G. Sachs, and E. Teller, Phys. Rev. 59 (1941) 673; the proof follows closely M. Born and K. Huang: Dynamical Theory of Crystal Lattices, p.82. Oxford: Clarendon Press. 1954.Google Scholar
  54. [1]
    A.C. Beer: Galvanomagnetic Effects in Semiconductors, in: Solid State Physics (E Seitz and D. Turnbull, eds.), Suppl. 4, p. 286. New York: Acad. Press. 1963.Google Scholar
  55. [1]
    R. Stratton, Proc. Roy. Soc. (London) A 246 (1958) 406; J. Phys. Soc. Japan 17 (1962) 590.CrossRefGoogle Scholar
  56. [2]
    E. M. Conwell: High Field Transport in Semiconductors, Solid State Physics, (F. Seitz, D. Turnbull, and H. Ehrenreich, eds.), Suppl. 9, chap. V. 7. New York: Acad. Press. 1967.Google Scholar
  57. [2]
    E. M. Conwell: High Field Transport in Semiconductors, Solid State Physics, (F. Seitz, D. Turnbull, and H. Ehrenreich, eds.), Suppl. 9, chap. V. 7. New York: Acad. Press. 1967.Google Scholar
  58. [1]
    H. J. G. Meyer, Phys. Rev. 112 (1958) 298.ADSCrossRefGoogle Scholar
  59. [2]
    W. Shockley, Bell. Syst. Tech. J. 30 (1951) 990; W. A. Harrison, Phys. Rev. 104 (1956) 1281.Google Scholar
  60. [3]
    K. Hess and K. Seeger, Zeitschr. f. Physik 218 (1969) 431; 237 (1970) 252; K. Hess, thesis, Univ. Wien, Austria. 1970.Google Scholar
  61. [4]
    T. N. Morgan and C. E. Kelly, Phys. Rev. 137 (1965) A 1573.Google Scholar
  62. [5]
    K. Seeger, Zeitschr. f. Physik 172 (1963) 68.ADSCrossRefGoogle Scholar
  63. [6]
    A. F. Gibson, J. W. Granville, and E. G. S. Paige, J. Phys. Chem. Solids 19 (1961) 198.ADSCrossRefGoogle Scholar
  64. [3]
    K. Hess and K. Seeger, Zeitschr. f. Physik 218 (1969) 431; 237 (1970) 252; K. Hess, thesis, Univ. Wien, Austria. 1970.Google Scholar
  65. [4]
    T. N. Morgan and C. E. Kelly, Phys. Rev. 137 (1965) A 1573.Google Scholar
  66. [5]
    K. Seeger, Zeitschr. f. Physik 172 (1963) 68.ADSCrossRefGoogle Scholar
  67. [6]
    A. F. Gibson, J. W. Granville, and E. G. S. Paige, J. Phys. Chem. Solids 19 (1961) 198.ADSCrossRefGoogle Scholar
  68. [7]
    E. M. Conwell, Solid State Physics (F. Seitz, D. Turnbull, and H. Ehrenreich, eds.) Suppl. 9, p. 171. New York: Acad. Press. 1967.Google Scholar
  69. [8]
    I. Adawi, Phys. Rev. 120 (1960) 118.ADSCrossRefMATHGoogle Scholar
  70. [9]
    K. Hess (unpublished).Google Scholar
  71. [9]
    K. Hess (unpublished). 2 2Google Scholar
  72. [1]
    D. J. Howarth and E. H. Sondheimer, Proc. Roy. Soc. (London) A219 (1953) 53.ADSCrossRefMATHGoogle Scholar
  73. [2]
    H. Ehrenreich, J. Appl. Phys. 32 Suppl. (1961) 2155.Google Scholar
  74. [3]
    E. M. Conwell, Phys. Rev. 143 (1966) 657.ADSCrossRefGoogle Scholar
  75. [4]
    K. Hess and H. Kahlert, J. Phys. Chem. Solids 32 (1971) 2262.Google Scholar
  76. [5]
    F. Kuchar, A. Philipp, and K. Seeger, Solid State Comm. 11 (1972) 965.ADSCrossRefGoogle Scholar
  77. [6]
    G. Bauer and H. Kahlert, Phys. Rev. B5 (1972) 566.ADSCrossRefGoogle Scholar
  78. [7]
    R. Stratton, Proc. Roy. Soc. (London) A 246 (1958) 406.ADSCrossRefMATHGoogle Scholar
  79. [4]
    K. Hess and H. Kahlert, J. Phys. Chem. Solids 32 (1971) 2262.Google Scholar
  80. [5]
    F. Kuchar, A. Philipp, and K. Seeger, Solid State Comm. 11 (1972) 965.ADSCrossRefGoogle Scholar
  81. [6]
    G. Bauer and H. Kahlert, Phys. Rev. B5 (1972) 566.ADSCrossRefGoogle Scholar
  82. [7]
    R. Stratton, Proc. Roy. Soc. (London) A 246 (195 8 ) 406.Google Scholar
  83. [8]
    H. Fröhlich and B. V. Paranjape, Proc. Phys. Soc. (London) B69 (1956) 21; see also E. M. Conwell: Solid State Physics (F. Seitz, D. Turnbull, and H. Ehrenreich, eds.) Suppl. 9, p. 200. New York: Academic Press. 1967. For “dielectric breakdown” see H. Fröhlich, Proc. Roy. Soc. (London) A160 (1937) 230; Adv. Physics 3 (1961) 325.Google Scholar
  84. [9]
    R. Stratton, J. Phys. Soc. Japan 17 (1962) 590.CrossRefGoogle Scholar
  85. [10]
    T. Kurosawa, Proc. Int. Conf. Phys. Semicond. Kyoto 1966, J. Phys. Soc. J.pan 21 Suppl. (1966) 424; W. Fawcett, A. D. Boardmann, and S. Swain, J. Phys. Chem. Solids 31 (1970) 1963.Google Scholar
  86. [11]
    H. Budd, Proc. Int. Conf. Phys. Semicond. Kyoto 1966, J. Phys. Soc. Japan 21 Suppl. (1966) 420.Google Scholar
  87. [12]
    ; IBM J. Res. Develop. 13 (1969) 537.Google Scholar
  88. [13]
    Wien—New York: Springer. 1973; O. Zimmerl, thesis T. H. Wien 1972.Google Scholar
  89. [14]
    For a brief review and further literature see e.g. C. Kittel: Quantum Theory of Solids, p. 137. New York: J. Wiley and Sons. 1963.Google Scholar
  90. [15]
    D. M. Larsen, Phys. Rev. 135 (1964) A 419; 144 (1966) 697; D. M. Larsen and E. J. Johnson, Proc. Int. Conf. Phys. Semic., Kyoto, 1966 (J. Phys. Soc. Japan 21, Suppl.) p. 443, Phys. Soc. Japan, Tokyo, 1966.Google Scholar
  91. [16]
    ; J. W. Hodby, J. A. Borders, and F. C. Brown, J. Phys. C 3 (1970) 335.CrossRefGoogle Scholar
  92. [17]
    H. Ehrenreich, J. Phys. Chem. Solids 8 (1959) 130. Chap.6m.Google Scholar
  93. [1]
    J. Appel, Phys. Rev. 122 (1961) 1760.Google Scholar
  94. [2]
    R. T. Bate, R. D. Baxter, F. J. Reid, and A. C. Beer, J. Phys. Chem. Solids 26 (1965) 1205.Google Scholar
  95. [3]
    ; E. H. Sondheimer, Proc. Roy. Soc. (London) A203 (1950) 75.CrossRefGoogle Scholar
  96. [15]
    D. M. Larsen, Phys. Rev. 135 (1964) A 419; 144 (1966) 697; D. M. Larsen and E. J. Johnson, Proc. Int. Conf. Phys. Semic., Kyoto, 1966 (J. Phys. Soc. Japan 21, Suppl.) p. 443, Phys. Soc. Japan, Tokyo, 1966.Google Scholar
  97. [16]
    M. Mikkor and F. C. Brown, Phys. Rev. 162 (1967) 848; J. W. Hodby, J. A. Borders, and F. C. Brown, J. Phys. C 3 (1970) 335.CrossRefGoogle Scholar
  98. [17]
    H. Ehrenreich, J. Phys. Chem. Solids 8 (1959) 130. Chap.6m.Google Scholar
  99. [1]
    J. Appel, Phys. Rev. 122 (1961) 1760.Google Scholar
  100. [2]
    R. T. Bate, R. D. Baxter, F. J. Reid, and A. C. Beer, J. Phys. Chem. Solids 26 (1965) 1205.Google Scholar
  101. [3]
    M. Kohler, Zeitschr. f. Physik 124 (1948) 772; 125 (1949) 679; E. H. Sondheimer, Proc. Roy. Soc. (London) A203 (1950) 75.CrossRefGoogle Scholar
  102. [4]
    T. P. McLean and E. G. S. Paige, J. Phys. Chem. Solids 16 (1960) 220.ADSCrossRefGoogle Scholar
  103. [1]
    L. R. Weisberg, J. Appl. Phys. 33 (1962) 1817.Google Scholar
  104. [2]
    H. Fritzsche, J. Phys. Chem. Solids 6 (1958) 69.ADSCrossRefGoogle Scholar
  105. [1]
    L. R. Weisberg, J. Appl. Phys. 33 (1962) 1817.Google Scholar
  106. [2]
    H. Fritzsche, J. Phys. Chem. Solids 6 (1958) 69.ADSCrossRefGoogle Scholar
  107. [3]
    W. Klein and D. Geist, Zeitschr. f. Physik 201 (1967) 411.ADSCrossRefGoogle Scholar
  108. [4]
    M. Pollak and T. H. Geballe, Phys. Rev. 122 (1961) 1742.Google Scholar
  109. [1]
    J. Friedel: Dislocations. Oxford: Pergamon. 1964. S. Amelincks: The Direct Observation of Dislocations. Solid State Physics (F. Seitz and D. Turnbull, eds.) Suppl. 6. New York: Acad. Press. 1964.Google Scholar
  110. [2]
    G. L. Pearson, W. T. Read,Jr., and F. J. Morin, Phys. Rev. 93 (1954) 93.Google Scholar
  111. [3]
    W. Schröter, phys. stat. sol. 21 (1967) 211.ADSCrossRefGoogle Scholar
  112. [4]
    W. Schröter and R. Labusch, phys. stat. sol. 36 (1969) 539.CrossRefADSGoogle Scholar
  113. [5]
    W. T. Read,Jr., Phil. Mag. 46 (1955) 111.Google Scholar
  114. [6]
    V. L. Bonch-Bruevich and Sh. M. Kogan, Fiz. Tverd. Tela 1 (1959) 1221. [Engl. transi.: Sov. Phys. - Sol. State 1 (1959) 1118.]Google Scholar
  115. [7]
    B. Pödör, Acta Physica Acad. Sci. Hung. 23 (1967) 393; phys.stat.sol. 16 (1966) K 167.Google Scholar
  116. [8]
    J. H. P. van Weeren, R. Struikmans, and J. Blok, phys. stat. sol. 19 (1967) K 107.Google Scholar
  117. [7]
    B. Pödör, Acta Physica Acad. Sci. Hung. 23 (1967) 393; phys.stat.sol. 16 (1966) K 167.Google Scholar
  118. [8]
    J. H. P. van Weeren, R. Struikmans, and J. Blok, phys. stat. sol. 19 (1967) K 107.Google Scholar
  119. [9]
    A. F. Gibson, J. Phys. Chem. Solids 8 (1959) 147.ADSCrossRefGoogle 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

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