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Zur Theorie der elektrischen Leitungserscheinungen in Halbleitern und Metallen

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Festkörperprobleme V

Part of the book series: Advances in Solid State Physics ((ASSP,volume 5))

Abstract

The present state of the theory of electrical conduction in metals and semiconductors is described in two parts. Part I is devoted to the elementary transport theory based on the validity of the relaxation time approximation. There are two reasons for repeated treatment of this well-known subject: 1. it seems to be necessary to establish the assumptions under which the frequently used relations of the elementary transport theory are valid, and 2. it is shown that this theory cannot explain the galvanomagnetic effects in most cases. The last mentioned circumstance is caused by the fact that nearly all physical properties depend on the orientation to crystal axes due to the influence of the crystal potential. As it will be demonstrated in I. 6 especially the requirements of validity of the relaxation time approximation —i. e. isotropic scattering mechanism and spherical equi-energy surfaces—are not fulfilled under these conditions. In part II is described how the galvanomagnetic magnitudes may be calculated, if the scattering mechanism of the charge carriers is anisotropic and if the energy band structure is not spherical. The theory is developed for low and high magnetic fields as well. These considerations are based on the assumption that the Boltzmann equation holds. This formulation of the problem requires more detailed information on the scattering mechanism than the elementary transport theory. Problems are mentioned which arise in this connection.

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Literatur

  1. Vgl. die zusammenfassenden Darstellungen: H. Fröhlich, Elektronentheorie der Metalle, Berlin: Springer 1936. N. F. Mott und H. Jones, The Theory of the Properties of Metals and Alloys. Oxford: Clarendon Press 1936. F. Seitz, The Modern Theory of Solids. New York: McGraw-Hill Book Co. 1940. A. H. Wilson, The Theory of Metals. Cambridge: Cambridge University Press 1953. R. E. Peierls, Quantum Theory of Solids. Oxford: Clarendon Press 1955. H. Jones, Theory of the Electrical and Thermal Conductivity. In Handbuch der Physik (Flügge), Bd. XIX, Berlin-Göttingen-Heidelberg: Springer 1956. F. J. Blatt, Solid State Phys. (ed. F. Seitz und D. Turnbull) 4, 199 (1957). J. M. Ziman, Electrons and Phonons. Oxford: Clarendon Press 1960. O. Madelung, Halbleiterprobleme II, 376. Vieweg & Sohn, Braunschweig 1955. H. Eggert, Festkörperprobleme I, 274. Vieweg & Sohn, Braunschweig 1962. W. Schottky, Festkörperprobleme I, 316. Vieweg & Sohn, Braunschweig 1962.

    MATH  Google Scholar 

  2. V. M. Galitskii und A. B. Migdal, Žur. eksper. teor. Fiz. 34, 139 (1958), Sov. Phys. JETP 34, 96 (1958).

    MathSciNet  Google Scholar 

  3. J. M. Luttinger, Phys. Rev. 119, 1153 (1960); 121, 1251 (1961).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  4. J. S. Langer, Phys. Rev. 120, 714 (1960); 124, 1003 (1961); 127, 5 (1962).

    Article  ADS  MATH  Google Scholar 

  5. H. Jones und C. Zener, Proc. Roy. Soc. (Lond.) A 145, 268 (1934).

    Article  ADS  MATH  Google Scholar 

  6. M. Kohler, Ann. Phys. (Lpzg.) 20, 891 (1934).

    Article  ADS  MATH  Google Scholar 

  7. F. Herman und J. Callaway, Phys. Rev. 89, 518 (1953).

    Article  ADS  Google Scholar 

  8. F. Herman, Revs Mod. Phys. 30, 102 (1958).

    Article  ADS  Google Scholar 

  9. C. Herring, Bell System Techn. Journ. XXXIV, 237 (1955).

    Google Scholar 

  10. C. Herring und E. Vogt, Phys. Rev. 101, 944 (1956), 105, 1933 (1957).

    Article  ADS  MATH  Google Scholar 

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

    Article  ADS  MATH  Google Scholar 

  12. D. Langbein, Z. Physik 166, 22 (1962) und 167, 83 (1962).

    Article  ADS  Google Scholar 

  13. D. Langbein, Z. Physik 162, 542 (1961).

    Article  ADS  MathSciNet  Google Scholar 

  14. L. J. Davis, Phys. Rev. 56, 93 (1939).

    Article  ADS  MATH  Google Scholar 

  15. R. Olson und S. Rodriguez, Phys. Rev. 108, 1212 (1957).

    Article  ADS  Google Scholar 

  16. F. Garcia-Moliner, Proc. Phys. Soc. 72, 996 (1958).

    Article  ADS  Google Scholar 

  17. J. R. A. Cooper und S. Raines, Phil. Mag. 4, 145 und 1149 (1959).

    Article  ADS  Google Scholar 

  18. B. Lax und J. Mavroides, Phys. Rev. 100, 1650 (1955); 107, 1530 (1957) und 108, 1648 (1957).

    Article  ADS  MATH  Google Scholar 

  19. D. Blochinzev und L. Nordheim, Z. Physik 84, 168 (1933).

    Article  ADS  MATH  Google Scholar 

  20. M. Kohler, Ann. Phys. (Lpzg.) 5, 99 (1950).

    Google Scholar 

  21. I. M. Lifŝic, M. Ja. Azbel' und M. I. Kaganov, Žur. eksper. teor. Fiz. 31, 63 (1956); Sov. Phys. JETP 4, 41 (1957).

    Google Scholar 

  22. B. Abeles und S. Meiboom, Phys. Rev. 93, 1121 (1954) und 95, 31 (1954).

    ADS  Google Scholar 

  23. M. Shibuya, J. Phys. Soc. Jap. 9, 134 (1954) und Phys. Rev. 95, 1385 (1954).

    Article  ADS  Google Scholar 

  24. R. M. Broudy und J. D. Venables, Phys. Rev. 105, 1757 (1957).

    Article  ADS  Google Scholar 

  25. W. Shockley, Phys. Rev. 79, 191 (1950).

    Article  ADS  MathSciNet  Google Scholar 

  26. J. W. McClure, Phys. Rev. 101, 1642 (1956); Phys. Rev. 112, 715 (1958).

    Article  ADS  Google Scholar 

  27. R. G. Chambers, Proc. Roy. Soc. (Lond.) A 238, 344 (1957).

    Article  ADS  MATH  Google Scholar 

  28. A. C. Beer und R. K. Willardson, PHys. Rev. 110, 1286 (1958).

    Article  ADS  Google Scholar 

  29. J. Kolodziejczak, Acta Physica Polonica XX, 289 (1961).

    Google Scholar 

  30. H. Jones, Handbuch der Physik (S. Flügge) XIX, p. 255.

    Google Scholar 

  31. P. P. Debye und E. M. Conwell, Phys. Rev. 93, 693 (1954).

    Article  ADS  Google Scholar 

  32. R. Mansfield, Proc. Phys. Soc. B 69, 76 (1956).

    Article  ADS  Google Scholar 

  33. M. Kohler, Z. Physik 126, 495 (1949).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  34. J. W. Rutter und J. Reekie, Phys. Rev. 78, 70 (1950).

    Article  ADS  Google Scholar 

  35. C. W. Berghout, Physica 18, 978 (1952).

    Article  ADS  Google Scholar 

  36. A. N. Gerritsen und J. O. Linde, Physica 18, 877 (1952).

    Article  ADS  Google Scholar 

  37. E. Krautz und H. Schultz, Z. Naturf. 9a, 125 (1954); 12a, 710 (1957).

    ADS  Google Scholar 

  38. P. Alley und B. Serin, Phys. Rev. 116, 334 (1959).

    Article  ADS  Google Scholar 

  39. D. J. Howarth und E. H. Sondheimer, Proc. Roy. Soc. (Lond.) A 219, 53 (1953).

    Article  ADS  MATH  Google Scholar 

  40. A. H. Wilson, The Theory of Metals, Cambridge 1954.

    Google Scholar 

  41. W. Schottky, Ann. Phys. (Lpzg.) 6, 193 (1949) sowie Festkörperphysik I, S. 316, Vieweg, Braunschweig 1962.

    MATH  Google Scholar 

  42. C. Herrig und E. Vogt, Phys. Rev. 101, 944 (1956); 105, 1933 (1957).

    Article  ADS  Google Scholar 

  43. G. Dresselhaus, A. Kip und C. Kittel, Phys. Rev. 95, 568 (1954).

    Article  ADS  Google Scholar 

  44. E. O. Kane, J. Phys. Chem. Sol. 1, 249 (1957).

    Article  ADS  Google Scholar 

  45. H. Ehrenreich, J. Phys. Chem. Sol. 9, 129 (1959).

    Article  ADS  Google Scholar 

  46. W. Kohn und J. M. Luttinger, Phys. Rev. 108, 590 (1957).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  47. J. M. Luttinger und W. Kohn, Phys. Rev. 109, 1892 (1958).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  48. G. V. Chester und A. Thellung, Proc. Phys. Soc. Lond. 73, 745 (1959).

    Article  MATH  ADS  Google Scholar 

  49. E. Verboven, Physica 26, 1091 (1960) sowie Phil. Mag. 5, 753 (1960).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  50. P. N. Argyres, J. Phys. Chem. Sol. 19, 66 (1961).

    Article  ADS  Google Scholar 

  51. I. G. Lang, Fiz. Tverdogo Tela 2, 2330 (1960); 3, 2573 (1961). Soviet. Phys. Solid State. 2, 2077 (1961); 3, 1871 (1962).

    Google Scholar 

  52. R. Kubo, Canad. J. Phys. 34, 1274 (1956); J. Phys. Soc. Jap. 12, 570 (1957).

    Article  MathSciNet  ADS  Google Scholar 

  53. L. Van Hove, Physica 21, 517 (1955); 23, 441 (1957); 25, 268 (1959) sowie in Fundamental Problems in Statistical Mechanics (Ed. E. G. D. Cohen), North-Holland-Publishing Company, Amsterdam 1962.

    MathSciNet  MATH  Google Scholar 

  54. S. F. Edwards, Phil. Mag. 3, 1020 (1958).

    Article  MATH  ADS  Google Scholar 

  55. O. V. Konstantinov und V. I. Perel', Žur. Eksptl. i. Teor. Fiz. 39, 197 (1960); Soviet Physics JETP 12, 142 (1961).

    MathSciNet  Google Scholar 

  56. D. N. Zubarev, Usp. Fiz. Nauk 71, 71 (1960); Fortschritte der Physik 9, 275 (1961).

    MathSciNet  Google Scholar 

  57. J. S. Langer, Phys. Rev. 120, 714 (1960); 124, 1003 (1961); 127, 5 (1962).

    Article  ADS  MATH  Google Scholar 

  58. N. Matsudaira, Progr. Theor. Phys. 25, 153 (1961): Scient. Pap. College General Education Univ. Tokyo, 11, 25 (1961).

    Article  ADS  MATH  Google Scholar 

  59. T. Izuyama, Progr. Theor. Phys. 25, 964 (1961).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  60. N. M. Plakida, Dokl. Akad. Nauk S. S. S. R., 147, 1067 (1962).

    Google Scholar 

  61. R. G. Chambers, in W. A. Harrison und M. B. Webb, “The Fermi Surface” John-Wiley & Sons, New York-London (1960).

    Google Scholar 

  62. R. B. Stinchcombe, Proc. Phys. Soc. 78, 275 (1961).

    Article  MathSciNet  MATH  ADS  Google Scholar 

  63. P. N. Argyres und E. N. Adams, Phys. Rev. 104, 900 (1956).

    Article  ADS  MATH  Google Scholar 

  64. I. M. Lifŝic, Žur. Eksper. i Teor. Fiz. 30, 814 (1956); Soviet Physics JETP 3, 774 (1956); J. Phys. Chem. Sol. 4, 11 (1958).

    Google Scholar 

  65. P. N. Argyres, J. Phys. Chem. Sol. 4, 19 (1958); 8, 124 (1959); Phys. Rev. 109, 1115 (1958); 117, 315 (1960).

    Article  ADS  Google Scholar 

  66. R. Kubo, H. Hasegawa und N. Hashitsume, J. Phys. Soc. Jap. 14, 56 (1959).

    Article  ADS  MATH  Google Scholar 

  67. E. N. Adams und T. D. Holstein, J. Phys. Chem. Sol. 10, 254 (1959).

    Article  ADS  Google Scholar 

  68. P. N. Argyres und L. M. Roth, J. Phys. Chem. Sol. 12, 89 (1959).

    Article  MathSciNet  ADS  Google Scholar 

  69. V. L. Gureviĉ und Yu. A. Firsov, Žur. Eksptl. i Teor. Fiz. 40, 198 (1961); 41, 512 (1961); Soviet Physics JETP 13, 137 (1961); 14, 367 (1962).

    Google Scholar 

  70. J. Hajdu, Z. Phys. 160, 481 (1960) und 163, 108 (1961).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  71. W. Schottky, Festkörperphysik I, S. 316, Vieweg, Braunschweig (1962).

    Book  Google Scholar 

  72. M. Kohler, Z. Physik 124, 772 (1948); 125, 679 (1949) und 126, 495 (1949).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  73. D. Enskog, Dissertation, Upsala 1917.

    Google Scholar 

  74. E. H. Sondheimer, Proc. Roy. Soc. (Lond.) A 203, 75 (1950).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  75. D. J. Howarth und E. H. Sondheimer, Proc. Roy. Soc. (Lond.) A 219, 53 (1953).

    Article  ADS  MATH  Google Scholar 

  76. H. Bross und A. Seeger, J. Phys. Chem. Sol. 4, 161 (1958).

    Article  ADS  Google Scholar 

  77. M. Tsuji, J. Phys. Soc. Jap. 13, 133, 818 und 979 (1958).

    Article  ADS  Google Scholar 

  78. G. E. Tauber, Journ. Franklin Inst. 268, 175 (1959).

    Article  MathSciNet  Google Scholar 

  79. D. Langbein, Z. Phys. 162, 542 (1961).

    Article  ADS  MathSciNet  Google Scholar 

  80. H. Ehrenreich, J. Phys. Chem. Sol. 2, 131 (1957); 9, 129 (1959).

    Article  ADS  Google Scholar 

  81. H. Bross, Z. Naturf. 15a, 859 (1960).

    ADS  Google Scholar 

  82. F. Garcia-Moliner, Proc. Roy. Soc. (Lond.) A 249, 73 (1958).

    Article  ADS  MathSciNet  Google Scholar 

  83. G. E. Tauber und L. Soffer, J. Phys. Chem. Sol. 8, 138 (1959).

    Article  ADS  Google Scholar 

  84. J. Hajdu, Z. Physik 160, 47 (1960).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  85. M. Kohler, Ann. Phys. (Lpzg.) 40, 601 (1941).

    ADS  MATH  Google Scholar 

  86. F. Garcia-Moliner und S. Simons, Proc. Cambr. Phil. Soc. 53, 848 (1957).

    Article  Google Scholar 

  87. M. Tsuji, J. Phys. Soc. Jap. 13, 979 (1958).

    Article  ADS  Google Scholar 

  88. H. Bross, Z. Naturf. 14a, 560 (1959).

    MathSciNet  ADS  Google Scholar 

  89. H. Bross, Phys. kondens. Materie 3, 349 (1965).

    Article  ADS  Google Scholar 

  90. H. Gabriel und R. Klein, Z. Naturf. 19a, 524 (1964).

    MathSciNet  ADS  Google Scholar 

  91. Ch. H. Müntz, Math. Ann. 87, 131 (1922).

    Article  Google Scholar 

  92. M. Bailyn, Phys. Rev. 126, 2040 (1962).

    Article  ADS  MathSciNet  Google Scholar 

  93. M. Kohler, Ann. Phys. (Lpzg.) 5, 89 (1950) und 6, 18 (1949).

    Google Scholar 

  94. vgl. H. Bross, “Elektronentheorie der Metalle”, in “Moderne Probleme der Metallphysik” herausgegeben von A. Seeger, Springer-Verlag, Berlin-Göttingen-Heidelberg.

    Google Scholar 

  95. H. Bross und A. Holz, Z. Naturf. 19a, 1611 (1964) und 20a, 504 (1964).

    ADS  Google Scholar 

  96. N. F. Mott, Proc. Cambr. Phil Soc. 32, 281 (1936).

    Article  MATH  Google Scholar 

  97. R. B. Dingle, Phil. Mag. 46, 831 (1955).

    MATH  Google Scholar 

  98. H. Ehrenreich, J. Phys. Chem. Sol. 2, 131 (1957); 8, 130 (1959).

    Article  ADS  Google Scholar 

  99. J. Kolodziejczak, Acta Physica Polonica XX, 289 (1961).

    Google Scholar 

  100. J. Bardeen und W. Shockely, Phys. Rev. 80, 72 (1950).

    Article  ADS  MATH  Google Scholar 

  101. S. C. Hunter und F. R. N. Nabarro, Proc. Roy. Soc. (Lond.) A 220, 542 (1953).

    Article  ADS  MATH  Google Scholar 

  102. A. Seeger und H. Bross, Z. Natuf. 15a, 663 (1960).

    ADS  Google Scholar 

  103. J. Bardeen, Phys. Rev. 52, 688 (1937).

    Article  ADS  Google Scholar 

  104. H. Ehrenreich und M. H. Cohen, Phys. Rev. 115, 786 (1959).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  105. M. Bailyn, Phys. Rev. 117, 974 (1960) und 120, 381 (1960).

    Article  ADS  MathSciNet  Google Scholar 

  106. D. Hone, Phys. Rev. 120, 1600 (1960).

    Article  ADS  MathSciNet  Google Scholar 

  107. S. Shinohara, Progr. Theor. Phys. (Kyoto) 26, 420 (1961) und J. Phys. Soc. Japan 16, 1963 (1961).

    Article  ADS  Google Scholar 

  108. J. S. Langer und S. H. Vosko, J. Phys. Chem. Sol. 12, 196 (1960).

    Article  ADS  Google Scholar 

  109. H. Bross und A. Holz, Z. Naturforschg. 20a, 504 (1965).

    ADS  Google Scholar 

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  1. Sektion Physik der Universität, Schellingstraße 2-8, München 13

    H. Bross

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  1. H. Bross
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Fritz Sauter

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© 1966 Friedr. Vieweg & Sohn Braunschweig

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Bross, H. (1966). Zur Theorie der elektrischen Leitungserscheinungen in Halbleitern und Metallen. In: Sauter, F. (eds) Festkörperprobleme V. Advances in Solid State Physics, vol 5. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0119273

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  • DOI: https://doi.org/10.1007/BFb0119273

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