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Charge and Energy Transport in a Nondegenerate Electron Gas

  • Karlheinz Seeger
Part of the Springer Series in Solid-State Sciences book series (SSSOL, volume 40)

Abstract

In the preceding chapters, we have seen that a mobile charge carrier in a semiconductor has an effective mass m which is different from the free electron mass m 0. The effective mass takes care of the fact that the carrier is subject to the crystal field. In discussing the velocity distribution of the gas of carriers, we found that the Fermi-Dirac distribution holds in general and that the Maxwell-Boltzmann distribution f (v) ∝ exp(−mv 2/2k B T) is an approximation of the former which is valid for nondegenerate semiconductors. Here the carrier density is small compared with the effective density of states N c in the conduction band and N v in the valence band (3.1.12). For these distributions, no externally applied electric fields were assumed to be present. Instead, the calculations were based on the assumption of thermal equilibrium.

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References

  1. 4.1
    L. Onsager: Phys. Rev. 37, 405 (1931)CrossRefGoogle Scholar
  2. L. Onsager: Phys. Rev. 38, 2265 (1931)CrossRefGoogle Scholar
  3. A.C. Smith, J.F. Janak, R.B. Adler: Electronic Conduction in Solids (McGraw-Hill, New York 1967) Sect. 3. 5Google Scholar
  4. 4.2
    S.R. de Groot: Thermodynamics of Irreversible Processes (North-Holland Amsterdam 1953)Google Scholar
  5. 4.3
    A.C. Beer: In The Hall Effect and its Applications,ed. by C.L. Chien, C.R. Westgate (Plenum, New York 1980) p.299 (review)Google Scholar
  6. 4.4
    E.H. Putley: The Hall Effect and Related Phenomena ( Butterworth, London 1960 )Google Scholar
  7. 4.5
    A.H. Wilson: The Theory of Metals, 2nd edn. ( Cambridge Univ. Press, London 1965 )Google Scholar
  8. 4.6
    O. Madelung, H. Weiss: Z. Naturforsch. 91, 527 (1954)Google Scholar
  9. 4.7
    N.I. Volokobinskaya, V.V. Galavanov, D.N. Nasledov: Fiz. Tverd. Tela 1, 756 (1959)Google Scholar
  10. N.I. Volokobinskaya, V.V. Galavanov, D.N. Nasledov: Engl Soy. Phys.-Solid State 1, 687 (1959)Google Scholar
  11. 4.8
    N.Z. Lupu, N.M. Tallan, D.S. Tannhauser: Rev. Sci. Instrum. 38, 1658 (1967)CrossRefGoogle Scholar
  12. 4.9
    H.H. Wieder: Laboratory Notes on Electrical and Galvanomagnetic Measurements ( Elsevier, Amsterdam 1979 )Google Scholar
  13. 4.10
    L.J. van der Pauw: Philips Techn. Rundsch. 20, 230 (1959)Google Scholar
  14. L.J. van der Pauw: Philips Res. Rep. 16, 187 (1961)Google Scholar
  15. 4.11
    J. Hornstra, L.J. van der Pauw: J. Electron. Control 7, 169 (1959), describing a method for measuring electrical resistivities of anisotropic materialsGoogle Scholar
  16. 4.12
    H.C. Montgomery: J. Appl. Phys. 42, 2971 (1971)CrossRefGoogle Scholar
  17. 4.13
    B. Schwartz (ed.): Ohmic Contacts to Semiconductors ( The Electrochemical Society, New York 1968 )Google Scholar
  18. 4.14
    R.K. Willardson, T. Harman, A.C. Beer: Phys. Rev. 96, 1512 (1954)CrossRefGoogle Scholar
  19. 4.15
    A. Kawabata: J. Phys. Soc. Jpn. 49, 628 (1980)CrossRefGoogle Scholar
  20. 4.16
    O.M. Corbino: Phys. Z. 12, 561 (1911)Google Scholar
  21. 4.17
    H. Welker, H. Weiss: Z. Physik 138, 322 (1954)CrossRefGoogle Scholar
  22. 4.18
    W. Röss, A. Philipp, K. Seeger, K. Ehinger, K. Menke, S. Roth: Solid State Commun. 45, 933 (1983)CrossRefGoogle Scholar
  23. 4.19
    R.F. Wick: J. Appl. Phys. 25, 741 (1954)CrossRefGoogle Scholar
  24. 4.20
    A.H. Thompson, G.S. Kino: J. Appl. Phys. 41, 3064 (1976)CrossRefGoogle Scholar
  25. 4.21
    R.W. Rendell, S.M. Girvin: Phys. Rev. B 23, 6610 (1981)Google Scholar
  26. 4.22
    P.M. Morse, H. Feshbach: Methods of Theoretical Physics, Pt. I (McGraw-Hill, New York 1953 ) p. 707Google Scholar
  27. 4.23
    B. Neudecker, K.H. Hoffmann: Solid State Commun. 62, 135 (1987)CrossRefGoogle Scholar
  28. 4.24
    J.A.M. Dikhoff: Solid-State Electronics 1, 202 (1960)CrossRefGoogle Scholar
  29. 4.25
    P.R. Camp: J. Appl. Phys. 25, 459 (1954)CrossRefGoogle Scholar
  30. 4.26
    F. Kuhn-Kuhnenfeld: J. Electrochem. Soc. Solid State Science and Technology 119, 1063 (1972)Google Scholar
  31. 4.27
    D.C. Miller, G.A. Rozgonyi: In Handbook on Semiconductors,Vol.3, ed. by S.P. Keller (North-Holland, Amsterdam 1980) p.217 (review)Google Scholar
  32. 4.28
    H. Rupprecht, R. Weber, H. Weiss: Z. Naturforsch. 15a, 783 (1960)Google Scholar
  33. 4.29
    C. Herring: J. Appl. Phys. 31, 1939 (1960)CrossRefGoogle Scholar
  34. 4.30
    H. Weiss: J. Appl. Phys. Suppl. 32, 2064 (1961)CrossRefGoogle Scholar
  35. 4.31
    D.J. Ryden: J. Phys. C 7, 2655 (1974)CrossRefGoogle Scholar
  36. 4.32
    J.Y.W. Seto: J. Appl. Phys. 46, 5247 (1975)CrossRefGoogle Scholar
  37. 4.33
    J.W. Orton, M.J. Powell: Rep. Prog. Phys. 43, 1263 (1980)CrossRefGoogle Scholar
  38. 4.34
    C. Yamanouchi, K. Mizuguchi, W. Sasaki: J. Phys. Soc. Jpn. 22, 859 (1967)CrossRefGoogle Scholar
  39. 4.35
    C. Goldberg, R.E. Davis: Phys. Rev. 94, 1121 (1954)CrossRefGoogle Scholar
  40. 4.36
    L. Grabner: Phys. Rev. 117, 689 (1960)CrossRefGoogle Scholar
  41. 4.37
    A.C. Smith, J.F. Janak, R.B. Adler: Electronic Conduction in Solids (McGraw-Hill, New York 1967 ) Appendix IGoogle Scholar
  42. 4.38
    M. Sze: Physics of Semiconductor Devices, 2nd edn. ( Wiley, New York 1981 )Google Scholar
  43. 4.39
    J. Appel: Progress in Semiconductors,Vol.5, ed. by A.F. Gibson, R.E. Burgess (Temple, London 1960) p.142 (review)Google Scholar
  44. 4.40
    T.H. Geballe, G.W. Hull: Phys. Rev. 110, 773 (1958)CrossRefGoogle Scholar
  45. 4.41
    H. Weiss: In Halbleiter und Phosphore, ed. by M. Schön, H. Welker ( Vieweg, Braunschweig 1957 ) p. 497Google Scholar
  46. 4.42
    J. Schröder: Rev. Sci. Instrum. 34, 615 (1963)CrossRefGoogle Scholar
  47. 4.43
    W. Fulkerson, J.P. Moore, R.K. Williams, R.S. Graves, D.L. McElroy: Phys. Rev. 167, 765 (1968)CrossRefGoogle Scholar
  48. 4.44
    O. Madelung: Introduction to Solid-State Theory, Springer Ser. Solid-State Sci., Vol. 2 ( Springer, Berlin, Heidelberg 1978 )Google Scholar
  49. 4.45
    H.M. Rosenberg: Low Temperature Solid State Physics (Oxford Univ. Press, London 1965 ) P 8Google Scholar
  50. F. Pobell: Matter and Methods at Low Temperatures, 2nd. edn. (Springer, Berlin, Heidelberg 1996 )Google Scholar
  51. 4.46
    M.W. Zemansky: Heat and Thermodynamics, 4th edn. ( McGraw-Hill, New York 1957 ) p. 192Google Scholar
  52. 4.47
    A.H. Wilson: The Theory of Metals, 2nd edn. ( Cambridge Univ. Press, Cambridge 1965 ) p. 205Google Scholar
  53. 4.48
    A.V. Gold, D.K.C. McDonald, W.B. Pearson, I.M. Templeton: Philos. Mag. 5, 765 (1960)CrossRefGoogle Scholar
  54. 4.49
    T.H. Geballe, G.W. Hull: Phys. Rev. 98, 940 (1955)CrossRefGoogle Scholar
  55. 4.50
    T.H. Geballe, G.W. Hull: Phys. Rev. 94, 1134 (1954)CrossRefGoogle Scholar
  56. 4.51
    L.J. Kroko, A.G. Milnes: Solid-State Electron. 8, 829 (1965)CrossRefGoogle Scholar
  57. 4.52
    C. Herring: In Halbleiter und Phosphore, ed. by M. Schön, H. Welker ( Vieweg, Braunschweig 1958 ) p. 184Google Scholar
  58. 4.53
    H.P.R. Frederikse: Phys. Rev. 91, 491 (1953)Google Scholar
  59. H.P.R. Frederikse: Phys. Rev. 92, 248 (1953)CrossRefGoogle Scholar
  60. 4.54
    L. Sosnowski: Semiconductors,Proc. Int’l School of Physics XXII (Academic, London 1963) p.436 (review)Google Scholar
  61. 4.55
    J. Bardeen, C. Herring: In: Imperfections in Nearly Perfect Crystals, ed. by F. Seitz ( Wiley, New York 1952 )Google Scholar
  62. 4.56
    R. Becker: Theory of Heat, 2nd edn ( Springer, Berlin, Heidelberg 1967 ) Chap. 95CrossRefGoogle Scholar
  63. R. Becker: Theorie der Wärme, 3rd edn, Heidelberger Taschenbücher, Vol. 10 ( Springer, Berlin, Heidelberg 1985 )Google Scholar
  64. W. Brenig: Statistical Theory of Heat (Springer, Berlin, Heidelberg 1989 )Google Scholar
  65. 4.57
    R. Bowers, R.W. Ure, Jr., J.E. Bauerle, A.J. Cornish: J. Appl. Phys. 30, 930 (1959)Google Scholar
  66. 4.58
    A.F. Joffé: Semiconductor Thermoelements and Thermoelectric Cooling ( Infosearch, London 1958 )Google Scholar
  67. 4.59
    H.P.R. Frederikse, V.A. Johnson, W.W. Scanlon: Solid State Physics Vo 6B, ed. by K. Lark-Horowitz, V.A. Johnson ( Academic, New York 1959 ) p. 114Google Scholar
  68. 4.60
    R. Wolfe: Semiconductor Products 6, 23 (1963)Google Scholar
  69. R. Wolfe: Sci. Am. 210, 70 (1964)CrossRefGoogle Scholar
  70. 4.61
    H. Wagini: Z. Naturforsch. 19a, 1541 (1964)Google Scholar
  71. 4.62
    A.C. Beer, J.A. Armstrong, 1.N. Greenberg: Phys. Rev. 107, 1506 (1957)CrossRefGoogle Scholar
  72. 4.63
    L. Sosnowski: Proc. Int’l Conf. Phys. Semicond. Paris 1964 ( Dunod, Paris 1964 ) p. 341Google Scholar
  73. 4.64
    D.N. Nasledov: J. Appl. Phys. 32, Suppl., 2140 (1961)Google Scholar
  74. 4.65
    S. Minomura, H.G. Drickamer: J. Phys. Chem. Solids 23, 451 (1962)CrossRefGoogle Scholar
  75. 4.66
    C. Kittel: Introduction to Solid State Physics, 4th edn. ( Wiley, New York 1965 ) Chap. 4Google Scholar
  76. 4.67
    B.K. Vainshtein: Fundamentals of Crystals, 2nd edn., Modern Crystallography I, Springer Ser. Solid-State Sci., Vol. 15 ( Springer, Berlin, Heidelberg 1994 )Google Scholar
  77. 4.68
    E.G.S. Paige: In Progress in Semiconductors, Vol. 8, ed. by A.F. Gibson, R.E. Burgess ( Temple, London 1964 ) p. 159Google Scholar
  78. 4.69
    C.S. Smith: Solid State Physics 6, 175 ( Academic, New York 1958 )Google Scholar
  79. 4.70
    W. Voigt: Lehrbuch der Kristallphysik ( Teubner, Leipzig 1928 )Google Scholar
  80. 4.71
    C.S. Smith: Phys. Rev. 94, 42 (1954)CrossRefGoogle Scholar
  81. 4.72
    F.J. Morin, T.H. Geballe, C. Herring: Phys. Rev. 105, 525 (1957)CrossRefGoogle Scholar
  82. 4.
    R.W. Keyes: Solid State Physics 11, 172 (Table V) and 176 (Table VI) (Academic, New York 1960), ed. by F. Seitz, D. TurnbullGoogle Scholar
  83. 4.74
    E.J. Ryder, W. Shockley: Phys. Rev. 81, 139 (1951)CrossRefGoogle Scholar
  84. 4.75
    E.J. Ryder: Phys. Rev. 90, 766 (1953)CrossRefGoogle Scholar
  85. 4.76
    H. Heinrich, K. Seeger: Verh. Dtsch. Phys. Ges. (VI) 2, 26 (1967)Google Scholar
  86. K. Seeger: Acta Phys. Austriaca 27, 1 (1968)Google Scholar
  87. 4.77
    H. Heinrich, G. Bauer, D. Kasperkovitz: Phys. Status Solidi 28, K51 (1968)CrossRefGoogle Scholar
  88. 4.78
    H. Heinrich, W. Jantsch: Solid State Commun. 7, 377 (1969)CrossRefGoogle Scholar
  89. 4.79
    A. Alberigi-Quaranta, C. Jacoboni, G. Ottaviani: Riv. Nuovo Cimento 1, 445 (1971)Google Scholar
  90. 4.80
    A.G.R. Evans: Electron. Lett. 8, 195 (1972)CrossRefGoogle Scholar
  91. 4.81
    K. Seeger: J. Appl. Phys. 63, 5439 (1988); Appl. Phys. Lett. 54, 1268 (1989)Google Scholar
  92. 4.82
    K. Seeger: Synth. Metals 15, 361 (1986)CrossRefGoogle Scholar
  93. 4.83
    K. Seeger, K.F. Hess: Z. Physik 237, 252 (1970)CrossRefGoogle Scholar
  94. 4.84
    A. van der Ziel: Noise, Measurement and Characterization ( Prentice-Hall, Englewood Cliffs NJ 1970 )Google Scholar
  95. 4.85
    D. Wolf (ed.): Noise in Physical Systems, Springer Ser. Electrophys., Vol. 2 ( Springer, Berlin Heidelberg 1978 )Google Scholar
  96. 4.86
    H. Nyquist: Phys. Rev. 32, 110 (1928)CrossRefGoogle Scholar
  97. 4.87
    A.L. McWhorter: In Semiconductor Surface Physics, ed. by R.H. Kingston ( Univ. of Pennsylvania Press, Philadelphia 1957 ) p. 207Google Scholar
  98. R.H. Kingston, A.L. McWhorter: Phys. Rev. 103, 534 (1956)CrossRefGoogle Scholar
  99. 4.88
    T.G. Maple, L. Bess, H.A. Gebbie: J. Appl. Phys. 26, 490 (1955)CrossRefGoogle Scholar
  100. 4.89
    D. Sautter, K. Seiler: Z. Naturforsch. 12a, 490 (1957)Google Scholar
  101. 4.90
    W. Shockley: Electrons and Holes in Semiconductors ( Van Nostrand, Princeton, NJ 1950 ) p. 345Google Scholar
  102. 4.91
    G. Lautz, M. Pilkuhn: Naturwissenschaften 47, 198, 394 (1960)CrossRefGoogle Scholar
  103. M. Pilkuhn: Rauschuntersuchungen an Germanium-Einkristallen bei tiefen Temperaturen, Dissertation, TH Braunschweig (1960)Google Scholar
  104. 4.92
    E. Erlbach, J.B. Gunn: Proc. Int. Conf. Phys. Semicond., Exeter ( Institute of Physics, London 1962 ) p. 128Google Scholar
  105. 4.93
    C.A. Bryant: Bull. Am. Phys. Soc. (Ser. II) 9, 62 (1964)Google Scholar
  106. 4.94
    P.J. Price: In Fluctuation Phenomena in Solids,ed. by R.E. Burgess (Academic, New York 1964) Chap. 8Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Karlheinz Seeger
    • 1
    • 2
  1. 1.WienAustria
  2. 2.Institut für MaterialphysikUniversität WienWienAustria

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