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Quantum Effects in Transport Phenomena

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Semiconductor Physics
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Abstract

In Chap. 2 we learnt how the quantization of the atomic energy levels results in the band structure of the crystalline solid. However, this is not the only domain of quantum mechanics in semiconductivity. Although most transport phenomena can be explained by assuming a classical electron gas, there are some which can be understood only by quantum mechanical arguments. In Sect. 9.1 we will treat phenomena which rely on the quantum mechanical tunnel effect, while in Sects. 9.2–9.4 the quantization of electron orbits in a strong magnetic field with the formation of Landau levels will be the basis for an understanding of the oscillatory behavior of transport phenomena.

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References

  1. L. Esaki: Phys. Rev. 109, 603 (1958)

    Article  CAS  Google Scholar 

  2. W.K. Chow: Principles of Tunnel Diode Circuits (Wiley, New York 1964) (review)

    Google Scholar 

  3. S.M. Sze: Physics of Semiconductor Devices (Wiley, New York 1969)

    Google Scholar 

  4. D. Böhm: Quantum Theory (Prentice Hall, Englewood Cliffs, NJ 1951)

    Google Scholar 

  5. E.O. Kane: J. Appl. Phys. 32, 83 (1961);

    Article  Google Scholar 

  6. E.O. Kane: J. Phys. Chem. Solids 2, 181 (1960)

    Article  Google Scholar 

  7. J. Karlovsky: Phys. Rev. 127, 419 (1962)

    Article  Google Scholar 

  8. E.O. Kane: Phys. Rev. 131, 79 (1963)

    Article  Google Scholar 

  9. P. Thomas, H.J. Queisser: Phys. Rev. 175, 983 (1968)

    Article  CAS  Google Scholar 

  10. P. Thomas: Fachberichte DPG (Teubner, Stuttgart 1968) p. 114 (review) H. Zetsche: Fachberichte DPG (Teubner, Stuttgart 1970) p.172

    Google Scholar 

  11. C. Zener: Proc. Roy. Soc. London 145, 523 (1934)

    Article  CAS  Google Scholar 

  12. K.B. McAfee, E.J. Ryder, W. Shockley, M. Sparks: Phys. Rev. 83, 650 (1951)

    Article  Google Scholar 

  13. S.L. Miller. Phys. Rev. 99, 1234 (1955)

    Article  CAS  Google Scholar 

  14. L. Esaki, R. Tsu: IBM J. Res. Dev. 14, 61 (1970)

    Article  CAS  Google Scholar 

  15. A.Y. Cho: Thin Solid Films 100, 291 (1983)

    Article  CAS  Google Scholar 

  16. P.D. Dapkus: J. Crystal Growth 68, 345 (1984)

    Article  CAS  Google Scholar 

  17. W. Richter: Festkörperprobleme I Advances in Solid State Physics 26, 335, ed. by P. Grosse (Vieweg, Braunschweig 1986)

    Google Scholar 

  18. R. Tsu, L. Esaki: Appl. Phys. Lett. 22, 562 (1973)

    Article  CAS  Google Scholar 

  19. H. Morkoc, J. Chen, U.K. Reddy, T. Henderson, S. Luryi: Appl. Phys. Lett. 49, 70 (1986)

    Article  CAS  Google Scholar 

  20. S. Luryi: In High-Speed Semiconductor Devices, ed. by S.M. Sze, (Wiley, New York 1990)

    Google Scholar 

  21. S. Luryi: In Heter o junction Band Discontinuities: Physics and Device Applications, ed. by F. Capasso, G. Margaritondo, (Elsevier, Amsterdam 1987) p.489

    Google Scholar 

  22. T.C.L.G. Sollner, W.D. Goodhue, P.E. Tannenwald, C.D. Parker, D.D. Peck: Appl. Phys. Lett. 43, 588 (1983)

    Article  CAS  Google Scholar 

  23. T.C.L.G. Sollner, P.E. Tannenwald, D.D. Peck, W.D. Goodhue: Appl. Phys. Lett. 45, 1319 (1984)

    Article  CAS  Google Scholar 

  24. F. Capasso, R.A. Kiehl: J. Appl. Phys. 58, 1366 (1985)

    Article  CAS  Google Scholar 

  25. F. Capasso, S. Sen, A.C. Gossard, A.L. Hutchinson, J.E. English: IEEE EDL-7, 573 (1986)

    Article  Google Scholar 

  26. M. Jonson: In Quantum Transport in Semiconductors ed. by D.K. Ferry, C. Jakoboni (Plenum, New York 1991) p. 193

    Google Scholar 

  27. B.D. McCombe, A. Petrou: In Handbook on Semiconductors ed. by T.S. Moss, M. Balkanski (Elsevier, Amsterdam 1994) Vol. 2, p.285 ff

    Google Scholar 

  28. T.P. Pearsall, J.M. Vandenberg, R. Hall, J. Bonar: Phys. Rev. Lett. 63, 2104 (1989)

    Article  CAS  Google Scholar 

  29. F.H. Pollak: In Handbook on Semiconductors ed. by T.S. Moss (Elsevier, Amsterdam 1994) Vol. 2, p.527

    Google Scholar 

  30. W. Wegscheider, J. Olajos, U. Menczigar, W. Dondl, G. Abstreiter: J. Crystal Growth 123, 75 (1992)

    Article  CAS  Google Scholar 

  31. G. Abstreiter, J. Olajos, R. Schorer, P. Vogl, W. Wegscheider: Semicond. Sci. Technol. 8, S6 (1993)

    Article  Google Scholar 

  32. J. Allègre, J. Calayud, B. Gil, H. Mathieu, H. Tuffigo, G. Lentz, N. Magnea, H. Mariette: Phys. Rev. B 41, 8195(1990)

    Article  Google Scholar 

  33. G.H. Döhler: Phys. Status. Solidi (b) 53, 73, 533 (1972)

    Article  Google Scholar 

  34. K.K. Choi, B.F. Levine, R.J. Malik, J. Walker, C.G. Bethea: Phys. Rev. B 35, 4172 (1987)

    Article  CAS  Google Scholar 

  35. J. Kastrup, R. Hey, K.H. Ploog, H.T. Grahn, L.L. Bonilla, M. Kindelau, M. Moscoso, A. Wacker, J. Galan: Phys. Rev. B 55, 2476 (1997)

    Article  CAS  Google Scholar 

  36. G.H. Wannier: Elements of Solid State Theory (Cambridge Univ. Press, Cambridge (England) 1959);

    Google Scholar 

  37. G.H. Wannier: Rev. Mod. Phys. 34, 645 (1962);

    Article  Google Scholar 

  38. G.H. Wannier: Phys. Rev. 181, 1364 (1969)

    Article  Google Scholar 

  39. G. Bastard, J.A. Brum, R. Ferreira: Solid State Physics Vol. 44, ed. by H. Ehrenreich, D. Turnbull (Academic, New York 1991) p.316

    Google Scholar 

  40. E.E. Méndez, F. Agulló-Rueda, J.M. Hong: Phys. Rev. Lett. 60, 2426 (1988)

    Article  Google Scholar 

  41. G. von Plessen, P. Thomas: Phys. Rev. B 45, 9185 (1992)

    Article  Google Scholar 

  42. J. J. Bleuse, G. Bastard, P. Voisin: Phys. Rev. Lett. 60, 220 (1988)

    Article  CAS  Google Scholar 

  43. P. Voisin, G. Bastard, M. Voos: Phys. Rev. B 29, 935 (1984)

    Article  CAS  Google Scholar 

  44. E.E. Méndez, G. Bastard: Phys. Today 46, 34 (June 1993)

    Article  Google Scholar 

  45. G. Bastard: Wave Mechanics Applied to Semiconductor Heterostructures (Les Editions de Physique, Les Ulis Cedex, France, 1987) p.26

    Google Scholar 

  46. K. Unterrainer, B.J. Keay, M.C. Wanke, S.J. Allen, D. Leonhard, G. Medeiros-Ribeiro, U. Bhattacharya, M.J.W. Rodwell: Phys. Rev. Lett. 76, 2973 (1996)

    Article  CAS  Google Scholar 

  47. A.A. Ignatov, A.P. Jauho: J. Appl. Phys. 85, 3643 (1999)

    Article  CAS  Google Scholar 

  48. S. Winnerl, E. Schomburg, J. Grenzer, H.J. Regl, A.A. Ignatov, A.D. Semenov, K.F. Renk, D.G. Pavel’ev, Yu. Koscharinov, B. Melzer, V. Ustinov, S. Ivanov, S. Schaposchnikov, P.S. Kop’ev: Phys. Rev. B 56, 10303 (1997)

    Article  CAS  Google Scholar 

  49. L.D. Landau: Z. Physik 64, 629 (1930)

    Article  CAS  Google Scholar 

  50. O. Madelung: Festkörper-Probleme V, 87 (Vieweg, Braunschweig 1960)

    Google Scholar 

  51. R.G. Chambers: Can. J. Phys. 34, 1395 (1956)

    Article  CAS  Google Scholar 

  52. G. Bauer, H. Kahlert: Phys. Rev. B 5, 566 (1972); Proc. Int’l Conf. Phys. Semicond., Cambridge MA, 1970 (USAEC, Oak Ridge, TN 1970) p.65

    Article  Google Scholar 

  53. L. Shubnikov, W.J. de Haas: Leiden Commun. 207a, 207c, 207d, 210a (1930)

    Google Scholar 

  54. E.N. Adams, T.D. Holstein: J. Phys. Chem. Solids 10, 254 (1959)

    Article  CAS  Google Scholar 

  55. L.I. Schiff: Quantum Mechanics (McGraw-Hill, New York 1968) p.441

    Google Scholar 

  56. M. Cardona: J. Phys. Chem. Solids 24, 1543 (1963)

    Article  CAS  Google Scholar 

  57. R.B. Dingle: Proc. Roy. Soc. London A 211, 517 (1952)

    Article  CAS  Google Scholar 

  58. R.A. Isaacson, F. Bridges: Solid State Commun. 4, 635 (1966)

    Article  CAS  Google Scholar 

  59. G. Bauer, H. Kahlert: Phys. Lett. 41, A351 (1972); also Ref. 9.54 below

    Article  CAS  Google Scholar 

  60. L.M. Roth, P.N. Argyres: Semiconductors and Semimetals 1, ed. by R.K. Willardson, A.C. Beer (Academic, New York 1966) p. 159

    Google Scholar 

  61. S.M. Puri, T.H. Geballe: Semiconductors and Semimetals 1, ed. by R.K. Willardson, A.C. Beer (Academic, New York 1966) p.203 (thermomagnetic effects)

    Google Scholar 

  62. W.J. de Haas, P.M. van Alphen: Leiden Commun. 208d, 212a (1930); 220d (1933)

    Google Scholar 

  63. R.A. Smith: The Physical Principles of Thermodynamics (Chapman and Hall, London 1952) p.154

    Google Scholar 

  64. R.A. Smith: Wave Mechanics of Crystalline Solids (Chapman and Hall, London 1961) p.384

    Google Scholar 

  65. J.M. Ziman: Principles of the Theory of Solids (Cambridge Univ. Press, Cambridge 1964) Sect.9.7

    Google Scholar 

  66. D. Shoenberg: In The Physics of Metals 1. Electrons, ed. by J.M. Ziman (Cambridge Univ. Press, Cambridge 1969)

    Google Scholar 

  67. Y. Yafet, R.W. Keyes, E.N. Adams: J. Phys. Chem. Solids 1, 137 (1956)

    Article  Google Scholar 

  68. R.W. Keyes, R.J. Sladek: J. Phys. Chem. Solids 1, 143 (1956)

    Article  Google Scholar 

  69. E.H. Putley: Proc. Phys. Soc. London 76, 802 (1960);

    Article  CAS  Google Scholar 

  70. E.H. Putley: J. Phys. Chem. Solids 22, 241 (1961)

    Article  CAS  Google Scholar 

  71. L.J. Neuringer: Proc. Int’l Conf. Phys. Semicond., Moscow 1968 (Nauka, Leningrad 1968) p.715

    Google Scholar 

  72. E.H. Putley: Semiconductors and Semimetals 1, ed. by R.K. Willardson, A.C. Beer (Academic, New York 1966) p.289

    Google Scholar 

  73. E.H. Putley: Phys. Status Solidi 6, 571 (1964)

    Article  CAS  Google Scholar 

  74. E.R. Brown, M.J. Wengler, T.G. Phillips: J. Appl. Phys. 58, 2051 (1985)

    Article  CAS  Google Scholar 

  75. V.L. Gurevich, Yu.A. Firsov: Zh. Eksp. Teor. Fiz. 40, 199 (1961) [Engl, transi.: Sov. Phys. -JETP 13, 137(1961)]

    Google Scholar 

  76. M.I. Klinger: Fiz. Tverd. Tela 3, 1342 (1961) [Engl, transl.: Sov. Phys. — Solid State 3, 974 (1961)]

    Google Scholar 

  77. Yu.A. Firsov, V.L. Gurevich, R.V. Parfeniev, S.S. Shalyt: Phys. Rev. Lett. 12, 660 (1964) for a degenerate electron gas

    Article  Google Scholar 

  78. A.L. Efros: Fiz. Tverd. Tela 3, 2848 (1961) [Engl, transi. Sov. Phys. — Solid State 3, 2079 (1962)]

    Google Scholar 

  79. L. Eaves, R.A. Stradling, R.A. Wood: Proc. Int’l Conf Phys. Semicond., Cambridge MA, 1970, ed. by S.P. Keller, J.C. Hensel, F. Stern (USAEC, Oak Ridge, TN 1970) p.816

    Google Scholar 

  80. V.L. Gurevich, Yu.A. Firsov: Zh. Eksp. Teor. Fiz. 47, 734 (1964) [Engl, transi.: Sov. Phys. -JETP 20, 489(1964)]

    CAS  Google Scholar 

  81. R.A. Stradling, R.A. Wood: J. Physique C 1, 1711 (1968)

    Article  Google Scholar 

  82. A.L. Mears, R.A. Stradling, E.K. Inall: J. Physique C 1, 821 (1968)

    Article  Google Scholar 

  83. R.A. Reynolds: Solid State Electron. 11, 385 (1968)

    Article  CAS  Google Scholar 

  84. R.A. Wood, R.A. Stradling, I.P. Molodyan: J. Phys. Paris C 3, LI54 (1970)

    Google Scholar 

  85. S.M. Puri, T.H. Geballe: Semiconductors and Semimetals 1, 203 (Academic, New York 1966)

    Article  Google Scholar 

  86. J. Bardeen, L.N. Cooper, J.R. Schrieffer: Phys. Rev. 108, 1157 (1957)

    Article  Google Scholar 

  87. J.R. Tucker: IEEE J. QE-15, 1234 (1979)

    Article  Google Scholar 

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Seeger, K. (1999). Quantum Effects in Transport Phenomena. In: Semiconductor Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03797-3_9

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  • DOI: https://doi.org/10.1007/978-3-662-03797-3_9

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