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Surface quantization in semiconductors

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Festkörperprobleme 13

Part of the book series: Advances in Solid State Physics ((ASSP,volume 13))

Abstract

The surface electric field associated with a semiconductor inversion or accumulation layer quantizes the motion normal to the surface. The bulk energy bands split into subbands near the surface forming a two-dimensional electron (hole) gas. A self-consistent formulation of the problem is given in the form of coupled Schrödinger and Poisson equations. A review of approximate results of simple limiting cases is given. The condition of surface semiconductor layer in applied magnetic field, causing Landau levels, is discussed. The analogy of the quantum size effect in thin semiconductor films to the quantum effect in the surface layer is outlined. A number of experimental techniques, as magnetoconductivity (Shubnikov-de Haas oscillations), Hall effect, capacitance, magnetocapacitance, piezoresistance, tunneling, and photoresponse measurements were carried out to verify the surface quantization in inversion and accumulation layers of silicon and other semiconductors from the low temperature region up to room temperatures.

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References

  1. F. Braun, Pogg. Ann. Bd. 153, 556 (1874).

    Google Scholar 

  2. W. Schottky, Z. Physik 113, 367 (1939); 118, 539 (1942).

    Article  MATH  ADS  Google Scholar 

  3. N. F. Mott, Proc. Roy. Soc. (London) A 171, 27 (1939).

    Article  MATH  ADS  Google Scholar 

  4. B. Davydov, J. Phys. (USSR) 1, 167 (1939).

    Google Scholar 

  5. J. Bardeen, Phys. Rev. 71, 717 (1947).

    Article  ADS  Google Scholar 

  6. I. E. Tamm, Z. Phys. 76, 849 (1932), Phys. Z. Sowjet. 1, 733 (1932).

    Article  ADS  Google Scholar 

  7. W. Shockley, Phys. Rev. 56, 317 (1939).

    Article  MATH  ADS  Google Scholar 

  8. J. Bardeen and W. H. Brattain, Phys. Rev. 74, 230 (1948); 75, 203 (1949).

    Article  ADS  Google Scholar 

  9. A. Many, Y. Goldstein, and N. B. Grover, Semiconductor Surfaces, Ch. 4, North-Holland Publishing Co., Amsterdam 1965.

    Google Scholar 

  10. B. Hoeneisen and C. A. Mead, Solid-State Electronics 15, 819 (1972).

    Article  ADS  Google Scholar 

  11. J. R. Schrieffer, Semiconductor Surface Physics, ed., R. H. Kingston, p. 55, Univ. of Pennsylvania Press, Philadephia (1957).

    Google Scholar 

  12. C. B. Duke, Phys. Rev. 159, 632 (1967).

    Article  ADS  Google Scholar 

  13. C. B. Duke, Phys. Rev. 168, 816 (1968).

    Article  ADS  Google Scholar 

  14. F. Stern and W. E. Howard, Phys. Rev. 163, 816 (1967).

    Article  ADS  Google Scholar 

  15. Joel A. Appelbaum and G. A. Baraff, Phys. Rev. B 4, 1235 (1971).

    Article  ADS  Google Scholar 

  16. G. A. Baraff and Joel A. Appelbaum, Phys. Rev. B 5, 475 (1972).

    Article  ADS  Google Scholar 

  17. A. P. Gnädinger and H. E. Talley, Solid-State Electronics 13, 1301 (1970).

    Article  ADS  Google Scholar 

  18. F. Stern, Phys. Rev. B 5, 4891 (1972).

    Article  ADS  Google Scholar 

  19. P. Handler and S. Eisenhour, Surface Sci. 2, 64 (1964).

    Article  ADS  Google Scholar 

  20. N. St. J. Murphy, Surface Sci. 2, 86 (1964).

    Article  ADS  Google Scholar 

  21. F. Proix and P. Handler, Surface Sci. 5, 81 (1966).

    Article  ADS  Google Scholar 

  22. F. F. Fang and W. E. Howard, Phys. Rev. Letters 16, 797 (1966).

    Article  ADS  Google Scholar 

  23. S. Kawaji and Y. Kawaguchi, J. Phys. Soc. Japan Suppl. 21, 336 (1966).

    Google Scholar 

  24. S. Kawaji and H. C. Gatos, Surface Sci. 6, 362 (1967); 7, 215 (1967).

    Article  ADS  Google Scholar 

  25. A. B. Fowler, F. F. Fang, W. E. Howard, and P. J. Stiles, Phys. Rev. Letters 16, 901 (1966); J. Phys. Soc. Japan Suppl. 21, 331 (1966).

    Article  ADS  Google Scholar 

  26. F. Stern, in Proc., 10th Int. Conf. Phys. Sem. p. 451, Cambridge, Massachusetts (1970); Proc. 1971 Int. Sonf. Solid Surfaces, p. 752, Boston, Mass.(1971).

    Google Scholar 

  27. F. Stern, J. Comput. Phys. 6, 56 (1970).

    Article  MATH  ADS  Google Scholar 

  28. D. Colman, R. T. Bate, and J. P. Mize, J. Appl. Phys. 39, 1923 (1968).

    Article  ADS  Google Scholar 

  29. G. Noti, Solid-State Electronics 15, 723 (1972).

    Article  ADS  Google Scholar 

  30. J. A. Pals, Phys. Letters 39A, 101 (1972).

    ADS  Google Scholar 

  31. J. A. Pals, Thesis, Technical University, Eindhoven 1972; Philips Res. Repts. Suppl. 1972, No. 7.

    Google Scholar 

  32. O. V. Konstantinov and A. Ya. Shik, Eksperim. i. Teor. Fiz. 58, 1662 (1970); Sov. Phys. JETP 31, 891 (1970).

    Google Scholar 

  33. Yu. F. Ogrin, V. N. Lutskij and M. I. Elinson, Zh. Exp. Toer. Fiz., Pisma, 3, 114 (1966); Sov. Phys. JETP Letters 3, 71 (1966).

    Google Scholar 

  34. V. N. Lutskij, D. N. Korneev, and M. I. Elinson, Zh. Exp. Teor. Fiz., Pisma, 4, 267 (1966).

    Google Scholar 

  35. V. B. Sandomirskij, Zh. Exp. Teor. Fiz., 52, 158 (1967); Sov. Phys. JETP 25, 101 (1967).

    Google Scholar 

  36. M. I. Elinson, V. A. Volkov, V. N. Lutskij, and T. N. Pinsker, Thin Solid Films 12, 383 (1972).

    Article  ADS  Google Scholar 

  37. B. A. Tavger and V. Ya. Demikhovskij, Sov. Phys. Uspekhi 11, 644 (1969).

    Article  ADS  Google Scholar 

  38. S. Kawaji, J. Phys. Soc. Japan 27, 906 (1969).

    Article  ADS  Google Scholar 

  39. J. Bardeen and W. Shockley, Phys. Rev. 80, 72 (1950).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  40. H. Ezawa, T. Kuroda, and K. Nakamura, Surface Sci. 24, 654 (1971).

    Article  ADS  Google Scholar 

  41. H. Ezawa, S. Kawaji, T. Kuroda, and K. Nakamura, Surface Sci. 24, 659 (1971).

    Article  ADS  Google Scholar 

  42. H. Ezawa, S. Kawaji, and K. Nakamura, Surface Sci. 27, 218 (1971).

    Article  ADS  Google Scholar 

  43. H. Ezawa, Ann. Phys. (N.Y.) 67, 438 (1971).

    Article  ADS  Google Scholar 

  44. S. Kawaji, H. Ezawa, and K. Nakamura, Proc. 1971 Int. Conf. Solid Surfaces, p. 762, Boston, Mass. (1971).

    Google Scholar 

  45. A. A. Guzev, G. L. Kurishev, and S. P. Sinitsa, phys. stat. sol. (a) 14, 41 (1972).

    Article  ADS  Google Scholar 

  46. E. D. Siggia and P. C. Kwok, Phys. Rev. B 2, 1024 (1970).

    Article  ADS  Google Scholar 

  47. R. F. Greene and R. W. O'Donnell, Phys. Rev. 147, 599 (1966).

    Article  ADS  Google Scholar 

  48. Y. Matsumoto, to be published.

    Google Scholar 

  49. T. I. Kamins and N. C. MacDonald, Phys. Rev. 167, 754 (1968).

    Article  ADS  Google Scholar 

  50. T. H. Ning and C. T. Sah, Phys. Rev. B 6, 4605 (1972).

    Article  ADS  Google Scholar 

  51. C. T. Sah, T. H. Ning, and L. L. Tschopp, Surface Sci. 30, 131 (1972).

    Google Scholar 

  52. T. Ando and Y. Uemura, J. Phys. Soc. Japan 30, 632 (1971).

    Article  ADS  Google Scholar 

  53. T. Ando, Y. Matsumoto, Y. Uemura, M. Kobayashi, and K. F. Komatsubara, J. Phys. Soc. Japan 32, 859 (1972).

    Article  ADS  Google Scholar 

  54. F. F. Fang and P. Stiles, Phys. Rev. 174, 823 (1968).

    Article  ADS  Google Scholar 

  55. J. F. Janak, Phys. Rev. 178, 1416 (1969).

    Article  ADS  Google Scholar 

  56. J. L. Smith and P. J. Stiles, Phys. Rev. Letters 29, 102 (1972).

    Article  ADS  Google Scholar 

  57. Y. Katayama, N. Kotera, and K. F. Komatsubara, Proc. 10th Int. Conf. Phys. Sem., p. 464, Cambridge, Mass. (1970).

    Google Scholar 

  58. N. Kotera, Y. Katayama, and K. F. Komatsubara, Phys. Rev. B 5, 3065 (1972).

    Article  ADS  Google Scholar 

  59. K. von Klitzing and G. Landwehr, Solid State Comm.9, 2201 (1971).

    Article  ADS  Google Scholar 

  60. D. J. Ben Daniel and C. B. Duke Phys. Rev. 160, 679 (1967).

    Article  ADS  Google Scholar 

  61. D. C. Tsui, Phys. Rev. Letters 24, 303 (1970); Phys. Rev. B4, 4438 (1971).

    Article  ADS  Google Scholar 

  62. D. C. Tsui, Solid State Comm. 9, 1789 (1971).

    Article  ADS  Google Scholar 

  63. D. C. Tsui, Proc. 10th Int. Conf. Phys. Sem., p. 468, Cambridge, Mass. (1970); Proc. 11th Int. Conf. Phys. Sem., p. 109, Warsaw, Poland (1972).

    Google Scholar 

  64. M. Kaplit and J. N. Zemel, Phys. Rev. Letters 21, 212 (1968); Surface Sci. 13, 17 (1969).

    Article  ADS  Google Scholar 

  65. A. M. Voshchenkov, PhD Thesis, University of Pennsylvania, Philadelphia, Pa. (1972).

    Google Scholar 

  66. K. Ohta, Japan J. Appl. Phys. 10, 850 (1971).

    Article  ADS  Google Scholar 

  67. A. F. Tasch, Jr., D. D. Buss, R. T. Bate, and B. H. Breazeale, Proc. 10th Int. Conf. Phys. Sem., p. 458, Cambridge, Mass. (1970).

    Google Scholar 

  68. J. A. Pals, Phys. Rev. B 5, 4208 (1972).

    Article  ADS  Google Scholar 

  69. J. A. Pals, Phys. Rev. B7, Jan. (1973).

    Google Scholar 

  70. G. Dorda, Appl. Phys. Letters 17, 406 (1970).

    Article  ADS  Google Scholar 

  71. G. Dorda, J. Appl. Phys. 42, 2053 (1971).

    Article  ADS  Google Scholar 

  72. G. Dorda, H. Friedrich, and E. Preuß, J. Vac. Sci. Technol. 9, 759 (1972); G. Dorda, I. Eisele, and E. Preuß, Proc. 11th Int. Conf. Phys. Sem., vol. 2, p. 1468, Warsaw, Poland (1972).

    Article  ADS  Google Scholar 

  73. G. Dorda, I. Eisele, and E. Preuß, Solid State Comm. 11, 1625 (1972).

    Article  ADS  Google Scholar 

  74. C. T. Sah, J. R. Edwards, and T. H. Ning, phys. stat. sol. (a) 10, 153 (1972).

    Article  ADS  Google Scholar 

  75. H. Sakaki and T. Sugano, Japan J. Appl. Phys. 10, 1016 (1971).

    Article  ADS  Google Scholar 

  76. H. Sakaki and T. Sugano, Proc. 3rd Conf. Solid State Devices, Tokyo 1971, Suppl. to Oyo Buturi, 41, 141 (1972).

    Google Scholar 

  77. S. Tansal, A. B. Fowler, and R. F. Cotellessa, Phys. Rev. 178, 1326 (1969).

    Article  ADS  Google Scholar 

  78. Y. Uemura and Y. Matsumoto, J. Japan Soc. Appl. Phys. Suppl. 40, 205 (1971).

    Google Scholar 

  79. R. G. Wheeler and R. W. Ralston, Phys. Rev. Letters 27, 925 (1971).

    Article  ADS  Google Scholar 

  80. Y. Katayama, N. Kotera, and K. F. Komatsubara, J. Japan Soc. Appl. Phys. Suppl. 40, 214 (1971).

    Google Scholar 

  81. R. Ito, J. Appl. Phys. 43, 735 (1972).

    Article  ADS  Google Scholar 

  82. F. F. Fang and A. B. Fowler, Phys. Rev. 169, 619 (1968).

    Article  ADS  Google Scholar 

  83. N. Kotera, Y. Katayama, I. Yoshida, and K. F. Komatsubara, J. Vac. Sci. Technol. 9, 754 (1972).

    Article  ADS  Google Scholar 

  84. H. Sakaki, K. Hoh, and T. Sugano, IEEE Trans. Electron Devices, ED-17, 892 (1970).

    Article  Google Scholar 

  85. T. Sugano, H. Sakaki, and K. Hoh, J. Japan Soc. Appl. Phys. 39, 192 (1970).

    Google Scholar 

  86. V. N. Dobrovolskij, Yu. S. Zharkikh, L. N. Abessonova, Soc. Phys.-Semic.5, 633 (1971)

    Google Scholar 

  87. C. A. Ribeiro and J. C. Pfister, Solid State Comm. 10, 63 (1972).

    Article  ADS  Google Scholar 

  88. A. Ohwada, H. Maeda, and K. Tanaka, Japan J. Appl. Phys. 8, 629 (1969).

    Article  ADS  Google Scholar 

  89. T. Sato, Y. Takeishi, H. Hara, and Y. Okamoto, Phys. Rev. B 4, 1950 (1971).

    Article  ADS  Google Scholar 

  90. F. F. Fang and A. B. Fowler, J. Appl. Phys. 41, 1825 (1970).

    Article  ADS  Google Scholar 

  91. T. Sato, Y. Takeishi, and H. Hara, Japan J. Appl. Phys. 8, 588 (1969).

    Article  ADS  Google Scholar 

  92. T. Sato, Y. Takeishi, H. Tango, H. Ohnuma, and Y. Okamoto, J. Phys. Soc. Japan 31, 1846 (1971).

    Article  ADS  Google Scholar 

  93. Y. Takeishi, T. Sato, H. Maeda, and K. Hirabayashi, J. Vac. Sci. Technol. 9, 769 (1972).

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Forschungslaboratorien Siemens AG, München

    Gerhard Dorda

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  1. Gerhard Dorda
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H. J. Queisser

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© 1973 Friedr. Vieweg+Sohn GmbH, Verlag

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Dorda, G. (1973). Surface quantization in semiconductors. In: Queisser, H.J. (eds) Festkörperprobleme 13. Advances in Solid State Physics, vol 13. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0108573

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  • DOI: https://doi.org/10.1007/BFb0108573

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  • Print ISBN: 978-3-528-08019-8

  • Online ISBN: 978-3-540-75335-3

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