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Coulomb-Blockade Oscillations in Semiconductor Nanostructures

  • Chapter
Single Charge Tunneling

Part of the book series: NATO ASI Series ((NSSB,volume 294))

Abstract

Coulomb-blockade oscillations of the conductance are a manifestation of single-electron tunneling through a system of two tunnel junctions in series (see Fig. 1) [1]–[5]. The conductance oscillations occur as the voltage on a nearby gate electrode is varied. This setup is the SET transistor described in Sec. 6 of Chap. 2. The number N of conduction electrons on an island (or dot) between two tunnel barriers is an integer, so that the charge Q = — Ne. on the island can only change by discrete amounts e. In contrast, the electrostatic potential difference of island and leads changes continuously as the electrostatic potential φext due to the gate is varied. This gives rise to a net charge imbalance Cφext —Ne between the island and the leads, which oscillates in a saw-tooth pattern with gate voltage (C is the mutual capacitance of island and leads). Tunneling is blocked at low temperatures, except near the degeneracy points of the saw-tooth, where the charge imbalance jumps from +e/2 to φ e/2. At these points the Coulomb blockade of tunneling is lifted and the conductance exhibits a peak. In metals treated in the previous chapters, these “Coulomb-blockade oscillations” are essentially a classical phenomenon [6, 7]. Because the energy level separation ΔE in the island is much smaller than the thermal energy k B T, the energy spectrum may be treated as a continuum. Furthermore, provided that the tunnel resistance is large compared to the resistance quantum h/e 2, the number N of electrons on the island may be treated as a sharply defined classical variable.

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References

  1. L. S. Kuz’min and K. K. Likharev, Pis’ma Zh. Eksp. Teor. Fiz. 45, 389 (1987) [JETP Lett. 45, 495 (1987)].

    Google Scholar 

  2. T. A. Fulton and G. J. Dolan, Phys. Rev. Lett. 59, 109 (1987).

    Article  ADS  Google Scholar 

  3. K. Mullen, E. Ben-Jacob, R. C. Jaklevic, and Z. Schuss, Phys. Rev. B 37, 98 (1988).

    Article  ADS  Google Scholar 

  4. M. Amman, K. Mullen, and E. Ben-Jacob, J. Appl. Phys. 65, 339 (1989).

    Article  ADS  Google Scholar 

  5. K. K. Likharev, IBM J. Res. Dev. 32, 144 (1988).

    Article  Google Scholar 

  6. D. V. Averin and K. K. Likharev, in: Mesoscopic Phenomena in Solids, B. L. Al’tshuler, ed. by P. A. Lee, and R. A. Webb, (Elsevier, Amsterdam, 1991). This is a comprehensive review of single-electron tunneling in metals.

    Google Scholar 

  7. L. I. Glazman and R. I. Shekhter, J. Phys. Condens. Matter 1, 5811 (1989).

    Article  ADS  Google Scholar 

  8. R. I. Shekhter, Zh. Eksp. Teor. Fiz. 63, 1410 (5) [Sov. Phys. JETP 36, 747 (1973)].

    Google Scholar 

  9. I. O. Kulik and R. I. Shekhter, Zh. Eksp. Teor. Fiz. 68, 623 (1975) [Sov. Phys. JETP 41, 308 (1975)].

    Google Scholar 

  10. For a review of theoretical and experimental aspects of quantum transport in semiconductor nanostructures, see: C. W. J. Beenakker and H. van Houten, Solid State Physics 44, 1 (1991).

    Article  Google Scholar 

  11. J. H. F. Scott-Thomas, S. B. Field, M. A. Kastner, H. I. Smith, and D. A. Antoniadis, Phys. Rev. Lett. 62, 583 (1989).

    Article  ADS  Google Scholar 

  12. U. Meirav, M. A. Kastner, M. Heiblum, and S. J. Wind, Phys. Rev. B 40, 5871 (1989).

    Article  ADS  Google Scholar 

  13. S. B. Field, M. A. Kastner, U. Meirav, J. H. F. Scott-Thomas, D. A. Antoniadis, H. I. Smith, and S. J. Wind, Phys. Rev. B 42, 3523 (1990).

    Article  ADS  Google Scholar 

  14. A. A. M. Staring, H. van Houten, C. W. J. Beenakker, and C. T. Foxon, in: High Magnetic Fields in Semiconductor Physics III, ed. by G. Landwehr, (Springer, Berlin, 1991).

    Google Scholar 

  15. A. A. M. Staring, H. van Houten, C. W. J. Beenakker, and C. T. Foxon, Phys. Rev. B. to be published.

    Google Scholar 

  16. C. de Graaf, J. Caro, S. Radelaar, V. Lauer, and K. Heyers, submitted to Phys. Rev. B.

    Google Scholar 

  17. U. Meirav, M. A. Kastner, and S. J. Wind, Phys. Rev. Lett. 65, 771 (1990).

    Article  ADS  Google Scholar 

  18. L. P. Kouwenhoven, N. C. van der Vaart, A. T. Johnson, C. J. P. M. Harmans, J. G. Williamson, A. A. M. Staring, and C. T. Foxon, Festkörperprobleme / Advances in Solid State Physics 31 (Vieweg, Braunschweig, 1991)

    Google Scholar 

  19. J. G. Williamson, A. A. M. Staring, H. van Houten, L. P. Kouwenhoven, and C. T. Foxon, to be published; A. A. M. Staring, J. G. Williamson, H. van Houten, C. W. J. Beenakker, L. P. Kouwenhoven, and C. T. Foxon, Physica B, to be published

    Google Scholar 

  20. A. L. Efros and B. I. Shklovskii, in: Electron-Electron Interactions in Disordered Systems, ed. by A. L. Efros and M. Pollak, (North-Holland, Amsterdam, 1985).

    Google Scholar 

  21. C. W. J. Beenakker, Phys. Rev. B. 44, 1646 (1991).

    Article  ADS  Google Scholar 

  22. Y. Meir, N. S. Wingreen, and P. A. Lee, Phys. Rev. Lett. 66, 3048 (1991).

    Article  ADS  Google Scholar 

  23. M.A. Kastner, S. B. Field, U. Meirav, J. H. F. Scott-Thomas, D. A. Antoniadis, and H. I. Smith, Phys. Rev. Lett. 63, 1894 (1989).

    Article  ADS  Google Scholar 

  24. A. I. Larkin and P. A. Lee, Phys. Rev. B 17, 1596 (1978).

    Article  ADS  Google Scholar 

  25. P. A. Lee and T. M. Rice, Phys. Rev. B 19, 3970 (1979).

    Article  ADS  Google Scholar 

  26. D. V. Averin and K. K. Likharev, unpublished.

    Google Scholar 

  27. H. van Houten and C. W. J. Beenakker, Phys. Rev. Lett. 63, 1893 (1989).

    Article  ADS  Google Scholar 

  28. F. M. de Aguiar and D. A. Wharam, Phys. Rev. B 43, 15 April (1991).

    Article  Google Scholar 

  29. J. Masek and B. Kramer, submitted to Europhys. Lett.

    Google Scholar 

  30. B. J. van Wees, L. P. Kouwenhoven, C. J. P. M. Harmans, J. G. Williamson, C. E. Timmering, M. E. L Broekaart, C. T. Foxon, and J. J. Harris, Phys. Rev. Lett. 62, 2523 (1989).

    Article  ADS  Google Scholar 

  31. U. Sivan and Y. Imry, Phys. Rev. Lett. 61, 1001 (1988).

    Article  ADS  Google Scholar 

  32. U. Sivan, Y. Imry, and C. Hartzstein, Phys. Rev. B 39, 1242 (1989).

    Article  ADS  Google Scholar 

  33. C. W. J. Beenakker, H. van Houten, and A. A. M. Staring, Phys. Rev. B. 44, 657 (1991).

    Article  Google Scholar 

  34. C. W. J. Beenakker, H. van Houten, and A. A. M. Staring, in: Granular Nanoelectronics, ed. by D. K. Ferry, J. Barker, and C. Jacoboni, (Plenum, New York, 1991).

    Google Scholar 

  35. P. L. McEuen, E. B. Foxman, U. Meirav, M. A. Kastner, Y. Meir, N. S. Wingreen, and S. J. Wind, Phys. Rev. Lett. 66, 1926 (1991).

    Article  ADS  Google Scholar 

  36. P. A. Lee, Phys. Rev. Lett. 65, 2206 (1990).

    Article  ADS  Google Scholar 

  37. D. V. Averin and A. N. Korotkov, Zh. Eksp. Teor. Fiz. 97, 1661 (1990) [Sov. Phys. JETP 70, 937 (1990)].

    Google Scholar 

  38. A. N. Korotkov, D. V. Averin, and K. K. Likharev, Physica B 165 & 166, 927 (1990); D. V. Averin, A. N. Korotkov, and K. K. Likharev, submitted to Phys. Rev. B.

    Article  Google Scholar 

  39. A. Groshev, Phys. Rev. B 42, 5895 (1990).

    Article  ADS  Google Scholar 

  40. A. Groshev, T. Ivanov, and V. Valtchinov, Phys. Rev. Lett. 66, 1082 (1991).

    Article  ADS  Google Scholar 

  41. L. P. Kouwenhoven, A. T. Johnson, N. C. van der Vaart, C. J. P. M. Harmans, and C. T. Foxon, unpublished.

    Google Scholar 

  42. L. J. Geerligs, V. F. Anderegg, P. A. M. Holweg, J. E. Mooij, H. Pothier, D. Estève, C. Urbina, M. H. Devoret, Phys. Rev. Lett. 64, 2691 (1990).

    Article  ADS  Google Scholar 

  43. H. Pothier, P. Lafarge, C. Urbina, D. Estève, and M. H. Devoret, Europhys. Lett. 17, 249 (1992).

    Article  ADS  Google Scholar 

  44. M. A. Reed, J. N. Randall, R. J. Aggarwal, R. J. Matyi, T. M. Moore, and A. E. Wetsel, Phys. Rev. Lett. 60, 535 (1988).

    Article  ADS  Google Scholar 

  45. B. Su, V. J. Goldman, and J. E. Cunningham, preprint.

    Google Scholar 

  46. W. B. Kinard, M. H. Weichold, G. F. Spencer, and W. P. Kirk, in: Nanostructure Physics and Fabrication, ed. by M. A. Reed and W. P. Kirk, (Academic, New York, 1989).

    Google Scholar 

  47. H. van Houten, C. W. J. Beenakker, and B. J. van Wees, in: Nanostructured Systems, ed. by M. A. Reed, (a volume of Semiconductors and Semimetals, Academic, New York, 1991).

    Google Scholar 

  48. B. J. van Wees, H. van Houten, C. W. J. Beenakker, J. G. Williamson, L. P. Kouwenhoven, D. van der Marel, and C. T. Foxon, Phys. Rev. Lett. 60, 848 (1988).

    Article  ADS  Google Scholar 

  49. D. A. Wharam, T. J. Thornton, R. Newbury, M. Pepper, H. Ahmed, J. E. F. Frost, D. G. Hasko, D. C. Peacock, D. A. Ritchie, and G. A. C. Jones, J. Phys. C 21, L209 (1988).

    Article  ADS  Google Scholar 

  50. J. A. Nixon and J. H. Davies, Phys. Rev. B. 41, 7929 (1990).

    Article  ADS  Google Scholar 

  51. G. W. Bryant, Phys. Rev. Lett. 59, 1140 (1987).

    Article  ADS  Google Scholar 

  52. P. A. Maksym and T. Chakraborty, Phys. Rev. Lett. 65, 108 (1990).

    Article  ADS  Google Scholar 

  53. A. Kumar, S. E. Laux, and F. Stern, Phys. Rev. B 42, 5166 (1990).

    Article  ADS  Google Scholar 

  54. M. Büttiker, Phys. Rev. B 33, 3020 (1986).

    Article  ADS  Google Scholar 

  55. M. Büttiker, IBM J. Res. Dev. 32, 63 (1988).

    Article  Google Scholar 

  56. A. D. Stone and P. A. Lee, Phys. Rev. Lett. 54, 1196 (1985).

    Article  ADS  Google Scholar 

  57. R. Landauer, in: Localization, Interaction, and Transport Phenomena, ed. by B. Kramer, G. Bergmann, and Y. Bruynseraede, (Springer, Berlin, 1985).

    Google Scholar 

  58. D. V. Averin and A. A. Odintsov, Phys. Lett. A 140, 251 (1989).

    Article  ADS  Google Scholar 

  59. D. V. Averin and Yu. V. Nazarov, Phys. Rev. Lett. 65, 2446 (1990).

    Article  ADS  Google Scholar 

  60. L. I. Glazman and K. A. Matveev, Pis’ma Zh. Eksp. Teor. Fiz. 51, 425 (1990) [JETP Lett. 51, 484 (1990)].

    Google Scholar 

  61. Yu. V. Nazarov, Solid State Comm. 75, 669 (1990); A. N. Korotkov and Yu. V. Nazarov, Physica B, to be published.

    Article  ADS  Google Scholar 

  62. S. E. Laux, D. E. Frank, and F. Stern, Surf. Sci. 196, 101 (1988).

    Article  ADS  Google Scholar 

  63. L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media (Pergamon, New York, 1960).

    MATH  Google Scholar 

  64. K. K. Likharev, N. S. Bakhvalov, G. S. Kazacha, and S. I. Serdyukova, IEEE Trans. Magn. 25, 1436 (1989).

    Article  ADS  Google Scholar 

  65. M. Amman, E. Ben-Jacob, and K. Mullen, Physics Letters A 142, 431 (1989).

    Article  ADS  Google Scholar 

  66. A. B. Fowler, A. Hartstein, and R. A. Webb, Phys. Rev. Lett. 48, 196 (1982).

    Article  ADS  Google Scholar 

  67. R. A. Webb, A. Hartstein, J. J. Wainer, and A. B. Fowler, Phys. Rev. Lett. 54, 1577 (1985).

    Article  ADS  Google Scholar 

  68. R. F. Kwasnick, M. A. Kastner, J. Melngailis, and P. A. Lee, Phys. Rev. Lett. 52, 224 (1984).

    Article  ADS  Google Scholar 

  69. M. A. Kastner, R. F. Kwasnick, J. C. Licini, and D. J. Bishop, Phys. Rev. B 36, 8015 (1987).

    Article  ADS  Google Scholar 

  70. P. A. Lee, Phys. Rev. Lett. 53, 2042 (1984).

    Article  ADS  Google Scholar 

  71. R. K. Kalia, W. Xue, and P. A. Lee, Phys. Rev. Lett. 57, 1615 (1986).

    Article  ADS  Google Scholar 

  72. C. J. Adkins, in: Hopping and Related Phenomena, ed. by H. Fritsche and M. Pollak, (World Scientific, New Jersey, 1990).

    Google Scholar 

  73. B. L. Al’tshuler, Pis’ma Zh. Eksp. Teor. Fiz. 41, 530 (1985) [JETP Lett. 41, 648 (1985)].

    Google Scholar 

  74. P. A. Lee and A. D. Stone, Phys. Rev. Lett. 55, 1622 (1985).

    Article  ADS  Google Scholar 

  75. A. B. Fowler, G. L. Timp, J. J. Wainer, and R. A. Webb, Phys. Rev. Lett. 57, 138 (1986).

    Article  ADS  Google Scholar 

  76. A. B. Fowler, J. J. Wainer, and R. A. Webb, IBM J. Res. Dev. 32, 372 (1988).

    Article  Google Scholar 

  77. M. Green and M. Pollak, in: Hopping and Related Phenomena, ed. by H. Fritsche and M. Pollak, (World Scientific, New Jersey, 1990).

    Google Scholar 

  78. J. J. Wainer, A. B. Fowler, and R. A. Webb, Surf. Sci. 196, 134 (1988).

    Article  ADS  Google Scholar 

  79. T. E. Kopley, P. L. McEuen, and R. G. Wheeler, Phys. Rev. Lett. 61, 1654 (1988).

    Article  ADS  Google Scholar 

  80. T. K. Ng and P. A. Lee, Phys. Rev. Lett. 61, 1768 (1988).

    Article  ADS  Google Scholar 

  81. Y. Aharonov and D. Bohm, Phys. Rev. 115, 485 (1959).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  82. Y. Aharonov and D. Bohm, 123, 1511 (1961).

    Google Scholar 

  83. S. Washburn and R. A. Webb, Adv. Phys. 35, 375 (1986).

    Article  ADS  Google Scholar 

  84. A. G. Aronov and Yu. V. Sharvin, Rev. Mod. Phys. 59, 755 (1987).

    Article  ADS  Google Scholar 

  85. P. H. M. van Loosdrecht, C. W. J. Beenakker, H. van Houten, J. G. Williamson, B. J. van Wees, J. E. Mooij, C. T. Foxon, and J. J. Harris, Phys. Rev. B 38, 10162 (1988).

    Article  Google Scholar 

  86. T. Ando, A. B. Fowler, and F. Stern, Rev. Mod. Phys. 54, 437 (1982).

    Article  ADS  Google Scholar 

  87. M. Büttiker, Phys. Rev. B 38, 9375 (1988).

    Article  ADS  Google Scholar 

  88. V. Fock, Z. Phys. 47, 446 (1928).

    Article  ADS  MATH  Google Scholar 

  89. C. G. Darwin, Proc. Camb. Phil. Soc. 27, 86 (1930).

    Article  ADS  Google Scholar 

  90. F. Geerinckx, F. M. Peeters, and J. T. Devreese, J. Appl. Phys. 68, 3435 (1990).

    Article  ADS  Google Scholar 

  91. M. Büttiker, Y. Imry, and R. Landauer, Phys. Lett. A 96, 365 (1983).

    Article  ADS  Google Scholar 

  92. B. J. van Wees, E. M. M. Willems, C. J. P. M. Harmans, C. W. J. Beenakker, H. van Houten, J. G. Williamson, C. T. Foxon, and J. J. Harris, Phys. Rev. Lett. 62, 1181 (1989).

    Article  ADS  Google Scholar 

  93. J. K. Jain, Phys. Rev. Lett. 60, 2074 (1988).

    Article  ADS  Google Scholar 

  94. R. J. Brown, C. G. Smith, M. Pepper, M. J. Kelly, R. Newbury, H. Ahmed, D. G. Hasko, J. E. F. Frost, D. C. Peacock, D. A. Ritchie, and G. A. C. Jones, J. Phys. Condens. Matter 1, 6291 (1989).

    Article  ADS  Google Scholar 

  95. C. G. Smith, M. Pepper, H. Ahmed, J. E. F. Frost, D. G. Hasko, D. C. Peacock, D. A. Ritchie, and G. A. C. Jones, J. Phys. C 21, L893 (1989).

    Article  Google Scholar 

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  1. Philips Research Laboratories, 5600 JA, Eindhoven, The Netherlands

    H. Van Houten, C. W. J. Beenakker & A. A. M. Staring

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    Hermann Grabert

  2. Centre d’Etudes de Saclay, Gif-sur-Yvette, France

    Michel H. Devoret

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Van Houten, H., Beenakker, C.W.J., Staring, A.A.M. (1992). Coulomb-Blockade Oscillations in Semiconductor Nanostructures. In: Grabert, H., Devoret, M.H. (eds) Single Charge Tunneling. NATO ASI Series, vol 294. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-2166-9_5

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