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Correlation Effects on the Density of States and Hopping Conduction

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Electronic Properties of Doped Semiconductors

Part of the book series: Springer Series in Solid-State Sciences ((SSSOL,volume 45))

Abstract

In this chapter it is shown that the density of states has two humps in its dependence on energy. Because of Coulombic correlations, the density of states vanishes at the Fermi level. This has an important effect on the temperature dependence of hopping conduction, especially in the variablerange hopping region. The existence of correlation implies that the random resistor network model, which underlies the theory of hopping conduction desribed in the preceding chapters, becomes strictly speaking inadequate. The model remains useful for physical problems, but its use requires special justification.

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References

  1. M. Pollak: Effect of carrier-carrier interactions on some transport properties in disordered semiconductors. Disc. Faraday Soc. 50, 13 (1970)

    Article  Google Scholar 

  2. M. L. Knotek, M. Pollak: Correlation effects in hopping conduction: Hopping as multielectron transition. J. Non-Crystal. Solids 8: 10 (1972)

    Article  Google Scholar 

  3. Correlation effects in hopping conduction: A treatment in terms of multielectron transitions. Phys. Rev. B9, 644 (1974)

    Google Scholar 

  4. G. Srinivasan: Statistical mechanics of charged traps in an amorphous semiconductor. Phys. Rev. B4, 2581 (1971)

    Google Scholar 

  5. T. Kurosawa, H. Sugimoto: Effects of coulomb correlation on hopping conduction in disordered systems. Prog. Theor. Phys. Suppl. 57, 217 (1975)

    Article  ADS  Google Scholar 

  6. A. L. Efros, B. I. Shklovskii: Coulomb gap and low-temperature conductivity of disordered systems. J. Phys. C8, L49 (1975)

    ADS  Google Scholar 

  7. B. L. Gel’mont, A. L. Efros: Coulomb gap in disordered systems. Numerical experiment in the one-dimensional model. Zh. Eksp. Theor. Fiz. Pis. Red. 25, 77 (1977)

    Google Scholar 

  8. B. L. Gel’mont, A. L. Efros: English transi. JETP Lett. 25, 67 (1977)

    Google Scholar 

  9. S. D. Baranovskii, A. L. Efros, B. L. Gel’mont, B. I. Shklovskii: Coulomb gap in disordered systems. Computer simulation. Solid State Commun. 27, 1 (1978)

    Article  ADS  Google Scholar 

  10. A. L. Efros, Nguyen Van Lien, B. I. Shklovskii: Impurity band structure in lightly doped semiconductors. J. Phys. C12, 1869 (1979)

    ADS  Google Scholar 

  11. J. H. Davies, P. A. Lee, T. M. Rice: Electron glass. Phys. Rev. Lett. 49, 758 (1982)

    Article  ADS  Google Scholar 

  12. M. Grünewald, B. Pohlmann, L. Schweitzer, D. Wütz: Mean field approach to electron glass. J. Phys. C15, L1153 (1982)

    ADS  Google Scholar 

  13. A. L. Efros: Coulomb gap in disordered systems. J. Phys. C9, 2021 (1976)

    ADS  Google Scholar 

  14. S. D. Baranovskii, B. I. Shklovskii, A. L. Efros: Elementary excitations in disordered systems with localized electrons. Zh. Eksp. Theor. Fiz. 78, 395 (1980)

    Google Scholar 

  15. S. D. Baranovskii, B. I. Shklovskii, A. L. Efros: English transi. Soy. Phys.—JETP 51, 199 (1980)

    ADS  Google Scholar 

  16. N. F. Mott: The effect of electron interaction on variable-range hopping. Phil. Mag. 34, 643 (1976)

    Google Scholar 

  17. E. L. Wolf: Nonsuperconducting electron tunneling spectroscopy. Solid State Phys. 30, 1 (1975)

    Article  Google Scholar 

  18. M. Pollak, M. L. Knotek: Correlation effects in hopping transport. J. Non-Crystal. Solids 32, 141 (1979)

    Article  ADS  Google Scholar 

  19. A. G. Zabrodskii, K. N. Zinov’eva: Critical behavior of parameters of n-Ge in the vicinity of compensation-induced Anderson transition. Zh. Eksp. Theor. Fiz. Pis. Red. 37, 369 (1983)

    Google Scholar 

  20. A. G. Zabrodskii, K. N. Zinov’eva: English transi. Soy. Phys.—JETP Lett. 37 (1983)

    Google Scholar 

  21. A. G. Zabrodskii, K. N. Zinov’eva: Low tmeperature conductivity and the metal-insulator transition in compensated n-Ge. Zh. Eksp. Theor. Fiz. 85 (1983)

    Google Scholar 

  22. P. Belitz, A. Gold, W. Götze: J. Phys. B44, 273 (1981)

    ADS  Google Scholar 

  23. Y. Imry, Y. Gefen, G. J. Bergman: “Dielectric and Optical Anomalies near the Anderson Metal-Insulator Transition,” in Proc. Taniguchi Symp., ed. by Y. Nagaoka (Springer, Berlin, Heidelberg, New York 1982)

    Google Scholar 

  24. V. E. Dubrov, M. E. Levinshtein, M. S. Shur: Permittivity anomaly in metal-dielectric transitions. Theory and simulation. Zh. Eksp. Theor. Fiz. 70, 2014 (1976)

    Google Scholar 

  25. V. E. Dubrov, M. E. Levinshtein, M. S. Shur: English transi. Sov. Phys.—JETP 43, 1050 (1976)

    ADS  Google Scholar 

  26. A. L. Efros, B. I. Shklovskii: Critical behavior of conductivity and dielectric constant near the metal—non-metal transition threshold. Phys. Stat. Sol. B76, 475 (1976)

    Google Scholar 

  27. T. G. Castner, N. K. Lee, G. S. Cieloszyk, G. L. Sallinger: Dielectric anomaly and the metal-insulator transition in n-type silicon. Phys. Rev. Lett. 34, 1627 (1975)

    Article  ADS  Google Scholar 

  28. M. Capizzi, G. A. Thomas, F. DeRosa, R. N. Bhatt, T. M. Rice: Observation of the approach to a polarization catastrophe. Phys. Rev. Lett. 44, 1019 (1980)

    Article  ADS  Google Scholar 

  29. H. F. Hess, K. De Conde, T. F. Rosenbaum, G. A. Thomas: Giant dielectric constants at the approach to the insulator-metal transition. Phys. Rev. B25, 5578 (1982)

    Google Scholar 

  30. G. A. Thomas, Y. Ootuka, S. Katsumoto, S. Kobayashi, W. Sasaki: Evidence of localization effects in compensated semiconductors. Phys. Rev. B25, 4288 (1982)

    Google Scholar 

  31. P. Cheng, B. Abeles, Y. Arie: Hopping conductivity in granular metals. Phys. Rev. Lett. 31, 44 (1973)

    Article  ADS  Google Scholar 

  32. B. Abeles, Ping Sheng, M. D. Coutts, Y. Arie: Structural and electrical properties of granular metal films. Adv. Phys. 24, 407 (1975)

    Google Scholar 

  33. T. Chui, G. Deutscher, P. Lindenfeld, W. L. McLean: Conduction in granular aluminum near the metal-insulator transition. Phys. Rev. B23, 6172 (1981)

    Google Scholar 

  34. O. Entin-Wohlman, Y. Gefen, Y. Shapira: Variable-range hopping conductivity in granular materials. J. Phys. C16, 1161 (1983)

    ADS  Google Scholar 

  35. R. Kikuchi: “Cation Diffusion and Conductivity in Solid Electrolytes,” in Fast Ion Transport in Solids. Solid State Batteries and Devices (North-Holland, Amsterdam 1973) p. 248

    Google Scholar 

  36. P. M. Richards: Theory of one-dimensional hopping conductivity and diffusion. Phys. Rev. B16, 1393 (1977)

    MathSciNet  Google Scholar 

  37. P. M. Richards: Correlated hopping conductivity in general two-sublattice structure. J. Chem. Phys. 68, 2125 (1978)

    Article  ADS  Google Scholar 

  38. M. L. Knotek, M. Pollak: Comment on correlation effects in hopping conduction. Phil. Mag. 35, 1133 (1977)

    Google Scholar 

  39. M. Ortuno, M. Pollak: The activation energy of hopping transport with sequential correlations of hops due to coulomb interactions. J. Phys. C16, 1459 (1983)

    ADS  Google Scholar 

  40. M. Pollak: Effect of electron-electron interactions on hopping and delocalization. Phil. Mag. 42, 781 (1980)

    Google Scholar 

  41. M. Pollak, M. Ortuno: Many electron quantum effects in localized disordered systems with inter-site Coulomb interactions. In press.

    Google Scholar 

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Shklovskii, B.I., Efros, A.L. (1984). Correlation Effects on the Density of States and Hopping Conduction. In: Electronic Properties of Doped Semiconductors. Springer Series in Solid-State Sciences, vol 45. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-02403-4_10

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  • DOI: https://doi.org/10.1007/978-3-662-02403-4_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-02405-8

  • Online ISBN: 978-3-662-02403-4

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