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Disorder and localization in bandtail hopping transport: experiments and concepts

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Abstract

This review describes the main transport experiments (including Ohmic and nonlinear transport in both dc and ac regimes) and related concepts which can be used to derive quantitative information on the localized electronic states above the Fermi level and in the bandtails, in low carrier mobility materials governed by hopping conductivity. For bandtail hopping, a model based on the filling rate of electronic states near the preferred transport path shows a sharp decrease of the hopping mobility with increasing bandtail disorder. While the slope T 1/4 0, derived from lnσ vs T −1/4 plots, is weakly sensitive to the shape of the DOS distribution, the prefactor σ ∘; ∘; values are extremely sensitive to bandtail disorder; uniform and exponential distributions can be discriminated experimentally (σ ∘; ∘; ≫ 102 S.cm−1 for bandtail hopping).

As an illustration, the localized π states distribution in amorphous carbon nitride a-C1−x N x :H (x=0.23) is investigated in sandwich devices. Using a wide range of temperatures, electric fields and ac frequencies, several methods are proposed to derive some DOS parameters: density of states at the Fermi level, localization radius and disorder energy of the exponential bandtail distribution. In the field-enhanced bandtail hopping and in the activationless regimes, both apparent slope T 1/4 0 and prefactor σ ∘; ∘; values are also properly described. An analytical model, based on the filling rate of localized states near the preferred transport energy, shows that the (F S/T) scaling properties of nonlinear conductivity σ(F, T) (with S ≈; 2/3 in a-C1−x N x :H) are related to the field-dependent effective temperature describing the non-equilibrium distribution of π; ∗; electrons in the bandtail. In ac transport, the characteristic response time τ(F, T) shows a linear lnτ vs T −1/4 behaviour, with a smaller T-dependence as the field strength increases, closely related to the filling rate obtained from the dc hopping transport.

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References

  1. Blöm, P.W.M., Vissenberg, M.C.J.M., Mater. Sci. Eng. 27, 53 (2000)

    Article  Google Scholar 

  2. Vissenberg, M.C.J.M., Matters, M., Phys. Rev. B 57, 12964 (1998)

    Article  CAS  Google Scholar 

  3. Forbes, R.G., Solid State Electron. 45, 779 (2001)

    Article  CAS  Google Scholar 

  4. Silva, S.R.P., Carey, J.D., Guo, X., Tsang, W.M., Poa, C.H.P., Thin Solid Films 482, 79 (2005)

    Article  CAS  Google Scholar 

  5. Lmimouni, K., Legrand, C., Dufour, C., Chapoton, A., Belouet, C., Appl. Phys. Lett. 78, 2437 (2001)

    Article  CAS  Google Scholar 

  6. Cachet, H., Deslouis, C., Chouiki, M., Saidani, B., Conway, N.M.J., Godet, C., J. Electrochem. Soc. 149, E233 (2002)

    Article  CAS  Google Scholar 

  7. Egret, S., Robertson, J., Milne, W.I., Clough, F.J., Diam. Relat. Mater. 6, 879 (1997)

    Article  CAS  Google Scholar 

  8. Godet, C., J. Non-Cryst. Solids 299–302, 333 (2002)

    Article  Google Scholar 

  9. Godet, C., Kumar, S., Chu, V., Philos. Mag. 83, 3351 (2003)

    Article  CAS  Google Scholar 

  10. Nespurek, S., J. Non-Cryst. Solids 299–302, 1033 (2002)

    Google Scholar 

  11. Kanicki, J., In Skotheim, T.A. (ed) Handbook of Conducting Polymers, Vol. 1 (Marcel Dekker, New York, 1986) 543

    Google Scholar 

  12. Robertson, J., Mater. Sci. Eng., R Rep. 37, 129 (2002)

    Article  Google Scholar 

  13. Chen, C.W., Robertson, J., J. Non-Cryst. Solids 227–230, 602 (1998)

    Article  Google Scholar 

  14. Mycielsky, W., Staryga, E., Lipinski, A., Mitura, S., Sokolowska, A., Diam. Relat. Mater. 3, 858 (1994)

    Article  Google Scholar 

  15. Foulani, A., Laurent, C., Mebarki, B., Segui, Y., J. Appl. Phys. 80, 470 (1996)

    Article  CAS  Google Scholar 

  16. Clough, F.J., Milne, W.I., Kleinsorge, B., Robertson, J., Amaratunga, G.A.J., Roy, B.N., Electron. Lett. 32, 319 (1996)

    Article  Google Scholar 

  17. Maeng, S.L., Uchikoya, S., Clough, F.J., Tagliaferro, A., Flewitt, A.J., Robertson, J., Milne, W.I., Diam. Relat. Mater. 9, 805 (2000)

    Article  CAS  Google Scholar 

  18. Klibanov, L., Oksman, M., Seidman, A., Croitoru, N., Diam. Relat. Mater. 6, 1152 (1997)

    Article  CAS  Google Scholar 

  19. Anderson, P.W., Phys. Rev. 109, 1492 (1958)

    Article  CAS  Google Scholar 

  20. Mott, N.F., Davis, E.A., Electronic Processes in Non-Crystalline Materials, 2nd edn., (Oxford University Press, 1979)

  21. Godet, C., Diam. Relat. Mater. 12, 159 (2003) and references included.

    Article  CAS  Google Scholar 

  22. Catherinot, A., private communication

  23. Mott, N.F., Phil. Mag. 19, 835 (1969)

    CAS  Google Scholar 

  24. Hill, R.M., Phil. Mag. 24, 1307 (1971)

    CAS  Google Scholar 

  25. Godet, C., Adamopoulos, G., Kumar, S., Katsuno, T., Thin Solid Films 482, 24 (2005)

    Article  CAS  Google Scholar 

  26. Godet, C., Kleider, J.P., Gudovskikh, A.S. (submitted)

  27. Aharony, A., Zhang, Y., Sarachik, M.P., Phys. Rev. Lett. 68, 3900 (1992)

    Article  CAS  Google Scholar 

  28. Knoteck, M.L., Pollak, M., Donovan, T.M., Kurtzman, H., Phys. Rev. Lett. 30, 853 (1973)

    Article  Google Scholar 

  29. Yoffe, A.D., Phillips, R.T., In Kastner, M.A., Thomas, G.A., Ovshinsky, S.R. (eds.), Disordered Semiconductors (Plenum, New York, 1987) 499

    Google Scholar 

  30. Heitz, T., Drévillon, B., Bourée, J.E., Godet, C., Appl. Phys. Lett. 72, 780 (1998)

    Article  CAS  Google Scholar 

  31. Grünewald, M., Thomas, P., Phys. Stat. Solidi (b) 94, 125 (1979)

    Google Scholar 

  32. Shapiro, R., Adler, D., J. Non-Cryst. Solids 74, 189 (1985)

    Article  CAS  Google Scholar 

  33. Shklovskii, B.I., Levin, E.I., Fritzsche, H., Baranovskii, S.D. In Fritzsche H. (ed.), Advances in Disordered Semiconductors, Vol. 3 (1990, World Scientific) 161

  34. Nebel, C., Street, R.A., Johnson, N.M., Tsai, C.C., Phys. Rev. B 46, (1992) 6803; Nebel, C., Street, R.A., Int. J. Mod. Phys. B 7, 1207 (1993)

    Article  CAS  Google Scholar 

  35. Godet, C., Phil. Mag. B 81, 205 (2001)

    Article  CAS  Google Scholar 

  36. Godet, C., Phys. Stat. Solidi (b) 231, 499 (2002)

    Article  CAS  Google Scholar 

  37. Helmbold, A., Hammer, P., Thiele, J.U., Rohwer, K., Meissner, D., Phil. Mag. B 72, 335 (1995)

    CAS  Google Scholar 

  38. Kao, K.C., Hwang, W., Electrical transport in solids (Pergamon Press, Oxford, 1981) 314

    Google Scholar 

  39. Fröhlich, H., Proc. Roy. Soc. London A 188, 521 (1947)

    Article  Google Scholar 

  40. Marianer, S., Shklovskii, B., Phys. Rev. B 46, 13100 (1992)

    Article  Google Scholar 

  41. Cleve, B., Hartenstein, B., Baranovskii, S.D., Scheidler, M., Thomas, P. Baessler, H., Phys. Rev. B 51, 16705 (1995).

    Article  CAS  Google Scholar 

  42. Movaghar, B., Yelon, A., Meunier, M., Chem. Phys. 146, 389 (1990)

    Article  Google Scholar 

  43. Schottky, W., Z. Physik 15, 872 (1914)

    CAS  Google Scholar 

  44. Frenkel, J., Phys. Rev. 54, 647 (1938)

    Article  Google Scholar 

  45. Bässler, H., Philos. Mag. 50, 347 (1984)

    Google Scholar 

  46. Apsley, N., Hughes, H.P., Philos. Mag. 31, 1327 (1975)

    CAS  Google Scholar 

  47. Godet, C., Phil. Mag. Lett. 83, 691 (2003)

    Article  CAS  Google Scholar 

  48. Monroe, D., Phys. Rev. Lett. 54, 146 (1985)

    Article  CAS  Google Scholar 

  49. Monroe, D., In Kastner, M.A., Thomas, G.A., Ovshinsky, S.R. (eds.), Disordered Semiconductors (Plenum Press, New York, 1987) 705

    Google Scholar 

  50. Kumar, S., Godet, C., Goudovskikh, A., Kleider, J.P., Adamopoulos, G., Chu, V., J. Non-Cryst. Solids 338–340, 349 (2004)

    Article  CAS  Google Scholar 

  51. Van Der Meer, N., Schuchardt, R., Keiper, R., Phys. Stat. Solidi (b) 110, 571 (1982)

    Google Scholar 

  52. Pollak, M., Riess, I., J. Phys. C : Solid State Phys. 9, 2339 (1976)

    Article  Google Scholar 

  53. Shklovskii, B., Sov. Phys. Semicond. 6, 1964 (1973)

    Google Scholar 

  54. Palinginis, K.C., Cohen, J.D., Ilie, A., Conway, N.M.J., Milne, W.I., J. Non-Cryst. Solids 266–269, 1077 (2000)

    Article  Google Scholar 

  55. Racine, B., Benlahsen, M., Zellama, K., Bouzerar, R., Kleider, J.P., Von Bardeleben, H.J., Diam. Relat. Mater. 10, 200 (2001)

    Article  CAS  Google Scholar 

  56. Cohen, J.D., Lang, D.V., Phys. Rev. B 25, 5321 (1982)

    Article  CAS  Google Scholar 

  57. Michelson, C.E., Gelatos, A.V., Cohen, J.D., Appl. Phys. Lett. 47, 412 (1985)

    Article  CAS  Google Scholar 

  58. Austin, I.G., Mott, N.F., Adv. Phys. 18, 41 (1969)

    Article  CAS  Google Scholar 

  59. Abkowitz, M., Le Comber, P.G., Spear, W.E., Commun. Phys. 1, 175 (1976)

    CAS  Google Scholar 

  60. Long, A.R., Adv. Phys. 31, 553 (1992)

    Article  Google Scholar 

  61. Elliott, S.R., Adv. Phys. 36, 135 (1987)

    Article  CAS  Google Scholar 

  62. Dyre, J.C., J. Appl. Phys. 64, 2456 (1988)

    Article  Google Scholar 

  63. Dyre, J.C., Schroeder, T.B., Rev. Mod. Phys. 72, 873 (2000)

    Article  Google Scholar 

  64. Kleider, J.P., Gudovskikh, A. Godet, C., J. Non-Cryst. Solids (2006) to appear

  65. Arena, C., Kleinsorge, B., Robertson, J., Milne, W.I., Welland, M.E., J. Appl. Phys. 85, 1609 (1999)

    Article  CAS  Google Scholar 

  66. Andrienko, I., Prawer, S. In Silva, S.R.P. (ed.) Properties of amorphous carbon, Emis datareviews series, no. 29 (Inspec, London, 2003) 171

    Google Scholar 

  67. Reinke, P., In Silva, S.R.P. (Ed.) Properties of amorphous carbon, Emis datareviews series, no. 29, (Inspec, London, 2003) 74

    Google Scholar 

  68. Bouchet-Fabre, B., Zellama, K., Godet, C., Ballutaud, D., Minea, T., Thin Solid Films 482, 156 (2004)

    Article  CAS  Google Scholar 

  69. Godet, C., Conway, N.M.J., Bourée, J.E., Bouamra, K., Grosman, A., Ortega, C., J. Appl. Phys. 91, 4154 (2002)

    Article  CAS  Google Scholar 

  70. Angus, J.C., Jansen, F., J. Vac. Sci. Technol. A 6, 1778 (1988)

    Article  CAS  Google Scholar 

  71. Chévrier, J.B., Equer, B., J. Appl. Phys. 76, 7415 (1994)

    Article  Google Scholar 

  72. Katsuno, T., Godet, C., Loir, A.S., Garrélie, F., J. Non-Cryst. Solids (2006) to appear.

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Authors and Affiliations

  1. Laboratoire de Physique, Atomes, Lasers, Molécules, Surfaces, UMR 6627 CNRS – Université Rennes 1, 35000, Rennes-Cedex, France

    C. Godet

  2. Laboratoire de Génie Electrique de Paris, UMR 8507 CNRS, Ecole Supérieure d'Electricité, Universités Paris VI et Paris XI, 11 rue Joliot-Curie, Plateau de Moulon, 91192, Gif-sur-Yvette Cedex, France

    J. P. Kleider

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Godet, C., Kleider, J.P. Disorder and localization in bandtail hopping transport: experiments and concepts. J Mater Sci: Mater Electron 17, 413–426 (2006). https://doi.org/10.1007/s10854-006-8088-5

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