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Fractional differential kinetics of charge transport in unordered semiconductors

  • Amorphous, Vitreous, Porous, Organic, and Microcrystalline Semiconductors; Semiconductor Composites
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Abstract

In previous studies, we obtained an expression for the time dependence of the transient current in amorphous semiconductors during dispersive transport. The expression contains a stable density with a characteristic exponent equal to the dispersion parameter α < 1; excess carrier concentrations are expressed in terms of fractional stable densities with the characteristic exponent α. In this study, generalized equations of diffusion and carrier drift in unordered semiconductors for dispersive transport were derived. A main feature of these equations is the fractional-order partial time derivative. Solutions to these equations are expressed in terms of fractional stable densities. At α → 1, fractional stable distributions become normal, and generalized equations become ordinary diffusion and drift equations. Thus, the fractional differential approach allows the description of normal and dispersive transport within a unified mathematical model.

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Authors and Affiliations

  1. Ul’yanovsk State University, ul. L’va Tolstogo 42, Ul’yanovsk, 432700, Russia

    R. T. Sibatov & V. V. Uchaikin

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  1. R. T. Sibatov
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  2. V. V. Uchaikin
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Original Russian Text © R.T. Sibatov, V.V. Uchaikin, 2007, published in Fizika i Tekhnika Poluprovodnikov, 2007, Vol. 41, No. 3, pp. 346–351.

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Sibatov, R.T., Uchaikin, V.V. Fractional differential kinetics of charge transport in unordered semiconductors. Semiconductors 41, 335–340 (2007). https://doi.org/10.1134/S1063782607030177

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  • DOI: https://doi.org/10.1134/S1063782607030177

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