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Fractional differential approach to dispersive transport in semiconductors

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Ul'yanovsk State University, ul. L. Tolstogo 42, Ulyanovsk, 432700, Russian Federation

A novel approach using equations with fractional order derivatives to describe dispersive transport in disordered semiconductors is described. A relationship between the self-similarity of dispersive transport, stable limiting distributions, and kinetic equations with fractional derivatives is established. It is shown that unlike the well-known Scher — Montroll and Arkhipov — Rudenko models, which are in a sense alternatives to the normal transport model, fractional differential equations provide a unified mathematical framework for describing normal and dispersive transport. The fractional differential formalism allows the equations of ambipolar dispersive transport to be written down and transport in systems with a distributed dispersion parameter to be described. The relationship between fractional differential equations and the generalized limiting theorem reveals the probabilistic aspects of the phenomenon in which a dispersive-to-Gaussian transport transition occurs in a time-of-flight experiment as the applied voltage is decreased and/or the sample thickness increased.

Text can be downloaded in Russian. English translation is available on IOP Science.
PACS: 05.40.Fb, 72.20.−i, 73.40.−c (all)
DOI: 10.3367/UFNe.0179.200910c.1079
URL: https://ufn.ru/en/articles/2009/10/c/
Citation: Sibatov R T, Uchaikin V V "Fractional differential approach to dispersive transport in semiconductors" Phys. Usp. 52 1019–1043 (2009)
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Оригинал: Сибатов Р Т, Учайкин В В «Дробно-дифференциальный подход к описанию дисперсионного переноса в полупроводниках» УФН 179 1079–1104 (2009); DOI: 10.3367/UFNr.0179.200910c.1079

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