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Fractional differential approach to dispersive transport in semiconductors

,
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.

Fulltext is available at IOP
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

References (91) Cited by (41) Similar articles (20) ↓

  1. V.V. Uchaikin “Self-similar anomalous diffusion and Levy-stable laws46 821–849 (2003)
  2. L.A. Bol’shov, P.S. Kondratenko, L.V. Matveev “Nonclassical transport in highly heterogeneous and sharply contrasting media62 649–659 (2019)
  3. L.M. Zelenyi, A.V. Milovanov “Fractal topology and strange kinetics: from percolation theory to problems in cosmic electrodynamics47 749–788 (2004)
  4. V.V. Uchaikin “Fractional phenomenology of cosmic ray anomalous diffusion56 1074–1119 (2013)
  5. A.V. Gapontsev, V.V. Kondrat’ev “Hydrogen diffusion in disordered metals and alloys46 1077–1098 (2003)
  6. O.G. Bakunin “Reconstruction of streamline topology, and percolation models of turbulent transport56 243–260 (2013)
  7. V.V. Slezov, V.V. Sagalovich “Diffusive decomposition of solid solutions30 23–45 (1987)
  8. I.M. Lifshitz, M.I. Kaganov “Some problems of the electron theory of metals I. Classical and quantum mechanics of electrons in metals2 831–855 (1960)
  9. B.V. Alekseev “Physical fundamentals of the generalized Boltzmann kinetic theory of ionized gases46 139–167 (2003)
  10. B.V. Alekseev “Physical principles of the generalized Boltzmann kinetic theory of gases43 601–629 (2000)
  11. E.L. Shangina, V.T. Dolgopolov “Quantum phase transitions in two-dimensional systems46 777–787 (2003)
  12. S.S. Murzin “Electron transport in the extreme quantum limit in applied magnetic field43 349–364 (2000)
  13. A.S. Borukhovich “Quantum tunneling in multilayers and heterostructures with ferromagnetic semiconductors42 653–667 (1999)
  14. V.I. Alkhimov “The self-avoiding walk problem34 (9) 804–816 (1991)
  15. I.A. Smirnov, V.S. Oskotskii “Semiconductor-metal phase transition in rare-earth semiconductors (samarium monochalcogenides)21 117–140 (1978)
  16. I.A. Abroyan “The effect of ion bombardment on the physical properties of semiconductors14 242–262 (1971)
  17. A.M. Bykov, I.N. Toptygin “Instabilities of a multicomponent plasma with accelerated particles and magnetic field generation in astrophysical objects50 141–174 (2007)
  18. V.V. Zosimov, L.M. Lyamshev “Fractals in wave processes38 347–384 (1995)
  19. A.I. Olemskoi, A.Ya. Flat “Application of fractals in condensed-matter physics36 (12) 1087–1128 (1993)
  20. E.G. Berezhko, G.F. Krymskii “Acceleration of cosmic rays by shock waves31 27–51 (1988)

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