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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

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  1. Wlaźlak E, Przyczyna D et al Jpn. J. Appl. Phys. 59 SI0801 (2020)
  2. Sibatov R T, Sun HongGuang Fractal Fract 4 42 (2020)
  3. Marinov O, Deen M J et al Physics Reports 844 1 (2020)
  4. Morozova E V J. Phys.: Conf. Ser. 1695 012170 (2020)
  5. Likhomanova P, Kalashnikov I Phys. Rev. E 102 (2) (2020)
  6. Wlaźlak E, Marzec M et al ACS Appl. Mater. Interfaces 11 17009 (2019)
  7. Sibatov R T, Svetukhin V V et al Electronics 8 650 (2019)
  8. Alaria A, Khan A M et al Int. J. Appl. Comput. Math 5 (6) (2019)
  9. Li ZhiPeng, Sun HongGuang, Sibatov R T 22 1480 (2019)
  10. Almeida R, Malinowska A B, Monteiro M T T Math Meth Appl Sci 41 336 (2018)
  11. Alisultanov Z Z, Ragimkhanov G B Chaos, Solitons & Fractals 107 39 (2018)
  12. El-Nabulsi R A Eur. Phys. J. Plus 133 (10) (2018)
  13. Alisultanov Z Z, Agalarov A M et al Fractional Dynamics, Anomalous Transport and Plasma Science Chapter 7 (2018) p. 125
  14. Choo K Y, Muniandy S V et al Organic Electronics 41 157 (2017)
  15. Shulezhko V V, Morozova E V Semiconductors 51 1713 (2017)
  16. Rekhviashvili S Sh, Alikhanov A A Semiconductors 51 755 (2017)
  17. Sibatov R, Shulezhko V, Svetukhin V Entropy 19 463 (2017)
  18. Sibatov R, Morozova E Lecture Notes In Electrical Engineering Vol. Theory and Applications of Non-integer Order Systems407 Chapter 26 (2017) p. 287
  19. Rekhviashvili S Sh, Mamchuev M O, Mamchuev M O Phys. Solid State 58 788 (2016)
  20. Sibatov R T, Morozova E V Russ Phys J 59 722 (2016)
  21. Aguilar J F G, Córdova-Fraga T et al Mathematical Problems In Engineering 2016 1 (2016)
  22. Sabelfeld K K, Brandt O, Kaganer V M J Math Chem 53 651 (2015)
  23. Sibatov R T, Sibatov R T i dr Teoreticheskaya Matematicheskaya Fizika 183 460 (2015) [Sibatov R T, Svetukhin V V Theor Math Phys 183 846 (2015)]
  24. Choo K Y, Muniandy S V Int. J. Mod. Phys. Conf. Ser. 36 1560008 (2015)
  25. Sibatov R T, Uchaikin V V Journal Of Computational Physics 293 409 (2015)
  26. Sibatov R T, Morozova E V J. Exp. Theor. Phys. 120 860 (2015)
  27. Svetukhin V V, Sibatov R T J. Exp. Theor. Phys. 120 678 (2015)
  28. Giraldi F, Petruccione F J. Phys. A: Math. Theor. 47 395304 (2014)
  29. Uchaikin V V Uspekhi Fizicheskikh Nauk 183 1175 (2013) [Uchaikin V V Phys.-Usp. 56 1074 (2013)]
  30. Alisultanov Z Z, Meilanov R P J. Synch. Investig. 7 46 (2013)
  31. Korolev N A, Nikitenko V R, Tyutnev A P Semiconductors 47 1292 (2013)
  32. Alisultanov Z Z, Alisultanov Z Z i dr Teor. Mat. Fiz. 171 404 (2012) [Alisultanov Z Z, Meilanov R P Theor Math Phys 173 1445 (2012)]
  33. Alisultanov Z Z, Alisultanov Z Z i dr Teor. Mat. Fiz. 171 404 (2012) [Alisultanov Z Z, Meilanov R P Theor Math Phys 171 769 (2012)]
  34. UCHAIKIN VLADIMIR V, SIBATOV RENAT T Int. J. Mod. Phys. B 26 1230016 (2012)
  35. Alisultanov Z Z, Alisultanov Z Z i dr Teoreticheskaya Matematicheskaya Fizika 173 135 (2012)
  36. Shkilev V P J. Exp. Theor. Phys. 115 164 (2012)
  37. El-Nabulsi R A Computers & Mathematics With Applications 62 1568 (2011)
  38. Sibatov R T Phys. Scr. 84 025701 (2011)
  39. Sibatov R T Jetp Lett. 93 503 (2011)
  40. Sibatov R T, Uchaikin V V Communications In Nonlinear Science And Numerical Simulation 16 4564 (2011)
  41. Uchaikin V V, Sibatov R T J. Phys. A: Math. Theor. 44 145501 (2011)

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