On anomalous diffusion of fast electrons through the silicon crystal
- Authors: Syshchenko V.V.1, Tarnovsky A.I.1, Dronik V.I.1
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Affiliations:
- Belgorod State University
- Issue: No 9 (2024)
- Pages: 95-100
- Section: Articles
- URL: https://jdigitaldiagnostics.com/1028-0960/article/view/664753
- DOI: https://doi.org/10.31857/S1028096024090125
- EDN: https://elibrary.ru/EHPCIH
- ID: 664753
Cite item
Abstract
Anomalous diffusion is a random process in which the root-mean-square displacement of a particle from the starting point depends nonlinearly on time. The possibility of such behavior for high energy particles moving through the crystal under conditions close to axial channeling was found earlier. In this case, the rapid displacement of particles in a plane transverse to atomic strings (Lévi flights) is due to the temporary capture of the particles in planar channels. In this work, by means of numerical simulation, the anomalous diffusion exponent was found for different values of the energy of electron transverse motion in the (100) plane of a silicon crystal. It has been established that in the case of electrons with an energy exceeding by 1 eV the height of the saddle point of the potential of a system of atomic chains [100], the results are consistent with those obtained earlier. It has been confirmed that the anomalous nature of diffusion is due to the possibility of short-term capture of particles in planar channels. With increasing transverse energy, this possibility disappears, and diffusion becomes normal (Brownian).
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About the authors
V. V. Syshchenko
Belgorod State University
Author for correspondence.
Email: syshch@yandex.ru
Russian Federation, Belgorod, 308015
A. I. Tarnovsky
Belgorod State University
Email: syshch@yandex.ru
Russian Federation, Belgorod, 308015
V. I. Dronik
Belgorod State University
Email: syshch@yandex.ru
Belgorod, 308015
References
- Ахиезер А.И., Шульга Н.Ф. Электродинамика высоких энергий в веществе. М.: Наука, 1993. 344 с.
- Ахиезер А.И., Шульга Н.Ф., Трутень В.И., Гриненко А.А., Сыщенко В.В. // УФН. 1995. Т. 165. № 10. С. 1165. https://doi.org/10.3367/UFNr.0165.199510c.1165
- Gemmel D.S. // Rev. Mod. Phys. 1974. V. 46. P. 129. https://doi.org/10.1103/RevModPhys.46.129
- Uggerhøj U.I. // Rev. Mod. Phys. 2005. V. 77. P. 1131. https://doi.org/10.1103/RevModPhys.77.1131
- Lindhard J. // Kongel. Dan. Vidensk. Selsk., Mat.-Fys. Medd. 1965. V. 34. № 14. P. 1.
- Bouchaud J.-P., Georges A. // Phys. Rep. 1990. V. 195. P. 127. https://doi.org/10.1016/0370-1573(90)90099-N
- Shlesinger M.F., Zaslavsky G.M., Klafter J. // Nature. 1993. V. 363. P. 31. https://doi.org/10.1038/363031a0
- Metzler R., Klafter J. // Phys. Rep. 2000. V. 339. P. 1. https://doi.org/10.1016/s0370-15730000070-3
- Zaslavsky G.M. // Phys. Rep. 2002. V. 371. P. 461. https://doi.org/10.1016/S0370-1573(02)00331-9
- Chechkin A.V., Klafter J., Gonchar V.Yu., Metzler R., Tanatarov L.V. // Phys. Rev. E. 2003. V. 67. 010102 (R). https://doi.org/10.1103/PhysRevE.67.010102
- Тихонов А.Н., Самарский А.А. Уравнения математической физики. М.: Наука, 1977. 736 с.
- Мэтьюз Дж., Уокер Р. Математические методы физики. М.: Атомиздат, 1972. 392 с.
- Greenenko A.A., Chechkin A.V., Shul’ga N.F. // Phys. Lett. A. 2004. V. 324. P. 82. https://doi.org/10.1016/j.physleta.2004.02.053
- Shul’ga N.F., Greenenko A.A., Truten’ V.I. // Ukr. J. Phys. 2006. V. 51. № 2. P. 147.
- Шульга Н.Ф. Некоторые вопросы теории рассеяния быстрых частиц в веществе и во внешних полях. Киев: Наукова думка, 2010. 199 с.
- Ландау Л.Д., Лифшиц Е.М. Теория поля. М.: Наука, 1988. 512 с.
- Гулд Х., Тобочник Я. Компьютерное моделирование в физике. Ч. 1. М.: Мир, 1990. 349 с.
- Brockmann D., Geisel T. // Phys. Rev. Lett. 2003. V. 90. Р. 170601. https://doi.org/10.1103/PhysRevLett.90.170601
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