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Open AccessArticle

Fractional Derivative Phenomenology of Percolative Phonon-Assisted Hopping in Two-Dimensional Disordered Systems

by Renat Sibatov 1,*,†,‡, Vadim Shulezhko 1,‡ and Vyacheslav Svetukhin 1,2,‡
1
Ulyanovsk State University, 42 Leo Tolstoy str., Ulyanovsk 432017, Russia
2
Institute of Nanotechnology of Microelectronics of the Russian Academy of Sciences, 16a Nagatinskaya str., Moscow 115487, Russia
*
Author to whom correspondence should be addressed.
Current address: 49 Transportnaya street, Ulyanovsk 432063, Russia.
These authors contributed equally to this work.
Entropy 2017, 19(9), 463; https://doi.org/10.3390/e19090463
Received: 22 June 2017 / Revised: 28 August 2017 / Accepted: 28 August 2017 / Published: 1 September 2017
(This article belongs to the Special Issue Complex Systems and Fractional Dynamics)
Anomalous advection-diffusion in two-dimensional semiconductor systems with coexisting energetic and structural disorder is described in the framework of a generalized model of multiple trapping on a comb-like structure. The basic equations of the model contain fractional-order derivatives. To validate the model, we compare analytical solutions with results of a Monte Carlo simulation of phonon-assisted tunneling in two-dimensional patterns of a porous nanoparticle agglomerate and a phase-separated bulk heterojunction. To elucidate the role of directed percolation, we calculate transient current curves of the time-of-flight experiment and the evolution of the mean squared displacement averaged over medium realizations. The variations of the anomalous advection-diffusion parameters as functions of electric field intensity, levels of energetic, and structural disorder are presented. View Full-Text
Keywords: anomalous diffusion; hopping; fractional equation; dispersive transport; mesoporous semiconductor; polymer blend; percolation anomalous diffusion; hopping; fractional equation; dispersive transport; mesoporous semiconductor; polymer blend; percolation
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Sibatov, R.; Shulezhko, V.; Svetukhin, V. Fractional Derivative Phenomenology of Percolative Phonon-Assisted Hopping in Two-Dimensional Disordered Systems. Entropy 2017, 19, 463.

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