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

Entropy

卷:19

Renat Sibatov¹  Vyacheslav Svetukhin¹  Vadim Shulezhko¹ 

[1] Ulyanovsk State University, 42 Leo Tolstoy str., Ulyanovsk 432017, Russia;

关键词: anomalous diffusion;    hopping;    fractional equation;    dispersive transport;    mesoporous semiconductor;    polymer blend;    percolation;   

DOI  :  10.3390/e19090463

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown