Abstract
The approach based on fractional advection–diffusion equations provides an effective and meaningful tool to describe the dispersive transport of charge carriers in disordered semiconductors. A fractional generalization of Fick’s law containing the Riemann–Liouville fractional derivative is related to the well-known fractional Fokker–Planck equation, and it is consistent with the universal characteristics of dispersive transport observed in the time-of-flight experiment (ToF). In the present paper, we consider the generalized Fick laws containing other forms of fractional time operators with singular and non-singular kernels and find out features of ToF transient currents that can indicate the presence of such fractional dynamics. Solutions of the corresponding fractional Fokker–Planck equations are expressed through solutions of integer-order equation in terms of an integral with the subordinating function. This representation is used to calculate the ToF transient current curves. The physical reasons leading to the considered fractional generalizations are elucidated and discussed.
Highlights
Fractional advection–diffusion equations provide effective and meaningful approach to description of dispersive charge carrier transport in disordered semiconductors [1,2,3,4,5]
In Ref. [18], it is shown that the universality of the transient current curves I(t) and the power-law dependence of the transient time tT on the sample thickness L, observed in the time-of-flight experiment (ToF) experiment, unambiguously indicate the fractional-differential kinetics of dispersive transport of nonequilibrium charge carriers
We study dispersive transport in a sample of finite width, and try to find out features of ToF transient currents that can indicate the generalized fractional dynamics
Summary
Fractional advection–diffusion equations provide effective and meaningful approach to description of dispersive charge carrier transport in disordered semiconductors [1,2,3,4,5]. This geometry is more appropriate to measure transient currents in organic nanocomposites, bulk heterojunctions, and perovskite solar cells. [18], it is shown that the universality of the transient current curves I(t) and the power-law dependence of the transient time tT on the sample thickness L, observed in the ToF experiment, unambiguously indicate the fractional-differential kinetics of dispersive transport of nonequilibrium charge carriers. We study dispersive transport in a sample of finite width, and try to find out features of ToF transient currents that can indicate the generalized fractional dynamics. The physical reasons leading to the considered fractional generalizations are discussed
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