(Color online) (a) Schematic of the Boltzmann-weighted hopping model. (b) The fractional error in the charge density, relative to a Boltzmann distribution, at the favored surface perpendicular to the field (•), and the surfaces parallel to the field (▪) at different times. The vertical lines delineate the average number of hops made parallel to the field. The insets depict the relaxation of the charge density over time. Note that dots represent densities rather than individual charges, and that our studies are exclusively at the limit of low charge densities.
(Color online) AFM micrographs showing directionally crystallized P3HT fibers in a well crystallized film (a), a possible inter-fiber break (encircled) (b), and an atypical disordered region (c) in a very defective film. Taken in tapping mode, images show phase (a, c), and height (b).
(Color online) Experimental temperature dependence of and . The dotted lines correspond to the average of our fitted mobilities, and the error bars twice their standard deviation. Data from Ref. 19.
(Color online) (a) The average mobility parallel to fibers and its standard deviation between devices . Lines are fitted as described in the text. (b) The average activation energy Ea of , as a function of the intra-fiber break density. Ea was calculated with a sample measuring 5 50 , with the long axis aligned with the fibers and and set to 10 and 78 meV, respectively. The line is fitted by eye. The cartoon depicts intra-fiber breaks, which partition otherwise continuous fibers.
The dependence of on device length at varying intra-fiber break densities. The device width is fixed at 50 , and the parameters are the same as those used in Fig. 4.
(Color online) The distribution anisotropies in films containing 10, 50, and 100 inter-fiber breaks measuring 2.5, and 1175 breaks measuring 500 nm. In each case are sampled from 4000 films, each with a random arrangement of inter-fiber breaks. The experimental anisotropy is marked by the dotted line. The cartoons depict two films with identical defect densities, one of which has an unhindered transport pathway. All lines are fitted by eye.
(Color online) The effect of amorphous regions on and and the ratio between them. The length of the error bars correspond to twice the standard deviation in .
Parameters of the Boltzmann-weighted hopping model fitted to experimental mobilities in directionally crystallized P3HT.
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