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Distribution of charge carrier transport properties in organic semiconductors with Gaussian disorder

The charge carrier drift mobility in disordered semiconductors is commonly graphically extracted from time-of-flight (ToF) photocurrent transients yielding a single transit time. However, the term transit time is ambiguously defined and fails to deliver a mobility in terms of a statistical average. Here, we introduce an advanced computational procedure to evaluate ToF transients, which allows to extract the whole distribution of transit times and mobilities from the photocurrent transient, instead of a single value. This method, extending the work of Scott et al. (Phys. Rev. B 46, 8603), is applicable to disordered systems with a Gaussian density of states (DOS) and its accuracy is validated using one-dimensional Monte Carlo simulations. We demonstrate the superiority of this new approach by comparing it to the common geometrical analysis of hole ToF transients measured on poly(3-hexyl thiophene-2,5-diyl) (P3HT). The extracted distributions provide access to a very detailed and accurate analysis of the charge carrier transport. For instance, not only the mobility given by the mean transit time, but also the mean mobility can be calculated. Whereas the latter determines the macroscopic photocurrent, the former is relevant for an accurate determination of the energetic disorder parameter $σ$ within the Gaussian disorder model (GDM). $σ$ derived by using the common geometrical method is, as we show, underestimated instead.