Role of transport band edge variation on delocalized charge transport in high-mobility crystalline organic semiconductors

We demonstrate that the degree of charge delocalization has a strong impact on polarization energy and thereby on the position of the transport band edge in organic semiconductors. This gives rise to long-range potential fluctuations, which govern the electronic transport through delocalized states in organic crystalline layers. This concept is employed to formulate an analytic model that explains a negative field dependence coupled with a positive temperature dependence of the charge mobility observed by a lateral time-of-flight technique in a high-mobility crystalline organic layer. This has important implications for the further understanding of the charge transport via delocalized states in organic semiconductors.

Figure 1

Evolution of the electronic structure upon charge delocalization for the case of a monolayer of pentacene molecules. (a) Possible delocalization geometries in a monolayer of pentacene; for each case, we consider delocalization of a positive charge over $N=5$ molecules and tabulate the corresponding polarization energy $P$. (b) Sketch of the charge delocalization impact on the electron and hole transport band energies. (c) As the charge delocalization expands over more molecules, $P$ decreases; correspondingly, the hole transport energy $E_h$ approaches the HOMO level of a neutral pentacene molecule (6.6 eV). Note that this represents an upper limit of the effect due to an idealized equalized charge density distribution over $N$ molecules being used to model the delocalization [16]; a nonuniform distribution leads to less strong shifts.

Figure 2

TOF photocurrent transients measured in ${\mathrm{C}}_8$-BTBT crystalline film at 323 K under different $V_b$ (a) and at constant bias $V_b=150\mathrm{V}$ for different temperatures (b). Dashed asymptotic lines were used to estimate the transit times (indicated by arrows). Inset in (a) shows a schematic view of the TOF photocurrent measurement.

Figure 3

(a) Field dependences of the TOF mobility measured (symbols) at different temperatures, and (b) the mobility temperature dependences at different $V_b$ in ${\mathrm{C}}_8$-BTBT crystalline films. Fitting by the present EMA model is shown by solid curves. Electric field was estimated as $E=V_b/L$.