Polaron Structure and Transport in Fullerene Materials: Insights from First-Principles Calculations

Organic semiconductors have attracted much attention as alternatives to traditional silicon-based inorganic electronics, showing promise as active materials in a range of technologies including field-effect transistors (FETs), light-emitting diodes (LEDs), and organic photovoltaics (OPVs). A major limiting factor, however, is their rate of charge transport. Increasing the intermolecular couplings, and thus the speed of this slow journey to the electrode, has the potential to increase the efficiency and economic viability of organic semiconductor technology.

One factor that must be considered in the modeling of charge transport is the influence of other charges. In particular, the question of charge density effects is relevant to FETs, which operate at fairly high charge densities of 10¹⁸-10¹⁹ cm^-3. Previous literature has suggested that charge density increases charge transport when excess charges fill the traps in the material that are caused by structural or chemical defects. It is argued that when additional charges fill these traps, the remaining charges are allowed to experience trap-free transport. Of the various materials that have been explored as possible electron acceptors in FETs, C₆₀ and C₇₀ fullerenes have been used in a large number of studies and have shown some of the more promising electron mobilities. C₇₀ has also been studied extensively as an electron-acceptor in OPVs, with C₇₀-based acceptors offering increased photoabsorption over a large energy range relative to C₆₀-based acceptors. Because of the usefulness of this increased photoabsorption, we treat C₇₀ in this study of fullerenes. Although we treat only C₇₀, the results are likely to be at least qualitatively relevant to charge transport between other fullerene molecules.   

In this study, we use density functional theory (DFT) to take a more detailed look at the effect of nearby charges on polarons in C₇₀ fullerenes, examining whether perturbations by adjacent charges can affect the charge carrier electronic structure and electronic couplings in a way that influences the transport process beyond the effects of  filling traps. The arrangement of charges that we study corresponds to an extremely high charge density and addresses the question of whether these effects become irrelevant at the charge densities that occur in current C₇₀ devices. This work makes no assumptions about the nature of the charge transport process: our results are relevant to charge transport in C₇₀ systems regardless of whether polarons travel via thermally activated hopping or via band transport.

First, we examine the effects of nearby charges on the structure of the charge density distribution of a polaron on a C₇₀ molecule. Next, we apply DFT to calculate the effect of nearby charges on electronic couplings between two C₇₀ molecules.

The fact that adjacent charges will to some extent repel the electron density of a polaron on a fullerene molecule is expected; however, by rigorously calculating the charge density of a polaron and visualizing its isosurface, we gain insight into the range of distances over which these effects are significant. We find that these effects drop off quickly as the distance of the point charges is increased, suggesting that such an effect would only be present in regions with extremely high charge density. When the effect of charges on electronic couplings in dimers is calculated, we find that the presence of nearby charges has an effect of maximizing coupling: while dimer orientations for which coupling is already relatively high are insensitive to charges, orientations with low initial couplings experience increases in electronic coupling of >100% when charges are placed very close to the edges of the fullerenes. As in the case of effects on the polaron charge density of a monomer, the effect of nearby charges on electronic couplings drops off quickly as the distance between the charges and the fullerenes is increased. This rapid drop-off with distance suggests that these charge density effects are insignificant in most regions of current C₇₀ devices.

Our results indicate that the positive correlation between charge density and mobility that has been presented in a range of experimental studies may, in limited regions with high charge density, be partially mediated by effects on electronic structure and couplings. These results are not in conflict with the common hypothesis that charge density influences mobility by allowing trap-free transport; rather, both mechanisms may contribute to the observed trends. In limited regions with extremely high charge density, increased density may promote charge transport not only via trap-filling but also via the mechanism of altered electronic couplings. Whether this infrequent event influences overall mobility will depend on the importance of these limited regions in charge transport in a particular device.