How Do Disorder, Reorganization, and Localization Influence the Hole Mobility in Conjugated Copolymers?

Abstract

In order to unravel the intricate interplay between disorder effects, molecular reorganization, and charge carrier localization, a comprehensive study was conducted on hole transport in a series of conjugated alternating phenanthrene indenofluorene copolymers. Each polymer in the series contained one further comonomer comprising monoamines, diamines, or amine-free structures, whose influence on the electronic, optical, and charge transport properties was studied. The series covered a wide range of highest occupied molecular orbital (HOMO) energies as determined by cyclovoltammetry. The mobility, inferred from time-of-flight (ToF) experiments as a function of temperature and electric field, was found to depend exponentially on the HOMO energy. Since possible origins for this effect include energetic disorder, polaronic effects, and wave function localization, the relevant parameters were determined using a range of methods. Disorder and molecular reorganization were established first by an analysis of absorption and emission measurements and second by an analysis of the ToF measurements. In addition, density functional theory calculations were carried out to determine how localized or delocalized holes on a polymer chain are and to compare calculated reorganization energies with those that have been inferred from optical spectra. In summary, we conclude that molecular reorganization has little effect on the hole mobility in this system while both disorder effects and hole localization in systems with low-lying HOMOs are predominant. In particular, as the energetic disorder is comparable for the copolymers, the absolute value of the hole mobility at room temperature is determined by the hole localization associated with the triarylamine moieties.

Unified description for hopping transport in organic semiconductors including both energetic disorder and polaronic contributions

“…25 We recently investigated hole transport in a series of π -conjugated copolymers. 39 When measuring the temperature dependence of the hole mobility σ values have been obtained ranging from 91 to 109 meV, quite consistent with many other disordered organic semiconductors 2 and significantly higher than the σ values of triplets. Values for E a , inferred from DFT calculations, range between 25 and 46 meV, 39 i.e., half that for triplet exciton transport (see above).…”

“…39 When measuring the temperature dependence of the hole mobility σ values have been obtained ranging from 91 to 109 meV, quite consistent with many other disordered organic semiconductors 2 and significantly higher than the σ values of triplets. Values for E a , inferred from DFT calculations, range between 25 and 46 meV, 39 i.e., half that for triplet exciton transport (see above). The corresponding values for the C factor are 0.40 to 0.44 and the T c values are between 1100 and 1300 K. It is obvious that the increased disorder combined with the lower reorganization energy of charge carriers ensures that at an experimentally relevant temperature range charge transport is dominated by disorder, tractable in terms of Miller-Abrahams rate instead of the computationally more demanding Marcus rates.…”

Chain conformations dictate multiscale charge transport phenomena in disordered semiconducting polymers

“…The reorganization energies of a few hundred millielectronvolts and electronic couplings of a few millielectronvolts agree well with recent calculations in a variety of systems (36)(37)(38)(39). A recent study of phenanthrene indenofluorene copolymers suggests that reorganization energies are lower than those calculated by DFT, so disorder and hole localization effects are predominant (40). Introducing a small amount of energetic disorder (35 meV) to our simulations resulted in lower reorganization energies but no change in the remaining fitting parameters.…”

Fabrication of poly(3-hexylthiophene) nanowires for high-mobility transistors

“…6(b) presents this comparison of m TOF as a function of 1/T 2 . The resulting s is reduced from 94 meV to 78 meV upon solvation, which compares favorably with the values expected for disordered polymer layers [62,64].…”