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Suppressing molecular vibrations in organic semiconductors by inducing strain

Organic molecular semiconductors are solution processable, enabling the growth of large-area single-crystal semiconductors. Improving the performance of organic semiconductor devices by increasing the charge mobility is an ongoing quest, which calls for novel molecular and material design, and improved processing conditions. Here we show a method to increase the charge mobility in organic single-crystal field-effect transistors, by taking advantage of the inherent softness of organic semiconductors. We compress the crystal lattice uniaxially by bending the flexible devices, leading to an improved charge transport. The mobility increases from 9.7 to 16.5 cm2 V−1 s−1 by 70% under 3% strain. In-depth analysis indicates that compressing the crystal structure directly restricts the vibration of the molecules, thus suppresses dynamic disorder, a unique mechanism in organic semiconductors. Since strain can be easily induced during the fabrication process, we expect our method to be exploited to build high-performance organic devices.

For device A, compression and decompression shows a substantial hysteresis while for device F, the hysteresis is much smaller. This results show that when applying a strain below 2% the effect of the strain is totally reversible and the mobility increase is reproducible over several cycles.

Supplementary Tables
Supplementary

Supplementary Note 1 | Band structure calculations
The band structure of unstrained/strained C 10 -DNBDT-NW was calculated using two different methods to ensure the accuracy of the results and hence the conclusions. As a first method, we used the VASP software with the rev-vdW-DF2 functional using plane waves as a basis set with a kinetic energy cutoff of 875.0 eV. The k-point sampling was done in 2 × 2 × 2 (Monkhorst-Pack mesh). As a second method we used the Gaussian 09 software with the PBEPBE functional and 6-31G(d) as a basis set. The crystal structure used to extract those parameters was optimized with VASP, as mentioned in the main text. The two calculation methods give slightly different results regarding the shape of the band diagram ( Supplementary Fig. 9), and the absolute values for the bandwidth as well as the effective mass (Supplementary Table 1). The relative changes between the unstrained and strained crystal structure, however, are essentially the same. Therefore, the conclusion drawn from the band structure calculations does not depend on the calculation method. More specifically, the change in effective mass is the same for both models and can thus not explain the large mobility increase under strain.

Supplementary Note 2 | Calculations of transfer integrals and their fluctuation
In the main text we calculated the effective mass of the charge carrier using the band transport picture. Here we discuss the changes of the transfer integrals upon applying strain and their fluctuations due to molecular vibrations. It needs to be pointed out, that in a system with extended wave functions the effective mass is the relevant parameter describing the mobility, whereas the results discussed here from the transfer integrals are more applicable to a hopping system, which we do not have. Nevertheless, the discussion of transfer integrals brings additional insights into the mechanisms governing charge transport. As mentioned in the main text, the position and orientation of the core, without the alkyl chains, of a set of 7 nearest-neighbor molecules from the optimized crystal structure without and with strain were extracted ( Supplementary Fig. 10 Table 3.
The They found that for very small molecules the fluctuations are on the same order of magnitude as the transfer integral itself 2 .The ratio is lower for larger and more complex molecules, but still larger than the results presented here 3,4 . Therefore, the simplifications used in our approach are expected to result in an underestimation of the fluctuations. The relative change of the fluctuations upon compression, however, can be estimated using our approach.
Upon compressive bending by a 3% strain, the transfer integral increases by 19% for the pair parallel to the c axis and by 7.2% for the pair transversal to the c axis (Supplementary Table 3). At the same time, the fluctuations reduce by 6.3 to 13% depending on the direction.
Finally, the tight binding approximation is used to calculate mobility from the transfer integrals.
Therefore, the results are not directly comparable to the results from the band structure calculations.
In the tight binding model, the mobility is proportional to (a t/Δt) 2 derived from Fermi's golden rule 5 , where a stands for the crystal axis length. If the ratio of Δt to t becomes smaller, the scattering of the charge carriers is suppressed. As in Supplementary Table 3, the increase of (a t/Δt) 2 parallel to the channel is about 77%, where static changes of the crystal lattice and the molecular vibrations contribute equally to the mobility increase. This is in very good quantitative agreement with the experimental results where a mobility increase of up to 70% was observed. Therefore, in both models, in the band transport picture and in the transfer integral picture, the suppression of the molecular fluctuation is a crucial ingredient to explain the mobility increase under strain.