[1]Benzothieno[3,2-b][1]benzothiophene derivatives with high air stability have recently displayed excellent charge transport properties in field-effect devices. In particular, the average charge mobilities can reach as high as 16.4 ± 6.1 cm2 V−1 s−1 in devices with a high quality semiconductor/insulator interface, which is comparable to the performance for a rubrene single-crystal device. To better understand these excellent charge transport properties, a multiscale approach combining molecular dynamics and quantum-chemical calculations was used in this work to assess the structure–property relationship for three of the [1]benzothieno[3,2-b][1]benzothiophene derivatives with different alkyl side chains. It is indicated that the extremely large electronic couplings along the a-axis direction are responsible for the excellent charge transport properties in these systems. While the molecular packings are centrosymmetrical in the ab plane, the lattice vibrations were found to hamper the charge transport in optimized crystal structures at the COMPASS molecular mechanics level which is opposite to the recent findings that the lattice dynamics should have a negligible effect on the charge mobility in the centrosymmetrical plane. The reason for such behavior was analyzed and the predicted order of the overall charge mobilities for the studied systems was consistent with the experiments. Meanwhile, how well the force field reproduces the observed crystal structures and dimer intermolecular separations and orientations is discussed in this work. In addition, it is shown that the present charge transport model can not only predict the magnitude of the charge mobility but also the measured “band-like” charge transport in experiments, so the nuclear tunneling effect is very important for charge transport in organic semiconductors as was demonstrated in recent theoretical work.

Crystal packing has strong influence on the charge mobility for organic semiconductors, so the elucidation of the structure-property relationship is important for the design of high-performance organic semiconductors. Halogen substitution has been shown to be a promising strategy to alter the crystal structure without significantly changing the molecular size in previous reports. This paper studies the influence of halogenation on charge transport in single crystals of chrysene derivatives from a theoretical standpoint. The structure-property relationship is first rationalized by investigating the reorganization energy and electronic coupling from the density functional theory calculations. Based on the Marcus charge transfer theory, the mobilities in the molecular monolayer are then calculated with the random walk simulation technique from which the angular resolution anisotropic mobilities are obtained on the fly. It is shown that the mobilities become much larger for holes than those for electrons in the molecular monolayer when the halogenation occurs. Furthermore, the intra-layer charge transport is little influenced by the inter-layer pathways in the single crystals of the halogenated chrysene derivatives, while the opposite case is shown for the crystal of the nonhalogenated chrysene derivative. The reason for the variations of charge transport is discussed theoretically.

The influence of lattice dynamics on carrier mobility has received much attention in organic crystalline semiconductors, because the molecular components are held together by weak interactions and the transfer integrals between neighboring molecular orbitals are extremely sensitive to small nuclear displacements. Recently, it has been shown that the dynamic disorder has little effect on hole mobility in the ab plane of pentacene, but a reasonable explanation is absent for such a puzzle. To better understand the effect of lattice vibrations on carrier transport, a further study is required for other organic materials. In this work, a mixed molecular dynamic and quantum-chemical methodology is used to assess the effect of nuclear dynamics on hole mobility in the dianthra[2,3-b:2′,3′-f]-thieno[3,2-b]thiophene (DATT) crystals which exhibit high air stability with the hole mobility as large as that in rubrene-based devices. It is found that the lattice vibrations lead to an increasing encumbrance for hole transport in the ab plane of the DATT crystals as the temperature increases. By comparing the crystal structures of DATT and pentacene, the reduced hole mobility in DATT is attributed to the unsymmetric arrays of nearest-neighboring molecular dimers in the ab plane, because the electronic coupling exhibits unbalanced thermal fluctuations for the nearest-neighboring dimers which then induces a stronger oscillation for carriers along the directions with asymmetric packing. To further relate the dynamic disorder with hole transport, the variations of anisotropic mobilities are also analyzed. As a result, the negligible effect of lattice dynamics on the hole mobility in pentacene is explained by the centrosymmetric molecular packing of the nearest-neighboring molecular pairs in the ab plane.

The electronic coupling between adjacent molecules is an important parameter for the charge transport properties of organic semiconductors. In a previous paper, a semiclassical generalized nonadiabatic transition state theory was used to investigate the nonperturbative effect of the electronic coupling on the charge transport properties, but it is not applicable at low temperatures due to the presence of high-frequency modes from the intramolecular conjugated carbon–carbon stretching vibrations [G. J. Nan et al., J. Chem. Phys., 2009, 130, 024704]. In the present paper, we apply a quantum charge transfer rate formula based on the imaginary-time flux–flux correlation function without the weak electronic coupling approximation. The imaginary-time flux–flux correlation function is then expressed in terms of the vibrational-mode path average and is evaluated by the path integral approach. All parameters are computed by quantum chemical approaches, and the mobility is obtained by kinetic Monte-Carlo simulation. We evaluate the intra-layer mobility of sexithiophene crystal structures in high- and low-temperature phases for a wide range of temperatures. In the case of strong coupling, the quantum charge transfer rates were found to be significantly smaller than those calculated using the weak electronic coupling approximation, which leads to reduced mobility especially at low temperatures. As a consequence, the mobility becomes less dependent on temperature when the molecular packing leads to strong electronic coupling in some charge transport directions. The temperature-independent charge mobility in organic thin-film transistors from experimental measurements may be explained from the present model with the grain boundaries considered. In addition, we point out that the widely used Marcus equation is invalid in calculating charge carrier transfer rates in sexithiophene crystals.

Charge mobility in polycrystalline organic semiconductors is often thermally activated, so a semiclassical Marcus charge transfer rate theory has long been used to investigate the charge transport properties of organic semiconductors. However, the classical treatment for the nuclear degrees of freedom and the first-order perturbative nature of electronic coupling in the semiclassical Marcus charge transfer rate theory is often invalid in organic semiconductors. Furthermore, traps in polycrystalline organic semiconductors are not considered during the simulations with the semiclassical Marcus charge transfer rate theory. In the present work, we propose a model to study charge transport properties in polycrystalline organic semiconductors which consist of trap-free crystallitic grains separated by boundaries between them. The charge transfer rate in grains is evaluated with a quantum charge transfer rate theory without weak electronic coupling approximation while the charge transport at grain boundaries is limited by energy barriers there. We find that a thermally activated mobility can be obtained from the quantum charge transfer rate theory when traps at grain boundaries are considered. Meanwhile, a roughly linear dependence of mobility on grain size is shown for large grain size while a rapid variation of mobility with grain size is observed when the grain size is small, which reconciles the discrepancy of the mobility versus grain size in experiments. In addition, the different mobilities for sexithiophene crystal structures in high- and low-temperature phases show that the mobility in polycrystalline organic semiconductors not only depends on the boundary property between grains but also the molecular packing in grains.Graphical abstractHighlights► A model is proposed to study charge transport in polycrystalline sexithiophene. ► The charge transfer rate in grains is evaluated with a quantum rate theory. ► The charge transport is limited by energy barriers at boundaries between grains. ► A thermally activated mobility can be obtained when the traps are considered.

The electron transfer rate formalism based on stationary phase approximation for imaginary-time flux–flux correlation function is often used to investigate the dynamic processes of complex systems in condensed phase, but the applicability of the electron transfer rate formula from stationary phase approximation has never been clarified. In this paper, we evaluated the electron transfer rates for spin-boson model with Debye spectral density from nonadiabatic to adiabatic regime. The comparison between the electron transfer rates from stationary phase approximation and the accurate results from the hierarchical equations of motion were made. The results from several approximate electron transfer methods were also shown. We found that the electron transfer rate formalism from stationary phase approximation can reasonably predict the electron transfer rates from nonadiabatic to intermediate regime and is invalid in adiabatic regime. The merit of the electron transfer rate formalism from stationary phase approximation was discussed.Graphical abstractHighlights► Reliability of electron transfer rate from stationary phase approximation is shown. ► The hierarchical equations of motion is used as a benchmark for comparison. ► Stationary phase approximation is reliable from nonadiabatic to intermediate regime. ► The spectral density is free for stationary phase approximation.

[1]Benzothieno[3,2-b][1]benzothiophene derivatives with high air stability have recently displayed excellent charge transport properties in field-effect devices. In particular, the average charge mobilities can reach as high as 16.4 ± 6.1 cm2 V−1 s−1 in devices with a high quality semiconductor/insulator interface, which is comparable to the performance for a rubrene single-crystal device. To better understand these excellent charge transport properties, a multiscale approach combining molecular dynamics and quantum-chemical calculations was used in this work to assess the structure–property relationship for three of the [1]benzothieno[3,2-b][1]benzothiophene derivatives with different alkyl side chains. It is indicated that the extremely large electronic couplings along the a-axis direction are responsible for the excellent charge transport properties in these systems. While the molecular packings are centrosymmetrical in the ab plane, the lattice vibrations were found to hamper the charge transport in optimized crystal structures at the COMPASS molecular mechanics level which is opposite to the recent findings that the lattice dynamics should have a negligible effect on the charge mobility in the centrosymmetrical plane. The reason for such behavior was analyzed and the predicted order of the overall charge mobilities for the studied systems was consistent with the experiments. Meanwhile, how well the force field reproduces the observed crystal structures and dimer intermolecular separations and orientations is discussed in this work. In addition, it is shown that the present charge transport model can not only predict the magnitude of the charge mobility but also the measured “band-like” charge transport in experiments, so the nuclear tunneling effect is very important for charge transport in organic semiconductors as was demonstrated in recent theoretical work.

The electronic coupling between adjacent molecules is an important parameter for the charge transport properties of organic semiconductors. In a previous paper, a semiclassical generalized nonadiabatic transition state theory was used to investigate the nonperturbative effect of the electronic coupling on the charge transport properties, but it is not applicable at low temperatures due to the presence of high-frequency modes from the intramolecular conjugated carbon–carbon stretching vibrations [G. J. Nan et al., J. Chem. Phys., 2009, 130, 024704]. In the present paper, we apply a quantum charge transfer rate formula based on the imaginary-time flux–flux correlation function without the weak electronic coupling approximation. The imaginary-time flux–flux correlation function is then expressed in terms of the vibrational-mode path average and is evaluated by the path integral approach. All parameters are computed by quantum chemical approaches, and the mobility is obtained by kinetic Monte-Carlo simulation. We evaluate the intra-layer mobility of sexithiophene crystal structures in high- and low-temperature phases for a wide range of temperatures. In the case of strong coupling, the quantum charge transfer rates were found to be significantly smaller than those calculated using the weak electronic coupling approximation, which leads to reduced mobility especially at low temperatures. As a consequence, the mobility becomes less dependent on temperature when the molecular packing leads to strong electronic coupling in some charge transport directions. The temperature-independent charge mobility in organic thin-film transistors from experimental measurements may be explained from the present model with the grain boundaries considered. In addition, we point out that the widely used Marcus equation is invalid in calculating charge carrier transfer rates in sexithiophene crystals.

The influence of lattice dynamics on carrier mobility has received much attention in organic crystalline semiconductors, because the molecular components are held together by weak interactions and the transfer integrals between neighboring molecular orbitals are extremely sensitive to small nuclear displacements. Recently, it has been shown that the dynamic disorder has little effect on hole mobility in the ab plane of pentacene, but a reasonable explanation is absent for such a puzzle. To better understand the effect of lattice vibrations on carrier transport, a further study is required for other organic materials. In this work, a mixed molecular dynamic and quantum-chemical methodology is used to assess the effect of nuclear dynamics on hole mobility in the dianthra[2,3-b:2′,3′-f]-thieno[3,2-b]thiophene (DATT) crystals which exhibit high air stability with the hole mobility as large as that in rubrene-based devices. It is found that the lattice vibrations lead to an increasing encumbrance for hole transport in the ab plane of the DATT crystals as the temperature increases. By comparing the crystal structures of DATT and pentacene, the reduced hole mobility in DATT is attributed to the unsymmetric arrays of nearest-neighboring molecular dimers in the ab plane, because the electronic coupling exhibits unbalanced thermal fluctuations for the nearest-neighboring dimers which then induces a stronger oscillation for carriers along the directions with asymmetric packing. To further relate the dynamic disorder with hole transport, the variations of anisotropic mobilities are also analyzed. As a result, the negligible effect of lattice dynamics on the hole mobility in pentacene is explained by the centrosymmetric molecular packing of the nearest-neighboring molecular pairs in the ab plane.