Modelling charge transport in organic semiconductors: from quantum dynamics to soft matter

The charge carrier dynamics in organic semiconductors has been traditionally discussed with the models used in inorganic crystalline and amorphous solids but this analogy has severe limitations because of the more complicated role of nuclear motions in organic materials. In this perspective, we discuss how a new approach to the modelling of charge transport is emerging from the alliance between the conventional quantum chemical methods and the methods more traditionally used in soft-matter modelling. After describing the conventional limit cases of charge transport we discuss the problems arising from the comparison of the theory with the experimental and computational results. Several recent applications of numerical methods based on the propagation of the wavefunction or kinetic Monte Carlo methods on soft semiconducting materials are reviewed.     

Negative field-dependent charge mobility in crystalline organic semiconductors with delocalized transport

Charge-carrier mobility has been investigated by time-of-flight (TOF) transient photocurrent in a lateral transport configuration in highly crystalline thin films of 2,7-dioctyl[1]benzothieno [3,2-b][1] benzothiophene (C₈-BTBT) grown by a zone-casting alignment technique. High TOF mobility has been revealed that it is consistent with the delocalized nature of the charge transport in this material, yet it featured a positive temperature dependence at \( T \ge 295\,{\text{K}} \). Moreover, the mobility was surprisingly found to decrease with electric field in the high-temperature region. These observations are not compatible with the conventional band-transport mechanism. We have elaborated an analytic model based on effective-medium approximation to rationalize the puzzling findings. The model considers the delocalized charge transport within the energy landscape formed by long-range transport band-edge variations in imperfect organic crystalline materials and accounts for the field-dependent effective dimensionality of charge transport percolative paths. The results of the model calculations are found to be in good agreement with experimental data.     

Facile synthesis of fluorine-substituted benzothiadiazole-based organic semiconductors and their use in solution-processed small-molecule organic solar cells

A facile new protocol for the synthesis of iodinated derivatives of fluorinated benzothiadiazoles is demonstrated for the production of p-type semiconducting materials. The newly synthesized small-molecule compounds bis[TPA-diTh]-MonoF-BT and bis[TPA-diTh]-DiF-BT exhibited a power conversion efficiency of 2.95?% and a high open-circuit voltage of 0.85?V in solution-processed small-molecule organic solar cells.     

Hopping charge transport in organic materials

General properties of the transport of charge carriers (electrons and holes) in disordered organic materials are discussed. It was demonstrated that the dominant part of the total energetic disorder in organic material is usually provided by the electrostatic disorder, generated by randomly located and oriented dipoles and quadrupoles. For this reason this disorder is strongly spatially correlated. Spatial correlation directly governs the field dependence of the carrier drift mobility. Shape of the current transients, which is of primary importance for a correct determination of the carrier mobility, is considered. A notable feature of the electro-static disorder is its modification in the vicinity of the electrode, and this modification takes place without modification of the structure of the material. It is shown how this phenomenon affects characteristics of the charge injection. We consider also effect of inter-charge interaction on charge transport.     

The role of acoustic phonon scattering in charge transport in organic semiconductors: a first-principles deformation-potential study

The electron-acoustic phonon scattering for charge transport in organic semiconductors has been studied by first-principles density functional theory and the Boltzmann transport equation with relaxation time approximation. Within the framework of deformation-potential theory, the electron-longitudinal acoustic phonon scattering probability and the corresponding relaxation time have been obtained for oligoacene single crystals (naphthalene, anthracene, tetracene and pentacene). Previously, the electron-optic...     

Energy spectrum and transport phenomena in organic semiconductors

Kinetic phenomena in anisotropic organic crystals of the anthracene and naphthalene type are considered. Expressions are obtained from the kinetic equation for the kinetic coefficients. Instead of the conventional isotropic relaxation time, a relaxation time matrix is introduced. The values obtained by means of this matrix for anisotropy in mobility are in considerably better agreement with the experimental values than are those reported in the literature.The material contained in this paper was presented at the Fourth All-Union Conference on Quantum Chemistry, Kiev, October 1966.     

Exciton dissociation and charge carrier recombination processes in organic semiconductors

Exciton dissociation and charge recombination processes in organic semiconductors, with thermal effects taken into account, are described in this paper. Here, we analyzed the mechanisms of polaron-excitons dissociation into free charge carriers and the consequent recombination of those carriers under thermal effects on two parallel π-conjugated polymers chains electronically coupled. Our results suggest that exciton dissociation in a single molecule give rise to localized, polaron-like charge carrier. Besides, we concluded that in the case of interchain processes, the bimolecular polaron recombination does not lead to an usual exciton state. Rather, this type of recombination leads to an oscillating dipole between the two chains. The recombination time obtained here for these processes are in agreement with the experimental results. Finally, our results show that temperature effects are essential to the relaxation process leading to polaron formation in a single chain, as in the absence of temperature, this process was not observed. In the case of two chains, we conclude that temperature effects also help the bimolecular recombination process, as observed experimentally.     

Techniques for characterization of charge carrier mobility in organic semiconductors

The charge transport characteristics of organic semiconductors are one of the key attributes that impacts the performance of organic electronic and optoelectronic devices in which they are utilized. For improved performance in organic photovoltaic cells, light-emitting diodes, and field-effect transistors (FETs), efficient transport of the charge carriers within the organic semiconductor is especially critical. Characterization of charge transport in these organic semiconductors is important both from scientific and technological perspectives. In this review, we shall mainly discuss the techniques for measuring the charge carrier mobility and not the theoretical underpinnings of the mechanism of charge transport. Mobility measurements in organic semiconductors and particularly in conjugated polymers, using space-charge-limited current, time of flight, carrier extraction by linearly increasing voltage, double injection, FETs, and impedance spectroscopy are discussed. The relative merits, as well as limitations for each of these techniques are reviewed. © 2012 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2012     

Simultaneous studies of pressure effect on charge transport and photophysical properties in organic semiconductors: A theoretical investigation

High-mobility and strong luminescent materials are essential as an important component of organic photodiodes, having received extensive attention in the field of organic optoelectronics. Beyond the conventional chemical synthesis of new molecules, pressure technology, as a flexible and efficient method, can tune the electronic and optical properties reversibly. However, the mechanism in organic materials has not been systematically revealed. Here, we theoretically predicted the pressure-depended luminescence and charge transport properties of high-performance organic optoelectronic semiconductors, 2,6-diphenylanthracene (DPA), by first-principle and multi-scale theoretical calculation methods. The dispersion-corrected density functional theory (DFT-D) and hybrid quantum mechanics/molecular mechanics (QM/MM) method were used to get the electronic structures and vibration properties under pressure. Furthermore, the charge transport and luminescence properties were calculated with the quantum tunneling method and thermal vibration correlation function. We found that the pressure could significantly improve the charge transport performance of the DPA single crystal. When the applied pressure increased to 1.86 GPa, the hole mobility could be doubled. At the same time, due to the weak exciton coupling effect and the rigid flat structure, there is neither fluorescence quenching nor obvious emission enhancement phenomenon. The DPA single crystal possesses a slightly higher fluorescence quantum yield ～ 0.47 under pressure. Our work systematically explored the pressure-dependence photoelectric properties and explained the inside mechanism. Also, we proposed that the external pressure would be an effective way to improve the photoelectric performance of organic semiconductors.     

Theory of kinetic transport coefficients for organic semiconductors

The magnetoresistance is calculated in the semiclassical approximation for a system with narrow bands. It is found that the conductivity in this case increases in the field and is governed by the size of the crystalline regions.     

Intermolecular charge transfer between heterocyclic oligomers. Effects of heteroatom and molecular packing on hopping transport in organic semiconductors

For electron or hole transfer between neighboring conducting polymer strands or oligomers, the intrinsic charge-transfer rate is dictated by the charge-resonance integral and by the reorganization energy due to geometric relaxation. To explain conduction anisotropy and other solid-state effects, a multivariate, systematic analysis of bandwidth as a function of intermolecular orientations is undertaken for a series of oligoheterocycles, using first-principles methods. While cofacial oligomers show the greatest bandwidths at a given intermolecular C-C contact distance, for a fixed center-to-center intermolecular distance, tilted pi-stacking increases pi-overlap (particularly for LUMO orbitals) and decreases electrostatic repulsion, yielding optimum tilt angles for packing of approximately 40-60 degrees at small intermolecular separations. The calculations also reveal that bandwidths and intrinsic mobilities of holes and electrons in conjugated oligoheterocycles can be quite comparable.     

Hole injection/transport materials derived from Heck and sol-gel chemistry for application in solution-processed organic electronic devices

An organosilicate polymer, based on N,N'-diphenyl-N,N'-bis(4-((E)-2-(triethoxysilyl)vinyl)phenyl)biphenyl-4,4'-diamine (TEVS-TPD) with extended conjugation between the Si atom and the aromatic amine, was prepared under mild conditions via sequential Heck and sol-gel chemistry and used as an alternative to poly(3,4-ethylenedioxythiophene):poly(styrenesulfonate) (PEDOT:PSS), the most widely used planarizing hole injection/transport layer in solution-processed organic electronic devices. Spin-coating TEVS-TPD polymer solutions yield defect-free, uniform, thin films with excellent adhesion to the ITO electrode. Upon thermal cross-linking at 180 °C, the cross-linked polymer exhibits excellent solvent resistance and electrochemical stability. Solution-processed organic light emitting diode (OLED) devices using iridium-based triplet emitting layers and cross-linked TEVS-TPD films as a hole injection/transport layer show significantly improved performance including lower leakage current, lower turn-on voltage, higher luminance, and stability at high current density, as compared to the control device prepared with PEDOT:PSS.     

Influence of polymorphism on charge transport properties in isomers of fluorenone-based liquid crystalline semiconductors

We measured the charge carrier mobilities for two isomers of fluorenone-based liquid crystalline organic semiconductors from their isotropic down to crystalline states through one or two mesophases. Improved charge transport properties of melt-processed crystalline films were obtained for the isomer exhibiting a highly ordered mesophase below its disordered smectic phase.     

Influences of molecular packing on the charge mobility of organic semiconductors: from quantum charge transfer rate theory beyond the first-order perturbation

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.     

Monte Carlo simulation based on dynamic disorder model in organic semiconductors: from coherent to incoherent transport

The dynamic disorder model for charge carrier transport in organic semiconductors has been extensively studied in recent years. Although it is successful on determining the value of bandlike mobility in the organic crystalline materials, the incoherent hopping, the typical transport characteristic in amorphous molecular semiconductors, cannot be described. In this work, the decoherence process is taken into account via a phenomenological parameter, say, decoherence time, and the projective and Monte Carlo method are applied for this model to determine the waiting time and thus the diffusion coefficient. It is obtained that the type of transport is changed from coherent to incoherent with a sufficiently short decoherence time, which indicates the essential role of decoherence time in determining the type of transport in organics. We have also discussed the spatial extent of carriers for different decoherence time, and the transition from delocalization (carrier resides in about 10 molecules) to localization is observed. Based on the experimental results of spatial extent, we estimate that the decoherence time in pentacene has the order of 1 ps. Furthermore, the dependence of diffusion coefficient on decoherence time is also investigated, and corresponding experiments are discussed.     

Master equation approach to charge injection and transport in organic insulators

We develop a master equation model of a disordered organic insulator sandwiched between metallic electrodes by treating as rate processes both the injection and the internal transport. We show how the master equation model allows for the inclusion of crucial correlation effects in the charge transport, particularly of the Pauli exclusion principle and of space-charge effects, besides, being dependent on just the microscopic form of the transfer rate between the localized electronic states, it allows for the investigation of different microscopic scenarios in the organic, such as polaronic hopping, correlated energy levels, interaction with image charge, etc. The model allows for a separate analysis of the injection and the recombination currents. We find that the disorder, besides increasing the injection current, eliminates the possibility of observation of a Fowler-Nordheim injection current at zero temperature, and that it does not alter the Schottky barrier size of the zero-field thermionic injection current from the value based on the energy difference between the electrode Fermi level and the highest occupied molecular orbital/lowest unoccupied molecular orbital levels in the organic, but it makes the Arrhenius temperature dependence appear at larger temperatures. We investigate how the I(V) characteristics of a device is affected by the presence of correlations in the site energy distribution and by the form of the internal hopping rate, specifically the Miller-Abrahams rate and the Marcus or small-polaron rate. We show that the disorder does not modify significantly the ebeta square root E field dependence of the net current due to the Schottky barrier lowering caused by the attraction between the charge and its image in the electrode.     

A theoretical description of charge reorganization energies in molecular organic P‐type semiconductors

Charge transport properties of materials composed of small organic molecules are important for numerous optoelectronic applications. A material's ability to transport charges is considerably influenced by the charge reorganization energies of the composing molecules. Hence, predictions about charge‐transport properties of organic materials deserve reliable statements about these charge reorganization energies. However, using density functional theory which is mostly used for the predictions, the computed reorganization energies depend strongly on the chosen functional. To gain insight, a benchmark of various density functionals for the accurate calculation of charge reorganization energies is presented. A correlation between the charge reorganization energies and the ionization potentials is found which suggests applying IP‐tuning to obtain reliable values for charge reorganization energies. According to benchmark investigations with IP‐EOM‐CCSD single‐point calculations, the tuned functionals provide indeed more reliable charge reorganization energies. Among the standard functionals, ωB97X‐D and SOGGA11X yield accurate charge reorganization energies in comparison with IP‐EOM‐CCSD values. © 2016 Wiley Periodicals, Inc.     

High-performance,solution-processed organic thin film transistors from a novel pentacene precursor

The Lewis acid-catalyzed Diels-Alder reaction of the organic semiconductor pentacene with N-sulfinylacetamide yields a soluble adduct. Spin-coated thin films of this adduct undergo solid-phase conversion to form thin films of pentacene at moderate temperatures. Organic thin film transistors fabricated by spin-coating this adduct, followed by thermal conversion to pentacene, exhibit the highest mobility reported to date for a solution-processed organic semiconductor.