Impact of Fluoroalkylation on the n-Type Charge Transport of Two Naphthodithiophene Diimide Derivatives

In this work, we investigate two recently synthesized naphthodithiophene diimide (NDTI) derivatives featuring promising n-type charge transport properties. We analyze the charge transport pathways and model charge mobility with the non-adiabatic hopping mechanism using the Marcus-Levich-Jortner rate constant formulation, highlighting the role of fluoroalkylated substitution in α (α-NDTI) and at the imide nitrogen (N-NDTI) position. In contrast with the experimental results, similar charge mobilities are computed for the two derivatives. However, while α-NDTI displays remarkably anisotropic mobilities with an almost one-dimensional directionality, N-NDTI sustains a more isotropic charge percolation pattern. We propose that the strong anisotropic charge transport character of α-NDTI is responsible for the modest measured charge mobility. In addition, when the role of thermally induced transfer integral fluctuations is investigated, the computed electron–phonon couplings for intermolecular sliding modes indicate that dynamic disorder effects are also more detrimental for the charge transport of α-NDTI than N-NDTI. The lower observed mobility of α-NDTI is therefore rationalized in terms of a prominent anisotropic character of the charge percolation pathways, with the additional contribution of dynamic disorder effects.     

Charge carrier transport in poly[methyl(phenyl)silylene]: the effect of additives

Poly[methyl(phenyl)silylene], PMPSi, was doped with compounds of the electron acceptor type. The charge carrier mobility increases with increasing electron affinity of the acceptors having zero dipole moments. At the same time the energy distribution of hopping states narrows. On the other hand, the hole drift mobility is influenced by the dipole moment of the dopand. The electrostatic charge carrier‐dipole interaction causes a broadening of the energy distribution of transport states which results in a decrease in the charge carrier mobility. The charge carrier transport can be explained by the disordered polaronic theory, according to which the activation energy of charge carrier mobility has contributions based on the dynamic disorder, i.e. the polaronic barrier, and on the static disorder, i.e. the variation of the energy of transport states as a result of the environment. Copyright © 2001 John Wiley & Sons, Ltd.     

Charge transport in high mobility molecular semiconductors: classical models and new theories

The theories developed since the fifties to describe charge transport in molecular crystals proved to be inadequate for the most promising classes of high mobility molecular semiconductors identified in the recent years, including for example pentacene and rubrene. After reviewing at an elementary level the classical theories, which still provide the language for the understanding of charge transport in these systems, this tutorial review outlines the recent experimental and computational evidence that prompted the development of new theories of charge transport in molecular crystals. A critical discussion will illustrate how very rarely it is possible to assume a charge hopping mechanism for high mobility organic crystals at any temperature. Recent models based on the effect of non-local electron-phonon coupling, dynamic disorder, coexistence of localized and delocalized states are reviewed. Additionally, a few more recent avenues of theoretical investigation, including the study of defect states, are discussed.     

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.     

The effect of charged centers on the transport of charge carriers in molecularly doped polymers

The effect of charged centers on the mobility of charge carriers in molecularly doped polycarbonate is experimentally studied by the method of accelerated electrons for the generation of charge carriers in the surface layer and in the polymer bulk. The hypersensitivity of mobility toward the presence of charged sites that is predicted by the theory of correlated disorder (dipolar glass) is not found. With accumulation of charged centers, transformation of the time-of-flight curves with a well-pronounced plateau region, which is indicative of quasiequilibrium transport according to theory, proceeds in full agreement with the classical concepts on the role of a space charge or bimolecular recombination during high-signal irradiation. Transport of charge carriers in the molecularly doped polymer is not quasiequilibrium but dispersive.     

Organic Semiconductors: Impact of Disorder at Different Timescales

The charge transport in organic materials, from molecular crystals to polymers, is determined by their degree of disorder. The dynamic disorder in ideal molecular crystals at room temperature and the static disorder in disordered polymers are just two limiting cases of the timescale of the fluctuations in the electronic Hamiltonian caused by nuclear motions. In fact, a very large number of important materials (e.g. liquid crystalline semiconductors) are actually in an intermediate regime where the disorder is neither purely static nor purely dynamic. This Minireview discusses the recent contribution of computational chemistry (molecular dynamics and quantum chemistry) to the characterization of these transport regimes and outlines the theoretical methods that can be used to relate the system characteristics to the measurable mobility.     

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.     

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.     

Effects of disordered interchain interactions on polaron dynamics in semiconducting polymers

Polaron dynamics in a system of two randomly coupled polymer chains is simulated using a nonadiabatic evolution method. The simulations are performed within the framework of the Su-Schrieffer-Heeger model modified to include disordered interchain interactions and an external electric field. By analysing the polaron velocity statistically, we find that the polaron motion is determined by the competition between the electric field and the disordered interchain interactions. Polaron dynamics are classified into two types, weak-coupling dynamics and strong-coupling dynamics. It is found that the strength of interchain interactions is the dominant factor controlling charge propagation in weak-coupling dynamics, whereas the effects of disorder are dominant in strong-coupling dynamics. The charge carriers tend to have higher mobility for stronger interchain coupling, and interchain coupling disorder can be favorable for charge transport depending on the coupling strength and the electric field.     

Hopping charge transport in amorphous organic and inorganic materials with spatially correlated random energy landscape

The general properties of the hopping transport of charge carriers in amorphous organic and inorganic materials are discussed. The case where the random energy landscape in the material is strongly spatially correlated is considered. This situation is typical of organic materials with the Gaussian density of states (DOS) and may also be realized in some materials with the exponential DOS. It is demonstrated that the different DOS types can lead to very different functional forms of the mobility field dependence even for the identical correlation function of random energy. Important arguments are provided in favor of the significant contribution of the local orientational order to the total magnitude of energetic disorder in organic materials. A simple but promising model of charge transport in highly anisotropic composites materials is proposed.     

Roles of inter- and intramolecular vibrations and band-hopping crossover in the charge transport in naphthalene crystal

We calculate the hole and electron mobilities in naphthalene crystal from 10 to 300 K within the framework of the Holstein-Peierls model coupled with first-principles density-functional-theory-projected tight-binding band structures. All the electron-phonon coupling constants, including both local and nonlocal parts for inter- and intramolecular vibrations, have been taken into considerations through density functional theory. The band-hopping crossover transition temperature for the electron transport in the c' axis is calculated to be around 23 K. We have identified a few high frequency intramolecular vibrations which are very important to the charge transport in naphthalene crystal due to their comparatively large electron-phonon coupling constants. However, their contributions to the temperature dependence of mobility are minor because of the small phonon occupations and small nonlocal coupling strengths. The low frequency intermolecular modes (longitudinal optical modes) are found to be the major contributions to the temperature dependent charge transfer properties in naphthalene crystal. Even though the calculated qualitative temperature dependence is in agreement with experiment, the predicted absolute mobility is about one to two orders of magnitude larger.     

Electron transport and recombination in dye-sensitized mesoporous TiO2 probed by photoinduced charge-conductivity modulation spectroscopy with Monte Carlo modeling

We present a combined experimental and theoretical investigation into the charge transport and recombination in dye-sensitized mesoporous TiO2. We electronically probe the photoinduced change in conductivity through in-plane devices while simultaneously optically probing signatures of the charge species. Our quasi-continuous wave technique allows us to build data sets of electron mobility and recombination versus charge density over a wide temperature range. We observe that the charge density dependence of mobility in TiO2 is strong at high temperatures and gradually reduces with reducing temperature, to an extent where at temperatures below 260 K the mobility is almost independent of charge density. The mobility first increases and then decreases with reducing temperature at any given charge density. These observed trends are surprising and consistent with the multiple-trapping model for charge transport only if the trap density-of-states (DoS) is allowed to become less deep and narrower as the temperature reduces. Our recombination measurements and simulations over a broad range of charge density and temperature are also consistent with the above-mentioned varying DoS function when the recombination rate constant is allowed to increase with temperature, itself consistent with a thermally activated charge-transfer process. Further to using the Monte Carlo simulations to model the experimental data, we use the simulations to aid our understanding of the limiting factors to charge transport and recombination. According to our model, we find that the charge recombination is mainly governed by the recombination reaction rate constant and the charge density dependence is mainly a result of the bimolecular nature of the recombination process. The implication to future material design is that if the mobility can be enhanced without increasing the charge density in the film, for instance by reducing the average trap depth, then this will not be at the sacrifice of comparably enhanced recombination and it will greatly increase the charge carrier diffusion lengths in dye-sensitized or mesoscopic solar cells.     

第一性原理的形变势理论研究声学声子散射对电荷传输的影响

本文应用密度泛函理论和玻尔兹曼方程,在形变势理论的框架和驰豫时间近似下,研究了分子晶体中电子与声学声子散射对电荷传输的影响.针对蒽、萘、丁省和并五苯的计算表明,非局域化电子的传输过程主要受到来自于声学声子的散射.对于蒽晶体,与以前的Holstein-Peierls模型计算结果相比,发现纵向声学声子对空穴的散射强度是光学声子的3倍,所得到的空穴迁移率更接近超纯单晶样品的实验测量结果.同时,我们发现电子的本征迁移率比空穴还要大,应用前线轨道交叠分析可以合理地解释这一结果.     

A general gel layer model for the transport of colloids and macroions in dilute solution

A general boundary element methodology for studying the dilute solution transport of rigid macroions that contain gel layers on their outer surfaces is developed and applied to several model systems. The methodology can be applied to particles of arbitrary size, shape, charge distribution, and gel layer geometry. Account is also taken of the steady state distortion of the ion atmosphere from equilibrium, which makes it applicable to the transport of highly charged structures. The coupled field equations (Poisson, ion-transport, low-Reynolds-number Navier-Stokes, and Brinkman) are solved numerically and from this, transport properties (diffusion constants, electrophoretic mobilities, excess viscosities) can be computed. In the present work, the methodology is first applied to a gel sphere model over a wide range of particle charge and the resulting transport properties are found to be in excellent agreement with independent theory under those conditions where independent theory is available. It is then applied to several prolate spheroidal models of a particular silica sol sample in an attempt to identify possible solution structures. A single model, that is able to account simultaneously for all of the transport behavior, which does not undergo significant conformational change with salt concentration, could not be found. A model with a thin (相似文献   

Polaron effects and electric field dependence of the charge carrier mobility in conjugated polymers

Charge transport in conjugated polymers has been investigated using Monte Carlo simulations implemented on top of the Marcus theory for donor-acceptor transition rates. In particular, polaron effects and the dependency of the mobility on the temperature and the applied electric field have been studied. The conclusions are that while the qualitative temperature dependence is similar to that predicted by Miller-Abrahams theory in the Gaussian disorder model (GDM), the electric field dependence is characterized by a crossover into the Marcus inverted region, not present in the GDM. Furthermore, available analytical approximations to describe the electric field dependence of the mobility in Marcus theory fail to fit the simulation data and hence cannot be used to directly draw conclusions about the importance of polaron effects for charge transport in conjugated polymers.     

Temperature dependence of charge mobility in model discotic liquid crystals

We address the calculation of charge carrier mobility of liquid-crystalline columnar semiconductors, a very promising class of materials in the field of organic electronics. We employ a simple coarse-grained theoretical approach and study in particular the temperature dependence of the mobility of the well-known triphenylene family of compounds, combining a molecular-level simulation for reproducing the structural changes and the Miller-Abrahams model for the evaluation of the transfer rates within the hopping regime. The effects of electric field, positional and energetic disorder are also considered. Simulations predict a low energetic disorder (~0.05 eV), slightly decreasing with temperature within the crystal, columnar and isotropic phases, and fluctuations of the square transfer integral of the order of 0.003 eV(2). The shape of the temperature-dependent mobility curve is however dominated by the variation of the transfer integral and barely affected by the disorder. Overall, this model reproduces semi-quantitatively all the features of experimentally measured mobilities, on one hand reinforcing the correctness of the hopping transport picture and of its interplay with system morphology, and on the other suggesting future applications for off-lattice modeling of organic electronics devices.     

Charge transport and electronic properties of N-heteroquinones: quadruple weak hydrogen bonds and strong π–π stacking interactions

The charge transport and photophysical properties of N-heteroquinones, which can function as n-type organic semiconductors in organic field-effect transistors (OFETs) with high electron mobility, were systematically investigated using hopping model, band theory, and time-dependent density functional theory (TDDFT). The calculated absorption spectra and electron mobility are in good agreement with experimental results. To the studied compounds, subtle structural modifications can greatly reduce the reorganization energy. There are two main kinds of intermolecular interaction forces of the studied compounds in the crystal, which result from intermolecular π–π and hydrogen bonds interactions, respectively. The results of hopping model show that the electron transport properties are mainly determined by pathways containing intermolecular π–π interactions, and hole transport properties are mainly determined by pathways containing intermolecular hydrogen bonds from the standpoint of transfer integral. Moreover, electronic transfer integral value increases with the enhancement of intermolecular overlap corresponding to the overlap extent of π–π packing. Hole transfer integral value decreases with decreasing the number of hydrogen bonds. This means that charge transport properties can be efficiently tuned by controlling the relative positions of the molecules and the number of hydrogen bonds. The analysis of band structure also supports the conclusion of hopping model.     

Effect of side-chain length on charge mobilities in neutral poly(3-alkylthiophene)s: Determination from dielectric measurement

For neutral poly(3-alkylthiophene)s (P3ATs), the electric modulus formalism of dielectric relaxation measurement together with the use of nonexponential decay function can be applied to describe the behavior of conductivity relaxation and carrier transport. The charge mobilities of neutral P3ATs calculated from conductivity relaxation with the use of the defect-diffusion model are in agreement with the data from field-effect transistor measurement. The temperature dependence of charge mobility exhibits a local maximum right after the end of glass transition region, which can be attributed to the transition of soft conformons in the disordered phase to localized conformons. The charge mobilities and activation energies of mobilities for P3ATs are dependent on conjugation length and volume fraction of conducting units. © 1994 John Wiley & Sons, Inc.     

Charge transport properties for carbazolyl groups pendant poly(glutamate)

Carbazolyl groups pendant poly(glutamate) (PCLG) was prepared to analyze its charge‐transport properties by employing mobility measurements and thermally‐stimulated current (TSC) measurements. The mobility induced TSC (MITSC) model proposed by I.Chen was employed to evaluate the experimental TSC spectra with mobility results. Simulated MITSC spectra showed good agreement in its peak temperature with experimental TSC spectra for PCLG. This suggests that the carrier transport followed the trap‐limited mechanism estimated by the mobility results. Further, the peaks in experimental TSC spectra appeared over the same temperature range as that in thermally‐stimulated polarization current (TSPC) spectra. Since the TSPC spectra were found to be correlated with the dielectric tan δ spectra for PCLG, the peaks in TSPC spectra are attributed to the side‐chain relaxation for PCLG. Therefore, the similarity between TSPC and TSC spectra indicates that the charge‐transport mechanism for PCLG was considerably affected by side‐chain relaxation for PCLG, which would vary the energy state of trap sites and effectively reduces the energy for the release of the carriers trapped on the illuminated surface. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 61–69, 1999