Charge Transport In Organic Crystals Research Articles

Machine learning based charge mobility prediction for organic semiconductors.

Transfer integral is a crucial parameter that determines the charge mobility of organic semiconductors, and it is very sensitive to molecular packing motifs. The quantum chemical calculation of transfer integrals for all the molecular pairs in organic materials is usually an unaffordable task; fortunately, it can be accelerated by the data-driven machine learning method now. In this work, we develop machine learning models based on artificial neutral networks to predict transfer integrals accurately and efficiently for four typical organic semiconductor molecules: quadruple thiophene (QT), pentacene, rubrene, and dinaphtho[2,3-b:2',3'-f]thieno[3,2-b]thiophene (DNTT). We test various forms of features and labels and evaluate the accuracy of different models. With the implementation of a data augmentation scheme, we have achieved a very high accuracy with the determination coefficient of 0.97 and mean absolute error of 4.5meV for QT, and similar accuracy for the other three molecules. We apply these models to studying charge transport in organic crystals with dynamic disorders at 300K and obtain the charge mobility and anisotropy in perfect agreement with the brutal force quantum chemical calculation. If more molecular packings representing the amorphous phase of organic solids are supplemented to the dataset, the current models can be refined to study charge transport in organic thin films with polymorphs and static disorders.

Charge Transport through Discrete Crystalline Architectures

Multitudes of novel π-conjugated materials have gained tremendous attention with potential applications in next-generation electronic devices as they are chemically programmable, mechanically flexible, and lightweight. Modulating the intermolecular interactions emerging from the π-conjugated molecules govern crystal packing and plays a pivotal role in designing molecular organic semiconductors. Determining the dynamic origin of charge transport in organic crystals from a molecular perspective has often proved challenging. In this Perspective, we have compiled effective methods to regulate the charge transport characteristics of functional organic materials in their crystalline phase. The ardent efforts in designing advanced materials with desirable charge transport properties from a theoretical perspective by our group are emphasized.

Intermediate polaronic charge transport in organic crystals from a many-body first-principles approach

Charge transport in organic molecular crystals (OMCs) is conventionally categorized into two limiting regimes − band transport, characterized by weak electron-phonon (e-ph) interactions, and charge hopping due to localized polarons formed by strong e-ph interactions. However, between these two limiting cases there is a less well understood intermediate regime where polarons are present but transport does not occur via hopping. Here we show a many-body first-principles approach that can accurately predict the carrier mobility in this intermediate regime and shed light on its microscopic origin. Our approach combines a finite-temperature cumulant method to describe strong e-ph interactions with Green-Kubo transport calculations. We apply this parameter-free framework to naphthalene crystal, demonstrating electron mobility predictions within a factor of 1.5−2 of experiment between 100 and 300 K. Our analysis reveals the formation of a broad polaron satellite peak in the electron spectral function and the failure of the Boltzmann equation in the intermediate regime.

Backbone charge transport in double-stranded DNA.

Understanding charge transport in DNA molecules is a long-standing problem of fundamental importance across disciplines1,2. It is also of great technological interest due to DNA's ability to form versatile and complex programmable structures. Charge transport in DNA-based junctions has been reported using a wide variety of set-ups2-4, but experiments so far have yielded seemingly contradictory results that range from insulating5-8 or semiconducting9,10 to metallic-like behaviour11. As a result, the intrinsic charge transport mechanism in molecular junction set-ups is not well understood, which is mainly due to the lack of techniques to form reproducible and stable contacts with individual long DNA molecules. Here we report charge-transport measurements through single 30-nm-long double-stranded DNA (dsDNA) molecules with an experimental set-up that enables us to address individual molecules repeatedly and to measure the current-voltage characteristics from 5 K up to room temperature. Strikingly, we observed very high currents of tens of nanoamperes, which flowed through both homogeneous and non-homogeneous base-pair sequences. The currents are fairly temperature independent in the range 5-60 K and show a power-law decrease with temperature above 60 K, which is reminiscent of charge transport in organic crystals. Moreover, we show that the presence of even a single discontinuity ('nick') in both strands that compose the dsDNA leads to complete suppression of the current, which suggests that the backbones mediate the long-distance conduction in dsDNA, contrary to the common wisdom in DNA electronics2-4.

A Unification of the Holstein Polaron and Dynamic Disorder Pictures of Charge Transport in Organic Crystals

By unifying two prominent theories of electron-phonon coupling, a new theoretical framework provides an efficient and realistic toolkit for improving the performance of organic-based semiconductors and superconductors.

Two-dimensional electronic and charge-transport properties of a monolayer organic crystal: Impacts of the collinear transfer-integral correlations

Abstract Electronic transfer integrals between the frontier orbitals of adjacent molecules represent the most important parameter governing charge transport in organic crystals. Different transfer integrals may be significantly modulated by the same modes of molecular vibrations as a result of nonlocal electron-phonon couplings, leading to spatial correlations between the transfer integrals. Here, by employing a multiscale modeling approach, we investigate theoretically the impacts of transfer-integral correlations (TICs) on the two-dimensional electronic and charge-transport properties of a monolayer pentacene crystal. In particular, we focus on the collinear TICs that are present between molecular pairs along the same direction of molecular packings in the crystal. We reveal that the interplay of the collinear TICs along different directions leads to diverse landscapes of nonlocal electron-phonon couplings in reciprocal space, of which the impacts explicitly manifest themselves in the band structures at finite temperatures. We also evaluate the anisotropic hole mobility of the pentacene monolayer and demonstrate that the consequence of the collinear TICs can be reflected in the behaviors of the temperature-dependent band-like mobility observed in experiment. These findings provide an insight into how nonlocal electron-phonon couplings operate through TICs to impact the electronic and electrical properties of organic crystals in two dimension.

Improving the theoretical description of charge transport in organic crystals.

Charge hopping based on Marcus theory is often used to predict charge carrier mobilities in organic crystals, although it is known to systematically underestimate the values. Here we show that this deficiency may lie on a fundamental aspect of quantum statistical averages, rather than on the approximation itself. Under adequate Boltzmann weighing procedure used to evaluate electron and hole transfer integrals, a kinetic Monte Carlo model is employed to describe mobilities in an azacene derivative. The values are in good agreement with experimental data suggesting that the evaluation of transfer integrals may be the weak link in hopping transport models.

Charge transport in organic molecular semiconductors from first principles: The bandlike hole mobility in a naphthalene crystal

Predicting charge transport in organic molecular crystals is notoriously challenging. Carrier mobility calculations in organic semiconductors are dominated by quantum chemistry methods based on charge hopping, which are laborious and only moderately accurate. We compute from first principles the electron-phonon scattering and the phonon-limited hole mobility of naphthalene crystal in the framework of ab initio band theory. Our calculations combine GW electronic bandstructures, ab initio electron-phonon scattering, and the Boltzmann transport equation. The calculated hole mobility is in very good agreement with experiment between 100$-$300 K, and we can predict its temperature dependence with high accuracy. We show that scattering between inter-molecular phonons and holes regulates the mobility, though intra-molecular phonons possess the strongest coupling with holes. We revisit the common belief that only rigid molecular motions affect carrier dynamics in organic molecular crystals. Our work provides a quantitative and rigorous framework to compute charge transport in organic crystals, and is a first step toward reconciling band theory and carrier hopping computational methods.

Dichotomy between the band and hopping transport in organic crystals: insights from experiments.

The molecular understanding of charge-transport in organic crystals has often been tangled with identifying the true dynamical origin. While in two distinct cases where complete delocalization and localization of charge-carriers are associated with band-like and hopping-like transports, respectively, their possible coalescence poses some mystery. Moreover, the existing models are still controversial at ambient temperatures. Here, we review the issues in charge-transport theories of organic materials and then provide an overview of prominent transport models. We explored ∼60 organic crystals, the single-crystal hole/electron mobilities of which have been predicted by band-like and hopping-like transport models, separately. Our comparative results show that at room-temperature neither of the models are exclusively capable of accurately predicting mobilities in a very broad range. Hopping-like models well-predict experimental mobilities around μ ∼ 1 cm2 V-1 s-1 but systematically diverge at high mobilities. Similarly, band-like models are good at μ > ∼50 cm2 V-1 s-1 but systematically diverge at lower mobilities. These results suggest the development of a unique and robust room-temperature transport model incorporating a mixture of these two extreme cases, whose relative importance is associated with their predominant regions. We deduce that while band models are beneficial for rationally designing high mobility organic-semiconductors, hopping models are good to elucidate the charge-transport of most organic-semiconductors.

Charge transport in organic crystals: critical role of correlated fluctuations unveiled by analysis of Feynman diagrams.

Organic crystals have unique charge transport properties that lie somewhere between delocalised band-type transport and localised hopping transport. In this paper, we use a stochastic tight-binding model to explore how dynamical disorder in organic crystals affects charge transport. By analysing the model in terms of Feynman diagrams (virtual processes), we expose the crucial role of correlated dynamical disorder to the charge transport dynamics in the model at short times in the order of a few hundred femtoseconds. Under correlated dynamical disorder, the random motions of molecules in the crystal allow for low-energy "bonding"-type interactions between neighboring molecular orbitals can persist over long periods of time. On the other hand, the dependence of charge transport on correlated dynamical disorder also tends to localize the charge, as correlated disorder cannot persist far in space. This concept of correlation may be the "missing link" for describing the intermediate regime between band transport and hopping transport that occurs in organic crystals.

Organic/Inorganic Hybrid Materials: Challenges for ab Initio Methodology

CONSPECTUS: Organic/inorganic hybrid structures are most exciting since one can expect new properties that are absent in either of their building blocks. They open new perspectives toward the design and tailoring of materials with desired features and functions. Prerequisite for real progress is, however, the in-depth understanding of what happens on the atomic and electronic scale. In this respect, hybrid materials pose a challenge for electronic-structure theory. Methods that proved useful for describing one side may not be applicable for the other one, and they are likely to fail for the interfaces. In this Account, we address the question to what extent we can quantitatively describe hybrid materials and where we even miss a qualitative description. We note that we are dealing with extended systems and thus adopt a solid-state approach. Therefore, density-functional theory (DFT) and many-body perturbation theory (MBPT), the GW approach for charged and the Bethe-Salpeter equation for neutral excitations, are our methods of choice. We give a brief summary of the used methodology, focusing on those aspects where problems can be expected when materials of different character meet at an interface. These issues are then taken up when discussing hybrid materials. We argue when and why, for example, standard DFT may fall short when it comes to the electronic structure of organic/metal interfaces or where the framework of MBPT can or must take over. Selected examples of organic/inorganic interfaces, structural properties, electronic bands, optical excitation spectra, and charge-transport properties as obtained from DFT and MBPT highlight which properties can be reliably computed for such materials. The crucial role of van der Waals forces is shown for sexiphenyl films, where the subtle interplay between intermolecular and molecule-substrate interactions is decisive for growth and morphologies. With a PTCDA monolayer on metal surfaces we discuss the performance of DFT in terms of interfacial electronic structure. We face the problem of a so far hidden variable, namely, electron-vibrational coupling, regarding level alignment at interfaces between organic and inorganic semiconductors. Poly(para-phenylene) adsorbed on graphene and encapsulated in carbon nanotubes represent case studies to demonstrate the impact of polarization effects and exciton delocalization in optoelectronic excitations, respectively. Polaron-induced band narrowing and its consequences for charge transport in organic crystals is exemplified for the HOMO bandwidth in naphthalene crystals. On the basis of these prototypical systems, we discuss what is missing to reach predictive power on a quantitative level for organic/inorganic hybrid materials and, thus, open a perspective toward the computational discovery of new materials for optoelectronic applications.

Flexible Surface Hopping Approach to Model the Crossover from Hopping to Band-like Transport in Organic Crystals.

Two distinct pictures are usually evoked when modeling charge transport in organic crystals, that is, band and hopping models, the signature of which is conveyed by a characteristic temperature dependence of mobility. Here, we present a novel flexible surface hopping approach compliant with general Hamiltonians that is able to grasp the crossover from hopping to band-like transport regimes. This approach is applied to solve a one-dimensional mixed quantum-classical model and to calculate the temperature dependence of charge mobility along with the degree of charge spatial localization. It is found that the roles of both local and nonlocal electron-phonon couplings strongly depend on the intrinsic charge localization strength.

Charge carrier dynamics in phonon-induced fluctuation systems from time-dependent wavepacket diffusion approach

A time-dependent wavepacket diffusion method is proposed to deal with charge transport in organic crystals. The electron-phonon interactions in both site energies and electronic couplings are incorporated by the time-dependent fluctuations which are generated from the corresponding spectral density functions. The numerical demonstrations reveal that the present approach predicts the consistent charge carrier dynamics with the rigorous quantum approaches. In addition, the diffusion coefficients obtained from the Marcus formula are well reproduced at the weak electronic coupling and high temperature limits. It is also found that the charge mobility feature of the crossover from the band-like to the hopping-type cannot be predicted from the fluctuations induced by the linear electron-phonon interactions with an Ohmic spectral density; however, it indeed appears as the electronic coupling fluctuation exponentially depends on the nuclear coordinates. Finally, it should be noted that although the present approach neglects the imaginary fluctuation, it essentially incorporates the coherent motion of the charge carrier and quantum effect of the phonon motion with a broad regime of the fluctuations for symmetric systems. Besides, the approach can easily be applied to systems having thousands of sites, which allows one to investigate charge transport in nanoscale organic crystals.

Charge transport in organic crystals: Theory and modelling

AbstractEfficient charge transport in organic semiconductors is the key for their application in Organic Electronics. Therefore the most important design ansatz is directed to improve carrier mobilities by means of available tools such as chemical and/or structural modifications of the organic materials. Thereby theoretical input can provide guidelines towards possible realizations of high‐mobility or, more general, highly functional materials. In particular the structure–property relationship is at the heart of theoretical studies which are extremely helpful if they achieve predictive power. In this paper we systematically review several charge‐transport approaches and illustrate their relationship in order to display their capabilities regarding this goal. Special focus is put on the transport mechanism, the mobility anisotropy and temperature dependence of charge‐carrier transport. As the central concept the inclusion of the strong coupling of the carriers with the vibrating lattice and, hence, the dressing of carriers to polarons is described. The availability of material parameters is tremendously important for transport description. We highlight their computation by ab initio theory in order to arrive at a satisfactory level beyond phenomenological approaches.

Characteristics of small- and large-polaron motion in organic crystals

Based on a generalized theory of charge transport in organic crystals we investigate themotion of polarons of arbitrary size. Within this theory, we analyze the influence ofcharacteristic electronic, vibronic, and thermal energies and their role for the transportregimes. The polaron bandwidth is identified as the central temperature-dependentquantity. The size of the dressed charge carriers is used to analyze the correlation betweenthe polaron size and transport mechanism. In addition, we propose that the band andhopping transport can be distinguished by investigating the mobility anisotropy.To do this only electronic structure parameters are necessary for comparison.

Charge Transport in Organic Crystals: Role of Disorder and Topological Connectivity

We analyze the relationship among the molecular structure, morphology, percolation network, and charge carrier mobility in four organic crystals: rubrene, indolo[2,3-b]carbazole with CH(3) side chains, and benzo[1,2-b:4,5-b']bis[b]benzothiophene derivatives with and without C(4)H(9) side chains. Morphologies are generated using an all-atom force field, while charge dynamics is simulated within the framework of high-temperature nonadiabatic Marcus theory or using semiclassical dynamics. We conclude that, on the length scales reachable by molecular dynamics simulations, the charge transport in bulk molecular crystals is mostly limited by the dynamic disorder, while in self-assembled monolayers the static disorder, which is due to the slow motion of the side chains, enhances charge localization and influences the transport dynamics. We find that the presence of disorder can either reduce or increase charge carrier mobility, depending on the dimensionality of the charge percolation network. The advantages of charge transporting materials with two- or three-dimensional networks are clearly shown.

Charge transport in organic crystals: interplay of band transport, hopping and electron–phonon scattering

We present an ab initio description of charge transport in organic semiconductors based on a recently developed theory that goes beyond small-polaron and/or narrow-band models. The mobility expression is evaluated with parameters from density functional theory, and application to naphthalene crystals demonstrates substantial progress in the simulated temperature dependence and relative magnitudes for all transport directions. The scattering by phonons is described in a manner that goes beyond the Holstein model for small polarons and, consequently, significantly improves the temperature dependence and anisotropy of carrier mobility with respect to the previous narrow-band theory. The contributions of coherent and incoherent scattering processes are analyzed. Special emphasis is placed on the origin and understanding of the transition from band transport at low temperatures to hopping at high temperatures, both of which are fully included in the theory. Additionally, in contrast to earlier narrow-band theories, the unphysical divergence at zero temperatures is removed.

Theory of charge transport in organic crystals: Beyond Holstein’s small-polaron model

We present a theory for charge transport in organic crystals. A mobility expression is derived based on the evaluation of the Kubo formula and the Holstein Hamiltonian. It covers the whole temperature range from low $T$, where it reproduces an expression from the Boltzmann equation for band transport, via elevated $T$, where it generalizes Holstein's small-polaron theory to finite bandwidths, up to high $T$, for which a temperature dependence equal to Marcus' electron transfer theory is obtained. The general expression treats coherent band transport and thermally induced hopping on equal footing. By avoiding the approximation of narrow polaron bands the theory allows for the description of large and small polarons.

Electronic polarization effects on charge carriers in anthracene: A valence bond study

A semiempirical quantum-chemical model based on a fragment orbital formalism is presented to assess molecular parameters relevant to charge transport in organic crystals. The mixed valence bond/Hartree--Fock approach provides an efficient integrated framework to evaluate the electronic polarization effects induced by localized charge carriers and the associated impact on the matrix elements mediating electron migration in the hopping regime. This formalism, applied here to anthracene clusters of increasing sizes and dimensionalities, yields the electrostatic and polarization contributions to the total interaction energy of the neutral and charged aggregates and leads to a reduction in the effective bandwidth by $\ensuremath{\sim}10%--20%$ as a result of the polarization cloud.

Elastomeric transistor stamps: reversible probing of charge transport in organic crystals.

We introduce a method to fabricate high-performance field-effect transistors on the surface of freestanding organic single crystals. The transistors are constructed by laminating a monolithic elastomeric transistor stamp against the surface of a crystal. This method, which eliminates exposure of the fragile organic surface to the hazards of conventional processing, enables fabrication of rubrene transistors with charge carrier mobilities as high as approximately 15 cm2/V.s and subthreshold slopes as low as 2nF.V/decade.cm2. Multiple relamination of the transistor stamp against the same crystal does not affect the transistor characteristics; we exploit this reversibility to reveal anisotropic charge transport at the basal plane of rubrene.