Mechanism of charge transport in self-organizing organic materials

Entropy-ruled nonequilibrium charge transport in thiazolothiazole-based molecular crystals: a quantum chemical study

The charge and energy fluctuations in molecular solids are crucial factors for a better understanding of charge transport (CT) in organic semiconductors. The energetic disorder-coupled molecular charge transport is still not well-established. Moreover, the conventional Einstein's diffusion (D)-mobility (μ) relation fails to explain the quantum features of organic semiconductors, including nonequilibrium and degenerate transport systems, where kB is the Boltzmann constant, T is the temperature and q is the electric charge. To overcome this issue, a unified version of the entropy-ruled D/μ relation was proposed by Navamani (J. Phys. Chem. Lett., 2024, 15, 2519-2528) for hopping and band transport systems as where d, η and heff are the dimension (d = 1, 2, 3), chemical potential and effective entropy, respectively. Within this context, we investigate the CT properties of 2,5-bis(4-methoxyphenyl)thiazolo[5,4-d]thiazole (MOP-TZTZ) and 2,5-bis(2,4,5 trifluorophenyl)-thiazolo[5,4-d]thiazole (TFP-TZTZ) molecular solids using electronic structure calculations and the entropy-ruled method. The CT key parameters such as charge transfer integral and site energy are computed by matrix elements of the Kohn-Sham Hamiltonian. Using Marcus theory, the charge transfer rate is numerically calculated for MOP-TZTZ and TFP-TZTZ molecular crystals under different site energy disorder (ΔEij(E⃑)) situations. Using our entropy-ruled method, the exact diffusion-mobility (D/μ) and other transport quantities such as thermodynamic density of states, conductivity, and current density are calculated for these derivatives at different applied electric field values via the site energy disorder. The theoretical results show that the molecule TFP-TZTZ has good hole mobility (∼0.012 cm2 V-1 s-1) at a site energy disorder value of 90 meV. The obtained ideality factor from the Navamani-Shockley diode current density equation categorizes the typical transport as either the Langevin-type or Shockley-Read-Hall mechanism in the studied molecular solids. Our analysis clearly shows that both the electron and hole transport in these MOP-TZTZ and TFP-TZTZ molecules follow the trap-free Langevin mechanism, which is indeed ideal for designing charge-transporting molecular devices.

Possible NLO response and electrical/charge transfer capabilities of natural anthraquinones as p-type organic semiconductors: a DFT approach

CONTEXT

Organic semiconductors (OSCs) have attracted a great deal of interest in recent days. There are various types of OSCs, among which small molecules have various inherent benefits. Further research is needed to advance this new kind of material because the field is still developing, and the current focus is on creating small molecules that exist naturally for OSCs. OSCs with nonlinear optical (NLO) characteristics offer a significant advantage over others. Thus, this study theoretically investigates naturally occurring anthraquinones such as chrysophanol and rhein as potential OSCs, as well as their NLO properties. The calculated properties include the ionization potential (IP), electron affinity (EA), and bandgap (Eg). The FMO energy levels together with the Eg, IP (8.17-8.53 eV), and EA (1.87-2.44 eV) suggest the semiconductor nature of the studied compounds. The calculated values of reorganization energy (λ) and transfer integrals (V) suggest the p-type character of both molecules. Rhein has the lowest λh (0.19 eV) and Eg (3.28 eV) and the highest Vh, predominantly because of its better p-type character. The polarizability increases due to the presence of an electron-withdrawing substituent, leading to better NLO performance for Rhein, which is supported by its lower LUMO and Eg values.

METHODS

The studied molecules were optimized with the DFT/B3LYP-GD3/6-31+G(d,p) method using Gaussian 16 software. The crystal structure was simulated with Materials Studio 7.0, and the V values were calculated with the ADF package. The CDD and DOS plots were obtained with the Multiwfn 3.8 program.

A model analysis of centimeter-long electron transport in cable bacteria

The recent discovery of cable bacteria has greatly expanded the known length scale of biological electron transport, as these multi-cellular bacteria are capable of mediating electrical currents across centimeter-scale distances. To enable such long-range conduction, cable bacteria embed a network of regularly spaced, parallel protein fibers in their cell envelope. These fibers exhibit extraordinary electrical properties for a biological material, including an electrical conductivity that can exceed 100 S cm-1. Traditionally, long-range electron transport through proteins is described as a multi-step hopping process, in which the individual hopping steps are described by Marcus electron transport theory. Here, we investigate to what extent such a classical hopping model can explain the conductance data recorded for individual cable bacterium filaments. To this end, the conductive fiber network in cable bacteria is modelled as a set of parallel one-dimensional hopping chains. Comparison of model simulated and experimental current(I)/voltage(V) curves, reveals that the charge transport is field-driven rather than concentration-driven, and there is no significant injection barrier between electrodes and filaments. However, the observed high conductivity levels (>100 S cm-1) can only be reproduced, if we include much longer hopping distances (a > 10 nm) and lower reorganisation energies (λ < 0.2 eV) than conventionally used in electron relay models of protein structures. Overall, our model analysis suggests that the conduction mechanism in cable bacteria is markedly distinct from other known forms of long-range biological electron transport, such as in multi-heme cytochromes.

Robust estimation of charge carrier diffusivity using transient photoluminescence microscopy

Transient microscopy has emerged as a powerful tool for imaging the diffusion of excitons and free charge carriers in optoelectronic materials. In many excitonic materials, extraction of diffusion coefficients can be simplified because of the linear relationship between signal intensity and local excited state population. However, in materials where transport is dominated by free charge carriers, extracting diffusivities accurately from multidimensional data is complicated by the nonlinear dependence of the measured signal on the local charge carrier density. To obtain accurate estimates of charge carrier diffusivity from transient microscopy data, statistically robust fitting algorithms coupled to efficient 3D numerical solvers that faithfully relate local carrier dynamics to raw experimental measurables are sometimes needed. Here, we provide a detailed numerical framework for modeling the spatiotemporal dynamics of free charge carriers in bulk semiconductors with significant solving speed reduction and for simulating the corresponding transient photoluminescence microscopy data. To demonstrate the utility of this approach, we apply a fitting algorithm using a Markov chain Monte Carlo sampler to experimental data on bulk CdS and methylammonium lead bromide (MAPbBr3) crystals. Parameter analyses reveal that transient photoluminescence microscopy can be used to obtain robust estimates of charge carrier diffusivities in optoelectronic materials of interest, but that other experimental approaches should be used for obtaining carrier recombination constants. Additionally, simplifications can be made to the fitting model depending on the experimental conditions and material systems studied. Our open-source simulation code and fitting algorithm are made freely available to the scientific community.

Efficient Surface Hopping Approach for Modeling Charge Transport in Organic Semiconductors

The trajectory surface hopping (TSH) method is nowadays widely applied to study the charge/exciton transport process in organic semiconductors (OSCs). In the present study, we systematically examine the performance of two approximations in the fewest switched surface hopping (FSSH) simulations for charge transport (CT) in several representative OSCs. These approximations include (i) the substitution of the nuclear velocity scaling along the nonadiabatic coupling vector (NCV) by rescaling the hopping probability with the Boltzmann factor (Boltzmann correction (BC)) and (ii) a phenomenological approach to treat the quantum feedback from the electronic system to the nuclear system (implicit charge relaxation (IR)) in the OSCs. We find that charge mobilities computed by FSSH-BC-IR are in very good agreement with the mobilities obtained by standard FSSH simulations with explicit charge relaxation (FSSH-ER), however, at reduced computational cost. A key parameter determining the charge carrier mobility is the reorganization energy, which is sensitively dependent on DFT functionals applied. By employing the IR approximation, the FSSH method allows systematic investigation of the effect of the reorganization energies obtained by different DFT functionals like B3LYP or ωB97XD on CT in OSCs. In comparison to the experiments, FSSH-BC-IR using ωB97XD reorganization energy underestimates mobilities in the low-coupling regime, which may indicate the lack of nuclear quantum effects (e.g., zero point energy (ZPE)) in the simulations. The mobilities obtained by FSSH-BC-IR using the B3LYP reorganization energy agree well with experimental values in 3 orders of magnitude. The accidental agreement may be the consequence of the underestimation of the reorganization energy by the B3LYP functional, which compensates for the neglect of nuclear ZPE in the simulations.

Charge Transport and Optical Absorption Properties of Dibenzocoronene Tetracarboxdiimide Based Liquid Crystalline Molecules: A Theoretical Study

Structure, optical absorption, and charge transport properties of dibenzocoronene tetracarboxdiimide (DCDI) based molecules were studied using electronic structure calculations. Based on the optimized neutral, cationic, and anionic geometries the ionized state properties, such as ionization potential, electron affinity, hole extraction potential, electron extraction potentials, and reorganization energy, were calculated. On the basis of the ground state geometry of the studied molecules, the absorption spectra were calculated using the time-dependent density functional theory (TDDFT) method at the PBE0/def-TZVP level of theory. It has been observed that the substitution of different functional groups significantly alters the absorption spectra of DCDI. The methoxy- (OCH₃-) substituted DCDI molecule has a maximum absorption wavelength of 529 nm. The charge transport parameters, such as the charge transfer integral, spatial overlap integral, and the site energy, are calculated directly from the Kohn-Sham matrix elements. The reorganization energy for the presence of excess positive and negative charges and the charge transfer rate calculated from Marcus' theory were used to find the mobility of charge carriers. The computed results show that the mobility of charge carriers is strongly influenced by the functional groups present on the DCDI molecule. The effect of intermolecular structural fluctuations on charge transport properties was studied through molecular dynamics and Monte Carlo simulations based on the polaron hopping mechanism. The calculated charge carrier mobility shows that the cyano- (CN-) substituted DCDI molecules are having n-type semiconducting property while, methoxy- (OCH₃-) and thiol- (SH-) substituted DCDI molecules exhibit ambipolar semiconducting properties.

Understanding charge transport in wavy 2D covalent organic frameworks

Understanding charge transport in 2D covalent organic frameworks is crucial to increase their performance. Herein a new wavy 2D covalent organic framework has been designed, synthesized and studied to shine light on the structural factors that dominate charge transport.

Charge Mobility in Discotic Liquid Crystals

Discotic (disk-shaped) molecules or molecular aggregates may form, within a certain temperature range, partially ordered phases, known as discotic liquid crystals, which have been extensively studied in the recent past. On the one hand, this interest was prompted by the fact that they represent models for testing energy and charge transport theories in organic materials. However, their long-range self-assembling properties, potential low cost, ease of processability with a variety of solvents and the relative ease of tailoring their properties via chemical synthesis, drove the attention of researchers also towards the exploitation of their semiconducting properties in organic electronic devices. This review covers recent research on the charge transport properties of discotic mesophases, starting with an introduction to their phase structure, followed by an overview of the models used to describe charge mobility in organic substances in general and in these systems in particular, and by the description of the techniques most commonly used to measure their charge mobility. The reader already familiar or not interested in such details can easily skip these sections and refer to the core section of this work, focusing on the most recent and significant results regarding charge mobility in discotic liquid crystals.

Delocalised kinetic Monte Carlo for simulating delocalisation-enhanced charge and exciton transport in disordered materials

Charge transport is well understood in both highly ordered materials (band conduction) or highly disordered ones (hopping conduction). In moderately disordered materials-including many organic semiconductors-the approximations valid in either extreme break down, making it difficult to accurately model the conduction. In particular, describing wavefunction delocalisation requires a quantum treatment, which is difficult in disordered materials that lack periodicity. Here, we present the first three-dimensional model of partially delocalised charge and exciton transport in materials in the intermediate disorder regime. Our approach is based on polaron-transformed Redfield theory, but overcomes several computational roadblocks by mapping the quantum-mechanical techniques onto kinetic Monte Carlo. Our theory, delocalised kinetic Monte Carlo (dKMC), shows that the fundamental physics of transport in moderately disordered materials is that of charges hopping between partially delocalised electronic states. Our results reveal why standard kinetic Monte Carlo can dramatically underestimate mobilities even in disordered organic semiconductors, where even a little delocalisation can substantially enhance mobilities, as well as showing that three-dimensional calculations capture important delocalisation effects neglected in lower-dimensional approximations.

Computational modeling of charge hopping dynamics along a disordered one-dimensional wire with energy gradients in quantum environments

This computational study investigates the effects of energy gradients on charge hopping dynamics along a one-dimensional chain of discrete sites coupled to quantum bath, which is modeled at the level of Pauli master equation (PME). This study also assesses the performance of different approximations for the hopping rates. Three different methods for solving the PME, a fourth order Runge-Kutta method, numerical diagonalization of the rate matrix followed by analytic propagation, and kinetic Monte Carlo simulation method, are tested and confirmed to produce virtually identical values of time dependent mean square displacement, diffusion constant, and mobility. Five different rate expressions, exact numerical evaluation of Fermi's Golden Rule (FGR) rate, stationary phase interpolation (SPI) approximation, semiclassical approximation, classical Marcus rate, and Miller-Abrahams rate, are tested to help understand the effects of approximations in representing quantum environments in the presence of energy gradients. The results based on direct numerical evaluation of FGR rate exhibit transition from diffusive to non-diffusive behavior with the increase in the gradient and show that the charge transport in the quantum bath is more sensitive to the magnitude of the gradient and the disorder than in the classical bath. Among all the four approximations for the hopping rates, the SPI approximation is confirmed to work best overall. A comparison of two different methods to calculate the mobility identifies drift motion of the population distribution as the major source of non-diffusive behavior and provides more reliable information on the contribution of quantum bath.

Nature (Hole or Electron) of Charge-Transfer Ability of Substituted Cyclopyrenylene Hoop-Shaped Compounds

We theoretically investigate here by means of DFT methods how the selective substitution in cyclic organic nanorings composed of pyrene units may promote semiconducting properties, analyzing the energy needed for a hole- or electron-transfer accommodation as a function of the substitution pattern and the system size (i.e., number of pyrene units). We choose to study both [3]Cyclo-2,7-pyrenylene ([3]CPY) and [4]Cyclo-2,7-pyrenylene ([4]CPY) compounds, the latter already synthesized, with substituents other than hydrogen acting in ipso and ortho positions, as well as the effect of the per-substitution. As substituents, we selected a set of electroactive halogen atoms (F, Cl, and Br) and groups (CN) to disclose structure-property relationships allowing thus to anticipate the use of these systems as organic molecular semiconductors.

Performance of Mixed Quantum-Classical Approaches on Modeling the Crossover from Hopping to Bandlike Charge Transport in Organic Semiconductors

In the present study, several mixed quantum-classical (MQC) methods are applied to on-the-fly nonadiabatic molecular dynamics simulations of hole transport in molecular organic semiconductors (OSCs). The tested MQC methods contain the mean-field Ehrenfest (MFE), trajectory surface hopping (TSH) approaches based on Tully's fewest switches surface hopping (FSSH) and the global flux surface hopping (GFSH), the latter in the diabatic/adiabatic representation, and a Landau-Zener type trajectory surface hopping (LZSH). We also tested several correction schemes which were proposed to identify trivial crossings and to remove unphysical long-range charge transfers due to decoherence corrections. In addition, several cost-effective approaches for the nuclear velocity adjustment after an energy-allowed/energy-forbidden hop are investigated with respect to detailed balance and internal consistency conditions. To model a broad spectrum of OSCs with different charge transport characteristics, we derived from the anthracene structural model the construction of two additional models by uniformly scaling down the electronic couplings by the factors of 0.1 and 0.5. Anthracene shows a bandlike charge transport mechanism, characterized by slightly delocalized charge carriers 'diffusing' through the crystal. For smaller couplings, the mechanism changes to a hopping type, characteristically differing in the charge delocalization and temperature dependence. The MFE and corrected adiabatic TSH approaches are able to quantitatively reproduce the expected behavior, while the diabatic LZSH method fails for large couplings, as do approaches which are based on the hopping of localized charge between neighboring sites. Moreover, we find that while the hole mobility of the anthracene crystal simulated using the celebrated Marcus theory is in good agreement with the experimental value, its agreement has to be regarded as an accident due to the overestimation of the prefactor in the Marcus rate equation.

Shortcuts for Electron-Transfer through the Secondary Structure of Helical Oligo-1,2-Naphthylenes

Atropisomeric 1,2-naphthylene scaffolds provide access to donor-acceptor compounds with helical oligomer-based bridges, and transient absorption studies revealed a highly unusual dependence of the electron-transfer rate on oligomer length, which is due to their well-defined secondary structure. Close noncovalent intramolecular contacts enable shortcuts for electron transfer that would otherwise have to occur over longer distances along covalent pathways, reminiscent of the behavior seen for certain proteins. The simplistic picture of tube-like electron transfer can describe this superposition of different pathways including both the covalent helical backbone, as well as noncovalent contacts, contrasting the wire-like behavior reported many times before for more conventional molecular bridges. The exquisite control over the molecular architecture, achievable with the configurationally stable and topologically defined 1,2-naphthylene-based scaffolds, is of key importance for the tube-like electron transfer behavior. Our insights are relevant for the emerging field of multidimensional electron transfer and for possible future applications in molecular electronics.

Effect of site energy fluctuation on charge transport in disordered organic molecules

Effect of dynamics of site energy disorder on charge transport in organic molecular semiconductors is not yet well-established. In order to study the relationship between the dynamics of site energy disorder and charge transport, we have performed a multiscale study on dialkyl substituted thienothiophene capped benzobisthiazole (BDHTT-BBT) and methyl-substituted dicyanovinyl-capped quinquethiophene (DCV5T-Me) molecular solids. In this study, we explore the structural dynamics and correlated charge transport by electronic structure calculations, molecular dynamics, and kinetic Monte-Carlo simulations. We have also proposed the differential entropy dependent diffusion and charge density equations to study the electric field drifted diffusion property and carrier density. In this investigation, we have addressed the transformation mechanism from dynamic to static disorder in the extended stacked molecular units. Here, the decrease in the charge transfer rate due to site energy fluctuations reveals the dispersion transport along the extended π-stacked molecules. Furthermore, the calculated current density for a different set of site energy difference values shows the validity and the limitations of the Einstein relation. Based on the calculated ideality factor, we have classified the charge transport in these molecules as either the Langevin or the Shockley-Read-Hall type mechanism. Through the calculated mobility, current density, and ideality factor analysis, we categorize the applicability of molecules of interest for photovoltaic or light emitting diode applications.

Quantum localization and delocalization of charge carriers in organic semiconducting crystals

Charge carrier transport in organic semiconductors is at the heart of many revolutionary technologies ranging from organic transistors, light-emitting diodes, flexible displays and photovoltaic cells. Yet, the nature of charge carriers and their transport mechanism in these materials is still unclear. Here we show that by solving the time-dependent electronic Schrödinger equation coupled to nuclear motion for eight organic molecular crystals, the excess charge carrier forms a polaron delocalized over up to 10-20 molecules in the most conductive crystals. The polaron propagates through the crystal by diffusive jumps over several lattice spacings at a time during which it expands more than twice its size. Computed values for polaron size and charge mobility are in excellent agreement with experimental estimates and correlate very well with the recently proposed transient localization theory.

Enhancing the supramolecular stability of monolayers by combining dipolar with amphiphilic motifs: a case of amphiphilic push-pull-thiazole

Equipping a thiazole dye with push and pull moieties adds dipolar intermolecular interactions and two hydrophilic anchors to a centrally anchored π-stacking and otherwise mono-amphiphilic dye. We show that, despite the resulting irregular shape of the tripodal amphiphile, the enhanced intermolecular interactions and amphiphilicity yield smooth and stable thin films. Furthermore, we present a first approach for deriving supramolecular binding energies from the Langmuir-Blodgett hysteresis data.

Arylic versus Alkylic-Hydrophobic Linkers Determine the Supramolecular Structure and Optoelectronic Properties of Tripodal Amphiphilic Push-Pull Thiazoles

The supramolecular structures and their constituents essentially determine the optoelectronic properties of thin films. The introduction of amphiphilicity to the constituents and interface assembly is one established technique to control supramolecular structures and resulting material properties. To yield amphiphilicity, rather hydrophobic chromophores are linked to hydrophilic head groups via flexible alkyl chains. In the present work, we investigate whether replacement of the alkyl linkers by a phenylene linker, that is, replacing an electrically isolating moiety with a potentially semiconducting one, increases the conductivity through the resulting layers. After investigating the influence of the linker on molecular properties of the 2-(4- N, N-dimethylaminophenyl)-4-hydroxy-5-nitrophenyl-1,3 thiazoles exemplarily used in this work, we produce supramolecular structures by means of the Langmuir-Blodgett (LB) technique. Atomic force microscopy (AFM) and UV-vis absorption spectroscopy reveal that thin films made from the more rigid thiazole bearing the arylic linker feature a more homogeneous and stable supramolecular structure as compared to those made from the thiazole dye containing the flexible alkylic linker. Finally, conductive AFM (cAFM) results disclose that the LB films made from the thiazole bearing the π-conjugated arylic linker are less conductive than their counterparts based on the alkylic linkers. In the latter layers, the alkylic linkers provide sufficient motional degrees of freedom to allow for supramolecular rearrangement upon electrical operation during cAFM measurements, hence yielding supramolecular structures featuring increased conductivity with successive cAFM measurements. This work highlights the importance of supramolecular structures for optoelectronic properties by presenting a case where supramolecular effects excel the property changes introduced by molecular modifications.

Assembly of T-Shaped Amphiphilic Thiazoles on the Air-Water Interface: Impact of Polar Chromophore Moieties, as Well as Dipolarity and π-Extension of the Chromophore on the Supramolecular Structure

The supramolecular structure essentially determines the properties of organic thin films. In this work, we systematically investigate the influence of the chromophore on the supramolecular structure formation at air-water interfaces by means of the Langmuir-Blodgett technique. Therefore, we focus on the recently introduced class of double-anchor T-shaped amphiphilic dyes, namely, 4-hydroxy-thiazole chromophores that are centrally equipped with an amphiphilicity-inducing hexanoic acid. The thiazoles contain hydrophilic subphase-anchor groups in the 2-position (4- N, N-dimethylaminophenyl (Am), 2-pyridyl (Py), and 4-nitrophenyl (Ni)), whereas the chromophores are systematically extended in the 5-position with various substituents. The combination of the Langmuir technique with online fluorescence measurements revealed that the π-π interactions that are pronounced in the case of 4-methoxybiphenyl derivatives yield the most distinct supramolecular structures. Whereas in the case of Py and Ni derivatives ordered J-type supramolecular structures in microdomains are formed, the Am derivative forms ordered supramolecular structures that are more homogeneous, which are, however, not stabilized by J-type dipolar interactions. Because of the synergetic π-π and dipolar stabilizations, the Ni derivative bearing the 4-methoxybiphenyl unit forms exceptionally stable quasi-two-dimensional Langmuir monolayers reaching very high surface pressures beyond 60 mN/m without any sign of disturbance of the Langmuir monolayer.

Fluorination-Induced Evolution of Columnar Packing in Fluorous Triphenylenes and Benzotriphenylenes

Use of D_3h -symmetrical triphenylene (TRPH) as a substrate for high-temperature radical reactions with C₄ F₈ I₂ under varying conditions resulted in the introduction of four types of fluorinated substituents: ω-C₄ F₈ H, c-C₄ F₈ , c-C₄ F₄ , and c-C₄ HF₃ . In contrast to the previous work on direct (poly)substitutions with R_F groups in polycyclic aromatic hydrocarbons (PAHs), in this work regiospecificity, selectivity, and high yield were achieved for TRPH(C₄ F₈ ) and TRPH(C₄ F₈ )₃ . New single-crystal structural data for seven compounds combined with literature crystallographic data allowed for the first detailed and precise analysis of the effects of fluorous substituent types, their number, and their position(s) on the TRPH core on the solid-state packing, and more specifically, the degree of π-π overlap between neighboring molecules, which is linked to charge transport properties. Comparison of isostructural partially fluorinated benzotriphenylenes, 2,3-TRPH(C₄ F₄ ) and 2,3-TRPH(C₄ HF₃ ), revealed an unexpectedly large (30 %) drop of π-π overlap, when only one fluorine atom was replaced with the hydrogen atom in a C₄ F₄ moiety. Theoretical and potentially practical implications of this work may include further testing and elaboration of computational methods describing solid-state interactions and predictions of transport properties of organic semiconductors, and further advances in the molecular design of high-performing TRPH-based organic materials and supramolecular architectures for organic optoelectronics.

Polaron States in Fullerene Adducts Modeled by Coarse-Grained Molecular Dynamics and Tight Binding

Strong electron-phonon coupling leads to polaron localization in molecular semiconductor materials and influences charge transport, but it is expensive to calculate atomistically. Here, we propose a simple and efficient model to determine the energy and spatial extent of polaron states within a coarse-grained representation of a disordered molecular film. We calculate the electronic structure of the molecular assembly using a tight-binding Hamiltonian and determine the polaron state self-consistently by perturbing the site energies by the dielectric response of the surrounding medium to the charge. When applied to fullerene derivatives, the method shows that polarons extend over multiple molecules in C60 but localize on single molecules in higher adducts of phenyl-C61-butyric-acid-methyl-ester (PCBM) because of packing disorder and the polar side chains. In PCBM, polarons localize on single molecules only when energetic disorder is included or when the fullerene is dispersed in a blend. The method helps to establish the conditions under which a hopping transport model is justified.

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.

Modelling of the charge carrier mobility in disordered linear polymer materials

We introduced a molecular-scale description of disordered on-chain charge carrier states into a theoretical model of the charge carrier transport in polymer semiconductors. The presented model combines the quantum mechanical approach with a semi-classical solution of the inter-chain charge hopping. Our model takes into account the significant local anisotropy of the charge carrier mobility present in linear conjugated polymers. Contrary to the models based on the effective medium approximation, our approach allowed avoiding artefacts in the calculated concentration dependence of the mobility originated in its problematic configurational averaging. Monte Carlo numerical calculations show that, depending on the degree of the energetic and structural disorder, the charge carrier mobility increases significantly with increasing charge concentration due to trap filling. At high charge carrier concentrations, the effect of the energetic disorder disappears and the mobility decreases slightly due to the lower density of unoccupied states available for the hopping transport. It could explain the experimentally observed mobility degradation in organic field-effect transistors at high gate voltage.

Theoretical modeling of charge transport in triphenylamine–benzimidazole based organic solids for their application as host-materials in phosphorescent OLEDs

The dynamic disorder and electric field effects on charge transport in triphenylamine–benzimidazole based molecular solids have been investigated using electronic structure calculations, molecular dynamics and Monte-Carlo simulations. During the charge propagation, the energy loss of the carrier in each hopping step is monitored by Monte-Carlo simulation. We derive a survival probability correlated momentum–energy distribution for drift-diffusion analysis and we demonstrate the dispersion initiated charge trapping mechanism which is indeed ideal for light emission efficiency via recombination. In the present model, the proposed carrier drift energy–current density expression and Shockley diode current density equation are used to study the current density–voltage characteristics; accordingly the ideality factor (∼1.8–2.0) dictates the deviation of Einstein's classical diffusion–mobility relation (where the ideality factor is unity). The dual mechanism of electric field assisted site energy gap on coherent-like transport and the electric field stretched dispersion on recombination are observed in tris(3′-(1-phenyl-1H-benzimidazole-2-yl)biphenyl-4-yl)amine (TBBI) and tris(4′-(1-phenyl-1H-benzimidazole-2-yl)biphenyl-4-yl)amine (TIBN) molecular systems, which can be used as host materials in organic light emitting diodes (OLEDs). We find the transport going from coherent to incoherent, due to the conversion mechanism of dynamic to static disorder. This can also be a controlled by applied electric field. By adjusting the applied electric field, film thickness and changing the π-stacked molecular aggregation via substitutions, one can fix the dispersive parameter and accordingly calculate the charge transport properties to design efficient host-materials for photovoltaic and light emitting diode devices.

Dynamic disorder and electric field affect the charge (hole and electron) transport in host-materials for OLEDs.

On the Control of Chromophore Orientation, Supramolecular Structure, and Thermodynamic Stability of an Amphiphilic Pyridyl-Thiazol upon Lateral Compression and Spacer Length Variation

The supramolecular structure essentially determines the properties of organic thin films. Therefore, it is of utmost importance to understand the influence of molecular structure modifications on supramolecular structure formation. In this article, we demonstrate how to tune molecular orientations of amphiphilic 4-hydroxy thiazole derivatives by means of the Langmuir-Blodgett (LB) technique and how this depends on the length of an alkylic spacer between the thiazole chromophore and the polar anchor group. Therefore, we characterize their corresponding supramolecular structures, thermodynamic, absorption, and fluorescence properties. Particularly, the polarization-dependence of the fluorescence is analyzed to deduce molecular orientations and their possible changes after annealing, i.e., to characterize the thermodynamic stability of the individual solid state phases. Because the investigated thiazoles are amphiphilic, the different solid state phases can be formed and be controlled by means of the Langmuir-Blodgett (LB) technique. This technique also allows to deduce atomistic supramolecular structure motives of the individual solid phases and to characterize their thermodynamic stabilities. Utilizing the LB technique, we demonstrate that subtle molecular changes, like the variation in spacer length, can yield entirely different solid state phases with distinct supramolecular structures and properties.

Charge-transport properties of 4-(1,2,2-tri-phenyl-vinyl)-aniline salicylaldehyde hydrazone: tight-packing induced molecular 'hardening'

Based on first-principles calculations, the relationship between molecular packing and charge-transport parameters has been investigated and analysed in detail. It is found that the crystal packing forces in the flexible organic molecule 4-(1,2,2-triphenylvinyl)-aniline salicylaldehyde hydrazone (A) can apparently overcome the dynamic intramolecular rotations and the intramolecular steric repulsion, effectively enhancing the molecular rigidity and decreasing the internal reorganization energy. The conducting properties of A have also been simulated within the framework of hopping models, and the calculation results show that the intrinsic electron mobility in A is much higher than the corresponding intrinsic hole mobility. These theoretical investigations provide guidance for the efficient and targeted control of the molecular packing and charge-transport properties of organic small-molecule semiconductors and conjugated polymeric materials.

Ferroelectric self-assembled molecular materials showing both rectifying and switchable conductivity

Advanced molecular materials that combine two or more physical properties are typically constructed by combining different molecules, each being responsible for one of the properties required. Ideally, single molecules could take care of this combined functionality, provided they are self-assembled correctly and endowed with different functional subunits whose strong electronic coupling may lead to the emergence of unprecedented and exciting properties. We present a class of disc-like semiconducting organic molecules that are functionalized with strong dipolar side groups. Supramolecular organization of these materials provides long-range polar order that supports collective ferroelectric behavior of the side groups as well as charge transport through the stacked semiconducting cores. The ferroelectric polarization in these supramolecular polymers is found to couple to the charge transport and leads to a bulk conductivity that is both switchable and rectifying. An intuitive model is developed and found to quantitatively reproduce the experimental observations. In a larger perspective, these results highlight the possibility of modulating material properties using the large electric fields associated with ferroelectric polarization.

Structure, transport and photoconductance of PbS quantum dot monolayers functionalized with a copper phthalocyanine derivative

We simultaneously surface-functionalize PbS nanocrystals with Cu 4,4′,4′′,4′′′-tetraaminophthalocyanine and assemble this hybrid material into macroscopic monolayers.

Photovoltaic concepts inspired by coherence effects in photosynthetic systems

The past decade has seen rapid advances in our understanding of how coherent and vibronic phenomena in biological photosynthetic systems aid in the efficient transport of energy from light-harvesting antennas to photosynthetic reaction centres. Such coherence effects suggest strategies to increase transport lengths even in the presence of structural disorder. Here we explore how these principles could be exploited in making improved solar cells. We investigate in depth the case of organic materials, systems in which energy and charge transport stand to be improved by overcoming challenges that arise from the effects of static and dynamic disorder - structural and energetic - and from inherently strong electron-vibration couplings. We discuss how solar-cell device architectures can evolve to use coherence-exploiting materials, and we speculate as to the prospects for a coherent energy conversion system. We conclude with a survey of the impacts of coherence and bioinspiration on diverse solar-energy harvesting solutions, including artificial photosynthetic systems.

Photogeneration and Mobility of Charge Carriers in Atomically Thin Colloidal InSe Nanosheets Probed by Ultrafast Terahertz Spectroscopy

The implementation of next generation ultrathin electronics by applying highly promising dimensionality-dependent physical properties of two-dimensional (2D) semiconductors is ever increasing. In this context, the van der Waals layered semiconductor InSe has proven its potential as photodetecting material with high charge carrier mobility. We have determined the photogeneration charge carrier quantum yield and mobility in atomically thin colloidal InSe nanosheets (inorganic layer thickness 0.8-1.7 nm, mono/double-layers, ≤ 5 nm including ligands) by ultrafast transient terahertz (THz) spectroscopy. A near unity quantum yield of free charge carriers is determined for low photoexcitation density. The charge carrier quantum yield decreases at higher excitation density due to recombination of electrons and holes, leading to the formation of neutral excitons. In the THz frequency domain, we probe a charge mobility as high as 20 ± 2 cm²/(V s). The THz mobility is similar to field-effect transistor mobilities extracted from unmodified exfoliated thin InSe devices. The current work provides the first results on charge carrier dynamics in ultrathin colloidal InSe nanosheets.

Critical analysis of fragment-orbital DFT schemes for the calculation of electronic coupling values

We present a critical analysis of the popular fragment-orbital density-functional theory (FO-DFT) scheme for the calculation of electronic coupling values. We discuss the characteristics of different possible formulations or "flavors" of the scheme which differ by the number of electrons in the calculation of the fragments and the construction of the Hamiltonian. In addition to two previously described variants based on neutral fragments, we present a third version taking a different route to the approximate diabatic state by explicitly considering charged fragments. In applying these FO-DFT flavors to the two molecular test sets HAB7 (electron transfer) and HAB11 (hole transfer), we find that our new scheme gives improved electronic couplings for HAB7 (-6.2% decrease in mean relative signed error) and greatly improved electronic couplings for HAB11 (-15.3% decrease in mean relative signed error). A systematic investigation of the influence of exact exchange on the electronic coupling values shows that the use of hybrid functionals in FO-DFT calculations improves the electronic couplings, giving values close to or even better than more sophisticated constrained DFT calculations. Comparing the accuracy and computational cost of each variant, we devise simple rules to choose the best possible flavor depending on the task. For accuracy, our new scheme with charged-fragment calculations performs best, while numerically more efficient at reasonable accuracy is the variant with neutral fragments.

Switchable Charge Injection Barrier in an Organic Supramolecular Semiconductor

We disclose a supramolecular material that combines semiconducting and dipolar functionalities. The material consists of a discotic semiconducting carbonyl-bridged triarylamine core, which is surrounded by three dipolar amide groups. In thin films, the material self-organizes in a hexagonal columnar fashion through π-stacking of the molecular core and hydrogen bonding between the amide groups. Alignment by an electrical field in a simple metal/semiconductor/metal geometry induces a polar order in the interface layers near the metal contacts that can be reversibly switched, while the bulk material remains nonpolarized. On suitably chosen electrodes, the presence of an interfacial polarization field leads to a modulation of the barrier for charge injection into the semiconductor. Consequently, a reversible switching is possible between a high-resistance, injection-limited off-state and a low-resistance, space-charge-limited on-state. The resulting memory diode shows switchable rectification with on/off ratios of up to two orders of magnitude. This demonstrated multifunctionality of a single material is a promising concept toward possible application in low-cost, large-area, nonvolatile organic memories.

Regioisomeric donor–acceptor–donor triads based on benzodithiophene and BODIPY with distinct optical properties and mobilities

Two regioisomeric donor–acceptor–donor triads composed of benzodithiophene and BODIPY exhibit distinct optical and charge transfer properties, and mobilities of ∼10⁻⁴ cm² V⁻¹ s⁻¹.

High charge mobility in two-dimensional percolative networks of PbSe quantum dots connected by atomic bonds

Two-dimensional networks of quantum dots connected by atomic bonds have an electronic structure that is distinct from that of arrays of quantum dots coupled by ligand molecules. We prepared atomically coherent two-dimensional percolative networks of PbSe quantum dots connected via atomic bonds. Here, we show that photoexcitation leads to generation of free charges that eventually decay via trapping. The charge mobility probed with an AC electric field increases with frequency from 150±15 cm² V⁻¹ s⁻¹ at 0.2 terahertz to 260±15 cm² V⁻¹ s⁻¹ at 0.6 terahertz. Gated four-probe measurements yield a DC electron mobility of 13±2 cm² V⁻¹ s⁻¹. The terahertz mobilities are much higher than for arrays of quantum dots coupled via surface ligands and are similar to the highest DC mobilities reported for PbSe nanowires. The terahertz mobility increases only slightly with temperature in the range of 15–290 K. The extent of straight segments in the two-dimensional percolative networks limits the mobility, rather than charge scattering by phonons.

The effect of nanocrystal structure on electronic properties is of considerable interest for optoelectronic devices. Here, Evers et al. study the charge transport in two-dimensional percolative networks of PbSe and find excellent terahertz mobility of charge carriers.

Forth-back oscillated charge carrier motion in dynamically disordered hexathienocoronene molecules: a theoretical study

Electronic structure calculations were performed to investigate the charge transport properties of hexathienocoronene (HTC) based molecules. The effective displacement of the charge carrier along the π-orbital of nearby molecules is calculated by monitoring the forth and back oscillations of the charge carrier through kinetic Monte Carlo simulation. The charge transport parameters such as charge transfer rate, mobility, hopping conductivity, localized charge density, time average effective mass and degeneracy pressure are calculated and used to study the charge transport mechanism in the studied molecules. The existence of degeneracy levels facilitates the charge transfer and is analyzed through degeneracy pressure. Theoretical results show that the site energy difference in the dynamically disordered system controls the forth-back oscillation of charge carrier and facilitates the unidirectional charge transport mechanism along the sequential localized sites. The ethyl substituted HTC has good hole and electron hopping conductivity of 415 and 894 S cm(-1), respectively, whereas unsubstituted HTC has the small hole mobility of 0.06 cm(2) V(-1) s(-1) which is due to large average effective mass of 1.42 × 10(-28) kg.

Quantitative prediction of charge mobilities of π-stacked systems by first-principles simulation

This protocol is intended to provide chemists and physicists with a tool for predicting the charge carrier mobilities of π-stacked systems such as organic semiconductors and the DNA double helix. An experimentally determined crystal structure is required as a starting point. The simulation involves the following operations: (i) searching the crystal structure; (ii) selecting molecular monomers and dimers from the crystal structure; (iii) using density function theory (DFT) calculations to determine electronic coupling for dimers; (iv) using DFT calculations to determine self-reorganization energy of monomers; and (v) using a numerical calculation to determine the charge carrier mobility. For a single crystal structure consisting of medium-sized molecules, this protocol can be completed in ∼4 h. We have selected two case studies (a rubrene crystal and a DNA segment) as examples of how this procedure can be used.

Field effect transistors based on semiconductive microbially synthesized chalcogenide nanofibers

Microbial redox activity offers a potentially transformative approach to the low-temperature synthesis of nanostructured inorganic materials. Diverse strains of the dissimilatory metal-reducing bacteria Shewanella are known to produce photoactive filamentous arsenic sulfide nanomaterials by reducing arsenate and thiosulfate in anaerobic culture conditions. Here we report in situ microscopic observations and measure the thermally activated (79 kJ mol(-1)) precipitation kinetics of high yield (504 mg per liter of culture, 82% of theoretical maximum) extracellular As2S3 nanofibers produced by Shewanella sp. strain ANA-3, and demonstrate their potential in functional devices by constructing field effect transistors (FETs) based on individual nanofibers. The use of strain ANA-3, which possesses both respiratory and detoxification arsenic reductases, resulted in significantly faster nanofiber synthesis than other strains previously tested, mutants of ANA-3 deficient in arsenic reduction, and when compared to abiotic arsenic sulfide precipitation from As(III) and S(2-). Detailed characterization by electron microscopy, energy-dispersive X-ray spectroscopy, electron probe microanalysis and Tauc analysis of UV-vis spectrophotometry showed the biogenic precipitate to consist primarily of amorphous As2S3 nanofibers with an indirect optical band gap of 2.37 eV. X-ray diffraction also revealed the presence of crystalline As8S(9-x) minerals that, until recently, were thought to form only at higher temperatures and under hydrothermal conditions. The nanoscale FETs enabled a detailed characterization of the charge mobility (∼10(-5) cm(2) V(-1) s(-1)) and gating behavior of the heterogeneously doped nanofibers. These studies indicate that the biotransformation of metalloids and chalcogens by bacteria enables fast, efficient, sustainable synthesis of technologically relevant chalcogenides for potential electronic and optoelectronic applications.

A DFT approach to the charge transport related properties in columnar stacked π-conjugated N-heterocycle cores including electron donor and acceptor units

Theoretical design of new, ambipolar DLC donor–acceptor systems based on tris[1,2,4]triazolo[1,3,5]triazine cores.

Effect of dynamic disorder on charge carrier dynamics in Ph4DP and Ph4DTP molecules

Electronic structure calculations were used to study the charge transport and optical properties of 2,2′,6,6′-tetraphenyldipyranylidene (Ph4DP) and its sulfur analogue 2,2′,6,6′-tetraphenyldithiopyranylidene (Ph4DTP) based molecules.