Charge carrier motion in disordered conjugated polymers: a multiscale Ab initio study

Coarse-Grained Model for Prediction of Hole Mobility in Polyethylene

Electrical conductivity measurements of polyethylene indicate that the semicrystalline structure and morphology influence the conductivity. To include this effect in atomistic charge transport simulations, models that explicitly or implicitly take morphology into account are required. In the literature, charge transport simulations of amorphous polyethylene have been successfully performed using short oligomers to represent the polymer. However, a more realistic representation of the polymer structure is desired, requiring the development of fast and efficient charge transport algorithms that can handle large molecular systems through coarse-graining. Here, such a model for charge transport simulations in polyethylene is presented. Quantum chemistry calculations were used to define six segmentation rules on how to divide a polymer chain into shorter segments representing localized molecular orbitals. Applying the rules to amorphous systems yields distributions of segments with mode and median segment lengths relatively close to the persistence length of polyethylene. In an initial test, the segments of an amorphous polyethylene were used as hopping sites in kinetic Monte Carlo (KMC) simulations, which yielded simulated hole mobilities that were within the experimental range. The activation energy of the simulated system was lower compared to the experimental values reported in the literature. A conclusion may be that the experimental result can only be explained by a model containing chemical defects that generate deep traps.

Computational Approaches for Organic Semiconductors: From Chemical and Physical Understanding to Predicting New Materials

While a complete understanding of organic semiconductor (OSC) design principles remains elusive, computational methods─ranging from techniques based in classical and quantum mechanics to more recent data-enabled models─can complement experimental observations and provide deep physicochemical insights into OSC structure-processing-property relationships, offering new capabilities for in silico OSC discovery and design. In this Review, we trace the evolution of these computational methods and their application to OSCs, beginning with early quantum-chemical methods to investigate resonance in benzene and building to recent machine-learning (ML) techniques and their application to ever more sophisticated OSC scientific and engineering challenges. Along the way, we highlight the limitations of the methods and how sophisticated physical and mathematical frameworks have been created to overcome those limitations. We illustrate applications of these methods to a range of specific challenges in OSCs derived from π-conjugated polymers and molecules, including predicting charge-carrier transport, modeling chain conformations and bulk morphology, estimating thermomechanical properties, and describing phonons and thermal transport, to name a few. Through these examples, we demonstrate how advances in computational methods accelerate the deployment of OSCsin wide-ranging technologies, such as organic photovoltaics (OPVs), organic light-emitting diodes (OLEDs), organic thermoelectrics, organic batteries, and organic (bio)sensors. We conclude by providing an outlook for the future development of computational techniques to discover and assess the properties of high-performing OSCs with greater accuracy.

Even a little delocalization produces large kinetic enhancements of charge-separation efficiency in organic photovoltaics

In organic photovoltaics, charges can separate efficiently even if their Coulomb attraction is an order of magnitude greater than the available thermal energy. Delocalization has been suggested to explain this fact, because it could increase the initial separation of charges in the charge-transfer (CT) state, reducing their attraction. However, understanding the mechanism requires a kinetic model of delocalized charge separation, which has proven difficult because it involves tracking the correlated quantum-mechanical motion of the electron and the hole in large simulation boxes required for disordered materials. Here, we report the first three-dimensional simulations of charge-separation dynamics in the presence of disorder, delocalization, and polaron formation, finding that even slight delocalization, across less than two molecules, can substantially enhance the charge-separation efficiency, even starting with thermalized CT states. Delocalization does not enhance efficiency by reducing the Coulomb attraction; instead, the enhancement is a kinetic effect produced by the increased overlap of electronic states.

Stepping Out of Equilibrium: The Quest for Understanding the Role of Non-Equilibrium (Thermo-)Dynamics in Electronic and Electrochemical Processes

This editorial aims to interest researchers and inspire novel research on the topic of non-equilibrium Thermodynamics and Monte Carlo for Electronic and Electrochemical Processes. We present a brief outline on recent progress and challenges in the study of non-equilibrium dynamics and thermodynamics using numerical Monte Carlo simulations. The aim of this special issue is to collect recent advances and novel techniques of Monte Carlo methods to study non-equilibrium electronic and electrochemical processes at the nanoscale.

Phonon-Assisted Hopping through Defect States in MoS2: A Multiscale Simulation

Understanding the carrier transport mechanism in transition metal dichalcogenides (TMDs) is essential for their device application. Experiments demonstrated that at low carrier density and room temperature, the conductivity in TMDs is dominant by activation hopping transport through localized S-vacancy states. In this work, a multiscale model combining ab initio calculation and the Marcus theory is applied to study such transport. We identify phonon-assisted hopping (PAH) as the most possible mechanism for the activation hopping. It is found that the macroscopic conductivity is mainly contributed by a few microscopic percolation paths. Analysis on the hopping distance indicates nearest-neighbor hopping behavior. The dependence of PAH mobility on defect concentration, temperature, and energy mismatch between defect sites is discussed. It is shown that all these factors can strongly affect the mobility. We further proposed that alloying can be an efficient way to tune the mobility due to increased energy mismatch effect.

Efficient evaluation of Coulomb interactions in kinetic Monte Carlo simulations of charge transport

The application of predictive and reliable modeling techniques for the simulation of charge transport in functional materials is an essential step for the development of advanced platforms for electronics, optoelectronics, and photovoltaics. In this context, kinetic Monte Carlo (KMC) methods have emerged as a valuable tool, especially for the simulation of systems where charge transport can be described by the hopping of charge carriers across localized quantum states, as, for example, in organic semiconductor materials. The accuracy, computational efficiency, and reliability of KMC simulations of charge transport, however, crucially depend on the methods and approximations used to evaluate electrostatic interactions arising from the distribution of charges in the system. The long-range nature of Coulomb interactions and the need to simulate large model systems to capture the details of charge transport phenomena in complex devices lead, typically, to a computational bottleneck, which hampers the application of KMC methods. Here, we propose and assess computational schemes for the evaluation of electrostatic interactions in KMC simulations of charge transport based on the locality of the charge redistribution in the hopping regime. The methods outlined in this work provide an overall accuracy that outperforms typical approaches for the evaluation of electrostatic interactions in KMC simulations at a fraction of the computational cost. In addition, the computational schemes proposed allow a spatial decomposition of the evaluation of Coulomb interactions, leading to an essentially linear scaling of the computational load with the size of the system.

Unexpectedly Large Couplings Between Orthogonal Units in Anthraquinone Polymers

The unusual electronic properties of directly linked 1,4-polyanthraquinones (14PAQs) are investigated. The dihedral angle between the molecular planes of anthraquinones (AQs) is found to be close to 90°. Contrary to the prevailing notion that the interaction between orthogonal units is negligible due to broken π-electron conjugation, the coupling between neighboring AQ units does not have a minimum at 90° and is much larger than that expected. The unexpectedly large electronic coupling between orthogonal AQ units is explained by the interaction between the lone pairs of the carbonyl oxygen and the π system of the neighboring unit, which allows favorable overlap between frontier molecular orbitals at the orthogonal geometry. It is shown that this effect, which is described computationally for the first time, can be strengthened by adding more quinone units. The effect of thermal fluctuations on the couplings is assessed through ab initio molecular dynamics simulations. The distributions of the couplings reveal that electron transport is resilient to dynamic disorder in all systems considered, whereas the hole couplings are much more sensitive to disorder. Lone pair-π interactions are described, as a previously largely overlooked conjugation mechanism, for incorporation into a new class of disorder-resilient semiconducting redox polymers.

Toward Design of Novel Materials for Organic Electronics

Materials for organic electronics are presently used in prominent applications, such as displays in mobile devices, while being intensely researched for other purposes, such as organic photovoltaics, large-area devices, and thin-film transistors. Many of the challenges to improve and optimize these applications are material related and there is a nearly infinite chemical space that needs to be explored to identify the most suitable material candidates. Established experimental approaches struggle with the size and complexity of this chemical space. Herein, the development of simulation methods is addressed, with a particular emphasis on predictive multiscale protocols, to complement experimental research in the identification of novel materials and illustrate the potential of these methods with a few prominent recent applications. Finally, the potential of machine learning and methods based on artificial intelligence is discussed to further accelerate the search for new materials.

Effects of Disorder on Thermoelectric Properties of Semiconducting Polymers

Organic materials have attracted recent interest as thermoelectric (TE) converters due to their low cost and ease of fabrication. We examine the effects of disorder on the TE properties of semiconducting polymers based on the Gaussian disorder model (GDM) for site energies while employing Pauli's master equation approach to model hopping between localized sites. Our model is in good agreement with experimental results and a useful tool to study hopping transport. We show that stronger overlap between sites can improve the electrical conductivity without adversely affecting the Seebeck coefficient. We find that positional disorder aids the formation of new conduction paths with an increased probability of carriers in high energy sites, leading to an increase in electrical conductivity while leaving the Seebeck unchanged. On the other hand, energetic disorder leads to increased energy gaps between sites, hindering transport. This adversely affects conductivity while only slightly increasing Seebeck and results in lower TE power factors. Furthermore, positional correlation primarily affects conductivity, while correlation in site energies has no effect on TE properties of polymers. Our results also show that the Lorenz number increases with Seebeck coefficient, largely deviating from the Sommerfeld value, in agreement with experiments and in contrast to band conductors. We conclude that reducing energetic disorder and positional correlation, while increasing positional disorder can lead to higher TE power factors.

Generalized Kinetic Monte Carlo Framework for Organic Electronics

In this paper, we present our generalized kinetic Monte Carlo (kMC) framework for the simulation of organic semiconductors and electronic devices such as solar cells (OSCs) and light-emitting diodes (OLEDs). Our model generalizes the geometrical representation of the multifaceted properties of the organic material by the use of a non-cubic, generalized Voronoi tessellation and a model that connects sites to polymer chains. Herewith, we obtain a realistic model for both amorphous and crystalline domains of small molecules and polymers. Furthermore, we generalize the excitonic processes and include triplet exciton dynamics, which allows an enhanced investigation of OSCs and OLEDs. We outline the developed methods of our generalized kMC framework and give two exemplary studies of electrical and optical properties inside an organic semiconductor.

Getting excited: challenges in quantum-classical studies of excitons in polymeric systems

A combination of classical molecular dynamics (MM/MD) and quantum chemical calculations based on the density functional theory (DFT) was performed to describe the conformational properties of diphenylethyne (DPE), methylated-DPE and poly para phenylene ethynylene (PPE). DFT calculations were employed to improve and develop force field parameters for MM/MD simulations. Many-body Green's function theory within the GW approximation and the Bethe-Salpeter (GW-BSE) equation were utilized to describe the excited states of the systems. The reliability of the excitation energies based on the MM/MD conformations was examined and compared to the excitation energies from DFT conformations. The results show an overall agreement between the optical excitations based on MM/MD conformations and DFT conformations. This allows for the calculation of excitation energies based on MM/MD conformations.

Charge-patching method for the calculation of electronic structure of polypeptides

Based on the CPM method, the charge densities of polypeptides can be generated and their electronic structure can be further calculated.

Charge carrier mobility of disordered organic semiconductors with correlated energetic and spatial disorder

Kinetic Monte Carlo study of the impact of spatial and energetic disorder on charge mobility, current distribution and transport energy in organic semiconductors.

How Many Parameters Actually Affect the Mobility of Conjugated Polymers?

We describe charge transport along a polymer chain with a generic theoretical model depending in principle on tens of parameters, reflecting the chemistry of the material. The charge carrier states are obtained from a model Hamiltonian that incorporates different types of disorder and electronic structure (e.g., the difference between homo- and copolymer). The hopping rate between these states is described with a general rate expression, which contains the rates most used in the literature as special cases. We demonstrate that the steady state charge mobility in the limit of low charge density and low field ultimately depends on only two parameters: an effective structural disorder and an effective electron-phonon coupling, weighted by the size of the monomer. The results support the experimental observation [N. I. Craciun, J. Wildeman, and P. W. M. Blom, Phys. Rev. Lett. 100, 056601 (2008)PRLTAO0031-900710.1103/PhysRevLett.100.056601] that the mobility in a broad range of (polymeric) semiconductors follows a universal behavior, insensitive to the chemical detail.

Simulating charge transport in organic semiconductors and devices: a review

Charge transport simulation can be a valuable tool to better understand, optimise and design organic transistors (OTFTs), photovoltaics (OPVs), and light-emitting diodes (OLEDs). This review presents an overview of common charge transport and device models; namely drift-diffusion, master equation, mesoscale kinetic Monte Carlo and quantum chemical Monte Carlo, and a discussion of the relative merits of each. This is followed by a review of the application of these models as applied to charge transport in organic semiconductors and devices, highlighting in particular the insights made possible by modelling. The review concludes with an outlook for charge transport modelling in organic electronics.

Probing the relation between charge transport and supramolecular organization down to ångström resolution in a benzothiadiazole-cyclopentadithiophene copolymer

Molecular modeling shows that longitudinal displacement of the backbones by a couple of ångströms has a profound impact on the electronic coupling mediating charge transport in a conjugated copolymer. These changes can be probed by monitoring the calculated X-ray scattering patterns and NMR chemical shifts as a function of sliding of the polymer chains and comparing them to experiment.

Polymeric Thin Films for Organic Electronics: Properties and Adaptive Structures

This review deals with the correlation between morphology, structure and performance of organic electronic devices including thin film transistors and solar cells. In particular, we report on solution processed devices going into the role of the 3D supramolecular organization in determining their electronic properties. A selection of case studies from recent literature are reviewed, relying on solution methods for organic thin-film deposition which allow fine control of the supramolecular aggregation of polymers confined at surfaces in nanoscopic layers. A special focus is given to issues exploiting morphological structures stemming from the intrinsic polymeric dynamic adaptation under non-equilibrium conditions.

Electron and Hole Contributions to the Terahertz Photoconductivity of a Conjugated Polymer:Fullerene Blend Identified

Time-resolved terahertz spectroscopy was employed for the investigation of charge-transport dynamics in benzothiadiazolo-dithiophene polyfluorene ([2,7-(9,9-dioctyl-fluorene)-alt-5,5-(4',7'-di-2-thienyl-2',1',3'-benzothiadiazole)]) (APFO-3) polymers with various chain lengths and in its monomer form, all blended with an electron acceptor ([6,6]-phenyl-C61-butyric acid methyl ester, PCBM). Upon photoexcitation, charged polaron pairs are created, negative charges are transferred to fullerenes, while positive polarons remain on polymers/monomers. Vastly different hole mobility in polymer and monomer blends allows us to distinguish the hole and electron contributions to the carrier mobility.

Design rules for charge-transport efficient host materials for phosphorescent organic light-emitting diodes

The use of blue phosphorescent emitters in organic light-emitting diodes (OLEDs) imposes demanding requirements on a host material. Among these are large triplet energies, the alignment of levels with respect to the emitter, the ability to form and sustain amorphous order, material processability, and an adequate charge carrier mobility. A possible design strategy is to choose a π-conjugated core with a high triplet level and to fulfill the other requirements by using suitable substituents. Bulky substituents, however, induce large spatial separations between conjugated cores, can substantially reduce intermolecular electronic couplings, and decrease the charge mobility of the host. In this work we analyze charge transport in amorphous 2,8-bis(triphenylsilyl)dibenzofuran, an electron-transporting material synthesized to serve as a host in deep-blue OLEDs. We show that mesomeric effects delocalize the frontier orbitals over the substituents recovering strong electronic couplings and lowering reorganization energies, especially for electrons, while keeping energetic disorder small. Admittance spectroscopy measurements reveal that the material has indeed a high electron mobility and a small Poole-Frenkel slope, supporting our conclusions. By linking electronic structure, molecular packing, and mobility, we provide a pathway to the rational design of hosts with high charge mobilities.

First-principles prediction of charge mobility in carbon and organic nanomaterials

We summarize our recent progresses in developing first-principles methods for predicting the intrinsic charge mobility in carbon and organic nanomaterials, within the framework of Boltzmann transport theory and relaxation time approximation. The electron-phonon couplings are described by Bardeen and Shockley's deformation potential theory, namely delocalized electrons scattered by longitudinal acoustic phonons as modeled by uniform lattice dilation. We have applied such methodology to calculating the charge carrier mobilities of graphene and graphdiyne, both sheets and nanoribbons, as well as closely packed organic crystals. The intrinsic charge carrier mobilities for graphene sheet and naphthalene are calculated to be 3 × 10(5) and ∼60 cm(2) V(-1) s(-1) respectively at room temperature, in reasonable agreement with previous studies. We also present some new theoretical results for the recently discovered organic electronic materials, diacene-fused thienothiophenes, for which the charge carrier mobilities are predicted to be around 100 cm(2) V(-1) s(-1).

Microscopic Simulations of Charge Transport in Disordered Organic Semiconductors

Charge carrier dynamics in an organic semiconductor can often be described in terms of charge hopping between localized states. The hopping rates depend on electronic coupling elements, reorganization energies, and driving forces, which vary as a function of position and orientation of the molecules. The exact evaluation of these contributions in a molecular assembly is computationally prohibitive. Various, often semiempirical, approximations are employed instead. In this work, we review some of these approaches and introduce a software toolkit which implements them. The purpose of the toolkit is to simplify the workflow for charge transport simulations, provide a uniform error control for the methods and a flexible platform for their development, and eventually allow in silico prescreening of organic semiconductors for specific applications. All implemented methods are illustrated by studying charge transport in amorphous films of tris-(8-hydroxyquinoline)aluminum, a common organic semiconductor.

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.