Charge Diffusion in Semiconducting Polymers: Analytical Relation between Polymer Rigidity and Time Scales for Intrachain and Interchain Hopping

Screening semiconducting polymers to discover design principles for tuning charge carrier mobility

We employ a rapid method for computing the electronic structure and orbital localization characteristics for a sample of 36 different polymer backbone structures. This relatively large sample derived from recent literature is used to identify the features of the monomer sequence that lead to greater charge delocalization and, potentially, greater charge mobility. Two characteristics contributing in equal measure to large localization length are the reduced variation of the coupling between adjacent monomers due to conformational fluctuations and the presence of just two monomers in the structural repeating units. For such polymers a greater mismatch between the HOMO orbitals of the fragments and, surprisingly, a smaller coupling between them is shown to favour greater delocalization of the orbitals. The underlying physical reasons for such observations are discussed and explicit and constructive design rules are proposed.

Local structuring of diketopyrrolopyrrole (DPP)-based oligomers from molecular dynamics simulations

The microscopic structure of high mobility semiconducting polymers is known to be essential for their performance but it cannot be easily deduced from the available experimental data. A series of short oligomers of diketopyrrolopyrrole (DPP)-based materials that display high charge mobility are studied by molecular dynamics simulations to understand their local structuring at an atomic level. Different analyses are proposed to compare the ability of different oligomers to form large aggregates and their driving force. The simulations show that the tendency for this class of materials to form aggregates is driven by the interaction between DPP fragments, but this is modulated by the other conjugated fragments of the materials which affect the rigidity of the polymer and, ultimately, the size of the aggregates that are formed. The main structural features and the electronic structure of the oligomers are fairly similar above the glass transition temperature and at room temperature.

Rapid Method for Calculating the Conformationally Averaged Electronic Structure of Conjugated Polymers

We developed a rapid method to calculate the average electronic structure properties of large ensembles of conjugated polymer chains sampling their conformational space. This is achieved by using the localized molecular orbital (MO) method to rapidly compute the MOs and their energies for isolated polymer chains and through using a calibration scheme to further correct the obtained energies by comparison with a few accurate calculations. The method is applied to the study of the density of states and orbital localization characteristics for five polymers. It is shown that all key properties of the individual chain related to the charge mobility can be rationalized in terms of the properties of the constituent monomers, their interaction, and the conformational flexibility of the chain. More specifically we identify the features that lead to greater charge delocalization. Finally, we discuss the prospect of using this method for a computational high-throughput screening of conjugated polymers.

Redox-Active Polymeric Ionic Liquids with Pendant N-Substituted Phenothiazine

Polymers that are elastic while supporting charge transport are desirable for flexible and soft electronics. Many polymers with bulky and conjugated redox-active pendant units have high glass transition temperatures (T_g) in their neutral form that will not lead to elasticity at room temperature. Their behavior in charged form in the solid state without an electrolyte has not been extensively studied. Here, the design strategy of polymeric ionic liquid where two weakly interacting ionic groups are used to maintain a low T_g is shown to lead to flexible redox active polymers. The use of a flexible ethylene backbone and redox-active phenothiazine (PTZ)-based pendant group resulted in polymers with relatively low T_g that are electrically conductive. PTZ that was N-substituted with 2-(2-ethoxyethoxy)ethoxy)ethyl was found to promote solubility of the polymer and lower the T_g of the neutral polymer by ∼150 °C relative to that of the T_g of a variant without the N-substituent. Doping with trifluoromethanesulfonimide leads to an electrically conductive polymer without significantly increasing the T_g. Physical characterization by UV-vis-NIR spectroscopy, electron spin resonance spectroscopy, and impedance spectroscopy verified that the molecular design leads to an efficient charge hopping between the PTZ groups.

Thermally activated charge transport in carbon atom chains

Charge transport through single molecules is at the heart of molecular electronics for realizing the practical use of the rich quantum characteristics of electrode-molecule-electrode systems. Despite the extensive studies reported in the past, little experimental efforts have been focused on the electron transport mechanism at a temperature higher than the ambient temperature. In this work, we have reported the observation of the subtle interplay between electron tunneling and charge hopping in carbon chains connected to two Au electrodes at elevated temperatures. We measured the single-molecule conductance of Au-alkanedithiol-Au molecular junctions at various temperatures from 300 K to 420 K in vacuum. The temperature dependence of conductance suggested substantial roles of superexchange with inter-chain charge hopping under elevated temperatures for alkane chains longer than heptane. This finding provides a guide to design functional molecular junctions under practical conditions.

Tuning the Ambipolar Character of Copolymers with Substituents: A Density Functional Theory Study

Ambipolar copolymers play a vital role in reducing the cost and simplifying the fabrication of ambipolar organic field-effect transistors (OFETs). However, the development of them lags behind that of p-type and n-type copolymers. Herein, we aim to obtain ambipolar copolymers by introducing appropriate substituents into DPP-TVT [diketopyrrolopyrrole-(E)-1,2-di(2-thienyl)ethane]. We study the effects of substituents (-NH₂, -OCH₃, -F, -CF₃, and -CN) on backbone planarity, electronic structures, and charge carrier mobility by density functional simulations. Electronic structure analyses show that the CN-substituted DPP-TVT lies in the trap-free energy window and has the narrowest band gap, suggesting promising ambipolar character. This was further confirmed by the results of its charge carrier mobility along both intra- and interchain directions. Besides the -CN group, the -NH₂ group also proved to be effective in turning DPP-TVT into the ambipolar copolymer. Our study provides insights into modulating the performances of OFETs by introducing appropriate substituents into the copolymers to achieve ambipolar character.

Exploring Disordered Morphologies of Blends and Block Copolymers for Light-Emitting Diodes with Mesoscopic Simulations

Recently, disordered blends of semiconducting and insulating polymers have been used to prepare light-emitting diodes with increased luminous efficiency. Because the thermodynamic stability of the disordered phase in blends is limited, equivalent diblock copolymers (BCPs) could be an alternative. However, the choice between disordered blends and BCPs requires understanding structural differences and their effect on charge carrier transport. Using a hybrid mesoscopic model, we simulate blends and equivalent BCPs of two representative semiconducting and insulating polymers: poly(p-phenylene vinylene) (PPV) and polyacrylate. The immiscibility is varied to mimic annealing at different temperatures. We find stable or metastable disordered morphologies until we reach the mean-field (MF) spinodal. Disordered morphologies are heterogeneous because of thermal fluctuations and local segregation. Near the MF spinodal, segregation is stronger in BCPs than in the blends, even though the immiscibility, normalized by the MF spinodal, is the same. We link the spatial distribution of PPV with electric conductance. We predict that the immiscibility (temperature at which the layer is annealed) affects electrical percolation much stronger in BCPs than in blends. Differences in the local structure and percolation between blends and BCPs are enhanced at a high insulator content.

Atomistic simulations of bulk heterojunctions to evaluate the structural and packing properties of new predicted donors in OPVs

Organic photovoltaic materials (OPVs), with low cost and structure flexibility, are of great interest and importance for their application in solar cell device development. However, the optimization of new OPV structures and the study of the structure arrangements and packing morphologies when materials are blended takes time and consumes raw materials, thus theoretical models could be of considerable value. In this work, we performed molecular dynamics simulations of present OPVs to understand the morphological packing of the donor-acceptor (DA) phases and DA heterojunction during evaporation and annealing processes, following inter and intramolecular properties like frontier orbitals, π-π stacking, coordination, distances, angles, and aggregation. Our considered donor molecules were selected from already proved experimental studies and also from predicted optimal compounds, designed through high throughput studies. The acceptor molecule employed in all our studied systems was PCBM ([6,6]-phenyl-C61-butyric acid methyl ester). Furthermore, we also analyze the influence of including different lateral aliphatic chains on the structural properties of the resulting DA packing morphologies. Our results can guide the design of new OPVs and subsequent studies applying charge transport and charge separation models.

Tying Together Multiscale Calculations for Charge Transport in P3HT: Structural Descriptors, Morphology, and Tie-Chains

Evaluating new, promising organic molecules to make next-generation organic optoelectronic devices necessitates the evaluation of charge carrier transport performance through the semi-conducting medium. In this work, we utilize quantum chemical calculations (QCC) and kinetic Monte Carlo (KMC) simulations to predict the zero-field hole mobilities of ∼100 morphologies of the benchmark polymer poly(3-hexylthiophene), with varying simulation volume, structural order, and chain-length polydispersity. Morphologies with monodisperse chains were generated previously using an optimized molecular dynamics force-field and represent a spectrum of nanostructured order. We discover that a combined consideration of backbone clustering and system-wide disorder arising from side-chain conformations are correlated with hole mobility. Furthermore, we show that strongly interconnected thiophene backbones are required for efficient charge transport. This definitively shows the role "tie-chains" play in enabling mobile charges in P3HT. By marrying QCC and KMC over multiple length- and time-scales, we demonstrate that it is now possible to routinely probe the relationship between molecular nanostructure and device performance.

Glassy phases in organic semiconductors

Organic semiconductors may be processed from fluids using graphical arts printing and patterning techniques to create complex circuitry. Because organic semiconductors are weak van der Waals solids, the creation of glassy phases during processing is quite common. Because structural disorder leads to electronic disorder, it is necessary to understand these phases to optimize and control the electronic properties of these materials. Here we review the significance of glassy phases in organic semiconductors. We examine challenges in the measurement of the glass transition temperature and the accurate classification of phases in these relatively rigid materials. Device implications of glassy phases are discussed. Processing schemes that are grounded in the principles of glass physics and sound glass transition temperature measurement will more quickly achieve desired structure and electronic characteristics, accelerating the exciting progress of organic semiconductor technology development.

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.

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.

Anomalous Charge Transport in Conjugated Polymers Reveals Underlying Mechanisms of Trapping and Percolation

While transport in conjugated polymers has many similarities to that in crystalline inorganic materials, several key differences reveal the unique relationship between the morphology of polymer films and the charge mobility. We develop a model that directly incorporates the molecular properties of the polymer film and correctly predicts these unique transport features. At low degree of polymerization, the increase of the mobility with the polymer chain length reveals trapping at chain ends, and saturation of the mobility at high degree of polymerization results from conformational traps within the chains. Similarly, the inverse field dependence of the mobility reveals that transport on single polymer chains is characterized by the ability of the charge to navigate around kinks and loops in the chain. These insights emphasize the connection between the polymer conformations and the transport and thereby offer a route to designing improved device morphologies through molecular design and materials processing.

A Comprehensive study of the Effects of Chain Morphology on the Transport Properties of Amorphous Polymer Films

Organic semiconductors constitute one of the main components underlying present-day paradigm shifting optoelectronic applications. Among them, polymer based semiconductors are deemed particularly favorable due to their natural compatibility with low-cost device fabrication techniques. In light of recent advances in the syntheses of these classes of materials, yielding systems exhibiting charge mobilities comparable with those found in organic crystals, a comprehensive study of their charge transport properties is presented. Among a plethora of effects arising from these systems morphological and non morphological attributes, it is shown that a favorable presence of several of these attributes, including that of rapid on-chain carrier propagation and the presence of elongated conjugation segments, can lead to an enhancement of the system's mobility by more than 5 orders of magnitude with respect to 'standard' amorphous organic semiconductors. New insight for the formulation of new engineering strategies for next generation polymer based semiconductors is thus gathered.

Percolation, Tie-Molecules, and the Microstructural Determinants of Charge Transport in Semicrystalline Conjugated Polymers

Semiconducting polymers play an important role in a wide range of optical and electronic material applications. It is widely accepted that the polymer ordering impacts charge transport in such devices. However, the connection between molecular ordering and device performance is difficult to predict due to the current need for a mathematical theory of the physics that dictate charge transport in semiconducting polymers. We present an analytical and computational description of semicrystalline conjugated polymer materials that captures the impact of polymer conformation on charge transport in heterogeneous thin films. We first develop an analytical theory for the statistical behavior of a polymer chain emanating from a crystallite, predicting the average distance to the first kink that would trap a charge. This analysis is used to define the conditions where percolation would lead to efficient transport through a semicrystalline material. We then establish a model that predicts the multiscale charge transport. This model is used to identify the speed limits of charge transport at short and long time scales for varying fraction of crystallinity. This work provides a rational framework to connect molecular organization to device performance.

The Next Breakthrough for Organic Photovoltaics?

While the intense focus on energy level tuning in organic photovoltaic materials has afforded large gains in device performance, we argue here that strategies based on microstructural/morphological control are at least as promising in any rational design strategy. In this work, a meta-analysis of ∼150 bulk heterojunction devices fabricated with different materials combinations is performed and reveals strong correlations between power conversion efficiency and morphology-dominated properties (short-circuit current, fill factor) and surprisingly weak correlations between efficiency and energy level positioning (open-circuit voltage, enthalpic offset at the interface, optical gap). While energy level positioning should in principle provide the theoretical maximum efficiency, the optimization landscape that must be navigated to reach this maximum is unforgiving. Thus, research aimed at developing understanding-based strategies for more efficient optimization of an active layer microstructure and morphology are likely to be at least as fruitful.

Multi-length-scale relationships between the polymer molecular structure and charge transport: the case of poly-naphthalene diimide bithiophene

Charge transport in organic polymer semiconductors is a complex phenomenon affected by structural and electronic properties ranging over different length scales, from the molecular one up to the macro-scale.

Narrower bands with better charge transport: the counterintuitive behavior of semiconducting copolymers

The narrower bands formed by donor-acceptor polymers are not detrimental to transport, as the reduced electronic coupling along the chain is more than compensated by a reduced activation energy for transport. These polymers are less sensitive to the conformational disorder of the chain as long as the bandwidth is larger than a threshold.