2.2. Materials 929 2.3. Factors Influencing Charge Mobility 931 2.3.1. Molecular Packing 931 2.3.2. Disorder 932 2.3.3. Temperature 933 2.3.4. Electric Field 934 2.3.5. Impurities 934 2.3.6. Pressure 934 2.3.7. Charge-Carrier Density 934 2.3.8. Size/molecular Weight 935 3. The Charge-Transport Parameters 935 3.1. Electronic Coupling 936 3.1.1. The Energy-Splitting-in-Dimer Method 936 3.1.2. The Orthogonality Issue 937 3.1.3. Impact of the Site Energy 937 3.1.4. Electronic Coupling in Oligoacene Derivatives 938

Charge transport in organic semiconductors.

Conjugated polymer chains have many degrees of conformational freedom and interact weakly with each other, resulting in complex microstructures in the solid state. Understanding charge transport in such systems, which have amorphous and ordered phases exhibiting varying degrees of order, has proved difficult owing to the contribution of electronic processes at various length scales. The growing technological appeal of these semiconductors makes such fundamental knowledge extremely important for materials and process design. We propose a unified model of how charge carriers travel in conjugated polymer films. We show that in high-molecular-weight semiconducting polymers the limiting charge transport step is trapping caused by lattice disorder, and that short-range intermolecular aggregation is sufficient for efficient long-range charge transport. This generalization explains the seemingly contradicting high performance of recently reported, poorly ordered polymers and suggests molecular design strategies to further improve the performance of future generations of organic electronic materials. The recent demonstration that highly disordered polymer films can transport charges as effectively as polycrystalline semiconductors has called into question the relationship between structural order and mobility in organic materials. It is now shown that, in high-molecular-weight polymers, efficient charge transport is allowed due to a network of interconnected aggregates that are characterized by short-range order.

A general relationship between disorder, aggregation and charge transport in conjugated polymers

2.3. Medical Devices and Sensors 9 2.4. Radio Frequency Applications 10 3. Materials 12 3.1. Organic Electronics Materials 12 3.2. Semiconducting Polymer Design 13 3.3. Poly(3-alkylthiophenes) 14 3.4. Poly(thieno(3,2-b)thiophenes 15 3.5. Benchmark Polymer Semiconductors 15 3.6. High Performance Polymer Semiconductors 15 4. Device Stability 16 4.1. Bias Stress in Organic Transistors 17 4.1.1. Bias Stress Characterization 17 4.1.2. Bias Stress Mechanism 18 4.2. Short Channel Effects in Organic Transistors 19 5. Materials Patterning and Integration 20 6. Conclusions 22 7. Acknowledgments 22 8. References 22

Materials and applications for large area electronics: solution-based approaches.

Organic (opto)electronic materials have received considerable attention due to their applications in thin-film-transistors, light-emitting diodes, solar cells, sensors, photorefractive devices, and many others. The technological promises include low cost of these materials and the possibility of their room-temperature deposition from solution on large-area and/or flexible substrates. The article reviews the current understanding of the physical mechanisms that determine the (opto)electronic properties of high-performance organic materials. The focus of the review is on photoinduced processes and on electronic properties important for optoelectronic applications relying on charge carrier photogeneration. Additionally, it highlights the capabilities of various experimental techniques for characterization of these materials, summarizes top-of-the-line device performance, and outlines recent trends in the further development of the field. The properties of materials based both on small molecules and on conjug...

Organic Optoelectronic Materials: Mechanisms and Applications

Organic solar cells have the potential to be low-cost and efficient solar energy converters, with a promising energy balance. They are made of carbon-based semiconductors, which exhibit favourable light absorption and charge generation properties, and can be manufactured by low temperature processes such as printing from solvent-based inks, which are compatible with flexible plastic substrates or even paper. In this review, we will present an overview of the physical function of organic solar cells, their state-of-the-art performance and limitations, as well as novel concepts to achieve a better material stability and higher power conversion efficiencies. We will also briefly review processing and cost in view of the market potential.

https://iopscience.iop.org/article/10.1088/0034-4885/73/9/096401/pdf

Polymer–fullerene bulk heterojunction solar cells

From a numerical solution of the master equation for hopping transport in a disordered energy landscape with a Gaussian density of states, we determine the dependence of the charge-carrier mobility on temperature, carrier density, and electric field. Experimental current-voltage characteristics in devices based on semiconducting polymers are excellently reproduced with this unified description of the mobility. At room temperature it is mainly the dependence on carrier density that plays an important role, whereas at low temperatures and high fields the electric field dependence becomes important. Omission in the past of the carrier-density dependence has led to an underestimation of the hopping distance and the width of the density of states in these polymers.

/pdf/unified-description-of-charge-carrier-mobilities-in-1jhj71d3g1.pdf

Unified Description of Charge-Carrier Mobilities in Disordered Semiconducting Polymers

We present a scaling theory for charge transport in disordered molecular semiconductors that extends percolation theory by including bonds with conductances close to the percolating one in the random-resistor network representing charge hopping. A general and compact expression is given for the charge mobility for Miller-Abrahams and Marcus hopping on different lattices with Gaussian energy disorder, with parameters determined from numerically exact results. The charge-concentration dependence is universal. The model-specific temperature dependence can be used to distinguish between the hopping models.

/pdf/scaling-theory-for-percolative-charge-transport-in-2rnthr5l7o.pdf

Scaling theory for percolative charge transport in disordered molecular semiconductors.

We model charge transport in disordered semiconducting polymers by hopping of charges on a regular cubic lattice of sites. A large on-site Coulomb repulsion prohibits double occupancy of the sites. Disorder is introduced by taking random site energies from a Gaussian distribution. Recently, it was demonstrated that this model leads to a dependence of the charge-carrier mobilities on the density of charge carriers that is in agreement with experimental observations. The model is conveniently solved within a mean-field approximation, in which the correlation between the occupational probabilities of different sites is neglected. This approximation becomes exact in the limit of vanishing charge-carrier densities, but needs to be checked at high densities. We perform this check by dividing the lattice in pairs of neighboring sites and taking into account the correlation between the sites within each pair explicitly. This pair approximation is expected to account for the most important corrections to the mean-field approximation. We study the effects of varying temperature, charge-carrier density, and electric field. We demonstrate that in the parameter regime relevant for semiconducting polymers used in practical devices the corrections to the mobilities calculated from the mean-field approximation will not exceed a few percent, so that this approximation can be safely used.

/pdf/calculating-charge-carrier-mobilities-in-disordered-m3vd78giqp.pdf

Calculating charge-carrier mobilities in disordered semiconducting polymers: Mean field and beyond

We recently introduced a scaling theory for charge transport in molecular semiconductors with uncorrelated Gaussian energetic disorder, considering Miller-Abrahams as well as Marcus hopping and different lattice structures [ Cottaar et al. Phys. Rev. Lett. 107 136601 (2011)]. A compact expression was derived for the dependence of the charge-carrier mobility on temperature and carrier concentration. We show here that for Miller-Abrahams hopping the theory can also be applied to non-Gaussian energetic disorder, without parameter changes. Moreover, we show how it can be applied to correlated energetic disorder as obtained from randomly oriented molecular dipoles, which experiments suggest to be often more suitable. The same compact expression still describes the charge-carrier mobility, with new parameter values as determined from numerically exact results. The critical scaling exponent for correlated disorder is about twice as large as for uncorrelated disorder, which is caused by a different topology of the percolating network. The temperature dependence of the mobility for correlated disorder is significantly weaker than for uncorrelated disorder, while the carrier-concentration dependence is slightly weaker, due to small deviations of the density of states from a Gaussian. We indicate how comparison with experiments could distinguish between the different models.

/pdf/scaling-theory-for-percolative-charge-transport-in-molecular-3mi37pwkov.pdf

Scaling theory for percolative charge transport in molecular semiconductors: Correlated versus uncorrelated energetic disorder

We model charge transport in disordered semiconducting polymers by hopping of charge carriers on a square lattice of sites with Gaussian on-site energy disorder, using Fermi-Dirac statistics. From numerically exact solutions of the Master equation, we study the dependence of the charge-carrier mobility on temperature, carrier density, and electric field. Our results are used in calculating current-voltage characteristics of hole-only polymer diodes. It is found that very good fits to experimental current-voltage characteristics can be obtained at different temperatures, with reasonable fitting parameters for the width of the Gaussian density of states and the lattice constant. In agreement with the experiments we find that the density dependence is dominant over the field dependence. Only at high fields and low temperatures the field dependence becomes noticeable. The potential and current distribution show strong inhomogeneities, which may have important consequences for the operation of polymer opto-electronic devices.

/pdf/charge-carrier-mobilities-in-disordered-semiconducting-87my7hxalt.pdf

J Jeroen Cottaar

Papers

Unified Description of Charge-Carrier Mobilities in Disordered Semiconducting Polymers

Scaling theory for percolative charge transport in disordered molecular semiconductors.

Calculating charge-carrier mobilities in disordered semiconducting polymers: Mean field and beyond

Scaling theory for percolative charge transport in molecular semiconductors: Correlated versus uncorrelated energetic disorder

Charge‐carrier mobilities in disordered semiconducting polymers: effects of carrier density and electric field