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## Charge transport in organic materials

#### University of Bremen, Germany

#### Organisers

Charge transport modelling of organic materials is an extremely challenging and interdisciplinary field. This is due to the wide variety of transport regimes, the crucial role played by defects, chemical environment, thermal fluctuations, mesoscopic and microscopic morphology of the material. The electronic states themselves can be delocalized (bandlike or small polaron models), strongly localized (hopping models, or big polaron) or dynamically localized by the adiabatic coupling with the nuclear structure and the surrounding environment (DNA, Liquid Crystals). Building a solid theoretical framework to describe charge transport in such materials is still a challenge, and it is of fundamental importance to support the engineering of optoelectronic devices with reliable simulation tools. Different models have been proposed, such as Gaussian Disordered Models, Polaron Band Transport and Time Resolved Wave Function Propagation. The aim of the proposed workshop is to get the main theoretical and experimental contributors together and investigate the range of applicability of the different models and their comparability with state-of-art available experimental techniques. By this, we will find the limitations and propose possible improvements in order to investigate possible multidisciplinar synergies and the integration of different models in multiphysics/multiscale simulation schemes, with the goal of realizing end-user Computer Aided Design (CAD) tools for organic electronics.

Several efforts have been devoted to understanding charge transport properties of organic materials in the last years, due to the impressive growth in the number of proposed electronic devices based on organic compounds. A wide class of organic conjugated materials exhibiting semiconducting or metallic properties have been employed as constitutive material for the realization of transistors (TFT, OFET) [1, 2, 3], Organic Light Emitting Devices (OLED) [4], solar cells [5, 6, 7]. Besides available applications, the enormous interest in understanding charge transport in organic materials comes from the potential applications in the fields of biocompatible and biodegradable sensors and DNA sequencing [8]. Being a field of interest with such a wide range of application, from consumer electronics to energy harvesting to healthcare, the impressive amount of academic and industrial research in this direction is easily justified.

Nevertheless, a comprehensive solid theoretical framework on charge transport in organic materials is missing. Due to the large number of physical and chemical phenomena involved, a reliable modelling of such materials and devices is extremely challenging. Charge transport is generally well understood only in two limiting cases: bandlike transport in highly crystalline materials and hopping transport in highly disordered materials.

In ordered crystalline systems, where translational invariance is preserved, the carriers are unlocalized on a large number of unit cells and the charge transport physics resembles the behaviour of a crystalline semiconductor. In a tight binding picture, this means that the coupling between adjacent sites is much bigger compared to any contribution due to the interaction with the environment, i.e. electron-phonon, electron-electron and defect scattering can be included as effective collision rates in a semiclassical approach, and extensions of Drude model have been used, possibly including local electron-phonon correction [9] or grain boundaries effects [10]. For devices or molecular chains shorter than the smallest collision length, the semiclassical picture fails but it’s still possible to tackle the transport problem using Non Equilibrium Green’s Function [11, 12], where interactions can be included as a renormalization in the quasi-particle picture.

In amorphous organic material the translational symmetry is broken, and it is reasonable to question whether the unlocalized picture will hold. In inorganic amorphous material, it’s well known from the pioneering work of Mott [13] and several others that localized states the conductance can be non zero, and the process leading to carrier transport is thermally activated hopping. In this model the electron-phonon interaction dominates the transport [9] and can be hardly captured within a small perturbation picture. Parameter-free multiscale schemes have been proposed by several authors. Simple phenomenological Miller-Abrahams hopping rates can be used when the electron-phonon coupling is weak; Marcus-Hush [14] theory can be used for systems with a strong electron-phonon adiabatic coupling [15]. The parameters are usually calculated on a on subset of structures. The QC calculation of hopping rates is then combined with Molecular Dynamics in a Kinetic Monte Carlo simulation to extract the charge mobility [16, 17]. The advantage of these scheme is that they rely on a multiscale approach which allows to calculate mobility on a scale length of hundred nanometers, hence taking into account static disorder due to morphology fluctuations. A similar multiscale scheme, based on a Master Equation approach in a 4 step calculation, has been proposed by Vukmirovic and Wang [18]. These model can include static disorder and large polaron effects, but clearly some assumptions on the molecular orbital involved in the charge transfer process must be done and it is therefore hard, if not impossible, to capture more complicated situation where the localization of the charge itself depends on nuclear motion on a wide range of frequencies.

Besides these limiting cases, a large system can be in an intermediate regime where dynamic and static disorder are combined. The electron-phonon interactions, considered in general as the interaction between the electronic and the nuclear degrees of freedom and thus including electron-vibron coupling (polaron), can exhibit dynamic fluctuations in the same order of magnitude of intermolecular couplings [19]. In this regime, the carriers themselves are nearly localized. Their localization is dynamically depending on thermal fluctuations, with a characteristic localized carrier residence time in the order of hundreds of femtoseconds, such that spectroscopy measurements can lead to ambiguous results. Such a mechanism has been proposed to apply to crystalline organic semiconductors [20], discotic liquid crystal [19] and DNA strands [21]. Different techniques have been proposed to calculate charge mobility, including multiscale approach combining Classical Molecular Dynamics (CMD), ab-initio Density Functional Theory (DFT) and Langevin Dynamics [19], combining CMD and semi-empirical DFT with Born-Oppenheimer [22] or Ehrenfest [21] wave function propagation or Green’s function coherent transport [23].

In conclusion, the landscape of theoretical techniques available to model organic electronics is very wide, due mainly to the interplay between dynamic and static disorder [24]. Difficulties that arise from the same disorder lead to a large deviation of experimental measurements of quantities of interest such as mobility. Moreover, to take into account different kind of disorder, we must necessarily rely on multiscale techniques, since a comprehensive quantum treatment of a device several computationally unmanageable. Hence, a joint effort between the experimental and theoretical community should be aimed to the possible integration of different simulation techniques in multiscale schemes, a clear understanding of their range of applicability and their degree of accuracy respect to different kind of disorder.

## References

**Germany**

Denis Andrienko (Max Planck Institute for Polymer Research) - Organiser & speaker

Marcus Elstner (Karlsruhe Institute of Technology) - Organiser

Thomas Frauenheim (University of Bremen) - Organiser

Gabriele Penazzi (University of Bremen, BCCMS) - Organiser

**Italy**

Aldo Di Carlo (University of Rome "Tor Vergata") - Organiser