The (Non-)Local Density of States of Electronic Excitations in Organic Semiconductors

The rational design of organic semiconductors for optoelectronic devices relies on a detailed understanding of how their molecular and morphological structure condition the energetics and dynamics of charged and excitonic states. Investigating the role of molecular architecture, conformation, orientation and packing, this work reveals mechanisms that shape the spatially resolved densities of states in organic, small-molecular and polymeric heterostructures and mesophases. The underlying computational framework combines multiscale simulations of the material morphology at atomistic and coarse-grained resolution with a long-range-polarized embedding technique to resolve the electronic structure of the molecular solid. We show that long-range electrostatic interactions tie the energetics of microscopic states to the mesoscopic structure, with a qualitative and quantitative impact on charge-carrier level profiles across organic interfaces. The computational approach provides quantitative access to the charge-density-dependent open-circuit voltage of planar heterojunctions. The derived and experimentally verified relationships between molecular orientation, architecture, level profiles and open-circuit voltage rationalize the acceptor-donor-acceptor pattern for donor materials in high-performing solar cells. Proposing a pathway for barrier-less dissociation of charge transfer states, we highlight how mesoscale fields generate charge splitting and detrapping forces in systems with finite interface roughness. The associated design rules reflect the dominant role played by lowest-energy configurations at the interface

Exciton transport in molecular organic semiconductors boosted by transient quantum delocalization

Designing molecular materials with very large exciton diffusion lengths would remove some of the intrinsic limitations of present-day organic optoelectronic devices. Yet, the nature of excitons in these materials is still not sufficiently well understood. Here we present Frenkel exciton surface hopping, an efficient method to propagate excitons through truly nano-scale materials by solving the time-dependent Schrödinger equation coupled to nuclear motion. We find a clear correlation between diffusion constant and quantum delocalization of the exciton. In materials featuring some of the highest diffusion lengths to date, e.g. the non-fullerene acceptor Y6, the exciton propagates via a transient delocalization mechanism, reminiscent to what was recently proposed for charge transport. Yet, the extent of delocalization is rather modest, even in Y6, and found to be limited by the relatively large exciton reorganization energy. On this basis we chart out a path for rationally improving exciton transport in organic optoelectronic materials

Modelling charge and exciton transport in polymeric and molecular systems

In this thesis some fundamental aspects of charge transport and exciton dynamics in organic semiconductors are explored from a theoretical and computational point of view. After a brief review of the field of organic electronics, the theoretical methods most commonly used to describe exciton dynamics and charge transport are summarised, with an emphasis on the specific methods employed in this thesis (chapter 1). A very general kinetic rate of hopping between electronic states in the incoherent regime is then derived (chapter 2). This rate contains the most commonly used rates (Miller-Abrahams, Marcus, Marcus-Levich-Jortner) as special cases. The excitonic couplings between molecules determine the properties of excited states in biological and artificial molecular aggregates. A large number of excitonic couplings in these systems are computed (chapters 3 and 4) including both the Coulombic and the short-range (non-Coulombic) contributions as well as the thermal fluctuation of the coupling (dynamic disorder). The effect of thermal fluctuations in crystalline materials is found to be important when evaluating exciton dynamics (chapter 3). The short-range component of the coupling needs to be included when the interacting molecules are in close contact (chapter 3). The characteristics of charge transport in disordered polymers depend in principle on many parameters. With the aim of accounting for the complicated nature of these materials, a very general charge transport model is presented here (chapter 5). A detailed electronic structure with variable localization of the electronic states is obtained from a simple model Hamiltonian depending on just a few parameters. Using the hopping rate derived in chapter 2, the charge mobility along disordered polymer chains is computed. The proposed model includes features of both variable range hopping (VRH) and mobility edge (ME) models, but it starts from fewer assumptions. Donor-acceptor copolymers have a narrower transport band which in principle should result in lower mobility. Instead, the narrower band is found to enhance mobility if the other parameters are kept constant. By exploring the large parameter space of this model, the temperature dependence of mobility is found to follow a universal Arrhenius behaviour in agreement with experimental data (chapter 6). The activation energy for transport depends only on the effective electronic disorder of the polymer chain. When the 3D structure of the polymer chains and the role of inter-chain hopping are also considered (chapter 7), the mobility is found to be linearly dependent on the persistence length. The activation energy is found to depend only on the electronic disorder and not on chain rigidity

Electronic transport in nano-scale organic semiconductors from non-adiabatic molecular dynamics

New electronic devices fabricated from organic molecules have been greatly improved over the past two decades. Yet, understanding the electronic transport mechanism of free carriers and excitons (bound electron-hole pairs) in organic semiconductors (OSs) is still a pertinent challenge. The soft molecular nature of these materials gives rise to an intricate interplay between electronic and nuclear motion as well as unique solid-state physical properties. Standard (analytic) treatments describing electronic transport often rely on one of two extremes: a travelling wave propagating through the material or a particle hopping from one molecular unit to the next. These are often unsuitable to fully describe the complex dynamics, which falls in between these regimes. In this regard, non-adiabatic molecular dynamics simulations permit a direct view into the transport mechanism, thus providing new important insights. In this thesis, I have further developed and improved in terms of efficiency and accuracy a fully atomistic non-adiabatic molecular dynamics algorithm, called fragment orbital-based surface hopping (FOB-SH). This allows the propagation of the coupled electron-nuclear motion in large nano-scale systems. After validating the accuracy of this methodology and discussing important physical requirements (i.e. energy conservation, detailed balance and internal consistency), I will present the application of FOB-SH to the calculation of room temperature charge mobility of a series of molecular organic crystals. I will discuss the agreement with experimental mobility values and the role of the disorder, induced by thermal fluctuations, on the delocalization of the states and the subsequent formation of a polaronic charge state. This polaronic charge propagates through the crystal by diffusive jumps over several lattice spacings at a time during which expands to more than twice its size. I will show that FOB-SH can recover the crossover from hopping to band-like transport depending on the strength of the electronic coupling and the temperature, thus successfully bridging the gap between these two extreme transport regimes. Finally, I will discuss a further extension of FOB-SH to the treatment of exciton transport in OSs. This opens up new exciting avenues for the application of FOB-SH to the study of electronic processes occurring in organic photovoltaic cells

Computations on non-covalent assemblies: Supramolecular organization and transport properties

The aim of this Thesis is to rationalize, from a theoretical perspective, the structural, electronic, optical and transport properties of different electroactive non-covalent assemblies of special relevance in the field of organic electronics. The ultimate goal is to establish valuable supramolecular structure-property relationships. In particular, this Thesis is focused on three types of systems: hole transporting materials (HTM), donor–acceptor supramolecular complexes and supramolecular polymers. For each system, the spotlight has been put on different relevant electronic processes. In the first part, the structural organization of several supramolecular polymers is studied. In particular, the relation between the supramolecular organization and the properties of interest (e.g. chiral behavior, or optical properties) of the selected systems. In the second part the charge transport properties of hole transporting materials, donor–acceptor supramolecular complexes are studied. On one hand the effect of H-bonding and the size of the HTM in the electronic mobilities is investigated. On the other hand, the kinectics of the photoinduced electron transfer on donor–acceptor supramolecular complexes in solution is simulated. Finally, the effects that become relevant for energy transport at the typical distances found in non-covalent assemblies are analyzed. These findings are used to simulate the exciton dynamics along one supramolecular polymer and, in particular the role of the charge transfer states in the exciton transport is analyzed

Methodological contributions to the simulation of charge and energy transport in molecular materials

Diese Arbeit beschäftigt sich mit methodischen Entwicklungen zur Untersuchung von Ladungs- und Energietransportprozessen in molekularen Materialien. Damit ist gemeint, dass neue Ansätzen zur Untersuchung solcher Prozesse eingeführt und getestet, nicht etwa spezielle Prozesse im Detail ergründet, werden. Insbesondere liegt der Fokus auf Methoden zur Untersuchung organischer, halbleitender Materialien mit hohen Ladungsträgermobilitäten oder effizienter Ekzitonendiffusion, wobei die vorgestellten Methoden weitaus breiter anwendbar sind. Zunächst wenden wir eine ursprünglich für den Ladungstransport in DNA-Strängen entwickelte, und später von Heck et al. für organische Halbleiter adaptierte, Methode auf Anthrazenkristalle an. Wir berechnen damit die korrekte Temperaturabhängigkeit der Lochmobilität. Diese ist eng mit dem zugrundeliegenden Transportmechanismus verwoben und kann im Falle von bandartigem Transport, wie in Anthrazen, nicht mit hoppingbasierten Methoden reproduziert werden. Daraufhin führen wir eine Methode zur Berechnung von Ekzitonendiffusionskonstanten in molekularen Materialien auf Basis der direkten Propagation der Ekzitonenwellenfunktion ein. Um solche Rechnungen möglich zu machen, werden unter Ausnutzung der molekularen Struktur Näherungen auf verschiedenen Ebenen eingeführt. Die neue Methode wird, um sie zu testen, auf Ekzitonentransport in Anthrazen angewendet und wir diskutieren dabei auch technische Details, die für die obig angesprochenen Ladungstransportstudien ebenfalls relevant sind. Bei der Propagation der Ekzitonenwellenfunktion müssen viele elektronische Strukturrechnungen angeregter Zustände durchgeführt werden, so dass dazu eine sehr schnelle Methode notwendig ist. Wir verwenden die approximative TD-DFTB Methode, die auf DFT mit einem GGA Funktional basiert. Es ist bekannt, dass GGA Funktionale für ausgedehnte π-Elektronensysteme, wie sie in organischen Halbleitern ständig vorkommen, nicht zuverlässig sind. Innerhalb von DFT lösen sogenannte long-range corrected (LC) Funktionale das Problem. Wir führen LC Funktionale in TD-DFTB ein, was Änderung am Formalismus erfordert. Wir zeigen, dass damit typische Probleme mit π-Systemen und Ladungstransferanregungen gelöst werden, bei tausendfach schnelleren Rechnungen als mit konventionellem TD-DFT. Abschließend beschäftigen wir uns mir der DFTB Methode selbst. LC Funktionale haben einen Parameter, der idealerweise systemspezifisch gewählt wird. Bei jeder Anpassung müssen für DFTB neue Parameter berechnet werden. Ein Satz von atompaarweisen Funktionen, genannt Repulsivpotentiale, erfordern dabei bisher viel Handarbeit. Wir versuchen diesen Vorgang zu automatisieren, indem wir DFTB mit Methoden aus der künstlichen Intelligenz verbinden

Electronic coupling calculations for modelling charge transport in organic semiconductors

Charge transport in organic semiconductors (OSCs) depends on a number of molecular properties, one of which is the electronic coupling matrix element for charge transfer between the molecules forming the material. They are the off-diagonal elements of the electronic Hamiltonian in the charge-localised (or diabatic) basis. The focus of this work is on the development of a method for a fast calculation of these matrix elements for OSCs. After addressing the different methods of their calculation, I present a program to estimate the off-diagonal elements of the Hamiltonian with a fast yet accurate semi-empirical method. This model approximates the off-diagonal elements of the Hamiltonian to be proportional to the overlap between the orbitals of the molecules, which are projected onto a very small basis set. The analytical results are in a reasonable agreement with accurate ab initio and fragment orbital DFT calculations and the speed-up is up to six orders of magnitude compared to DFT calculations. Following on from this, the analytic overlap method was implemented in two programs for charge carrier propagation, one based on Kinetic Monte Carlo simulation of charge carrier hopping (presented here), the other on surface hopping non-adiabatic molecular dynamics. I also show that the analytic overlap method can be used to estimate non-adiabatic coupling vectors very efficiently, which is an important quantity in surface hopping simulations

OPTICAL AND ELECTRICAL PROPERTIES OF ORGANIC SEMICONDUCTORS: EXPERIMENT AND SIMULATION

This dissertation focuses on the charge transport of organic semiconductors, particularly in the presence of traps and defects. Rather than attempting to ultimately pure materials, intentional mixtures were made and studied. The materials were characterized by electrochemistry, UV/Vis spectroscopy and computational studies using density functional theory (DFT) and time dependent DFT (TDDFT). In experiment, the phthalocyanine films were prepared from solution. We explored how to improve the coatings of organic semiconductors on different substrates. Moreover, the effect of how intentionally introduced traps or barriers change the charge transport was studied using the spin-coated octabutoxy phthalocyanine and naphthalocyanine mixed films. It was found that the introduced barriers decreased the mobility. And a negative differential resistance was observed in the saturated region of the Field-effect-transistor (FET) measurements in the mixed films. In simulation, density functional theory (DFT) and time-dependent density functional theory (TDDFT) calculations were performed to predict optical and electrical parameters of the semiconducting materials. In the calculations of phthalocyanine molecules with different metal or ligand substitutions, it was found that the electrical and optical properties of the phthalocyanine semiconductors could be tuned more with different organic ligands than by modifying the metal centers. For the mixed valence (MV) bipyridine bridged triarylamine systems, the simulation perfectly predicted the absorption of the spectra and the blue-shift of the spectra with different solvents reported by our collaborator in experiments