Can lattice models predict the density of states of amorphous organic semiconductors?

Charge transport in the spatially correlated exponential random energy landscape: effect of the nonpositive correlation function

Charge transport in amorphous semiconductors having spatially correlated exponential density of states (DOS) has been considered for the arbitrary behavior of the correlation function of random energies. Average carrier velocity is exactly calculated for the quasi-equilibrium (nondispersive) transport regime. For the symmetric exponential DOS with exponential tails for low and high energies and nonpositive correlation function the temperature of the transition to the dispersive transport regime depends on correlation properties and becomes greater than the traditional estimation based on the DOS decay energy kT = U₀. Another new feature of the transport in the landscape having nonpositive correlation function is the decrease of the mobility with the field in the low field region and development of the universal mobility field dependence for stronger fields.

Effects of MEH-PPV Molecular Ordering in the Emitting Layer on the Luminescence Efficiency of Organic Light-Emitting Diodes

We investigated the effects of molecular ordering on the electro-optical characteristics of organic light-emitting diodes (OLEDs) with an emission layer (EML) of poly[2-methoxy-5-(2-ethylhexyloxy)-1,4-phenylenevinylene] (MEH-PPV). The EML was fabricated by a solution process which can make molecules ordered. The performance of the OLED devices with the molecular ordering method was compared to that obtained through fabrication by a conventional spin coating method. The turn-on voltage and the luminance of the conventional OLEDs were 5 V and 34.75 cd/m², whereas those of the proposed OLEDs were 4.5 V and 120.3 cd/m², respectively. The underlying mechanism of the higher efficiency with ordered molecules was observed by analyzing the properties of the EML layer using AFM, SE, XRD, and an LCR meter. We confirmed that the electrical properties of the organic thin film can be improved by controlling the molecular ordering of the EML, which plays an important role in the electrical characteristics of the OLED.

Improving organic photovoltaic cells by forcing electrode work function well beyond onset of Ohmic transition

As electrode work function rises or falls sufficiently, the organic semiconductor/electrode contact reaches Fermi-level pinning, and then, few tenths of an electron-volt later, Ohmic transition. For organic solar cells, the resultant flattening of open-circuit voltage (V_oc) and fill factor (FF) leads to a ‘plateau’ that maximizes power conversion efficiency (PCE). Here, we demonstrate this plateau in fact tilts slightly upwards. Thus, further driving of the electrode work function can continue to improve V_oc and FF, albeit slowly. The first effect arises from the coercion of Fermi level up the semiconductor density-of-states in the case of ‘soft’ Fermi pinning, raising cell built-in potential. The second effect arises from the contact-induced enhancement of majority-carrier mobility. We exemplify these using PBDTTPD:PCBM solar cells, where PBDTTPD is a prototypal face-stacked semiconductor, and where work function of the hole collection layer is systematically ‘tuned’ from onset of Fermi-level pinning, through Ohmic transition, and well into the Ohmic regime.

Both open-circuit voltage and fill factor of organic solar cells are affected by the metal-organic semiconductor interface. Here, the authors demonstrate that the voltage can continue to rise when the Fermi level is forced up to the semiconductor density-of-states tail.

Evolutionary Approach to Constructing a Deep Feedforward Neural Network for Prediction of Electronic Coupling Elements in Molecular Materials

We present a general framework for the construction of a deep feedforward neural network (FFNN) to predict distance and orientation dependent electronic coupling elements in disordered molecular materials. An evolutionary algorithm automatizes the selection of an optimal architecture of the artificial neural network within a predefined search space. Systematic guidance, beyond minimizing the model error with stochastic gradient descent based backpropagation, is provided by simultaneous maximization of a model fitness that takes into account additional physical properties, such as the field-dependent carrier mobility. As a prototypical system, we consider hole transport in amorphous tris(8-hydroxyquinolinato)aluminum. Reference data for training and validation is obtained from multiscale ab initio simulations, in which coupling elements are evaluated using density-functional theory, for a system containing 4096 molecules. The Coulomb matrix representation is chosen to encode the explicit molecular pair coordinates into a rotation and translation invariant feature set for the FFNN. The final optimized deep feedforward neural network is tested for transport models without and with energetic disorder. It predicts electronic coupling elements and mobilities in excellent agreement with the reference data. Such a FFNN is readily applicable to much larger systems at negligible computational cost, providing a powerful surrogate model to overcome the size limitations of the ab initio approach.

Electronic Excitations in Complex Molecular Environments: Many-Body Green's Functions Theory in VOTCA-XTP

Many-body Green's functions theory within the GW approximation and the Bethe-Salpeter Equation (BSE) is implemented in the open-source VOTCA-XTP software, aiming at the calculation of electronically excited states in complex molecular environments. Based on Gaussian-type atomic orbitals and making use of resolution of identity techniques, the code is designed specifically for nonperiodic systems. Application to a small molecule reference set successfully validates the methodology and its implementation for a variety of excitation types covering an energy range from 2 to 8 eV in single molecules. Further, embedding each GW-BSE calculation into an atomistically resolved surrounding, typically obtained from Molecular Dynamics, accounts for effects originating from local fields and polarization. Using aqueous DNA as a prototypical system, different levels of electrostatic coupling between the regions in this GW-BSE/MM setup are demonstrated. Particular attention is paid to charge-transfer (CT) excitations in adenine base pairs. It is found that their energy is extremely sensitive to the specific environment and to polarization effects. The calculated redshift of the CT excitation energy compared to a nucelobase dimer treated in vacuum is of the order of 1 eV, which matches expectations from experimental data. Predicted lowest CT energies are below that of a single nucleobase excitation, indicating the possibility of an initial (fast) decay of such an UV excited state into a binucleobase CT exciton. The results show that VOTCA-XTP's GW-BSE/MM is a powerful tool to study a wide range of types of electronic excitations in complex molecular environments.

Introducing correlations into carrier transport simulations of disordered materials through seeded nucleation: impact on density of states, carrier mobility, and carrier statistics

Disorder in organic semiconductors has made it challenging to achieve performance gains; this is a result of the many competing and often nuanced mechanisms effecting charge transport. In this article, we attempt to illuminate one of these mechanisms in the hopes of aiding experimentalists in exceeding current performance thresholds. Using a heuristic exponential function, energetic correlation has been added to the Gaussian disorder model (GDM). The new model is grounded in the concept that energetic correlations can arise in materials without strong dipoles or dopants, but may be a result of an incomplete crystal formation process. The proposed correlation has been used to explain the exponential tail states often observed in these materials; it is also better able to capture the carrier mobility field dependence, commonly known as the Poole-Frenkel dependence, when compared to the GDM. Investigation of simulated current transients shows that the exponential tail states do not necessitate Montroll and Scher fits. Montroll and Scher fits occur in the form of two distinct power law curves that share a common constant in their exponent; they are clearly observed as linear lines when the current transient is plotted using a log-log scale. Typically, these fits have been found appropriate for describing amorphous silicon and other disordered materials which display exponential tail states. Furthermore, we observe the proposed correlation function leads to domains of energetically similar sites separated by boundaries where the site energies exhibit stochastic deviation. These boundary sites are found to be the source of the extended exponential tail states, and are responsible for high charge visitation frequency, which may be associated with the molecular turnover number and ultimately the material stability.

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.

Diffusion of a particle in the spatially correlated exponential random energy landscape: Transition from normal to anomalous diffusion

Diffusive transport of a particle in a spatially correlated random energy landscape having exponential density of states has been considered. We exactly calculate the diffusivity in the nondispersive quasi-equilibrium transport regime for the 1D transport model and found that for slow decaying correlation functions the diffusivity becomes singular at some particular temperature higher than the temperature of the transition to the true non-equilibrium dispersive transport regime. It means that the diffusion becomes anomalous and does not follow the usual ∝ t^1/2 law. In such situation, the fully developed non-equilibrium regime emerges in two stages: first, at some temperature there is the transition from the normal to anomalous diffusion, and then at lower temperature the average velocity for the infinite medium goes to zero, thus indicating the development of the true dispersive regime. Validity of the Einstein relation is discussed for the situation where the diffusivity does exist. We provide also some arguments in favor of conservation of the major features of the new transition scenario in higher dimensions.

Hopping charge transport in amorphous semiconductors with the spatially correlated exponential density of states

Hopping charge transport in amorphous semiconductors having spatially correlated exponential density of states has been considered. Average carrier velocity is exactly calculated for the quasi-equilibrium (nondispersive) transport regime. We suggest also a heuristic approach for the consideration of the carrier velocity for the non-equilibrium dispersive regime.

Electrostatic phenomena in organic semiconductors: fundamentals and implications for photovoltaics

This review summarizes the current understanding of electrostatic phenomena in ordered and disordered organic semiconductors, outlines numerical schemes developed for quantitative evaluation of electrostatic and induction contributions to ionization potentials and electron affinities of organic molecules in a solid state, and illustrates two applications of these techniques: interpretation of photoelectron spectroscopy of thin films and energetics of heterointerfaces in organic solar cells.

Parameter-free continuous drift-diffusion models of amorphous organic semiconductors

Continuous drift-diffusion models are routinely used to optimize organic semiconducting devices. Material properties are incorporated into these models via dependencies of diffusion constants, mobilities, and injection barriers on temperature, charge density, and external field. The respective expressions are often provided by the generic Gaussian disorder models, parametrized on experimental data. We show that this approach is limited by the fixed range of applicability of analytic expressions as well as approximations inherent to lattice models. To overcome these limitations we propose a scheme which first tabulates simulation results performed on small-scale off-lattice models, corrects for finite size effects, and then uses the tabulated mobility values to solve the drift-diffusion equations. The scheme is tested on DPBIC, a state of the art hole conductor for organic light emitting diodes. We find a good agreement between simulated and experimentally measured current-voltage characteristics for different film thicknesses and temperatures.

Impact of mesoscale order on open-circuit voltage in organic solar cells

Structural order in organic solar cells is paramount: it reduces energetic disorder, boosts charge and exciton mobilities, and assists exciton splitting. Owing to spatial localization of electronic states, microscopic descriptions of photovoltaic processes tend to overlook the influence of structural features at the mesoscale. Long-range electrostatic interactions nevertheless probe this ordering, making local properties depend on the mesoscopic order. Using a technique developed to address spatially aperiodic excitations in thin films and in bulk, we show how inclusion of mesoscale order resolves the controversy between experimental and theoretical results for the energy-level profile and alignment in a variety of photovoltaic systems, with direct experimental validation. Optimal use of long-range ordering also rationalizes the acceptor-donor-acceptor paradigm for molecular design of donor dyes. We predict open-circuit voltages of planar heterojunction solar cells in excellent agreement with experimental data, based only on crystal structures and interfacial orientation.

An Effective Two-Orbital Quantum Chemical Model for Organic Photovoltaic Materials

We present a coarse-grained quantum chemical model of organic photovoltaic materials, which is based on the classic idea that the main physical processes involve the electrons occupying the frontier orbitals (HOMO and LUMO) of each molecule or "site". This translates into an effective electronic Hamiltonian with two electrons and two orbitals per site. The on-site parameters (one- and two-electron integrals) can be rigorously related to the ionization energy, electron affinity, and singlet and triplet first excitation energies of that site. The intersite Hamiltonian parameters are introduced in a way that is consistent with classical electrostatics, and for the one-electron part, we use a simple approximation that could be refined using information from atomistic quantum chemical calculations. The model has been implemented within the GAMESS-US package. This allows the exploration of the physics of these materials using state-of-the art quantum chemical methods on relatively large systems (hundreds of electron-donor and electron-acceptor sites). To illustrate this point, we present ground- and excited-state calculations on dimers and two-dimensional arrays of sites using the Hartree-Fock, configuration interaction, and coupled-cluster methods. The calculations provide evidence for the possibility of low-energy, long-range electron transfer in donor-acceptor heterojunctions characterized by a moderate degree of disorder.

Molecular-scale simulation of electroluminescence in a multilayer white organic light-emitting diode

In multilayer white organic light-emitting diodes the electronic processes in the various layers--injection and motion of charges as well as generation, diffusion and radiative decay of excitons--should be concerted such that efficient, stable and colour-balanced electroluminescence can occur. Here we show that it is feasible to carry out Monte Carlo simulations including all of these molecular-scale processes for a hybrid multilayer organic light-emitting diode combining red and green phosphorescent layers with a blue fluorescent layer. The simulated current density and emission profile are shown to agree well with experiment. The experimental emission profile was obtained with nanometre resolution from the measured angle- and polarization-dependent emission spectra. The simulations elucidate the crucial role of exciton transfer from green to red and the efficiency loss due to excitons generated in the interlayer between the green and blue layers. The perpendicular and lateral confinement of the exciton generation to regions of molecular-scale dimensions revealed by this study demonstrate the necessity of molecular-scale instead of conventional continuum simulation.