Methodological assessment of kinetic Monte Carlo simulations of organic photovoltaic devices: The treatment of electrostatic interactions

Knowledge-driven design of solid-electrolyte interphases on lithium metal via multiscale modelling

Due to its high energy density, lithium metal is a promising electrode for future energy storage. However, its practical capacity, cyclability and safety heavily depend on controlling its reactivity in contact with liquid electrolytes, which leads to the formation of a solid electrolyte interphase (SEI). In particular, there is a lack of fundamental mechanistic understanding of how the electrolyte composition impacts the SEI formation and its governing processes. Here, we present an in-depth model-based analysis of the initial SEI formation on lithium metal in a carbonate-based electrolyte. Thereby we reach for significantly larger length and time scales than comparable molecular dynamic studies. Our multiscale kinetic Monte Carlo/continuum model shows a layered, mostly inorganic SEI consisting of LiF on top of Li2CO3 and Li after 1 µs. Its formation is traced back to a complex interplay of various electrolyte and salt decomposition processes. We further reveal that low local Li+ concentrations result in a more mosaic-like, partly organic SEI and that a faster passivation of the lithium metal surface can be achieved by increasing the salt concentration. Based on this we suggest design strategies for SEI on lithium metal and make an important step towards knowledge-driven SEI engineering.

Utilizing Data-Driven Optimization to Automate the Parametrization of Kinetic Monte Carlo Models

Kinetic Monte Carlo (kMC) simulations are a popular tool to investigate the dynamic behavior of stochastic systems. However, one major limitation is their relatively high computational costs. In the last three decades, significant effort has been put into developing methodologies to make kMC more efficient, resulting in an enhanced runtime efficiency. Nevertheless, kMC models remain computationally expensive. This is in particular an issue in complex systems with several unknown input parameters where often most of the simulation time is required for finding a suitable parametrization. A potential route for automating the parametrization of kinetic Monte Carlo models arises from coupling kMC with a data-driven approach. In this work, we equip kinetic Monte Carlo simulations with a feedback loop consisting of Gaussian Processes (GPs) and Bayesian optimization (BO) to enable a systematic and data-efficient input parametrization. We utilize the results from fast-converging kMC simulations to construct a database for training a cheap-to-evaluate surrogate model based on Gaussian processes. Combining the surrogate model with a system-specific acquisition function enables us to apply Bayesian optimization for the guided prediction of suitable input parameters. Thus, the amount of trial simulation runs can be considerably reduced facilitating an efficient utilization of arbitrary kMC models. We showcase the effectiveness of our methodology for a physical process of growing industrial relevance: the space-charge layer formation in solid-state electrolytes as it occurs in all-solid-state batteries. Our data-driven approach requires only 1-2 iterations to reconstruct the input parameters from different baseline simulations within the training data set. Moreover, we show that the methodology is even capable of accurately extrapolating into regions outside the training data set which are computationally expensive for direct kMC simulation. Concluding, we demonstrate the high accuracy of the underlying surrogate model via a full parameter space investigation eventually making the original kMC simulation obsolete.

Mass transport and charge transfer through an electrified interface between metallic lithium and solid-state electrolytes

All-solid-state Li-ion batteries are one of the most promising energy storage devices for future automotive applications as high energy density metallic Li anodes can be safely used. However, introducing solid-state electrolytes needs a better understanding of the forming electrified electrode/electrolyte interface to facilitate the charge and mass transport through it and design ever-high-performance batteries. This study investigates the interface between metallic lithium and solid-state electrolytes. Using spectroscopic ellipsometry, we detected the formation of the space charge depletion layers even in the presence of metallic Li. That is counterintuitive and has been a subject of intense debate in recent years. Using impedance measurements, we obtain key parameters characterizing these layers and, with the help of kinetic Monte Carlo simulations, construct a comprehensive model of the systems to gain insights into the mass transport and the underlying mechanisms of charge accumulation, which is crucial for developing high-performance solid-state batteries.

Systematic kMC Study of Doped Hole Injection Layers in Organic Electronics

Organic light emitting diodes (OLED) play an important role in commercial displays and are promising candidates for energy-efficient lighting applications. Although they have been continuously developed since their discovery in 1987, some unresolved challenges remain. The performance of OLEDs is determined by a multifaceted interplay of materials and device architectures. A commonly used technique to overcome the charge injection barrier from the electrodes to the organic layers, are doped injection layers. The optimization of doped injection layers is critical for high-efficiency OLED devices, but has been driven mainly by chemical intuition and experimental experience, slowing down the progress in this field. Therefore, computer-aided methods for material and device modeling are promising tools to accelerate the device development process. In this work, we studied the effect of doped hole injection layers on the injection barrier in dependence on material and layer properties by using a parametric kinetic Monte Carlo model. We were able to quantitatively elucidate the influence of doping concentration, material properties, and layer thickness on the injection barrier and device conductivity, leading to the conclusion that our kMC model is suitable for virtual device design.

Molecular Mechanism for the Self-Supported Synthesis of Graphitic Carbon Nitride from Urea Pyrolysis

Quantum chemical calculations combined with kinetic Monte Carlo simulations are performed to decipher the kinetics for the one-pot synthesis of two-dimensional graphitic carbon nitride (g-C₃N₄) from urea pyrolysis. Two mechanisms are considered, one involving ammelide as the intermediate compound and the other considering cyanuric acid. Different grid growing patterns are investigated, and the size, shape, and density of the grids as well as the number and position of the defects are evaluated. We find that the mechanistic pathway involving ammelide is preferred. Larger g-C₃N₄ grids with lower density are achieved when the rate constant for melon growing is inversely proportional to the number of local reaction sites, while nearly filled smaller grids are obtained in the opposite scenario. Larger defects appear at the grid periphery while smaller holes appear throughout the grid. The synthesis of extended g-C₃N₄ structures is favored if the g-C₃N₄ growing propensity is directly proportional to the number of reaction sites.

Efficient evaluation of Coulomb interactions in kinetic Monte Carlo simulations of charge transport

The application of predictive and reliable modeling techniques for the simulation of charge transport in functional materials is an essential step for the development of advanced platforms for electronics, optoelectronics, and photovoltaics. In this context, kinetic Monte Carlo (KMC) methods have emerged as a valuable tool, especially for the simulation of systems where charge transport can be described by the hopping of charge carriers across localized quantum states, as, for example, in organic semiconductor materials. The accuracy, computational efficiency, and reliability of KMC simulations of charge transport, however, crucially depend on the methods and approximations used to evaluate electrostatic interactions arising from the distribution of charges in the system. The long-range nature of Coulomb interactions and the need to simulate large model systems to capture the details of charge transport phenomena in complex devices lead, typically, to a computational bottleneck, which hampers the application of KMC methods. Here, we propose and assess computational schemes for the evaluation of electrostatic interactions in KMC simulations of charge transport based on the locality of the charge redistribution in the hopping regime. The methods outlined in this work provide an overall accuracy that outperforms typical approaches for the evaluation of electrostatic interactions in KMC simulations at a fraction of the computational cost. In addition, the computational schemes proposed allow a spatial decomposition of the evaluation of Coulomb interactions, leading to an essentially linear scaling of the computational load with the size of the system.

Disorder compensation controls doping efficiency in organic semiconductors

Conductivity doping of inorganic and organic semiconductors enables a fantastic variety of highly-efficient electronic devices. While well understood for inorganic materials, the mechanism of doping-induced conductivity and Fermi level shift in organic semiconductors remains elusive. In microscopic simulations with full treatment of many-body Coulomb effects, we reproduce the Fermi level shift in agreement with experimental observations. We find that the additional disorder introduced by doping can actually compensate the intrinsic disorder of the material, such that the total disorder remains constant or is even reduced at doping molar ratios relevant to experiment. In addition to the established dependence of the doping-induced states on the Coulomb interaction in the ionized host-dopant pair, we find that the position of the Fermi level and electrical conductivity is controlled by disorder compensation. By providing a quantitative model for doping in organic semiconductors we enable the predictive design of more efficient redox pairs.

Though conductivity doping in organic semiconductors has been widely studied in organic electronics, a clear mechanistic picture that explains the phenomenon is still lacking. Here, the authors report a theoretical approach to elucidate the role of disorder compensation in doped organic materials.

Toward Design of Novel Materials for Organic Electronics

Materials for organic electronics are presently used in prominent applications, such as displays in mobile devices, while being intensely researched for other purposes, such as organic photovoltaics, large-area devices, and thin-film transistors. Many of the challenges to improve and optimize these applications are material related and there is a nearly infinite chemical space that needs to be explored to identify the most suitable material candidates. Established experimental approaches struggle with the size and complexity of this chemical space. Herein, the development of simulation methods is addressed, with a particular emphasis on predictive multiscale protocols, to complement experimental research in the identification of novel materials and illustrate the potential of these methods with a few prominent recent applications. Finally, the potential of machine learning and methods based on artificial intelligence is discussed to further accelerate the search for new materials.

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.

Charge carrier mobility of disordered organic semiconductors with correlated energetic and spatial disorder

Kinetic Monte Carlo study of the impact of spatial and energetic disorder on charge mobility, current distribution and transport energy in organic semiconductors.

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.

Influence of permittivity and energetic disorder on the spatial charge carrier distribution and recombination in organic bulk-heterojunctions

Gaining insight into the spatial charge carrier distribution and its relation to geminate and nongeminate recombination in bulk-heterojunction organic solar cells.

Charge carrier thermalization in organic diodes

Charge carrier mobilities of organic semiconductors are often characterized using steady-state measurements of space charge limited diodes. These measurements assume that charge carriers are in a steady-state equilibrium. In reality, however, energetically hot carriers are introduces by photo-excitation and injection into highly energetic sites from the electrodes. These carriers perturb the equilibrium density of occupied states, and therefore change the overall charge transport properties. In this paper, we look into the effect of energetically hot carriers on the charge transport in organic semiconductors using steady state kinetic Monte Carlo simulations. For injected hot carriers in a typical organic semiconductor, rapid energetic relaxation occurs in the order of tens of nanoseconds, which is much faster than the typical transit time of a charge carrier throught the device. Furthermore, we investigate the impact of photo-generated carriers on the steady-state mobility. For a typical organic voltaic material, an increase in mobility of a factor of 1.1 is found. Therefore, we conclude that the impact of energetically hot carriers on normal device operation is limited.

Simulations of singlet exciton diffusion in organic semiconductors: a review

Recent advances in exciton diffusion simulations in conjugated materials are presented in this review.

How high local charge carrier mobility and an energy cascade in a three-phase bulk heterojunction enable >90% quantum efficiency

Charge generation in champion organic solar cells is highly efficient in spite of low bulk charge-carrier mobilities and short geminate-pair lifetimes. In this work, kinetic Monte Carlo simulations are used to understand efficient charge generation in terms of experimentally measured high local charge-carrier mobilities and energy cascades due to molecular mixing.

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.

A multiscale modeling study of loss processes in block-copolymer-based solar cell nanodevices

Flexible photovoltaic devices possess promising perspectives in opto-electronic technologies, where high mobility and/or large-scale applicability are important. However, their usefulness in such applications is currently still limited due to the low level of optimization of their performance and durability. For the improvement of these properties, a better understanding and control of small-scale annihilation phenomena involved in the photovoltaic process, such as exciton loss and charge carrier loss, is necessary, which typically implicates multiple length- and time-scales. Here, we study the causes for their occurrence on the example of nanostructured diblock- and triblock-copolymer systems by making use of a novel solar-cell simulation algorithm and explore new routes to optimize their photovoltaic properties. A particular focus is set on the investigation of exciton and charge carrier loss phenomena and their dependence on the inter-monomeric interaction strength, chain architecture, and external mechanical loading. Our simulation results reveal that in the regime from low up to intermediate χ-parameters an increasing number of continuous percolation paths is created. In this parameter range, the internal quantum efficiency (IQE) increases up to a maximum, characterized by a minimum in the number of charge losses due to charge recombination. In the regime of high χ-parameters both block-copolymer systems form nanostructures with a large number of bottlenecks and dead ends. These lead to a large number of charge losses due to charge recombination, charge trapping, and a deteriorated exciton dissociation, resulting in a significant drop in the IQE. Moreover, we find that the photovoltaic performance of the triblock-copolymer material decreases with increasing mechanical loading, caused by a growing number of charge losses due to charge recombination and charge accumulation. Finally, we demonstrate that the process of charge trapping in defects can be reversed by changing the polarity of the electrodes, which confers these materials the ability to be used as charge storage media.

Anomalous thickness-dependence of photocurrent explained for state-of-the-art planar nano-heterojunction organic solar cells

Due to their simple geometry and design, planar heterojunction (PHJ) solar cells have advantages both as potential photovoltaics with more efficient charge extraction than their bulk heterojunction (BHJ) counterparts, and as idealized interfaces to study basic device operation. The main reason for creating BHJs was the limited exciton diffusion length in the active materials of the PHJ: if an exciton is generated at a distance greater than its diffusion length from the hetero-interface of the PHJ, it would be very unlikely to be able to contribute to the photocurrent. Based on this argument one expects a maximum in the photocurrent of PHJs for a thickness of the active layer equal to the exciton diffusion length (~10 nm). However, in two recently developed PHJs that have appeared in the literature, a maximum photocurrent is observed for 60-65 nm of poly(3-hexylthiophene) (P3HT). In this work, we explore this anomaly by combining both an optical T-matrix and a kinetic Monte Carlo simulation that tracks the exciton behavior in the PHJs. The two systems considered are a P3HT/single walled carbon nanotube (SWNT) device, and a P3HT/phenyl-C61-butyric acid methyl ester (PCBM) device. The model demonstrates how a bulk exciton sink can explain the shifted maximum in the P3HT/SWNT case, whereas in the P3HT/PCBM case the maximum is mainly determined by PCBM molecules interdiffusing in the P3HT upon annealing. Based upon the results of this model it will be possible to more intelligently design nanostructured photovoltaics and optimize them toward higher efficiencies.