Experimentally Calibrated Kinetic Monte Carlo Model Reproduces Organic Solar Cell Current-Voltage Curve

Kinetic Monte Carlo (KMC) simulations are a powerful tool to study the dynamics of charge carriers in organic photovoltaics. However, the key characteristic of any photovoltaic device, its current-voltage ($J$-$V$) curve under solar illumination, has proven challenging to simulate using KMC. The main challenges arise from the presence of injecting contacts and the importance of charge recombination when the internal electric field is low, i.e., close to open-circuit conditions. In this work, an experimentally calibrated KMC model is presented that can fully predict the $J$-$V$ curve of a disordered organic solar cell. It is shown that it is crucial to make experimentally justified assumptions on the injection barriers, the blend morphology, and the kinetics of the charge transfer state involved in geminate and nongeminate recombination. All of these properties are independently calibrated using charge extraction, electron microscopy, and transient absorption measurements, respectively. Clear evidence is provided that the conclusions drawn from microscopic and transient KMC modeling are indeed relevant for real operating organic solar cell devices.Comment: final version; license update

Non-Equilibrium Charge Motion in Organic Solar Cells

Organic photovoltaic (OPV) devices based on semiconducting polymers and small molecules allow for a low cost alternative to inorganic solar cells. Recent developments show power conversion efficiencies as high as 10-12%, highlighting the potential of this technology. Nevertheless, further improvements are necessary to achieve commercialization. To a large extent the performance of these devices is dictated by their ability to extract the photo-generated charge, which is related to the charge carrier mobility. Various time-resolved and steady-state techniques are available to probe the charge carrier mobility in OPVs but often lead to different mobility values for one and the same system. Despite such conflicting observations it is generally assumed that charge transport in OPV devices can be described by well-defined charge carrier mobilities, typically obtained using a single steady-state technique. This thesis shows that the relevance of such well-defined mobilities for the charge separation and extraction processes is very limited. Although different transient techniques probe different time scales after photogeneration, they are mutually consistent as they probe the same physical mechanism governing charge motion – gradual thermalization of the photo-generated carriers in the disorder broadened density of states (DOS). The photo-generated carriers gradually lose their excess energy during transport to the extracting electrodes, but not immediately. Typically not all excess energy is dissipated as the photo-generated carriers tend to be extracted from the OPV device before reaching quasi-equilibrium. Carrier motion is governed by thermalization, leading to a time-dependent carrier mobility that is significantly higher than the steady-state mobility. This picture is confirmed by several transient techniques: Time-resolved Terahertz Spectroscopy (TRTS), Time-resolved Microwave Conductance (TRMC) combined with Transient Absorption (TA), electrical extraction of photo-induced charges (photo-CELIV). The connection between transient and steady-state mobility measurements (space-charge limited conductivity, SCLC) is described. Unification of transient opto-electric techniques to probe charge motion in OPVs is presented. Using transient experiments the distribution of extraction times of photo-generated charges in an operating OPV device has been determined and found to be strongly dispersive, spanning several decades in time. In view of the strong dispersion in extraction times the relevance of even a well-defined time-dependent mean mobility is limited. In OPVs a continuous ‘percolating’ donor network is often considered necessary for efficient hole extraction, whereas if the network is discontinuous, hole transport is thought to deteriorate significantly, limiting device performance. Here, it is shown that even highly diluted donor sites (5.7-10 %) in a buckminsterfullerene (C60) matrix enable reasonably efficient hole transport. Using transient measurements it is demonstrated that hole transport between isolated donor sites can occur by long-range hole tunneling (over distances of ~4 nm) through several C60 molecules – even a discontinuous donor network enables hole transpor

Nonequilibrium drift-diffusion model for organic semiconductor devices

Two prevailing formalisms are currently used to model charge transport in organic semiconductor devices. Drift-diffusion calculations, on the one hand, are time effective but assume local thermodynamic equilibrium, which is not always realistic. Kinetic Monte Carlo models, on the other hand, do not require this assumption but are computationally expensive. Here, we present a nonequilibrium drift-diffusion model that bridges this gap by fusing the established multiple trap and release formalism with the drift-diffusion transport equation. For a prototypical photovoltaic system the model is shown to quantitatively describe, with a single set of parameters, experiments probing (1) temperature-dependent steady-state charge transport-space-charge limited currents, and (2) time-resolved charge transport and relaxation of nonequilibrated photocreated charges. Moreover, the outputs of the developed kinetic drift-diffusion model are an order of magnitude, or more, faster to compute and in good agreement with kinetic Monte Carlo calculations

Automated open-source software for charge transport analysis in single-carrier organic semiconductor diodes

Organic electronics is an emerging technology with numerous applications in which the active layer is composed of an organic semiconductor (OSC) or blends of multiple OSC. One of the key performance parameters for such devices is the charge carrier mobility which can be evaluated by different measurement techniques. Here, we review different formalisms for extraction and analysis of hole mobilities from temperature-dependent space-charge limited conductivity (SCLC) measurements for pristine OSC as well as for binary and ternary blends as used in e.g. photovoltaic applications. The model is also applicable to n-type materials. Possible sources of measurement errors, such as the presence of traps and series resistance, are discussed. We show that by a simple method of selecting a proper experimental data range these errors can be avoided. The Murgatroyd-Gill analytical model in combination with the Gaussian Disorder Model is used to extract zero-field hole mobilities as well as estimates of the Gaussian energetic disorder in the HOMO level from experimental data. The resulting mobilities are in excellent agreement with those found from more elaborate fits to a full drift-diffusion model that includes a temperature, field and density dependent charge carrier mobility; the same holds for the Gaussian disorder of pure materials and blends with low fullerene concentration. The zero-field mobilities are also analyzed according to an Arrhenius model that was previously argued to reveal a universal mobility law; for most -but not all- material systems in the present work this framework gave an equally good fit to the experimental data as the other models. An automated fitting freeware, incorporating the different models, is made openly available for download and minimizes error, user input and SCLC data analysis time; e.g. SCLC current-voltage curves at several different temperatures can be globally fitted in a few seconds.Funding Agencies|Knut and Alice Wallenberg Foundation [KAW 2016.0494]</p

Design Rule for Improved Open-Circuit Voltage in Binary and Ternary Organic Solar Cells

Mixing different compounds to improve functionality is one of the pillars of the organic electronics field. Here, the degree to which the charge transport properties of the constituent materials are simply additive when materials are mixed is quantified. It is demonstrated that in bulk heterojunction organic solar cells, hole mobility in the donor phase depends critically on the choice of the acceptor material, which may alter the energetic disorder of the donor. The same holds for electron mobility and disorder in the acceptor. The associated mobility differences can exceed an order of magnitude compared to pristine materials. Quantifying these effects by a state-filling model for the open-circuit voltage (<i>V</i>_OC) of ternary Donor:Acceptor1:Acceptor2 (D:A₁:A₂) organic solar cells leads to a physically transparent description of the surprising, nearly linear tunability of the <i>V</i>_OC with the A₁:A₂ weight ratio. It is predicted that in binary OPV systems, suitably chosen donor and acceptor materials can improve the device power conversion efficiency (PCE) by several percentage points, for example from 11 to 13.5% for a hypothetical state-of-the-art organic solar cell, highlighting the importance of this design rule

Buildup of Triplet-State Population in Operating TQ1:PC71BM Devices Does Not Limit Their Performance

Triplet generation in organic solar cells has been considered a major loss channel. Determining the density of the triplet-state population in an operating device is challenging. Here, we employ transient absorption (TA) spectroscopy on the quinoxaline-thiophene copolymer TQ1 blended with PC71BM, quantify the transient charge and tripletstate densities, and parametrize their generation and recombination dynamics. The charge recombination parameters reproduce the experimentally measured current-voltage characteristics in charge carrier drift-diffusion simulations, and they yield the steady-state charge densities. We demonstrate that triplets are formed by both geminate and nongeminate recombination of charge carriers and decay primarily by triplet-triplet annihilation. Using the charge densities in the rate equations describing triplet-state dynamics, we find that triplet-state densities in devices are in the range of charge carrier densities. Despite this substantial triplet-state buildup, TQ1:PC71BM devices exhibit only moderate geminate recombination and significantly reduced nongeminate charge recombination, with reduction factors between 10(-4) and 10(-3) compared to Langevin recombination.Funding Agencies|King Abdullah University of Science and Technology (KAUST) Office of Sponsored Research (OSR) [OSR2018-CARF/CCF-3079]; Knut and Alice Wallenberg FoundationKnut &amp; Alice Wallenberg Foundation [KAW 2016.0494]</p

Role of coherence and delocalization in photo-induced electron transfer at organic interfaces

Photo-induced charge transfer at molecular heterojunctions has gained particular interest due to the development of organic solar cells (OSC) based on blends of electron donating and accepting materials. While charge transfer between donor and acceptor molecules can be described by Marcus theory, additional carrier delocalization and coherent propagation might play the dominant role. Here, we describe ultrafast charge separation at the interface of a conjugated polymer and an aggregate of the fullerene derivative PCBM using the stochastic Schrödinger equation (SSE) and reveal the complex time evolution of electron transfer, mediated by electronic coherence and delocalization. By fitting the model to ultrafast charge separation experiments, we estimate the extent of electron delocalization and establish the transition from coherent electron propagation to incoherent hopping. Our results indicate that even a relatively weak coupling between PCBM molecules is sufficient to facilitate electron delocalization and efficient charge separation at organic interfaces

Photo-generated carriers lose energy during extraction from polymer-fullerene solar cells

In photovoltaic devices, the photo-generated charge carriers are typically assumed to be in thermal equilibrium with the lattice. In conventional materials, this assumption is experimentally justified as carrier thermalization completes before any significant carrier transport has occurred. Here, we demonstrate by unifying time-resolved optical and electrical experiments and Monte Carlo simulations over an exceptionally wide dynamic range that in the case of organic photovoltaic devices, this assumption is invalid. As the photo-generated carriers are transported to the electrodes, a substantial amount of their energy is lost by continuous thermalization in the disorder broadened density of states. Since thermalization occurs downward in energy, carrier motion is boosted by this process, leading to a time-dependent carrier mobility as confirmed by direct experiments. We identify the time and distance scales relevant for carrier extraction and show that the photo-generated carriers are extracted from the operating device before reaching thermal equilibrium.Funding Agencies|Swedish Science Council and Energimyndigheten; Knut and Alice Wallenberg foundation; Deutsche Forschungsgemeinschaft [SPP1355]</p