Yield of geminate pair dissociation in an energetically random hopping system

What We have Learnt from PM6:Y6

Over the past three years, remarkable advancements in organic solar cells (OSCs) have emerged, propelled by the introduction of Y6-an innovative A-DA'D-A type small molecule non-fullerene acceptor (NFA). This review provides a critical discussion of the current knowledge about the structural and physical properties of the PM6:Y6 material combination in relation to its photovoltaic performance. The design principles of PM6 and Y6 are discussed, covering charge transfer, transport, and recombination mechanisms. Then, the authors delve into blend morphology and degradation mechanisms before considering commercialization. The current state of the art is presented, while also discussing unresolved contentious issues, such as the blend energetics, the pathways of free charge generation, and the role of triplet states in recombination. As such, this review aims to provide a comprehensive understanding of the PM6:Y6 material combination and its potential for further development in the field of organic solar cells. By addressing both the successes and challenges associated with this system, this review contributes to the ongoing research efforts toward achieving more efficient and stable organic solar cells.

Extremely Non-Equilibrium Hopping Transport and Photogeneration Efficiency in Organic Semiconductors: An Analytic Approach

An analytical model of highly nonequilibrium hopping transport of charge carriers in disordered organic semiconductors has been developed. In particular, the initial time interval is considered when transport is controlled by hops down in energy. The model is applied to the calculation of the separation probability of geminate pairs in a semiconductor with a Gaussian energy distribution of localized states. This probability determines the photogeneration efficiency. The temperature dependence of the separation probability is obtained and shown to be much weaker than predicted by the classical Onsager model, in agreement with experiment and Monte Carlo simulations. The field dependence is taken into account using a modified effective temperature method.

On Analytical Modeling of Hopping Transport of Charge Carriers and Excitations in Materials with Correlated Disorder

Spatial-energy correlations strongly influence charge and exciton transport in weakly ordered media such as organic semiconductors and nanoparticle assemblies. Focusing on cases with shorter-range interparticle interactions, we develop a unified analytic approach that allows us to calculate the temperature and field dependence of charge carrier mobility in organic quadrupole glasses and the temperature dependence of the diffusion coefficient of excitons in quantum dot solids. We obtain analytic expressions for the energy distribution of hopping centers, the characteristic escape time of charge/exciton from the energy well stemming from energy correlations around deep states, and the size of the well. The derived formulas are tested with Monte Carlo simulation results, showing good agreement and providing simple analytic expressions for analysis of charge and exciton mobility in a broad range of partially ordered media.

Disorder and Photogeneration Efficiency in Organic Semiconductors

An analytical description of the separation probability of a geminate pair in organic semiconductors is given. The initial diffusion of "hot" twins is anomalously strong due to energy disorder. This circumstance significantly increases the photogeneration quantum yield at low temperatures and weakens its temperature dependence relative to predictions of the Onsager model, in agreement with Monte Carlo and experimental results.

Dynamics of Excitons in Conjugated Molecules and Organic Semiconductor Systems

The exciton, an excited electron-hole pair bound by Coulomb attraction, plays a key role in photophysics of organic molecules and drives practically important phenomena such as photoinduced mechanical motions of a molecule, photochemical conversions, energy transfer, generation of free charge carriers, etc. Its behavior in extended π-conjugated molecules and disordered organic films is very different and very rich compared with exciton behavior in inorganic semiconductor crystals. Due to the high degree of variability of organic systems themselves, the exciton not only exerts changes on molecules that carry it but undergoes its own changes during all phases of its lifetime, that is, birth, conversion and transport, and decay. The goal of this review is to give a systematic and comprehensive view on exciton behavior in π-conjugated molecules and molecular assemblies at all phases of exciton evolution with emphasis on rates typical for this dynamic picture and various consequences of the above dynamics. To uncover the rich variety of exciton behavior, details of exciton formation, exciton transport, exciton energy conversion, direct and reverse intersystem crossing, and radiative and nonradiative decay are considered in different systems, where these processes lead to or are influenced by static and dynamic disorder, charge distribution symmetry breaking, photoinduced reactions, electron and proton transfer, structural rearrangements, exciton coupling with vibrations and intermediate particles, and exciton dissociation and annihilation as well.

The Role of Delocalization and Excess Energy in the Quantum Efficiency of Organic Solar Cells and the Validity of Optical Reciprocity Relations

The photon energy dependence of long-range charge separation is studied for two prototypical polymer:fullerene systems. The internal quantum efficiency (IQE) of PCDTBT:PC₆₁BM is experimentally shown to be independent of the excitation energy. In contrast, for TQ1:PC₇₁BM the IQE is strongly energy-dependent for excitation energies close to charge transfer (CT) electroluminescence peak maximum while it becomes energy-independent at higher excitation energies. Kinetic Monte Carlo simulations reproduce the experimental IQE and reveal that the photon energy-dependence of the IQE is governed by charge delocalization. Efficient long-range separation at excitation energies corresponding to the CT electroluminescence peak maximum or lower requires an initial separation of the hole-electron pair by ∼4-5 nm, whereas delocalization is less important for charge separation at higher photon energies. Our modeling results suggest that a phenomenological reciprocity between CT electroluminescence and external quantum efficiency does not necessarily prove that commonly employed reciprocity relations between these spectra are valid from a fundamental perspective.

Disorder vs Delocalization: Which Is More Advantageous for High-Efficiency Organic Solar Cells?

We investigate the combined influence of energetic disorder and delocalization on electron-hole charge-transfer state separation efficiency in donor-acceptor organic photovoltaic systems using an analytical hopping model and Monte Carlo calculations, coupled with an effective mass model. Whereas energetic disorder increases the separation yield at intermediate and low electric fields for low-efficiency blends with strongly localized carriers, we find that it reduces dramatically the fill factors and power conversion efficiencies in high-efficiency solar cells that require high carrier delocalization within the conjugated segment and high mobility-lifetime product. We further demonstrate that the initial electron-hole distance and thermalization processes play only a minor role in the separation dynamics.

Photogenerated Charge Transport in Organic Electronic Materials: Experiments Confirmed by Simulations

The performance of organic optoelectronic devices, such as organic photovoltaic (OPV) cells, is to a large extent dictated by their ability to transport the photogenerated charge, with relevant processes spanning a wide temporal (fs-µs) and spatial (1-100 nm) range. However, time-resolved techniques can access only a limited temporal window, and often contradict steady-state measurements. Here, commonly employed steady-state and time-resolved techniques are unified over an exceptionally wide temporal range (fs-µs) in a consistent physical picture. Experimental evidence confirmed by numerical simulations shows that, although various techniques probe different time scales, they are mutually consistent as they probe the same physical mechanisms governing charge motion in disordered media-carrier hopping and thermalization in a disorder-broadened density of states (DOS). The generality of this framework is highlighted by time-resolved experimental data obtained on polymer:fullerene, polymer:polymer, and small-molecule blends with varying morphology, including recent experiments revealing that low donor content OPV devices operate by long-range hole tunneling between non-nearest-neighbor molecules. The importance of nonequilibrium processes in organic electronic materials is reviewed, with a particular focus on experimental data and understanding charge transport physics in terms of material DOS.

Probing the pathways of free charge generation in organic bulk heterojunction solar cells

The fact that organic solar cells perform efficiently despite the low dielectric constant of most photoactive blends initiated a long-standing debate regarding the dominant pathways of free charge formation. Here, we address this issue through the accurate measurement of the activation energy for free charge photogeneration over a wide range of photon energy, using the method of time-delayed collection field. For our prototypical low bandgap polymer:fullerene blends, we find that neither the temperature nor the field dependence of free charge generation depend on the excitation energy, ruling out an appreciable contribution to free charge generation though hot carrier pathways. On the other hand, activation energies are on the order of the room temperature thermal energy for all studied blends. We conclude that charge generation in such devices proceeds through thermalized charge transfer states, and that thermal energy is sufficient to separate most of these states into free charges.

Contradictory models are being debated on the dominant pathways of charge generation in organic solar cells. Here Kurpiers et al. determine the activation energy for this fundamental process and reveal that the main channel is via thermalized charge transfer states instead of hot exciton dissociation.

The Enhancement of Interfacial Exciton Dissociation by Energetic Disorder Is a Nonequilibrium Effect

The dissociation of excited electron-hole pairs is a microscopic process that is fundamental to the performance of photovoltaic systems. For this process to be successful, the oppositely charged electron and hole must overcome an electrostatic binding energy before they undergo ground state recombination. It has been observed previously that the presence of energetic disorder can lead to a reduction in recombination losses. Here we investigate this effect using a simple model of charge dynamics at a donor-acceptor interface. We consider the effect of spatial variations in electronic energy levels, such as those that arise in disordered molecular systems, on dissociation yield and demonstrate that it is maximized with a finite amount of disorder. We demonstrate that this is a nonequilibrium effect that is mediated by the dissipation driven formation of partially dissociated intermediate states that are long-lived because they cannot easily recombine. We present a kinetic model that incorporates these states and show that it is capable of reproducing similar behavior when it is parametrized with nonequilibrium rates.

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.

Encounter-limited charge-carrier recombination in phase-separated organic semiconductor blends

The theoretical effects of phase separation on encounter-limited charge carrier recombination in organic semiconductor blends are investigated using kinetic Monte Carlo simulations of pump-probe experiments. Using model bulk heterojunction morphologies, the dependence of the recombination rate on domain size and charge carrier mobility are quantified. Unifying competing models and simulation results, we show that the mobility dependence of the recombination rate can be described using the power mean of the electron and hole mobilities with a domain-size-dependent exponent. Additionally, for domain sizes typical of organic photovoltaic devices, we find that phase separation reduces the recombination rate by less than one order of magnitude compared to the Langevin model and that the mobility dependence can be approximated by the geometric mean.

Temperature dependence of charge carrier generation in organic photovoltaics

The charge generation mechanism in organic photovoltaics is a fundamental yet heavily debated issue. All the generated charges recombine at the open-circuit voltage (V_{OC}), so that investigation of recombined charges at V_{OC} provides a unique approach to understanding charge generation. At low temperatures, we observe a decrease of V_{OC}, which is attributed to reduced charge separation. Comparison between benchmark polymer:fullerene and polymer:polymer blends highlights the critical role of charge delocalization in charge separation and emphasizes the importance of entropy in charge generation.

Charge generation in polymer-fullerene bulk-heterojunction solar cells

Charge generation in organic solar cells is a fundamental yet heavily debated issue. This article gives a balanced review of different mechanisms proposed to explain efficient charge generation in polymer-fullerene bulk-heterojunction solar cells. We discuss the effect of charge-transfer states, excess energy, external electric field, temperature, disorder of the materials, and delocalisation of the charge carriers on charge generation. Although a general consensus has not been reached yet, recent findings, based on both steady-state and transient measurements, have significantly advanced our understanding of this process.

Photophysics and dynamics of surface plasmon polaritons-mediated energy transfer in the presence of an applied electric field

The possibility to transfer energy between molecular excitons across a metal film up to 150 nm thick represents a very attractive solution to control and improve the performances of thin optoeletronic devices. This process involves the presence of coupled surface plasmon polaritons (SPPs) at the two dielectric-metal interfaces, capable of mediating the interactions between donor and acceptor, located on opposite sides of the metal film. In this Article, the photophysics and the dynamics of an efficient SPP-mediated energy transfer between a suitable dye and a conjugated polymer is characterized by means of steady-state and time-resolved photoluminescence techniques. The process is studied in model multilayer structures (donor/metal/acceptor) as well as in electrically pumped heterostructures (donor/metal cathode/acceptor/anode), to verify the effects of applied electric fields on the efficiency and the dynamics of SPP-mediated energy transfer. A striking enhancement of the overall luminescence was recorded in a particular range of applied bias, suggesting the presence of cooperative effects between optical and electrical stimulations.

Effect of charge trapping on geminate recombination and polymer solar cell performance

In this letter, we examine the effect of charge trapping on geminate recombination and organic photovoltaic performance using a Monte Carlo model. We alter the degree of charge trapping by considering energetic disorder to be spatially uncorrelated or correlated. On correlating energetic disorder, and so reducing the degree of trapping, it is found that power conversion efficiency of blend and bilayer devices improves by factors of 3.1 and 2.6, respectively. These results are related to the experimental data and quantum chemical calculations for poly[9,9-dioctylfluorene-co-bis-N,N'-(4-butylphenyl)-bis-N,N'-phenyl-1,4-phenylenediamine] (PFB)/poly(9,9-dioctylfluorene-co-benzothiadiazole) (F8BT) as well as poly(3-hexylthiophene) (P3HT)/(6,6)-phenyl-C(61)-butyric acid methyl ester (PCBM) solar cell systems. The minimization of traps at the heterojunction between electron- and hole-accepting materials, perhaps by molecular design, appears to be a promising strategy to achieve large gains in PV performance. It is also shown that macroscopically measurable quantities such as mobility and energetic disorder are not necessarily good predictors of nanoscale geminate recombination process.

Exact solution for hopping dissociation of geminate electron-hole pairs in a disordered chain

A universal theoretical description of the dissociation problem for electron-hole pair on a one-dimensional chain in the hopping regime is proposed. Widely used results of Frenkel and Onsager theories are obtained as particular cases of the general solution. The application of the analytical theory to disordered chains shows that disorder enhances dissociation of geminate electron-hole pairs at low electric fields and suppresses at high fields.

Precursor states for charge carrier generation in conjugated polymers probed by ultrafast spectroscopy

Photocurrent experiments using two femtosecond laser pulses are performed on a photodiode using a ladder-type conjugated polymer as the active layer. With a photon energy of 3.1 eV the first pulse excites singlet excitons. A time-delayed second pulse with a photon energy of 2.49 eV leads to a decrease of the photocurrent by exciton depletion due to stimulated emission. S1 excitons being dissociated during their entire lifetime are identified as the only relevant channel for charge carrier generation. Intrachain polaron pairs are also formed on an ultrafast time scale with a yield of approximately 10%. They can be efficiently dissociated by reexcitation with photons of an energy of 1.9 eV.