Ultrafast Long-Range Charge Separation in Organic Photovoltaics: Promotion by Off-Diagonal Vibronic Couplings and Entropy Increase

Endothermic Charge Separation Occurs Spontaneously in Non-Fullerene Acceptor/Polymer Bulk Heterojunction

Organic photovoltaics (OPVs) based on non-fullerene acceptors (NFAs) have achieved a power conversion efficiency close to 20%. These NFA OPVs can generate free carriers efficiently despite a very small energy level offset at the donor/acceptor interface. Why these NFAs can enable efficient charge separation (CS) with low energy losses remains an open question. Here, the CS process in the PM6:Y6 bulk heterojunction is probed by time-resolved two-photon photoemission spectroscopy. It is found that the CS, the conversion from bound charge transfer (CT) excitons to free carriers, is an endothermic process with an enthalpy barrier of 0.15 eV. The CS can occur spontaneously despite being an endothermic process, which implies that it is driven by entropy. It is further argued that the morphology of the PM6:Y6 film and the anisotropic electron delocalization restrict the electron and hole wavefunctions within the CT exciton such that they can primarily contact each other through point-like junctions. This configuration can maximize the entropic driving force.

Theoretical investigation of distal charge separation in a perylenediimide trimer

An exciton-phonon (ex-ph) model based on our recently developed block interaction product basis framework is introduced to simulate the distal charge separation (CS) process in aggregated perylenediimide (PDI) trimer incorporating the quantum dynamic method, i.e., the time-dependent density matrix renormalization group. The electronic Hamiltonian in the ex-ph model is represented by nine constructed diabatic states, which include three local excited (LE) states and six charge transfer (CT) states from both the neighboring and distal chromophores. These diabatic states are automatically generated from the direct products of the leading localized neutral or ionic states of each chromophore's reduced density matrix, which are obtained from ab initio quantum chemical calculation of the subsystem consisting of the targeted chromophore and its nearest neighbors, thus considering the interaction of the adjacent environment. In order to quantum-dynamically simulate the distal CS process with massive coupled vibrational modes in molecular aggregates, we used our recently proposed hierarchical mapping approach to renormalize these modes and truncate those vibrational modes that are not effectively coupled with electronic states accordingly. The simulation result demonstrates that the formation of the distal CS process undergoes an intermediate state of adjacent CT, i.e., starts from the LE states, passes through an adjacent CT state to generate the intermediates (∼200 fs), and then formalizes the targeted distal CS via further charge transference (∼1 ps). This finding agrees well with the results observed in the experiment, indicating that our scheme is capable of quantitatively investigating the CS process in a realistic aggregated PDI trimer and can also be potentially applied to exploring CS and other photoinduced processes in larger systems.

Surface hopping simulations on charge separation in an organic donor-acceptor system

Charge separation in organic solar cells is a long-lasting and heavily debated issue. Here, we use the surface hopping method based on the Pariser-Parr-Pople (PPP) Hamiltonian and configuration interaction singles (CIS) approximation to simulate the charge separation process in an organic donor-acceptor system. The system is composed of one donor polymer chain and four acceptor polymer chains, and they are all stacked face-to-face. We let the system to relax from a photoexcited state, and then we observed that the electron is transferred from the donor chain to different acceptor chains and the hole is left on the donor chain, forming polaron pairs with different electron-hole distances. By performing statistical analysis on a number of trajectories, we found that the electron and the hole are fully separated before the system relaxes to its lowest excited state. The yield of free charges shows a significant dependence on the donor-acceptor band offset which provides the driving force for charge separation, while showing negligible dependence on the photoexcitation energy. The external electric field has a remarkable effect on the yield of free charges.

New Density Matrix Renormalization Group Approaches for Strongly Correlated Systems Coupled with Large Environments

Thanks to the high compression of the matrix product state (MPS) form of the wave function and the efficient site-by-site iterative sweeping optimization algorithm, the density matrix normalization group (DMRG) and its time-dependent variant (TD-DMRG) have been established as powerful computational tools in accurately simulating the electronic structure and quantum dynamics of strongly correlated molecules with a large number (10^1-2) of quantum degrees of freedom (active orbitals or vibrational modes). However, the quantitative characterization of the quantum many-body behaviors of realistic strongly correlated systems requires a further consideration of the interaction between the embedded active subsystem and the remaining correlated environment, e.g., a larger number (10^2-3) of external orbitals in electronic structure or infinite condensed-phase phononic modes in nucleus dynamics. To this end, we introduced three new post-DMRG and TD-DMRG approaches, namely (1) DMRG2sCI-MRCI and DMRG2sCI-ENPT by the reconstruction of selected configuration interaction (sCI) type of compact reference function from DMRG coefficients and the use of externally contracted MRCI (multireference configuration interaction) and Epstein-Nesbet perturbation theory (ENPT), without recourse to the expensive high order n-electron reduced density matrices (n-RDMs). (2) DMRG combined with RR-MRCI (renormalized residue-based MRCI), which improves the computational accuracy and efficiency of internally contracted (ic) MRCI by renormalizing the contracted bases with small-sized buffer environment(s) of a few external orbitals as probes based on quantum information theory. (3) HM (hierarchical mapping)-TD-DMRG in which a large environment is reduced to a small number of renormalized environmental modes (which accounts for the most vital system-environment interactions) through stepwise mapping transformation. These advances extend the efficacy of highly accurate DMRG/TD-DMRG computations to the quantitative characterization of the electronic structure and quantum dynamics in realistic strongly correlated systems coupled with large environments and are reviewed in this paper.

Exciton Dissociation in a Model Organic Interface: Excitonic State-Based Surface Hopping versus Multiconfigurational Time-Dependent Hartree

Quantum dynamical simulations are essential for a molecular-level understanding of light-induced processes in optoelectronic materials, but they tend to be computationally demanding. We introduce an efficient mixed quantum-classical nonadiabatic molecular dynamics method termed eXcitonic state-based Surface Hopping (X-SH), which propagates the electronic Schrödinger equation in the space of local excitonic and charge-transfer electronic states, coupled to the thermal motion of the nuclear degrees of freedom. The method is applied to exciton decay in a 1D model of a fullerene-oligothiophene junction, and the results are compared to the ones from a fully quantum dynamical treatment at the level of the Multilayer Multiconfigurational Time-Dependent Hartree (ML-MCTDH) approach. Both methods predict that charge-separated states are formed on the 10-100 fs time scale via multiple "hot-exciton dissociation" pathways. The results demonstrate that X-SH is a promising tool advancing the simulation of photoexcited processes from the molecular to the true nanomaterials scale.

The role of entropy gains in the exciton separation in organic solar cells

In organic solar cell (OSC), the lower dielectric constant of organic semiconductor material induces a strong Coulomb attraction between electron-hole pairs, which leads to a low exciton separation efficiency, especially the charge transfer (CT) state. The CT state formed at the electron-donor (D) and electron-acceptor (A) interface is regarded as an unfavorable property of organic photovoltaic devices. Since the OSC works in a nonzero temperature condition, the entropy effect would be one of the main reasons to overcome the Coulomb energy barrier and must be taken into account. In this review, we review the present understanding of the entropy-driven charge separation and describe how factors such as the dimensionality of the organic semiconductor, energy disorder effect, the morphology of the active layer, and the nonequilibrium effect affect the entropy contribution in compensating the Coulomb dissociation barrier for CT exciton separation and charge generation process. We focus on the investigation of the entropy effect on exciton dissociation mechanism from both theoretical and experimental aspects, which provides pathways for understanding the underlying mechanisms of exciton separation and further enhancing the efficiency of OSCs. This article is protected by copyright. All rights reserved.

Why ultrafast charge separation occurs in bulk-heterojunction organic solar cells: a multichain tight binding model study

Bulk-heterojunction (BHJ) organic solar cells (OSCs) exhibit ultrafast charge separation (UCS) which enables lower geminate charge recombination and high internal quantum efficiency. Unravelling why UCS occurs in BHJ-OSCs is important for the exploration of devices in future, however it is still far from clear. In this work, we build a multichain tight-binding model to study the conditions for realizing UCS. We propose that two conditions are important: (i) the BHJ-OSC has a morphology with donor and acceptor molecules being individually aggregated; (ii) the ratio of the donor/acceptor interfacial coupling to the internal donor/donor and acceptor/acceptor coupling should be smaller than a threshold. In addition, we suggest that increasing the donor/acceptor energetic offset will boost the UCS efficiency. As a fundamental theoretical analysis on the underlying mechanism of UCS, our work provides design rules for optimizing high-performance BHJ OSCs.

Ultrafast Charge Transfer and Relaxation at a Donor-Acceptor Interface

The efficiency of charge separation in organic photovoltaic materials is crucially determined by the underlying dynamics of the charge transfer (CT) excitons and their dissociation into free electrons and holes. To unravel the main principles of the underlying mechanism on a molecular level, we construct a toy model of electronically coupled donors interacting with a manifold of CT exciton states. In particular, we set up a ladder of CT site energies to model the exciton dissociation. To mimic the complexity of the exciton dynamics at the donor-acceptor interface, the electronic CT manifold is designed to include two vibrational modes that are vibronically coupled to the excitons. We examine the impact of the electronic and vibrational coherences and the structure of the vibronic manifold on the transfer efficiency and charge recombination. Optimal configurations of the vibronic CT manifold are revealed. In particular, the rate of charge recombination can be minimized when the transient dynamics are carefully explored. Such a toy model can be used as a guide for the design of organic materials for efficient photovoltaic devices.

Nonequilibrium Thermodynamics of Charge Separation in Organic Solar Cells

This work presents a novel theoretical description of the nonequilibrium thermodynamics of charge separation in organic solar cells (OSCs). Using stochastic thermodynamics, we take realistic state populations derived from the phonon-assisted dynamics of electron-hole pairs within photoexcited organic bilayers to connect the kinetics with the free energy profile of charge separation. Hereby, we quantify for the first time the difference between nonequilibrium and equilibrium free energy profile. We analyze the impact of energetic disorder and delocalization on free energy, average energy, and entropy. For a high disorder, the free energy profile is well-described as equilibrated. We observe significant deviations from equilibrium for delocalized electron-hole pairs at a small disorder, implying that charge separation in efficient OSCs proceeds via a cold but nonequilibrated pathway. Both a large Gibbs entropy and large initial electron-hole distance provide an efficient charge separation, while a decrease in the free energy barrier does not necessarily enhance charge separation.

Vibration-mediated resonant charge separation across the donor-acceptor interface in an organic photovoltaic device

Examination of a recent open-system Ehrenfest dynamics simulation suggests that a vibration-mediate resonance may play a pivotal role in the charge transfer across a donor-acceptor interface in an organic solar cell. Based on this, a concise dissipative two-level electronic system coupled to a molecular vibrational mode is proposed and solved quantum mechanically. It is found that the charge transfer is enhanced substantially when the vibrational energy quanta is equal to the electronic energy loss across the interface. This vibration-mediate resonant charge transfer process is ultrafast, occurring within 100 fs, comparable to experimental findings. The open-system Ehrenfest dynamics simulation of the two-level model is carried out, and similar results are obtained, which confirms further that the earlier open-system Ehrenfest dynamics simulation indeed correctly predicted the occurrence of the resonant charge transfer across the donor-acceptor interface.

Vibrationally Resolved Absorption Spectra and Exciton Dynamics in Zinc Phthalocyanine Aggregates: Effects of Aggregation Lengths and Remote Exciton Transfer

The vibrationally resolved absorption spectra and exciton dynamics in the α-zinc phthalocyanine aggregates are theoretically investigated by using a non-Markovian stochastic Schrödinger equation. The model Hamiltonian adopted for spectral and dynamic simulations explicitly includes the couplings for both nearest-neighbor and remote exciton transfer, and it is parametrized from first-principles calculations. The results indicate that aggregation lengths and remote exciton transfer significantly influence the relative energy alignment between delocalized Frenkel exciton (FE) and charge transfer (CT) states, which in turn strongly affects the relative intensities of the two absorption peaks in the Q-band region. Analytical formulas are derived to establish quantitative structure-spectra relationships in aggregates, and they offer simple patterns to extract electronic-state properties directly from absorption spectra. The dynamics simulations reveal that the light absorption can directly generate mixed states with both FE and CT features, but it is hard for the photoexcitation from the Q-band region to generate free carriers due to the high energies of charge-separated states.

Charge transfer via deep hole in the J51/N2200 blend

In recently developed non-fullerene acceptor (NFA) based organic solar cells (OSCs), both the donor and acceptor parts can be excited by absorbing light photons. Therefore, both the electron transfer and hole transfer channels could occur at the donor/acceptor interface for generating free charge carriers in NFA based OSCs. However, in many molecular and DNA systems, recent studies revealed that the high charge transfer (CT) efficiency cannot be reasonably explained by a CT model with only highest occupied molecular orbitals (HOMOs) and lowest unoccupied molecular orbitals (LUMOs) of donor and acceptor molecules. In this work, taking an example of a full-polymer blend consisting of benzodithiophene-alt-benzotriazole copolymers (J51) as donor and naphthalene diimide-bithiophene (N2200) as acceptor, in which the ultrafast hole transfer has been recently reported, we investigate its CT process and examine the different roles of various frontier molecular orbitals (FMOs). Through a joint study of quantum mechanics electronic structure calculation and nonadiabatic dynamics simulation, we find that the hole transfer between HOMOs of J51 and N2200 can hardly happen, but the hole transfer from HOMO of N2200 to HOMO - 1 of J51 is much more efficient. This points out the underlying importance of the deep hole channel in the CT process and indicates that including FMOs other than HOMOs and LUMOs is highly necessary to build a robust physical model for studying the CT process in molecular optoelectronic materials.

Reduced Nonradiative Voltage Loss in Terpolymer Solar Cells

The dissociation of hybrid local exciton and charge transfer excitons (LE-CT) in efficient bulk-heterojunction nonfullerene solar cells contributes to reduced nonradiative photovoltage loss, a mechanism that still remains unclear. Herein we studied the energetic and entropic contribution in the hybrid LE-CT exciton dissociation in devices based on a conjugated terpolymer. Compared with reference devices based on ternary blends, the terpolymer devices demonstrated a significant reduction in the nonradiative photovoltage loss, regardless of the acceptor molecule, be it fullerene or nonfullerene. Fourier transform photocurrent spectroscopy revealed a significant LE-CT character in the terpolymer-based solar cells. Temperature-dependent hole mobility and photovoltage confirm that entropic and energetic effects contribute to the efficient LE-CT dissociation. The energetic disorder value measured in the fullerene- or nonfullerene-based terpolymer devices suggested that this entropic contribution came from the terpolymer, a signature of higher disorder in copolymers with multiple aromatic groups. This gives new insight into the fundamental physics of efficient LE-CT exciton dissociation with smaller nonradiative recombination loss.

Exciton dissociation and charge separation at donor–acceptor interfaces from quantum-classical dynamics simulations

Nonadiabatic dynamics simulations based on the quantum-classical Liouville equation are employed to study the real-time dynamics of exciton dissociation and charge separation at a model donor–acceptor interface.

Charge-transfer state dynamics in all-polymer solar cells: formation, dissociation and decoherence

All-polymer solar cells have made substantial achievements in recent years, offering numerous unsettled subjects for mechanical researchers. In order to quantitatively study the influence of the molecular electrostatic potential on the charge generation proposed by the experimenter, we simulate the ultrafast dynamics of the charge-transfer (CT) state at the interface between two polymer chains, which are respectively regarded as the donor and acceptor in all-polymer solar cells. The formation of a stable CT state is found to be sensitive to the distance between two oppositely charged polarons and the relevant critical electrostatic potential is thus quantified, which is in good agreement with experiments. In order to get insight into the dependence of the dissociation of the CT state on the width of the interfacial layer, two quantities are calculated: one is the Coulomb capture radius between the two polarons and the other is the quantum trace distance which serves as the fingerprint of the quantum coherence between them. The dissociation of the CT state is found to take place within an ultrafast timescale for an optimum interfacial width. The classical spatial distance and the quantum trace distance manifest a converging trend, suggesting a decoherence scenario for the charge separation in all-polymer solar cells.

Optimum driving energy for achieving balanced open-circuit voltage and short-circuit current density in organic bulk heterojunction solar cells

Organic bulk heterojunction solar cells generally suffer from a trade-off between the open circuit voltage (Voc) and the short circuit current density (Jsc) under a given donor/acceptor (D/A) interfacial energetic offset (or the so-called driving force). Here we theoretically investigate the optimum driving energy required for achieving the balanced Jsc and Voc simultaneously. To this end, the Jscversus the driving force ΔE curves are calculated under two different charge separation mechanisms by employing the drift-diffusion method. For the Marcus incoherent mechanism, the curve features a high plateau in a broad range of ΔE starting from 0.2 eV, which is due to the accumulation of undissociated excitons within their lifetime and signifies the possibility of obtaining a sizable Jsc under a ΔE value much smaller than the reorganization energy. After incorporating both the electron and hole transfer pathways into the device model, the calculated J-V curves are comparable to experimentally measured ones foractual blended systems of different driving forces. For the coherent mechanism, it is demonstrated that the maximum Jsc can also be achieved under the ΔE of 0.2 eV if a large proportion of the high-lying delocalized states are harvested through tuning the density of states for the charge transfer excitons to reduce the sub-gap states. This theoretical work revealed quantitatively the relationship between the interfacial energy offsets and device performance, and also provides some guidelines for identifying the macroscopic features of the actual charge separation mechanisms in bulk heterojunction solar cells.

Full Quantum Dynamics Simulation of a Realistic Molecular System Using the Adaptive Time-Dependent Density Matrix Renormalization Group Method

The accurate theoretical interpretation of ultrafast time-resolved spectroscopy experiments relies on full quantum dynamics simulations for the investigated system, which is nevertheless computationally prohibitive for realistic molecular systems with a large number of electronic and/or vibrational degrees of freedom. In this work, we propose a unitary transformation approach for realistic vibronic Hamiltonians, which can be coped with using the adaptive time-dependent density matrix renormalization group (t-DMRG) method to efficiently evolve the nonadiabatic dynamics of a large molecular system. We demonstrate the accuracy and efficiency of this approach with an example of simulating the exciton dissociation process within an oligothiophene/fullerene heterojunction, indicating that t-DMRG can be a promising method for full quantum dynamics simulation in large chemical systems. Moreover, it is also shown that the proper vibronic features in the ultrafast electronic process can be obtained by simulating the two-dimensional (2D) electronic spectrum by virtue of the high computational efficiency of the t-DMRG method.

Partial atomic multipoles for internally consistent microelectrostatic calculations

An extension of the extant microelectrostatic methodologies, based on the concept of distributed generalized polarizability matrix derived from the Coupled Perturbed Hartree-Fock (CPHF) equations, is proposed for self-consistent calculation of charge carrier and charge-transfer (CT) state electrostatic energies in molecular solids, including the doped, defected and disordered ones. The CPHF equations are solved only once and the generalized molecular polarizability they yield enables low cost iterations that mutually adjust the molecular electronic distributions and the local electric field in which the molecules are immersed. The approach offers a precise picture of molecular charge densities, accounting for atomic partial multipoles up to order 2, which allows one to reproduce the recently reported large charge-quadrupole contributions to CT state energies in low-symmetry local environments. It is particularly well suited for repetitive calculations for large clusters (up to 300,000 atoms), and may potentially be useful for describing electrostatic solvent effects. © 2017 Wiley Periodicals, Inc.

Effect of Infrared Pulse Excitation on the Bound Charge-Transfer State of Photovoltaic Interfaces

The nature and dynamics of the bound charge-transfer (CT) state in the exciton dissociation process in organic solar cells are of critical importance for the understanding of these devices. It was recently demonstrated that this state can be probed by a new experiment in which an infrared (IR) push-pulse is used to dissociate charges from the bound excited state. Here we proposed a simple quantum dynamics model to simulate the excitation of the IR pulse on the bound CT state with model parameters extracted from quantum chemical calculations. We show that the pulse dissociates the CT state following two different mechanisms: one, fairly expected, is the direct excitation of higher energy CT states leading to charge separation; the other, proposed here for the first time, is a rebound mechanism in which the negative charge is transferred in the opposite direction to form the neutral Frenkel exciton state from where it dissociates.

Determining the Conduction Band-Edge Potential of Solar-Cell-Relevant Nb2O5 Fabricated by Atomic Layer Deposition

Often key to boosting photovoltages in photoelectrochemical and related solar-energy-conversion devices is the preferential slowing of rates of charge recombination-especially recombination at semiconductor/solution, semiconductor/polymer, or semiconductor/perovskite interfaces. In devices featuring TiO₂ as the semiconducting component, a common approach to slowing recombination is to install an ultrathin metal oxide barrier layer or trap-passivating layer atop the semiconductor, with the needed layer often being formed via atomic layer deposition (ALD). A particularly promising barrier layer material is Nb₂O₅. Its conduction-band-edge potential E_CB is low enough that charge injection from an adsorbed molecular, polymeric, or solid-state light absorber and into the semiconductor can still occur, but high enough that charge recombination is inhibited. While a few measurements of E_CB have been reported for conventionally synthesized, bulk Nb₂O₅, none have been described for ALD-fabricated versions. Here, we specifically determine the conduction-band-edge energy of ALD-fabricated Nb₂O₅ relative to that of TiO₂. We find that, while the value for ALD-Nb₂O₅ is indeed higher than that for TiO₂, the difference is less than anticipated based on measurements of conventionally synthesized Nb₂O₅ and is dependent on the thermal history of the material. The implications of the findings for optimization of competing interfacial rate processes, and therefore photovoltages, are briefly discussed.