Exciton Diffusion Constant Research Articles

Nonadiabatic Simulation of Exciton Dynamics in Organic Semiconductors Using Neural Network-Based Frenkel Hamiltonian and Gradients.

In this study, we present a multiscale method to simulate the propagation of Frenkel singlet excitons in organic semiconductors (OSCs). The approach uses neural network models to train a Frenkel-type Hamiltonian and its gradient, obtained by the long-range correction version of density functional tight-binding with self-consistent charges. Our models accurately predict site energies, excitonic couplings, and corresponding gradients, essential for the nonadiabatic molecular dynamics simulations. Combined with the fewest switches surface hopping algorithm, the method was applied to four representative OSCs: anthracene, pentacene, perylenediimide, and diindenoperylene. The simulated exciton diffusion constants align well with experimental and reported theoretical values and offer valuable insights into exciton dynamics in OSCs.

Molecular beam epitaxy of GaN/AlGaN quantum wells on bulk GaN substrate in the step-flow or step meandering regime: Influence on indirect exciton diffusion

GaN/AlxGa1−xN quantum wells were grown by molecular beam epitaxy on high quality bulk (0001) GaN substrates. The quantum well thickness was set in the 6–8 nm range to favor the photoluminescence emission of indirect excitons. Indeed, such excitons are known to be spatially indirect due to the presence of the internal electric field which spatially separates the electron and hole wave functions. The growth conditions were optimized in view of minimizing the photoluminescence peak broadening. In particular, the impact of growth temperature (up to 900 °C) on the surface morphology, structural, and photoluminescence properties was studied. The diffusion of indirect excitons on the scale of tens of micrometers was measured with a micro-photoluminescence setup equipped with a spatially resolved detection. A dedicated model and its analysis allow us to extract from these measurements the exciton diffusion constant and to conclude on the optimum growth conditions for the GaN/AlxGa1−xN quantum well structures suited for studies of quantum collective effects in indirect exciton liquids.

Perylene Diimide Based Fluorescent Sensors for Drug Simulant Detection: The Effect of Alkyl-Chain Branching on Film Morphology, Exciton Diffusion, Vapor Diffusion, and Sensing Response.

Luminescence-based sensing has been demonstrated to be a powerful method for rapid trace detection of chemical vapors (analytes). Analyte diffusion has been shown to be the critical factor for real-time luminescence-based detection of explosive analytes via photoinduced electron transfer in amorphous films of conjugated polymers and dendrimers. However, similar studies to determine the critical factors for sensing have not been performed on materials that employ photoinduced hole transfer (PHT) to detect low electron affinity analytes such as illicit drugs. Nor have such studies been performed on semicrystalline sensing films. We have developed a family of perylene diimide-based sensing materials capable of undergoing PHT with amine-group containing analytes. It was found that the choice of branched alkyl chain [1-hexylheptyl (PHH), 2-hexyloctyl (PHO), or 2,2-dihexyloctyl (PDHO)] attached to the nitrogen atoms of the imide moiety strongly affected the solution-processed film morphology. PHH and PHO were found to contain crystalline phases, whereas PDHO was essentially amorphous. The degree of crystallinity strongly influenced exciton diffusion, with PHH and PHO exhibiting exciton diffusion coefficients that were 20× and 10× greater than the value of the amorphous PDHO. The degree of film crystallinity was also found to be critical when the films were applied to detect N-methylphenethylamine (MPEA), a simulant of methamphetamine. While PHH had the largest exciton diffusion coefficient [(1.0 ± 0.2) × 10-2 cm2 s-1] and analyte uptake (12.3 ± 1.8 ng) it showed the smallest quenching efficiency (2.6% ng-1). In contrast, PHO, which sorbed the least analyte (6.1 ± 0.4 ng) of the three compounds, had the largest quenching efficiency (7.1% ng-1) due to its molecular packing and hence exciton diffusion coefficient [(4.5 ± 1.4) × 10-3 cm2 s-1] not being affected by sorption of the analyte. These results show that when applying fluorescent films in practical detection scenarios there is a potential trade-off between a high exciton diffusion constant and analyte diffusion for semicrystalline sensing materials and that a high exciton diffusion coefficient in an as-cast film does not necessarily translate into a more efficient fluorescent quenching. The results also show that sensing materials that form semicrystalline films, whose packing is not disrupted by analyte diffusion, provide a route for overcoming these effects and achieving high sensitivity.

Efficient 2D to 0D Energy Transfer in HgTe Nanoplatelet-Quantum Dot Heterostructures through High-Speed Exciton Diffusion.

Large area absorbers with localized defect emission are of interest for energy concentration via the antenna effect. Transfer between 2D and 0D quantum-confined structures is advantageous as it affords maximal lateral area antennas with continuously tunable emission. We report the quantum efficiency of energy transfer in in situ grown HgTe nanoplatelet (NPL)/quantum dot (QD) heterostructures to be near unity (>85%), while energy transfer in separately synthesized and well separated solutions of HgTe NPLs to QDs only reaches 47 ± 11% at considerably higher QD concentrations. Using Kinetic Monte Carlo simulations, we estimate an exciton diffusion constant of 1-10 cm2/s in HgTe NPLs, the same magnitude as that of 2D semiconductors. We also simulate in-solution energy transfer between NPLs and QDs, recovering an R-4 dependence consistent with 2D-0D near-field energy transfer even in randomly distributed NPL/QD mixtures. This highlights the advantage of NPLs 2D morphology and the efficiency of NPL/QD heterostructures and mixtures for energy harvesting.

Exciton annihilation in molecular aggregates suppressed through quantum interference.

Exciton-exciton annihilation (EEA), an important loss channel in optoelectronic devices and photosynthetic complexes, has conventionally been assumed to be an incoherent, diffusion-limited process. Here we challenge this assumption by experimentally demonstrating the ability to control EEA in molecular aggregates using the quantum phase relationships of excitons. We employed time-resolved photoluminescence microscopy to independently determine exciton diffusion constants and annihilation rates in two substituted perylene diimide aggregates featuring contrasting excitonic phase envelopes. Low-temperature EEA rates were found to differ by more than two orders of magnitude for the two compounds, despite comparable diffusion constants. Simulated rates based on a microscopic theory, in excellent agreement with experiments, rationalize this EEA behaviour based on quantum interference arising from the presence or absence of spatial phase oscillations of delocalized excitons. These results offer an approach for designing molecular materials using quantum interference where low annihilation can coexist with high exciton concentrations and mobilities.

Supramolecular Tuning of Exciton Transport in Pi-Peptide Assemblies

We demonstrate the use of sequence-dependent interactions between peptide-functionalized pi-conjugated pigments to tune exciton transport behavior in their supramolecular assemblies in aqueous solutions. Peptide sequences attached to a perylene diimide (PDI) core were selected based on their ability to foster a wide range of excitonic coupling strengths within organized assemblies, as reflected by experimentally measured steady-state absorption and emission spectra. Photoresponses of organized assemblies of weakly interacting PDIs closely resemble those observed for weakly assembled chromophores. In contrast, organized assemblies that support strong intermolecular coupling exhibit significant excitonic delocalization and transport, as observed through distinct transient signatures of fluence-dependent singlet–singlet annihilation and a short-lived biexcitonic state at high initial exciton densities. A one-dimensional (1D) diffusion model appropriately accounts for exciton–exciton encounters in assemblies, with effective exciton diffusion constants that scale with interchromophore coupling strength, ranging between 0 and 7 sites2/ps (0–1 nm2/ps or LD ranging from 0 to 40 nm). Variations in effective diffusion constant arise from peptide-tuned variations in interchromophore alignment and wavefunction overlap, with mixed Frenkel-CT exciton coupling identified as the key interaction that facilitates site-to-site exciton diffusion within PDI stacks. This work demonstrates the potential to use simple peptide sequence variation as a tool for rational engineering of exciton transport and other excited-state behaviors in supramolecular materials.

Scaling relations of exciton diffusion in linear aggregates with static and dynamic disorder.

Exciton diffusion plays an important role in many opto-electronic processes and phenomena. Understanding the interplay of intermolecular coupling, static energetic disorder, and dephasing caused by environmental fluctuations (dynamic disorder) is crucial to optimize exciton diffusion under various physical conditions. We report on a systematic analysis of the exciton diffusion constant in linear aggregates using the Haken-Strobl-Reinekermodel to describe this interplay. We numerically investigate the static-disorder scaling of (i) the diffusion constant in the limit of small dephasing rate, (ii) the dephasing rate at which the diffusion is optimized, and (iii) the value of the diffusion constant at the optimal dephasing rate. Three scaling regimes are found, associated with, respectively, fully delocalized exciton states (finite-size effects), weakly localized states, and strongly localized states. The scaling powers agree well with analytically estimated ones. In particular, in the weakly localized regime, the numerical results corroborate the so-called quantum Goldilocks principle to find the optimal dephasing rate and maximum diffusion constant as a function of static disorder, while in the strong-localization regime, these quantities can be derived fully analytically.

Signatures of Dimensionality and Symmetry in Exciton Band Structure: Consequences for Exciton Dynamics and Transport

Exciton dynamics, lifetimes, and scattering are directly related to the exciton dispersion or band structure. Here, we present a general theory for exciton band structure within both ab initio and model Hamiltonian approaches. We show that contrary to common assumption, the exciton band structure contains nonanalytical discontinuities—a feature which is impossible to obtain from the electronic band structure alone. These discontinuities are purely quantum phenomena, arising from the exchange scattering of electron–hole pairs. We show that the degree of these discontinuities depends on materials’ symmetry and dimensionality, with jump discontinuities occurring in 3D and different orders of removable discontinuities in 2D and 1D, whose details depend on the exciton degeneracy and material thickness. We connect these features to the early stages of exciton dynamics, radiative lifetimes, and diffusion constants, in good correspondence with recent experimental observations, revealing that the discontinuities in the band structure lead to ultrafast ballistic transport and suggesting that measured exciton diffusion and dynamics are influenced by the underlying exciton dispersion.

Excitonic Transport and Intervalley Scattering Dynamics in Large‐Size Exfoliated MoSe2 Monolayer Investigated by Heterodyned Transient Grating Spectroscopy

AbstractExciton intervalley scattering, annihilation, relaxation dynamics, and diffusive transport in monolayer transition metal dichalcogenides are central to the functionality of devices based on them. Here, these properties in a large‐size exfoliated high‐quality monolayer MoSe2 are addressed directly using heterodyned transient grating spectroscopy at room temperature. While the free exciton population is found to be long‐lived (≈230 ps), an extremely fast intervalley scattering (≤170 fs) is observed, leading to a negligible valley polarization, consistent with steady state photoluminescence measurements and theoretical calculation. The exciton population decay shows an appreciable contribution from the exciton–exciton annihilation, with an annihilation rate of ≈0.01 cm2 s−1. The annihilation process also leads to a significant distortion of the transient grating evolution. Taking this distortion into account, consistent exciton diffusion constants D ≈ 1.4 cm2 s−1 are found by a model simulation in the excitation density range of 1011–1012 cm−2. The presented results highlight the importance of correctly considering the many‐body annihilation processes to obtain a pronounced understanding of the excitonic properties of monolayer transition metal dichalcogenides.

Charge and Exciton Transfer Simulations Using Machine-Learned Hamiltonians.

Quantum-mechanical simulations of charge and exciton transfer in molecular organic materials are a key method to increase our understanding of organic semiconductors. Our goal is to build an efficient multiscale model to predict charge-transfer mobilities and exciton diffusion constants from nonadiabatic molecular dynamics simulations and Marcus-based Monte Carlo approaches. In this work, we apply machine learning models to simulate charge and exciton propagation in organic semiconductors. We show that kernel ridge regression models can be trained to predict electronic and excitonic couplings from semiempirical density functional tight binding (DFTB) reference data with very good accuracy. In simulations, the models could reproduce hole mobilities along the anthracene crystal axes to within 8.5% of the DFTB reference and 34% of the experimental results with only 1000 training data points. Using these models decreased the cost of exciton transfer simulations by one order of magnitude.

Long-range exciton transport and slow annihilation in two-dimensional hybrid perovskites

Two-dimensional hybrid organic-inorganic perovskites with strongly bound excitons and tunable structures are desirable for optoelectronic applications. Exciton transport and annihilation are two key processes in determining device efficiencies; however, a thorough understanding of these processes is hindered by that annihilation rates are often convoluted with exciton diffusion constants. Here we employ transient absorption microscopy to disentangle quantum-well-thickness-dependent exciton diffusion and annihilation in two-dimensional perovskites, unraveling the key role of electron-hole interactions and dielectric screening. The exciton diffusion constant is found to increase with quantum-well thickness, ranging from 0.06 ± 0.03 to 0.34 ± 0.03 cm2 s−1, which leads to long-range exciton diffusion over hundreds of nanometers. The exciton annihilation rates are more than one order of magnitude lower than those found in the monolayers of transition metal dichalcogenides. The combination of long-range exciton transport and slow annihilation highlights the unique attributes of two-dimensional perovskites as an exciting class of optoelectronic materials.

Direct observation of exciton\u2013exciton interactions

Natural light harvesting as well as optoelectronic and photovoltaic devices depend on efficient transport of energy following photoexcitation. Using common spectroscopic methods, however, it is challenging to discriminate one-exciton dynamics from multi-exciton interactions that arise when more than one excitation is present in the system. Here we introduce a coherent two-dimensional spectroscopic method that provides a signal only in case that the presence of one exciton influences the behavior of another one. Exemplarily, we monitor exciton diffusion by annihilation in a perylene bisimide-based J-aggregate. We determine quantitatively the exciton diffusion constant from exciton–exciton-interaction 2D spectra and reconstruct the annihilation-free dynamics for large pump powers. The latter enables for ultrafast spectroscopy at much higher intensities than conventionally possible and thus improves signal-to-noise ratios for multichromophore systems; the former recovers spatio–temporal dynamics for a broad range of phenomena in which exciton interactions are present.

Direct Imaging of Frenkel Exciton Transport by Ultrafast Microscopy.

Long-range transport of Frenkel excitons is crucial for achieving efficient molecular-based solar energy harvesting. Understanding of exciton transport mechanisms is important for designing materials for solar energy applications. One major bottleneck in unraveling of exciton transport mechanisms is the lack of direct measurements to provide information in both spatial and temporal domains, imposed by the combination of fast energy transfer (typically ≤1 ps) and short exciton diffusion lengths (typically ≤100 nm). This challenge requires developing experimental tools to directly characterize excitation energy transport, and thus facilitate the elucidation of mechanisms. To address this challenge, we have employed ultrafast transient absorption microscopy (TAM) as a means to directly image exciton transport with ∼200 fs time resolution and ∼50 nm spatial precision. By mapping population in spatial and temporal domains, such approach has unraveled otherwise obscured information and provided important parameters for testing exciton transport models. In this Account, we discuss the recent progress in imaging Frenkel exciton migration in molecular crystals and aggregates by ultrafast microscopy. First, we establish the validity of the TAM methods by imaging singlet and triplet exciton transport in a series of polyacene single crystals that undergo singlet fission. A new singlet-mediated triplet transport pathway has been revealed by TAM, resulting from the equilibrium between triplet and singlet exciton populations. Such enhancement of triplet exciton transport enables triplet excitons to migrate as singlet excitons and leads to orders of magnitude faster apparent triplet exciton diffusion rate in the picosecond and nanosecond time scales, favorable for solar cell applications. Next we discuss how information obtained by ultrafast microscopy can evaluate coherent effects in exciton transport. We use tubular molecular aggregates that could support large exciton delocalization sizes as a model system. The initial experiments measure exciton diffusion constants of 3-6 cm2 s-1, 3-5 times higher than the incoherent limit predicted by theory, suggesting that coherent effects play a role. In summary, combining ultrafast spectroscopic methods with microscopic techniques provides a direct approach for obtaining important parameters to unravel the underlying exciton transport mechanisms in molecular solids. We discuss future directions to bridge the gap in understanding of fundamental energy transfer theories to include coherent and incoherent effects. We are still in the infancy of ultrafast microscopy, and the vast potential is not limited to the systems discussed in this Account.

Direct Imaging of Exciton Transport in Tubular Porphyrin Aggregates by Ultrafast Microscopy.

Long-range exciton transport is a key challenge in achieving efficient solar energy harvesting in both organic solar cells and photosynthetic systems. Self-assembled molecular aggregates provide the potential for attaining long-range exciton transport through strong intermolecular coupling. However, there currently lacks an experimental tool to directly characterize exciton transport in space and in time to elucidate mechanisms. Here we report a direct visualization of exciton diffusion in tubular molecular aggregates by transient absorption microscopy with ∼200 fs time resolution and ∼50 nm spatial precision. These direct measurements provide exciton diffusion constants of 3-6 cm2 s-1 for the tubular molecular aggregates, which are 3-5 times higher than a theoretical lower bound obtained by assuming incoherent hopping. These results suggest that coherent effects play a role, despite the fact that exciton states near the band bottom crucial for transport are only weakly delocalized (over <10 molecules). The methods presented here establish a direct approach for unraveling the mechanisms and main parameters underlying exciton transport in large molecular assemblies.

Room-Temperature Micron-Scale Exciton Migration in a Stabilized Emissive Molecular Aggregate.

We report 1.6 ± 1 μm exciton transport in self-assembled supramolecular light-harvesting nanotubes (LHNs) assembled from amphiphillic cyanine dyes. We stabilize LHNs in a sucrose glass matrix, greatly reducing light and oxidative damage and allowing the observation of exciton-exciton annihilation signatures under weak excitation flux. Fitting to a one-dimensional diffusion model, we find an average exciton diffusion constant of 55 ± 20 cm2/s, among the highest measured for an organic system. We develop a simple model that uses cryogenic measurements of static and dynamic energetic disorder to estimate a diffusion constant of 32 cm2/s, in agreement with experiment. We ascribe large exciton diffusion lengths to low static and dynamic energetic disorder in LHNs. We argue that matrix-stabilized LHNS represent an excellent model system to study coherent excitonic transport.

Direct Imaging of Long-Range Exciton Transport in Quantum Dot Superlattices by Ultrafast Microscopy.

Long-range charge and exciton transport in quantum dot (QD) solids is a crucial challenge in utilizing QDs for optoelectronic applications. Here, we present a direct visualization of exciton diffusion in highly ordered CdSe QDs superlattices by mapping exciton population using ultrafast transient absorption microscopy. A temporal resolution of ∼200 fs and a spatial precision of ∼50 nm of this technique provide a direct assessment of the upper limit for exciton transport in QD solids. An exciton diffusion length of ∼125 nm has been visualized in the 3 ns experimental time window and an exciton diffusion coefficient of (2.5 ± 0.2) × 10(-2) cm(2) s(-1) has been measured for superlattices constructed from 3.6 nm CdSe QDs with center-to-center distance of 6.7 nm. The measured exciton diffusion constant is in good agreement with Förster resonance energy transfer theory. We have found that exciton diffusion is greatly enhanced in the superlattices over the disordered films with an order of magnitude higher diffusion coefficient, pointing toward the role of disorder in limiting transport. This study provides important understandings on energy transport mechanisms in both the spatial and temporal domains in QD solids.

Influences of Exciton Diffusion and Exciton-Exciton Annihilation on Photon Emission Statistics of Carbon Nanotubes.

Pump-dependent photoluminescence imaging and second-order photon correlation studies have been performed on individual single-walled carbon nanotubes (SWCNTs) at room temperature. These studies enable the extraction of both the exciton diffusion constant and the Auger recombination coefficient. A linear correlation between these parameters is attributed to the effect of environmental disorder in setting the exciton mean free path and capture-limited Auger recombination at this length scale. A suppression of photon antibunching is attributed to the creation of multiple spatially nonoverlapping excitons in SWCNTs, whose diffusion length is shorter than the laser spot size. We conclude that complete antibunching at room temperature requires an enhancement of the exciton-exciton annihilation rate that may become realizable in SWCNTs allowing for strong exciton localization.

Roles of local and nonlocal electron-phonon couplings in triplet exciton diffusion in the anthracene crystal

Triplet exciton migration in the anthracene single crystal is modeled using a kinetic Monte Carlo scheme based on fully atomistic hopping rates. These account for the coupling of the triplet excitations to both intramolecular vibrations and lattice phonons from first principles. Thermal fluctuations in site energies and excitonic couplings obtained within the fragmented excitation difference approach yield triplet exciton diffusion constants in quantitative agreement with experiment.

Exciton diffusion in near-infrared absorbing solution-processed organic thin films

We report on singlet-singlet annihilation and exciton diffusion in as-prepared p-type and annealed n-type thin films of the low-bandgap quinoidal quaterthiophene [QQT(CN)4] using ultrafast transient absorption measurements. The decay dynamics of exciton populations are well described by a one-dimensional diffusion-limited bimolecular recombination, indicating that the singlet excitons migrate preferentially along the stacking direction. Our results show that the exciton diffusion constants in QQT(CN)4 films do not vary significantly upon thermal annealing. Exciton diffusion lengths are measured to be as high as 4 and 5 nm in as-prepared and annealed QQT(CN)4 films, respectively. We also observe an influence of the excitation densities on the singlet exciton diffusion, which is attributed to phonon scattering. Because of the possibility of patterning p-n regions in QQT(CN)4 films by thermal nanolithography techniques, this study provides important insight not only into the photophysical properties of quinoidal oligothiophene derivatives but also for their future integration into high-performance p-n nanostructured near infrared light-sensing devices.

Förster-mediated spectral diffusion in disordered organic materials

A model that describes exciton diffusion in disordered organic materials is introduced that is capable of quantitatively describing the effects of inhomogeneous broadening and energetic disorder on the energy transfer. The model is tested on a system that consists of a polymer matrix containing the perylene bisimide dye Perylene Red at high concentration as active sites. Excitons can be efficiently exchanged between the dye molecules by F\"orster energy transfer, resulting in a fairly high mobility of the excitons. Compared to polymers, the investigated system provides better insight into the parameters controlling the mobility of the excitons. Using femtosecond absorption spectroscopy, clear signatures for dispersive energy migration are found, namely, a shift of the exciton energy to lower energies within the first picoseconds and an anisotropy decay that deviates slightly from the predictions of classical F\"orster theory. Both effects are quantitatively reproduced by the model, which extends previous theories and takes explicitly into account the dependence of the F\"orster radius on the donor and the acceptor energy in a disordered sample of equal chromophores. The model predicts correctly the order of the exciton diffusion constant and provides a quantitative linkage between the exciton mobility and the inhomogeneous line width.