Prolonged Exciton Lifetime Is Achieved in Porphyrin Nanoring by Template Engineering: A Nonadiabatic Tight Binding Approach

Porphyrin nanoring has been attracting immense attention due to its light harvesting capacity and potential applications in optical, catalysis, sensor, and electronic devices. We demonstrate by nonadiabatic quantum dynamics simulations that the photovoltaic efficiency can be enhanced by template engineering. Altering the hexadentate template (T6) with two tridentate templates (2T3) within the porphyrin ring (P6) cavity accelerated the electron transfer twice and suppressed the electron-hole recombination by nearly three times. The atomistic tight-binding simulation rationalized the dynamics by different localizations of charge of the band edge states, changes in nonadiabatic coupling, alteration in quantum coherence, and involvement of diverse electron-phonon vibrational modes. Further 2T3 templates more strongly hold the P6 ring than T6, reducing the structural fluctuation. As a result, the nonadiabatic coupling becomes weaker and suppresses the carrier recombination. Current atomistic simulation presents a template engineering strategy to enhance the exciton lifetime along with ultrafast charge separation, crucial factors for photovoltaic applications.

Estimating Nonradiative Excited-State Lifetimes in Photoactive Semiconducting Nanostructures

The time evolution of the exciton generated by light adsorption in a photocatalyst is an important feature that can be approached from full nonadiabatic molecular dynamics simulations. Here, a crucial parameter is the nonradiative recombination rate between the hole and the electron that form the exciton. In the present work, we explore the performance of a Fermi's golden rule-based approach on predicting the recombination rate in a set of photoactive titania nanostructures, relying solely on the coupling of the ground and first excited state. In this scheme the analysis of the first excited state is carried out by invoking Kasha's rule thus avoiding computationally expensive nonadiabatic molecular dynamics simulations and resulting in an affordable estimate of the recombination rate. Our results show that, compared to previous ones from nonadiabatic molecular dynamics simulations, semiquantitative recombination rates can be predicted for the smaller titania nanostructures, and qualitative values are obtained from the larger ones. The present scheme is expected to be useful in the field of computational heterogeneous photocatalysis whenever a complex and computationally expensive full nonadiabatic molecular dynamics cannot be carried out.

Two-Dimensional Octuple-Atomic-Layer M2Si2N4 (M = Al, Ga and In) with Long Carrier Lifetime

Bulk III-nitride materials MN (M = Al, Ga and In) and their alloys have been widely used in high-power electronic and optoelectronic devices, but stable two-dimensional (2D) III-nitride materials, except h-BN, have not been realized yet. A new kind of 2D III-nitride material M2Si2N4 (M = Al, Ga and In) is predicted by choosing Si as the appropriate passivation element. The stability, electronic and optical properties of 2D M2Si2N4 materials are studied systematically based on first-principles calculations. The results show that Al2Si2N4 and Ga2Si2N4 are found to be indirect bandgap semiconductors, while In2Si2N4 is a direct bandgap semiconductor. Moreover, Al2Si2N4 and In2Si2N4 have good absorption ability in the visible light region, while Ga2Si2N4 is an ultraviolet-light-absorbing material. Furthermore, the carrier lifetimes of Ga2Si2N4 and In2Si2N4 are as large as 157.89 and 103.99 ns, respectively. All these desirable properties of M2Si2N4 materials make them attractive for applications in electronics and photoelectronics.

Symmetrical Linkage in Porphyrin Nanoring Suppressed the Electron-Hole Recombination Demonstrated by Nonadiabatic Molecular Dynamics

Macromolecular porphyrin nanorings are receiving significant attention because of their excellent optoelectronic properties. However, their efficiencies as potential solar materials are significantly affected by nonradiative charge recombination. To understand the recombination mechanism by alternating structural parameters and using tight-binding nonadiabatic molecular dynamics, we demonstrate that charge recombination depends strongly on the mode of the linker in the porphyrin nanoring. The nanoring having all-butadiyne-linkage (pristine-P8) inhibits carrier relaxation. In contrast, a partially fused nanoring (fused-P8) expedites the rate of quantum transition. An extension of the lifetime by a factor of 4 is due to the larger optical gap in pristine-P8 that reduces the NA coupling by decreasing the overlap between band edge states. Additionally, an intense phonon peak in the low-frequency region and rapid coherence loss within the electronic subsystem favors prolonging the carrier lifetime. This study provides an atomistic realization for the design of macromolecular porphyrin nanorings for the potential use in photovoltaic materials.

Two Dimensional MOene: From Superconductors to Direct Semiconductors and Weyl Fermions

The number of semiconducting MXenes with direct band gaps is extremely low; thus, it is highly desirable to broaden the MXene family beyond carbides and nitrides to expand the palette of desired chemical and physical properties. Here, we theoretically report the existence of the single-layer (SL) dititanium oxide 2H-Ti₂O MOene (MXene-like 2D transition oxides), showing an Ising superconducting feature. Moreover, SL halogenated 2H- and 1T-Ti₂O monolayers display tunable semiconducting features and strong light-harvesting ability. In addition, the external strains can induce Weyl fermions via quantum phase transition in 2H-Ti₂OF₂ and Ti₂OCl₂ monolayers. Specifically, 2H- and 1T-Ti₂OF₂ are direct semiconductors with band gaps of 0.82 and 1.18 eV, respectively. Furthermore, the carrier lifetimes of SL 2H- and 1T-Ti₂OF₂ are evaluated to be 0.39 and 2.8 ns, respectively. This study extends emerging phenomena in a rich family of 2D MXene-like MOene materials, which provides a novel platform for next-generation optoelectronic and photovoltaic fields.

Interpolating Nonadiabatic Molecular Dynamics Hamiltonian with Inverse Fast Fourier Transform

Nonadiabatic (NA) molecular dynamics (MD) allows one to investigate far-from-equilibrium processes in nanoscale and molecular materials at the atomistic level and in the time domain, mimicking time-resolved spectroscopic experiments. Ab initio NAMD is limited to about 100 atoms and a few picoseconds, due to computational cost of excitation energies and NA couplings. We develop a straightforward methodology that can extend ab initio quality NAMD to nanoseconds and thousands of atoms. The ab initio NAMD Hamiltonian is sampled and interpolated along a trajectory using a Fourier transform, and then, it is used to perform NAMD with known algorithms. The methodology relies on the classical path approximation, which holds for many materials and processes. To achieve a complete ab initio quality description, the trajectory can be obtained using an ab initio trained machine learning force field. The method is demonstrated with charge carrier trapping and relaxation in hybrid organic-inorganic and all-inorganic metal halide perovskites that exhibit complex dynamics and are actively studied for optoelectronic applications.

Increasing Efficiency of Nonadiabatic Molecular Dynamics by Hamiltonian Interpolation with Kernel Ridge Regression

Nonadiabatic (NA) molecular dynamics (MD) goes beyond the adiabatic Born-Oppenheimer approximation to account for transitions between electronic states. Such processes are common in molecules and materials used in solar energy, optoelectronics, sensing, and many other fields. NA-MD simulations are much more expensive compared to adiabatic MD due to the need to compute excited state properties and NA couplings (NACs). Similarly, application of machine learning (ML) to NA-MD is more challenging compared with adiabatic MD. We develop an NA-MD simulation strategy in which an adiabatic MD trajectory, which can be generated with a ML force field, is used to sample excitation energies and NACs for a small fraction of geometries, while the properties for the remaining geometries are interpolated with kernel ridge regression (KRR). This ML strategy allows for one to perform NA-MD under the classical path approximation, increasing the computational efficiency by over an order of magnitude. Compared to neural networks, KRR requires little parameter tuning, saving efforts on model building. The developed strategy is demonstrated with two metal halide perovskites that exhibit complicated MD and are actively studied for various applications.

Dependence between Structural and Electronic Properties of CsPbI3: Unsupervised Machine Learning of Nonadiabatic Molecular Dynamics

Using unsupervised machine learning on the trajectories from a nonadiabatic molecular dynamics simulation with time-dependent Kohn-Sham density functional theory, we elucidated the structural parameters with the largest influence on nonradiative recombination of charge carriers in CsPbI₃, which forms the basis for solar energy and optoelectronic applications. The I-I-I angles between PbI₆ octahedra, followed by the Cs-I distance, have the strongest impact on the bandgap and the nonadiabatic coupling. The importance of the Cs-I distance is unexpected, because Cs does not contribute to electron and hole wave functions. The nonadiabatic coupling is most influenced by static properties, which is also surprising, given its explicit dependence on atomic velocities.

Ultrafast Orbital Depolarization and Defect-Localized Phonon Dynamics Induced by Quantum Resonance between Multi-Nitrogen Vacancy Defects

Proximate nitrogen-vacancy (NV) defects with interdefect interaction may establish a new kind of quantum qubit network to explore controlled multibody quantum dynamics. In particular, by introducing the critical distance and favorable orientation between a pair of NV defects, the quantum resonance (QR) can be induced. Here, we present the first real-time depolarization and phonon dynamics on the excited state at ambient temperature which are intrinsic to the proximate multi-NV defects. We computationally demonstrate that the QR can effectively change the major properties of the multi-NV defects, such as orbital degeneracy, orbital delocalization, local phonon modes, electron-phonon coupling, and orbital depolarization dynamics, elucidating the physical mechanisms and finding the key factors to control them. The physical insights provide a starting point for the positioning accuracy of NV defects and creation protocols with broad implications for magnetometry, quantum information, nanophotonics, sensing, and spectroscopy, allowing the QR to be a new means of physical manipulation.

Hydrogen Passivated Silicon Grain Boundaries Greatly Reduce Charge Recombination for Improved Silicon/Perovskite Tandem Solar Cell Performance: Time Domain Ab Initio Analysis

By performing nonadiabatic molecular dynamics simulations, we demonstrate that grain boundaries (GBs) can induce the indirect-to-direct transition of the silicon band gap. However, missing a silicon atom creates an electron trap state in the GBs. Electron trapping by the silicon vacancy occurs on tens of picoseconds followed by recombination of the trapped electron and valence band hole on sub-100 ps, which operates parallel to recombination of the free electron and hole on a similar time scale. The recombination is greatly accelerated by 2 orders of magnitude compared to the GBs without a silicon vacancy. Hydrogen passivation eliminates the trap state and notably delays the charge recombination due to an increased band gap and a shortened coherence time, extending the excited-state lifetime to sub-10 ns. Our study provides an atomistic description of how charge recombination in the silicon can be efficiently reduced, suggesting a rational route to enhance silicon/perovskite tandem solar cells performance.

Strong Influence of Ti Adhesion Layer on Electron-Phonon Relaxation in Thin Gold Films: Ab Initio Nonadiabatic Molecular Dynamics

Electron-phonon relaxation in thin metal films is an important consideration for many ultrasmall devices and ultrafast applications. Recent time-resolved experiments demonstrate a significant, more than a factor of five, increase in the electron-phonon coupling and acceleration in the electron-phonon relaxation rate when a narrow Ti adhesion layer is introduced between an Au film and a nonmetal substrate. Using nonadiabatic molecular dynamics combined with real-time time-dependent density functional theory, we identify the reasons that give rise to this strong effect. First, the Ti layer greatly enhances the density of states (DOS) in the energy region starting at 1 eV below the Fermi level and extending several electronvolts above it. Second, Ti atoms are four times lighter than Au atoms and therefore generate larger nonadiabatic (NA) electron-phonon coupling. Because the transition rates depend on coupling and DOS, both the factors accelerate the dynamics. Showing good agreement with the experiments, the time-domain atomistic simulations provide a detailed mechanistic understanding of the electron-phonon relaxation dynamics in thin gold films and related nanomaterials.

Control of Multiple Exciton Generation and Electron-Phonon Coupling by Interior Nanospace in Hyperstructured Quantum Dot Superlattice

The possibility of precisely manipulating interior nanospace, which can be adjusted by ligand-attaching down to the subnanometer regime, in a hyperstructured quantum dot (QD) superlattice (QDSL) induces a new kind of collective resonant coupling among QDs and opens up new opportunities for developing advanced optoelectric and photovoltaic devices. Here, we report the first real-time dynamics simulations of the multiple exciton generation (MEG) in one-, two-, and three-dimensional (1D, 2D, and 3D) hyperstructured H-passivated Si QDSLs, accounting for thermally fluctuating band energies and phonon dynamics obtained by finite-temperature ab initio molecular dynamics simulations. We computationally demonstrated that the MEG was significantly accelerated, especially in the 3D QDSL compared to the 1D and 2D QDSLs. The MEG acceleration in the 3D QDSL was almost 1.9 times the isolated QD case. The dimension-dependent MEG acceleration was attributed not only to the static density of states but also to the dynamical electron-phonon couplings depending on the dimensionality of the hyperstructured QDSL, which is effectively controlled by the interior nanospace. Such dimension-dependent modifications originated from the short-range quantum resonance among component QDs and were intrinsic to the hyperstructured QDSL. We propose that photoexcited dynamics including the MEG process can be effectively controlled by only manipulating the interior nanospace of the hyperstructured QDSL without changing component QD size, shape, compositions, ligand, etc.

Decoherence Allows Model Reduction in Nonadiabatic Dynamics Simulations

A nonadiabatic (NA) molecular dynamics (MD) simulation requires calculation of NA coupling matrix elements, the number of which scales as a square of the number of basis states. The basis size can be huge in studies of nanoscale materials, and calculation of the NA couplings can present a significant bottleneck. A quantum-classical approximation, NAMD overestimates coherence in the quantum, electronic subsystem, requiring decoherence correction. Generally, decoherence times decrease with increasing energy separation between pairs of states forming coherent superpositions. Since rapid decoherence stops quantum dynamics, one expects that decoherence-corrected NAMD can eliminate the need for calculation of NA couplings between energetically distant states, notably reducing the computational cost. Considering several types of dynamics in a semiconductor quantum dot, we demonstrate that indeed, decoherence allows one to reduce the number of needed NA coupling matrix elements. If the energy levels are spaced closer than 0.1 eV, one obtains good results while including only three nearest-neighbor couplings, and in some cases even with just the first nearest-neighbor coupling scheme. If the energy levels are spaced by about 0.4 eV, the nearest-neighbor model fails, while three or more nearest-neighbor schemes also provide good results. In comparison, the results of NAMD simulation without decoherence vary continuously with changes in the number of NA couplings. Thus, decoherence effects induced by coupling to a quantum-mechanical environment not only provide the physical mechanism for NAMD trajectory branding and improve the accuracy of NAMD simulations, but also afford significant computational savings.

Evidence of Phonon-Assisted Auger Recombination and Multiple Exciton Generation in Semiconductor Quantum Dots Revealed by Temperature-Dependent Phonon Dynamics

Auger processes, multiple exciton generation, and Auger recombination, provide and disturb a potential route to increase solar cell efficiencies by creating multiple charge carriers, respectively. Physical mechanisms of the Auger processes can be deduced from the temperature dependence. Our real-time ab initio simulation found logarithmic temperature dependence of the Auger rates in semiconductor quantum dots (QDs), which agrees well with the recent experimental observations. This anomalous temperature dependence is not only determined by static electronic structures of the QDs depending on temperature, but also attributed to dynamical electron-phonon couplings, directly demonstrating that the Auger processes are actually induced by the electron-phonon couplings and can be controlled by phonon modes. Our findings suggest that high-frequency and broad phonon modes of a QD including the surface ligands dictate efficient Auger dynamics in a QD.

Exciton multiplication from first principles

Third-generation photovolatics require demanding cost and power conversion efficiency standards, which may be achieved through efficient exciton multiplication. Therefore, generating more than one electron-hole pair from the absorption of a single photon has vast ramifications on solar power conversion technology. Unlike their bulk counterparts, irradiated semiconductor quantum dots exhibit efficient exciton multiplication, due to confinement-enhanced Coulomb interactions and slower nonradiative losses. The exact characterization of the complicated photoexcited processes within quantum-dot photovoltaics is a work in progress. In this Account, we focus on the photophysics of nanocrystals and investigate three constituent processes of exciton multiplication, including photoexcitation, phonon-induced dephasing, and impact ionization. We quantify the role of each process in exciton multiplication through ab initio computation and analysis of many-electron wave functions. The probability of observing a multiple exciton in a photoexcited state is proportional to the magnitude of electron correlation, where correlated electrons can be simultaneously promoted across the band gap. Energies of multiple excitons are determined directly from the excited state wave functions, defining the threshold for multiple exciton generation. This threshold is strongly perturbed in the presence of surface defects, dopants, and ionization. Within a few femtoseconds following photoexcitation, the quantum state loses coherence through interactions with the vibrating atomic lattice. The phase relationship between single excitons and multiple excitons dissipates first, followed by multiple exciton fission. Single excitons are coupled to multiple excitons through Coulomb and electron-phonon interactions, and as a consequence, single excitons convert to multiple excitons and vice versa. Here, exciton multiplication depends on the initial energy and coupling magnitude and competes with electron-phonon energy relaxation. Multiple excitons are generated through impact ionization within picoseconds. The basis of exciton multiplication in quantum dots is the collective result of photoexcitation, dephasing, and nonadiabatic evolution. Each process is characterized by a distinct time-scale, and the overall multiple exciton generation dynamics is complete by about 10 ps. Without relying on semiempirical parameters, we computed quantum mechanical probabilities of multiple excitons for small model systems. Because exciton correlations and coherences are microscopic, quantum properties, results for small model systems can be extrapolated to larger, realistic quantum dots.

Molecular Design of Porphyrins for Dye-Sensitized Solar Cells: A DFT/TDDFT Study

To design efficient sensitizers for dye-sensitized solar cells (DSSCs), a series of porphyrin sensitizers with different electron-donating and withdrawing substituents are investigated using the density functional theory (DFT) and time-dependent DFT approach. We found that the designed dyes have smaller highest occupied molecular orbital to lowest unoccupied molecular orbital (HOMO-LUMO) energy gap values, and the absorption bands are broadened and shifted to longer wavelengths compared to the so far best sensitizer (YD2-o-C8). Importantly, our designed dyes have larger contributions of the anchoring group to the LUMOs, which enhance the electron injection process. Our calculation results indicated that the new systems should have better performance than the existing efficient dyes due to their improved optical properties.

Photoexcited electron and hole dynamics in semiconductor quantum dots: phonon-induced relaxation, dephasing, multiple exciton generation and recombination

Photoexcited dynamics of electrons and holes in semiconductor quantum dots (QD), including phonon-induced relaxation, multiple exciton generation, fission and recombination (MEG, MEF and MER), were simulated by combining ab initio time-dependent density functional theory and non-adiabatic molecular dynamics. These nonequilibrium phenomena govern the optical properties and photoexcited dynamics of QDs, determining the branching between electronic processes and thermal energy losses. Our approach accounts for QD size and shape as well as defects, core-shell distribution, surface ligands and charge trapping, which significantly influence the properties of photoexcited QDs. The method creates an explicit time-domain representation of photoinduced processes and describes various kinetic regimes owing to the non-perturbative treatment of quantum dynamics. QDs of different sizes and materials, with and without ligands, are considered. The simulations provide direct evidence that the high-frequency ligand modes on the QD surface play a pivotal role in the electron-phonon relaxation, MEG, MEF and MER. The insights reported here suggest novel routes for controlling the photoinduced processes in semiconductor QDs and lead to new design principles for increasing the efficiencies of photovoltaic devices.

Multiple exciton generation and recombination dynamics in small Si and CdSe quantum dots: an ab initio time-domain study

Multiple exciton generation and recombination (MEG and MER) dynamics in semiconductor quantum dots (QDs) are simulated using ab initio time-dependent density functional theory in combination with nonadiabatic molecular dynamics. The approach differs from other MEG and MER theories because it provides atomistic description, employs time-domain representation, allows for various dynamical regimes, and includes electron-phonon interactions. MEG rapidly accelerates with energy, reflecting strong energy dependence of double exciton (DE) density of states. At early times, MEG is Gaussian rather than exponential. Exponential dynamics, assumed in rate theories, starts at a later time and becomes more important in larger QDs. Phonon-assisted MEG is observed at energies below the purely electronic threshold, particularly in the presence of high-frequency ligand vibrations. Coupling to phonons is essential for MER since higher-energy DEs must relax to recombine into single excitons (SEs), and SEs formed during MERs must lose some of their energy to avoid recreating DEs. MER simulated starting from a DE is significantly slower than MER involving an optical excitation of a SE, followed by MEG and then MER. The latter time scale agrees with experiment, emphasizing the importance of quantum-mechanical superpositions of many DEs for efficient MER. The detailed description of the interplay between MEG and MER coupled to phonons provides important insights into the excited state dynamics of semiconductor QDs and nanoscale materials in general.

Time-domain ab initio study of Auger and phonon-assisted auger processes in a semiconductor quantum dot

We developed time-domain ab initio simulation of Auger phenomena, including multiple exciton generation (MEG) and recombination (MER). It is the first approach describing phonon-assisted processes and early dynamics. MEG starts below the electronic threshold, strongly accelerating with energy. Ligands are particularly important to phonon-assisted MEG, which therefore can be probed with infrared spectroscopy. Short-time gaussian component gives 5-10% of MEG, justifying rate theories that assume exponential dynamics. MER is preceded by electron-phonon relaxation to low energies.

Photoinduced dynamics in semiconductor quantum dots: insights from time-domain ab initio studies

Nanoscale clusters of bulk materials, also known as quantum dots (QDs), exhibit both molecular and bulk properties. Unlike either bulk or molecular materials, QD properties can be modified continuously by changing QD shape and size. However, the chemical and physical properties of molecular and bulk materials often contradict each other, which can lead to differing viewpoints about the behavior of QDs. For example, the molecular view suggests strong electron-hole and charge-phonon interactions, as well as slow energy relaxation due to mismatch between electronic energy gaps and phonon frequencies. In contrast, the bulk view advocates that the kinetic energy of quantum confinement is greater than electron-hole interactions, that charge-phonon coupling is weak, and that the relaxation through quasi-continuous bands is rapid. By synthesizing the bulk and molecular viewpoints, this Account clarifies the controversies and provides a unified atomistic picture of the nature and dynamics of photoexcited states in semiconductor QDs. Based on the state-of-the-art ab initio approaches in both the energy and time domains, the Account presents a comprehensive discussion of the dynamical processes in QDs, ranging from the initial photon absorption to the final emission. The atomistic description of QDs complements phenomenological models, provides important details, and creates new scientific paradigms. The ab initio approaches are particularly useful for studying geometric and electronic structure of QDs because they treat bulk, surface, ligands, and defects on equal footing and incorporate electronic correlation effects. Nonadiabatic molecular dynamics simulations most closely mimic the complex coupled evolutions of charges, phonons, and spins as they occur in nature. The simulations show that the underlying atomic structure, thermal fluctuations, and surface effects lift electronic state degeneracies predicted by phenomenological models and that excitonic electron-hole interactions are strong in small QDs. Stoichiometric surfaces self-heal. However, only molecular ligands and core/shell designs can eliminate traps associated with dangling chemical bonds, missing atoms, and other defects. Ligands create charge traps and provide high-frequency phonons. The phonon-induced dephasing of electronic excitations is ultrafast, ranging from tens to hundreds of femtoseconds. The dependence of the relaxation on the excitation energy and the density of states clarify the controversies regarding the phonon bottleneck in the photoexcited electron relaxation, and the participation of low-frequency phonons explains the temperature dependence of the relaxation rate. We rationalize the ultrafast generation of multiple excitons without the phononbottleneck by strong Coulomb interactions between the charge carriers. The QD charging and defects explain the large variation in the experimental data on multiple exciton generation. The issues raised here with the electronic states and semiconductor QDs are similar to those found with the spin states and metallic QDs. Assemblies of QDs with other materials, such as organic chromophores and inorganic semiconductors, will present new sets of questions. Time-domain ab initio approaches will allow scientists to address these challenges directly in the near future.