Electron-Volt Fluctuation of Defect Levels in Metal Halide Perovskites on a 100 ps Time Scale

Machine learning accelerated nonadiabatic dynamics simulations of materials with excitonic effects

This study presents an efficient methodology for simulating nonadiabatic dynamics of complex materials with excitonic effects by integrating machine learning (ML) models with simplified Tamm-Dancoff approximation (sTDA) calculations. By leveraging ML models, we accurately predict ground-state wavefunctions using unconverged Kohn-Sham (KS) Hamiltonians. These ML-predicted KS Hamiltonians are then employed for sTDA-based excited-state calculations (sTDA/ML). The results demonstrate that excited-state energies, time-derivative nonadiabatic couplings, and absorption spectra from sTDA/ML calculations are accurate enough compared with those from conventional density functional theory based sTDA (sTDA/DFT) calculations. Furthermore, sTDA/ML-based nonadiabatic molecular dynamics simulations on two different materials systems, namely chloro-substituted silicon quantum dot and monolayer black phosphorus, achieve more than 100 times speedup than the conventional linear response time-dependent DFT simulations. This work highlights the potential of ML-accelerated nonadiabatic dynamics simulations for studying the complicated photoinduced dynamics of large materials systems, offering significant computational savings without compromising accuracy.

Point defects at grain boundaries can create structural instabilities and persistent deep traps in metal halide perovskites

Metal halide perovskites (MHPs) have attracted strong interest for a variety of applications due to their low cost and excellent performance, attributed largely to favorable defect properties. MHPs exhibit complex dynamics of charges and ions that are coupled in unusual ways. Focusing on a combination of two common MHP defects, i.e., a grain boundary (GB) and a Pb interstitial, we developed a machine learning model of the interaction potential, and studied the structural and electronic dynamics on a nanosecond timescale. We demonstrate that point defects at MHP GBs can create new chemical species, such as Pb-Pb-Pb trimers, that are less likely to occur with point defects in bulk. The formed species create structural instabilities in the GB and prevent it from healing towards the pristine structure. Pb-Pb-Pb trimers produce deep trap states that can persist for hundreds of picoseconds, having a strong negative influence on the charge carrier mobility and lifetime. Such stable chemical defects at MHP GBs can only be broken by chemical means, e.g., the introduction of excess halide, highlighting the importance of proper defect passivation strategies. Long-lived GB structures with both deep and shallow trap states are found, rationalizing the contradictory statements in the literature regarding the influence of MHP GBs on performance.

Surface Defects Control Bulk Carrier Densities in Polycrystalline Pb-Halide Perovskites

The (opto)electronic behavior of semiconductors depends on their (quasi-)free electronic carrier densities. These are regulated by semiconductor doping, i.e., controlled "electronic contamination". For metal halide perovskites (HaPs), the functional materials in several device types, which already challenge some of the understanding of semiconductor properties, this study shows that doping type, density and properties derived from these, are to a first approximation controlled via their surfaces. This effect, relevant to all semiconductors, and already found for some, is very evident for lead (Pb)-HaPs because of their intrinsically low electrically active bulk and surface defect densities. Volume carrier densities for most polycrystalline Pb-HaP films (<1 µm grain diameter) are below those resulting from even < 0.1% of surface sites being electrically active defects. This implies and is consistent with interfacial defects controlling HaP devices in multi-layered structures with most of the action at the two HaP interfaces. Surface and interface passivation effects on bulk electrical properties are relevant to all semiconductors and are crucial for developing those used today. However, because bulk dopant introduction in HaPs at controlled ppm levels for electronic-relevant carrier densities is so difficult, passivation effects are vastly more critical and dominate, to first approximation, their optoelectronic characteristics in devices.

Strong Dependence of Point Defect Properties in Metal Halide Perovskites on Description of van der Waals Interaction

Weaker than ionic and covalent bonding, van der Waals (vdW) interactions can have a significant impact on structure and function of molecules and materials, including stabilities of conformers and phases, chemical reaction pathways, electro-optical response, electron-vibrational dynamics, etc. Metal halide perovskites (MHPs) are widely investigated for their excellent optoelectronic properties, stemming largely from high defect tolerance. Although MHPs are primarily ionic compounds, we demonstrate that vdW interactions contribute ∼5% to the total energy, and that static, dynamics, electronic and optical properties of point defects in MHPs depend significantly on the vdW interaction model used. Focusing on widely studied CsPbBr3 with the common Br vacancy and interstitial defects, we compare the PBE, PBE+D3, PBE+TS, PBE+TS/HI and PBE+MBD-NL models and show that vdW interactions strongly alter the global and local geometric structure, and change the fundamental bandgap, midgap state energies and electron-vibrational coupling. The vdW interaction sensitivity stems from involvement of heavy and highly polarizable chemical elements and the soft MHP structure.

Extreme Electron-Photon Interaction in Disordered Perovskites

The interaction of light with solids can be dramatically enhanced owing to electron-photon momentum matching. This mechanism manifests when light scattering from nanometer-sized clusters including a specific case of self-assembled nanostructures that form a long-range translational order but local disorder (crystal-liquid duality). In this paper, a new strategy based on both cases for the light-matter-interaction enhancement in a direct bandgap semiconductor - lead halide perovskite CsPbBr3 - by using electric pulse-driven structural disorder, is addressed. The disordered state allows the generation of confined photons, and the formation of an electronic continuum of static/dynamic defect states across the forbidden gap (Urbach bridge). Both mechanisms underlie photon-momentum-enabled electronic Raman scattering (ERS) and single-photon anti-Stokes photoluminescence (PL) under sub-band pump. PL/ERS blinking is discussed to be associated with thermal fluctuations of cross-linked [PbBr6]4- octahedra. Time-delayed synchronization of PL/ERS blinking causes enhanced spontaneous emission at room temperature. These findings indicate the role of photon momentum in enhanced light-matter interactions in disordered and nanostructured solids.

Unraveling the excitonics of light emission from metal-halide perovskite quantum dots

Metal halide semicondictor perovskites have been under intense investigation for their promise in light absorptive applications like photovoltaics. They have more recently experienced interest for their promise in light emissive applications. A key aspect of perovskites is their glassy, ionic lattice that exhibits dynamical disorder. One possible result of this dynamical disorder is their strong coupling between electronic and lattice degrees of freedom which may confer remarkable properties for light emission such as defect tolerance. How does the system, comprised of excitons, couple to the bath, comprised of lattice modes? How does this system-bath interaction give rise to novel light emissive properties and how do these properties give insight into the nature of these materials? We review recent work from this group in which time-resolved photoluminescence spectroscopy is used to reveal such insights. Based upon a fast time resolution of 3 ps, energy resolution, and temperature dependence, a wide variety of insights are gleaned. These insights include: lattice contributions to the emission linewidths, multiexciton formation, hot carrier cooling, excitonic fine structure, single dot superradiance, and a breakdown of the Condon approximation, all due to complex structural dynamics in these materials.

Experimental evidence for defect tolerance in Pb-halide perovskites

The term defect tolerance (DT) is used often to rationalize the exceptional optoelectronic properties of halide perovskites (HaPs) and their devices. Even though DT lacked direct experimental evidence, it became a "fact" in the field. DT in semiconductors implies that structural defects do not translate to electrical and optical effects (e.g., due to charge trapping), associated with such defects. We present pioneering direct experimental evidence for DT in Pb-HaPs by comparing the structural quality of 2-dimensional (2D), 2D-3D, and 3D Pb-iodide HaP crystals with their optoelectronic characteristics using high-sensitivity methods. Importantly, we get information from the materials' bulk because we sample at least a few hundred nanometers, up to several micrometers, from the sample's surface, which allows for assessing intrinsic bulk (and not only surface-) properties of HaPs. The results point to DT in 3D, 2D-3D, and 2D Pb-HaPs. Overall, our data provide an experimental basis to rationalize DT in Pb-HaPs. These experiments and findings will help the search for and design of materials with real DT.

Photocatalytic activity of dual defect modified graphitic carbon nitride is robust to tautomerism: machine learning assisted ab initio quantum dynamics

Two-dimensional graphitic carbon nitride (GCN) is a popular metal-free polymer for sustainable energy applications due to its unique structure and semiconductor properties. Dopants and defects are used to tune GCN, and dual defect modified GCN exhibits superior properties and enhanced photocatalytic efficiency in comparison to pristine or single defect GCN. We employ a multistep approach combining time-dependent density functional theory and nonadiabatic molecular dynamics (NAMD) with machine learning (ML) to investigate coupled structural and electronic dynamics in GCN over a nanosecond timescale, comparable to and exceeding the lifetimes of photo-generated charge carriers and photocatalytic events. Although frequent hydrogen hopping transitions occur among four tautomeric structures, the electron-hole separation and recombination processes are only weakly sensitive to the tautomerism. The charge separated state survives for about 10 ps, sufficiently long to enable photocatalysis. The employed ML-NAMD methodology provides insights into rare events that can influence excited state dynamics in the condensed phase and nanoscale materials and extends NAMD simulations from pico- to nanoseconds. The ab initio quantum dynamics simulation provides a detailed atomistic mechanism of photoinduced evolution of charge carriers in GCN and rationalizes how GCN remains photo-catalytically active despite its multiple isomeric and tautomeric forms.

Compression Eliminates Charge Traps by Stabilizing Perovskite Grain Boundary Structures: An Ab Initio Analysis with Machine Learning Force Field

Grain boundaries (GBs) play an important role in determining the optoelectronic properties of perovskites, requiring an atomistic understanding of the underlying mechanisms. Strain engineering has recently been employed in perovskite solar cells, providing a novel perspective on the role of perovskite GBs. Here, we theoretically investigate the impact of axial strain on the geometric and electronic properties of a common CsPbBr3 GB. We develop a machine learning force field and perform ab initio calculations to analyze the behavior of GB models with different axial strains on a nanosecond time scale. Our results demonstrate that compressing the GB efficiently suppresses structural fluctuations and eliminates trap states originating from large-scale distortions. The GB becomes more amorphous under compressive strain, which makes the relationship between the electronic structure and axial strain nonmonotonic. These results can help clarify the conflicts in perovskite GB experiments.

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.

Exploring the formation of gold/silver nanoalloys with gas-phase synthesis and machine-learning assisted simulations

While nanoalloys are of paramount scientific and practical interest, the main processes leading to their formation are still poorly understood. Key structural features in the alloy systems, including the crystal phase, chemical ordering, and morphology, are challenging to control at the nanoscale, making it difficult to extend their use to industrial applications. In this contribution, we focus on the gold/silver system that has two of the most prevalent noble metals and combine experiments with simulations to uncover the formation mechanisms at the atomic level. Nanoparticles were produced using a state-of-the-art inert-gas aggregation source and analyzed using transmission electron microscopy and energy-dispersive X-ray spectroscopy. Machine-learning-assisted molecular dynamics simulations were employed to model the crystallization process from liquid droplets to nanocrystals. Our study finds a preponderance of nanoparticles with five-fold symmetric morphology, including icosahedra and decahedra which is consistent with previous results on mono-metallic nanoparticles. However, we observed that gold atoms, rather than silver atoms, segregate at the surface of the obtained nanoparticles for all the considered alloy compositions. These segregation tendencies are in contrast to previous studies and have consequences on the crystallization dynamics and the subsequent crystal ordering. We finally showed that the underpinning of this surprising segregation dynamics is due to charge transfer and electrostatic interactions rather than surface energy considerations.

Breaking the Condon Approximation for Light Emission from Metal Halide Perovskite Nanocrystals

The idea that the electronic transition dipole moment does not depend upon nuclear excursions is the Condon approximation and is central to most spectroscopy, especially in the solid state. We show a strong breakdown of the Condon approximation in the time-resolved photoluminescence from CsPbBr3 metal halide perovskite semiconductor nanocrystals. Experiments reveal that the electronic transition dipole moment increases on the 30 ps time scale due to structural dynamics in the lattice. Ab initio molecular dynamics calculations quantitatively reproduce experiments by considering excitation-induced structural dynamics.

Machine-Learning Accelerated First-Principles Accurate Modeling of the Solid-Liquid Phase Transition in MgO under Mantle Conditions

While accurate measurements of MgO under extreme high-pressure conditions are needed to understand and model planetary behavior, these studies are challenging from both experimental and computational modeling perspectives. Herein, we accelerate density functional theory (DFT) accurate calculations using deep neural network potentials (DNPs) trained over multiple phases and study the melting behavior of MgO via the two-phase coexistence (TPC) approach at 0-300 GPa and ≤9600 K. The resulting DNP-TPC melting curve is in excellent agreement with existing experimental studies. We show that the mitigation of finite-size effects that typically skew the predicted melting temperatures in DFT-TPC simulations in excess of several hundred kelvin requires models with ∼16 000 atoms and >100 ps molecular dynamics trajectories. In addition, the DNP can successfully describe MgO metallization well at increased pressures that are captured by DFT but missed by classical interatomic potentials.

Efficient Modeling of Quantum Dynamics of Charge Carriers in Materials Using Short Nonequilibrium Molecular Dynamics

Nonadiabatic molecular dynamics provides essential insights into excited-state processes, but it is computationally intense and simplifications are needed. The classical path approximation provides critical savings. Still, long heating and equilibration steps are required. We demonstrate that practical results can be obtained with short, partially equilibrated ab initio trajectories. Once the system's structure is adequate and essential fluctuations are sampled, the nonadiabatic Hamiltonian can be constructed. Local structures require only 1-2 ps trajectories, as demonstrated with point defects in metal halide perovskites. Short trajectories represent anharmonic motions common in defective structures, an essential improvement over the harmonic approximation around the optimized geometry. Glassy systems, such as grain boundaries, require different simulation protocols, e.g., involving machine learning force fields. 10-fold shorter trajectories generate 10-20% time scale errors, which are acceptable, given experimental uncertainties and other approximations. The practical NAMD protocol enables fast screening of excited-state dynamics for rapid exploration of new materials.

Interpolating Nonadiabatic Molecular Dynamics Hamiltonian with Bidirectional Long Short-Term Memory Networks

Essential for understanding far-from-equilibrium processes, nonadiabatic (NA) molecular dynamics (MD) requires expensive calculations of the excitation energies and NA couplings. Machine learning (ML) can simplify computation; however, the NA Hamiltonian requires complex ML models due to its intricate relationship to atomic geometry. Working directly in the time domain, we employ bidirectional long short-term memory networks (Bi-LSTM) to interpolate the Hamiltonian. Applying this multiscale approach to three metal-halide perovskite systems, we achieve two orders of magnitude computational savings compared to direct ab initio calculation. Reasonable charge trapping and recombination times are obtained with NA Hamiltonian sampling every half a picosecond. The Bi-LSTM-NAMD method outperforms earlier models and captures both slow and fast time scales. In combination with ML force fields, the methodology extends NAMD simulation times from picoseconds to nanoseconds, comparable to charge carrier lifetimes in many materials. Nanosecond sampling is particularly important in systems containing defects, boundaries, interfaces, etc. that can undergo slow rearrangements.

Development and Validation of Versatile Deep Atomistic Potentials for Metal Oxides

Machine learning interatomic potentials powered by neural networks have been shown to readily model a gradient of compositions in metallic systems. However, their application to date on ionic systems tends to focus on specific compositions and oxidation states owing to their more heterogeneous chemical nature. Herein we show that a deep neural network potential (DNP) can model various properties of metal oxides with different oxidation states without additional charge information. We created and validated DNPs for Ag_xO_y, Cu_xO_y Mg_xO_y, Pt_xO_y, and Zn_xO_y, whereby each system was trained without any limitations on oxidation states. We illustrate how the database can be augmented to enhance the DNP transferability for a new polymorph, surface energies, and thermal expansion. In addition, we show that these potentials can correctly interpolate significant pressure and temperature ranges, exhibit stability over long molecular dynamics simulation time scales, and replicate nonharmonic thermal expansion, consistent with experimental results.

Grain boundary sliding and distortion on a nanosecond timescale induce trap states in CsPbBr3: ab initio investigation with machine learning force field

Grain boundaries (GBs) in perovskite solar cells and optoelectronic devices are widely regarded as detrimental defects that accelerate charge and energy losses through nonradiative carrier trapping and recombination, but the mechanism is still under debate owing to the diversity of GB configurations and behaviors. We combine ab initio electronic structure and machine learning force field to investigate evolution of the geometric and electronic structure of a CsPbBr₃ GB on a nanosecond timescale, which is comparable with the carrier recombination time. We demonstrate that the GB slides spontaneously within a few picoseconds increasing the band gap. Subsequent structural oscillations dynamically produce midgap trap states through Pb-Pb interactions across the GB. After several hundred picoseconds, structural distortions start to occur, increasing the occurrence of deep midgap states. We identify a distinct correlation of the average Pb-Pb distance and fluctuations in the ion coordination numbers with the appearance of the midgap states. Suppressing GB distortions through annealing and breaking up Pb-Pb dimers by passivation can efficiently alleviate the detrimental effects of GBs in perovskites. The study provides new insights into passivation of the detrimental GB defects, and demonstrates that structural and charge carrier dynamics in perovskites are intimately coupled.

Fluctuations at Metal Halide Perovskite Grain Boundaries Create Transient Trap States: Machine Learning Assisted Ab Initio Analysis

All-inorganic perovskites are promising candidates for solar energy and optoelectronic applications, despite their polycrystalline nature with a large density of grain boundaries (GBs) due to facile solution-processed fabrication. GBs exhibit complex atomistic structures undergoing slow rearrangements. By studying evolution of the Σ5(210) CsPbBr₃ GB on a nanosecond time scale, comparable to charge carrier lifetimes, we demonstrate that GB deformations appear every ∼100 ps and increase significantly the probability of deep charge traps. However, the deep traps form only transiently for a few hundred femtoseconds. In contrast, shallow traps appear continuously at the GB. Shallow traps are localized in the GB layer, while deep traps are in a sublayer, which is still distorted from the pristine structure and can be jammed in unfavorable conformations. The GB electronic properties correlate with bond angles, with notable exception of the Br-Br distance, which provides a signature of halide migration along GBs. The transient nature of trap states and localization of electrons and holes at different parts of GBs indicate that charge carrier lifetimes should be long. At the same time, charge mobility can be reduced. The complex, multiscale evolution of geometric and electronic structures of GBs rationalize the contradictory statements made in the literature regarding both benign and detrimental roles of GBs in perovskite performance and provide new atomistic insights into perovskite properties.

Anion Doping Delays Nonradiative Electron-Hole Recombination in Cs-Based All-Inorganic Perovskites: Time Domain ab Initio Analysis

Using time-domain density functional theory combined with nonadiabatic (NA) molecular dynamics, we demonstrate that composition engineering of the X-site anions has a strong influence on the nonradiative electron-hole recombination and thermodynamic stability of cesium-based all-inorganic perovskites. Partial substitution of iodine(I) with bromine (Br) and acetate (Ac) anions reduces the NA electron-vibrational coupling by minimizing the overlap between the electron and hole wave functions and suppressing atomic fluctuations. The doping also widens the energy gap to further reduce the NA coupling and to enhance the open-circuit voltage of perovskite solar cells. These factors increase the charge carrier lifetime by an order of magnitude and improve structural stability in the series CsPbI_1.88BrAc_0.12 > CsPbI₂Br > CsPbI₃. The fundamental atomistic insights into the influence of anion doping on the photophysical properties of the all-inorganic lead halide perovskites guide the design of efficient optoelectronic materials.

Interplay of structural fluctuations and charge carrier dynamics is key for high performance of hybrid lead halide perovskites

Interplay of organic cation rotation and inorganic lattice fluctuation maintains the high performance of hybrid organic–inorganic perovskites.