Effect of disorder on transport properties in a tight-binding model for lead halide perovskites

Nuclear Quantum Effects Accelerate Hot Carrier Relaxation but Slow Down Recombination in Metal Halide Perovskites

Inorganic semiconductors are composed of heavy elements whose vibrational motions are well described by classical mechanics. Heavy elements, such as Pb and I, support charge carriers in metal halide perovskites. Nevertheless, the soft structure and strong coupling between the organic and inorganic components create conditions in which nuclear quantum effects (NQEs) can play important roles. By combining ab initio, ring-polymer, and nonadiabatic molecular dynamics approaches with time-domain density functional theory, we demonstrate how NQEs influence structural and electronic properties and electron-vibrational dynamics in hybrid organic-inorganic (MAPbI3) and all-inorganic (CsPbI3) perovskites. Quantum zero-point fluctuations enhance structural disorder, reduce the band gap, and accelerate elastic electron-vibrational scattering responsible for coherence loss. NQEs have opposite influences on intraband carrier relaxation and interband recombination. These inelastic scattering events are governed by the product of the overlap-like electron-phonon matrix element and atomic velocity. NQEs reduce the overlap and increases the velocity. The intraband carrier relaxation involves many states. Reduction of overlap between some states is offset by other pathways, while an increased velocity makes intraband relaxation faster. Electron-hole overlap in band-edge states plays a key role in the recombination, and its reduction by NQEs-enhanced disorder makes the recombination slower. This phenomenon is seen with both MAPbI3 and CsPbI3 and is much more pronounced when a light organic component is present. This study offers a detailed understanding of the role of NQEs in the carrier relaxation processes of perovskites, offering important theoretical insights into hot carriers and carrier recombination that govern the performance of solar cells and other optoelectronic devices.

Effect of Sb-Bi alloying on electron-hole recombination time of Cs2AgBiBr6 double perovskite

The double perovskite material Cs2AgBiBr6, characterized by high stability, low toxicity, and excellent optoelectronic properties, has emerged as a promising alternative to lead-based halide perovskites in photovoltaic applications. However, its photovoltaic conversion efficiency after integration into solar cell devices is less than 3%, significantly lower than that of traditional perovskite solar cells. While alloying methods have been widely applied in the design of photovoltaic materials, their specific role in modulating the lifetime of photo-generated charge carriers in double-perovskite solar cells remains inadequately explored. In this study, through nonadiabatic molecular dynamics (NAMD) simulations, the excited-state dynamics properties of Cs2AgBiBr6 and alloyed Cs2AgSb0.375Bi0.625Br6 samples were compared. The results revealed that the introduction of Sb ions into the double perovskite structure induces lattice deformation upon heating to 300 K, leading to distortion of Bi-Br bonds and enhanced valence band delocalization. Using the decoherence-induced surface hopping method, the capture and recombination processes of charge carriers between different states were simulated. It was suggested that hole lifetime serves as the primary limiting factor for carrier lifetime in Cs2AgBiBr6, and replacing 0.375 proportion of Bi with Sb can decelerate the hole capture rate, extending carrier lifetime by 3-4 times. This study demonstrates that alloying offers a viable approach to optimizing the optoelectronic performance of the Cs2AgBiBr6 perovskite, thereby advancing the application of double perovskite materials in the field of photovoltaics.

The effective prolongation of the excited-state carrier lifetime of CsPbI2Br with applying strain

In recent years, all-inorganic perovskites CsPbX3 (X = Cl, Br, I) have emerged as excellent candidates for solar cells due to their remarkable thermal stability and suitable bandgaps. Among them, CsPbI2Br is a hotspot in perovskite material research currently. Non-radiative electron-hole recombination often leads to significant energy losses, impacting the efficiency of solar cells, so a thorough understanding of carrier recombination mechanisms is crucial. Our work investigated the carrier recombination dynamics in detail and proved that strains can effectively reduce nonradiative recombination. In this study, using first-principles calculations combined with nonadiabatic (NA) molecular dynamics (MD), we demonstrate that applying 2% tensile and 2% compressive strains to CsPbI2Br can modify the bandgap, induce moderate disorder, reduce the overlap of electron-hole wavefunctions, decrease NA coupling, and shorten decoherence time, thereby minimizing non-radiative recombination and extending the carrier lifetime. Especially the 2% tensile strain exhibits more effective control performance, significantly reducing non-radiative electron-hole recombination and extending the charge carrier lifetime to 14.59 ns, nearly five times that of the pristine CsPbI2Br system (3.12 ns). This study reveals the impact mechanism of strain on carrier behavior in perovskite solar cells, providing a new non-chemical strategy for modulating the lifetime of photo-generated carriers and enhancing the efficiency of all-inorganic perovskite solar cells.

Computation of the Spatial Distribution of Charge-Carrier Density in Disordered Media

The space- and temperature-dependent electron distribution n(r,T) determines optoelectronic properties of disordered semiconductors. It is a challenging task to get access to n(r,T) in random potentials, while avoiding the time-consuming numerical solution of the Schrödinger equation. We present several numerical techniques targeted to fulfill this task. For a degenerate system with Fermi statistics, a numerical approach based on a matrix inversion and one based on a system of linear equations are developed. For a non-degenerate system with Boltzmann statistics, a numerical technique based on a universal low-pass filter and one based on random wave functions are introduced. The high accuracy of the approximate calculations are checked by comparison with the exact quantum-mechanical solutions.

Nuclear Quantum Effects Accelerate Charge Recombination but Boost the Stability of Inorganic Perovskites in Mild Humidity

Experiments have demonstrated that mild humidity can enhance the stability of the CsPbBr3 perovskite, though the underlying mechanism remains unclear. Utilizing ab initio molecular dynamics, ring polymer molecular dynamics, and non-adiabatic molecular dynamics, our study reveals that nuclear quantum effects (NQEs) play a crucial role in stabilizing the lattice rigidity of the perovskite while simultaneously shortening the charge carrier lifetime. NQEs reduce the extent of geometric disorder and the number of atomic fluctuations, diminish the extent of hole localization, and thereby improve the electron-hole overlap and non-adiabatic coupling. Concurrently, these effects significantly suppress phonon modes and slow decoherence. As a result, these factors collectively accelerate charge recombination by a factor of 1.42 compared to that in scenarios excluding NQEs. The resulting sub-10 ns recombination time scales align remarkably well with experimental findings. This research offers novel insight into how moisture resistance impacts the stability and charge carrier lifetime in all-inorganic perovskites.

Twist Angle-Dependent Intervalley Charge Carrier Transfer and Recombination in Bilayer WS2

A twist angle at a van der Waals junction provides a handle to tune its optoelectronic properties for a variety of applications, and a comprehensive understanding of how the twist modulates electronic structure, interlayer coupling, and carrier dynamics is needed. We employ time-dependent density functional theory and nonadiabatic molecular dynamics to elucidate angle-dependent intervalley carrier transfer and recombination in bilayer WS2. Repulsion between S atoms in twisted configurations weakens interlayer coupling, increases the interlayer distance, and softens layer breathing modes. Twisting has a minor influence on K valleys while it lowers Γ valleys and raises Q valleys because their wave functions are delocalized between layers. Consequently, the reduced energy gaps between the K and Γ valleys accelerate the hole transfer in the twisted structures. Intervalley electron transfer proceeds nearly an order of magnitude faster than hole transfer. The more localized wave functions at K than Q values and larger bandgaps result in smaller nonadiabatic couplings for intervalley recombination, making it 3-4 times slower in twisted than high-symmetry structures. B2g breathing, E2g in-plane, and A1g out-of-plane modes are most active during intervalley carrier transfer and recombination. The faster intervalley transfer and extended carrier lifetimes in twisted junctions are favorable for optoelectronic device performance.

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.

Structural Disorder in Higher-Temperature Phases Increases Charge Carrier Lifetimes in Metal Halide Perovskites

Solar cells and optoelectronic devices are exposed to heat that degrades performance. Therefore, elucidating temperature-dependent charge carrier dynamics is essential for device optimization. Charge carrier lifetimes decrease with temperature in conventional semiconductors. The opposite, anomalous trend is observed in some experiments performed with MAPbI₃ (MA = CH₃NH₃⁺) and other metal halide perovskites. Using ab initio quantum dynamics simulation, we establish the atomic mechanisms responsible for nonradiative electron-hole recombination in orthorhombic-, tetragonal-, and cubic MAPbI₃. We demonstrate that structural disorder arising from the phase transitions is as important as the disorder due to heating in the same phase. The carrier lifetimes grow both with increasing temperature in the same phase and upon transition to the higher-temperature phases. The increased lifetime is rationalized by structural disorder that induces partial charge localization, decreases nonadiabatic coupling, and shortens quantum coherence. Inelastic and elastic electron-vibrational interactions exhibit opposite dependence on temperature and phase. The partial disorder and localization arise from thermal motions of both the inorganic lattice and the organic cations and depend significantly on the phase. The structural deformations induced by thermal fluctuations and phase transitions are on the same order as deformations induced by defects, and hence, thermal disorder plays a very important role. Since charge localization increases carrier lifetimes but inhibits transport, an optimal regime maximizing carrier diffusion can be designed, depending on phase, temperature, material morphology, and device architecture. The atomistic mechanisms responsible for the enhanced carrier lifetimes at elevated temperatures provide guidelines for the design of improved solar energy and optoelectronic materials.

Correlated organic-inorganic motion enhances stability and charge carrier lifetime in mixed halide perovskites

Organic cations are believed to have little influence on the charge carrier lifetime in hybrid organic-inorganic perovskites. Experiments defy this expectation. We consider formamidinium lead iodide (FAPbI₃) doping with and without Br as two prototypical systems, and perform ab initio time-domain nonadiabatic (NA) molecular dynamics simulations to investigate nonradiative electron-hole recombination. The simulations demonstrate that correlated organic-inorganic motion stabilizes the lattice and inhibits nonradiative charge recombination in FAPbI₃ upon Br doping. Br doping suppresses the rotation of FA and the vibrations of both organic and inorganic components, and leads to hole localization and the extent of localization is enhanced upon thermal impact, notably reducing the NA coupling by decreasing the overlap between the electron and hole wave functions. Doping also slightly increases the bandgap for further decreasing NA coupling and enhances the open-circuit voltage of perovskite solar cells. The small NA coupling and large bandgap beat the slow coherence loss, delaying electron-hole recombination and extending the charge carrier lifetime to 1.5 ns in Br-doped FAPbI₃, which is on the order of 1.1 ns in pristine FAPbI₃. The obtained time scales are in good agreement with experiments. Multiple phonon modes, including those of both the inorganic and organic components, couple to the electronic subsystem and accommodate the excess electronic energy lost during nonradiative charge recombination. The study reveals the unexpected atomistic mechanisms for the reduction of electron-hole recombination upon Br doping, rationalizes the experiments, and advances our understanding of the excited-state dynamics of perovskite solar cells.

Metal-to-Semiconductor Transition in Two-Dimensional Metal-Organic Frameworks: An Ab Initio Dynamics Perspective

Two-dimensional (2D) π-stacked layered metal-organic frameworks (MOFs) are permanently porous and electrically conductive materials with easily tunable crystal structures. Here, we provide an accurate examination of the correlation between structural features and electronic properties of Ni₃(HITP)₂, HITP = 2,3,6,7,10,11-hexaiminotriphenylene, as an archetypical 2D MOF. The main objective of this work is to unravel the responsive nature of the layered architecture to external stimuli such as temperature and show how the layer flexibility translates to different conductive behaviors. To this end, we employ a combination of quantum mechanical tools, ab initio molecular dynamics (AIMD) simulations, and electronic band structure calculations. We compare the band structure and projected density of states of equilibrated system at 293 K to that of the 0 K optimized structure. Effect of interlayer π-π and intralayer d-π interactions on charge mobility is disentangled and studied by increasing the distance between layers of Ni₃(HITP)₂ and comparison to an exemplary case of Zn₃(HITP)₂ 2D MOF. Our findings show how a structural change, which can be deformations along the layers, slipping of layers, or change of the interlayer distance, can induce metal-to-semiconductor or indirect-to-direct semiconductor transition, suggesting a way to adjust or even switch between the intralayer vs interlayer conductive anisotropy in Ni₃(HITP)₂, in particular, and 2D MOFs in general.

Why Hybrid Tin-Based Perovskites Simultaneously Improve the Structural Stability and Charge Carriers' Lifetime: Ab Initio Quantum Dynamics

Much effort has been dedicated to boost the development of lead-free perovskite solar cells. However, their performance and stability are still much less competitive to the lead-bearing counterparts. By exploiting a mixed Sn-Ge cation strategy for the development of lead-free perovskites, we perform ab initio electronic structure calculations and quantum dynamics simulations on MASn_0.5Ge_0.5I₃ and compare them to MASnI₃. The calculations demonstrate that the hybrid cation strategy can improve simultaneously the perovskite stability and the lifetime of charge carriers. The stability increases due to a larger space of possible structures within the favorable range of the structural parameters, such as the Goldschmidt tolerance and octahedron factors. By exploring the larger structure space, mixed perovskites find stable configurations with lower free energies and better fitting components that exhibit reduced fluctuations around the equilibrium geometries. Charge carriers live longer in mixed perovskites because cation mixing results in an additional and moderate disorder that separates electrons and holes, reducing their interactions while still maintaining efficient band-like charge transport. These general and fundamental principles established by the analysis of the simulation results are useful for the design of advanced materials for solar energy and construction of optoelectronic devices.

Isotopic Exchange Extends Charge Carrier Lifetime in Metal Lead Perovskites by Quantum Dynamics Simulations

One may expect that isotopic exchange has no influence on charge carrier lifetime and perovskite solar cell performance because isotopic effects do not affect the fundamental electronic structure of materials. Experiments defy this expectation. By performing nonadiabatic (NA) molecular dynamics simulations, we demonstrate that hydrogen and deuterium exchange significantly enhances the excited-state lifetime and stability of CH₃NH₃PbI₃. Replacing lighter hydrogen with heavier deuterium suppresses the collective motions of organic and inorganic components, thus enhancing lattice stiffness and decreasing the NA coupling. Isotopic exchange further reduces NA coupling by localizing electron wave functions for separation of electrons and holes, which beats the extended coherence time, slowing down nonradiative electron-hole recombination from CH₃ND₃PbI₃ to CD₃ND₃PbI₃ with respect to the pristine system. The unchanged fundamental electronic structure together with the prolonged carrier lifetime and enhanced stability rationalize the improvement of the deuterated CH₃NH₃PbI₃ solar cells. Our work provides valuable insights into isotope effects for the design of high-performance perovskite photovoltaic and optoelectronic devices.

Edge Influence on Charge Carrier Localization and Lifetime in CH3NH3PbBr3 Perovskite: Ab Initio Quantum Dynamics Simulation

The distribution of charge carriers in metal halide perovskites draws strong interest from the solar cell community, with experiments demonstrating that edges of various microstructures can improve material performance. This is rather surprising because edges and grain boundaries are often viewed as the main source of charge traps. We demonstrate by ab initio quantum dynamics simulations that edges of the CH₃NH₃PbBr₃ perovskite create shallow trap states that mix well with the valence and conduction bands of the bulk and therefore support mobile charge carriers. Charges are steered to the edges energetically, facilitating dissociation of photo-generated excitons into free carriers. The edge-driven charge separation extends carrier lifetimes because of decreased overlap of the electron and hole wave functions, which leads to reduction of the nonadiabatic coupling responsible for nonradiative electron-hole recombination. Reduction of spatial symmetry near the edges activates additional vibrational modes that accelerate coherence loss within the electronic subsystem, further extending carrier lifetimes. Enhanced atomic motions at edges increase fluctuations of edge energy levels, enhancing mixing with band states and improving charge mobility. The simulations contribute to the atomistic understanding of the unusual properties of metal halide perovskites, generating the fundamental knowledge needed to design high-performance optoelectronic devices.

Modeling nonadiabatic dynamics in condensed matter materials: some recent advances and applications

This review focuses on recent developments in the field of nonadiabatic molecular dynamics (NA-MD), with particular attention given to condensed-matter systems. NA-MD simulations for small molecular systems can be performed using high-level electronic structure (ES) calculations, methods accounting for the quantization of nuclear motion, and using fewer approximations in the dynamical methodology itself. Modeling condensed-matter systems imposes many limitations on various aspects of NA-MD computations, requiring approximations at various levels of theory-from the ES, to the ways in which the coupling of electrons and nuclei are accounted for. Nonetheless, the approximate treatment of NA-MD in condensed-phase materials has gained a spin lately in many applied studies. A number of advancements of the methodology and computational tools have been undertaken, including general-purpose methods, as well as those tailored to nanoscale and condensed matter systems. This review summarizes such methodological and software developments, puts them into the broader context of existing approaches, and highlights some of the challenges that remain to be solved.

Anomalous Temperature-Dependent Charge Recombination in CH3NH3PbI3 Perovskite: Key Roles of Charge Localization and Thermal Effect

Optimizing metal halide perovskite solar cells necessitates understanding of nonradiative electron-hole recombination because it comprises a dominant route for charge and energy losses. In principle, the electron-hole recombination rate increases as temperature grows due to enhanced electron-phonon coupling. Experiments defy this expectation in MAPbI₃ (MA = CH₃NH₃⁺). By performing nonadiabatic (NA) molecular dynamics analyses combined with time-domain density functional theory simulations, we demonstrate that nonradiative electron-hole recombination in MAPbI₃ at high temperature occurs more slowly than that at low temperature. First and most important, increasing temperature enhances thermal disorder and leads to significant distortion of the inorganic Pb-I framework, giving rise to electron and hole wave functions locating spatial separation and reducing NA coupling by a factor of 28% in comparison with low temperature. Second, rising temperature enhances the thermal fluctuations of both the inorganic and organic components that accelerate decoherence process by a factor of 12%. Both factors, particularly the small NA coupling, contribute to suppressing electron-hole recombination at high temperature. The simulations show excellent agreement with experiments and emphasize how the charge localization driven by thermal effects impacts electron-hole recombination in perovskites and advances our understanding of the unusual charge dynamics.

Role of Quantum Confinement in 10 nm Scale Perovskite Optoelectronics

Quantum confinement-driven band structure engineering of metal halide perovskites (MHPs) is examined for realistically sized structures that consist of up to 10⁵ atoms. The structural and compositional effects on band gap energies are simulated for crystalline CH₃NH₃PbX₃ (X = I/Br/Cl) with a tight-binding approach that has been well-established for electronic structure calculations of multimillion atomic systems. Solid maps of band gap energies achievable with quantum dots, nanowires, and nanoplatelets concerning sizes, shapes, and halide compositions are presented, which should be informative to experimentalists for band gap designs. The pathway to suppress band gap instability that appeared in mixed halide perovskites is proposed, revealing that the red shift induced by halide phase separation can be hugely diminished by reducing sizes and adopting halides of lower electronegativity. Our modeling results on finite MHP structures of over 10 nm dimensions show a blueprint for designs of stable light-emitting sources with precisely controlled wavelengths.

How Lattice and Charge Fluctuations Control Carrier Dynamics in Halide Perovskites

Here we develop a microscopic approach aimed at the description of a suite of physical effects related to carrier transport in, and the optical properties of, halide perovskites. Our theory is based on the description of the nuclear dynamics to all orders and goes beyond the common assumption of linear electron-phonon coupling in describing the carrier dynamics and band gap characteristics. When combined with first-principles calculations and applied to the prototypical MAPbI₃ system, our theory explains seemingly disparate experimental findings associated with both the charge-carrier mobility and optical absorption properties, including their temperature dependencies. Our findings demonstrate that orbital-overlap fluctuations in the lead-halide structure plays a significant role in determining the optoelectronic features of halide perovskites.