Session X54: Halide Perovskites III: Theory

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Halide perovskites (HaPs) have shown great promise as materials for use in energy and optoelectronic devices owing to their fascinating microscopic properties. Of particular scientific interest is the coupling of electronic to lattice-dynamical properties of HaPs, because a comprehensive understanding of it is key to predicting and further improving charge-carrier mobility and defect characteristics. In this talk, I will present our recent theoretical findings on electron-lattice relaxation phenomena in HaPs. Specifically, using molecular dynamics in conjunction with electronic-structure theory, it will be shown that the soft, polar lattice of paradigmatic HaPs leads to a range of very interesting electron-lattice relaxation effects. These include structural anharmonicities, nonlinear electron-phonon couplings and short-range correlated disorder potentials. The impact of these phenomena on charge-carrier mobilities, optical absorption and defect characteristics will be discussed.   

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Hybrid lead halide perovskites are a class of materials that have unique photophysical properties due to their anharmonic lattices and predominately ionic bonding. Recently, layered perovskites have been synthesized with large organic cations. These flexible structures have optical properties that can in principle be easily controlled by composition and thickness, enabling their use in a variety of optoelectronic applications. The interplay between organic cations and the inorganic framework significantly affects the material properties, resulting in flexible lattices with significant dynamic disorder and soft vibrational modes. In this work, we aim to elucidate the effects of anharmonicity and study the relaxation dynamics of the lattice due to photogenerated excitons by using advanced molecular dynamics simulations. This work may provide the foundation for future studies on novel electron-phonon interactions in these materials.   

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Structural dynamics in halide perovskites (HaPs) include several interesting phenomena that can be expected to contribute significant amounts of disorder to the material at room temperature. This anticipated disorder is seemingly in contrast with the known small Urbach energies of HaPs allowing for fabrication of efficient solar-cell devices. Using density functional theory (DFT) calculations and DFT-based molecular dynamics, we study structural dynamics and its implications on electronic states in HaPs[1]. Interrelations of anharmonicity in the structural dynamics and their spatial correlations with disorder potentials for the electronic states are investigated and discussed. We observe that particularly A-site and X-site ionic motion results in dynamic confinements of disorder potentials to interatomic distances in various HaPs. These short correlation lengths of the disorder potential lead to small Urbach energies, which are a key parameter for efficient collection of solar light with HaP absorber materials.

[1] C. Gehrmann & D. A. Egger, Nat. Commun. 10, 3141 (2019).   

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The formation of large polarons due to the interaction between charge carriers and the crystal lattice has been proposed to have wide-ranging effects on charge carrier dynamics in organometal halide perovskites (OHPs), with an underlying hypothesis that charge carriers are “protected” from scattering [1, 2]. We derive expressions for the rates of scattering of polarons by polar optical phonons, acoustic phonons and ionised impurities, and quantify them for electrons and holes in the OHPs MAPbI₃, MAPbBr₃ and CsPbI₃. We then compute polaron momentum distribution functions which satisfy the Boltzmann transport equation using a semiclassical Monte Carlo method, from which we extract temperature dependent mobilities. By carrying out analogous calculations for bare band carriers, we conclude that polaronic effects on the scattering and mobilities of charge carriers in OHPs are limited, contrary to claims in the recent literature.

[1] Zhu, X. and Podzorov, V. J. Phys. Chem. Lett. 6, 4758 (2015)
[2] Ghosh, D. et al. J. Phys. Chem. Lett. 11, 9, 3271 (2020)   

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Halide perovskites show promising photovoltaic and optoelectronic properties, despite large, nonlinear lattice fluctuations at room temperature. Theoretical calculation of thermally disordered electronic structure requires accurate prediction of local electronic interactions in terms of atomic structure, but the length scales of such disorder are too large for plane wave DFT calculations. We present an atomic orbital tight binding model of MAPbI3 capable of extending the accuracy of ab initio calculations to the length and time scales of thermal disorder. Our model predicts the atomic orbital Hamiltonian from atomic structures using either physical fits or machine learning, including the fluctuations in orbital energy, bond geometry, and spin orbit coupling. Benchmarking against DFT shows quantitative accuracy of both individual matrix elements and overall band structure across a range of temperatures and phases. We present applications to temperature dependence of carrier mass and bandgap, as well as differentiating the relative effects of increased bond lengths and disorder on these quantities. Finally this model suggests methods for treating dynamical spin splitting, polaron formation, surfaces, defects, nanocrystals, and other materials.   

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Density functional theory (DFT) is a well-established theoretical tool helping to reveal origins of the fascinating optoelectronic properties of halide perovskites (HaPs). However, DFT presents too high computational costs for large-scale simulations of HaPs, which prompts us to search for an alternative theoretical approach. Therefore, following previous work [1] we propose a tight binding (TB) model as a computationally efficient tool to model large-scale system sizes and calculate optoelectronic properties of HaPs. By parametrizing the TB model with the help of DFT calculations and applying it to force-field molecular dynamics trajectories, we will demonstrate computation of optoelectronic properties, such as band gap distributions, for several HaPs. This helps rationalizing various interesting physical properties of HaPs, such as the coincidence of small Urbach energies and large amounts of dynamic disorder around room temperature.


References
[1] M. Z. Mayers, L. Z. Tan, D. A. Egger, A. M. Rappe and D. R. Reichman. How Lattice and Charge Fluctuations Control Carrier Dynamics in Halide Perovskites. Nano Lett. 18, 8041 – 8046 (2018).   

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Hybrid organic-inorganic semiconductors (HOIS), particularly perovskites, form a diverse group of semiconductor materials with tunable properties through targeted variations of both organic and inorganic components. We here describe the current status of the HybriD³ database (https://materials.hybrid3.duke.edu), a curated database of both experimentally and computationally assessed HOIS materials and their properties. Over 400 unique compounds are currently included in the database, including, where available, synthesis information, crystal and band structures, optoelectronic, magnetic, thermal and other properties. We showcase the use of the HybriD³ database for several examples and also highlight the underlying MatD³ software [1], a package that enables the creation of other individual web-facing materials databases beyond HOIS. As a community resource, the HybriD³ database is open for external user data input.

[1] Journal of Open Source Software 5, 1945 (2020). DOI: 10.21105/joss.01945   

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Control over carrier type, carrier concentration, and Fermi level are critical in semiconductor technology and typically accomplished by doping. We study Bi as a potential dopant of the paradigmatic layered (so-called 2D) hybrid organic-inorganic perovskite phenethylammonium lead iodide ((PEA)2PbI4 or "PEPI"). Total-energy calculations (density-functional theory using the van der Waals corrected PBE functional) show that Bi can be incorporated either as a substitutional defect (dopant) or in conjunction with charge-compensating Pb vacancies (non-doping), depending on the synthesis conditions of a PEPI crystal. Energy band structure calculations using spin-orbit coupled hybrid density functional theory for supercell sizes above 750 atoms show that the energy levels introduced by Bi defects are found below the conduction band levels in the gap in either case. We compare the results to experimental findings including optoelectronic properties and photoelectron spectroscopy.   

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Low dimensional halide perovskite nanostructures, such as 2D sheets and nanoparticles, are known to have tunable optical gaps and improved structural stability. Using first-principles calculations, we show that dimensional reduction leads to modified excited state dynamics. In 2D hybrid organic–inorganic perovskites, we find that the formation of localized layer edge states leads to efficient electron–hole dissociation. These layer edge states are stabilized by internal electric fields created by polarized molecular alignment of organic cations in 2D perovskites two layers or thicker, suggesting that control over these molecular components would lead to control over layer edge optoelectronic properties.   

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In this study, we investigated the structural properties of perovskite solar cell (PSC) through simulations that would help to select optimum parameters before the actual fabrication process. In the present study, a numerical simulation using Solar Cell Capacitance Simulator 1-D (SCAPS-1D) was performed. For the study, a cell architecture FTO/ZnO/CH₃NH₃PbI₃/Ag is investigated. The effect of variations in absorbing layer thickness and n/i interface defect densities on the solar cell performance was simulated. The simulation showed that the thickness can be optimized for the better performance of the PSC. The thickness of the absorber layer was increased from 2 μm to 27 μm in the simulation to find the optimum thickness for maximum conversion efficiency. Our studies showed that a minimum of 10 μm thickness is necessary for improving the efficiency of PSC. The n/i defect density was also varied from 10¹³ cm^-3 to 10¹⁸ cm^-3 and observed higher efficiency with the density 10¹³ cm^-3. By optimization of the respective thickness and the defect density, the best power conversion efficiency of over 18% is predicted by the simulation. Overall, our study may ultimately result in providing practical guides for the fabrication of high-performance perovskite solar cells.   

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The lead-free halide double perovskite Cs₂AgBiBr₆ has emerged as a promising candidate for applications in tandem perovskite solar cells. The measured low carrier mobility, under 11 cm²/Vs, poses a challenge in developing efficient devices. Furthermore, the relative importance of defects and phonons in the scattering of the charge carriers remains unclear. In this first-principles investigation, we employ density functional perturbation theory (DFPT), Wannier-Fourier interpolation, and the Boltzmann transport equation (BTE) to calculate the electronic and phonon band structures, electron-phonon vertices, and intrinsic mobilities of electrons and holes in Cs₂AgBiX₆ (X=Br,Cl) at finite temperature. We find that phonon scattering accounts for the measured mobility at room temperature, and we identify the dominant electron-phonon scattering process in Cs₂AgBiX₆ (X=Br,Cl). Our findings provide an atomic-scale explanation for the low intrinsic carrier mobilities in these important solar cell candidate materials.   

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Numerous symmetry-breaking anomalies, e.g., octahedral tilting in cubic oxide SrTiO₃ and halide CsSnI₃ perovskites were traditionally ascribed to thermal motions whose time-average is zero. We point out that for many cubic perovskites, the internal energy U can be lowered due to intrinsic Distortions off Wyckoff Positions (DOWP’s) before the contribution of thermal motion sets in. Such intrinsic DOWP’s do not time-average to zero, representing non-stochastic, bonding-induced static deformations. We studied for a few cubic oxide/halide perovskites the intrinsic DOWP’s by minimizing the DFT internal energy U at T=0 in a supercell constrained to the cubic shape, followed by observing the dynamic behavior from MD equilibration of G=U-TS at finite T. We propose that these intrinsic DOWP’s form the kernel configurations from which thermally excited stochastic distortions seen in MD simulation. As a result, these intrinsic DOWP’s lead to blueshift band gap in cubic oxide/halide perovskites (e.g., SrTiO₃, CsPbI₃) compared to the nominal cubic (Pm-3m) perovskites. After temperature set in, thermal-induced distortions in cubic SrTiO₃ lead to redshift band gap. Interestingly, the intrinsic DOWP’s in cubic SrTiO₃ lead to a development of distinct Γ-Γ direct band gap.   

On Demand

In recent years, great effort has been devoted to deducing the fundamental mechanisms that enable the high efficiency of hybrid perovskites. One widely accepted proposition is that, while high concentrations of point defects are present in hybrid perovskites, these defects do not cause nonradiative recombination; hence the concept of “defect tolerance”. We explicitly calculate the defect-assisted nonradiative recombination rates in the prototypical hybrid perovskite MAPbI₃ (MA=CH₃NH₃) with the multiphonon emission methodology. To achieve accurate and reliable results, all of our first-principles calculations are based on hybrid density functional theory with spin-orbit coupling included. We show that hybrid perovskites actually do suffer from defect-assisted recombination, i.e., they are not “defect tolerant”. The iodine interstitial is a strong nonradiative recombination center, and is likely responsible for the experimentally observed nonradiative recombination rates. These insights should put an end to misguided attempts to analyze and design device characteristics based on erroneous assumptions, and point to the actual fruitful directions of defect engineering toward improved efficiencies.