(349d) Kinetic Monte Carlo Simulation of Anisotropy in CsPbBr3 Nanocrystals

CsPbBr₃ nanocrystals have recently garnered a lot of attention owing to its applications in solar cells, next-generation displays and other optoelectronic devices¹ that can surpass the performance of currently existing semiconductor nanocrystals. The photoluminescence peaks are readily tunable by both size-tuned quantum confinement and chemical tuning of the bulk bandgap via facile anion exchange. However, to reap the benefits of the fascinating properties of CsPbBr₃ it is imperative to have a narrow particle size distribution. Furthermore, previous studies have shown that nanocrystals of different anisotropic shapes exhibiting varying anisotropic photophysical properties are possible for CsPbBr₃ nanocrystals viz. nanoribbons (NRs), nano-platelets (NPs) and nanowires (NWs)² which means that the crystal growth rate is not uniform in all directions despite near-cubic lattice symmetry. This anisotropic crystal behavior depends on the temperature of operation, the precursor concentration and the choice of different ligands³. The observation that one of the dimensions of this crystal follows kinetic control while the size of the other two dimensions are controlled by thermodynamics has made it very difficult to predict the morphology of these NCs⁴. The aforementioned reasons make it of extreme importance to understand the crystallization mechanism which can be employed to predict the size and morphological anisotropy of these NCs and tailor them for use in a specific optoelectronic device or other application. As of now, there are rarely any studies in this direction. Consequently, there is a paucity of modelling parameters for simulating this crystallization process. The goal of this research is to address these lacunae by proposing a probable mechanism of the crystal growth which will explain the anisotropic crystal growth and estimate the model parameters of the CsPbBr₃ crystallization process.

In this study, a single crystal with simultaneous growth on (001), (010) and (100) faces has been modeled by implementation of a kinetic Monte Carlo (KMC) algorithm. This KMC is based upon a solid-on-solid⁵ model for crystal growth which considers three types of event viz, adsorption, migration, and desorption with the fundamental particle being a single unit-cell of CsPbBr₃. The growth on each face has been modeled using a 50 by 50 2-Dimensional lattice. On each of these three lattices, adsorption, migration and desorption events are being considered. For the adsorption event, it is assumed that each lattice site is energetically equal to the other and is available for the attachment, and thus the attachment rate is uniform over the lattice. Conversely, the rates of the migration of a particle and the dissolution of the particle in the solution are dependent on the number of the nearest neighbors of the particle. The local environment of each particle can have up to 6 neighbors, and this allows us to classify each lattice site into a separate class depending on the number of nearest neighbors that each lattice site has. This book-keeping technique helps us increase the computational efficiency. The rates for these events can be calculated based on the average binding energy of the lattice (φ), average bonding energy per bond between the neighbors (E_pb) and the attachment coefficient (K_o⁺). To explain the anisotropic crystal growth, an anisotropic factor (γ) has been introduced in the direction of (001) face. Extensive simulations were performed to determine these four parameters and γ by corroborating with the experimental results. The experimental results are being generated by our experimental collaborator to facilitate precise determination of parameter⁴. Extensive simulation studies are carried out to evaluate the influence of temperature and supersaturation on the shape and size CsPbBr₃ NC at the end of a batch.

References

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