Modeling Metal-Halide Perovskite Thin Film: Deterministic Voronoi Diagrams Based on Stochastic Correlated Nuclei

Metal-halide perovskite thin films, composed of grains, exhibit microstructures with regularity and intriguing geometries. However, the underlying geometric principles shaping these patterns remain unclear. In this study, the geometric and statistical properties of grain structures are investigated. Grain shapes are characterized by using equivalent radius and shape parameters such as circularity, aspect ratio, convexity, and solidity. These shape parameters with those of Voronoi diagrams generated from various models are compared, including correlated and uncorrelated center distributions. These findings reveal that the statistical properties, including means and standard deviation of the shape parameters, align closely with Voronoi diagrams based on random close packing of circle centers. This suggests that such Voronoi diagrams provide an accurate mathematical model for describing perovskite thin-film morphology. Furthermore, by integrating the correlated center distribution and Voronoi framework with the Avrami–Johnson–Mehl method, a model is proposed for nucleation, grain growth, and morphology evolution in perovskite thin films. This work offers a foundational perspective for understanding the film formation mechanisms of perovskite thin films, paving the way for enhanced control over their microstructures.