Fractal-Theory-Based Control of the Shape and Quality of CVD-Grown 2D Materials

The precise control of the shape and quality of 2D materials during chemical vapor deposition (CVD) processes remains a challenging task, due to a lack of understanding of their underlying growth mechanisms. The existence of a fractal-growth-based mechanism in the CVD synthesis of several 2D materials is revealed, to which a modified traditional fractal theory is applied in order to build a 2D diffusion-limited aggregation (2D-DLA) model based on an atomic-scale growth mechanism. The strength of this model is validated by the perfect correlation between theoretically simulated data, predicted by 2D-DLA, and experimental results obtained from the CVD synthesis of graphene, hexagonal boron nitride, and transition metal dichalcogenides. By applying the 2D-DLA model, it is also discovered that the single-domain net growth rate (SD-NGR) plays a crucial factor in governing the shape and quality of 2D-material crystals. By carefully tuning SD-NGR, various fractal-morphology high-quality single-crystal 2D materials are synthesized, achieving, for the first time, the precise control of 2D-material CVD growth. This work lays the theoretical foundation for the precise adjustment of the morphologies and physical properties of 2D materials, which is essential to the use of fractal-shaped nanomaterials for the fabrication of new-generation neural-network nanodevices.