Critical role of precursor flux in modulating nucleation density in 2D material synthesis revealed by a digital twin.

Chemical vapor deposition (CVD) is the most widespread approach for two-dimensional (2D) material synthesis, yet control of nucleation density remains a major hurdle towards large-area growth. We find that precursor flux, a function of gas velocity and precursor concentration, is the critical parameter controlling nucleation. We observe that for a vertically aligned substrate, the presence of a cavity/slot in the substrate-supporting plate creates an enhanced growth zone for 2D-MoS₂. The effect of this confined space on nucleation density is experimentally verified by electron microscopy. To understand this intriguing observation, we developed a hyper-realistic multiphysics computational fluid dynamics model, i.e., a digital twin of our CVD reactor, which reveals that space confinement achieves nearly-zero gas velocities. Digital twin-informed calculations indicate a significantly lower metal precursor flux at the confined space during the initial stages of growth, while precursor concentration is uniform across the substrate. The digital twin also makes an important prediction regarding a large time-lag between the set temperature, reactor environmental temperature, and substrate temperature, with implications for nucleation and growth. We offer a framework for designing confined spaces to control nucleation via regulating precursor flux, and for simulating reactor parameters for rapid optimization via the digital-twin model.