Accelerating Optimal Synthesis of Atomically Thin MoS2: A Constrained Bayesian Optimization Guided Brachistochrone Approach

A machine learning (ML) guided approach is presented for the accelerated optimization of chemical vapor deposition (CVD) synthesis of 2D materials toward the highest quality, starting from low-quality or unsuccessful synthesis conditions. Using 26 sets of these synthesis conditions as the initial training dataset, our method systematically guides experimental synthesis towards optoelectronic-grade monolayer MoS2 flakes. A-exciton linewidth (sigma(A)) as narrow as 38 meV could be achieved in 2D MoS2 flakes after only an additional 35 trials (reflecting 15% of the full factorial design dataset for training purposes). In practical terms, this reflects a decrease of the possible experimental time to optimize the parameters from up to one year to about two months. This remarkable efficiency was achieved by formulating a constrained sequencing optimization problem solved via a combination of constraint learning and Bayesian Optimization with the narrowness of sigma(A) as the single target metric. By employing graph-based semi-supervised learning with data acquired through a multi-criteria sampling method, the constraint model effectively delineates and refines the feasible design space for monolayer flake production. Additionally, the Gaussian Process regression effectively captures the relationships between synthesis parameters and outcomes, offering high predictive capability along with a measure of prediction uncertainty. This method is scalable to a higher number of synthesis parameters and target metrics and is transferrable to other materials and types of reactors. This study envisions that this method will be fundamental for CVD and similar techniques in the future.