Nonparametric localized Gaussian process models for accelerated meso-scale Monte Carlo simulation-based design and control of Carbon nanotube synthesis in chemical vapor deposition process

This research investigates development of nonparametric localized Gaussian process (GP) models for atomistic simulation of nanostructure synthesis process, especially carbon nanotubes (CNT) in chemical vapor deposition (CVD), towards providing platforms for integrated process planning and control. The current production and yield rate of nanostructures remains rather low (hover in 10-20%), as the synthesis mechanism is not well understood. Atomistic simulation models are useful to study those nano-scale phenomena, and predictive analytics is employed to accelerate the atomistic simulations and investigate process design and control. Coarse-grained (CG) potential function fitting: Heavy computational overhead hampers the simulation only to several tens of nanoseconds of the synthesis process. CG atomistic simulation and correspondingly CG potential function is needed to enlarge the investigation scale. Graph-theory based CG potential fitting is developed, which consolidates a group of atoms into CG nodes to reduce the system degree-of-freedom. Spectrum features for the CG graph are extracted and mapped to the CG energy via neural network model. Accelerated CG Monte Carlo Simulation: However, CNTs only up to 80 nm can be obtained through CG atomistic Monte Carlo (MC) simulation due to the heavy computational expense. An accelerated CG atomistic MC simulation is built to model synthesis of vertically aligned CNTs. A local Gaussian process model based on capturing local topological patterns is developed to track evolution of the growth increments to initialize relaxation in MC simulation. This procedure has reduced 70% of the computation time, leading to one of the longest CNTs from atomistic simulation models (~194 nm). Process design: Initial process design of CNT synthesis based on the accelerated CG MC simulation is investigated to identify key parameters to optimize structure properties. Catalyst diameter, synthesis temperature, and CNT length are studied towards optimizing the Young's modulus. in situ quality control: Process design may only partly address the optimization issues, as the main cause for low yield and quality can go beyond sub-optimal process design. To handle the considerable spatiotemporal variation in the process, in situ control using Dirichlet process based mixture Gaussian process (DPMG) model is developed. DPMG can capture multi-step variation of CNT growth increments, and decision theory is used to detect the end point (EPD) of the synthesis process. CNTs generated through this EPD approach are within the 1 nm variation of the specifications.