Physics-driven Bayesian hierarchical modeling of the nanowire growth process at each scale

Despite significant advances in nanoscience, current physical models are unable to predict nanomanufacturing processes under uncertainties. This research work aims to model the nanowire (NW) growth process at any scale of interest. The main idea is to integrate available data and physical knowledge through a Bayesian hierarchical framework with consideration of scale effects. At each scale the NW growth model describes the time–space evolution of NWs at different sites on a substrate. The model consists of two major components: NW morphology and local variability. The morphology component represents the overall trend characterized by growth kinetics. The area-specific variability is less understood in nanophysics due to complex interactions among neighboring NWs. The local variability is therefore modeled by an intrinsic Gaussian Markov random field to separate it from the growth kinetics in the morphology component. Case studies are provided to illustrate the NW growth process model at coarse and fine scales, respectively.