Statistical Weight Kinetics Modeling and Estimation for Silica Nanowire Growth Catalyzed by Pd Thin Film

Abstract

This work intends to understand and model the kinetic aspect or the change of substrate weight over time in the selective growth of silica nanowires (NWs) catalyzed through Pd thin film. Various adsorption-induced, diffusion-induced, or unified vapor-liquid-solid (VLS) growth models have been developed to describe the NW length varying with time. Since NW length has been difficult to be measured, substrate weight change is therefore used as an alternative in this study to investigate growth kinetics of NWs. We investigate six different weight kinetics models in predicting weight changes during growth. Model estimation and comparison are conducted using both maximum-likelihood estimation (MLE) and Bayesian approaches. Owing to the embedded kinetics information in the nonlinear growth models, the Bayesian hierarchical model is shown to be more desirable when process data is limited.