Logistic regression for crystal growth process modeling through hierarchical nonnegative garrote-based variable selection

Single-crystal silicon ingots are produced from a complex crystal growth process. Such a process is sensitive to subtle process condition changes, which may easily become failed and lead to the growth of a polycrystalline ingot instead of the desired monocrystalline ingot. Therefore, it is important to model this polycrystalline defect in the crystal growth process and identify key process variables and their features. However, to model the crystal growth process poses great challenges due to complicated engineering mechanisms and a large amount of functional process variables. In this article, we focus on modeling the relationship between a binary quality indicator for polycrystalline defect and functional process variables. We propose a logistic regression model with hierarchical nonnegative garrote-based variable selection method that can accurately estimate the model, identify key process variables, and capture important features. Simulations and a case study are conducted to illustrate the merits of the proposed method in prediction and variable selection.