In-situ and Non-contact Etch Depth Prediction in Plasma Etching via Machine Learning (ANN & BNN) and Digital Image Colorimetry

Precise monitoring of etch depth and the thickness of insulating materials, such as Silicon dioxide and silicon nitride, is critical to ensuring device performance and yield in semiconductor manufacturing. While conventional ex-situ analysis methods are accurate, they are constrained by time delays and contamination risks. To address these limitations, this study proposes a non-contact, in-situ etch depth prediction framework based on machine learning (ML) techniques. Two scenarios are explored. In the first scenario, an artificial neural network (ANN) is trained to predict average etch depth from process parameters, achieving a significantly lower mean squared error (MSE) compared to a linear baseline model. The approach is then extended to incorporate variability from repeated measurements using a Bayesian Neural Network (BNN) to capture both aleatoric and epistemic uncertainty. Coverage analysis confirms the BNN's capability to provide reliable uncertainty estimates. In the second scenario, we demonstrate the feasibility of using RGB data from digital image colorimetry (DIC) as input for etch depth prediction, achieving strong performance even in the absence of explicit process parameters. These results suggest that the integration of DIC and ML offers a viable, cost-effective alternative for real-time, in-situ, and non-invasive monitoring in plasma etching processes, contributing to enhanced process stability, and manufacturing efficiency.

The Association Between SOC and Land Prices Considering Spatial Heterogeneity Based on Finite Mixture Modeling

An understanding of how Social Overhead Capital (SOC) is associated with the land value of the local community is important for effective urban planning. However, even within a district, there are multiple sections used for different purposes; the term for this is spatial heterogeneity. The spatial heterogeneity issue has to be considered when attempting to comprehend land prices. If there is spatial heterogeneity within a district, land prices can be managed by adopting the spatial clustering method. In this study, spatial attributes including SOC, socio-demographic features, and spatial information in a specific district are analyzed with Finite Mixture Modeling (FMM) in order to find (a) the optimal number of clusters and (b) the association among SOCs, socio-demographic features, and land prices. FMM is a tool used to find clusters and the attributes' coefficients simultaneously. Using the FMM method, the results show that four clusters exist in one district and the four clusters have different associations among SOCs, demographic features, and land prices. Policymakers and managerial administration need to look for information to make policy about land prices. The current study finds the consideration of closeness to SOC to be a significant factor on land prices and suggests the potential policy direction related to SOC.