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This paper proposes a linear regression model for scalar-valued responses and two-way functional (bivariate) predictors. Our motivation stems from the quality evaluation of products based on optical emission spectroscopy data from virtual metrology of semiconductor manufacturing. We focus on multivariate cases where the smoothness and shapes of the data vary significantly across variables. We propose a two-step solution to this problem, consisting of decomposition and prediction. First, we decompose the two-way functional data into pairs of component functions using functional singular value decomposition. Next, we build functional linear models for the decomposed functional variables and obtain the final predictor by averaging the models. Results from numerical studies, including simulation studies and real data analysis, demonstrate the promising empirical properties of the proposed approach, especially when the number of predictors is large. [ABSTRACT FROM AUTHOR]

This paper addresses the quality control of the photolithography process in the semiconductor industry. Overlay errors in the process seriously affect the wafer yield, and cause the wafer to be forced to rework and affect the production efficiency of the equipment. We examine the current state of its process control, develop a novel overlay predict model, and verify the prediction results. This study proposes a Global Attention Generative Adversarial Networks (GAGAN) model to precisely predict the overlay error for the feed-forward data of the front layer, which is used as the important information and process parameters for the advanced process control of the current layer. Experiment results on a semiconductor shop-floor confirms that our proposed method achieves high predictive performance while maintaining extensibility and visual quality. [ABSTRACT FROM AUTHOR]

Semiconductor manufacturing consists of multiple sequential processes. In addition, even in a single process, a wafer must pass several steps. Accordingly, a dataset generated in semiconductor manufacturing has sequential information. Thus, the sequential information between steps and processes must be considered when predicting a target variable such as a yield or defect status. This paper proposes a method that utilizes the concept of residual learning to capture sequential information. Specifically, we propose to learn several modules that use data gathered starting from different steps and obtain a final decision by combining all modules’ decisions. In each module including multiple models, the first model is trained to predict the target variable using the data from the earliest step, and the remaining models are trained to predict the residuals that cannot be explained by the models for the previous steps based on the concept of residual learning. We conducted extensive experiments using two real-world semiconductor manufacturing datasets and found that even though each module’s performance was not good, the final decision obtained by combining all the modules’ decisions achieved a significant performance improvement. As a result, the proposed method significantly outperformed the baseline models. [ABSTRACT FROM AUTHOR]