Translation-Invariant Multiscale Energy-Based PCA for Monitoring Batch Processes in Semiconductor Manufacturing

The overwhelming majority of processes taking place in semiconductor manufacturing operate in a batch mode by imposing time-varying conditions to the products in a cyclic and repetitive fashion. These conditions make process monitoring a very challenging task, especially in massive production plants. Among the state-of-the-art approaches proposed to deal with this problem, the so-called multiway methods incorporate the batch dynamic features in a normal operation model at the expense of estimating a large number of parameters. This makes these approaches prone to overfitting and instability. Moreover, batch trajectories are required to be well aligned in order to provide the expected performance. To overcome these issues and other limitations of the conventional methodologies for process monitoring in semiconductor manufacturing, we propose an approach, translation-invariant multiscale energy-based principal component analysis, that requires a much lower number of estimated parameters. It is free of process trajectory alignment requirements and thus easier to implement and maintain, while still rendering useful information for fault detection and root cause analysis. The proposed approach is based on implementing a translation-invariant wavelet decomposition along the time series profile of each variable in one batch. The normal operational signatures in the time-frequency domain are extracted, modeled, and then used for process monitoring, allowing prompt detection of process abnormalities. The proposed procedure was tested with real industrial data and it proved to effectively detect the existing faults as well as to provide reliable indications of their underlying root causes. Note to Practitioners-Monitoring batch processes in the semiconductor manufacturing is currently a challenge. Methods available require complex preliminary alignment and modeling stages. We propose a new methodology for monitoring batch processes. This methodology is particularly suited to the applications found in this sector-it is simpler and more parsimonious than current two-way and three-way approaches (therefore less prone to over-fitting), flexible (can accommodate batches with different lengths), sensitive to process upsets, and does not require the complex and time-consuming alignment step in data pretreatment. Through validating with real data from semiconductor manufacturing industry, we demonstrate the practicability of the proposed translation-invariant multiscale energy-based principal component analysis method.