Exponentially weighted moving average-based procedure with adaptive thresholding for monitoring nonlinear profiles: Monitoring of plasma etch process in semiconductor manufacturing

Recently, there are many situations where the quality of a process is characterized by a relationship of functional data (or profiles) such as time series and image data. Such data have been used for detecting out-of-process and quality improvement in many engineering applications such as semiconductor manufacturing, automobile manufacturing, and nano-machining systems. The functional data contain high dimensionality, high feature correlation, non-stationality, and large amount of noise. Due to such characteristics, most classic statistical process control (SPC) may not perform on-line monitoring satisfactorily on functional data. In addition, local shift monitoring with functional data is more significant than the detection of global shifting patterns. In this paper, wavelet-based exponentially weighted moving average (EWMA) test statistic with adaptive thresholding method, which extracts several significant coefficients from original functional data in the wavelet domain and monitors out-of-control events, is proposed. Instead of monitoring global shifting, the local shifting in functional data is of major significance in our study. Throughout this study, we use a spectroscopy in monitoring of plasma etching process from semiconductor manufacturing to illustrate the implementation of the proposed approach. Experiment studies show that the proposed approach quickly detects smaller local shifts compared with the well-known methods.