A Multiscale Bayesian SPRT Approach for Online Process Monitoring

Online monitoring of complex processes, such as semiconductor manufacturing processes, often requires the need to analyze sensor data with multiple characteristics. Some of these characteristics include nonstationary behavior, non-Gaussian distribution, high frequency of data generation, and multiscale (multiple frequencies) noise that mask the true nature of the process. Furthermore, it is necessary to implement process monitoring schemes that take into consideration the cost associated with sampling and incorrect decision making without sacrificing sensitivity, robustness, and ease of implementation. In this paper, a novel multiscale Bayesian sequential probability ratio test (MBSPRT) is developed, which is shown to be efficient in monitoring processes with the above characteristics. The MBSPRT method is also made suitable for online application by developing a moving block data processing strategy, which can match the data processing speed with the rate of data acquisition. The efficacy of the MBSPRT method was tested via detection of the end point occurrence in a chemical-mechanical planarization (CMP) process of semiconductor manufacturing using coefficient of friction (CoF) data. The proposed methodology offers a cost effective alternative to the traditional end point method, which is based on expensive metrology. Test results from both oxide and copper metal CMP are presented which show that MBSPRT is uniquely capable of identifying the start and finish of the end point event.