Sampling algorithm for qualitative (non-numerical) metrology in a FAB
Elena Malkes, M.sc student Advisor: Prof. Evgeni Khmelnitsky
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In semiconductor manufacturing, various sampling models are commonly used, including those based on statistical data analysis like APC and SPC for dynamic sampling, and those based on metrology machine learning like AMS and FDC for adaptive sampling. The latest development in sampling is Virtual Metrology (VM), which predicts whether a lot requires actual measurements in the metrology area. However, these models rely solely on numerical feedback from previous lots and cannot be applied to metrology tools that provide qualitative, non-numerical feedback. This thesis presents a new sampling model for a non-numerical metrology station called Viper, located in the photolithography department. The model utilizes an algorithm that calculates the total hourly cost of the photolithography process and minimizes the cost by adjusting the skip size. The cost function includes process and waiting costs, where process costs are determined based on the probability of detecting defects, leading to rework or scrap procedures, and waiting costs are associated with the time that a lot spends waiting for measurement at the Viper station. The model verification is conducted for two base cases: one with 20 lot types with identical production rates and the other with 20 lot types with different production rates. The sensitivity of the sampling model is analyzed with respect to various system parameters, including the Viper server rate, the number of servers, the time needed for any lot to pass through the process in the next FAB department, the cost of scrap, and the nominal waiting cost. The results show that the system performance is comparable for both base cases. Since the Viper station capacity is limited by the server rate and by the number of servers, the cost function cannot be optimized for low server rates or small number of servers. We analyze the dependence of the cost function on some critical parameters, such as the time needed for any lot to pass through the next department process, the cost of scrap and the nominal waiting cost.
Elena is an M.Sc. student at the department of Industrial Engineering in Tel Aviv University, specializing in Operations Research and Data Science. Elena holds B.Sc. and M.Sc. degrees in Chemical Engineering from Technion, Israel Institute of Technology. Her research focuses on sampling models in semiconductor manufacturing. The research is supervised by Prof. Evgeni Khmelnitsky
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