A fuzzy set approach for yield learning modeling in wafer manufacturing

The yield of semiconductor manufacturing can be improved through a learning process. A learning model is usually used to describe the learning process and to predict future yields. However, in traditional learning models such as Gruber´s general yield model, the uncertainty and variation inherent in the learning process are not easy to consider. Also there are many strict assumptions about parameter distributions that need to be made. These result in the unreliability and imprecision of yield prediction. To improve the reliability and precision of yield prediction, expert opinions are consulted to evaluate and modify the learning model in this study. The fuzzy set theory is applied to facilitate this consulting process. At first, fuzzy forecasts are generated to predict future yields. The necessity of specifying strict parameter distributions is thus relaxed. Fuzzy yield forecasts can be defuzzified, or their α-cuts can be considered in capacity planning. The interpretation of such a treatment is also intuitive. Then, experts are requested to evaluate the learning model and express their opinions about the parameters in suitable fuzzy numbers or linguistic terms defined in advance. Two correction functions are designed to incorporate expert opinions in the learning model. Some examples are used for demonstration. The advantages of the proposed method are then discussed