Modeling and analyzing semiconductor yield with generalized linear mixed models

As the challenges and opportunities of using 'big data' expand, there is a need to explore different ways of analyzing large datasets. The semiconductor industry is a good example of a manufacturing process where many data are collected throughout the fabrication of the product. These massive datasets are used for various purposes, primarily to detect problems and determine root causes, control the process, and build models that predict yield. The yield predictions are used for process planning, optimization, and control. However, many current approachesto yield modeling are limited because the actual processes violate the model assumptions, limiting the power of the models' use. This paper explores the use of generalized linear mixed models (GLMMs) to predict semiconductor yield and to provide significant information about the process using a large semiconductor yield dataset. Both batch-specific and population-averaged GLMM approaches are used and compared. Differences in link functions, sample sizes, and levels of aggregation (die-level and wafer-level models) are also compared with each other and with the results from generalized linear models (GLMs). The results of this study show that GLMMs are a reasonable approach to analyzing large datasets by providing additional insight into the fabrication process while maintaining or even improving prediction power compared with GLMs and some prior yield models found in the literature. This paper also provides a modeling strategy through suggestions regarding level of aggregation, link function, and sample size that are appropriate for different research goals.