Modeling and analyzing semiconductor yield with generalized linear mixed models

Abstract

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 approaches to 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.

A Review of Data Mining with Big Data towards Its Applications in the Electronics Industry

“…One of the research papers deals with predicting the performance (yield) of a manufacturing process or system in terms of critical functional characteristics. Months may pass before a chip is completed; hence, there is a great interest in mining production data to predict its performance prior to the final testing of the wafers [100][101][102][103][104][105][106][107][108]. In order to infer to the possible causes of faults and manufacturing process variations in semiconductor manufacturing after the whole fab process is completed, the clustering, classification, and association analyses are conducted based on different DMTs such as k-means, SOM, SVM, and decision tree to identify critical poor yield factors and determine the root cause of low yield.…”

Simultaneous and temporal autoregressive network models

“…Placing our proposed methods within the GLMM framework allows us to use other link functions such as a logit() for logistic regression, as well as allowing us to model other types of non-Gaussian data; e.g., should our network data be count, as is often the case, we may use a log link corresponding to a Poisson or Negative Binomial family of distributions. Countless texts describe these models, and in fact GLMMs are so prevalent that many fields have books or articles demonstrating how to apply GLMMs to their specific subject area (e.g., Bolker et al, 2009;Gbur, 2012;Krueger & Montgomery, 2014;Bharadwaj, 2016).…”

Optimization of Gas Sensors Based on Advanced Nanomaterials through Split-Plot Designs and GLMMs

“…Therefore, the main theoretical characteristics for GLMMs [ 15 , 16 ] can be summarized in two key-points: (i) the distributional assumption for the response variable Y ; and (ii) the evaluation of fixed and random effects involved in the model as independent variables. Obviously, the GLMM theory and the advantages obtained by applying this class of models cannot be restricted to two key-points alone; in [ 17 ], GLMMs were applied to improve the semiconductor yield and to provide significant information when using a large dataset; however, these two key-points were essential for the theory applied in this study.…”