Application of Virtual Metrology in Semiconductor Manufacturing
Dekong Zeng and Costas J. Spanos
The purpose of this research is to develop a novel Virtual Metrology scheme to utilize tool data collected from wafer fabrication tools to create predictive models for the resulting wafer properties. An effective Virtual Metrology system can significantly reduce the need for actual metrology, reducing both cost and cycle time. A practical Virtual Metrology model must operate without adaptation over a long time, while providing accurate predictions. This is very challenging, since wafer processing tools are known to be aging over time and many process parameter excursions happen randomly. Therefore, the framework for building VM consists of three components: data quality assurance, input variable selection, and modeling methods exploration.
Data quality assurance is responsible for data compression, outlier detection, and data scaling. Data compression extracts the summary statistics from the time series based trace data. This requires us to explore various transient analysis schemes. Outliers are detected and removed based on their large contributions to the prediction error in the VM model; therefore we employ statistical distance and time series analysis for data anomaly detection. Missing values and normalization of data are also investigated in this work.
High dimensionality and collinearity in the data structures require appropriate variable selection for modeling. Our work in this area falls into two areas. The first, vector selection, is to be considered during the model building process. Here we use genetic algorithms where variable selection is based on numerous regression models built by different subsets of the predictors. The second selection technique is derived from information theory. By exploiting knowledge of the physical meanings of the sensor data, we can use entropy minimization, and clustering techniques in combination with logistic regression to select variables that are meaningful to the system operation.
There have been a variety of different modeling techniques investigated in different industries for data with high dimension and dynamic structure. For our work, we mainly focus on using partial least squares and neural networks for modeling.
Application of virtual metrology in the fault detection and classification (FDC) area is also investigated in our work. There are two main directions for FDC: statistical pattern recognition-based fault-finding and principle of sensors-based diagnostic.
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