T2 Statistic Error Detection in Semiconductor Fabrication
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Solution Overview
Problem
Existing semiconductor fabrication processes face high false alarm rates in error detection, leading to unnecessary shutdowns of fabrication tools and reduced productivity due to the inability to accurately correlate measurements across multiple wafers and parameters, especially when data is incomplete or delayed.
Innovation Solution
A method involving the creation of measurement vectors, correlation matrices, autocorrelation matrices, and combined matrices to calculate a T2 value, which is compared to a chi-square distribution value to determine if a semiconductor fabrication tool should be stopped, allowing for real-time assessment and reduction of false alarms by continuously updating the analysis as new data becomes available.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If traditional error detection methods are used in semiconductor fabrication, then fabrication errors can be detected, but the false alarm rate is high causing unnecessary tool shutdowns and reduced productivity
Solution Approach 1:
The system continuously monitors multiple process parameters and uses feedback loops to update the multivariate statistical model in real-time. The T2 statistic provides continuous feedback about process state, allowing the system to distinguish between normal variation and actual errors, reducing false alarms while maintaining high detection accuracy
Solution Approach 2:
The invention transforms multiple correlated process parameters into a single T2 statistic that captures the overall process state. By changing from monitoring individual parameters to monitoring the composite T2 value against a dynamic control limit, the system achieves more reliable error detection with fewer false alarms, thereby maintaining tool availability and productivity
2Reliability
If multiple parameters are monitored to improve detection accuracy, then error detection reliability improves, but the complexity of data analysis increases
Solution Approach 1:
The invention merges multiple correlated process parameters into a single T2 statistic using multivariate statistical analysis. The control limit merges information from historical data and process correlations. This consolidation simplifies the analysis complexity while maintaining high detection accuracy by capturing the joint behavior of all parameters in a single metric
Solution Approach 2:
The system transforms the complex multivariate parameter space into a univariate T2 statistic that can be easily monitored. This parameter transformation reduces analytical complexity from handling multiple correlated variables to monitoring a single composite value, while the underlying multivariate model maintains high detection accuracy
3Reliability
If real-time monitoring is implemented to reduce false alarms, then detection reliability improves, but the computational requirements and processing time increase
Solution Approach 1:
The system performs preliminary calculations by pre-computing the inverse of the covariance matrix and storing historical process data. This preliminary action prepares the statistical model in advance, allowing real-time T2 calculations to be performed quickly without extensive computation during critical monitoring moments, thus reducing processing time while maintaining high reliability
Solution Approach 2:
The control limit is dynamically adjusted based on the estimated process state and confidence level, allowing the system to adapt to changing process conditions. This dynamic approach enables efficient real-time computation by focusing computational resources on the most relevant parameters and timeframes, reducing overall processing time while maintaining high detection reliability
Data Source
AI summary
Methods and computer program products for performing automatically determining when to shut down a fabrication tool, such as a semiconductor wafer fabrication tool, are provided herein. The methods include, for example, creating a measurement vector including process parameters of semiconductor wafers, creating a correlation matrix of correlations between measurements of parameters obtained of each wafer, creating autocorrelation matrixes including correlations between measurements of the parameter obtained for pairs of wafers; creating a combined matrix of correlation and autocorrelation matrixes, obtaining a T2 value from the measurement vector and combined matrix, and stopping a semiconductor wafer fabrication tool if the T2 value exceeds a critical value.