T2 Statistic Error Detection in Semiconductor Fabrication
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Solution Overview
Problem
Existing semiconductor fabrication error detection methods have high false alarm rates, leading to unnecessary shutdowns of fabrication tools and reduced productivity, as they fail to accurately account for correlations between multiple parameters measured across different wafers and the availability of data in real-time.
Innovation Solution
A method involving the creation of measurement vectors, correlation 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 shut down, allowing for real-time analysis and reducing false alarms by considering correlations between parameters measured on the same and different wafers.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If traditional error detection methods are used to monitor fabrication parameters, then fabrication errors can be detected, but the false alarm rate is high causing unnecessary shutdowns
Solution Approach 1:
The patent segments the error detection problem by creating separate correlation matrices for different parameter relationships: (1) correlation matrix for parameters within the same wafer, and (2) autocorrelation matrix for the same parameter across different wafers. This segmentation allows independent analysis of intra-wafer parameter correlations and inter-wafer parameter consistency, reducing false alarms by distinguishing real errors from normal variations.
Solution Approach 2:
The patent merges the correlation matrix and autocorrelation matrix into a combined matrix to create a comprehensive statistical model. This combined matrix integrates both intra-wafer parameter correlations and inter-wafer parameter consistency, enabling the T2 statistic to evaluate overall process health more accurately and reduce false alarms compared to using either matrix alone.
2Measurement precision
If multiple parameters are monitored across multiple wafers to improve detection accuracy, then error detection capability increases, but the complexity of data analysis increases
Solution Approach 1:
The patent implements feedback by continuously updating the correlation and autocorrelation matrices as new wafer data becomes available. The T2 statistic is calculated based on these updated matrices, providing real-time feedback on process health. This feedback mechanism enables dynamic adaptation to process variations while maintaining manageable complexity through standardized matrix operations.
Solution Approach 2:
The patent transforms multiple parameter measurements into a unified statistical framework by changing parameters from raw measurement values to correlation coefficients and T2 statistics. This parameter transformation simplifies the analysis complexity by converting complex multi-parameter relationships into standardized statistical metrics that are easier to interpret and act upon.
3Productivity
If real-time analysis of fabrication parameters is performed to enable timely error detection, then productivity is maintained, but the computational requirements increase
Solution Approach 1:
The patent performs preliminary action by pre-calculating and storing the correlation and autocorrelation matrices based on historical process data. When new wafer measurements are available, the system only needs to calculate the T2 statistic using the pre-computed matrices, significantly reducing real-time computational requirements. This preliminary preparation enables rapid error detection without excessive computational burden during production.
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.