Production Correlation Analysis for Sparse Semiconductor Measurements
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Solution Overview
Problem
Conventional methods fail to reliably analyze correlations between sparse and overspecified data sets in semiconductor processes, particularly due to high missing values and low sampling rates, which hinders efficient control and optimization of production parameters.
Innovation Solution
A computer-implemented method that involves drawing random samples, calculating correlation matrices, determining significance values, and using Explainable Boosting Machines (EBM) to identify precise dependencies between inline and PCM measurements, allowing for the adjustment of production processes based on these correlations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Loss of time
If a sampling mechanism is used to monitor processes, then test time is shortened and cycle time is reduced, but the data set becomes sparse with high missing values and low sampling rate
Solution Approach 1:
The patent applies preliminary action by performing multiple imputation procedures before correlation analysis to reconstruct missing measurement values. This preliminary data completion enables reliable statistical analysis despite the sparse sampling data, resolving the contradiction between reduced test time and data completeness.
2Extent of automation
If conventional machine learning approaches are used, then analysis can be performed, but they fail when the number of missing values is very high in combination with very low sampling rate
Solution Approach 1:
The patent segments the analysis process into distinct stages: multiple imputation to handle missing values, correlation matrix calculation, and significance testing. This segmentation allows each stage to address specific data quality issues, enabling reliable analysis where conventional machine learning approaches fail.
Solution Approach 2:
The patent changes the approach from direct machine learning on raw sparse data to a statistical methodology that transforms the data through multiple imputation and correlation analysis. This parameter change in the analytical method enables reliable results with high missing values and low sampling rates.
3Loss of information
If expert knowledge is used for analysis, then correlations can be identified, but the method is unreliable for sparse and overspecified data sets
Solution Approach 1:
The patent replaces the mechanical approach of expert knowledge with a systematic statistical methodology involving multiple imputation and correlation analysis. This substitution provides objective, reproducible results that are reliable for sparse and overspecified data sets where expert judgment becomes unreliable.
Data Source
AI summary
A method is disclosed for determining correlations between first measurements and second measurements after respectively different production steps for optimizing the production steps. The method includes multiple repetition of the following steps: drawing random samples from the set of measurements and calculating a correlation matrix between the first and the second measurements contained in the randomly drawn sample. After the repetitions have been completed, a mean correlation matrix is determined over the correlation matrices and a standard variance matrix of the correlation matrices. Then follows a determination of significance values based on a division of absolute value of the mean correlation matrix element by element with the absolute values of the standard variance matrix. Depending on the significance values, one of the production steps can be adjusted.