Trace Feature Identification via Regression Residuals
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Solution Overview
Problem
In semiconductor manufacturing, identifying significant trace features that are insensitive to secondary factors such as temporal drifts, equipment age, and environmental factors is challenging, as these factors often cause deviations in process outputs from specifications, making it difficult to distinguish between true causal relationships and correlations affected by consumables.
Innovation Solution
A method involving a computer-based approach to compute residuals in multiple regressions, calculate coefficients of determination, and rank trace feature sets to determine significant trace features that are insensitive to secondary factors, thereby isolating true causal relationships from those influenced by consumables.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional regression methods are used to identify trace features, then all potential trace features including those affected by secondary factors are included, but the accuracy of identifying true causal relationships deteriorates due to contamination from consumable-related variations
Solution Approach 1:
The patent extracts and removes the influence of secondary factors (consumables) from the trace feature analysis by performing regression of secondary factors on targets and subtracting these effects. This isolation technique separates true causal relationships from spurious correlations, directly resolving the contradiction between comprehensive feature inclusion and accurate causal identification.
Solution Approach 2:
The patent segments the analysis into multiple components: (1) regression of secondary factors on targets, (2) regression of secondary factors on trace features, and (3) analysis of residuals. This segmentation allows systematic removal of consumable effects while preserving genuine trace feature relationships, thereby improving measurement precision without losing important information.
2Reliability
If comprehensive trace feature sets are analyzed, then all potential causes are considered, but the complexity of distinguishing significant features from those affected by secondary factors increases
Solution Approach 1:
The patent performs preliminary regression analysis of secondary factors on both targets and trace features before the main analysis. This preliminary action pre-computes the consumable effects that need to be removed, simplifying the subsequent identification of significant trace features while maintaining comprehensive analysis of all potential causes.
Solution Approach 2:
The patent introduces residuals as an intermediary variable that mediates between comprehensive trace feature sets and significant feature identification. By analyzing residuals after removing secondary factor effects, the patent simplifies the discrimination process while maintaining reliability of the comprehensive analysis.
3Measurement precision
If secondary factors are removed from analysis, then true causal relationships are isolated, but the ability to account for all sources of variation in process outputs is reduced
Solution Approach 1:
The patent extracts secondary factor influences through regression analysis and removes them from the trace feature analysis. This extraction isolates true causal relationships while the extracted secondary factor models are preserved for separate analysis, preventing complete loss of information about consumable effects.
Solution Approach 2:
The patent applies partial removal of secondary factors - only removing the portion that confounds trace feature analysis while retaining the ability to analyze secondary factor effects separately. This partial action maintains isolation of true causal relationships while preserving information about secondary factor influences for other purposes.
Data Source
AI summary
A method, a computer program product, and a computer system for identifying significant and consumable-insensitive trace features. A computer computes a residual in a first regression of one or more secondary factors on a target. The computer computes residuals in a second regression of the one or more secondary factors on each of one or more trace features in one or more trace feature sets. The computer computes, for the one or more trace feature sets, coefficients of determination in a third regression of the residuals in the second regression on the residual in the first regression. The computer ranks the one or more trace feature sets by sorting the coefficient of determination. The computer determines, based on rankings of the one or more trace feature sets, significant trace feature sets.