Non-Normal SPC Index for Semiconductor Wafer Control
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Solution Overview
Problem
Statistical Process Control (SPC) methods, which rely on normal distribution data, are ineffective for controlling semiconductor processes with non-normal distribution data, as seen in new product wafer production, failing to accurately identify abnormal states.
Innovation Solution
A method involving a database-based approach that samples non-normal distribution data, filters it, forms a non-normal distribution diagram, calculates a value-at-risk and median, and uses proportion formulas to derive state and index values, enabling the identification of abnormal states through comparison.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If traditional SPC methods are used for controlling semiconductor processes, then the control mechanism works well for normal distribution data, but it cannot accurately identify abnormal states when the data presents non-normal distribution (as in new product wafer production)
Solution Approach 1:
The patent transforms the control approach by changing the statistical parameters from normal distribution-based (mean, standard deviation) to non-normal distribution-based parameters (value-at-risk, median, and their ratios). This parameter transformation enables the control mechanism to accurately identify abnormal states in non-normal distribution data while maintaining reliability
Solution Approach 2:
The patent introduces intermediate calculation steps including value-at-risk calculation, median calculation, and the derivation of state values and index values through specific formulas. These intermediaries bridge the gap between raw non-normal distribution data and the final abnormal state identification, making the control mechanism adaptable to non-normal data while maintaining accuracy
2Measurement precision
If SPC index values (Cp, Cpk, Cpmk) are established with normal distribution data, then the control mechanism is simple and well-established, but it lacks sensitivity and cannot provide suitable index values for non-normal distribution groups
Solution Approach 1:
The patent replaces traditional SPC parameters (Cp, Cpk, Cpmk) with new parameters specifically designed for non-normal distribution: value-at-risk, median, state values, and index values. This parameter change increases measurement precision and sensitivity for detecting abnormal states in non-normal data, while the systematic approach keeps the mechanism manageable
Solution Approach 2:
The patent segments the control mechanism into distinct calculation stages: data sampling, value-at-risk calculation, median calculation, state value calculation, and index value calculation. This segmentation makes the complex mechanism more manageable and implementable while maintaining high sensitivity for abnormal state detection
Data Source
AI summary
A specification establishing method for controlling semiconductor process, the steps includes: sampling a plurality of sample groups from a population, each sample group being a non-normal distribution; filtering the sample groups; summarizing the filtered sample groups to form a non-normal distribution diagram; getting a value-at-risk and a median by calculating from the non-normal distribution diagram; getting a critical value by calculating the value-at-risk and the median with a critical formula; getting a plurality of state values by calculating the filtered sample groups with a proportion formula; and getting an index value by calculating the non-normal distribution diagram with the proportion formula. Thus, the state values indicate the states of the sample groups are abnormal or not by comparing the state values to the index value.