Kriging-Based Overlay Error Calibration for Semiconductor Wafers
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Solution Overview
Problem
Semiconductor fabrication processes often result in uneven processing outcomes due to irregular errors, requiring continuous calibration of process conditions to achieve uniform results.
Innovation Solution
The implementation of the Kriging method from geostatistics to calibrate overlay errors and process parameters by measuring, sampling, and estimating errors across multiple areas of a workpiece, using weight values and outlier removal to generate calibrated data for improved processing.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If traditional error measurement and calibration methods are used, then manufacturing precision can be improved, but measurement time and processing complexity increase
Solution Approach 1:
The patent divides the workpiece into multiple discrete areas and processes each area independently through separate measurement and estimation steps. This segmentation allows parallel processing of different regions, reducing total measurement time while maintaining precision through localized error analysis and calibration
Solution Approach 2:
The patent measures errors in only some areas of the workpiece rather than all areas, using statistical estimation to infer errors in unmeasured regions. This partial measurement approach significantly reduces measurement time while maintaining acceptable precision through the relationship between measured and unmeasured area errors
2Manufacturing precision
If comprehensive error measurement across all areas is performed, then manufacturing precision improves, but device complexity and processing time increase
Solution Approach 1:
The patent introduces statistical estimation methods as an intermediary between direct measurement and final calibration. Instead of measuring all areas directly, the system uses measured data from selected areas as intermediaries to estimate errors in unmeasured areas, simplifying the measurement system while maintaining calibration accuracy
Solution Approach 2:
The patent creates a statistical model that copies the error patterns observed in measured areas to estimate errors in unmeasured areas. This copying approach through statistical relationships reduces the need for direct measurement of every area, simplifying the overall processing system
3Manufacturing precision
If outlier data is included in calibration, then measurement completeness is maintained, but manufacturing precision deteriorates due to irregular errors
Solution Approach 1:
The patent extracts and removes outlier data points from the measurement set before performing calibration. By identifying and taking out these irregular error measurements that would skew results, the system improves calibration accuracy while maintaining reliability through selective data inclusion
Data Source
AI summary
A processing method includes processing a wafer based on initial data, measuring errors for each of the plurality of areas, calculating an error similarity of at least some of the plurality of areas as a function of a separation distance between each pair of some of the areas, selecting a first area and a plurality of second areas adjacent to the first area, calculating weight values for the second areas based on the error similarities between each pair of second areas and the error similarities between the first area and each second area, calculating an estimated error of the first area based on the measured errors of the second areas and the weight values for the second areas, and generating estimated data based on the estimated errors for each of the plurality of areas.