An MILP Approach to Wafer Sampling and Selection

This paper introduces a novel algorithm for selecting the optimal wafers for measurement given a set of selection rules. The algorithm is based on assigning a penalty to each of the sampling rules and then using a mixed-integer linear program to pick the wafers which minimize the sum of the penaltie...

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Bibliographic Details
Published in:IEEE transactions on semiconductor manufacturing 2007-11, Vol.20 (4), p.400-407
Main Authors: Good, R.P., Purdy, M.A.
Format: Article
Language:English
Subjects:
Adaptive sampling
Algorithms
Applied sciences
Chambers
Electronics
Exact sciences and technology
Frequency
History
Mathematical analysis
Metrology
Microelectronic fabrication (materials and surfaces technology)
mixed-integer programming
Monitoring
Optimization
Process control
Production facilities
Sampling
Sampling methods
Semiconductor device manufacture
Semiconductor electronics. Microelectronics. Optoelectronics. Solid state devices
Semiconductors
wafer sampling
wafer-level control
Wafers
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Description
Summary:This paper introduces a novel algorithm for selecting the optimal wafers for measurement given a set of selection rules. The algorithm is based on assigning a penalty to each of the sampling rules and then using a mixed-integer linear program to pick the wafers which minimize the sum of the penalties. By waiting until the metrology step to determine the best wafers to measure, a real-time decision can be made based on which wafers have previously been measured, the tools and chambers on which wafers were processed, and other user-specified selection criteria. The penalties can also be increased after a rule violation to ensure that each of the selection rules are satisfied at a finite frequency.
ISSN:0894-6507
1558-2345
DOI:10.1109/TSM.2007.907616