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 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.