On temporally bounded spatial dynamic sampling for metrology optimization

In smart semiconductor manufacturing, wafer metrology plays an important role in ensuring production quality and efficiency. Extensive production metrology however implicates substantial costs in terms of equipment and time needed to perform the measurements. Achieving efficient metrology plans is therefore highly desirable. When the characteristics being monitored are spatially correlated it is possible to develop dynamic sampling strategies that exploit this correlation to reduce the number of measurement sites needed for full process visibility. These approaches typically employ historical data to identify the subset of locations to measure for each wafer, and statistical models that can reconstruct the complete data from the reduced set of measurements. Existing dynamic sampling strategies have focused on trading off reconstruction accuracy with the number of measurements points, without considering constraints on the temporal horizon, that is, the number of wafers that need to be processed before all available locations are measured at least once. This is an important parameter in practical applications as it defines the maximum number of wafers for which previously unseen abnormal behavior can go undetected. In this paper we formulate the temporally bounded dynamical sampling problem and explore a number of different strategies for solving it. These strategies focus on the best way to select new sites to visit for each wafer in order to comply with the temporal constraint, while minimizing the impact on process visibility. The effectiveness of the proposed methods is tested using both simulated and real world semiconductor manufacturing case studies. Results show that an algorithm, denoted DFSCA-Greedy, that distributes the number of forced sites evenly across the measurement plan, and selects the sites with a variant of the FSCA optimum site selection algorithm, achieves the best overall performance.