A mathematical programming approach for optimizing control plans in semiconductor manufacturing

In a globally competitive environment, sustaining high yield with a minimum number of quality controls is key for manufacturing plants to remain competitive. In modern semiconductor manufacturing facilities, with the moves to ever smaller geometries and the variety among products to be run concurrently, designing efficient control plans is becoming increasingly complex. Since a 100% of inspection is neither feasible nor interesting because of the cost and reliability of each control, dynamically identifying the right product to inspect is one of the keys to achieve high yield and reduce the cycle time. However, when control parameters are over- or under-estimated, a dynamic sampling static sampling strategy can lead to poor results. In this paper we propose an integer linear programming approach to optimize the use of inspection capacity through dynamic sampling. The goal is to determine two key parameters (called warning limit and inhibit limit) that are related to the resulting level of risk and the available inspection capacity. The model has been implemented on a commercial solver and tested using actual industrial data. Results show that the overall risk can be strongly reduced without any additional capacity.