Modeling and scheduling stepper operations in the photolithography process in wafer fabrication

Abstract

The development of mathematical models to schedule lots using slot-based continuous-time representation for stepper operations in the photolithography process in wafer fabrication was discussed. The model allowed the scheduling of multiple lots of the same type of product/device in a single slot to handle larger problems. Optimal allocation of steppers to different types of lots, while minimizing the setup or changeover times and costs, was essential for maximizing the productivity and profits. Numerical test show that the integer variables as opposed to binary variables had much less effect on the model performance. Around 30000 wafers were scheduled on steppers in about 20 seconds.