Workload Balancing for Photolithography Machines in Semiconductor Manufacturing via Estimation of Distribution Algorithm Integrating Kmeans Clustering

Abstract

This work focuses on the scheduling of a photolithography area with multiple machine groups and each one consists of a predetermined number of photolithography machines (PMs). PMs belonging to the same machine group should have identical processing capacities. Additionally, all PMs are designated with downward processing compatibility. This means that the wafers requiring relatively low pattern precision can be processed by the PMs used to deal with high pattern precision. After executing a photolithography process, a circuit pattern is transferred from an auxiliary resource called a reticle onto the wafer surface. Moreover, when processing wafers with different reticle and processing environment requirements, the machine setup is necessary. With those complex processing requirements, the objective is to minimize the difference between the longest and shortest working time of PMs so as to balance the workloads among all PMs. To do so, a mixed-integer linear programming model is built and then solved by using CPLEX for the small-sized problem. For medium- and large-sized problems, a designed estimation of distribution algorithm integrating a Kmeans clustering is constructed to improve the productivity of the photolithography area. Comparison results show that the proposed method outperforms the compared algorithms regardless of problem sizes.