Efficient dual-armed cluster tool performance via branch and cut optimization algorithm

Fab is the facility that produces silicon wafers. Capital investment of semiconductor fab has grown to 3-4 billions. Semiconductor equipments' cost per fab may count up to 74% of the capital investment. The semiconductor manufacturing industry is moving towards an efficient cluster approach for semiconductor equipments to create a higher throughput for wafer processing. Physical Vapor Deposition (PVD) is one of the most important processing for wafers' production. To improve fab production, the key issues are to make a near-optimal tool sequence optimization in a computationally efficient manner and be able to assess the quality of the near-optimal results for PVD cluster tools. In this paper, based on the Petri net for the PVD cluster tools, the tool sequence optimization problem is formulated to minimize the makespan of the wafers processing time with the PVD cluster tools, and then the formulation is converted to linear to be solved by the branch-and-cut method in the standard commercial solver CPLEX. Special methods for the linear conversion are highlighted. Effective search strategy, proper time unit and suitable solution gap selection and proper management for the sparse matrix are adopted to reduce the CPU calculation time base on the characteristic of tool sequence optimization problem. Numerical testing demonstrated that the models and algorithms developed can effectively optimize production and improve the quality of fab production.