Simulations-based and solver-based optimization approaches for batch processes in semiconductor manufacturing

Klemmt,; Weigert,; Hielscher,

doi:10.1109/wsc.2008.4736300

Cited by 23 publications

(9 citation statements)

References 7 publications

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“…It also has been reduced to n(T × R × Z + )/N for each iteration in the decomposed model. In constraint structure perspectives, equality assignment constraint (1) in the full MILP model is stricter than inequality constraint (9) in the decomposed model. It makes the decomposed model yield more feasible solutions than the full MILP model.…”

Section: Computational Advantage Of the Decomposition Methodsmentioning

confidence: 99%

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An Effective Problem Decomposition Method for Scheduling of Diffusion Processes Based on Mixed Integer Linear Programming

Jung

Pabst

Ham

et al. 2014

IEEE Trans. Semicond. Manufact.

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Diffusion processes in semiconductor fabrication facilities (Fabs) refer to the series of processes from wafer cleaning processes to furnace processes. Most furnace tools are batch tools, with large batch sizes, and have relatively long process times, when compared to the other processes. Strict time window constraints link cleaning processes with furnace processes for quality control. Those operational requirements for diffusion processes make their scheduling very difficult. This paper proposes an advanced scheduling approach based on a rolling horizon scheduling concept. Due to the combinatorial nature of the scheduling problem, the complexity of the problem increases exponentially, when the number of jobs and tools increase. However, the computation time allowed for the scheduler is limited in practice, because the variability in most Fabs requires schedulers to update the schedule in short intervals. We suggest an mixed integer linear programming model for diffusion processes, and propose an effective decomposition method to deal with this complexity problem. The decomposition method repeats multiple scheduling iterations, as it gradually extends the number of runs on tools, enabling the scheduler to generate near-optimal schedules in limited time intervals. The scheduler could make large improvements on key performance indicators, such as time window violation rates, batch sizes, throughput, etc. The software architecture of the scheduler implementation is also addressed in this paper.Index Terms-Diffusion processes, scheduling, batch tools, time window constraints, mixed integer linear programming, decomposition method. 0894-6507

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Section: Computational Advantage Of the Decomposition Methodsmentioning

confidence: 99%

“…Simulation based approaches were proposed in [1], [2]. MILP based approaches can be found in [3], [4].…”

Section: Introductionmentioning

confidence: 99%

An Effective Problem Decomposition Method for Scheduling of Diffusion Processes Based on Mixed Integer Linear Programming

Jung

Pabst

Ham

et al. 2014

IEEE Trans. Semicond. Manufact.

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“…The suggested MIP is similar to the MIP suggested by Klemmt et al (2008). Some modifications concerning constraints and objective become necessary.…”

Section: Mip Approachmentioning

confidence: 99%

“…The VNS approach of Almeder und Mönch (2009) is further extended in this paper to tackle these specific process constraints. Klemmt et al (2008) describe MIP models as well as a simulation-based optimization approach which was performed together with a genetic algorithm for unrelated parallel batch problems. Here, the objective was to minimize makespan and queuing time.…”

Section: Previous Related Workmentioning

confidence: 99%

A comparison of MIP-based decomposition techniques and VNS approaches for batch scheduling problems

Klemmt

Weigert²,

Almeder

et al. 2009

Proceedings of the 2009 Winter Simulation Conference (WSC)

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This research is motivated by a scheduling problem found in the diffusion and oxidation areas of semiconductor wafer fabrication facilities. With respect to some practical motivated process constraints, like equipment dedication and unequal batchsizes, we model the problem as unrelated parallel batch machines problem with incompatible job families and unequal ready times of the jobs. Our objective is to minimize the total weighted tardiness (TWT) of the jobs. Given that the problem is NPhard, we propose two different solution approaches. The first approach works with a time window-based mixed integer programming (MIP) decomposition. The second approach uses a variable neighbourhood search (VNS). Using randomly generated test instances, we show that the proposed algorithms outperform common dispatching rules that cannot deal with the given constraints effectively. INTRODUCTIONThe planning and optimization of semiconductor manufacturing is a very complex task. Especially, in the field of wafer processing in the front-end a lot of different processing steps have to be performed. These steps are, for example, typical batch tool operations like oven processes and wet-etch processes, or typical cluster tool operations like dry-etch, implant or lithography processes having complex setup strategies. A batching machine allows that several jobs can be processed at the same time. Because of several specific constraints and dependencies, it is challenging to schedule the jobs. Moreover, meeting customer due dates is one of the important manufacturing objectives. Because of the complex nature of the process, the customer due date is set for each operation as operation due date (ODD) (cf. Rose 2003). The task to be solved consists in meeting these due dates for each job within each work center as good as possible with respect to different job priorities.In this paper, we focus on diffusion and oxidation operations which are performed on batch machines, i.e. furnaces. Because of the long processing times of batch tools an effective scheduling of the furnace operation has an huge impact on global manufacturing objectives (cf. Mehta and Uzsoy 1998). Though several jobs can be processed simultaneously on these batch processing machines, the process restrictions require that only jobs belonging to the same family can be processed together at the same time. Further process restrictions specify that not all families can be processed by every machine (equipment dedication) and that machines can have different capacities. These equipment dedication constraints mainly represent different equipment qualifications. Especially for research and development wafer fabs with high product mixtures and constantly new developments, these constraints make the manufacturing control more sophisticated. In addition, the jobs to be processed have different priorities/weights, due dates, and ready times. So, in the case of unequal ready times, it is sometimes advantageous to form a non-full batch while in other situations it is a better strategy to wai...

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“…Approaches for Batch Processes In Semiconductor Manufacturing" (Klemmt, et al 2008) discusses how these factors are addressed in a semi conductor fabrication process. In the problem described in the article looks to optimize the scheduling of a special oven machine group using different strategies.…”

Section: Optimization Approaches For Batch Processesmentioning

confidence: 99%

Using simulation as a tool to improve a multi-product paint process.

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Simulations-based and solver-based optimization approaches for batch processes in semiconductor manufacturing

Cited by 23 publications

References 7 publications

An Effective Problem Decomposition Method for Scheduling of Diffusion Processes Based on Mixed Integer Linear Programming

An Effective Problem Decomposition Method for Scheduling of Diffusion Processes Based on Mixed Integer Linear Programming

A comparison of MIP-based decomposition techniques and VNS approaches for batch scheduling problems

Using simulation as a tool to improve a multi-product paint process.

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