In semiconductor manufacturing, to improve the throughput of cluster tools, process modules (PMs) are designed to have multiple spaces such that more than one wafers can be processed in a PM concurrently. For multiple-space PMs, the internal chamber of a PM can rotate to make a wafer correctly loaded/unloaded into/from a space at the door of the PM. This makes that the wafer residency time in PMs is affected by both rotation operations of the internal chambers of PMs and the robot tasks. Also, satisfying constraints on the residency time of wafers is quite challenging in this kind of tools. Thus, with a single-arm robot and two-space PMs, this work is conducted to solve the challenging scheduling problems of cluster tools. To do so, by a presented two-wafer backward strategy, the properties of the system are presented. According to those properties, sufficient and necessary schedulability conditions under the two-wafer backward strategy are established and theoretical proofs are given. Also, if such a tool is schedulable, an optimal schedule can be found by an efficient algorithm developed in this work. Finally, case studies are carried out to show the applications of the proposed method.

In semiconductor manufacturing, multi-space process modules (PMs) are adopted in some cluster tools for wafer processing. With multi-space PMs, a PM can have multiple wafers concurrently. Also, the internal chamber in a PM should rotate to make the robot able to load/unload a wafer into/from a space in the PM. This means that the wafer staying time in PMs is affected by both the rotation operations of the internal chambers of PMs and the robot tasks. Thus, minimizing the wafer delay time is quite challenging. In this work, for cluster tools with single-arm robots and two-space PMs, efforts are made for wafer delay minimization in scheduling the tools. Specifically, a two-wafer backward strategy is presented to operate the tools in a steady state. Then, the workloads of each processing step and the robot are analyzed. Further, to find optimal schedules with the objective of minimizing the total wafer delay time, efficient algorithms are established. Finally, case studies show that the wafer delay time at some steps can be totally eliminated by the proposed method. In the meantime, in all cases, the proposed method can work well in reducing the total wafer delay time at all steps.

To increase productivity, more sophisticated cluster tools are developed. To achieve this, one of the ways is to increase the number of spaces in a process module (PM) and the number of fingers on a robot arm as well, leading to a cluster tool with multi-space PMs and a multi-finger-arm robot. This paper discusses the scheduling problem of cluster tools with four-space PMs and a four-finger-arm robot, a typical tool with multi-space PMs and a multi-finger-arm robot adopted in modern fabs. With two arms in such a tool, one is used as a clean one, while the other is used as a dirty one. In this way, wafer quality can be improved. However, scheduling such cluster tools to ensure the residency time constraints is very challenging, and there is no research report on this issue. This article conducts an in-depth analysis of the steady-state scheduling for this type of cluster tools to explore the effect of different scheduling strategies. Based on the properties, four robot task sequences are presented as scheduling strategies. With them, four linear programming models are developed to optimize the cycle time of the system and find feasible schedules. The performance of these strategies is dependent on the activity parameters. Experiments are carried out to test the effect of different parameters on the performance of different strategies. It shows that, given a group of parameters, one can apply all the strategies and choose the best result obtained by one of the strategies.

In order to improve quality assurance in wafer manufacturing, there are strict process requirements. Besides the well-known residency time constraints (RTCs), a dual-arm cluster tool also requires each robot arm to execute a specific set of tasks. We call such a tool an arm task-constrained dual-arm cluster tool (ATC-DACT). To do this, one of the arms is identified as the dirty one and the other as the clean one. The dirty one can deal with raw wafers, while the clean one can deal with processed wafers. This requirement raises a new problem for scheduling a cluster tool. This paper discusses the scheduling problem of ATC-DACTs with RTCs. Due to the arm task constraints, the proven, effective swap strategy is no longer applicable to ATC-DACTs, making the scheduling problem difficult. To address this problem, we explicitly describe the robot waiting as an event and build a Petri net (PN) model. Then, we propose a hybrid task sequence (HTS) as an operation strategy by combining the swap and backward strategies. Based on the HTS, the necessary and sufficient conditions for schedulability are established; also, a linear programming model is developed. We then develop an algorithm using these results to optimally schedule the system. Industrial case studies demonstrate the application of this method.