Cluster tools, which combine several single-wafer processing modules with wafer handling robots in a closed environment, have been increasingly used for most wafer fabrication processes. We review tool architectures, operational issues, and scheduling requirements. We then explain recent progress in tool science and engineering for scheduling and control of cluster tools.

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A review of scheduling theory and methods for semiconductor manufacturing cluster tools

Cluster tools are automated production cells which are largely used for semiconductor manufacturing. They consist of several processing modules (PMs) and a transportation robot. Since cluster tools have limited buffers and diverse scheduling requirements such as complex wafer flow patterns, parallel PMs, wafer residency time constraints, and dual-arm robot, and so on, their scheduling problems are difficult. Due to the diversity of scheduling problems, dealing with those problems one by one may be impractical. Computational complexity is another difficulty. In this paper, we propose an efficient scheduling method to deal with diverse complex cluster tool scheduling problems by using timed Petri nets (TPN). We propose TPN models of cluster tools with various scheduling requirements. Then, based on the TPN models and their state equations, we develop a new mixed integer programming (MIP) model that can efficiently determine the optimal cyclic schedules. We show that many kinds of scheduling requirements such as parallel, reentrant and multiple material flows, a dual-armed robot, and time constrained PMs can be dealt with by the MIP model. Through experiments, we also show that the MIP model can efficiently solve most practical cluster tool scheduling problems.

An Efficient Mixed Integer Programming Model Based on Timed Petri Nets for Diverse Complex Cluster Tool Scheduling Problems

Cluster tools, each of which consists of multiple processing modules, one material handling robot, and loadlocks, are widely used for wafer fabrication processes, such as lithography, etching, and deposition. There have been many approaches and algorithms for cyclic scheduling of cluster tools in which the robot repeats a specified sequence for processing identical wafers. However, the lot order size has recently been decreasing due to the larger wafer size and circuit width reductions. In modern fabs, each wafer lot can have different flow patterns and process times for the same process step, and heterogeneous lots are processed consecutively in a tool. Even some tools in a fab have idle time waiting for wafer lots depending on the work-in-process fluctuations. Such different wafer lots and frequent tool state changes cannot be handled with cyclic scheduling methods, and accordingly noncyclic scheduling methods for such cases are required. Therefore, we develop an efficient branch and bound (B&B) procedure for noncyclic scheduling problems of cluster tools to minimize the makespan. Since a timed Petri net (TPN) is known for its powerful modeling ability and analysis capability, the algorithm is developed based on a TPN. We verify the efficiency of the B&B procedure with various cluster tool scheduling problems.

Noncyclic Scheduling of Cluster Tools With a Branch and Bound Algorithm

A cluster tool that consists of several processing modules, a transport robot, and loadlocks is widely used for wafer processing in the semiconductor industry. The cluster tool repeats an identical operational sequence for processing wafers in a lot, and such a cyclic operation sequence is determined by the wafer flow pattern and process times of a wafer lot. When a wafer lot changes, the tool operation sequence should be switched accordingly. Switching from a cyclic tool operation sequence to another is subject to deadlocks and unnecessary task delays to avoid scheduling complexity. Hence, it is necessary to have a scheduling method for such frequent lot switchings that prevents a deadlock and reduces the switching time. In this paper, we first develop a Petri net model for lot switching operations and then utilize a mixed integer programming model for an optimal schedule. However, since its practical value is limited, we develop effective heuristic methods for lot switching in single-armed and dual-armed cluster tools. The scheduling strategies adapt prevalent cyclic tool scheduling rules, such as backward and swap sequences. By computational experiments, we prove the efficiency and effectiveness of the proposed scheduling rules.

Scheduling Lot Switching Operations for Cluster Tools

We examine a scheduling problem of cluster tools that concurrently process two wafer types in a cyclic operational sequence. Whereas the process steps for different wafer types are assigned to different processing modules (PMs), the wafer loading and unloading tasks at the PMs are performed by a single robot. For a given cycle plan, which is a mix of different wafers for each cycle, we wish to determine the robot task sequence so as to minimize the tool cycle time. When a single wafer type is processed, the backward and swap sequences are optimal for single-armed and dual-armed tools, respectively. They are being prevalently used because of their simplicity and robustness. To maintain such advantages in concurrent processing, we introduce and define the concurrent backward and swap sequences (CBSs and CSSs, respectively). We then develop conditions on process times, robot task times, and the number of wafers produced in a cycle for which such CBSs and CSSs are still optimal for concurrent processing. We also show that, for some special cases, the two wafer types can achieve their maximum throughput rates as if each wafer type exclusively uses the tool regardless of other wafer types in progress. When the developed conditions do not hold, an effective mixed integer programming (MIP) model based on the CBSs and CSSs is used for robot task sequencing. Finally, we experimentally verify its efficiency and effectiveness by comparing to the existing scheduling methods for optimal scheduling of cluster tools.

Scheduling Cluster Tools for Concurrent Processing of Two Wafer Types

In a dual-armed cluster tool, the swap operation method that exchanges a wafer on a robot arm with another wafer at a chamber has been mostly used. It is known to minimize the tool cycle time although it restricts the robot task sequence. Recent cluster tools have new scheduling requirements such as reentrant wafer flows for atomic layer deposition processes, constraints on the wafer delay times within chambers after processing, and concurrent processing of different wafer types. The restricted swap operation method may neither minimize the tool cycle time nor satisfy the wafer delay constraints, and even cause a deadlock. We examine new robot task sequences for dual-armed cluster tools that use the two robot arms more flexibly without the swap restriction. We first propose a Petri net modeling method without the swap restriction. From the model, we identify necessary conditions for which deadlocks are prevented. We then systematically develop a mixed integer programming model that determines an optimal robot task sequence. From experiments, we show that deadlock prevention constraints, not required for the model, together with the initial branching rule for a branch and bound procedure reduce the solution space significantly.

Jin-Heum Paek

Papers

Optimal scheduling of dual-armed cluster tools without swap restriction