Petri net-based response policies to process module failure in time-constrained single-arm cluster tools

In semiconductor manufacturing, wafer residency time constraints make the scheduling problem of cluster tools complicated. A process module (PM) in cluster tools is prone to failure. It is crucial to deal with any such failure in a proper and timely manner. If there are feasible periodic schedules in operating a cluster tool before and after a PM failure, it is desired to make it operate continuously when such a failure occurs. However, due to wafer residency time constraints, it is highly challenging to control a tool such that it can be correctly transferred from a feasible schedule before failure to another after it. To solve this problem, a Petri net model is developed to describe the dynamic behavior of a single-arm cluster tool and failure response policies are proposed. The proposed policies are formulated via simple control laws for their easy implementation. Examples are given to show them.

Cyclic scheduling and operation of a residency time- constrained single-arm cluster tool with failure-prone process modules are highly challenging. In some cases, when a fail- ure occurs, there still exists a feasible cyclic schedule for the performance-degraded tool. In other cases, such a schedule no longer exists. For the latter, it is highly desired to respond to a process module failure properly such that the tool can continue working and the wafers in the tool can be completed in a feasi- ble way. This work is the first one to study this important issue. The idea is to apply Petri nets to describe the dynamic behav- ior of a single-arm cluster tool. With the developed Petri net model, this paper formulates failure response policies to control the cluster tool such that it can keep working without violat- ing any residency time constraint. The failure response policies are implemented via efficient real-time control laws. Illustrative examples are presented to show their usage. Index Terms—Wafer fabrication, Cluster tools, Petri net, Scheduling, Failure response.

In semiconductor manufacturing, a process module (PM) failure in cluster tools (CTs) happens from time to time. To effectively operate a CT, such a failure should be handled in a proper and timely manner. This issue becomes much more complicated because wafer residency time constraints (WRTCs) must be met to ensure the quality for some wafer fabrication processes. With such constraints, if a tool is operated under a periodic schedule and a PM fails, it is desired that the tool can still operate under a periodic schedule if it is possible. Nevertheless, the periodic schedule after a PM failure must be different from that before its failure since in this case the tool is degraded. Thus, there must be a transient process between them. It is a great challenge to operate a tool such that it can go through such a transient process with WRTCs being always satisfied. This paper aims to solve this problem by proposing PM failure response policies which can successfully transfer a CT to the feasible schedule after failure from the one before a failure. Then, efficient algorithms are developed to improve these response policies. The proposed policies are composed of simple control laws such that they can be realized in real time and online. Illustrative examples are presented to show their applications.

Scheduling of time-constrained single-arm cluster tools with purge operations in wafer fabrications

We examine cyclic scheduling of single-armed and dual-armed cluster tools that concurrently process two wafer types by sharing a process module (PM). Because a PM is shared by two different wafers, the backward and swap sequences, which are prevalently used for single-armed and dual-armed tools without such complexity, respectively, are not effective. We therefore propose new sequences, called alternating backward and alternating swap sequences, for steady cycles of single-armed and dual-armed tools, respectively. We then develop optimality conditions for which the proposed sequences achieve the minimum cycle times in a fundamental cycle, and show that the optimality conditions hold for most practical cases. We also develop a condition for which a shared PM becomes the bottleneck and hence the PM sharing increases the cycle time. For general cycles, we propose heuristic scheduling methods that combine both the alternating backward (or swap) sequence and the conventional backward (or swap) sequence. Finally, we experimentally verify the efficiency and effectiveness of the proposed algorithm for dual-armed cluster tools.

The next generation sub-micron devices requires control of wafer environment and the interfaces between film layers. A wafer must not be exposed to atmosphere between some processing steps. To meet these requirements, multiple processing integrated system or "Cluster" tool for IC fabrication has been a major tooling development in the last few years. This leads to the concept of open architecture system and the development of interface standards. This also creates new demands on the system control and user interfaces. An open architecture integrated system must operate in a seamless fashion with real-time control and communication among the process modules and the wafer transport platform. Furthermore, it must present the user with a single interface mechanism with all the flexibility and functions required from the process modules as well as the wafer transport platform. The user interface will need to be configurable to die unique requirements of each process modules. In essence, the user should have all the flexibility in selecting their process module of choice without any penalty in performance. This paper describes the control and communication architecture and methods used in an open architecture cluster host platform. The architecture provides the basis of an environment that is easily adaptable to the various requirements in this type of tool. Functions such as flexible wafer routing, process recipe selection and editing, interface with multiple modules are shown. Other useful functions such as data logging, system performance record and "intelligent process parameter control" are also described. Finally, the authors will discuss developments directions that will provide complete and quick integration between the process modules and cluster host platform while still retaining the unique identity of each supplier in the future.

Scheduling a cluster tool with wafer residency time constraints is challenging and important in wafer manufacturing. With a backward strategy, the scheduling problem of such singlerobot-arm cluster tools is well-studied in the literature. It is much more challenging to schedule a more general case whose optimal scheduling strategy is not limited to the backward one. This work uses a timed Petri net (PN) to model the dynamic behavior of the system and presents a method to determine the optimal scheduling strategy for the system. Based on its PN model and the obtained strategy, it reveals that the key issue to schedule such a tool is to determine when and how long the robot should wait for. Based on this finding, this work establishes for the first time the necessary and sufficient conditions regarding the existence of an optimal and feasible one-wafer cyclic schedule for singlerobot-arm cluster tools. It then formulates a computationally efficient linear program to find it if existing, and finally gives industrial examples to show the application and power of the proposed method.

As wafer circuit widths shrink down, wafer fabrication processes require stringent quality control. Therefore, fabs recently tend to clean a chamber after processing each wafer, in order to remove chemical residuals within the chamber. Such chamber cleaning, called purge operation, increases scheduling complexity in robotized cluster tools. In this paper, we examine scheduling problems of single-armed cluster tools with purge operations for series-parallel chambers. By extending the wellknown backward sequence, we propose a backward(z) sequence that allows partial loading for parallel chambers, where vector z specifies how many chambers zi of each process step i are kept empty for cleaning. We then propose a way of finding optimal vector z* and identify when backward(z*) achieves the minimum cycle time among all possible sequences. We present experimental results on the accuracy of backward(z*).

Scheduling of multicluster tools has received much attention due to its complexity of interaction among cluster tools. A cluster tool comprises several modules such as processing modules, a transfer module with a single or dual-armed handling robot, and loadlock modules. A multicluster tool comprises two, three, or more cluster tools that are interconnected with each other. In this paper, we propose a deadlock prevention policy for noncyclic scheduling of dual-armed multicluster tools. The proposed deadlock prevention policy is effective for generating an efficient schedule for two or three-connected multicluster tools with a single or a dual-path flow. This is proven by analyzing the strict minimal siphon of the Petri net model. The performance of the proposed method is compared with that of a maximal permissible deadlock prevention policy. The results demonstrate that the proposed method is computationally efficient for larger state spaces and more suitable than conventional deadlock prevention policies for generating effective schedules for noncyclic scheduling of multicluster tools. Note to Practitioners —Scheduling of multicluster tools has recently attracted attention in the growing semiconductor manufacturing industry. Most conventional studies on multicluster tools focus on cyclic scheduling to minimize cycle time with swap strategy. The challenge addressed by this paper is to derive a deadlock-free schedule for multicluster tools with noncyclic operations. We propose a simple deadlock prevention policy that can be applied to large-scale timed Petri net (PN) model of general multicluster tools without enumeration of siphon computations or solution of mixed integer programming. A timed PN model is developed for noncyclic operations of dual-armed multicluster tools with a dual ath. The computational results show that the approximately 10% of the total throughput of the proposed method is better than those of the conventional methods. It enables more efficient operations for noncyclic scheduling under transient periods including cleaning operations.

In a cluster tool where process modules have residency constraints, an optimal schedule may need to buffer the partially processed wafers. In previous approaches, one of the active resources (i.e. the transport module) was used as a temporary buffer. In this approach we try to use a resource that is usually available in cluster tools and is only used for tool maintenance reasons. This passive module that we refer to as buffer module, can hold the partially processed wafers, and free the transport module (TM). Our experiment shows that in 57% of the cases, because the TM can perform other actions while the wafer is buffered in the buffer module, a schedule with better throughput was found.

Modeling and implementing a real-time scheduler for dual-armed cluster tools

Motivated by the expansion of the modern wafer semiconductor industry, where the manufacturing process consists of multiple cluster tools, including robots and process modules, a coordination tool is developed based on supervisory control theory. The tool is parametric with respect to the number of cluster tools, the number of process modules of each cluster tool, and the number of product types, treated simultaneously in the cluster tools. In the present paper, a fully parametric model of semiconductor manufacturing processes will be developed, using the models of the robots and the models of the process modules. The desired operational specifications for the coordination of the subsystems of the process will be developed. The development of the supervisor design, realizing these specifications, will be initiated by the translation of the specifications to appropriate sets of regular languages. Next, each regular language will be realized by a respective supervisor automaton, expressed in parametric form. The supervisor design will be completed by the determination of the automaton of the total controlled process and the examination of its satisfactory performance, by proving the controllability of the desired languages and the nonblocking property of the total controlled process.

A single-wafer cluster tool refers to a group of single-wafer process modules organized around a group of wafer transporters to perform a series of process steps on a wafer. To achieve high throughput, redundant modules and transporters are added to the cluster tool. The networking of the many redundant modules and transporters brings about complex wafer flow which requires complex coordination of wafer processing and transporting. Invariably, occur in transporting the wafer. If the occur at a gating module, the throughput slows down. If they occur in critical process modules, the on-wafer results are adversely affected. Furthermore, the process results will not be consistent because the wafers are not processed in similar flow paths. This paper presents a method for reducing the wafer flow complexity. By introducing planned delays to the process times of noncritical process modules, it is shown that (a) zero transport can be assured in gating modules and critical process modules; (b) periodicity can be introduced into the wafer flow. The consequence of (a) is an improvement in quality and throughput. The consequence of (b) is a drastic reduction in the number of possible wafer flow paths, thus ensuring consistent process results. A real life example of queueing to reduce the complexity in a photoresist processing system is presented to illustrate the concept and methodology.

ABSTRACTTo improve the efficiency of wafer fabrication, this work addresses the scheduling and control problems of mixed-processing with multiple wafer types in cluster tools. Then, based on a developed Petri net (PN) model, it presents a general model for cluster tools with multiple wafer types and the conventional swap strategy. By analyzing the coordination mechanism between wafers processing and robot tasks, necessary and sufficient conditions are established to check the schedulability of the system that is operated by using the conventional swap strategy. If the system is not schedulable checked by such schedulability conditions, a constraint-guided heuristic algorithm and a conflicts-avoiding algorithm are developed to obtain a reasonable schedule. Finally, illustrative examples are presented to show the applications of the proposed method.

There are wafer fabrication processes in cluster tools that require wafer revisiting. If a swap strategy is applied to dual-arm cluster tools handling wafer revisiting, a three-wafer periodical process is formed with three wafers completed in each period. Such a period contains three cycles in a revisiting process and three cycles in a nonrevisiting one. Hence, analysis and scheduling of such tools become very complicated. In this paper, a Petri net (PN) model is developed to describe their operations. Based on it, it is found that, if a swap strategy is applied, such tools are always in a transient state. A systematic method is then presented to analyze their performance. With the help of the proposed PN model, this work, for the first time, derives the optimality conditions of three-wafer period scheduling. Industrial application examples are given to show the results.