Simulation analysis of cluster tool operations in wafer fabrication

Cluster tools play an important role in the semiconductor fabrication industry. Optimization of an individual cluster tool maximizes productivity of mass fabrication. Optimizing the scheduler results in increased throughput. The cluster tool is a real-time, dynamic environment in which different parts interact. That is why it is necessary to have a dynamic scheduler that makes its decisions online and within an acceptable computation time in the presence of unexpected sporadic events. Our contribution is to develop and implement a scheduler for a cluster tool. Attributes of the scheduler are predictive, periodic and dynamic to satisfy real-time characteristics of the cluster tool. The major characteristic of the scheduler is that it is optimized to produce high throughput and low complexity, i.e. time to schedule as overhead. First steady-state and transient-state of the cluster tool are analyzed. Then different scheduling algorithms are experimented with and compared. As the results of experiments demonstrate, throughput is optimized in steady-state and transient-state of the scheduler with low overhead.

Most cluster tool scheduling studies assume identical access times between chambers or do not discuss the impact of access times. However, the optimal scheduling rule and the cycle time can depend on the access times or physical configuration of parallel chambers. Therefore, we examine cyclic scheduling problems for cluster tools that have nonidentical access times. We first develop Petri net models for tool behaviors and analyze the cycle time by identifying the workloads of the process steps. We prove that the conventional backward and swap sequencing strategies are still optimal for single-armed and dual-armed cluster tools, respectively, when a process step is the bottleneck and the tool repeats a minimal cyclic work cycle. We also present a closed-form formula for the cycle time and identify a coprime condition on the number of parallel chambers for which the cycle time is independent of the order of using parallel chambers. Finally, we develop a mixed integer programming model for cases in which the coprime requirement is not satisfied.

By extrapolating technological trends, one can expect future fabs to consist largely of highly reliable cluster tools. Such trends raise the issues of how cluster tools should be configured (i.e., how modules should be grouped together), and the impact of configuration on optimal lot size. This paper generates equation-based models to compare the throughput and cycle time of different systems that perform the same sequence of process steps, with the same total number of modules grouped in different ways into multiple cluster tools. The two extremes of the spectrum of possible cluster tool configurations are considered: the serial configuration, in which a wafer visits each module in the cluster tool, and the parallel configuration, in which all of the modules in the cluster tool are identical. The models predict the following for typical cluster tool parameters and process times. When all process step times are identical, systems of serial-configured tools can achieve the same throughputs with lower cycle times, as their parallel-configured counterparts. However, if process times in the sequence significantly differ from one another, then systems of parallel-configured tools may achieve lower cycle times than their serial-configured counterparts at high throughputs. Finally, the serial configuration significantly reduces the lot size required to achieve total throughput capacity.

For the past few years, integrated machines (i.e. cluster tools) in wafer fabrication have been widely used to achieve reductions in cycle time, contamination, operator handling, capital costs and required floor space. The integration among several processing steps can lead to savings in cycle time, labour costs and inventory, and often provides a dramatic opportunity for yield improvement by preventing contamination. However, because of its complex configurations, modelling and analysis on the activities of an integrated machine is not an easy task. In this paper, a hybrid approach is introduced in order to model and to analyse the activities of the integrated machine.

Green scheduling of dual-armed cluster tool based on cleaning scenarios

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*).

Test-driven simulation modelling: A case study using agent-based maritime search-operation simulation

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.

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.

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.

For wafer fabrication, a process module (PM) in cluster tools is prone to failure. It is crucial to deal with such failure in a proper and timely manner. With residency time constraints, 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. A Petri net model is developed to describe the dynamic behavior of a single-arm cluster tool and failure response policies are proposed to deal with a failure. The proposed policies are formulated via simple control laws for their real-time and on-line implementation. An example is presented to show their application.

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.

Analytical water quality model for biochemical oxygen demand simulation in River Gomti of Ganga Basin, India

In this paper authors propose the approach for investigation of photonic switches performance metrics in modern all-optical networks. The approach includes photonic switches analytical and simulation modeling. The analytical model of the $$4\times 4$$ -photonic switch is based on the M/M/1/4 queuing model using so-called probability translation matrix method that allows to investigate functioning of the system in transient mode. The analytical expressions of such performance metrics as a loss probability, a buffer size and a transient time are obtained. A comparison of analytical and simulation modeling results was carried out. The analysis show that the steady-state loss probability obtained in results of analytical modeling is greater than the analogous parameter obtained in results of simulation modelling by 8%. The study of simulation models of $$4\times 4$$ and $$16\times 16$$ -photonic switches show that the buffer size of these systems does not exceed one packet. Analysis of the $$16\times 16$$ -photonic switch buffer show that the buffer size of the first cascade is four times larger than the buffer of the second cascade. The results of the investigation show that the proposed type of photonic switches can be used in the high-performance all-optical network designed to transmit information from the ground module to tethered high-altitude unmanned module and vice versa.

The impact that scheduling can have on the performance of semi-conductor wafer fabrication facilities is assessed. The performance measure considered is the mean throughput time (sometimes called cycle time, turnaround time or manufacturing interval) for a lot of wafers. A variety of input control and sequencing rules are evaluated using a simulation model of a representative, but fictitious, semiconductor wafer fabrication. Certain of these scheduling rules are derived by restricting attention to the sub-set of stations that are heavily utilized, and by using a Brownian network model, which approximates a multi-class queuing network model with dynamic control capability. Three versions of the wafer fabrication model, which differ only by the number of servers present at particular stations, are studied. The three versions have one, two, and four stations, respectively, that are heavily utilized (near 90% utilization). The simulation results indicate that scheduling has a significant impact on average throughput time, with larger improvements coming from discretionary imput control than from lot sequencing. The effects that specific sequencing rules have are highly dependent on both the type of input control used and the number of bottleneck stations in the fabrication.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>