Short-Term Scheduling Model of Cluster Tool in Wafer Fabrication

Since last decade, the cluster tool has been mainstream in modern semiconductor manufacturing factories. In general, the cluster tool occupies 60% to 70% of production machines for advanced technology factories. The most characteristic feature of this kind of equipment is to integrate the relevant processes into one single machine to reduce wafer transportation time and prevent wafer contaminations as well. Nevertheless, cluster tools also increase the difficulty of production planning significantly, particularly for shop floor control due to complicated machine configurations. The main objective of this study is to propose a short-term scheduling model. The noteworthy goal of scheduling is to maximize the throughput within time constraints. There are two modules included in this scheduling model—arrival time estimation and short-term scheduling. The concept of the dynamic cycle time of the product’s step is applied to estimate the arrival time of the work in process (WIP) in front of machine. Furthermore, in order to avoid violating the time constraint of the WIP, an algorithm to calculate the latest time of the WIP to process on the machine is developed. Based on the latest process time of the WIP and the combination efficiency table, the production schedule of the cluster tools can be re-arranged to fulfill the production goal. The scheduling process will be renewed every three hours to make sure of the effectiveness and good performance of the schedule.

Clustering Using Student t Mixture Copulas

Tewari et al. (Parametric characterization of multimodal distributions with non-Gaussian modes, pp 286–292, 2011) introduced Gaussian mixture copula models (GMCM) for clustering problems which do not assume normality of the mixture components as Gaussian mixture models (GMM) do. In this paper, we propose Student t mixture copula models (SMCM) as an extension of GMCMs. GMCMs require weak assumptions, yielding a flexible fit and a powerful cluster tool. Our SMCM extension offers, in a natural way, even more flexibility than the GMCM approach. We discuss estimation issues and compare Expectation-Maximization (EM)-based with numerical simplex optimization methods. We illustrate the SMCM as a tool for image segmentation.

In silico rationalisation of selectivity and reactivity in Pd-catalysed C–H activation reactions

A computational approach has been developed to automatically generate and analyse the structures of the intermediates of palladium-catalysed carbon–hydrogen (C–H) activation reactions as well as to predict the final products. Implemented as a high-performance computing cluster tool, it has been shown to correctly choose the mechanism and rationalise regioselectivity of chosen examples from open literature reports. The developed methodology is capable of predicting reactivity of various substrates by differentiation between two major mechanisms – proton abstraction and electrophilic aromatic substitution. An attempt has been made to predict new C–H activation reactions. This methodology can also be used for the automated reaction planning, as well as a starting point for microkinetic modelling.

In Silico Rationalisation of Selectivity and Reactivity in Pd-Catalysed C-H Activation Reactions

<p>A computational approach has been developed to automatically generate and analyse the structures of the intermediates of palladium catalysed carbon-hydrogen (C-H) activation reactions as well as to predict the final products. Implemented as a high-performance computing cluster tool, it has been shown to correctly choose the mechanism and rationalise regioselectivity of chosen examples from open literature reports. The developed methodology is capable of predicting reactivity of various substrates by differentiation between two major mechanisms - proton abstraction and the electrophilic aromatic substitution. An attempt has been made to predict new C-H activation reactions. This methodology can also be used for the automated reaction planning, as well as a starting point for microkinetic modelling.</p>

In Silico Rationalisation of Selectivity and Reactivity in Pd-Catalysed C-H Activation Reactions

<p>A computational approach has been developed to automatically generate and analyse the structures of the intermediates of palladium catalysed carbon-hydrogen (C-H) activation reactions as well as to predict the final products. Implemented as a high-performance computing cluster tool, it has been shown to correctly choose the mechanism and rationalise regioselectivity of chosen examples from open literature reports. The developed methodology is capable of predicting reactivity of various substrates by differentiation between two major mechanisms - proton abstraction and the electrophilic aromatic substitution. An attempt has been made to predict new C-H activation reactions. This methodology can also be used for the automated reaction planning, as well as a starting point for microkinetic modelling.</p>

In Silico Rationalisation of Selectivity and Reactivity in Pd-Catalysed C-H Activation Reactions

<p>A computational approach has been developed to automatically generate and analyse the structures of the intermediates of palladium catalysed carbon-hydrogen (C-H) activation reactions as well as to predict the final products. Implemented as a high-performance computing cluster tool, it has been shown to correctly choose the mechanism and rationalise regioselectivity of chosen examples from open literature reports. The developed methodology is capable of predicting reactivity of various substrates by differentiation between two major mechanisms - proton abstraction and the electrophilic aromatic substitution. An attempt has been made to predict new C-H activation reactions. This methodology can also be used for the automated reaction planning, as well as a starting point for microkinetic modelling.</p>

Real-Time Scheduling and Control of Single-Arm Cluster Tools With Residency Time Constraint and Activity Time Variation by Using Resource-Oriented Petri Nets

In semiconductor manufacturing, when a wafer is processed, it requires unloading from its process module in a given time interval, otherwise it is scraped. This requirement is called wafer residency time constraints. Thus, it is crucial to schedule a cluster tool such that the wafer sojourn time in a process module is within a given time window to satisfy the wafer residency time constraints. Besides wafer residency time constraints, in a cluster tool, the activity time is subject to variation. The activity time variation can make a feasible schedule obtained under the assumption of deterministic activity times become infeasible. To solve this problem, it is important to reveal the wafer sojourn time fluctuations with bounded activity time variation. Such an issue is addressed in this chapter for single-arm cluster tools. A single-arm cluster tool is modeled by a resource-oriented Petri net to describe the wafer fabrication processes. Based on it, a real-time control policy is proposed such that it offsets the effect of the activity time variation as much as possible. Then, the wafer sojourn time delay in a process module is analyzed and analytical expressions are derived to calculate the upper bound. With the help of the real-time control policy and wafer sojourn time delay analysis results, schedulability conditions and scheduling algorithms for an off-line schedule are presented in this chapter. The schedulability conditions can be analytically checked. If schedulable, an off-line schedule can be analytically found. The off-line schedule together with the real-time control policy forms the real-time schedule for the system. It is optimal in terms of cycle time minimization. Examples are given to show the application of the proposed approach.