Wafer sojourn time fluctuation analysis for time-constrained dual-arm multi-cluster tools with activity time variation

Scheduling a multi-cluster tool with wafer residency time constraints is highly challenging yet important in ensuring high productivity of wafer fabrication. This paper presents a method to find an optimal one-wafer cyclic schedule for it. A Petri net is developed to model its dynamic behavior. By using this model, its schedule is found and analytically expressed as a function of robots' waiting time. In addition, this work establishes the necessary and sufficient conditions under which a feasible one-wafer cyclic schedule exists. Then, it gives efficient algorithms to find such a schedule that is optimal. These algorithms require one to determine the robots' waiting time via simple calculation and thus are efficient.

A multi-cluster tool is composed of a number of individual cluster tools linked by buffering modules (BMs). The capacity of a BM can be one or two. Aiming at finding an optimal one-wafer cyclic schedule, this paper explores the effect of two-space BMs on the performance of a multi-cluster tool. A Petri net (PN) model is developed to model it by extending resource-oriented PNs. The dynamic behavior of robot waiting and tasks, process modules, and buffers is well described by the model. This paper shows that there is always a one-wafer cyclic schedule that reaches the lower bound of the cycle time of a process-bound tool. Furthermore, a closed-form algorithm is revealed to find such a schedule for the first time for such multi-cluster tools. Illustrative examples are given to show the application and power of the proposed method.

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

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

With the requirements of physical vapor deposition and chemical vapor deposition processes, twin-cluster tools are widely used in the current wafer fabrication. Cycle scheduling ensures that wafers have the same quality, however, twin-cluster tools involve resource coordination between two tools, which makes cycle scheduling more sophisticated. A steady-state cycle scheduling problem of twin-cluster tools with a complete concurrent processing module is studied, considering the wafer residency time constraints. First, a Petri net model is constructed to describe the process of twin-cluster tools under a steady state with the wafer residency time constraints and the complete concurrent processing module, and a control strategy is proposed to avoid the system deadlock. The sufficient conditions for the system to reach the highest efficiency are obtained by analyzing the workload of the processing module and the robot task, and an algorithm is developed to obtain the robot schedule. Finally, examples are verified about the effectiveness of the algorithms.

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.

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.

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.

Enabling fail-operational behavior of safety-critical software is essential to achieve autonomous driving. At the same time, automotive vendors have to regularly deliver over-the-air software updates. Here, the challenge is to enable a flexible and dynamic system behavior while offering, at the same time, a predictable and deterministic behavior of time-critical software. Thus, it is necessary to verify that timing constraints can be met even during failover scenarios. For this purpose, we present a formal analysis to derive the worst-case application failover time. Without such an automated worst-case failover timing analysis, it would not be possible to enable a dynamic behavior of safety-critical software within safe bounds. We support our formal analysis by conducting experiments on a hardware platform using a distributed fail-operational neural network. Our randomly generated worst-case results are as close as 6.0% below our analytically derived exact bound. Overall, our presented worst-case failover timing analysis allows to conduct an automated analysis at run-time to verify that the system operates within the bounds of the over timing constraint such that a dynamic and safe behavior of autonomous systems can be ensured.

We describe in this paper the application of several neural network architectures to the problem of simulating and predicting the dynamic behavior of complex economic time series. We use several neural network models and training algorithms to compare the results and decide at the end, which one is best for this application. We also compare the simulation results with the traditional approach of using a statistical model. In this case, we use real time series of prices of consumer goods to test our models. Real prices of tomato and green onion in the U.S. show complex fluctuations in time and are very complicated to predict with traditional statistical approaches.

We describe in this paper the application of several neural network architectures to the problem of simulating and predicting the dynamic behavior of complex economic time series. We use several neural network models and training algorithms to compare the results and decide at the end, which one is best for this application. We also compare the simulation results with the traditional approach of using a statistical model. In this case, we use real time series of prices of consumer goods to test our models. Real prices of tomato and green onion in the U.S. show complex fluctuations in time and are very complicated to predict with traditional statistical approaches.

As gas and oil fields mature their operation becomes increasingly more complex, due to complex process dynamics, like slugging, gas coning, water breakthrough, salt or hydrate deposition. Moreover these phenomena also lead to production constraints in the upstream facilities. This complexity asks for operator support in how to optimally operate such an asset. In this paper we explore how, based on physical models of reservoirs, wells and top side separation and compression equipment, real-time optimization may be used in optimal operation of a maturing asset showing complex dynamic behavior and top side compressor constraints. In a joint industry project of Wintershall, GDF, EBN, Siemens and TNO the applicability of Real-Time Optimization is explored. Real-time optimization will be demonstrated on a maturing North Sea off-shore gas production asset consisting of eight wells and two separator and compression trains. The current results show how the optimization problem has been defined and implemented in a real-time architecture. First results are shown realizing the gas production set point and minimizing compressor power, while the production of individual wells suffer from degrading performance and (unplanned) shut-ins. The optimizer computes how the production must be dynamically distributed over the wells and how the compressor trains must be operated. Dynamic optimization strategies have been exploited successfully in downstream operations. A similar development is happening in upstream industry, while having to cope with the higher uncertainties typically present in upstream processes. As the paper shows Dynamic Optimization may lead to large benefits in Real-Time Operation of upstream production facilities.

Human epigenetic enzyme disruptor of telomeric silencing 1-like (DOT1L) is a key drug target for treating acute myeloid leukemia. Several nucleoside and non-nucleoside DOT1L inhibitors have been developed to inhibit its histone methyltransferase activity. Non-mechanism-based nucleoside DOT1L inhibitors have shown good inhibitory activity and high on-target residence times. Previous computational studies have explored the dynamic behavior of this group of molecules on DOT1L to design compounds with enhanced binding affinities. Nevertheless, it is well known that drug-target kinetics also plays a crucial role in the discovery of new drugs. Therefore, we performed τ-Random Acceleration Molecular Dynamics (τRAMD) simulations to estimate the residence times of nucleoside DOT1L inhibitors. The high correlation between the calculated and experimental residence times suggested that the method can reliably estimate the residence time of nucleoside DOT1L inhibitors when modifications are made to those substituents that occupy the buried hydrophobic pocket of the active site, exhibit hydrophobic interactions with F245 or that form H-bonds with D161 and G163. Overall, this study will be a step toward understanding the binding kinetics of nucleoside DOT1L inhibitors for the treatment of acute myeloid leukemia.

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 this paper, the turbulent attached cavitating flows around two different twisted hydrofoils, named as NACA0009 and Clark-y, are studied numerically, with emphasis on cavity shedding dynamic behavior and the turbulence flow structures. The computational method of large eddy simulation (LES) coupled with a homogeneous cavitation model is applied and assessed by previous experimental data. It was found that the predicted results were in good agreement with that of the experiment. The unsteady cavity morphology of the two hydrofoils undergoes a similar quasi-periodic process, but has different shedding dynamic behavior. The scale of the U-type shedding structures forming on the suction surface of NACA0009 is larger than that of Clark-y. This phenomenon is also present in the iso-surface distributions of Q-criterion. Otherwise, the time-averaged cavity morphology is dramatically different for the two hydrofoils, and it is found that the attached location of the cavity is closely related to the hydrofoil geometry. The time fluctuation of the lift force coefficients is affected significantly by the cavity shedding dynamics. Compared with NACA0009, the lift force of Clark-y shows more fluctuation, due to its complicated shedding behavior. Further analysis of the turbulent structure indicates that the more violent shedding behaviors can induce higher levels of turbulence velocity fluctuations.