Due-date based scheduling and control policies in a multiproductsemiconductor wafer fabrication facility

This paper focuses on lot release control and scheduling problems in a semiconductor wafer fab producing multiple products that have different due dates and different process flows. For lot release control, it is necessary to determine the type of a wafer lot and the time to release wafers into the wafer fab, while it is necessary to determine sequences of processing waiting lots in front of workstations for lot scheduling. New dispatching rules are developed for lot release control and scheduling considering special features of the wafer fabrication process. Simulation experiments are carried out to test the dispatching rules. Results show that lot release control and lot scheduling at photolithography workstations are more important than scheduling at other workstations. Also, it is shown that new dispatching rules work better in terms of tardiness of orders than existing rules such as the EDD (earliest due date) rule and other well-known dispatching rules for multimachine scheduling     

Stochastic wafer fabrication scheduling

To meet the challenge of integrating uncertainty analysis into wafer fabrication scheduling, this paper proposes a stochastic dynamic programming model for scheduling new releases and bottleneck processing by stage. Based on the paradigm of stochastic linear quadratic control (SLQ), the fab scheduling model incorporates considerable analysis of uncertainties in yields and demands. The SLQ scheduling model explicitly captures the reentrant flow structure characteristic of wafer fabrication. Moreover, the SLQ scheduling model removes a major weakness in applying dynamic programming to production control by accommodating noninteger values for lead times. Embedded in the SLQ scheduling model is what the authors term a degree-2 yield distribution that subsumes most popular yield distributions in the literature. As long as the underlying system dynamics behave in a degree-2 fashion, the corresponding optimal scheduling policy turns out to be a linear control rule that is easy to compute and implement. Industrial data are used to test the effectiveness and robustness of the SLQ machinery versus the LP rolling horizon and pull heuristic methodologies. Encouraging results and valuable insights are obtained from extensive numerical experiments that show promise for successfully managing uncertainties surrounding fab scheduling.     

Family-based scheduling rules of a sequence-dependent wafer fabrication system

Consider the dispatch problem for a wafer fabrication where production process is divided into hundreds of operations and takes a few months to complete. In the process, wafers have to go through similar operations several times repeatedly for different layers of circuit, called job re-entrances. General family-based scheduling rules are proved to perform better than the individual job scheduling rule in terms of machine utilization for multiserver and multiple job re-entrance manufacturing systems under the condition that with a positive possibility, a queue exists in front of steppers. Five special family-based scheduling rules are constructed, of which FCFS-F, SRPT-F, EDD-F, and LS-F are modified from previous well-known scheduling rules, while SDA-F is a rule-based algorithm, using threshold control and least slack principles. A simulation model is built to evaluate the performances of these five family-based rules by using the information collected from a wafer fab located in Hsin-Chu, Taiwan. As a result, SDA-F is shown to perform best among all five rules, followed by LS-F and FCFS-F.     

Performance measures and scheduling policies in ring networks

A unidirectional ring network is considered. A node may transmit at most one packet per slot to its downstream neighbor. Potentially all nodes may transmit at the same slot. The achievable performance is studied and policies are proposed for both the evacuation mode and continual operation. In the evacuation mode each node has initially an amount of packets destined for every other node of the ring, and no more packets are generated later. It is shown that the furthest destination first (FDF) policy, that gives priority to the packet with the longest way to go at each node, minimizes the time until every packet reaches its destination. Furthermore it is shown that the closest destination first (CDF) policy, that gives priority to the packet with the shortest way to go at each node, minimizes the average packet delivery time. A formula for the optimal evacuation time is obtained. The continual operation of the ring is considered then where packets are generated according to some arrival process. For any arrival sample path, the PDF maximizes the fraction of the time at which the ring is empty. The performance analysis of individual origin-destination traffic streams under FDF is facilitated based on the following. For each traffic stream, a single server priority queue is identified such that the average sojourn time of the traffic stream in the ring is equal to the aggregate transmission time plus the queueing delay of the low priority stream in the queue. Formulas for the sojourn time are obtained for iid arrivals. The performance of CDF and FIFO in continual operation is studied by simulation. It turns out that the CDF, minimum delay policy for the evacuation, has the worst performance in continual operation     

A new scheduling approach using combined dispatching criteria in wafer fabs

In this paper, a scheduling approach that combines multiple dispatching criteria into a single rule, with the objective of simultaneously optimizing multiple performance measures is proposed. This is accomplished using a linear combination with relative weights. The weights identify the contribution of the different criteria. The weights' assignments to the different criteria are optimized using a mixture design of experiments (DOE) and multiple response optimization. Results using this new approach show significant improvement versus the use of a single dispatching criterion.     

A problem reduction approach for scheduling semiconductor wafer fabrication facilities

Most scheduling procedures used in industry are based on the dispatching paradigm, where decisions are made based on the jobs available at the time the machine becomes free. While optimization-based scheduling procedures have repeatedly been shown to yield significantly better schedules under ideal circumstances, their practical implementation is hampered by high computational requirements. We present a problem reduction procedure that allows a workcenter-based global scheduling heuristic to be implemented in very low CPU times. The procedure partitions the workcenters in a fab into heavily loaded and lightly loaded classes and solves the global scheduling problem only for the heavily loaded workcenters. The proposed technique is tested on instances drawn from an International SEMATECH wafer fab model. The proposed problem reduction approach yields superior results with modest computational effort, enabling the practical use of the decomposition heuristic.     

Stable scheduling policies for fading wireless channels

We study the problem of stable scheduling for a class of wireless networks. The goal is to stabilize the queues holding information to be transmitted over a fading channel. Few assumptions are made on the arrival process statistics other than the assumption that their mean values lie within the capacity region and that they satisfy a version of the law of large numbers. We prove that, for any mean arrival rate that lies in the capacity region, the queues will be stable under our policy. Moreover, we show that it is easy to incorporate imperfect queue length information and other approximations that can simplify the implementation of our policy.     

无线网络链路传输调度策略研究综述

无线网络链路传输调度策略确定各个时间槽内进行传输的链路集合,这些链路互不冲突,能够同时进行传输.对于当前的无线网络链路传输调度策略建立一个全面的了解有助于对无线网络的性能做出客观评估,并且成为网络设计的基本依据之一.文章总结了当前主流的无线网络链路传输调度策略,并且给出了这一领域的后续发展趋势和主要挑战.在具体的介绍过程中,本文重点介绍了基于吞吐量的调度策略、基于链路服务质量的调度策略、基于应用的服务策略,以及应对于在线视频传输的策略.在后续挑战的介绍中,文章主要归纳了基于应用的调度策略的实施前提要求和挑战.     

Efficient scheduling policies to reduce mean and variance ofcycle-time in semiconductor manufacturing plants

The problem of reducing the mean and variance of cycle time in semiconductor manufacturing plants is addressed. Such plants feature a characteristic reentrant process flow, where lots repeatedly return at different stages of their production to the same service stations for further processing, consequently creating much competition for machines. We introduce a new class of scheduling policies, called Fluctuation Smoothing policies. Unanimously, our policies achieved the best mean cycle time and Standard Deviation of Cycle Time, in all the configurations of plant models and release policies tested. As an example, under the recommended Workload Regulation Release policy, for a heavily loaded Research and Development Fabrication Line model, our Fluctuation Smoothing policies achieved a reduction of 22.4% in the Mean Queueing Time, and a reduction of 52.0% in the Standard Deviation of Cycle Time, over the baseline FIFO policy. These conclusions are based on extensive simulations conducted on two models of semiconductor manufacturing plants. The first is a model of a Research and Development Fabrication Line. The second is an aggregate model intended to approximate a full scale production line. Statistical tests are used to corroborate our conclusions     

Queueing analysis of scheduling policies in copy networks ofspace-based multicast packet switches

Space-based multicast switches use copy networks to generate the copies requested by the input packets. In this paper our interest is in the multicast switch proposed by Lee (1988). The order in which the copy requests of the input ports are served is determined by the copy scheduling policy and this plays a major part in defining the performance characteristics of a multicast switch. In any slot, the sum of the number of copies requested by the active inputs of the copy network may exceed the number of output ports and some of the copy requests may need to be dropped or buffered. We first propose an exact model to calculate the overflow probabilities in an unbuffered Lee's copy network. Our exact results improve upon the Chernoff bounds on the overflow probability given by Lee by a factor of more than 10. Next, we consider buffered inputs and propose queueing models for the copy network for three scheduling policies: cyclic service of the input ports with and without fanout splitting of copy requests and acyclic service without fanout splitting. These queueing models obtain the average delay experienced by the copy requests. We also obtain the sustainable throughput of a copy network, the maximum load that can be applied to all the input ports without causing an unstable queue at any of the inputs, for the scheduling policies mentioned above     

节能调度背景下考虑不确定市场信息的机组检修计划

我国电力工业改革的重要措施之一是实施节能发电调度,交易方式有别于国外实时市场,发电公司检修策略肯定也有所不同。因此,有必要研究节能调度对检修计划制定的影响。检修策略是发电公司中长期生产计划的制订问题,需要考虑中长期负荷和非计划停运等不确定信息。在此背景下,计及负荷和非计划停运等不确定信息,建立机组检修计划制定策略的随机优化模型,研究节能调度实施后对机组检修计划的影响。算例分析表明了模型的有效性。     

Mechanisms of wafer sawing and impact on wafer properties

Silicon wafer wire‐sawing experiments were realized with different sets of sawing parameters, and the thickness, roughness, and cracks depth of the wafers were measured. The results are discussed in relation to assumptions underlying the rolling–indenting model, which describes the process. It was also found that the silicon surface at the bottom of the sawing groove is different from the wafer surface, implying different sawing conditions in the two positions. Furthermore, the measured parameters were found to vary along the wire direction, between the entrance of the wire in the ingot and its exit. Based on these observations, some improvements for the wire‐sawing model are discussed. Copyright © 2010 John Wiley & Sons, Ltd.     

Real-time multimedia scheduling policies for end-to-end delayjitter and loss guarantees across ATM satellite systems

We propose a simple first-in first-out (FIFO)-based service protocol which is appropriate for a multimedia ATM satellite system. The main area of interest is to provide real-time traffic with upper bounds on the end-to-end delay, jitter, and loss experienced at various service queues within a satellite network. Various service protocols, each based on a common underlying strategy, are developed in light of the requirements and limitations imposed at each of the satellite's subsystems. These subsystems include the uplink (UL) earth station (ES) service queue, on-board processing (OBP) queues, and the downlink (DL) ES service queue feeding into a wireline ATM network or directly to an end-user application. Numerous network simulation results demonstrate the tractability, efficiency, and versatility of the underlying service discipline. Key features of our strategy are its algorithmic and architectural simplicity, its non-ad-hoc scheduling approach, and its unified treatment of all real-time streams at all service queues. In addition, the delay and jitter bounds are uncoupled. In this way, end-to-end jitter can be tightly controlled even if medium access requires long indeterminate waiting durations     

Fast wafer level reliability monitoring as a tool to achieve automotive quality for a wafer process

This work describes and discusses fast wafer level reliability (fWLR) Monitoring as a supporting procedure on productive wafers to achieve stringent quality requirements of automotive, medical and/or aviation applications. Examples are given for the various reliability topics: dielectrics, devices, metallisation, plasma charging with respect to required test structures, stress methods and data analysis. Application areas of fWLR are highlighted and limitations considered. Further aspects such as relevant reliability parameters, sampling strategies and out of control action plans are discussed.     

Integrated resource scheduling in a distributed scheduling environment

The Space Station era presents a highly complex multimission planning and scheduling environment exercised over a highly distributed system. In order to automate the scheduling process, customers require a mechanism for communicating their scheduling requirements to NASA. An expressive scheduling notation that captures a wide range of customer requirements and scheduling options is one solution to this problem. This article describes a request language that a remotely located customer can use to specify his scheduling requirements to a NASA scheduler, thus automating the customer-scheduler interface. Additionally, this article describes a scheduler that can accept these requests, process them, generate schedules, and return schedule and resource availability information to the requester.     

Applying just-in-time in a wafer fab: a case study

The successful application of the just-in-time (JIT) manufacturing management philosophy within a wafer fab photoresist wet chemistry area is described. The JIT techniques that were applied included lot-size reduction, setup-time reduction, layout changes for improved work flow, and improved operator flexibility. These set the stage for the implementation of a demand-pull system that resulted in significant decreases in cycle times as well as corresponding decrease in inventory levels. Aspects related to quality improvement as well as other long-term issues are also discussed     

Thermal modeling of a wafer in a rapid thermal processor

A model, using geometric optics, has been developed to calculate the illumination of a wafer inside a rapid thermal processor. The main parameters of the model are: the processing chamber geometry, the lamp number and location, the reflector characteristics, and the wafer temperature. Each incident light component, i.e., direct or reflected, is identified, its contribution to the illumination of the wafer is calculated through a 3D analytical model, and the corresponding contour maps are depicted. Then, the heat diffusion equation is numerically solved in two dimensions, and thermal maps of a Si wafer are given versus various experimental conditions, such as the effect of patterning the reflectors, of individually adjusting the electrical power applied to each lamp, and the impact of rotating the wafer or using crossed lamp banks. The latter method, while being easy to implement, is shown to give excellent thermal uniformity     

On the stability of local scheduling policies in networks of packet switches with input queues

A significant research effort has been devoted to the design of simple and efficient scheduling policies for input queued (IQ) and combined input-output queued (CIOQ) packet switches. As a result, a number of switch control algorithms have been proposed. Among these, scheduling policies based on maximum weight matching (MWM) were identified as optimal, in the sense that they were proved to achieve 100% throughput under any admissible arrival process satisfying the strong law of large number. On the contrary, it has been shown that the usual MWM policies fail to guarantee 100% throughput in networks of interconnected IQ/CIOQ switches. Hence, new policies suited for networks of interconnected switches were proposed and proved to achieve 100% throughput. All of these new policies require coordination and cooperation among different switches. We identify scheduling policies that require no coordination among switches (and are, thus, said to be local), and that guarantee 100% throughput in a network of IQ/CIOQ switches. The only assumptions on the input traffic pattern are that it is stationary, satisfies the strong law of large numbers and does not oversubscribe any link in the network.     

Fast electromigration wafer mapping for wafer fab process monitoring and improvement

In this work, a set up for fast wafer level electromigration (WL-EM) is developed with the use of a standard electrical analyser, a semi-auto probe station with a hot chuck, and a PC. EM tests on multiple test structures are carried out simultaneously and tests are done at multiple locations (EM mapping) across the wafer. Measured data are imported into MS EXCEL and analysed with a macro automatically. Good correlations are demonstrated between the fast WL-EM test and classical package level EM at 0.1% failure rate. For several years reliable EM monitoring charts are created with the fast WL-EM set up. The fast EM mapping test does not only exploit the advantages of fast WL-EM test in terms of short throughput time and low cost (without packaging) for process monitoring, the additional information on EM performance across the wafer makes the test extremely valuable for process improvement.     

Assessment of ultra-thin Si wafer thickness in 3D wafer stacking

3D integration with multi-stacked wafers is a promising option to enhance device performance and density beyond traditional device scaling limits. However, to bring wafer stacking into reality, there are many technological challenges to be resolved, and one of those is the problem of uniform Si wafer thinning. For multi-stacked devices, Si wafers must be drastically thinned down to less than 50 μm. Problems associated with such ultra-thin Si wafers range from basic wafer handling to difficulty in accurately assessing the thickness of the thinned wafer across the wafer. In this study, bonded wafer pairs have been prepared with different bonding materials, and the stacks were ground down to about 30 μm. The thickness of the ultra-thin wafers was measured by Fourier transform infrared spectrometry (FTIR) technique, and its stability based on bonding status as well as measuring issues will be discussed.