# Browsing by Subject "Process control--Mathematical models"

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Item Electrical parameter control for semiconductor manufacturing(2007-12) Schoene, Clare Butler, 1979-; Qin, S. Joe; Edgar, Thomas F.Show more The semiconductor industry is highly competitive environment where modest improvements in the manufacturing process can translate to significant cost savings. An area where improvements can be realized is reducing the number of wafers that fail to meet their electrical specifications. Wafers that fail to meet electrical specifications are scrapped, which negatively impacts yield and increases manufacturing costs. Most of the existing semiconductor process control research has focused on controlling individual steps during the manufacturing process via run-to-run control, but almost no work has looked at directly controlling device electrical characteristics. Since meeting electrical specifications is so critical to reducing scrap a fab-wide electrical parameter control scheme is proposed to directly control electrical parameter values. The goal of the controller is reducing the variation in the electrical parameters. The control algorithm uses a model to predict electrical parameter values after each processing step. Based on this prediction the decision to make a control move is made. If a control move is necessary, optimal adjustments for the subsequent processing steps are determined. The process model is continually updated so that it reflects the current process. A simple implementation using a least squares model is first proposed. Simulations and an industrial case study demonstrate the potential improvements that can be achieved with the algorithm and the limitations of the simple implementation are discussed. A partial least squares modeling and control algorithm combined with missing data algorithms are proposed as enhancements to the electrical parameter control algorithm to address many of the issues faced when implementing such a control strategy in real manufacturing environments. The enhancements take the input variable correlations into account when making control moves and utilize the correlation structure to make better model predictions. Simulations are performed to determine the effectiveness of the enhancements. A cost function formulation and a Bayesian based alternative are also presented and evaluated. The cost function implementation uses a different method to determine the optimal set points for the subsequent processing steps than the other implementations use. Simulations are used to compare the cost function formulation with the other methods presented. The Bayesian implementation addresses the stochastic nature of the manufacturing process by dealing with the probabilities of events occurring. A simulation of the Bayesian algorithm is preformed and the algorithms limitations are discussed.Show more Item Semiconductor manufacturing inspired integrated scheduling problems : production planning, advanced process control, and predictive maintenance(2008-08) Cai, Yiwei; Kutanoglu, Erhan; Qin, SizhaoShow more This dissertation is composed of three major parts, each studying a problem related to semiconductor manufacturing. The first part of the dissertation proposes a high-level scheduling model that serves as an intermediate stage between planning and detailed scheduling in the usual planning hierarchy. The high-level scheduling model explicitly controls the WIP over time in the system and provides a more specific guide to detailed scheduling. WIP control is used to balance the WIP (Work In Process) level and to keep the bottleneck station busy to maintain a high throughput rate. A mini-fab simulation model is used to evaluate the benefits of different approaches to implementing such a high-level scheduling model, and to compare different WIP control policies. Extensive numerical studies show that the proposed approaches can achieve much shorter cycle times than the traditional planning-scheduling approach, with only a small increase in inventory and backorder costs. With increasing worldwide competition, high technology product manufacturing companies have to pay great attention to lower their production costs and guarantee high quality at the same time. Advanced process control (APC) is widely used in semiconductor manufacturing to adjust machine parameters so as to achieve satisfactory product quality. The interaction between scheduling and APC motivates the second part of this dissertation. First, a single-machine makespan problem with APC constraints is proved to be NPcomplete. For some special cases, an optimal solution is obtained analytically. In more general cases, the structure of optimal solutions is explored. An efficient heuristic algorithm based on these structural results is proposed and compared to an integer programming approach. Another important issue in manufacturing system is maintenance, which affects cycle time and yield management. Although there is extensive literature regarding maintenance policies, the analysis in most papers is restricted to conventional preventive maintenance (PM) policies, i.e., calendar-based or jobbased PM policies. With the rapid development of new technology, predictive maintenance has become more feasible, and has attracted more and more attention from semiconductor manufacturing companies in recent years. Thus, the third problem considered in this dissertation is predictive maintenance in an M/G/1 queueing environment. One-recipe and two-recipe problems are studied through semi-Markov decision processes (SMDP), and structural properties are obtained. Discounted SMDP problems are solved by linear programming and expected machine availabilities are calculated to evaluate different PM policies. The optimal policy can maintain a high machine availability with low long-run cost. The structures of the optimal PM policies show that it is necessary to consider multiple recipes explicitly in predictive maintenance models.Show more