Shengwei Ding

Multicluster tools scheduling: an integrated event graph and network model approach

Steady-state throughput and scheduling of a multicluster tool become complex as the number of modules and clusters grows. We propose a new methodology integrating event graph and network models to study the scheduling and throughput of multicluster tools. A symbolic decision-move-done graph modeling is developed to simplify discrete-event dynamics for the multicluster tool. This event graph is further used for searching feasible action sequences of the cluster tool. By representing sequences with networks, an extended critical path method is applied to calculate the corresponding cycle time. Grouping methods that are based on network are also introduced to reduce the searching complexity. Compared with optimization-based scheduling approaches, the proposed methodology can directly capture the cyclic characteristic of cluster tool schedules and be applied to analyze the impact of process and wafer flow variations on cycle time and robot schedules. We have successfully applied this new methodology to dozens of cluster tools at Intel Corporation. A chemical-mechanical planarization polisher is employed as an example to illustrate and validate the proposed methodology

Optimal Scheduling of Multicluster Tools With Constant Robot Moving Times, Part I: Two-Cluster Analysis

In semiconductor manufacturing, finding an efficient way for scheduling a multicluster tool is critical for productivity improvement and cost reduction. This two-part paper analyzes optimal scheduling of multicluster tools equipped with single-blade robots and constant robot moving times. In this first part of the paper, a resource-based method is proposed to analytically derive closed-form expressions for the minimal cycle time of two-cluster tools. We prove that the optimal robot scheduling of two-cluster tools can be solved in polynomial time. We also provide an algorithm to find the optimal schedule. Examples are presented to illustrate the proposed approaches and formulations.

Steady-State Throughput and Scheduling Analysis of Multicluster Tools: A Decomposition Approach

Cluster tools are widely used as semiconductor manufacturing equipment. While throughput analysis and scheduling of single-cluster tools have been well-studied, research work on multicluster tools is still at an early stage. In this paper, we analyze steady-state throughput and scheduling of multicluster tools. We consider the case where all wafers follow the same visit flow within a multicluster tool. We propose a decomposition method that reduces a multicluster tool problem to multiple independent single-cluster tool problems. We then apply the existing and extended results of throughput and scheduling analysis for each single-cluster tool. Computation of lower-bound cycle time (fundamental period) is presented. Optimality conditions and robot schedules that realize such lower-bound values are then provided using ldquopullrdquo and ldquoswaprdquo strategies for single-blade and double-blade robots, respectively. For an -cluster tool, we present lower-bound cycle time computation and robot scheduling algorithms. The impact of buffer/process modules on throughput and robot schedules is also studied. A chemical vapor deposition tool is used as an example of multicluster tools to illustrate the decomposition method and algorithms. The numerical and experimental results demonstrate that the proposed decomposition approach provides a powerful method to analyze the throughput and robot schedules of multicluster tools.

Optimal Scheduling of Multicluster Tools With Constant Robot Moving Times, Part II: Tree-Like Topology Configurations

In this paper, we analyze optimal scheduling of a tree-like multicluster tool with single-blade robots and constant robot moving times. We present a recursive minimal cycle time algorithm to reveal a multi-unit resource cycle for multicluster tools under a given robot schedule. For a serial-cluster tool, we provide a closed-form formulation for the minimal cycle time. The formulation explicitly provides the interaction relationship among clusters. We further present decomposition conditions under which the optimal scheduling of multicluster becomes much easier and straightforward. Optimality conditions for the widely used robot pull schedule are also provided. An example from industry production is used to illustrate the analytical results. The decomposition and optimality conditions for the robot pull schedule are also illustrated by Monte Carlo simulation for the industrial example.

Throughput Analysis of Linear Cluster Tools

In this paper, we analyze steady-state throughput and scheduling of linear cluster tools with single-blade robots in semiconductor manufacturing. We extend the existing research results in throughput and scheduling analysis for regular cluster tools to linear cluster tools. We analyze the tools throughput for typical single and separate input/output configurations. We also consider a general distribution of the parallel process modules. We present a few examples of linear cluster tools to illustrate the proposed decomposition method and algorithms. The numerical results demonstrate that the proposed approach provides a powerful method to analyze the throughput and robot schedules of newly developed linear cluster tools.

Steady-State Throughput and Scheduling Analysis of Multi-Cluster Tools for Semiconductor Manufacturing: A Decomposition Approach

Cluster tools are widely used as semiconductor manufacturing equipment. While throughput analysis and scheduling of single-cluster tools have been well-studied, the corresponding research on multi-cluster tools is still at the early stage. This paper analyzes steady-state throughput and scheduling of multi-cluster tools. A decomposition method is utilized to reduce a multi-cluster tool problem to multiple single-cluster tool problems. Existing research on the throughput and scheduling results is then applied to each single-cluster tool. For an M-cluster tool, an O(M) throughput calculation and robot scheduling algorithm is presented. A chemical-mechanical planarization (CMP) polisher is used as an example of the multi-cluster cluster tools to illustrate the proposed decomposition method and algorithms.

Excursion Yield Loss and Cycle Time Reduction in Semiconductor Manufacturing

The importance of cycle time reduction is well known to the semiconductor manufacturing industry in the sense of reduced inventory costs and faster response to the market. Less emphasized is the fact that the overall die yield is also closely related to cycle time. In particular, some yield losses are due to “excursions,” when process or equipment shift out of specifications. While some and perhaps most excursions are detected by in-line inspections, some are not detected until the wafers are tested in the probing area after fabrication. A long production cycle time will expose significant amounts of wafers in production to defective processing by such excursions. This paper introduces analytical formulas to quantify the revenue losses due to excursions not detected until end-of-line testing as a function of manufacturing cycle time, excursion probabilities and kill rates. The formulas provide a means to evaluate the revenue gains due to cycle time reduction, based on the assumption that the average selling prices of semiconductor products are declining steadily at predictable rates.

Optimal scheduling of k-unit production of cluster tools with single-blade robots

The main challenge in scheduling multi-cluster tools in semiconductor manufacturing is the interactions among clusters. These interactions create a k-unit optimal production that do not exist in single-cluster tools. This paper analyzes optimal scheduling of k-unit cycle production of multi-cluster tools with single-blade robots. A resource-based method is used to analytically derive closed-form expressions for the minimal cycle time of a multi-cluster tool. Conditions for decoupling multi-cluster tools and optimality conditions for the widely used pull schedule are also presented. An example from industry production is used to illustrate the derived formula and decoupling conditions.

On the Optimality of One-Unit Cycle Scheduling of Multi-Cluster Tools with Single-Blade Robots

In semiconductor manufacturing, finding an efficient way for scheduling a multi-cluster tool is crucial for productivity improvement and cost reduction. In this paper, we analyze optimal scheduling of multi-cluster tools under a general configuration with non-zero constant transfer robot traveling time. A resource-based method is developed to analyze optimal scheduling of single-cluster tools. Optimality conditions for obtaining minimum one-unit cycle time for multi-cluster tools are established. Under these conditions, it is shown that the optimal one-unit cycle can be achieved by first optimally scheduling each single-cluster tool separately and then combining the schedules to form the optimal schedule for the multi-cluster tool. A polynomial-time algorithm is presented to find the optimal one-unit cycle time and its corresponding schedules for a multi-cluster tool.

Stochastic Modeling for Serial-Batching Workstations with Heterogeneous Machines

The bottleneck workstation in semiconductor manufacturing is lithography. Lithography is a complex manufacturing system (CMS) and consists of multiple products, serial-batching operations, re-entrant process flows, and parallel non-identical machines. Existing stochastic models for such a CMS focus on simple extensions of the classical queueing theory. These models fail to question the applicability of the theory but try to modify model inputs on the first moment (average) and the second moment (variation). The implementation of these models has been unsatisfactory. In this paper, we provide a stochastic model of such a CMS. We model the arrival process of CMS by Poisson Process and the service process by Markov Decision Process. We propose a geometric-distribution based probabilistic dispatching model. The model is verified using a lithography workstation in a high-volume wafer fabrication facility. This study provides a theoretic framework and promis-ing results for serial-batching operation modeling in semicon-ductor manufacturing and other industries as well.