Scheduling Dual-Arm Multi-Cluster Tools With Regulation of Post-Processing Time

As wafer circuit width shrinks down to less than ten nanometers in recent years,stringent quality control in the wafer manufacturing process is increasingly important.Thanks to the coupling of neighboring cluster tools and coordination of multiple robots in a multi-cluster tool,wafer production scheduling becomes rather complicated.After a wafer is processed,due to high-temperature chemical reactions in a chamber,the robot should be controlled to take it out of the processing chamber at the right time.In order to ensure the uniformity of integrated circuits on wafers,it is highly desirable to make the differences in wafer post-processing time among the individual tools in a multicluster tool as small as possible.To achieve this goal,for the first time,this work aims to find an optimal schedule for a dual-arm multi-cluster tool to regulate the wafer post-processing time.To do so,we propose polynomial-time algorithms to find an optimal schedule,which can achieve the highest throughput,and minimize the total post-processing time of the processing steps.We propose a linear program model and another algorithm to balance the differences in the post-processing time between any pair of adjacent cluster tools.Two industrial examples are given to illustrate the application and effectiveness of the proposed method.

Scheduling method for single-arm cluster tools of wafer fabrications with residency and continuous reentrancy

In order to enhance the utilization of single-ann cluster tools and optimize the scheduling problems of dynamic reaching wafers with residency time and continuous reentrancy constraints, a structural heuristic scheduling algorithm is presented. A nonlinear programming scheduling model is built on the basis of bounding the scheduling problem domain. A feasible path search scheduling method of single-arm robotic operations is put forward with the objective of minimal makespan. Finally, simulation experiments are designed to analyze the scheduling algorithms. Results indicate that the proposed algorithm is feasible and valid to solve the scheduling problems of multiple wafer types and single-ann clusters with the conflicts and deadlocks generated by residency time and continuous reentrancy constraints.

Scheduling algorithm of dual-armed cluster tools with residency time and reentrant constraints

To solve the scheduling problem of dual-armed cluster tools for wafer fabrications with residency time and reentrant constraints,a heuristic scheduling algorithm was developed.Firstly,on the basis of formulating scheduling problems domain of dual-armed cluster tools,a non-integer programming model was set up with a minimizing objective function of the makespan.Combining characteristics of residency time and reentrant constraints,a scheduling algorithm of searching the optimal operation path of dual-armed transport module was presented under many kinds of robotic scheduling paths for dual-armed cluster tools.Finally,the experiments were designed to evaluate the proposed algorithm.The results show that the proposed algorithm is feasible and efficient for obtaining an optimal scheduling solution of dual-armed cluster tools with residency time and reentrant constraints.

Try and error-based scheduling algorithm for cluster tools of wafer fabrications with residency time constraints

To improve the productivity of cluster tools in semiconductor fabrications,on the basis of stating scheduling problems,a try and error-based scheduling algorithm was proposed with residency time constraints and an objective of minimizing Makespan for the wafer jobs in cluster tools.Firstly,mathematical formulations of scheduling problems were presented by using assumptions and definitions of a scheduling domain.Resource conflicts were analyzed in the built scheduling model,and policies to solve resource conflicts were built.A scheduling algorithm was developed.Finally,the performances of the proposed algorithm were evaluated and compared with those of other methods by simulations.Experiment results indicate that the proposed algorithm is effective and practical in solving the scheduling problem of the cluster tools.

Cycle Time Analysis for Wafer Revisiting Process in Scheduling of Single-arm Cluster Tools

Some wafer fabrication processes performed by cluster tools require revisiting. With wafer revisiting, a cluster tool is very difficult to be scheduled due to a large number of possible schedules for the revisiting process. Atomic layer deposition （ALD） is a typical process with wafer revisiting that should be performed by cluster tools. This paper discusses the scheduling problem of single-arm cluster tools for the ALD process. In scheduling such a system, the most difficult part is to schedule the revisiting process such that the cycle time is minimized. Thus, this paper studies the revisiting process of ALD with revisiting times k = 3, 4, and 5, and analytical expressions are obtained to calculate the cycle time for the k possible schedules. Then, the schedule with the minimal cycle time is the optimal one. In this way, the scheduling problem of such a revisiting process becomes very simple and this is a significant improvement in scheduling cluster tools with wafer revisiting. Illustrative example is presented to show the application of the proposed method.

Post-Processing Time-Aware Optimal Scheduling of Single Robotic Cluster Tools

Integrated circuit chips are produced on silicon wafers.Robotic cluster tools are widely used since they provide a reconfigurable and efficient environment for most wafer fabrication processes.Recent advances in new semiconductor materials bring about new functionality for integrated circuits.After a wafer is processed in a processing chamber,the wafer should be removed from there as fast as possible to guarantee its high-quality integrated circuits.Meanwhile,maximization of the throughput of robotic cluster tools is desired.This work aims to perform post-processing time-aware scheduling for such tools subject to wafer residencytime constraints.To do so,closed-form expression algorithms are derived to compute robot waiting time accurately upon the analysis of particular events of robot waiting for singlearm cluster tools.Examples are given to show the application and effectiveness of the proposed algorithms.

The Fuzzy Cluster Analysis in Identification of Key Temperatures in Machine Tool

The thermal-induced error is a very important sour ce of machining errors of machine tools. To compensate the thermal-induced machin ing errors, a relationship model between the thermal field and deformations was needed. The relationship can be deduced by virtual of FEM (Finite Element Method ), ANN (Artificial Neural Network) or MRA (Multiple Regression Analysis). MR A is on the basis of a total understanding of the temperature distribution of th e machine tool. Although the more the temperatures measured are, the more accura te the MRA is, too more temperatures will hinder the analysis calculation. So it is necessary to identify the key temperatures of the machine tool. The selectio n of key temperatures decides the efficiency and precision of MRA. Because of th e complexities and multi-input and multi-output structure of the relationships , the exact quantitative portions as well as the unclear portions must be taken into consideration together to improve the identification of key temperatures. I n this paper, a fuzzy cluster analysis was used to select the key temperatures. The substance of identifying the key temperatures is to group all temperatures b y their relativity, and then to select a temperature from each group as the repr esentation. A fuzzy cluster analysis can uncover the relationships between t he thermal field and deformations more truly and thoroughly. A fuzzy cluster ana lysis is the cluster analysis based on fuzzy sets. Given U={u i|i=0,...,N}, in which u i is the temperature measured, a fuzzy matrix R can be obta ined. The transfer close package t(R) can be deduced from R. A fuzzy clu ster of U then conducts on the basis of t(R). Based on the fuzzy cluster analysis discussed above, this paper identified the k ey temperatures of a horizontal machining center. The number of the temperatures measured was reduced to 4 from 32, and then the multiple regression relationshi p models between the 4 temperatures and the thermal deformations of the spindle were drawn. The remnant errors between the regression models and measured deform ations reached a satisfying low level. At the same time, the decreasing of tempe rature variable number improved the efficiency of measure and analysis greatly.

BioCluster:Tool for Identification and Clustering of Enterobacteriaceae Based on Biochemical Data

Presumptive identifcation of different Enterobaeteriaeeae species is routinely achieved based on biochemical properties. Traditional practice includes manual comparison of each biochem- ical property of the unknown sample with known reference samples and inference of its identity based on the maximum similarity pattern with the known samples. This process is labor- intensive, time-consuming, error-prone, and subjective. Therefore, automation of sorting and sim- ilarity in calculation would be advantageous. Here we present a MATLAB-based graphical user interface （GUI） tool named BioCluster. This tool was designed for automated clustering and iden- tification of Enterobacteriaceae based on biochemical test results. In this tool, we used two types of algorithms, i.e., traditional hierarchical clustering （HC） and the Improved Hierarchical Clustering （IHC）, a modified algorithm that was developed specifically for the clustering and identification of within this species. IHC takes into account the variability in result of 1-47 biochemical tests family. This tool also provides different options to optimize the clus- tering in a user-friendly way. Using computer-generated synthetic data and some real data, we have demonstrated that BioCluster has high accuracy in clustering and identifying enterobacterial species based on biochemical test data. This tool can be freely downloaded at http：//microbialgen.du.ac.bd/ biocluster/.