Petri Net Modeling and Wafer Sojourn Time Analysis of Single-Arm Cluster Tools With Residency Time Constraints and Activity Time Variation

2012 ◽  
Vol 25 (3) ◽  
pp. 432-446 ◽  
Author(s):  
Yan Qiao ◽  
NaiQi Wu ◽  
MengChu Zhou
Keyword(s):  
Petri Net ◽  
Time Variation ◽  
Sojourn Time ◽  
Time Constraints ◽  
Time Analysis ◽  
Activity Time ◽  
Cluster Tools ◽  
Residency Time

Wafer Residency Time Analysis for Time-Constrained Single-Robot-Arm Cluster Tools With Activity Time Variation

2020 ◽  
Vol 28 (4) ◽  
pp. 1177-1188 ◽  
Author(s):  
Fajun Yang ◽  
Xin Tang ◽  
Naiqi Wu ◽  
Chunjiang Zhang ◽  
Liang Gao
Keyword(s):  
Time Variation ◽  
Robot Arm ◽  
Time Analysis ◽  
Activity Time ◽  
Cluster Tools ◽  
Residency Time

Real-Time Scheduling and Control of Single-Arm Cluster Tools With Residency Time Constraint and Activity Time Variation by Using Resource-Oriented Petri Nets

2019 ◽  
pp. 850-886
Author(s):  
Yan Qiao ◽  
NaiQi Wu ◽  
MengChu Zhou
Keyword(s):  
Real Time ◽  
Time Variation ◽  
Sojourn Time ◽  
Control Policy ◽  
Time Constraints ◽  
Activity Time ◽  
Real Time Control ◽  
Time Control ◽  
Cluster Tool ◽  
Residency Time

In semiconductor manufacturing, when a wafer is processed, it requires unloading from its process module in a given time interval, otherwise it is scraped. This requirement is called wafer residency time constraints. Thus, it is crucial to schedule a cluster tool such that the wafer sojourn time in a process module is within a given time window to satisfy the wafer residency time constraints. Besides wafer residency time constraints, in a cluster tool, the activity time is subject to variation. The activity time variation can make a feasible schedule obtained under the assumption of deterministic activity times become infeasible. To solve this problem, it is important to reveal the wafer sojourn time fluctuations with bounded activity time variation. Such an issue is addressed in this chapter for single-arm cluster tools. A single-arm cluster tool is modeled by a resource-oriented Petri net to describe the wafer fabrication processes. Based on it, a real-time control policy is proposed such that it offsets the effect of the activity time variation as much as possible. Then, the wafer sojourn time delay in a process module is analyzed and analytical expressions are derived to calculate the upper bound. With the help of the real-time control policy and wafer sojourn time delay analysis results, schedulability conditions and scheduling algorithms for an off-line schedule are presented in this chapter. The schedulability conditions can be analytically checked. If schedulable, an off-line schedule can be analytically found. The off-line schedule together with the real-time control policy forms the real-time schedule for the system. It is optimal in terms of cycle time minimization. Examples are given to show the application of the proposed approach.

scholarly journals A Resource-Oriented Petri Net Approach to Scheduling and Control of Time-Constrained Cluster Tools in Semiconductor Fabrication

Robotics ◽  
2013 ◽  
pp. 970-1011
Author(s):  
NaiQi Wu ◽  
MengChu Zhou
Keyword(s):  
Real Time ◽  
Petri Net ◽  
Time Variation ◽  
Control Policy ◽  
Activity Time ◽  
Real Time Control ◽  
Time Control ◽  
Cluster Tools ◽  
Periodic Schedule ◽  
Residency Time

Because of residency time constraints and activity time variation for cluster tools, it is very challenging to schedule them. This chapter addresses their real-time scheduling issues and conducts their schedulability analysis in considering residency time constraints and bounded activity time variation. A Petri Net (PN) model, called Resource-Oriented PN (ROPN) is developed to model them. Such formal models describe not only the behavior of both initial transient and steady state processes of cluster tools but also determine the robot activity sequence with robot waits included. They are very compact, independent of wafer flow pattern, and useful for discrete-event control. It is due to the proposed models that scheduling cluster tools are converted into determining robot wait times. A two-level operational architecture is proposed to include an off-line periodic schedule and real-time controller. The former determines when a wafer should be placed into a process module for processing, while the latter regulates robot wait times on-line in order to reduce the effect of activity time variation on wafer sojourn times in process modules. Therefore, the system can adapt to random activity time variation. Based on the PN model, real-time operational architecture, and real-time control policy, it analyzes the effect of activity time variation on wafer sojourn time delay at a process module and presents its upper bounds. The upper bounds are given in an analytical form and can be easily evaluated. Then, it derives schedulability conditions that are in closed form expressions. If schedulable, an algorithm is developed to obtain an off-line periodic schedule. This schedule together with the real-time control policy forms a real-time schedule. It is optimal in terms of cycle time and can be analytically computed, which represents significant advance in this area. Several examples are used to show the applications of the proposed approach.

Real-Time Scheduling and Control of Single-Arm Cluster Tools with Residency Time Constraint and Activity Time Variation by Using Resource-Oriented Petri Nets

2013 ◽  
pp. 178-210
Author(s):  
Yan Qiao ◽  
NaiQi Wu ◽  
MengChu Zhou
Keyword(s):  
Real Time ◽  
Time Variation ◽  
Sojourn Time ◽  
Control Policy ◽  
Time Constraints ◽  
Activity Time ◽  
Real Time Control ◽  
Time Control ◽  
Cluster Tool ◽  
Residency Time

In semiconductor manufacturing, when a wafer is processed, it requires unloading from its process module in a given time interval, otherwise it is scraped. This requirement is called wafer residency time constraints. Thus, it is crucial to schedule a cluster tool such that the wafer sojourn time in a process module is within a given time window to satisfy the wafer residency time constraints. Besides wafer residency time constraints, in a cluster tool, the activity time is subject to variation. The activity time variation can make a feasible schedule obtained under the assumption of deterministic activity times become infeasible. To solve this problem, it is important to reveal the wafer sojourn time fluctuations with bounded activity time variation. Such an issue is addressed in this chapter for single-arm cluster tools. A single-arm cluster tool is modeled by a resource-oriented Petri net to describe the wafer fabrication processes. Based on it, a real-time control policy is proposed such that it offsets the effect of the activity time variation as much as possible. Then, the wafer sojourn time delay in a process module is analyzed and analytical expressions are derived to calculate the upper bound. With the help of the real-time control policy and wafer sojourn time delay analysis results, schedulability conditions and scheduling algorithms for an off-line schedule are presented in this chapter. The schedulability conditions can be analytically checked. If schedulable, an off-line schedule can be analytically found. The off-line schedule together with the real-time control policy forms the real-time schedule for the system. It is optimal in terms of cycle time minimization. Examples are given to show the application of the proposed approach.

A Resource-Oriented Petri Net Approach to Scheduling and Control of Time-Constrained Cluster Tools in Semiconductor Fabrication

2013 ◽  
pp. 136-177
Author(s):  
NaiQi Wu ◽  
MengChu Zhou
Keyword(s):  
Real Time ◽  
Petri Net ◽  
Time Variation ◽  
Control Policy ◽  
Activity Time ◽  
Real Time Control ◽  
Time Control ◽  
Cluster Tools ◽  
Periodic Schedule ◽  
Residency Time

Because of residency time constraints and activity time variation for cluster tools, it is very challenging to schedule them. This chapter addresses their real-time scheduling issues and conducts their schedulability analysis in considering residency time constraints and bounded activity time variation. A Petri Net (PN) model, called Resource-Oriented PN (ROPN) is developed to model them. Such formal models describe not only the behavior of both initial transient and steady state processes of cluster tools but also determine the robot activity sequence with robot waits included. They are very compact, independent of wafer flow pattern, and useful for discrete-event control. It is due to the proposed models that scheduling cluster tools are converted into determining robot wait times. A two-level operational architecture is proposed to include an off-line periodic schedule and real-time controller. The former determines when a wafer should be placed into a process module for processing, while the latter regulates robot wait times on-line in order to reduce the effect of activity time variation on wafer sojourn times in process modules. Therefore, the system can adapt to random activity time variation. Based on the PN model, real-time operational architecture, and real-time control policy, it analyzes the effect of activity time variation on wafer sojourn time delay at a process module and presents its upper bounds. The upper bounds are given in an analytical form and can be easily evaluated. Then, it derives schedulability conditions that are in closed form expressions. If schedulable, an algorithm is developed to obtain an off-line periodic schedule. This schedule together with the real-time control policy forms a real-time schedule. It is optimal in terms of cycle time and can be analytically computed, which represents significant advance in this area. Several examples are used to show the applications of the proposed approach.

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