Single-Arm Cluster Tool Start-Up Scheduling With Petri Net Models
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Current scheduling methods for single-arm cluster tools with wafer residency time constraints are not applicable, as they fail to derive an optimal feasible transient process, making existing research results infeasible for residency time-constrained single-arm cluster tools.
Innovation Solution
A method is developed using a Petri net model and scheduling algorithm to schedule the start-up process of a single-arm cluster tool, incorporating a linear programming model to regulate robot waiting times and ensure wafer residency time constraints are met, allowing the tool to transition to a steady state.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If existing scheduling methods are applied to single-arm cluster tools with wafer residency time constraints, then the scheduling complexity is reduced, but the feasibility of the schedule is compromised
Solution Approach 1:
The patent transforms the scheduling problem by changing the parameter representation from direct time scheduling to Petri net marking sequences. This parameter transformation allows the system to handle wafer residency time constraints effectively while maintaining scheduling feasibility, resolving the contradiction between simplicity and feasibility.
Solution Approach 2:
The patent introduces Petri nets as an intermediary formalism between the cluster tool control system and the scheduling algorithm. This intermediary enables precise modeling of wafer residency time constraints and facilitates the derivation of feasible schedules, bridging the gap between simplified scheduling and constraint satisfaction.
2Manufacturing precision
If wafer residency time constraints are enforced, then the manufacturing precision is improved, but the productivity is reduced
Solution Approach 1:
The patent employs dynamic scheduling strategies that adapt to wafer residency time constraints. By using Petri net models to dynamically determine optimal robot waiting times and wafer transfer sequences, the system maintains precise residency time control while maximizing throughput, resolving the contradiction between precision and productivity.
Solution Approach 2:
The patent changes the approach from static scheduling to dynamic parameter optimization. By adjusting robot waiting times and wafer processing sequences based on real-time constraints, the system achieves both precise residency time control and high productivity, transforming the trade-off into a coordinated optimization problem.
3Loss of time
If the start-up process is optimized, then the time to reach steady state is reduced, but the complexity of the scheduling algorithm increases
Solution Approach 1:
The patent applies preliminary action by pre-calculating optimal robot waiting times and wafer transfer sequences during the start-up phase using Petri net models. This preliminary optimization minimizes start-up time while the structured approach of the Petri net methodology keeps the algorithm complexity manageable through systematic state-space analysis.
Solution Approach 2:
The patent segments the start-up process into discrete Petri net states and transitions, allowing systematic optimization of each phase. This segmentation reduces overall start-up time by identifying critical paths and optimizing them independently, while the modular state-based approach prevents algorithmic complexity from becoming unmanageable.
Data Source
AI summary
Due to the trend of using larger wafer diameter and smaller lot size, cluster tools need to switch from processing one lot of wafers to another frequently. It leads to more transient periods in wafer fabrication. Their efficient scheduling and control problems become more and more important. It becomes difficult to solve such problems, especially when wafer residency time constraints must be considered. This work develops a Petri net model to describe the behavior during the start-up transient processes of a single-arm cluster tool. Then, based on the model, for the case that the difference of workloads among the steps is not too large and can be properly balanced, a scheduling algorithm to find an optimal feasible schedule for the start-up process is given. For other cases schedulable at the steady state, a linear programming model is developed to find an optimal feasible schedule for the start-up process.