Petri Net-Based Scheduling Analysis of Dual-Arm Cluster Tools with Wafer Revisiting

1. Petri Net-Based Scheduling Analysis of Dual-Arm Cluster Tools with Wafer Revisiting • Yan Qiao and Naiqi Wu • Guangdong University of Technology, • China • Mengchu Zhou • New Jersey Institute of Technology, • USA

2. Semiconductor Manufacturing TM PMs Transport module Cassette module Processing modules • Cluster Tools • Better utilization of Space • Higher yield • Better quality

3. Dual-Arm Cluster Tools • Configuration • A dual arm robot • Process modules (PM) • Loadlocks (LL) • No intermediate buffer • Operated by Swap Strategy

4. Consider Wafer Revisiting • Single wafer type • 3 steps (operations) • Operations 2 and 3 form a revisiting process: typical atomic layer deposition process • Situations considered: revisiting k = 2 times

5. Cycle Time Analysis • Processes with revisiting • Work by Lee et al. (Korea) • It is for single-arm cluster tools and not applicable for dual-arm ones • It involves complex computation • Work by Wu et al. (China) • The process never reaches steady-state • Two methods to operate the system • It is not optimal for some cases • Work by Qiao et al. (China) • Cycle time analysis for dual-arm cluster tools with k-time revisiting, k > 2 • It is not optimal for some cases

6. Cycle Time Analysis • A generic Petri net model • Properties of cluster tools scheduled by 3-wafer schedule • It is not optimal for some cases • A novel scheduling method • It is optimal

7. Petri Net Modeling • Places and Transitions • pL: loadlocks with K(p0)= • and M0(p0)=n • pi: wafer processing at step i • with K(pi)= 1 • tij: robot moving from Step i • to Step j • qij: model a robot arm • waiting at Step i • cp: a control place • Initial state • M0(pi) = K(pi) and M0(qij) = 0, iN3, jN3 • control function

8. Time Modeling

9. 3-Wafer Schedule • Wu et al • When k = 2 • System starts from the idle state • Three local cycles with PM2 and PM3 • Three global cycles with PM1, PM2 and PM3 • Three wafers are completed • 3-Wafer Schedule • It is not optimal for some cases

10. Dynamics in the Local Cycles • Example: A2=120, A3=125, =21,  = 2, starting from the idle state • The robot waiting times are changing with a number of cycles to reaching its steady state • Finally, the robot waits at Step i with Ai being the largest one and it does not wait at other steps • If the robot does not wait at Step i, the wafer sojourn time i > Ai, or a wafer processing delay occur

11. Notations • The state of the system: M = {1, 2, 3, 4} • i, iN3, represents the wafers in PMi, • 4 represents the wafers held by robot. • Wd(q) represents the d-th wafer is being processed or to be processed for q-th operation in pi.

12. A Novel Scheduling Method • Consider 2 times revisits • The marking evolution of the PN: M1 = {W4(1), W3(2), W2(3), W1(5)}  M2 = {W4(1), W2(4), W1(5), W3(3)}  M3 = {W5(1), W4(2), W3(3), W2(5)} M1 to M2: Firing sequence is {swapping at p3 t32 swapping at p2t23} M2 to M3: Firing sequence is{swapping at p3 t3LtL1 swapping at p1 t12 swapping at p2t23}

13. 1-Wafer Schedule • One local cycles with PM2 and PM3 • One global cycles with PM1, PM2 and PM3 • One wafers are completed • 1-Wafer Schedule • It is optimal

14. Conclusions • Contribution • A Petri net model for the ALD process • A novel scheduling method • It is optimal. • Future work • Consider wafer residency time constraint • Subject to bounded activity time variation

15. Thank you for attention!