1. Yan Qiao and Naiqi Wu Guangdong University of Technology, Guangdong University of Technology, China China Mengchu Zhou New Jersey Institute of Technology, New Jersey Institute of Technology, USA USA

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

3.  Configuration –A dual arm robot –Process modules (PM) –Loadlocks (LL) –No intermediate buffer  Operated by Swap Strategy

4.  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 Consider Wafer Revisiting

5.  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.  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.  Places and Transitions p L : loadlocks with K(p 0 )=  and M 0 (p 0 )=n p i : wafer processing at step i with K(p i )= 1 t ij : robot moving from Step i to Step j q ij : model a robot arm waiting at Step i c p : a control place  Initial state M 0 (p i ) = K(p i ) and M 0 (q ij ) = 0, i  N 3, j  N 3  control function

8. Transition or place Time duration t L1  +  t 12, t 23, t 32  t 3L  +  pipi aiai t i0 and t i0 qi1qi1 i1i1 qi2qi2 i2i2 qi3qi3 i3i3

9.  Wu et al – When k = 2 – System starts from the idle state – Three local cycles with PM 2 and PM 3 – Three global cycles with PM 1, PM 2 and PM 3 – Three wafers are completed – 3-Wafer Schedule – It is not optimal for some cases 3-Wafer Schedule

10. Example: A 2 =120, A 3 =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 A i 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 > A i, or a wafer processing delay occur CycleWaiting time before swapping at p 2 Waiting time before swapping at p 3 1745 25510 35015 44520 54025 ……… 12560 13065 14065

11.  The state of the system: M = {  1,  2,  3,  4 }   i, i  N 3, represents the wafers in PM i,   4 represents the wafers held by robot.  W d (q) represents the d-th wafer is being processed or to be processed for q-th operation in p i.

12.  Consider 2 times revisits  The marking evolution of the PN: M 1 = {W 4 (1), W 3 (2), W 2 (3), W 1 (5)}  M 2 = {W 4 (1), W 2 (4), W 1 (5), W 3 (3)}  M 3 = {W 5 (1), W 4 (2), W 3 (3), W 2 (5)} M 1 to M 2 : Firing sequence is {swapping at p 3  t 32  swapping at p 2  t 23 } M 2 to M 3 : Firing sequence is{swapping at p 3  t 3L  t L1  swapping at p 1  t 12  swapping at p 2  t 23 }

13.  One local cycles with PM 2 and PM 3  One global cycles with PM 1, PM 2 and PM 3  One wafers are completed  1-Wafer Schedule  It is optimal 1-Wafer Schedule

14.  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!