Analysis of Circular Cluster Tools: Transient Behavior and Semiconductor Equipment Models

1. Analysis of Circular Cluster Tools: Transient Behavior and Semiconductor Equipment Models YounghunAhn and James R. Morrison KAIST, Department of Industrial and Systems Engineering IEEE CASE 2010 Toronto, Canada August 22, 2010

2. Contents • Motivation • System description: Cluster tools • Methods • Transition analysis • Waiting times in the transitions • Cycle time analysis & simulation • Concluding remarks

3. Motivation • Semiconductor wafer fabrication is arguably the most complex of manufacturing processes with facility costs rising toward US $5 billion • Transient behavior in semiconductor manufacturing will be much more common • Until now, there has been substantial effort to model and control tools in steady state • Transients are brought about by setups, product changeovers and small lot sizes (few wafers per lot) • In the current & future, transient behavior is more common/frequent Goal: To develop rigorous models of wafer cycle time in cluster tools that include wafer transport robot and address transient behavior

4. Motivation • Existing research • Single-wafer Cluster Tool Performance: An Analysis of Throughput* • It doesn’t consider robot put / get time • It assumes that all chambers have same process time • We will call the PMGC approximation • Throughput Analysis of Linear Cluster Tools** • It doesn’t consider robot move, put / get time ( E is the alternative) • It assumes that all chambers have same process time • We will call the PM approximation • Our research Achievement • We consider robot move time, get / put time and different process time • Wemake a general equation and cyclic approximation • * T. Perkinson, P. McLarty, R. Gyurcsik, and R. Cavin, “Single-Wafer Cluster Tool Performance: An Analysis of Throughput,” IEEE Transactions Semiconductor Manufacturing, vol. 7, no. 3, pp. 369–373, 1994. • ** P. van derMeulen, “Linear Semiconductor Manufacturing Logistics and the Impact on Cycle Time,” in Proc. 18th Ann. IEEE/SEMI Adv Semiconduct. Manuf. Conf., Stresa, Italy, 2007.

5. System Description • Backward policy is considered • Wafer lots consist of up to 25 wafers • Each wafer must receive service from all process chambers in sequence • Robot move time is constant C2 C3 C1 C4 WTR VEC VEC aligner loadlock Circular cluster tool

6. System Description • RX,Y,Z , X: Robot action, Y: Index of wafer, Z: Location • X ∈{G, P, M, W}, Y ∈{0, 1, …, W}, Z∈{I, O, C1, C2, …, CN} • WCi(wj): Duration of time the robot waits after it reaches chamber i until wafer j is completed and ready for removing • δ: Robot move time • ε: Robot get / put time • Pi: Process time of chamber I • Aj, j∈{0, 1, 2, …, N} • Robot action of removing a wafer from chamber and placing it into chamber j+1 • AB=(AN,AN-1, …, A1, A0} • Transient control: use“backward sequence“ and systematically skip action that are not possible M3 M3 M2 M2 A1 M3 M3 M2 M2 M4 M4 M1 M1 M4 M4 M1 M1 input output input output input output input output M3 M2 M3 M3 M3 M2 M2 M2 M3 M3 M2 M2 M3 M3 M3 M3 M2 M2 M2 M2 M3 M3 M3 M3 M3 M2 M2 M2 M2 M2 M4 M1 AB M4 M4 M4 M3 M1 M1 M1 M2 M3 M3 M2 M2 M4 M4 M1 M1 M4 M4 M4 M4 M1 M1 M1 M1 M4 M4 M4 M4 M4 M1 M1 M1 M1 M1 M3 M3 M2 M2 M4 M1 M4 M4 M1 M1 input output input input input output output output input output input output input input input output output output input output M4 M4 M1 M1 input input input input input output output output output output input output input output input output input output input output

7. Transition Analysis • Example of robot behavior (initial part of robot sequence) ※ TX,Y,Z is the instant time at which event RX,Y,Z completes RG,1,I→ RM,1,C1→ RP,1,C1→ RW,1,C1→ RG,1,C1→ RM,1,C2→ RP,1,C2→ RM,0,C2→ RG,2,I→… → RP,W,O M3 M3 M3 M2 M2 M2 M3 M3 M2 M2 M3 M2 M3 M3 M2 M2 M4 M4 M4 M1 M1 M1 M4 M4 M1 M1 M4 M1 M4 M4 M1 M1 input input input output output output input input output output input output input input output output

8. Transition Analysis Lemma 1: Duration of the initial transition & cyclic period NOTE: we also find out the duration of the final transition in paper (Lemma 2) Proposition 1: General equation for the cycle time NOTE: we develop a recursive procedure to calculate WCi(wj) in paper

9. Cycle Time Analysis & Simulation • Idea for approximation • 1-unit cycle time for N chambers (backward sequence)* • Our approximation * * P2 3δ+4ε t P2+3δ+4ε Approximation 1: Cyclic approximation for cycle time * W. Dawande, H. Neil Geismar, P. Sethi, C. Sriskandarajam, “Throughput Optimization in Robotic Cells”, Springer, 2007.

10. Cycle Time Analysis & Simulation • Modified version of existing approximation Approximation 2: PMGC Approximation for Cycle Time Approximation 3: PM Approximation for Cycle Time

11. Cycle Time Analysis & Simulation • Application: Semiconductor wafer cluster tools • Measurement: The average time between lot departures (TBLD) • TS (Train size): The number of lots that are run consecutively • Simulation: 400 lots, 20 replications • Example 1: N=4, P1=80, P2=70, P3=110, P4=90 δ=1, ε=1

12. Cycle Time Analysis & Simulation • Application: Semiconductor wafer cluster tools • Example 1: N=4, P1=80, P2=70, P3=110, P4=90 δ=1, ε=1 μs CPU time(μs) in Example 1

13. Cycle Time Analysis & Simulation • Application: Semiconductor wafer cluster tools • Example 2: N=4, P1=6, P2=5, P3=4, P4=5 δ=1, ε=1

14. Concluding Remarks • Contribution • Exact equation: Transient analysis is possible • Cyclic approximation is less errors than existing approximations • Our models are good candidates for use in semiconductor manufacturing modeling and simulation • Future direction • Study other robot sequence for transient state • Consider parallel circular tool

15. Question & Answer