Analysis of Circular Cluster Tools:
Transient Behavior and Semiconductor Equipment Models
Younghun Ahn and James R. Morrison
KAIST, Department of Industrial and Systems Engineering
IEEE CASE 2010
Toronto, Canada
August 22, 2010
©2010 – IEEE CASE 2010 – Toronto – August 22, 2010
Contents
• Motivation
• System description: Cluster tools
• Methods
– Transition analysis
– Waiting times in the transitions
– Cycle time analysis & simulation
• Concluding remarks
©2010 – IEEE CASE 2010 – Toronto – August 22, 2010 – 2
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
©2010 – IEEE CASE 2010 – Toronto – August 22, 2010 – 3
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
We make 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 der Meulen, “Linear Semiconductor Manufacturing Logistics and the Impact on Cycle Time,” in Proc. 18th Ann. IEEE/SEMI Adv Semiconduct. Manuf. Conf., Stresa, Italy, 2007.
©2010 – IEEE CASE 2010 – Toronto – August 22, 2010 – 4
System Description
C2
• Backward policy is considered
C3
• Wafer lots consist of up to 25
C1
C4
wafers
VEC
VEC
WTR
• Each wafer must receive service
aligner
loadlock
Circular cluster tool
from all process chambers in
sequence
• Robot move time is constant
©2010 – IEEE CASE 2010 – Toronto – August 22, 2010 – 5
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, C2A, …, CN}
1
– WCi(wj): Duration of time the robot waits after it reaches
chamber
i until
M
M
wafer j is completed and ready for removing
– δ: Robot move time
M
M
– ε: Robot get / put time
– Pi: Process time of chamber I
3
2
4
1
• Aj, j∈{0, 1, 2, …, N}
input
output
AB
M
M
– Robot action of removing a wafer from chamber and placing
it into
chamber j+1
M
– AB=(AN,AN-1, …, A1, A0}
2
1
3
M4
• Transient control: use “backward sequence“ and systematically
input
output
skip action that are not possible
©2010 – IEEE CASE 2010 – Toronto – August 22, 2010 – 6
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
TM, O,I  0,
TG,1,I   ,
TM,1, C1     ,
TP,1,C1  2   ,
TW,1,C1  2    WC1 ( w1 )  2    P1 ,
TG,1,C1  3    WC1 ( w1 ),
M2
TM,1, C 2  3  2  WC1 ( w1 ),
M3
TP,1,C 2  4  2  WC1 ( w1 ),
M4
M1
input
output
TM, O,I  4  3  WC1 ( w1 ),
TG,2,I  5  3  WC1 ( w1 ),
TM,2, C1  5  4  WC1 ( w1 ),
TP,2,C1  6  4  WC1 ( w1 ),
TM,0, C 2  6  5  WC1 ( w1 ),
TW,1,C 2  6  5  WC1 ( w1 )  WC2 ( w1 ).
©2010 – IEEE CASE 2010 – Toronto – August 22, 2010 – 7
Transition Analysis
Lemma 1: Duration of the initial transition & cyclic period
RM , 0, I (i )  2( N  1)  2( N  1) 
i
W
j i 1 N
2( N  1)  (2 N  1)

where f ( N , i )  2( N  i )  (2 N  i )
0

Ci 1 j
( w j )  f ( N , i ),
,i  1


,1  i  N  for i  1,  , W .
, otherwise 
NOTE: we also find out the duration of the final transition in paper (Lemma 2)
Proposition 1: General equation for the cycle time
W
N 2
i 1
i 1
CT   RM , 0, I (i )   RP ,W ,O (i )  2    WC N ( wW  N  2 )
NOTE: we develop a recursive procedure to calculate WCi(wj) in paper
©2010 – IEEE CASE 2010 – Toronto – August 22, 2010 – 8
Cycle Time Analysis & Simulation
• Idea for approximation
– 1-unit cycle time for N chambers (backward sequence)*
max{ max Pi  3  4 , 2( N  1)  2( N  1) }
1i  N
• Our approximation
Approximation 1: Cyclic approximation for cycle time
*
P
CT  P1  3  4   {max{ max Pi  3  4 , 2( j  1)  2( j  12) }
N 1
j 2
1i  j
 (W  N  1) max{ max Pi  3  4 , 2( N  1)  2( N  1) }   P
 2+3δ+4ε

2
1i  N
N 1
 P4  3  4   {max{ max Pi  3  4 , 2( N  j  1)  2( N  j  1) }
j 2
j i  N
* W. Dawande, H. Neil Geismar, P. Sethi, C. Sriskandarajam, “Throughput Optimization in Robotic Cells”, Springer, 2007.
©2010 – IEEE CASE 2010 – Toronto – August 22, 2010 – 9
3δ+4ε
t
Cycle Time Analysis & Simulation
• Modified version of existing approximation
Approximation 2: PMGC Approximation for Cycle Time
CT 
N 1
z
N 1
k  z 1
K 1
K  z 1
 2 K '(W  N  1) max( P  4 ' ,2 ' ( N  1))   P  4 '  2( K  1) '3 ' ,
P
2

'
where z  min{ N  1, INT (
)}
2
 '     , P  max Pi
1i  N
Approximation 3: PM Approximation for Cycle Time
CT  ( P  E )  ( N  1)  ( P  E )  W
E  3  4 , P  max Pi
1i  N
©2010 – IEEE CASE 2010 – Toronto – August 22, 2010 – 10
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
Lemma 1-5 &
Proposition 1
TS=1
TS=2
TS=3
TS=4
TS=5
3189s
3057s
3013s
2991s
2977s
TS=1
TS=2
TS=3
TS=4
TS=5
Approximation 1:
0.31% 0.16% 0.10% 0.10% 0.06%
Cyclic
Approximation 2:
14.10% 7.78% 5.54% 4.41% 3.72%
PMGC
Approximation 3:
2.72% 1.40% 0.96% 0.70% 0.60%
PM
©2010 – IEEE CASE 2010 – Toronto – August 22, 2010 – 11
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
1,400
exact
1,200
Cyclic appx.
1,000
μs
PMGC appx.
PM appx.
800
600
400
200
0
TS=1
TS=2
TS=3
TS=4
TS=5
CPU time(μs) in Example 1
©2010 – IEEE CASE 2010 – Toronto – August 22, 2010 – 12
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
Lemma 1-5 &
Proposition 1
TS=1
TS=2
TS=3
TS=4
TS=5
525s
513s
508s
506s
505s
TS=1
TS=2
TS=3
TS=4
TS=5
0%
0%
Approximation 1:
-0.30% -0.20% -0.10%
Cyclic
Approximation 2:
-2.85% -1.55% -0.98% -0.60% -0.60%
PMGC
Approximation 3:
-30.6% -32.7% -33.4% -33.7% -34%
PM
©2010 – IEEE CASE 2010 – Toronto – August 22, 2010 – 13
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
©2010 – IEEE CASE 2010 – Toronto – August 22, 2010 – 14
Question & Answer
©2010 – IEEE CASE 2010 – Toronto – August 22, 2010 – 15