©2010 – ieee case 2010 – toronto – august 22, 2010 analysis of circular cluster tools:...

©2010 – IEEE CASE 2010 – Toronto – August 22, 2010

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

Younghun Ahn and James R. MorrisonKAIST, Department of Industrial and Systems Engineering

IEEE CASE 2010 Toronto, CanadaAugust 22, 2010

©2010 – IEEE CASE 2010 – Toronto – August 22, 2010 – 2

Contents• Motivation

• System description: Cluster tools

• Methods– Transition analysis– Waiting times in the transitions– Cycle time analysis & simulation

• Concluding remarks


Motivation

• Semiconductor wafer fabrication is arguably the most com-plex of manufacturing processes with facility costs rising to-ward 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


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

* T. Perkinson, P. McLarty, R. Gyurcsik, and R. Cavin, “Single-Wafer Cluster Tool Performance: An Analysis of Throughput,” IEEE Transactions Semiconductor Manufactur-ing, 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.

Achieve-ment

• We consider robot move time, get / put time and different process time• We make a general equation and cyclic approximation


System Description

• Backward policy is considered

• Wafer lots consist of up to 25

wafers

• Each wafer must receive service

from all process chambers in se-

quence

• Robot move time is constant

C1

C2 C3

C4

loadlock

aligner

WTRVEC VEC

Circular cluster tool


• RX,Y,Z , X: Robot action, Y: Index of wafer, Z: Location– X {G, P, M, W}, Y {0, 1, …, W}, Z {I, O, C∈ ∈ ∈ 1, 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

System Description

M4

M3

M1

M2

input output

M4

M3

M1

M2

input output

M4

M3

M1

M2

input output

M4

M3

M1

M2

input output

A1

M4

M3

M1

M2

inputout-put

M4

M3

M1

M2

inputout-put

M4

M3

M1

M2

inputout-put

M4

M3

M1

M2

inputout-put

M4

M3

M1

M2

inputout-put

M4

M3

M1

M2

inputout-put

M4

M3

M1

M2

inputout-put

M4

M3

M1

M2

inputout-put

M4

M3

M1

M2

inputout-put

M4

M3

M1

M2

inputout-put

M4

M3

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inputout-put

M4

M3

M1

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inputout-put

M4

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M2

inputout-put

M4

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inputout-put

M4

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M1

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inputout-put

M4

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inputout-put

M4

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inputout-put

M4

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M2

inputout-put

M4

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M1

M2

inputout-put

M4

M3

M1

M2

inputout-put

AB


Transition Analysis

).()(56T

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,0T

11CW,1,

1CM,0,

1CP,2,

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1CG,1,

11CW,1,

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CM,1,

IG,1,

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212

12

11

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wW

wW

PwW

CC

C

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C

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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

M4

M3

M1

M2

inputout-put

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M3

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inputout-put

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inputout-put

• Example of robot behavior (initial part of robot sequence) ※ TX,Y,Z is the instant time at which event RX,Y,Z completes


Transition Analysis

Lemma 1: Duration of the initial transition & cyclic pe-riod

.,,1

,0

1,)2()(2

1,)12()1(2

),(

),,()()1(2)1(2)(1

,0, 1

Wifor

otherwise

NiiNiN

iNN

iNfwhere

iNfwWNNiRi

NijjCIM ji

Proposition 1: General equation for the cycle time

)(2)()( 2

2

1,,

1,0,

NWC

N

iOWP

W

iIM wWiRiRCT

N

NOTE: we develop a recursive procedure to calculate WCi(wj) in paper

NOTE: we also find out the duration of the final transition in paper (Lemma 2)


Cycle Time Analysis & Simulation

• Idea for approximation– 1-unit cycle time for N chambers (backward sequence)*

• Our approximation

Approximation 1: Cyclic approximation for cycle time

})1(2)1(2,43max{max{43

2})1(2)1(2,43maxmax{)1(

})1(2)1(2,43max{max{43

1

24

1

1

21

1

N

ji

Nij

iNi

N

ji

ji

jNjNPP

NNPNW

jjPPCT

})1(2)1(2,43maxmax{1

NNPiNi

*

* W. Dawande, H. Neil Geismar, P. Sethi, C. Sriskandarajam, “Throughput Optimization in Robotic Cells”, Springer, 2007.

* P23δ+4

εP2+3δ+4ε t



Approximation 2: PMGC Approximation for Cycle Time

)}2

2'(,1min{

,'3')1(2'4))1('2,'4max()1('21

1 1

1

1

P

INTNzwhere

KPNPNWKCTN

zk

z

K

N

zK

Approximation 3: PM Approximation for Cycle Time

WEPNEPCT )()1()(

iNiPP

1max,'

iNiPPE

1max,43

• Modified version of existing approximation



• 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

TS=1 TS=2 TS=3 TS=4 TS=5

Lemma 1-5 &Proposition 1

3189s 3057s 3013s 2991s 2977s


Approximation 1:Cyclic

0.31% 0.16% 0.10% 0.10% 0.06%

Approximation 2:PMGC

14.10% 7.78% 5.54% 4.41% 3.72%

Approximation 3:PM

2.72% 1.40% 0.96% 0.70% 0.60%



• Application: Semiconductor wafer cluster tools– Example 1: N=4, P1=80, P2=70, P3=110, P4=90 δ=1, ε=1


200

400

600

800

1,000

1,200

1,400

exact

Cyclic appx.

PMGC appx.

PM appx.

μs

CPU time(μs) in Example 1



• 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

525s 513s 508s 506s 505s


Approximation 1:Cyclic

-0.30% -0.20% -0.10% 0% 0%

Approximation 2:PMGC

-2.85% -1.55% -0.98% -0.60% -0.60%

Approximation 3:PM

-30.6% -32.7% -33.4% -33.7% -34%


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 manufactur-

ing modeling and simulation

• Future direction– Study other robot sequence for transient state– Consider parallel circular tool


Question & Answer

©2010 – ieee case 2010 – toronto – august 22, 2010 analysis of circular cluster tools:...

Documents

wafer transport robot

wafer j

robot action

duration of time

time e

index of wafer

process time of chamber

waferseach wafer