jungyeon park – xs3d lab seminar – september 11 2014 - 1 xs3d lab seminar cycle time and...

Jungyeon Park – xS3D Lab Seminar – September 11 2014 - 1

xS3D Lab Seminar Cycle Time and Throughput Models of Clustered Photolithography Tools for Fab-Level Simulation

Jungyeon (John) Park

Department of Industrial and Systems Engineering KAIST, South Korea


Presentation Overview

• Motivation

• System description: Clustered photolithography tool (CPT)

• Equipment models Linear model Affine model Flow line model Exit recursion model

• Numerical experiments Same sample & same parameter Different sample & same parameter Different sample & different parameter

• Concluding remarks

http://www.google.co.kr/url?sa=i&rct=j&q=&esrc=s&frm=1&source=images&cd=&docid=IvY4lbzXOG-f2M&tbnid=3q_2miLbU3VYmM:&ved=0CAUQjRw&url=http://www.directindustry.com/prod/suss-microtec/photolithography-equipment-36187-1332469.html&ei=4kvoU7XAKJDm8AWnkYHABQ&bvm=bv.72676100,d.dGc&psig=AFQjCNFplYkBtRJhIcVRKapXX6evs63bRw&ust=1407818957680699


Motivation


Motivation (1)

• Semiconductor manufacturing • Global revenue in 2013: ₩ 323 조 (US$ 318 billion)

• Construction costs• 300 mm wafer fab: ₩ 5 조 (US$ 5 billion [2])• 450 mm wafer fab: ₩ 10-15 조 (US$10-

15 billion)

• Significant value for improvements• 1996-1999: Fab production control method earned Samsung ₩ 1 조

(US$ 1 billion [3]) additional revenue• 2005: IBM’s 30 independent supply chains merged into a single global

system and saved ₩ 6 조 (US$ 6 billion [4])• …

[1]


Motivation (2)

• Clustered photolithography tools (CPT)• Purchase cost of ₩ 205 억 – 1025 억 (US$ 20-100 M [5])• The most expensive tool in a fabricator• Typically the bottleneck of the fabricator• Key yield and cycle time contributor

[5]


Motivation (3)

• Want: Models for CPTs• Accurate: Predict throughput with less than 1%

error• Expressive: Incorporate fundamental behaviors• Computationally tractable: Very quick to calculate results

• For the purpose of: • Understanding toolset performance• Enabling capacity optimization• Toolset scheduling or optimization• Improving the quality of fab simulation models


System Description:Clustered Photolithography Tool (CPT)


System Description: CPT (1)

• Multi-cluster tool, robot in each cluster, IF buffers, STK buffer• Scanner is often the CPT bottleneck• Largely deterministic process times• Process time can vary by product• Setups between lots (reticle changes, pre-scan setup, …)• Wafer handling robot decision policy & deadlock prevention [6]

Clustered PhotolithographyTool

Scanner


System Description: CPT (2)

“ “


System Description: Performance Metrics

• Notational: Arrival time of lot l to the toolSl: Start time of lot l in the toolCl: Completion time of lot l from the tool

• Performance measuresCycle time of lot l: CTl := Cl - al Lot residency time of lot l: LRTl := Cl - Sl Throughput time of lot l: TTl := min{ LRTl , Cl – Cl-1 }

Lot 1Lot 2

Lot 3

Time

TT2TT3

TT1

Computation time


Equipment Models


Models for CPTs

• Models with various levels of detail

Affine Models

Exit Recursion Mod-els

Flow LineModels

A(k1), B

A(k1), B(k1, k2)

A(k1), B(k1)

With complete tool log data

With wafer in/out log data

With lot in/out log data

Parametric flow lines

Empirical flow lines

Linear Model A(k1)

Access Big Data

Data Analytics

Simulate models

Detailed Model “Every-thing”


Linear Model

• Referred to as the Ax equipment model or linear model• Time between wafer completions: Al

• Process time estimation:

TlPT = Ak1 ∙ w(l) ( w(l): the number of wafers of lot l )

Complete Model:l = max{ al , l-1 }l = l l = l + Ak1 ∙ w(l)l = l

• Pros:– Simple to understand– Fast computation

• Cons: – Exactly matched to single wafer tool, not to CPT

mAl

Ax Model for lot cycle time in a one machine tool

Wafersenter

Wafersexit


Affine Models

• Referred to as the Ax+B model• First wafer delay: Bl

• Time between wafer completions: Al

• Process time estimation: TlPT = Ak1∙ (w(l) – 1) + Bl ( w(l) : the number of wafers of lot l )

B can be generalized to B(k1), B(k1, k2)

Complete model:l = max{ al , l-1 }l = l l = l + B + Ak1 ∙ (w(l) - 1)l = l

• Pros:• Simple to understand • Fast computation

• Cons:• Only one module per process, so not matched to CPT• New lots enter only when the tool is empty


Flow Line Models: Elementary Evolution Equations

• Notation• aw : Arrival time of wafer w to the tool, aw aw-1• Xi(w) : Entry time of wafer w into process i of the tool• : Deterministic process time for process i

• Elementary Evolution Equations (EEEs)• X1(w) = max{aw , X2(w-1) }• Xi+1(w) = max{Xi(w) + , Xi+2(w-1) }• XM(w) = max{XM-1(w) + , XM(w-1) + } (M is the last process)

Process i

W-1W


Flow Line Models: Extensions

• Elementary Evolution Equations (EEEs) can be generalized to allow:• Different classes of wafer to be produced• Multiple modules per process• Consider robotic workload in process times of modules• Consider setups – reticle setup, pre-scan setup

• Parameter extraction• Parametric flow line model – Known process times, robot times, and setup times • Empirical flow line model – Parameters extracted from tool processing data

Wafersenter

Wafersexit


Flow Line Models: Exit Recursions

• Theorem: Exact recursion for customer completion (exit) times [7,8]

• Theorem: Recursive bound for customer completion (exit) times [9]

P1

t1

……

Wafer LotsArrive

P2

t2

PM

tMWafer Lots

Exit…

P3

t3

BM

M

mmkM kcakc ,max1

11

……

Customers Arrive

Customers Exit

…

R1=2 P2

R2=1

R3=3RM=2

)(

max1

)(max,max)( i

Ni

M

mmk ikCakC


Exit Recursion Model (1)

• Conceptually based on flow line exit recursions

• Complete model

)1(),()( ~

~ ikik

i1)k(i),k(i

21iik(i)1

ikii B1)(WAC1),(WAFWDamaxC

No Contention at bottleneck Contention at bottleneck

)(),()( ~~~ 1 ikik

i1)k(i),k(i

21iik(i)1

ikii B1)(WAC1),(WAFWDSmaxC

1)k(i),k(iii ELS ~~

1iii V, amax L ~

~

1)k(i),k(iii DCV ~~


Exit Recursion Model (2)

(k)Φl

k

1

lFWD(k)Φ

FWD )(1

1

(k)Φl(k)Φl

l

k

1

1

lAW

A )(11 1

1

(k)Φl(k)Φl

l

klA

WA

2

2

22 1

1)(

)k(kΦl

kk lB)k(kΦ

B212

21

212

1

,

, )(,

)k(kΦl

kk lD)k(kΦ

D210

21

210

1

,

, )(,

)k(kΦl

kk lE)k(kΦ

E210

21

210

1

,

, )(,

• Parameter extraction

• Populations used as a function of available category of data


Model Properties

Completion times in the exit recursion model exactly match those in a deterministic flow line from which the parameters are derived with

(i) A single class of wafers and constant setup between wafers , or

(ii) Multiple wafer classes with no setup, proportional service and geometric decay within channels

Proposition: Exactness on completion times in the exit recursion model

(i) All completion times in the linear model exactly match those in a single process deterministic flow line from which the parameters are derived..

(ii) Throughput time can be exactly achieved on average in a flow line with different structure..

Proposition: Exactness of completion times in the linear model

(i) Completion times in the affine model exactly match those in a deterministic flow line in which each lot starts on an empty tool (via full flush constraint) from which the parameters are derived.

(ii) Throughput time can be exactly achieved on average in a flow line with different structure..

Proposition: Exactness of completion times in the affine model


Numerical Experiments


Numerical Experiments

• LWP(Longest waiting pair) robot policy[6]: gives optimal steady state throughput• Dead lock avoidance rule• Setup time ~ Uniform(210, 260); Reticle alignment ~ Uniform(240, 420)• 13,000 lots x 30 replications• Assume detail simulation is true operation.

A : Linear Model B : Affine Model - A(k1),B C : Affine Model - A(k1),B(k1)D : Affine Model - A(k1),B(k1,k2) E : FL Model F : EFL Model

G : ER Model - Tool Log H : ER Model - Wafer Log I : ER Model - Lot Log

[1]


Same Sample, Same Parameter• loading level : 0.95, train level : 3, lot size : {22, 23, 24} with probability {0.25, 0.5, 0.25}, both setups

De-tail

A B C D E F G H I-5%

0%

5%

10%

15%

20%

25%

30%

35%

40%

Cycle Time36.36% 36.35% 36.28% 36.26%

-0.09% -0.13%2.60% 3.52% 3.17%

De-tail

A B C D E F G H I

-60%

-50%

-40%

-30%

-20%

-10%

0%

10%

Lot Residency Time

--51.32% -51.33%

2.74% 0.61% -2.59% 2.56% 2.34%

De-tail

A B C D E F G H I

-10%-8%-6%-4%-2%0%2%4%6%8%

10%

Throughput Time

0.00% -0.00 -0.01% -0.02% 0.00% 0.03% -0.09%

-51.33% -51.33%

-0.00 -0.00

• Linear model & Affine models are only good in throughput time.

• ER models & Flow line models are good in all times.


Same Sample, Same Parameter• loading level : 0.3, train level : 3, lot size : {22, 23, 24} with probability {0.25, 0.5, 0.25}, both setups

De-tail

A B C D E F G H I

-10%-8%-6%-4%-2%0%2%4%6%8%

10%

Cycle Time

De-tail

A B C D E F G H I

-20%

-15%

-10%

-5%

0%

5%

10%

Lot Residency Time

De-tail

A B C D E F G H I

-10%-8%-6%-4%-2%0%2%4%6%8%

10%

Throughput Time

2.16% 2.15% 2.15% 2.15%

-0.30% -0.57%

2.27% 2.33%

-0.04%

-17.28% 0.20% -0.09% 0.81%

3.97%

1.71%

-0.00% -0.00% -0.00% -0.00% -0.13% -0.35% 0.03% 0.07% -1.82%

-17.28% -17.28% -17.28%

• Linear model & Affine models are good in cycle time, and throughput time.

• ER models & Flow line models are good in all times


Different Sample, Same Parameter• loading level : 0.95, train level : 3, lot size : {22, 23, 24} with probability {0.25, 0.5, 0.25}, both setups

De-tail

A B C D E F G H I-10%

0%

10%

20%

30%

40%

50%

60%

70%

Cycle Time

De-tail

A B C D E F G H I

-60%

-50%

-40%

-30%

-20%

-10%

0%

10%

Lot Residency Time

De-tail

A B C D E F G H I

-10%-8%-6%-4%-2%0%2%4%6%8%

10%

Throughput Time

58.35%

43.43% 46.19% 47.40%

4.97% -0.37% 1.24% 2.70% 2.04%

-51.40% -51.31%

2.75% 0.62% -2.58% 2.77% 2.46%

-0.12% 0.05% 0.05% 0.06% 0.03% 0.01% 0.01% 0.04% -0.00%

-51.31% -51.31%

• Linear model & Affine models are only good in throughput time.

• ER models & Flow line models are good in all times.


Different Sample, Same Parameter• loading level : 0.3, train level : 3, lot size : {22, 23, 24} with probability {0.25, 0.5, 0.25}, both setups

De-tail

A B C D E F G H I

-10%-8%-6%-4%-2%0%2%4%6%8%

10%

Cycle Time

De-tail

A B C D E F G H I

-20%

-15%

-10%

-5%

0%

5%

10%

Lot Residency Time

De-tail

A B C D E F G H I

-10%-8%-6%-4%-2%0%2%4%6%8%

10%

Throughput Time

2.57% 2.65% 2.52% 2.42%

-0.17% -0.35%

2.30% 2.28%

0.44%

-17.22%0.29% -0.03% 0.84%

3.98%

2.23%

0.09% 0.19% 0.17% 0.17% -0.16% -0.37% 0.05% 0.14% -1.46%

-17.14% -17.16% -17.16%

• Linear model & Affine models are good in cycle time, and throughput time.

• ER models & Flow line models are good in all times


Different Sample, Different Parameter• From loading level : 0.95 & train level : 3, To lading level : 0.8 & train level : 1 With lot size : {22, 23, 24} with probability {0.25, 0.5, 0.25}, both setups

De-tail

A B C D E F G H I

-10%

-5%

0%

5%

10%

15%

20%

25%

Cycle Time

De-tail

A B C D E F G H I

-50%

-40%

-30%

-20%

-10%

0%

10%

Lot Residency Time

De-tail

A B C D E F G H I

-10%

-5%

0%

5%

10%

Throughput Time

-5.09% -4.05% -5.90% -4.12% -0.04% 0.43%

19.29% 20.21% 17.67%

-37.96%

0.11% 0.08% 2.17% 6.36% 5.67%

-5.19% -5.09% -5.09% -4.97% -0.00% -0.11% 0.00%-0.04% -0.42%

-37.89% -37.89% -37.81%

• Linear model & Affine models are slightly good in cycle time, and throughput time .

• ER models are good in lot residency time, and throughput time.

• Only FL models are good in all times.


Different Sample, Different Parameter• From lot size: {22, 23, 24} with {0.25, 0.5, 0.25}, to lot size: {12, 13, 14} with {0.25, 0.5, 0.25} with loading level : 0.95, train level : 3, both setups

De-tail

A B C D E F G H I

-40%

-30%

-20%

-10%

0%

10%

20%

30%

Cycle Time

De-tail

A B C D E F G H I

-70%-60%-50%-40%-30%-20%-10%

0%10%20%

Lot Residency Time

De-tail

A B C D E F G H I

-18%-16%-14%-12%-10%-8%-6%-4%-2%0%2%

Throughput Time

-33.18% -14.54% -15.85% -15.21% 0.29% -0.64%

17.66% 16.71%

-0.43%

-59.70% -56.67% -56.68% -56.67% 1.26% 0.39%3.56% 7.43%

0.38%

-16.21%

-9.92% -9.92% -9.92%

-0.13% -0.16% -0.17% 0.02% -3.78%

• Linear model & Affine models are bad in all times.

• ER models are good in lot residency time, and throughput time.

• Only FL models are good in all times.


Computational Comparison

Relative Computation Time

Linear Model 0.5

Affine Model 1

ER Model 2.4

FL Model 120

Detailed Simulation 13,000


Accuracy Comparison

• Errors relative to detailed model• Error of 20%+• Error 5-20%• Error 0-5%

Same Sample, Same Parame-ter

Different Sample, Same Param-eter

Different Sample, Different Parame-ter

Linear Model CT LRT TT CT LRT TT CT LRT TT

Affine Models CT LRT TT CT LRT TT CT LRT TT

ER Models CT LRT TT CT LRT TT CT LRT TT

Flow Line Models CT LRT TT CT LRT TT CT LRT TT


Concluding Remarks


Concluding Remarks

• CPT: Expensive & typically fab bottleneck toolset

• Models for CPT throughput time, process time & cycle time• Classic models: Linear, affine• Recent models: Flow line, exit recursion• Compare: Computation and accuracy

• Next directions• Improved models: Newer exit recursions, additional

parameters• Implementation: Fab simulation, optimization, etc.


References1. HIS iSuppli April 20112. Elpida Memory, Inc., available at http://www.eplida.com, 3. Leachman, Robert C., Jeenyoung Kang, and Vincent Lin. "SLIM: Short cycle time and low inventory in manufactur-

ing at samsung electronics." Interfaces32.1 (2002): 61-774. http://www.forbes.com/forbes/2003/0811/076.html5. Roger H. French and V. Hoang, “Immersion Lithography: Photomask and Wafer-Level Materials,” Tran. Annual

Review of Materials Research, Vol. 39, 93-1266. Hyun Joong Yoon and Doo Yong Lee, “Deadlock-free scheduling of photolithography equipment in semiconduc-

tor fabrication,” IEEE Trans. Semi. Mfg., vol. 17, no. 1, pp. 42-54, 20047. Avi-Itzhak, B. "A sequence of service stations with arbitrary input and regular service times." Management Sci-

ence 11.5 (1965): 565-5718. Friedman, Henry D. "Reduction methods for tandem queuing systems." Operations Research 13.1 (1965): 121-

1319. Park, Kyungsu, and James R. Morrison. "Performance evaluation of deterministic flow lines: Redundant modules

and application to semiconductor manufacturing equipment." Automation Science and Engineering (CASE), 2010 IEEE Conference on. IEEE, 2010

10. Morrison, James R. "Deterministic flow lines with applications." Automation Science and Engineering, IEEE Transactions on 7.2 (2010): 228-239

11. Morrison, James R. "Multiclass flow line models of semiconductor manufacturing equipment for fab-level simula-tion." Automation Science and Engineering, IEEE Transactions on 8.1 (2011): 81-94

Longest waiting pair: [7] Geismar, H.N.; Sriskandarajah, C.; Ramanan, N., "Increasing throughput for robotic cells with parallel Machines and multiple robots," IEEE Trans. Auto. Sci. and Eng., vol.1, no.1, pp.84,89, Jul 2004

jungyeon park – xs3d lab seminar – september 11 2014 - 1 xs3d lab seminar cycle time and...

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lot residency time of

arrival time of lot

completion time of lot

sl throughput time of

wafer fab

cycle time contributor

expensive tool

complete tool log data