statistical process control and computer integrated manufacturing

Lecture 16: From SPC to APC

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Statistical Process Controland

Computer Integrated Manufacturing

Run to Run ControlReal-Time SPC

Computer Integrated Manufacturing


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Auto-correlated DataOne important and widespread assumption in SPC is that the samples take random values that are independently andidentically distributed according to a normal distribution

With automated readings and high sampling rates, each reading statistically depends on its previous values. This implies the presence of autocorrelation defined as:

The IIND property must be restored before we apply any traditional SPC procedures.

yt = µ + et t = 1,2,... et ~ N (0, σ2)

ρk = Σ (yi - y)(yi+k - y)Σ (yi - y)2

= 0 k = 1,2,...


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Time Series Modeling

Various models have been used to describe and eliminate the autocorrelation from continuous data.A simple case exists when only one autocorrelation is present:

The IIND property can be restored if we use this model to "forecast" each new value and then use the forecasting error (an IIND random number) in the SPC procedure.

yt = µ + ϕ yt-1 + et et ~ N (0, σ2)µ' = µ / (1- ϕ), σ' = σ / 1-ϕ2

et = yt - yt


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Example: LPCVD Temperature Readings

Temps are not IIND since future readings can be predicted!

100806040200601

602

603

604

605

606

607

608

Temp Readings from LPCVD Tube

Time607605603601

601

602

603

604

605

606

607

608

LPCVD Temp Autocorrelation

Temp (t)

Temp(t+1) = 758 - 0.253 Temp(t)


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The Residuals of the Prediction can be Used for SPC..

100806040200601

602

603

604

605

606

607

608Temp. Readings from LPCVD Tube

Time100806040200

-3

-2

-1

0

1

2

3Temperature Residuals

Time


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Estimated Time Series

A "Time Series" is a collection of observations generated sequentially through time.Successive observations are (usually) dependent.

Our objectives are to:Describe - features of a time series processExplain - relate observations to rules of behaviorForecast - see into the futureControl - alter parameters of the model


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Two Basic Flavors of Time Series ModelsStationary data (i.e. time independent mean, variance and autocorrelation structure) can be modelled as:Autoregressive

Moving Average

Mixture (i.e. Autoregressive + Moving Average) models.

zt = ϕ1 zt-1 + et et ~ N (0, σ2)zt = yt - μ

zt = θ1 et-1 + et et ~ N (0, σ2)zt = yt - μ

yt = μ + ϕ1zt-1 + ϕ2zt-2 +...+ ϕpzt-p

+ et - θ1et-1 - θ2et-2 -...- θqet-q

ϕ: autoregressiveθ: moving average


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First Order Autoregressive Model AR(1)This model assumes that the next reading can be predicted from the last reading according to a simple regression equation.

zt = ϕ1 zt-1 + et et ~ N (0, σ2)zt = yt - μ

-0.6-0.5-0.4-0.3-0.2-0.10.00.10.20.30.40.50.6

35 40 45 50 55 60

sampleARForecastError


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Higher order AR(p) and ACF, PACF representationHigher order autoregressive models are common in engineering. Their structure can be inferred from acf and pacf plots.Autocorrelation Function (acf):

ρk = Σ (yi - y)(yi+k - y)Σ (yi - y)2

= 0 k = 1,2,...

Partial Autocorrelation Function (pacf):

zt = ϕ1zt-1zt = ϕ1zt-1 + ϕ2zt-2

zt = ϕ1zt-1 + ϕ2zt-2 + ϕ3zt-3zt = ϕ1zt-1 + ϕ2zt-2 + ϕ3zt-3+ ϕ4xt-4

...

k

k


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First Order Moving Average Model MA(1)This model assumes that the next reading can be predicted from the last residual according to a simple regression equation.

zt = θ1 et-1 + et et ~ N (0, σ2)zt = yt - μ

time

zt

0


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Mixed AR & MA Models: ARMA(p,q)

In general, each new value depends not only on past readings but on past residuals as well. The general form is:

This structure is called ARMA (autoregressive moving average). The particular model is an ARMA(p,q).If the data is differentiated to become stationary, we get an ARIMA (Autoregressive, Integrated Moving Average) model.Structures also exist that describe seasonal variations and multivariate processes.

yt = μ + ϕ1zt-1 + ϕ2zt-2 +...+ ϕpzt-p+ et - θ1et-1 - θ2et-2 -...- θqet-q

ϕ: autoregressiveθ: moving average


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Summary on Time Series Models

Time Series Models are used to describe the "autocorrelation structure" within each real-time signal.After the autocorrelation structure has been described, it can be removed by means of time series filtering.The models we use are known as Box-Jenkins linear models.The generation of these models involves some statistical judgment.


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Shewhart and CUSUM time series residuals


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Fitted ARIMA(0,1,1) ExampleData ARIMA(0,1,1) Residuals


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So, what is RTSPC?RTSPC reads real-time signals from processing tools.

It automatically does ACF and PACF analysis to build and save time series models.

During production, RTSPC ”filters” the real-time signals.

The filtered residuals are combined using T2 statistics.

This analysis is done simultaneously in several levels:

• Real-Time Signals

• Wafer Averages

• Lot Averages

The multivariate T2 chart provides a robust real-time summary of machine “goodness”.


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The Equipment ControllerToday, the operation of individual pieces of equipment can be streamlined with the help of external software applications. SPC is just one of them.

FaultDiagnosis

CIM database

Local Database(s)

Equipment Supervisor

Maintenance

Monitoring

StatisticalProcessControl

Modelingand

SimulationRecipe

Generation

WorkcellCoordinator


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The Workcell ControllerMost process steps are so interrelated that must be controlled together using feed forward and feedback loops.Crucial pieces of equipment must by controlled by SPC throughout this operation.

EquipmentModel

Step

EquipmentModel

Step

AdaptiveControl

AdaptiveControl

test test test


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Model Based Control

All actions are based on the comparison of response surface models to actual equipment behavior.

Malfunction alarms are detected using a multivariate extension of the regression chart on the prediction residuals of the model.

Control alarms are detected with a multivariate CUSUMchart of the prediction residuals.

Control limits are based on experimental errors as well as on the model prediction errors due to regression. Hard limitson equipment inputs are also used.


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The Idea of Statistically Based Feedback Control

xo

yo

original RSM

new RSM

yn

xf

yf 1

2 453

1. Original Operation2. Process Shifts3. Shift is detected by MBSPC4. RSM is adapted5. New Recipe is generated

controlling input

response


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Feedback ControlModel-based, adaptive Feedback Control has been employed on several processes.

InitialSettings

RecipeUpdate

Spin Coat& Bake

ParameterEstimator

EquipmentModel

Controller t Test

M

ModelUpdate?

yes

No


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Feedback Control in Resist Application

AdaptiveController

Spin-Coat& Bake

ThicknessIncoming Outgoing

Equipment& Refl ectanceMeasurement

Wafer Wafer

InputSettings


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Feedback Control in Resist Application (cont.)

11800

12000

12200

12400

12600

0 10 20 30 40 50 60

TargetModel Prediction

Experimental Data

20242832364044

0 10 20 30 40 50

Wafer Number

60

Target

Model Prediction

Experimental Data


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Alarms in Resist Application Control

048

121620

0 10 20 30 40 50 60

Alarm (a)

Alarm (b) Alarm (c)

UCL

0

5

10

15

0 10 20 30 40 50 60

AlarmAlarm

Wafer Number

Alarm

UCL


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Adapting the Regression ModelThe regression model has many coefficients that mayneed adaptation.

What can be adapted depends on what measurementsare available.

yn = aox2+b’nx +c’’nyo = aox2+box +co

yn = aox2+box +c’nyn = anx2+bnx +c’n

1

23

4


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Adapting the Regression Model (cont.)In multivariate situations it is often not clear which of the gain or higher order variables can be adapted in the original model.

x1

x2

y

AB

C

In these cases the model is “rotated” so that it has orthogonal coefficients, along the principal components of the available observations. These coefficients are updated one at a time.


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Model Adaptation in Resist Application Control

-15000

-14500

-14000

-13500

1.85

1.90

1.95

2.00

0 10 20 30 40 50 60

131

132

133

134

135

0 10 20 30 40 50 60

Wafer Number


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Feed-Forward ControlModels can also be used to predict the outcome and correct ahead of time if necessary.

Exposure M Develop

RecipeUpdate

Model ProjectedCD Spread

InSpec?

StandardSetting

Yes

No


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Modified Charts for Feed Forward Control

LSLUCLLCL

Yield Loss

USL

σ (equipment spread)

σ/√n (prediction spread)

No FF

False Alarm Probability


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Feed Forward/Feedback Control Results (cont)

78

80

82

84

86

88

90

92

0 5 10 15 20 25 30Wafer No

Open LoopFeedForward

Target = 88.75%


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Concurrent Control of Multiple Steps

SpinCoat

&Bake

Expose DevelopT&RMeas

R

Meas CDMeas

AdaptiveControl

AdaptiveControl

AdaptiveControl

Equip.

ModelEquip.Model

Equip.Model

InputsOriginal


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Resist Thickness Example

0 5 10 15 2011000

11500

12000Target = 11906Å

Wafer NumberClosed LoopOpen Loop


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Resist Thickness Input

0 5 10 15 2040

60

80

100

Wafer Number

Closed LoopOpen Loop


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Latent Image output

0 5 10 15 2070

80

90

100

Wafer Number

Target = 87.75%

Malfunction AlarmControl AlarmClosed Loop

Open Loop


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Latent Image Input

0 5 10 15 200.60

0.70

0.80

0.90

1.00

Wafer Number



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Developer Output

0 5 10 15 202.50

2.60

2.70

2.80

Wafer Number

Target = 2.66 um

Malfunction AlarmControl AlarmClosed Loop

Open Loop


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Developer Input

Wafer Number0 5 10 15 20


50

55

60

65


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Process Improvement Due to Run to Run Control

CD in μm CD in μm2.55 2.65

2

4

1

3

5

2.75 2.85 2.55 2.65

2

4

1

3

5

2.75 2.85

Closed Loop Operation Open Loop Operation

Target Target

Dev. Malf.


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Supervisory Control

The complete controller must be able to perform feedback and feed-forward control, along with automated diagnosis.

Feed-forward control must be performed in an optimum fashion over several pieces of the equipment that follow.

max Cpk

equip

control


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The Concept of Dynamic Specifications

ConstraintMapping

Step

Control

Model

Step

Control

Model

ConstraintMapping

Specs are enforced by a cost function which is defined in terms of the parameters passed between equipment.

A change is propagated upstream through the system by redefining specifications for all steps preceding the change.


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Specs to step A must change if step B "ages"

Step Step StepA B C

Fixed speclimits for BNew spec

limits for A

Out1A

Out2A

Out1B

Out2B

Mapping

Modelof B

PC2PC1


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Specs are outlined automatically - Stepper example

(Develop time varies between 55 and 65 seconds)Thickness


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An Example of Supervisory Control

0.80.91.01.11.21.31.41.51.61.71.81.9

CD (μm)0

5

10

15

20

Outliers

Target

0.80.91.01.11.21.31.41.51.61.71.81.9

CD (μm)0

5

10

15

20

Outliers

Target

0.80.91.01.11.21.31.41.51.61.71.81.9

CD(μm)0

5

10

15

20

Outliers

TargetBaseline FF/FB only Supervisory


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Results from Supervisory Control ApplicationBaseline FF/FB Only Supervisory

Th

PAC

LI


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Control Results - CD

Baseline FF/FB Only Supervisory


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Summary, so far• Real-time Statistical Process Control – Time

Series modeling.• Response surface models can be built based on

designed experiments and regression analysis.• Model-based Run-to-Run control is based on

control alarms and on malfunction alarms.• RSM models are being updated automatically as

equipment age.• Optimal, dynamic specifications can be used to

guide a complex process sequence.

• Next stop: a historical / industrial perspective


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Manufacturing Evolution…

Process/Equipment Model and Controller Real-time equipment model Diagnostic Engine


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DriftNoise

EquipmentModel

Advanced Process ControlAPC Requires Integrated RtRPC and FDC

(fromPrevioustool)

Post-ProcessMeasurementsFor Feed-forwardControl

Run to RunController

Real TimeEquipmentController

ProcessModel

EquipmentState

MetrologyProcessState

WaferState

AutomaticFault

Detection

Post-Process Measurements

In-Situ Sensors

(tonexttool)

UpdatedRecipe

ModifiedRecipe Unit Operation

SummarizedIn-Situ Measurements

Courtesy: Tom Sonderman / Advanced Micro Devices


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Supervisory Control Dynamic SchedulingPredictive Yield Modeling

Factory Wide ControlDemand Profile Manufacturing Constraints

Transistor/Isolation Island ofControl

CD

Masking

RtR

FDC

Etch

RtR

FDC CD

Deposition

RtR

FDC Thk

Polish

RtR

FDC Thk

E-Test

CD Target CD TargetThickness

TargetThickness

Target

Transistor Island of Control

Supervisory Control Dynamic Scheduling

BEOL Island of Control

Factory Wide Control (FWC)w/Real-Time Optimization (RTO)



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SORT RO

MP

STA

TIC

0

1

2

3

4

5

6

7

8

9

10

950975

10001025

10501075

11001125

11501175

12001225

12501275

13001325

13501375

14001425

14501475

15001525

15501575

16001625

16501675

17001725

1750

100MHz

3rd consecutive year > 30% sort RO improvement on bulk

Industry average: 21%

Q1-02 Q2-02 Q3-02 Q4-02

Rapid Technology Change34% Sort RO improvement in 2002



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Transistor ControlEffect on Microprocessor Speed Distributions

Initial Impact of APC on MPU Performance – 1998 – Narrower transistor drive current distribution allows AMD to push our process to the edge of the spec without fallout for high power or slow parts

AMD-K6® drive current distribution before Id,sat control

AMD-K6® drive current distribution after Id,sat control

Initial side-by-side comparison: Leff APC used ever since in F25 and from start-up in F30


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Lithography Overlay ControlPerformance improvement over 6+ years


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Why Did AMD Implement APC?

We saw the need to achieve precision processing beyond the tool capability so as to achieve competitive product performance at the leading edge.

We saw the potential to extend tool life.

We believed that it would become a major enabler in AMD’s dynamic manufacturing environment.

We believed that it was a natural extension of our SPC capability.

We saw it as a mechanism to reduce product costs while increasing the revenue potential from each wafer

We believed that the 130 nm and beyond technology nodes would demand automated control to achieve competitive yields!

We understood the competitive leverage of Precision Manufacturing!

We were right!



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Intel R+D and Transfer Strategy

• R+D for manufacturing

• Deliver PCS systems and infrastructure with the technology to manufacturing

• Copy Exactly! transfer to manufacturing

• Ramp and continuous improvement

Courtesy: Kumud Srinivasan / Intel


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Major Functional Groups

• R2R (Run to Run) • FD (Fault Detection)• FC (Fault Classification)• FP (Fault Prediction) • SPC (Statistical Process Control)

= EP= EP

= APC= APC



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Intel PCS Strategy

• PCS capability and applications have been growing with technology advancements

• Capable of: – Rapid detection, classification &

prediction of problems to control process & equipment and keep variability at minimum

• PCS dev. strategy: – Internal Development of the PCS FW– External Engagement to develop the

PCS Interfaces



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APC Applications

Completed APC Apps by Area (18)Implant

1Polish 2

Etch 2

TF/Diff4

Litho9

Completed APC Apps by Technology (Cum)

05

101520

P854 P856 P858 PX60 P1262

A B

APC Proposed Apps (28)

Litho10

TF/Diff7

Polish6

C43

Etch2

Control Points

02468

101214

CD Reg ThicknessControl Points

# of

App

s

Completed Proposed

D C



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Emerging Factory Control Structure

Workstream Recipe Management

Alarm Handler

Planningand SchedulingCentral SPC

Maintenance

"CIM-Bus"

SECSIIServer


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Automated Precision ManufacturingControl Evolution

Phase 3: Predictability

Tool-Level Control

Supervisory Control

IMWET/SORT

MetProcessMet

Dynamic Adaptive Sampling

Electrical Parameter ControlDynamic Targeting

IntegratedFDC/RtRPC



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Fab-Wide Control TechnologyFactors Influencing Sampling

Incorporation of control related inputs allows for “smarter”sampling based on factory performance.

Sampling Decisions

Control Requirements

Control Uncertainty

Process ToolEvents

ProcessMonitoring

MetrologyResults

ControlPerformance

ProductionPriority

MetrologyCapacity



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Fab-Wide Control TechnologyDynamic Production Control

Determine speed distribution for each lot based on in-line measurements and transistor model

Change priority of lot based on estimate of # of parts in speed bins and production outs requirements (based on user input of outs@speed / week)

Change equipment set for each lot based on equipment performance (defectivity, speed impact) and requirements for outs

Change starts based on current estimations of in-line yield@speed and requirements for outs

E-Test

FEOL MOL BEOL

Factory Control Model

Lot Priorities

Lot Priorities

Inline Measurements

Inline Measurements

Inline Measurements

Model Updates



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The SPC Server

Accesses data base and draws simple X-R charts.Disables machine upon alarmBenefits from automated data collectionPerforms arbitrary correlations across the processCan to build causal models across the processMonitors process capabilities of essential stepsMaintains 2000+ charts across a typical fabKeeps track of alarm explanations given by operators and engineers.


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Training for SPCOperators: understand and "own" basic charts.

Process Engineers: be able to decide what to monitor and what chart to use (grouping, etc.)

Equipment Engineers: be able to collect tool data. Understand how to control real-time tool data.

Manufacturing Manager: understand process capabilities. Monitor several charts collectively.

Fab Statistician: understand the technology and its limitations. Appreciate cost of measurements.


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Summary of SPC topicsRandom variables and distributions.Sampling and hypothesis testing.The assignable cause.Control chart and operating characteristic.p, c and u charts.XR, XS charts and pattern analysis.Process capability.Acceptance charts.Maximum likelihood estimation, CUSUM.Multivariate control.Evolutionary operation.Regression chart.Time series modeling.


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The 2002 Roadmap


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The 2004 Roadmap Update


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199719992001 2003 2006 2009 2012

Function/milicent0

5

10

15

20

Function/milice

Overall ProductionEfficiency up by ~20X (!) from 1997 to 2012.

The main metric is “Efficiency”


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Where will the Extra Productivity Come from?

(Jim Owens, Sematech)Time

Other Productivity - Equipment, etc.

Yield Improvement

Wafer Size

3%4%9%

12% Feature Size

12-14%

4%

7-10%2%

12-14%

<2%

<1%

9-15%Ln$

/ Fun

ctio

n

25% - 30% / Yr.Improvement


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The OpportunitiesYear 1997 1999 2001 2003 2006Feature nm 250 180 150 100 70Yield % 85 ~90 ~92 ~93 ?Equipment utilization % 35 ~50 ~60 ~70Test wafers % 5-15 5-15 5-15 5-15

OEE30%

Down Un15%Down Pl

3%No Prod7%

No Oper10%

Quality2%

Test Wafers8%

Setup10%

Speed15%


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Basic CD Economics

(D. Gerold et al, Sematech AEC/APC, Sept 97, Lake Tahoe, NV)


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Application of Run-to-Run Control at Motorola

Dosen = Dosen-1 - β (CDn-1 - CDtarget)(D. Gerold et al, Sematech AEC/APC, Sept 97, Lake Tahoe, NV)


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CD Improvement at Motorola

σLeff reduced by 60%(D. Gerold et al, Sematech AEC/APC, Sept 97, Lake Tahoe, NV)


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Why was this Improvement Important?

600k APC investment, recovered in two days...


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Less Tangible Opportunities

Reduce cost of second sourcing (facilitate technology transfer)

Dramatically increase flexibility (beat competition with more customized options)

Extend life span of older technologies

Cut time to market (by linking manufacturing to design)


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What is the current extend of “control” in our industry?

Widespread inspection and SPC

Systematic setup and calibration (DOE)

Widespread use of RSM / Taguchi techniques

Factory statistics is an established discipline


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Advances for the Semiconductor Industry

An old idea - ensure equipment integrity - automatically

A new idea - perform feedback control on the workpiece

Isolate performance from technologyIsolate technology from equipmentCreate a process with truly interchangeable parts


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Changing the “do not touch my process” attitudeA stable process is one that is locally characterized and locked. SPC is used to make sure it stays there.

An “agile” process is one that is characterized over a region of operation. Process data and control algorithms are used to obtain goals.

Can we reach the 2010 process goals with a “stable”process?


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In ConclusionSPC provides “open loop” control.

In-situ data can be used for tighter run-to-run and supervisory control.

Several technical (and some cultural) problems must be addressed before that happens:

• Need sensors that are simple, non-intrusive and robust.

• User interfaces suitable for the production floor.

Next step in the evolution of manufacturing: From hand crafted products, to hand crafted lines to lines with interchangeable parts.

statistical process control and computer integrated manufacturing

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