lecture 16 from SPC to APC

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Lecture 16: From SPC to APC

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1

Statistical Process Control

and

Computer Integrated Manufacturing

Run to Run Control

Real-Time SPC

Computer Integrated Manufacturing

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Auto-correlated Data

One important and widespread assumption in SPC is that the
samples take random values that are independently and
identically 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.

y

t

= µ + e

t

t = 1,2,... e

t

~ N (0,

σ

2

)

ρ

k

=

Σ (y

i

- y)(y

i+k

- y)

Σ(y

i

- 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.

y

t

= µ +

ϕ y

t-1

+ e

t

e

t

~ N (0,

σ

2

)

µ' = µ / (1-

ϕ), σ' = σ / 1-ϕ

2

e

t

= y

t

- y

t

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Example: LPCVD Temperature Readings

Temps are not IIND since future readings can be predicted!

100

80

60

40

20

0

601

602

603

604

605

606

607

608

Temp Readings from LPCVD Tube

Time

607

605

603

601

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..

100

80

60

40

20

0

601

602

603

604

605

606

607

608

Temp. Readings from LPCVD Tube

Time

100

80

60

40

20

0

-3

-2

-1

0

1

2

3

Temperature 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 process

Explain - relate observations to rules of behavior

Forecast - see into the future

Control - alter parameters of the model

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Two Basic Flavors of Time Series Models

Stationary data (i.e. time independent mean, variance and
autocorrelation structure) can be modelled as:

Autoregressive

Moving Average

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

z

t

=

ϕ

1

z

t-1

+ e

t

e

t

~ N (0,

σ

2

)

z

t

= y

t

-

μ

z

t

=

θ

1

e

t-1

+ e

t

e

t

~ N (0,

σ

2

)

z

t

= y

t

-

μ

y

t

=

μ + ϕ

1

z

t-1

+

ϕ

2

z

t-2

+...+

ϕ

p

z

t-p

+ e

t

-

θ

1

e

t-1

-

θ

2

e

t-2

-...-

θ

q

e

t-q

ϕ: autoregressive

θ: 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.

z

t

=

ϕ

1

z

t-1

+ e

t

e

t

~ N (0,

σ

2

)

z

t

= y

t

-

μ

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

35

40

45

50

55

60

sample

AR
Forecast

Error

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Higher order AR(p) and ACF, PACF representation

Higher order autoregressive models are common in
engineering. Their structure can be inferred from acf and
pacf plots.

Autocorrelation Function (acf):

ρ

k

=

Σ (y

i

- y)(y

i+k

- y)

Σ(y

i

- y)

2

= 0 k = 1,2,...

Partial Autocorrelation Function (pacf):

z

t

=

ϕ

1

z

t-1

z

t

=

ϕ

1

z

t-1

+

ϕ

2

z

t-2

z

t

=

ϕ

1

z

t-1

+

ϕ

2

z

t-2

+

ϕ

3

z

t-3

z

t

=

ϕ

1

z

t-1

+

ϕ

2

z

t-2

+

ϕ

3

z

t-3

+

ϕ

4

x

t-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.

z

t

=

θ

1

e

t-1

+ e

t

e

t

~ N (0,

σ

2

)

z

t

= y

t

-

μ

time

z

t

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.

y

t

=

μ + ϕ

1

z

t-1

+

ϕ

2

z

t-2

+...+

ϕ

p

z

t-p

+ e

t

-

θ

1

e

t-1

-

θ

2

e

t-2

-...-

θ

q

e

t-q

ϕ: autoregressive

θ: 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) Example

Data

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 T

2

statistics.

This analysis is done simultaneously in several levels:

• Real-Time Signals

• Wafer Averages

• Lot Averages

The multivariate T

2

chart provides a robust real-time

summary of machine “goodness”.

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The Equipment Controller

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

Fault

Diagnosis

CIM

database

Local

Database(s)

Equipment

Supervisor

Maintenance

Monitoring

Statistical

Process

Control

Modeling

and

Simulation

Recipe

Generation

Workcell

Coordinator

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The Workcell Controller

Most 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.

Equipment

Model

Step

Equipment

Model

Step

Adaptive

Control

Adaptive

Control

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 CUSUM
chart of the prediction residuals.

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

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The Idea of Statistically Based Feedback Control

x

o

y

o

original RSM

new RSM

y

n

x

f

y

f

1

2

4

5

3

1. Original Operation
2. Process Shifts
3. Shift is detected by MBSPC
4. RSM is adapted
5. New Recipe is generated

controlling input

response

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Feedback Control

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

Initial
Settings

Recipe
Update

Spin Coat
& Bake

Parameter
Estimator

Equipment
Model

Controller

t Test

M

Model
Update?

yes

No

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Feedback Control in Resist Application

Adaptive
Controller

Spin-Coat
& Bake

Thickness

Incoming

Outgoing

Equipment

& Refl ectance

Measurement

Wafer

Wafer

Input
Settings

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Feedback Control in Resist Application (cont.)

11800

12000

12200

12400

12600

0

10

20

30

40

50

60

Target

Model Prediction

Experimental Data

20

24

28

32

36

40

44

0

10

20

30

40

50

Wafer Number

60

Target

Model Prediction

Experimental Data

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Alarms in Resist Application Control

0

4

8

12

16

20

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

Alarm

Alarm

Wafer Number

Alarm

UCL

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Adapting the Regression Model

The regression model has many coefficients that may
need adaptation.

What can be adapted depends on what measurements
are available.

y

n

= a

o

x

2

+b’

n

x +c’’

n

y

o

= a

o

x

2

+b

o

x +c

o

y

n

= a

o

x

2

+b

o

x +c’

n

y

n

= a

n

x

2

+b

n

x +c’

n

1

2

3

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.

x

1

x

2

y

A

B

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 Control

Models can also be used to predict the outcome and
correct ahead of time if necessary.

Exposure

M

Develop

Recipe
Update

Model

Projected
CD Spread

In

Spec?

Standard
Setting

Yes

No

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28

Modified Charts for Feed Forward Control

LSL

UCL

LCL

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

30

Wafer No

Open Loop

FeedForward

Target = 88.75%

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Concurrent Control of Multiple Steps

Spin

Coat

&

Bake

Expose

Develop

T&R

Meas

R

Meas

CD

Meas

Adaptive

Control

Adaptive

Control

Adaptive

Control

Equip

.

Model

Equip.

Model

Equip.

Model

Inputs

Original

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Resist Thickness Example

0

5

10

15

20

11000

11500

12000

Target = 11906Å

Wafer Number

Closed Loop

Open Loop

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Resist Thickness Input

0

5

10

15

20

40

60

80

100

Wafer Number

Closed Loop

Open Loop

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Latent Image output

0

5

10

15

20

70

80

90

100

Wafer Number

Target = 87.75%

Malfunction Alarm

Control Alarm

Closed Loop

Open Loop

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Latent Image Input

0

5

10

15

20

0.60

0.70

0.80

0.90

1.00

Wafer Number

Closed Loop

Open Loop

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Developer Output

0

5

10

15

20

2.50

2.60

2.70

2.80

Wafer Number

Target = 2.66 um

Malfunction Alarm

Control Alarm

Closed Loop

Open Loop

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Developer Input

Wafer Number

0

5

10

15

20

Closed Loop

Open Loop

50

55

60

65

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Process Improvement Due to Run to Run Control

CD in

μm

CD in

μm

2.55

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

Constraint
Mapping

Step

Control

Model

Step

Control

Model

Constraint
Mapping

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

Step

A

B

C

Fixed spec
limits for B

New spec
limits for A

Out1

A

Out2

A

Out1

B

Out2

B

Mapping

Model

of B

PC

2

PC

1

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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

Target

Baseline

FF/FB only

Supervisory

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Results from Supervisory Control Application

Baseline

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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Drift

Noise

Equipment

Model

Advanced Process Control

APC Requires Integrated RtRPC and FDC

(from
Previous
tool)

Post-Process
Measurements
For Feed-
forward
Control

Run to Run

Controller

Real Time

Equipment

Controller

Process

Model

Equipment

State

Metrology

Process

State

Wafer

State

Automatic

Fault

Detection

Post-Process Measurements

In-Situ Sensors

(to
next
tool)

Updated

Recipe

Modified

Recipe

Unit Operation

Summarized
In-Situ
Measurements

Courtesy: Tom Sonderman / Advanced Micro Devices

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Supervisory Control

Dynamic Scheduling

Predictive Yield Modeling

Factory Wide Control

Demand Profile

Manufacturing Constraints

Transistor/Isolation Island of

Control

CD

M asking

RtR

FDC

Etch

RtR

FDC

CD

Deposition

RtR

FDC

Thk

Polish

RtR

FDC

Thk

E-Test

CD Target

CD Target

Thickness

Target

Thickness

Target

Transistor Island of Control

Supervisory Control

Dynamic Scheduling

BEOL Island of Control

Factory Wide Control (FWC)

w/Real-Time Optimization (RTO)

Courtesy: Tom Sonderman / Advanced Micro Devices

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SORT RO

MPSTATIC

0

1

2

3

4

5

6

7

8

9

10

950

975

1000

1025

1050

1075

1100

1125

1150

1175

1200

1225

1250

1275

1300

1325

1350

1375

1400

1425

1450

1475

1500

1525

1550

1575

1600

1625

1650

1675

1700

1725

1750

100MHz

3

rd

consecutive

year > 30% sort

RO improvement

on bulk
Industry average:

21%

Q1-02

Q2-02

Q3-02

Q4-02

Rapid Technology Change

34% Sort RO improvement in 2002

Courtesy: Tom Sonderman / Advanced Micro Devices

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Transistor Control

Effect 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 Control

Performance improvement over 6+ years

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Why Did AMD Implement APC?

¾ We saw the need to achieve precision processing beyond the tool capability

so as to achieve competitive product performance at the leading edge.

¾ We saw the potential to extend tool life.

¾ We believed that it would become a major enabler in AMD’s dynamic

manufacturing environment.

¾ We believed that it was a natural extension of our SPC capability.

¾ We saw it as a mechanism to reduce product costs while increasing the

revenue potential from each wafer

¾ We believed that the 130 nm and beyond technology nodes would demand

automated

control to achieve competitive yields!

¾ We understood the competitive leverage of

Precision Manufacturing

!

We were right!

Courtesy: Tom Sonderman / Advanced Micro Devices

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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

Courtesy: Kumud Srinivasan / Intel

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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

Courtesy: Kumud Srinivasan / Intel

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APC Applications

Completed APC Apps by Area (18)

Implant

1

Polish

2

Etch

2

TF/Diff

4

Litho

9

Completed APC Apps by

Technology (Cum)

0

5

10

15

20

P854

P856

P858

PX60

P1262

A

B

APC Proposed Apps (28)

Litho

10

TF/Diff

7

Polish

6

C4

3

Etch

2

Control Points

0

2

4

6

8

10

12

14

CD

Reg

Thickness

Control Points

# of

A

pps

Completed

Proposed

D

C

Courtesy: Kumud Srinivasan / Intel

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Emerging Factory Control Structure

Workstream

Recipe
Management

Alarm
Handler

Planning
and
Scheduling

Central SPC

Maintenance

"CIM-Bus"

SECSII
Server

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Automated Precision Manufacturing

Control Evolution

Phase 3: Predictability

Tool-Level Control

Supervisory Control

IM

WET/SORT

Met

Process

Met

Dynamic Adaptive Sampling

Electrical Parameter Control

Dynamic Targeting

Integrated

FDC/RtRPC

Courtesy: Tom Sonderman / Advanced Micro Devices

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Fab-Wide Control Technology

Factors Influencing Sampling

Incorporation of control related inputs allows for “smarter”

sampling based on factory performance.

Sampling Decisions

Control

Requirements

Control

Uncertainty

Process Tool

Events

Process

Monitoring

Metrology

Results

Control

Performance

Production

Priority

Metrology

Capacity

Courtesy: Tom Sonderman / Advanced Micro Devices

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Fab-Wide Control Technology

Dynamic 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

Courtesy: Tom Sonderman / Advanced Micro Devices

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The SPC Server

Accesses data base and draws simple X-R charts.

Disables machine upon alarm

Benefits from automated data collection

Performs arbitrary correlations across the process

Can to build causal models across the process

Monitors process capabilities of essential steps

Maintains 2000+ charts across a typical fab

Keeps track of alarm explanations given by operators
and engineers.

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Training for SPC

Operators: 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 topics

Random 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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19971999

2001 2003

2006

2009 2012

Function/milicent

0

5

10

15

20

Function/milice

Overall Production
Efficiency 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%

L

n

$

/

F

u

n

c

ti

o

n

25% - 30% / Yr.
Improvement

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The Opportunities

Year

1997 1999 2001 2003 2006

Feature nm

250

180

150

100

70

Yield %

85

~90

~92

~93

?

Equipment utilization %

35

~50

~60

~70

Test wafers %

5-15

5-15

5-15

5-15

OEE

30%

Down Un

15%

Down Pl

3%

No Prod

7%

No Oper

10%

Quality

2%

Test Wafers

8%

Setup

10%

Speed

15%

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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

Dose

n

= Dose

n-1

-

β (CD

n-1

- CD

target

)

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

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CD Improvement at Motorola

σ

Leff

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 technology
Isolate technology from equipment
Create a process with truly interchangeable parts

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Changing the “do not touch my process” attitude

A 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 Conclusion

SPC 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.


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