# Statistical Process Control Implementation in Semiconductor Manufacturing

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NCTS Industrial Statistics
Research Group Seminar

Electron Industrial Control Lab

Department of Electrical and

Control Engineering, NCTU

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1

of 56

Statistical Process Control
Implementation

in Semiconductor Manufacturing

Tzu
-
Cheng Lin

Taiwan Semiconductor Manufacturing Company, Ltd

tclinr@tsmc.com, edward.ece97g@nctu.edu.tw

March 26, 2010

NCTS Industrial Statistics
Research Group Seminar

Electron Industrial Control Lab

Department of Electrical and

Control Engineering, NCTU

Page
2

of 56

1.
MVA application
:

-
Variate Semiconductor Process Control Chart.

2.
MVA application
:

Yield2Equipment Events Mining.

3.
PLS application
:

Virtual Metrology of Deep Trench Chain.

4.
Time series application
:

KSI
-
Based to Predict Tool Maintenance.

5.

Survival application
:

-
Time to Yield Monitoring System.

6.

SPC chart application
:

Smart Process Capability Trend Monitoring System.

This presentation will cover the following topics:

Agenda:

NCTS Industrial Statistics
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Department of Electrical and

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3

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Case(1):
MVA application

-
Variate Semiconductor
Process Control Chart.

NCTS Industrial Statistics
Research Group Seminar

Electron Industrial Control Lab

Department of Electrical and

Control Engineering, NCTU

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4

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-
Variate Semiconductor

Process Control Chart

Process Variation = (
Process Metrology Value
) + (
Tool Healthy Quality
) + (
Metrology Tool Calibration
)

SPC monitoring system

FDC monitoring system

MSA calibration scheme

Motivation:

As you know,
In Line Process Control

is a great important task on semiconductor manufacturing.
We usually use the
SPC system

to monitor the process measurement data, and use the
FDC
system

to monitor the tool healthy index. Although engineers via theses two regular systems, they
could check the process is stable or not ?? BUT it is time consuming for engineers, ……..

FDC

SPC

Innovative idea !!

If we could build up the
Bi
-
Variate Process Control Chart

which based on the
relationships between
In
-
Line metrology data

and
FDC tool parameter monitoring
data
, and provide the
Ellipse Control Region

to real time tell engineers
what’s
current status for the latest process capability is stable or not??

In this way, it will give a big hand for engineers not only to monitor the
SPC chart

,
but also to monitor the
FDC chart

at the same time.

NCTS Industrial Statistics
Research Group Seminar

Electron Industrial Control Lab

Department of Electrical and

Control Engineering, NCTU

Page
5

of 56

-
Variate Semiconductor
Process Control Chart

Innovative idea profile:

(1)

The box is showing the process
information on this chart.
(2)
X
-
axis is the In
-
Line metrology value (X).
(3)

Y
-
axis is the FDC summary value (Y).
(4)

The light
-
gray area is the Ellipse Control
Region with 1 sigma.
(5)

The mid
-
gray area is the Ellipse Control
Region with 2 sigma.
(6)

The dark
-
gray area is the Ellipse Control
Region with 3 sigma.
(7)

The red point is contributed from (X,Y)
and draw it on this specific control chart.
(8)

When the point is out of 3 sigma area, it’ll
give a ‘x’ symbol to represent the OOC case.
(9)

When the point is OOC, it’ll also provide
the Wafer_ID nearby it.
(10)

The ‘green’, ‘yellow’, and ’red’ light will
point out the degree of stability on this
process.

In
-
Line Metrology Value (X)

FDC Summary Value (Y)

8

9

Process_A

(X,Y)

(1)

(2)

(3)

(6)

(5)

(4)

(7)

(9)

(8)

(10)

Remarks
:

NCTS Industrial Statistics
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Full
-
Line

Bi
-
Variate Semiconductor Process Control Chart

process control
chart, we’d be
more easily to
check the
process
status.

It can integrate semiconductor full
-
line process & tool information into one
system, and to be a kind of real time control tool for modern 12” iFab.

NCTS Industrial Statistics
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Department of Electrical and

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7

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Case study

Target

UCL

LCL

ALD NOLA Depth is a new process for new generation. So, we’re going to use this “
Bi
-
Variate Semiconductor Process Control Chart”

to monitor this critical process:

1) In
-
line metrology value: Depth (nm).

2) Equipment FDC parameters: Var1
-
Var25.

3) 34 raw data sets.

ALDA102
-
PM4

Trial data looks like…

NCTS Industrial Statistics
Research Group Seminar

Electron Industrial Control Lab

Department of Electrical and

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8

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Step(1):

Select Key Steps and Parameters

Due to for ALDA equipment has so many tool parameters, we need the
engineers/ vendors to provide the
key process steps

(some critical steps in
the recipe) and parameters where measurements have significant effect on
product quality.

Process step

Variables

the key parameter in corresponding step.

Identify the key steps
and variables.

NCTS Industrial Statistics
Research Group Seminar

Electron Industrial Control Lab

Department of Electrical and

Control Engineering, NCTU

Page
9

of 56

Step(2):

T
-
Score Transformation

TOOL:
ALDA102/PM4

ChamberPressure

PumpingPressure

MFC1

GasLineHeater1Temp

StageHeaterInTemp

StageHeaterOutTemp

Source1HeaterTemp

Source2HeaterTemp

ThrottleValveHeaterTemp

PumpingLineHeaterTemp

ChamberWallHeaterTemp

ChamberBottomHeaterTe
mp

SHInletHeaterTemp

VATValveHeaterTemp

Source1_Outlet_Pressure

……….

………

…..

..

.

*FDC Summary Value:

*Huge data reduce to only ONE index:

…..

Matrix [34X25]

Based on each wafer, we’d
provide the one index
-

FDC
summary value
, which could
represents all tool
parameters healthy status.

NCTS Industrial Statistics
Research Group Seminar

Electron Industrial Control Lab

Department of Electrical and

Control Engineering, NCTU

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10

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An ellipse centered at the point (
h
,
k
) and having its major axis parallel to the
x
-
axis may
be specified by the equation

This ellipse can be expressed parametrically as

where
t

may be restricted to the interval

Step(3):

Ellipse Control Region

So, we based on the historical raw data (w/ good wafers), to set up the Ellipse
control region, and use the
Confident
-
Interval concept

to calculate the 1 to 3 sigma
alarm region to be the SPC
-
like, Bi
-
Variate process control chart.

Ellipse Equations:

NCTS Industrial Statistics
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Department of Electrical and

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11

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Step(4):

Simulation for NOLA Depth process

These two points are OOC!!

These four points are in
warning control region.

Bi
-
Variate Semiconductor
Process Control Chart:

SPC+FDC information.

The 1 to 3 sigma
Ellipse control region.

(1)

(2)

(4)

(3)

NCTS Industrial Statistics
Research Group Seminar

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Department of Electrical and

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Conclusions

From the simulation testing, it seems that our innovative
proposal
-
Variate Semiconductor Process
Control Chart

can monitor the semiconductor
process
variation

successfully.

-
Variate Semiconductor Process Control Chart

approach not only can be used to monitor the
Process
Information (
SPC Chart)

, but also to monitor the
Tool
Information (
FDC Chart)

at the same time.

The degree of process capability

(like Traffic Lights) for
specific critical process also can be known via this novel
Bi
-
Variate process control chart. In this way, the
engineers could control process more easily and
efficiently.

NCTS Industrial Statistics
Research Group Seminar

Electron Industrial Control Lab

Department of Electrical and

Control Engineering, NCTU

Page
13

of 56

Case(2):
MVA application

Yield2Equipment Events Mining.

NCTS Industrial Statistics
Research Group Seminar

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Department of Electrical and

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14

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Yield2Equipment Events Mining

PM

PM

Tool
-
A

time/date

YB Yield

T
-
Score

Trend Down

Trend Up

MVA T
-
Score

Novel Idea:

T
-
Score

is an index to represent
all tool
parameters status
. If the T
-
Score is
larger than specific limit we can say that
this data point is
significant different
from the normal condition.

During this PM cycle,
the
Yield

and
T
-
Score

have high correlation

and T
-
Score is bigger
than
normal condition
.

In this way, we can induce that
this may
occur some critical issues in this specific
time period.

Another way to point
out the abnormal tool !!

NCTS Industrial Statistics
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Department of Electrical and

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15

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Variable & Key Step

selection

Data transformation

to T
-
Score

Key Step: certain time period

Variable: critical recipe/ process parameters

MVA Principal Component Analysis

MVA T
-
Score calculation

MSPC Hotelling T2 control limit set up [0, UCL]

Correlation analysis

between

Yield & Tool Events

Yield & T
-
score trend up/down monitoring

Pearson Correlation Analysis

Highlight the HIGH correlation PM Cycle to

conduct

Yield2Equipment Events Mining

Invention Program Flowchart

Root Cause Analysis

Identify suspected ill
-
parameters

NCTS Industrial Statistics
Research Group Seminar

Electron Industrial Control Lab

Department of Electrical and

Control Engineering, NCTU

Page
16

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Step(1):

Select Key Steps and Parameters

Due to for each equipment has so many tool parameters, we need the
engineers/ vendors to provide the
key process steps

(some critical steps in
the recipe) and parameters where measurements have significant effect on
product quality.

Process step

Variables

the key parameter in corresponding step.

Identify the key steps
and variables.

NCTS Industrial Statistics
Research Group Seminar

Electron Industrial Control Lab

Department of Electrical and

Control Engineering, NCTU

Page
17

of 56

Step(2):

T
-
Score Transformation

TOOL:
ALDA102 / PM5

ChamberPressure

PumpingPressure

MFC1

GasLineHeater1Temp

StageHeaterInTemp

StageHeaterOutTemp

Source1HeaterTemp

Source2HeaterTemp

ThrottleValveHeaterTemp

PumpingLineHeaterTemp

ChamberWallHeaterTemp

ChamberBottomHeaterTemp

SHInletHeaterTemp

VATValveHeaterTemp

Source1_Outlet_Pressure

……….

………

…..

..

.

*T2 Score

*Huge data reduce to
ONLY one index

NCTS Industrial Statistics
Research Group Seminar

Electron Industrial Control Lab

Department of Electrical and

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18

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Step(3):

Correlation Analysis

In this step, we’ll conduct the
Pearson’s linear correlation analysis

to find
out the most important
PM Cycle

in this process and it will be our Highlight
issues.

It has high significant correlation !!
And
then we can put more emphasized eyes
on this PM Cycle!!

Correlation Analysis Table

Pearson linear correlation analysis equation

PM

Tool
-
A

time/date

YB Yield

T
-
Score

NCTS Industrial Statistics
Research Group Seminar

Electron Industrial Control Lab

Department of Electrical and

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19

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Step(4):

RCA
-
R
oot
C
auses
A
nalysis

PCA Index

Raw Data

T1 Chart

Root Cause Analysis via
Multi
-
Variate Analysis

Highlight the suspected issued
parameter based on MVA Index!!

NCTS Industrial Statistics
Research Group Seminar

Electron Industrial Control Lab

Department of Electrical and

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Page
20

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Conclusions

From the simulation results, it seems that our
proposal
Yield2Equip Events Mining module

can
monitor PM Events

on
Yield effects

obviously.

The
Yield2Equip Events Mining

approach not only
can be used to
monitor

PM performance
, but also it
is useful to

when the
T
-
Score

and
Yield

have HIGH correlation relationship.

NCTS Industrial Statistics
Research Group Seminar

Electron Industrial Control Lab

Department of Electrical and

Control Engineering, NCTU

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21

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Case(3):
PLS application

Virtual Metrology of Deep Trench Chain.

NCTS Industrial Statistics
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Department of Electrical and

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22

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Virtual metrology of deep trench chain

DT Chain Process Flow:

If we could set up the virtual metrology model according to
DT Litho CD
,
DT PHMO CD
, and
DTMO
CD

to predict
DT final CD
. It will be more helpful to assist in on
-
line process control.

As you know, the deep trench control is more critical for process engineers.
Due to the process
time between
DTMO Etch

to
DT Etch

is about 1.5 days, during this time period no one can be
aware of the quality of DT final CD.

Innovative idea !!

DT

Litho

CD

DT

PHMO

CD

DT

MO

CD

DT

ETCH

CD

predicted

1.5 days

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Department of Electrical and

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23

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Methodology introduced
-

PLS modeling overview

NCTS Industrial Statistics
Research Group Seminar

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Department of Electrical and

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24

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Methodology introduced
-

PLS modeling geometric interpretation

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RMSE

Error Rate

PLSR

0.0017766

1.211%

LSER

0.0023455

1.618%

Tool: D90 OXEC103
-
chamber A

Simulation(1)
-

Predicted DT final CD via PLS/LSE

*From the chart, it seems that we could get the better DTME
predicted CD via
PLS modeling

technical.

Formula
:

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Tool: T90 OXEC107
-
chamber A

Simulation(2)
-

SPC for virtual metrology of DT final CD

It can correctly catch the
process alarm message !!

1) PLS model predicts the
virtual metrology values

by the pre
-
process metrology data.

2) At the same time,
SPC scheme

will monitor the prediction value of metrology parameter.

3) It will also give alarms to engineers when the prediction value is out of the specification.

→ So, via this virtual scheme, we could ensure that the process is within specification.

Summary:

NCTS Industrial Statistics
Research Group Seminar

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Department of Electrical and

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27

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Virtual Metrology of deep trench chain.

DT Chain Healthy Index set up.

Early alarm/detection system.

Process grouping for following process.

Improve throughputs for critical process.

Improve line stability.

Conclusions

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Department of Electrical and

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28

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Appendix

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Abstract:

When the number of X is large compared to the number of
observations, the multiple linear regression is no longer feasible ( because of
multicolinearity). In order to solve the problem, several approaches have been
developed. One is
principal component regression (PCR)

and the other is
Partial least squares regression (PLSR)

Goal:

To solve multicolinearity problem

To reduce data dimension

To predict Y from X and to describe their common structure

To get important X variables

Difference between PLSR and PCR:

PLSR finds components from
X that are also relevant for Y

Partial least squares regression (PLSR)

page.1

NCTS Industrial Statistics
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Department of Electrical and

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30

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t = Xw

Cov(t) = Cov(Xw) = w
T
Cov(X)w =

1

u = Yc

Cov(u) = Cov(Yc) = c
T
Cov(X)c =

2

To find two sets of weights
w

and
c

in order to create (respectively) a linear
combination of the columns of X and Y such that their covariance is maximum!!

page.2

Basic concept

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31

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Nonlinear Iterative Partial Least Squares Algorithm (NIPALS)

T is
score matrix

The columns of T are the
latent vectors

P is

j=0, E
0
=X
n
×
m
, F
0
=Y
n
×
p
, u
j
=any column of Y matrix, t = Xw, u = Yc

page.3

NCTS Industrial Statistics
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Case(4):
Time series application

KSI
-
Based to Predict Tool Maintenance.

NCTS Industrial Statistics
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Department of Electrical and

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33

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KSI
-
Based to Predict Tool Maintenance

Once this KSI is greater than a
pre
-
scribed limit (threshold).

Call for engineers &

Call for tool maintenance !!

KSI:
K
ey
S
ensitive
I
ndex.

PM

PM

Threshold

KSI

Time

Idea of invention:

However, we all know that
correct trend monitoring via tool signals

can be
used to determine approaching timing for preventive maintenance.

In this way,
our innovative idea can be described as following:

Due to the tool maintenance schedule is usually arranged by
date
,
wafer run
counts
,
RF hours
, and for the furnace process it will also consider the
equipment sidewall film thickness
, but all of them are not sensitive to catch tool
real status which need to conduct
PM

or not?.

NCTS Industrial Statistics
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Invention Program Flowchart

Variable & Key Step

selection

Correlation analysis

Key Step: certain time period

Variable: critical recipe/ process parameters

Correlation: the quantity of variables

Screen out key parameter & key step

Extract out the signal characteristics

Time series model

Time series models fit the trend of variables

Auto
-
correlation: the

q

of MA model

Partial Auto
-
correlation: the
p
of AR model

Defined Time Series
ARIMA
(p,d,q) model

KSI

would decide when to call tool maintenance

NCTS Industrial Statistics
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Department of Electrical and

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Step(1):

Select key steps and parameters

Due to for each equipment has so many tool parameters, we need the
engineers/ vendors to provide the key process steps (some critical steps in
the recipe) and parameters which measurements have significant effects on
product quality.

Process step

Variables

the key parameter in corresponding step.

Identify the key steps
and variables.

NCTS Industrial Statistics
Research Group Seminar

Electron Industrial Control Lab

Department of Electrical and

Control Engineering, NCTU

Page
36

of 56

The
KSV

(
K
ey
S
ensitive Process
V
ariables), may not be the measurements
itself in corresponding key step. However,
we can transform the original
tool signals into some statistic quantity
, such as slop, area, maxima and
minima…,etc., which can really represent the characteristics of tool status.

Step(2):

Extract out KSV from tool signals

How to extract out the useful tool
signal information ??

Tool signals

1. Time Length

2. Mean

3. Stdev

4. Median

5. Max

6. Min

7. Area

8. Quantile……………….

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Step(3):

Correlation analysis

In this step, we’ll conduct the
Pearson’s linear correlation analysis

to find
out the most important
KSV

in this process and it will be our
Time Series

Modeling variable.

It has high significant correlation !! And
then we can use it to be modeling item.

Correlation Analysis Table

Pearson linear correlation analysis equation

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Step(4):

Fitted the Time Series model to get KSI

Model: ARIMA(1,1,2)

Trend chart for Variable_3

Stdev

Fitted Time Series Model

How to fit this Time
Series model ??

According to the previous study, we can realize that

(Step_4)+(Variable_3)+(Stdev)

is the

KSV

in this process, and
correct trend monitoring

can be used to
determine appropriate timing for preventive maintenance.

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Step(5):

Compute KSI & Simulation

ARIMA(1,1,2) predicted model

Time Series Model can catch the
tool KSV decayed trend.

In this work, the
KSI

(
K
ey
S
ensitive
I
ndex)
based approach is proposed for process
trend monitoring.

Based
-
on

KSI

and
Threshold limit

we can predict when to do Preventive Maintenance !!

KSI
-
Based

PM

PM

PM

PM

KSI

KSI

KSI

Threshold

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Conclusions

From the simulation results, it seems that our proposal KSI can
catch the tool decayed trend, and when the KSI is greater than
users defined threshold, then we can suggest engineers to do
PM jobs.

The
KSI
-
Based to Predict Tool Maintenance

approach
not only

can be used for
Furnace
and
Etch

tools to assist engineers in
when to call for Preventive Maintenance,
but also

it is useful to
do process trend monitoring in
FDC

system.

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Case(5):
Survival application

-
Time to Yield
Monitoring System.

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As you know,
Q
-
Time Process Control

is a great important task on semiconductor manufacturing.
In Fabs, the following processes are also involved in Q
-
Time issues:

1. DT ME → Change FOUP (Q
-
Time < 3hrs)

2.
HSG Depo → HSG Recess (Q
-
Time < 10hrs)

3. RC1a → Poly1b (Q
-
Time < 6hrs) …,and so on.

Q time <

k hours

monitoring scheme to control these critical
processes.

Survival Function Based
-

-
Time2Yield Morning System

Motivation:

Process A

Process B

Process A
end time

(
t
1
)

Process B
start time

(
t
2
)

Q
-
Time = [t
2
-

t
1
]

Queue Time Definition:

Innovative idea !!

If we could build up the
Survival Function Model

which based on the relationships
between
Q
-
Time

and
Yield

decayed process, and provide the
probability of risks
-
degrees

to real time tell engineers what’s the current status for
yield detractor

and
how long could we wait for next process starting.

In this way, it will give a big hand for
not only

Q
-
Time process control,
but also

productivity scheduling and cycle time improvement
.

For chemical processes, they
usually
put the criteria for Q
-
Time
control to avoid excursions
. If the
Q
-
Time longer than the specific
specification, we can induce that
this may occur some critical
issues in this specific time period.

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Survival Function Introduction

Survival Function KPIs

1)
Survival function:

2)

3)
Hazard function:

Exponential Survival Function

If x
t
=2, then

Survival probability =0.2

4)
MTBF/ MTTF:

Survival analysis attempts to answer questions, such as:

1) What is the fraction of a population which will survive past a certain time?

2) What rate will they die or fail?

3) Can multiple causes of death or failure be taken into account?

4) How do particular circumstances or characteristics increase or decrease the

odds of survival?

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Q
-
Time and Yield data

collecting/mapping

Model parameters

fitting

based on distribution

Key process selecting from engineers Know
-
How.

Variable: critical WAT/ Yield data.

Likelihood function to fit parameters.

Kaplan
-
Meier estimator.

Reliability theory.

Survival distributions

selecting

RMSE/ MME/ TMSE evaluated.

Survival model validation.

Invention Program Flowchart

Survival function

KPIs calculating

Survival function.

Hazard Function.

MTTF/ MTBF.

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Step(1):

Q
-
Time and Response Data Mapping

From engineers Know
-
How, we could collect the specific
Q
-
Time control
processes
, and related
WAT

(electrical testing data)/
Yield

data.

And then, we are going to conduct the
Rank Correlation Analysis

to find out
the variables which are higher correlation between process and WAT
parameters.

Q
-
Time control process

WAT Variables

the highly correlation relationship.

Identify the sensitivity
process and variable.

NCTS Industrial Statistics
Research Group Seminar

Electron Industrial Control Lab

Department of Electrical and

Control Engineering, NCTU

Page
46

of 56

Step(2):

Survival Distribution Selecting

Weibul
distribution

Lognormal
distribution

Exponential
distribution

Normal
distribution

Model identification:

For the Survival function distribution
identification, we usually choose 4
popular distributions:
1) Weibul distribution
2) Lognormal distribution
3) Exponential distribution
4) Normal distribution

to be the initial testing model,and
based on the
“Anderson
-
Darling
value”,

we could select the best
fitted distribution as the Survival
function.

Probability Plots for 4 Survival distributions

Which one is better ??

NCTS Industrial Statistics
Research Group Seminar

Electron Industrial Control Lab

Department of Electrical and

Control Engineering, NCTU

Page
47

of 56

After identified the
process decayed distribution
, we need to estimate the model
parameters. Currently, there are two popular methods to figure out the model
parameter estimations:

1) Kaplan
-
Meier estimator:

2) Maximum Likelihood estimation(MLE):

Step(3):

Model Parameters Fitting

Fitted parameters to data:

From below CDF charts, it ‘s obviously to see
that
K
-
M estimator

could estimate the survival
function from
life
-
time data

as good as
original
distribution
.

NCTS Industrial Statistics
Research Group Seminar

Electron Industrial Control Lab

Department of Electrical and

Control Engineering, NCTU

Page
48

of 56

Step(4):

Survival Function KPIs Calculating

Survival KPIs:

1)
Survival probability:

2)

3)
Hazard function:

4)
MTBF/ MTTF:

We set
X
t
=10

to evaluate each KPI.

0.4346

0.0362

0.0833

12

X
t

Simulation Result:

We set the Q
-
Time controlled
process belongs to
Exp(Θ=12)

distribution, and its Survival
function is also shown here.

So, if the Lot queuing time in critical process
is
10 hours
, its Survival probability is
0.4346.

At the same time, RTD could reference this
Survival probability to dispatch FOUPs.

NCTS Industrial Statistics
Research Group Seminar

Electron Industrial Control Lab

Department of Electrical and

Control Engineering, NCTU

Page
49

of 56

Conclusions

From the simulation results, it seems that our innovative
proposal
Survival Function Based
-
-
Time2Yield
Morning System

can estimate the Q
-
Time controlled
process decayed behavior successfully.

The
Survival Function Based
-
-
Time2Yield
Morning System

approach not only can be used to monitor
queuing time between
process ended

to
next process
starting
, but also give the Survival probability function for
risks
-
degrees if wafer waited for a long time.

The Cycle Time and Productivity Scheduling efficiency will
also be improved, if Fab RTD System could reference this
Survival probability value to work logistic dispatch.

NCTS Industrial Statistics
Research Group Seminar

Electron Industrial Control Lab

Department of Electrical and

Control Engineering, NCTU

Page
50

of 56

Case(6):
SPC chart application

Smart Process Capability

Trend Monitoring System.

NCTS Industrial Statistics
Research Group Seminar

Electron Industrial Control Lab

Department of Electrical and

Control Engineering, NCTU

Page
51

of 56

Smart Process Capability

Trend Monitoring System

Problem:

Currently, we only can find problems when a tool violates Western Electric rules.
We can’t provide the pre
-
alert system when tools have potential problem
. Although our Yield system provide the C
pmk

index to
monitor the tool health, but there are no monitoring rules like SPC in it.

How:

Here we will use the
CUSUM (Cumulative sum control chart)

method to transform the C
pmk
value of tool in
our Yield system.
We not only provide the monitoring rules and
can find the trend down situation of tools.

At present, we use the SPC (Statistical Process Control) to monitor process capability and so on. The SPC
charts use
Western Electric rule

to monitor tools real
-

USL

LSL

CL

UCL

LCL

One point out of control limit (3 Sigma)

Hold

Western Electric rule

Hold

USL

LSL

CL

UCL

LCL

7 points increasing or decreasing

NCTS Industrial Statistics
Research Group Seminar

Electron Industrial Control Lab

Department of Electrical and

Control Engineering, NCTU

Page
52

of 56

Method Introduction

Cusum

Cumula瑩ve sum con瑲ol chart

It is out of control situation, that the upper sum
higher than H (decision interval) or the lower
sum lower than H. Normally

Cusum Concept:

Key Concept:

The
Cusum
method will calculate the
upper cusum value

and
lower cusum value

which base on last
cusum value. So we just need to monitor the cusum value of each period that there is trend down
situation in condition periods.

C
pmk

limit

Mean

Period/date

C
pmk

Value

Small trend down situation

Method equation:

NCTS Industrial Statistics
Research Group Seminar

Electron Industrial Control Lab

Department of Electrical and

Control Engineering, NCTU

Page
53

of 56

Simulation

Tool A

FAB: Cross Fab

Date range: 4/15
-
5/13

Condition 4 periods

Analysis result:

There is a trend down
situation in
periods 1
-
17

and
periods 32
-
50
.

NCTS Industrial Statistics
Research Group Seminar

Electron Industrial Control Lab

Department of Electrical and

Control Engineering, NCTU

Page
54

of 56

Conclusions

Provided a
new monitor index (CUSUM) for tools’
health

and
pre
-

when tools have potential
problems that engineers can
handle tools’ health
conveniently
&
prevent tools from occurring
significant problems
.

NCTS Industrial Statistics
Research Group Seminar

Electron Industrial Control Lab

Department of Electrical and

Control Engineering, NCTU

Page
55

of 56

Thank You.

NCTS Industrial Statistics
Research Group Seminar

Electron Industrial Control Lab

Department of Electrical and

Control Engineering, NCTU

Page
56

of 56

Published Papers