NCTS Industrial Statistics
Research Group Seminar
Electron Industrial Control Lab
Department of Electrical and
Control Engineering, NCTU
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Statistical Process Control
Implementation
in Semiconductor Manufacturing
Tzu

Cheng Lin
林資程
Advanced Control Program/ IIPD/ R&D
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
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2
of 56
1.
MVA application
:
Advanced Bi

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
:
Advanced Queue

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
Research Group Seminar
Electron Industrial Control Lab
Department of Electrical and
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Case(1):
MVA application
Advanced Bi

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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Advanced Bi

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
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Advanced Bi

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
Research Group Seminar
Electron Industrial Control Lab
Department of Electrical and
Control Engineering, NCTU
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Full

Line
Bi

Variate Semiconductor Process Control Chart
Via this advanced
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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Electron Industrial Control Lab
Department of Electrical and
Control Engineering, NCTU
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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 “
Advanced
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
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Department of Electrical and
Control Engineering, NCTU
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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
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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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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
Research Group Seminar
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Department of Electrical and
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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
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Department of Electrical and
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Conclusions
From the simulation testing, it seems that our innovative
proposal
Advanced Bi

Variate Semiconductor Process
Control Chart
can monitor the semiconductor
process
variation
successfully.
Advanced Bi

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
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Case(2):
MVA application
Yield2Equipment Events Mining.
NCTS Industrial Statistics
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Department of Electrical and
Control Engineering, NCTU
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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
Research Group Seminar
Electron Industrial Control Lab
Department of Electrical and
Control Engineering, NCTU
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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
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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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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
Control Engineering, NCTU
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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
Control Engineering, NCTU
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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
do RCA tasks
when the
T

Score
and
Yield
have HIGH correlation relationship.
NCTS Industrial Statistics
Research Group Seminar
Electron Industrial Control Lab
Department of Electrical and
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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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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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Methodology introduced

PLS modeling overview
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Department of Electrical and
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Methodology introduced

PLS modeling geometric interpretation
NCTS Industrial Statistics
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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
:
NCTS Industrial Statistics
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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
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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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Appendix
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Electron Industrial Control Lab
Department of Electrical and
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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
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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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Nonlinear Iterative Partial Least Squares Algorithm (NIPALS)
T is
score matrix
The columns of T are the
latent vectors
P is
loading matrix
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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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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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
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Electron Industrial Control Lab
Department of Electrical and
Control Engineering, NCTU
Page
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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.
NCTS Industrial Statistics
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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
Advanced Queue

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.
Nowadays, we usually set the
Q time <
k hours
monitoring scheme to control these critical
processes.
Survival Function Based

Advanced Q

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)
Lifetime distribution function:
3)
Hazard function:
Exponential Survival Function
If x
t
=2, then
Survival probability =0.2
How to read it ??
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.
•
Lifetime distribution function.
•
Hazard Function.
•
MTTF/ MTBF.
NCTS Industrial Statistics
Research Group Seminar
Electron Industrial Control Lab
Department of Electrical and
Control Engineering, NCTU
Page
45
of 56
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)
Lifetime distribution function:
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

Advanced Q

Time2Yield
Morning System
can estimate the Q

Time controlled
process decayed behavior successfully.
The
Survival Function Based

Advanced Q

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

time alert.
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

alert model
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.
Questions & Answers…
NCTS Industrial Statistics
Research Group Seminar
Electron Industrial Control Lab
Department of Electrical and
Control Engineering, NCTU
Page
56
of 56
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