Statistical Process Control Implementation in Semiconductor Manufacturing

1
Statistical Process Control Implementation in
Semiconductor Manufacturing
Tzu-Cheng Lin ???Advanced Control Program/
IIPD/ RDTaiwan Semiconductor Manufacturing
Company, Ltd tclinr_at_tsmc.com,
edward.ece97g_at_nctu.edu.tw

March 26, 2010
2
Agenda
This presentation will cover the following topics

• 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.

Leadership in Analytics
3
Case(1) MVA application Advanced Bi-Variate
Semiconductor Process Control Chart.
4
Advanced Bi-Variate Semiconductor Process
Control Chart
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, ..

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 whats 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.
5
Advanced Bi-Variate Semiconductor Process Control
Chart
Innovative idea profile
Remarks
(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,
itll give a x symbol to represent the OOC
case.
(9) When the point is OOC,
itll also provide the Wafer_ID nearby it.
(10) The
green, yellow, and red light will point out
the degree of stability on this process.
6
Full-Line Bi-Variate Semiconductor Process
Control Chart
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.
Via this advanced process control chart, wed be
more easily to check the process status.

7
Case study
ALD NOLA Depth is a new process for new
generation. So, were 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.
Trial data looks like
ALDA102-PM4
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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
Identify the key steps and variables.
Variables
the key parameter in corresponding step.
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Step(2) T-Score Transformation
TOOL ALDA102/PM4
ChamberPressure PumpingPressure MFC1 GasLineHeater
1Temp StageHeaterInTemp StageHeaterOutTemp Source1
HeaterTemp Source2HeaterTemp ThrottleValveHeaterTe
mp PumpingLineHeaterTemp ChamberWallHeaterTemp Cha
mberBottomHeaterTemp SHInletHeaterTemp VATValveHea
terTemp Source1_Outlet_Pressure . .. ..
.
Based on each wafer, wed provide the one index-
FDC summary value, which could represents all
tool parameters healthy status.
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Step(3) Ellipse Control Region

• Ellipse Equations

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                         
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.
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Step(4) Simulation for NOLA Depth process
These four points are in warning control region.
(4)
(3)
The 1 to 3 sigma Ellipse control region.
(2)
These two points are OOC!!
(1)
Bi-Variate Semiconductor Process Control Chart
SPCFDC information.
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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.

13
Case(2) MVA application Yield2Equipment Events
Mining.
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Yield2Equipment Events Mining
Novel Idea
MVA T-Score
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 !!
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Invention Program Flowchart

• Key Step certain time period
• Variable critical recipe/ process parameters

Variable Key Step selection

• MVA Principal Component Analysis
• MVA T-Score calculation
• MSPC Hotelling T2 control limit set up 0, UCL
  

Data transformation to T-Score

• Yield T-score trend up/down monitoring
• Pearson Correlation Analysis
• Highlight the HIGH correlation PM Cycle to
• conduct Yield2Equipment Events Mining

Correlation analysis between Yield Tool Events
Root Cause Analysis

• Identify suspected ill-parameters

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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
Identify the key steps and variables.
Variables
the key parameter in corresponding step.
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Step(2) T-Score Transformation
TOOL ALDA102 / PM5
ChamberPressure PumpingPressure MFC1 GasLineHeater
1Temp StageHeaterInTemp StageHeaterOutTemp Source1
HeaterTemp Source2HeaterTemp ThrottleValveHeaterTe
mp PumpingLineHeaterTemp ChamberWallHeaterTemp Cha
mberBottomHeaterTemp SHInletHeaterTemp VATValveHea
terTemp Source1_Outlet_Pressure . .. ..
.
Huge data reduce to ONLY one index
T2 Score
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Step(3) Correlation Analysis
In this step, well conduct the Pearsons linear
correlation analysis to find out the most
important PM Cycle in this process and it will be
our Highlight issues.
Pearson linear correlation analysis equation

Correlation Analysis Table
It has high significant correlation !! And then
we can put more emphasized eyes on this PM Cycle!!
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Step(4) RCA-Root Causes Analysis
T1 Chart
Root Cause Analysis via Multi-Variate Analysis
PCA Index
Raw Data
Highlight the suspected issued parameter based on
MVA Index!!
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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.

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Case(3) PLS application Virtual Metrology of
Deep Trench Chain.
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Virtual metrology of deep trench chain
1.5 days

• DT Chain Process Flow

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.
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.
Innovative idea !!
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Methodology introduced-PLS modeling overview
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Methodology introduced-PLS modeling geometric
interpretation
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Simulation(1)-Predicted DT final CD via PLS/LSE
Tool D90 OXEC103-chamber A
RMSE Error Rate
PLSR 0.0017766 1.211
LSER 0.0023455 1.618

Formula
From the chart, it seems that we could get the
better DTME predicted CD via PLS modeling
technical.
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Simulation(2)-SPC for virtual metrology of DT
final CD
Tool T90 OXEC107-chamber A
It can correctly catch the process alarm message
!!
Summary
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.
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Conclusions

• 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.

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Appendix
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page.1
Partial least squares regression (PLSR)

• 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

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page.2
Basic concept
t Xw ? Cov(t) Cov(Xw) wTCov(X)w l1 u Yc
? Cov(u) Cov(Yc) cTCov(X)c l2
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!!
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page.3

• Nonlinear Iterative Partial Least Squares
  Algorithm (NIPALS)

T is score matrix The columns of T are the latent
vectors P is loading matrix
j0, E0Xnm , F0Ynp , ujany column of Y
matrix, t Xw, u Yc
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Case(4) Time series application KSI-Based to
Predict Tool Maintenance.
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KSI-Based to Predict Tool Maintenance
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?.
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
Idea of invention
Once this KSI is greater than a pre-scribed limit
(threshold).
PM
PM
Threshold
KSI
Call for engineers Call for tool maintenance !!
Time
KSI Key Sensitive Index.
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Invention Program Flowchart

• Key Step certain time period
• Variable critical recipe/ process parameters

Variable Key Step selection

• Correlation the quantity of variables
• Screen out key parameter key step
• Extract out the signal characteristics

Correlation analysis

• 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

Time series model
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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
Identify the key steps and variables.
Variables
the key parameter in corresponding step.
36
Step(2) Extract out KSV from tool signals
The KSV (Key Sensitive Process Variables), 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.
How to extract out the useful tool signal
information ??
1. Time Length 2. Mean 3. Stdev 4. Median 5.
Max 6. Min 7. Area 8. Quantile.
37
Step(3) Correlation analysis
In this step, well conduct the Pearsons linear
correlation analysis to find out the most
important KSV in this process and it will be our
Time Series Modeling variable.
Correlation Analysis Table
It has high significant correlation !! And then
we can use it to be modeling item.
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Step(4) Fitted the Time Series model to get KSI
Trend chart for Variable_3 - Stdev
Fitted Time Series Model
Model ARIMA(1,1,2)
How to fit this Time Series model ??
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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 (Key Sensitive Index) based
approach is proposed for process trend
monitoring.
Based-on KSI and Threshold limit we can predict
when to do Preventive Maintenance !!

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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 applicationAdvanced Queue-Time
to Yield Monitoring System.
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Survival Function Based-Advanced Q-Time2Yield
Morning System
Motivation
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.
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 lt 3hrs)

2. HSG Depo ? HSG Recess (Q-Time lt 10hrs)

3.
RC1a ? Poly1b (Q-Time lt 6hrs) ,and so on.
Nowadays, we usually set the Q time lt k hours
monitoring scheme to control these critical
processes.
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 whats 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.
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Survival Function Introduction
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?
Survival Function KPIs
1) Survival function
2) Lifetime distribution function
3) Hazard function
4) MTBF/ MTTF
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Invention Program Flowchart

• Key process selecting from engineers Know-How.
• Variable critical WAT/ Yield data.

Q-Time and Yield data collecting/mapping

• RMSE/ MME/ TMSE evaluated.
• Survival model validation.

Survival distributions selecting

• Likelihood function to fit parameters.
• Kaplan-Meier estimator.
• Reliability theory.

Model parameters fitting based on distribution

• Survival function.
• Lifetime distribution function.
• Hazard Function.
• MTTF/ MTBF.

Survival function KPIs calculating
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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
Identify the sensitivity process and variable.
WAT Variables
the highly correlation relationship.
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Step(2) Survival Distribution Selecting

• 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 ??
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Step(3) Model Parameters Fitting

• Fitted parameters to data

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)
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.
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Step(4) Survival Function KPIs Calculating
Simulation Result
We set the Q-Time controlled process belongs to
Exp(T12) distribution, and its Survival function
is also shown here.

• Survival KPIs

We set Xt10 to evaluate each KPI.
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.
1) Survival probability
0.4346
2) Lifetime distribution function
0.0362
3) Hazard function
0.0833
12
4) MTBF/ MTTF
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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.

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Case(6) SPC chart application Smart Process
Capability Trend Monitoring System.
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Smart Process Capability Trend Monitoring System
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.
Western Electric rule
Problem Currently, we only can find problems
when a tool violates Western Electric rules. We
cant provide the pre-alert system when tools
have potential problem. Although our Yield system
provide the Cpmk 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 Cpmk value of tool in our Yield
system. We not only provide the monitoring rules
and can find the trend down situation of tools.
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Method Introduction
Cusum Concept
Small trend down situation
CpmkValue
Mean
Cpmk limit
Period/date
Key ConceptThe 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.
Method equation

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

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Simulation

• Tool A
• FAB Cross Fab
• Date range 4/15-5/13
• Condition 4 periods
• Analysis resultThere is a trend down situation
  in periods 1-17 and periods 32-50.

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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.

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Thank You.
Questions Answers
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Published Papers