lecture 16 from SPC to APC


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EE290H F05
Statistical Process Control
and
Computer Integrated Manufacturing
Run to Run Control
Real-Time SPC
Computer Integrated Manufacturing
Lecture 16: From SPC to APC
1
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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
yt = + et t = 1,2,... et ~ N (0, 2)
With automated readings and high sampling rates, each
reading statistically depends on its previous values. This
implies the presence of autocorrelation defined as:
 = Ł (yi -y)(yi+k -y) = 0 k = 1,2,...
k
(y
Ł -y)2
i
The IIND property must be restored before we apply any
traditional SPC procedures.
Lecture 16: From SPC to APC
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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:
yt = +  yt-1 + et et ~ N (0, 2)
' = / (1-), ' =  / 1-2
et = yt - yt
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.
Lecture 16: From SPC to APC
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Example: LPCVD Temperature Readings
Temp Readings from LPCVD Tube
LPCVD Temp Autocorrelation
Temp(t+1) = 758 - 0.253 Temp(t)
608
608
607
607
606
606
605
605
604
604
603
603
602
602
601
601
0 20 40 60 80 100
601 603 605 607
Time Temp (t)
Temps are not IIND since future readings can be predicted!
Lecture 16: From SPC to APC
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The Residuals of the Prediction can be Used for SPC..
Temp. Readings from LPCVD Tube
Temperature Residuals
608
3
607
2
606
1
605
0
604
-1
603
-2
602
601
-3
0 20 40 60 80 100
0 20 40 60 80 100
Time Time
Lecture 16: From SPC to APC
5
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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
Lecture 16: From SPC to APC
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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
zt = 1 zt-1 + et et ~ N (0, 2)
zt = yt - ź
Moving Average
zt = 1 et-1 + et et ~ N (0, 2)
zt = yt - ź
Mixture (i.e. Autoregressive + Moving Average) models.
yt = ź + 1zt-1 + 2zt-2 +...+ pzt-p
+ et - 1et-1 - 2et-2 -...- qet-q
: autoregressive
: moving average
Lecture 16: From SPC to APC
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First Order Autoregressive Model AR(1)
This model assumes that the next reading can be predicted
from the last reading according to a simple regression
equation.
zt = 1 zt-1 + et et ~ N (0, 2)
zt = yt - ź
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
AR
sample
Forecast
Error
Lecture 16: From SPC to APC
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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):
k
 = Ł (yi -y)(yi+k -y) = 0 k = 1,2,...
k
(y
Ł -y)2
i
Partial Autocorrelation Function (pacf):
zt = 1zt-1
k
zt = 1zt-1 + 2zt-2
zt = 1zt-1 + 2zt-2 + 3zt-3
zt = 1zt-1 + 2zt-2 + 3zt-3+ 4xt-4
...
Lecture 16: From SPC to APC
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First Order Moving Average Model MA(1)
This model assumes that the next reading can be predicted
from the last residual according to a simple regression
equation.
zt = 1 et-1 + et et ~ N (0, 2)
zt = yt - ź
zt
0
time
Lecture 16: From SPC to APC
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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:
yt = ź + 1zt-1 + 2zt-2 +...+ pzt-p
+ et - 1et-1 - 2et-2 -...- qet-q
: autoregressive
: moving average
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.
Lecture 16: From SPC to APC
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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.
Lecture 16: From SPC to APC
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Shewhart and CUSUM time series residuals
Lecture 16: From SPC to APC
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Fitted ARIMA(0,1,1) Example
Data
Residuals
ARIMA(0,1,1)
Lecture 16: From SPC to APC
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So, what is RTSPC?
RTSPC reads real-time signals from processing tools.
It automatically does ACF and PACF analysis to build and
save time series models.
During production, RTSPC  filters the real-time signals.
The filtered residuals are combined using T2 statistics.
This analysis is done simultaneously in several levels:
" Real-Time Signals
" Wafer Averages
" Lot Averages
The multivariate T2 chart provides a robust real-time
summary of machine  goodness .
Lecture 16: From SPC to APC
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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.
CIM
database
Maintenance
Workcell
Coordinator
Monitoring
Statistical
Process
Control
Equipment
Supervisor Fault
Diagnosis
Modeling
and
Simulation
Local
Recipe
Database(s)
Generation
Lecture 16: From SPC to APC
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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.
Adaptive Adaptive
Control
Control
Equipment Equipment
Model Model
test test test
Step Step
Lecture 16: From SPC to APC
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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.
Lecture 16: From SPC to APC
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The Idea of Statistically Based Feedback Control
1. Original Operation
2. Process Shifts
3. Shift is detected by MBSPC
response
4. RSM is adapted
5. New Recipe is generated
yn
2
4
3
5
new RSM
yf yo
1
original RSM
xo xf controlling input
Lecture 16: From SPC to APC
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Feedback Control
Model-based, adaptive Feedback Control has been
employed on several processes.
Initial
Parameter
Settings
Estimator
Equipment
yes
Model
Model
Recipe
Controller
t Test
Update?
Update
No
Spin Coat
M
& Bake
Lecture 16: From SPC to APC
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Feedback Control in Resist Application
Adaptive
Controller
Input
Settings
Incoming
Outgoing
Spin-Coat
Wafer Wafer
Thickness
& Bake
& Refl ectance
Equipment
Measurement
Lecture 16: From SPC to APC
21
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Feedback Control in Resist Application (cont.)
12600
Target
12400
Model Prediction
12200
Experimental Data
12000
11800
0 102030405060
Wafer Number
Model Prediction
44
40
Target
36
Experimental Data
32
28
24
0102030405060
20
Lecture 16: From SPC to APC
22
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Alarms in Resist Application Control
20
Alarm (a)
16
Alarm (b) Alarm (c)
12
8
UCL
4
0
010 2030405060
15
Alarm
Alarm
10
Alarm
UCL
5
0
0102030405060
Wafer Number
Lecture 16: From SPC to APC
23
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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.
3
2
1
yn = aox2+box +c n
4
yn = anx2+bnx +c n
yn = aox2+b nx +c  n
yo = aox2+box +co
Lecture 16: From SPC to APC
24
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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.
y
x2
C
A
B
x1
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.
Lecture 16: From SPC to APC
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Model Adaptation in Resist Application Control
2.00
-13500
1.95
-14000
1.90
-14500
1.85
-15000
0 1020304050 60
135
134
133
132
131
0 102030405060
Wafer Number
Lecture 16: From SPC to APC
26
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Feed-Forward Control
Models can also be used to predict the outcome and
correct ahead of time if necessary.
Projected
Model
CD Spread
No
In
Recipe
Spec?
Update
Yes
Standard
Setting
M
Exposure Develop
Lecture 16: From SPC to APC
27
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Modified Charts for Feed Forward Control
LCL UCL
LSL USL
/"n (prediction spread)
 (equipment spread)
No FF
Yield Loss False Alarm Probability
Lecture 16: From SPC to APC
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Feed Forward/Feedback Control Results (cont)
92
90
Target = 88.75%
88
86
84
82
Open Loop
80
FeedForward
78
0 5 10 15 20 25 30
Wafer No
Lecture 16: From SPC to APC
29
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Concurrent Control of Multiple Steps
Equip.
Equip.
Equip.
Model
Model
Model
Adaptive Adaptive Adaptive
Control
Control
Control
Original
Inputs
Spin
R
T&R
CD
Coat
Develop
Expose
&
Meas
Meas
Meas
Bake
Lecture 16: From SPC to APC
30
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Resist Thickness Example
12000
Target = 11906
11500
11000
0 5 10 15 20
Wafer Number
Closed Loop
Open Loop
Lecture 16: From SPC to APC
31
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Resist Thickness Input
100
80
Closed Loop
Open Loop
60
40
0 5 10 15 20
Wafer Number
Lecture 16: From SPC to APC
32
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Latent Image output
Closed Loop Control Alarm
100
Malfunction Alarm
Open Loop
90
Target = 87.75%
80
70
0 5 10 15 20
Wafer Number
Lecture 16: From SPC to APC
33
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Latent Image Input
Closed Loop
Open Loop
1.00
0.90
0.80
0.70
0.60
0 5 10 15 20
Wafer Number
Lecture 16: From SPC to APC
34
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Developer Output
Closed Loop Control Alarm
Malfunction Alarm
Open Loop
2.80
2.70
Target = 2.66 um
2.60
2.50
0 5 10 15 20
Wafer Number
Lecture 16: From SPC to APC
35
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Developer Input
Closed Loop
Open Loop
65
60
55
0 5 10 15 20
50
Wafer Number
Lecture 16: From SPC to APC
36
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Process Improvement Due to Run to Run Control
Target
Target
5 5
4 4
3 3
Dev. Malf.
2 2
1 1
2.85
2.85 2.55 2.65 2.75
2.75
2.55 2.65
CD in źm
CD in źm
Closed Loop Operation Open Loop Operation
Lecture 16: From SPC to APC
37
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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
control
equip
Lecture 16: From SPC to APC
38
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The Concept of Dynamic Specifications
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.
Model Model
Constraint
Constraint
Mapping
Mapping
Control Control
Step Step
Lecture 16: From SPC to APC
39
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Specs to step A must change if step B "ages"
Out2A Fixed spec
Out2B
New spec
limits for B
limits for A
Mapping
PC2
PC1
Model
of B
Out1A Out1B
Step Step Step
B
A C
Lecture 16: From SPC to APC
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Specs are outlined automatically - Stepper example
Thickness
(Develop time varies between 55 and 65 seconds)
Lecture 16: From SPC to APC
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An Example of Supervisory Control
Baseline
FF/FB only Supervisory
Tar
get
20 20
20
Tar Tar
get get
15 15
15
10
10
10
Outliers
Outliers
Outliers
5 5
5
0 0
0
0.8 1.0 1.2 1.5 1.7
0.9 1.1 1.31.4 1.6 1.81.9
0.8 1.0 1.21.3 1.5 1.7 1.9 0.8 1.0 1.21.3 1.5 1.7
0.9 1.1 1.4 1.6 1.8 0.9 1.1 1.4 1.6 1.81.9
CDź( CDź( CD(m)
m) m) ź
Lecture 16: From SPC to APC
42
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Results from Supervisory Control Application
Supervisory
FF/FB Only
Baseline
Th
PAC
LI
Lecture 16: From SPC to APC
43
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Control Results - CD
Supervisory
FF/FB Only
Baseline
Lecture 16: From SPC to APC
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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
Lecture 16: From SPC to APC
45
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Manufacturing Evolution&
Process/Equipment
Real-time equipment model Diagnostic Engine
Model and Controller
Lecture 16: From SPC to APC
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Advanced Process Control
APC Requires Integrated RtRPC and FDC
Post-Process Measurements
Automatic
Fault
Detection
Summarized
In-Situ Sensors
In-Situ
Measurements
(to
(from
Real Time
next
Previous
Run to Run
Equipment
tool)
tool)
Controller
Controller
Wafer
Process Metrology
Equipment
State
State
State
Post-Process Equipment
Process
Measurements Updated Model Modified
Model
Unit Operation
For Feed- Recipe Recipe
forward
Control
Drift
Noise
Courtesy: Tom Sonderman / Advanced Micro Devices
Lecture 16: From SPC to APC
47
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Factory Wide Control (FWC)
w/Real-Time Optimization (RTO)
Factory Wide Control
Demand Profile
Manufacturing Constraints
Supervisory Control
Predictive Yield Modeling Dynamic Scheduling
Transistor/Isolation Island of
BEOL Island of Control
Control
Transistor Island of Control
Dynamic Scheduling
Supervisory Control
Thickness Thickness
CD Target
CD Target
Target
Target
RtR
RtR
RtR RtR
FDC
FDC
FDC FDC
Thk
Thk
CD CD
E-Test
Deposition
Masking Etch Polish
Courtesy: Tom Sonderman / Advanced Micro Devices
Lecture 16: From SPC to APC
48
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Rapid Technology Change
34% Sort RO improvement in 2002
10
3rd consecutive
year > 30% sort
9
Q1-02 Q2-02 Q3-02 Q4-02
RO improvement
8
on bulk
Industry average:
7
21%
6
100MHz
5
4
3
2
1
0
950 1000 1050 1100 1150 1200 1250 1300 1350 1400 1450 1500 1550 1600 1650 1700 1750
975 1025 1075 1125 1175 1225 1275 1325 1375 1425 1475 1525 1575 1625 1675 1725
SORT RO
Courtesy: Tom Sonderman / Advanced Micro Devices
Lecture 16: From SPC to APC
49
MPSTATIC
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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 AMD-K6 drive current
distribution before Id,sat control distribution after Id,sat control
Initial side-by-side comparison: Leff APC used ever since in F25 and from start-up in F30
Lecture 16: From SPC to APC
50
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Lithography Overlay Control
Performance improvement over 6+ years
Lecture 16: From SPC to APC
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Why Did AMD Implement APC?
We saw the need to achieve precision processing beyond the tool capability
so as to achieve competitive product performance at the leading edge.
We saw the potential to extend tool life.
We believed that it would become a major enabler in AMD s dynamic
manufacturing environment.
We believed that it was a natural extension of our SPC capability.
We saw it as a mechanism to reduce product costs while increasing the
revenue potential from each wafer
We believed that the 130 nm and beyond technology nodes would demand
automated control to achieve competitive yields!
We understood the competitive leverage of Precision Manufacturing!
We were right!
Courtesy: Tom Sonderman / Advanced Micro Devices
Lecture 16: From SPC to APC
52
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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
Lecture 16: From SPC to APC
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Major Functional Groups
" R2R (Run to Run)
= APC
= APC
" FD (Fault Detection)
" FC (Fault Classification)
= EP
= EP
" FP (Fault Prediction)
" SPC (Statistical Process Control)
Courtesy: Kumud Srinivasan / Intel
Lecture 16: From SPC to APC
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Intel PCS Strategy
" PCS capability and applications have
been growing with technology
advancements
" Capable of:
 Rapid detection, classification &
prediction of problems to control process
& equipment and keep variability at
minimum
" PCS dev. strategy:
 Internal Development of the PCS FW
 External Engagement to develop the
PCS Interfaces
Courtesy: Kumud Srinivasan / Intel
Lecture 16: From SPC to APC
55
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APC Applications
Completed APC Apps by
Completed APC Apps by Area (18)
AB
Technology (Cum)
Implant
Polish
1
2
20
Etch
2
15
Litho
10
9
5
TF/Diff
0 4
P854 P856 P858 PX60 P1262
Control Points
APC Proposed Apps (28)
Completed Proposed
14
12 Etch
C4
10
2
3 Litho
8
6
10
4
2
Polish
0
CD Reg Thickness
6
Control Points
TF/Diff
DC
7
Courtesy: Kumud Srinivasan / Intel
Lecture 16: From SPC to APC
56
# of Apps
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Emerging Factory Control Structure
Planning
Alarm
and
Central SPC
Handler
Scheduling
"CIM-Bus"
Recipe
SECSII
Workstream
Maintenance
Management
Server
Lecture 16: From SPC to APC
57
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Automated Precision Manufacturing
Control Evolution
Phase 3: Predictability
Electrical Parameter Control
Supervisory Control
Dynamic Targeting
Tool-Level Control
Integrated
FDC/RtRPC
WET/SORT
Process
Met
IM
Met
Dynamic Adaptive Sampling
Courtesy: Tom Sonderman / Advanced Micro Devices
Lecture 16: From SPC to APC
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Fab-Wide Control Technology
Factors Influencing Sampling
Control Process Tool
Uncertainty Events
Control Process
Requirements Monitoring
Sampling Decisions
Control Production
Performance Priority
Metrology Metrology
Results Capacity
Incorporation of control related inputs allows for  smarter
sampling based on factory performance.
Courtesy: Tom Sonderman / Advanced Micro Devices
Lecture 16: From SPC to APC
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Fab-Wide Control Technology
Dynamic Production Control
FEOL MOL BEOL
Inline Inline Inline
Lot Lot
E-Test
Measurements Measurements Measurements
Priorities Priorities
Model
Updates
Factory Control Model
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
Courtesy: Tom Sonderman / Advanced Micro Devices
Lecture 16: From SPC to APC
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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.
Lecture 16: From SPC to APC
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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.
Lecture 16: From SPC to APC
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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.
Lecture 16: From SPC to APC
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The 2002 Roadmap
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The 2004 Roadmap Update
Lecture 16: From SPC to APC
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The main metric is  Efficiency
Function/milice
20
15
Overall Production
10
Efficiency up by
~20X (!)
5
from 1997 to 2012.
0
Function/milicent
19971999
2001
2003
2006
2009
2012
Lecture 16: From SPC to APC
66
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Where will the Extra Productivity Come from?
12%
Feature Size
9%
12-14%
12-14%
4%
3%
4%
Wafer Size
<2%
2%
Yield Improvement
<1%
7-10%
Other Productivity - Equipment, etc.
9-15%
25% - 30% / Yr.
Improvement
Time
(Jim Owens, Sematech)
Lecture 16: From SPC to APC
67
Ln $ / Function
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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
Speed
OEE
15%
30%
Setup
10%
Test Wafers
8%
Quality
Down Un
No Oper
2%
No Prod Down Pl
15%
10%
3%
7%
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Basic CD Economics
(D. Gerold et al, Sematech AEC/APC, Sept 97, Lake Tahoe, NV)
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Application of Run-to-Run Control at Motorola
Dosen = Dosen-1 -  (CDn-1 - CDtarget)
(D. Gerold et al, Sematech AEC/APC, Sept 97, Lake Tahoe, NV)
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CD Improvement at Motorola
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.
Lecture 16: From SPC to APC
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