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1FLCC
Comprehensive CD Uniformity Control in Lithography and Etch Process
Qiaolin Zhanga, Cherry Tangb, Tony Hsiehb, Nick Maccraeb, Bhanwar Singhb,
Kameshwar Poollaa, Costas Spanosa
aDept of EECS, UC BerkeleybSDC, Advanced Micro Devices
March 3, 2005
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2FLCC
Motivation • Importance of across-wafer (AW) CD (gate-length) uniformity
– Impacts IC performance spread and yield
– Large AW CDV large die-to-die performance variation
low yield
• How to cope with increasing AW CD variation?– Employ design tricks, ex. adaptive body biasing
• Has limitations
– Reduce AW CD variation during manufacturing• The most effective approach
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3FLCC
Across-wafer CD Variation Sources
Spin/Coat
PEB
Develop
ExposureDeposition
Etch
Total across-wafer CD Variation
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4FLCC
CD Uniformity Control Approach• Current litho clusters strive for uniform PEB profile of multi-zone
bake plate and contemplate die-to-die exposure dose compensation to improve CDU.
• Our approach is to manipulate across-wafer PEB profiles to compensate for other systematic across-wafer poly CD variation sources
Exposure PEB Develop EtchSpin/Coat/PAB
CD Metrology
Optimizer
Optimal zone offsets
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5FLCC
Multi-zone PEB Bake plate
Schematic setup of multi-zone bake plate (approximate)
Each zone is given an individual steady state target temperature,
by adjusting an offset value2
4
3
6
5 71
Zone offset knobs
PEB BakePlate
O ),( yxT
),( yxCD
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6FLCC
Develop Inspection (DI) CDU Control Methodology
• The across-wafer DI CD is a function of zone offsets
• Seen as a constrained nonlinear programming problem
• Minimize
• Subject to: Up
iLow OOO
baselineresistDI CDSTCD
721
72111
...,
...
...,
...
OOOg
OOOg
T
T
T
mm
baselineTTT
721
72111
...,
...
...,
...
OOOf
OOOf
CD
CD
CD
nn
DI
ettDI
T
ettDI CDCDCDCD argarg
7...2,1i
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zone 1 zone 2 zone 3
zone 4 zone 5 zone 6
zone 7
Snapshot of Derived CD-to-Offset Model • Empirically derived CD-to-offset model based on
temperature-to-offset model and resist PEB sensitivity
-2
-1
0
1
2
3
4
5
6
7
8
nm/offset unit
Zone 1 Zone 2 Zone 3
Zone 4 Zone 5 Zone 6
Zone 7
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Simulation Results of DI CDU Control
Dense Line Semi-isolated Line Isolated Line
CDU Improvement 72% 61% 69%
Baseline DI CD
134
136
138
140
Optimal DI CD
134
136
138
140
Dense Line Semi-isolated Line Isolated Line
Baseline DI CD
134
136
138
140
142
Optimal DI CD
134
136
138
140
142
Baseline DI CD
Optimal DI CD
150
152
154
156
158
150
152
154
156
158
Experimentally extracted
baseline CDU
Simulated optimal CDU after applying DI CDU
control
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9FLCC
Final Inspection (FI) CDU Control Methodology
• Across-wafer FI CD is function of zone offsets
baselineresistDI CDSTCD
• Now we minimize:
ettFI
T
ettFI CDCDCDCD argarg
DIFIsp CDCDCD
_
)...,(
...
)...,(
721
7211
_
OOOg
OOOg
CDCDCD
n
spDIFI
• Plasma etching induced AW CD Variation (signature)
Upi
Low OOO • Subject to: 7...2,1i
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Plasma Etching Induced AW CD Variation
• PEB-based DI control can be tuned to anticipate the plasma induced non-uniformity and cancel it.
• Use 3 plasma non-uniformity examples to simulate the proposed FI CDU control approach.
Bowl shape signature
-5
-4
-3
-2
-1
Dome shape signature
-5
-4
-3
-2
-1
Bowl Dome Tilt
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FI CDU Control Simulation - Bowl Plasma Signature Dense Semi-isolated Isolated Baseline DI CD
134
136
138
140
Optimal DI CD
138
140
142
144
Optimal FI CD
134136138140
Baseline DI CD
Optimal DI CD
Optimal FI CD
134
136
138
140
142
138
140
142
144
146
134136138140142
Baseline DI CD
Optimal DI CD
Optimal FI CD
150
152
154
156
158
154
156
158160
162
150152154156158
Experimentally extracted
baseline CDU
Simulated corrected DI CD after applying FI
CDU control
Simulated optimal FI CD after
applying FI CDU control
Dense Semi-isolated Isolated
CDU Improvement 57% 37% 53%
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12FLCC
FI CDU Control Simulation - Dome Plasma Signature
Baseline DI CD
150
152
154
156
158
Optimal DI CD
154
156
158
160
Optimal FI CD
150152154156158
Baseline DI CD
134
136
138
140
Optimal DI CD
138
140
142
144
Optimal FI CD
134136138140
Baseline DI CD
Optimal DI CD
Optimal FI CD
134
136
138
140
142
138140142144
134136138140142
Dense Semi-isolated Isolated
Experimentally extracted
baseline CDU
Simulated corrected DI CD after applying FI
CDU control
Simulated optimal FI CD after
applying FI CDU control
Dense Semi-isolated Isolated
CDU Improvement 69% 56% 65%
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13FLCC
FI CDU Control Simulation - Tilted Plasma Signature
Baseline DI CD
150
152
154
156
158
Optimal DI CD
154
156
158
160
Optimal FI CD
150152154156158
Baseline DI CD
134
136
138
140
Optimal DI CD
138
140
142
144
Optimal FI CD
134136138140
Baseline DI CD
Optimal DI CD
Optimal FI CD
134
136
138
140
142
138
140
142
144
146
134136138140142
Dense Semi-isolated Isolated
Experimentally extracted
baseline CDU
Simulated corrected DI CD after applying FI
CDU control
Simulated optimal FI CD after
applying FI CDU control
Dense Semi-isolated Isolated
CDU Improvement 56% 34% 52%
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14FLCC
• Multi-objective optimization of CDU for multiple targets
• Minimize the weighted sum of deviation of each target
– Subject to:
– Optimal zone offsets:
– The relative magnitude of the weighting factor indicates the importance of meeting the corresponding CD target
)_(1
2
minarg
n
iiii
O
opt TCDCDWO
Simultaneous CDU Control for Multiple CD Targets
n
iiii TCDCDWJ
1
2
_
10 iW ni 1
11
i
n
i
W
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15FLCC
Simultaneous CDU Control for Multiple CD Targets• What is the best improvement possible for multiple targets?
• How can we automatically find the corresponding weighting factors and optimal zone offsets?
• Minimax optimization– Weighting factors of the jth iteration along the optimal searching
trajectory:
– Minimax to find optimal weighting factors and offsets
Tjnjj WWW ,,1 ...
)_(1
2
,minarg
n
iiiji
O
j TCDCDWO
))...(max(... ,,1,,1 minarg jnj
W
Toptnoptopt
j
WWW
)_(1
2
,minarg
n
iiiopti
O
opt TCDCDWO
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Simultaneous CDU Control for Multiple CD Targets
Dense Line Semi-iso Line Iso Line
Wd =0.36; Ws =0.33 ; Wi =0.31 64.9% 40.7% 66.4%
Wd = 0.90; Ws =0.05 ; Wi =0.05 71.8% 15.9% 61.8%
Wd = 0.05; Ws =0.90 ; Wi =0.05 48.2% 60.7% 54.1%
Wd = 0.05; Ws =0.05 ; Wi =0.90 64.1% 32.4% 68.6%
Dense Semi-isolated Isolated
Baseline DI CD
150
152
154
156
158
Optimal DI CD
150
152154
156
158
Baseline DI CD
134
136
138
140
Optimal DI CD
134136138140
Baseline DI CD
134
136
138
140
142
Optimal DI CD
134136138140142
Experimentally extracted
baseline CDU
Simulated optimal FI CD after applying
simultaneous CDU control
Simulation of simultaneous CDU control for dense, semi-iso and iso lines
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Summary and Conclusions• Extracted CDU signatures of dense, iso and semi-iso
• CD-to-offset model enables DI & FI CDU control – The derived CD-to-offset model is based on temperature-to-offset
model and resist PEB sensitivity– Offers better fidelity than the old CD-to-offset model purely based on
CD measurement – Simulation indicates promise of DI & FI CDU control
• Multi-objective & minimax optimization schemes enable simultaneous CDU control for multiple CD targets
• Work in SDC at AMD are under way to validate this approach experimentally
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18FLCC
Technology/Circuit Co-Design:Technology/Circuit Co-Design:Impact of Spatial CorrelationImpact of Spatial Correlation
Paul FriedbergPaul FriedbergDepartment of Electrical Engineering and Computer SciencesDepartment of Electrical Engineering and Computer Sciences
University of California, BerkeleyUniversity of California, Berkeley
Feb. 14, 2005Feb. 14, 2005
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19FLCC
Outline
• Motivation
• Spatial Correlation Extraction
• Impact of Spatial Correlation on Circuit Performance
• How does process control impact spatial correlation?
• Conclusions/Future Plans
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20FLCC
Gate length, Vth, tox
Motivation: reality
Circuit design Manufacturingdesign rules
performance power
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21FLCC
Motivation: simulation
performance power
Canonical circuit Manuf. statisticsμ, σ, ρ
primary focus: spatial correlation
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22FLCC
Spatial Correlation Analysis• Exhaustive ELM poly-CD measurements (280/field):
• Z-score each CD point, using wafer-wide distribution:
• For each spatial separation, calculate correlation among all within-field pairs:
nzz ikijjk /*
jjijij xxz /
(CD data courtesy of Jason Cain)
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23FLCC
Spatial Correlation Dependence• Within-field correlation vs. horizontal/vertical distance,
evaluated for entire wafer:
• Statistical assumptions are violated (distribution is not stationary): we will address this later
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24FLCC
Spatial Correlation Model• Fit rudimentary linear model to spatial correlation
curve extracted from empirical data:
XL, characteristic
“correlation length”
Ignore this part of the curve— restrict critical paths to some reasonable length
BCharacteristic “correlation
baseline”
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25FLCC
Monte Carlo Simulations• Use canonical circuit of FO2 NAND-chain w/ stages
separated by 100m local interconnect, ST 90nm model:
• Perform several hundred Monte Carlo simulations for various combinations of XL, B, and (gate length variation)
• Measure resulting circuit delays, extract normalized delay variation (3 )
Input
100m
OutputStage i
100 m
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26FLCC
Delay Variability vs. XL, B,
• Scaling gate length variation directly: most impactful• Reducing spatial correlation also reduces variability,
increasingly so as decreases
Normalized delay variability (3/) (%)
Scaling factor
B = 0.2
B = 0.0
B = 0.4
0% 20% 40% 60% 80% 100%
XL scaling
L scaling
25
20
15
10
5
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27FLCC
• CD variation can be thought of as nested systematic variations about a true mean:
Origin of Spatial Correlation Dependence
Across-field
CDij = + mask + fi + wj + εij
Across-wafer
Spatial components
True mean
Wafer
Field
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28FLCC
Origin of Spatial Correlation Dependence• Within-die variation:
Average Field
Scan
Slit
Scaled Mask ErrorsNon-mask related across-field systematic variation
- =
Polynomial model of across-field
systematic variation
Removing this component of variation will simulate WID
process control
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29FLCC
Origin of Spatial Correlation Dependence• Across-wafer variation extraction:
- -
=
Average Wafer Scaled Mask Errors Across-Field Systematic Variation
Across-Wafer Systematic Variation
Polynomial Model
Removing this component of variation will simulate AW
process control
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30FLCC
Artificial WID Process Control• By removing the within-field component of variation,
we get distinctly different correlation curves:
• Shape of curve changes; correlation decreases for horizontal, but increases for vertical
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31FLCC
Artificial AW Process Control• Removing the across-wafer component only:
• Shape stays roughly the same; correlation decreases across the board
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32FLCC
Artificial AW+WID Process Control• Removing both AW and WID components, get a
cumulative effect larger than the sum of the parts:
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33FLCC
Additional process control• One more round of control: die-to-die dose control
- =
Horizontal separation Vertical separation
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34FLCC
Conclusions• Correlation effects are significant: should definitely
be included in MC simulation frameworks• Spatial correlation virtually entirely accounted for by
systematic variation Complete process control can almost completely reconcile correlation
• As process control is implemented, σ and ρ are simultaneously reduced: a double-win
• The closer to complete control, the greater the impact of additional control on correlation– Last “little bit” of systematic variance in the distribution
causes substantial correlation