Download Shot Noise, LER and Quantum Efficiency of EUV

Shot Noise, LER and Quantum Efficiency
of EUV Photoresists
Robert L. Brainard,a Peter Trefonas,a Jeroen H. Lammers,b Charlotte A. Cutler,a
Joseph F. Mackevich,a Alexander Trefonas and Stewart A. Robertsona
•
Introduction
•
EUV and DUV Base Titration Experiments
•
Poisson Statistics of LER vs. Esize
•
LER Simulation Model
•
Quantum Efficiency
•
New Resist Systems
•
Conclusions
Partial Support by
DARPA and EUV-LLC
a. Rohm and Haas Microelectronics
b. Philips Research
Brainard EUV 2004
1
I. Introduction
The 45 nm Node will require EUV Resists with Low LER and Esize:
LER = 2 nm
Esize = 2-15 mJ/cm2
Number of Photons / mJ
140
Shot Noise Limit1 =
x 10
13
120
100
Limit imposed by
80
statistical probability of
60
underexposing a pixel
40
20
0
DUV
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193 nm
EUV
(1) Neureuther & Wilson J. Vac. Sci. Tech. 1988.
2
Shot Noise Limits
In 1998, John Hutchinson2 compared Shot Noise Limits of 193 nm
and EUV resists using a theoretical model of LER.
193 nm
Shot Noise Limit (10 mJ/cm2): 1 nm
(1 mJ/cm2):
5 nm
13 nm (EUV)
8 nm LER
25 nm LER
Without considering secondary electrons or acid diffusion effects.
More recently,3 several excellent papers considered role of shot noise
in limiting the ability to print contact hole arrays.
(2) Hutchinson, SPIE 1998
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(3) O'Brien SPIE 2001, Cobb SPIE 2003, Lee SPIE 2003
3
Shot Noise Limits
In 2002, Dentinger et. al.4 compared the LER of 25 resist formulations
using DUV and EUV exposures. Ratio of LEREUV vs. LERDUV showed no
statistically significant increase in EUV LER as photospeed is increased.
EUV LER / DUV LER
Ratio of EUV LER/DUV LER vs. Esize
Dentinger et. al.
Authors' Reasoning:
Since DUV has 12X more
absorbed photons than EUV and
the LER ratios do not change with
Dose:
1.4
1.2
1
0.8
0.6
0.4
0.2
0
0
5
10
15
EUV E
size
20
25
2
(mJ/cm )
30
35
Shot noise does not effect LER
down to 3 mJ/cm2
Absorbed Photons = Esize x Abs x Photons/mJ
Brainard EUV 2004
(4) P. M. Dentinger, et. al. SPIE 1998
4
Materials
Experimental Resists based on EUV-2D
R2
O
O
R3
OH
Inhibiting
Onium PAG
Base Titration Study of EUV-2D
30
ArnE+ X-
Non-Nucleophilic Base
[Base]/[PAG] = 0 to 75%
3-Sigma LER (nm)
R1
Polymer
100 nm LER
150-200 nm LER
DUV 300-500 LER
25
20
DUV
Exposure
15
Increasing Base
10
5
EUV
Exposure
0
0
O
20
40
60
80
100
2
Esize (mJ/cm )
Ethyl Lactate
Solvent
O
100 nm Dense for EUV and 200 nm Dense for DUV
OH
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II. Base Titration
Allowed Us to Study:
Relationship between LER and Esize for Both EUV and DUV
Statistical Analysis of LER vs. Esize
Poisson Statistics
Acid - Base Simulation Program
Written for this Paper
Quantum Efficiency
C-Parameter
(Szmanda Method)
OD
(2004 SPIE Paper)
3-Sigma LER (nm)
30
EUV Exposure 100 nm Lines
EUV Exposure 150-200 nm Lines
DUV Exposure 300-500 nm Lines
25
20
EUV-2D
15
10
5
0
0
20
40
60
80
100
2
Esize (mJ/cm )
100 nm Dense for EUV and 200 nm Dense for DUV
Other Resist Systems
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III. Poisson Statistics of
LER vs. Esize
σN =
Poisson Statistics Apply to Absorption of Incident Photons:
N
N = number of absorbed photons per volume element ∝ dose.
Side wall roughness ∝ relative variation
Base titration curves show the
statistics of shot noise.
Why do both EUV and DUV
show the same linear behavior?
30
3-Sigma LER (nm)
σN
1
1
=
∝
LER ∝
N
N
dose
25
20
2
DUV r = 0.94
15
10
2
EUV r = 0.97
5
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1/2
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1/(Esize)
7
IV. LER Simulation Model
(6 0
00 n
gr m
id
un
its
)
15
Exposed
sk
Ma
EUV
Light
Unexposed
Output of Model
Schematic of Model
12.5 nm
(50 grid units)
100 nm
(400 grid units)
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Simulation Steps
Aerial Image
Unexposed
Exposed
10 mJ/cm2 exposure
1 Photon =
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Simulation Steps
Acid & Base Positions
10 mJ/cm2 exposure
Unexposed
Exposed
2.5Å film slice
1 Acid
=
1 Base
=
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10
Simulation Steps
Acid Latent Image
After Base Quench
Unexposed
Exposed
10 mJ/cm2 exposure
2.5Å film slice
1 Acid
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=
11
Simulation Steps
Deblocked Latent Image,
After acid diffusion
1.5 mJ/cm2 exposure
Unexposed
Exposed
2.5Å film slice
Rdiffusion = 32Å
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Simulation Steps
Deblocking Density by
Overlapping Spheres
Unexposed
Exposed
1.5 mJ/cm2 exposure
2.5Å film slice
Rdiffusion = 32Å
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Simulation Results
8
5.4 nm
2.9 nm
27 mJ/cm2
LER: 9.3 nm
exposed
3
unexposed
Dose: 1.5
1.6 nm
Increasing Base
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Simulated LER Results
Excellent Fit of (Dose)-1/2
Simulation LER (nm)
10
8
Simulated Results in
2
r = 0.95
Agreement with
Experimental Work
6
4
Number and Distribution
of Acids Define LER vs.
2
(Dose)-1/2 Behavior
0
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
(Dose)-1/2
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V. Quantum Efficiency
3-Sigma LER (nm)
30
25
20
Why do both EUV and DUV
show the same linear behavior?
2
DUV r = 0.94
15
10
2
EUV r = 0.97
5
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1/2
1/(Esize)
Quantum
Efficiency
Brainard EUV 2004
Number of Acids Generated
=
Number of Photons Absorbed
16
V. Quantum Efficiency
# Photons Absorbed
Need to Know:
• Absorption 125 nm
• Number of EUV Photons / mJ/cm2
0.1 mJ/cm2
EUV Photons
(41%)
(6.7 x 1013)
# Photons
= (0.1 mJ/cm2)(0.41)(6.7 x 1013 mJ/cm2)
Absorbed
1 cm x 1 cm x 125 nm
EUV-2D
0.5
Need to Know:
• C-Parameter
• [PAG]
• Avogadro's Number
0.4
[base]/[PAG]
# Acids
Generated
0.3
0.2
0.1
C-Parameter
= 0.051 cm2/mJ
0
-0.1
0
= [PAG](1 – e(-CE))(6.02 x 1023)
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2
4
6
8
10
12
14
Eo
Szmanda's Base
Titration Method
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Quantum Efficiency
of EUV-2D at DUV and 193 nm
Φ
OD (1/um)
C-Parameter
DUV
0.37
0.037
0.33
193 nm
24.5
0.12
0.14
PAG
H+
hν
92.5 eV
EUV Photon
PAG
C, H & O
Polymer
eee-
In principal, there is enough energy in an
EUV photon to activate ~20-30 PAGs
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PAG
PAG
H+
H+
H+
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Quantum Efficiency
of EUV-2D is 2.1!
Wavelength
Esize
2
(mJ/cm )
EUV
DUV
6.7
9.7
# of Photons
2
in 1 mJ/cm
13
x 10
Absoption
of 125 nm
Quantum
Efficiency
6.7
125
0.41
0.10
2.08
0.33
Number of Acids
Generated @ Esize
x 10
13
38.2
40.6
The number of acids generated at EUV and DUV are the same!
The LER vs. Esize Curves for both EUV and DUV are described by
Shot Noise (Poisson) Statistics:
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LER ∝ Dose-1/2
19
VI. Is EUV Limited by
LER (3-Sigma, nm)
14
Shot Noise?
12
EUV-2D
10
8
No Hard Barrier Yet
Resist Improvements
6
4
Although EUV-2D
2
0
10
20
30
40
50
60
70
80
2
14
LER (3-Sigma, nm)
follows a LER vs. Esize pattern
Esize (mJ/cm )
12
defined by
EUV-2D
shot noise statistics,
10
8
New improved resists show
6
Resist
Improvements
4
that performance is not
r2=
0.95 - 0.97
2
0
0.2
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0.4
0.6
0.8
(Esize)-1/2
1
1.2
1.4
limited by shot noise
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VII. Conclusions
Shot Noise observed at DUV and EUV for all resist systems
LER follows Poisson Statistical Rules: LER ∝ Dose-1/2
Although EUV-2D follows a LER vs. Esize pattern defined by
shot noise (Poisson) statistics, resists can be made with better
LER/Sensitivity performance
Earlier studies of shot noise and LER either predicted:
• Catastrophic LER failure, or
• Shot noise barrier not yet encountered
We conclude that shot noise statistics have been with us all
along in DUV and EUV
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What Don't We Know?
How are multiple acids from a single
photon arranged?
Will this arrangement affect LER?
hν
H+
H+
Brainard EUV 2004
hν
hν
H+
H+
hν hν hν hν
H+ + +
H+ + HH
H
H+
+
+
H
H
H+
H+
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VII. Acknowledgements
DARPA/SPAWAR
David Patterson
Cynthia Hanson
Donald Mullin
Sandia National Laboratories
Kevin McDonald
Jerry Sledge
Chip Stein
Dan Folk
John Goldsmith
Donna O’Connell
Shipley
Kathleen Spear
Kathleen O’Connell
Pramod Kandanarachchi
Doris Kang
Tom Penniman
Bob Blacksmith
Chuck Szmanda
Brainard EUV 2004
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