Line Edge Roughness - Applied Math SolutionsIt is impossible to list all the numerous references to...
Transcript of Line Edge Roughness - Applied Math SolutionsIt is impossible to list all the numerous references to...
02/21/2010 Gallatin SPIE 11
Line Edge Roughness
An introductory/intermediate course on measuring, modeling and understanding LER
Gregg M. Gallatin
Center for Nanoscale Science and TechnologyNational Institute of Standards and Technology
Gaithersburg, MD 20899 [email protected]
301-975-2140
02/21/2010 Gallatin SPIE 22
The full description of the procedures used in these course notes
requires the identification of certain commercial products and
their suppliers. The inclusion of such information should in no
way be construed as indicating that such products or suppliers
are endorsed by NIST or are recommended by NIST or that they
are necessarily the best materials, instruments, software or
suppliers for the purposes described.
Please read the following statement:
02/21/2010 Gallatin SPIE 33
Acknowledgements
Patrick Naulleau, Robert Brainard, Alex Liddle, Dimitra Niakoula, ElsayedHassanein, Bruno La Fontaine, Tom Wallow, Adam Pawlowski, David van
Steenwinckel, Robert Bristol, Pieter Kruit, Tor Sanstrom, Vivek Prabhu, Tony Novembre, Stuart Stanton, Victor Katsap, Yehiel Gotkis, Keith
Standiford, Andrew McCullough…. And many others
References
It is impossible to list all the numerous references to LER data, LER modeling, LER metrology, LER effects, etc.
The references listed on the following pages are those papers which I myself have found to be useful.
I humbly apologize to the authors of any references not listed.
02/21/2010 Gallatin SPIE 44
Data, General Properties, and Characterization of LER, Surface Roughness, and Resist Resolution:
He and Cerrina, J. Vac. Sci. Technol. 16 (1998)William D. Hinsberg, et. al., Proc. SPIE 3999, 148 (2000) Jonathan L. Cobb, et. al. Proc. SPIE 4688, 412 (2002)J. A. Hoffnagle, et. al., Opt. Letts. 27, 1776 (2002)J. A. Croon, et. al., IEDM (2002)V. Constantoudis, et. al., J. Vac. Sci. Technol. B21, 1019 (2003)William Hinsberg, et. al., Proc. SPIE 5039, 1 (2003) Atsuko Yamaguchi and Osamu Komuro, Jpn. J. Appl. Phys. 42, 3763 (2003) Charlotte A. Cutler, Proc. SPIE 5037, 406 (2003)Robert L. Brainard, et. al., Proc. SPIE 5374, 74 (2004)Gerard M. Schmid, et. al., Proc. SPIE 5376, 333 (2004)V. Constantoudis, et. al., J. Vac. Sci. Technol. B22, 1974 (2004)Adam R. Pawloski, et. al., Proc. SPIE 5376, 414 (2004)Gallatin, Proc. SPIE 5754 (2005)Adam R. Pawloski, et. al., J. Microlith., Microfab., Microsys. 5(2), 023001 (2006)Choi, et. al., Proc. SPIE 6519 (2007)Kang, et. al., Proc. SPIE 6519 (2007)Steenwinckel, et. al., Proc. SPIE 6519 (2007)Gallatin, et. al., Proc. SPIE 6921 (2008)Hassanein, et. al. Proc. SPIE 6921 (2008)Steenwinckel, et. al., J. Micro/Nanolith., MEMS, MOEMS. 7(2) (2008)Naulleau, et. al., J. Vac. Sci. Technol. 26 (2008)… and many many others…
Refe
renc
es
02/21/2010 Gallatin SPIE 55
Metrology and LER Data Analysis:Goldfarb, et. al., J. Vac. Sci. Technol. B22, 647 (2004)Constantoudis, et. al., Proc. SPIE 5752 (2005)Villarrubia and Bunday, Proc. SPIE 5752 (2005)Katz, et. al., Proc. SPIE 6152 (2006)Constantoudis, et. al., Proc. SPIE 6518 (2007)Wang, et. al., Proc. SPIE 6518 (2007)Naulleau and Cain, J. Vac. Sci. Technol. 25 (2007)Wang, et. al., Proc. SPIE 6922 (2008)Yamaguchi, et. al., Microelectronic Eng. 84 (2007)Constantoudis and Gogolides, Proc. SPIE 6922 (2008)Naulleau, et. al., J. Vac. Sci. Technol. 26 (2008)Orji, et. al., Proc. SPIE 7042 (2008)Bunday, et. al., Proc. SPIE 6922 (2008)
SEM and AFM Limitations, Modeling and Analysis:Stedman, Journal of Microscopy 152 (1988)Villarrubia, J. Research NIST 102 (1997)Cazaux, Nanotechnology 15 (2004)Villarrubia, et. al., Surf. Interface Anal. 37 (2005)Villarrubia, et. al., Proc. SPIE 6518 (2007)Chris Mack, Microlithography World, August 2008.
… and many others…
… and many others…
Refe
renc
es
02/21/2010 Gallatin SPIE 66
LER and LER-Related Resist Modeling:
P. C. Tsiartas, et. al., Macromolecules 30, 4656 (1997)L. W. Flanagin, et. al., Macromolecules 32, 5337 (1999) F. A. Houle, et. al., J. Vac. Sci. Technol. B18, 1874 (2000)Gallatin, Proc. SPIE 4404, 123 (2001) S. D. Burns, et. al., J. Vac. Sci. Technol. B20, 537 (2002)Hiroshi Fukuda, J. Photopolymer Sci. and Tech. 15, 389 (2002) F. A. Houle, et. al., J. Vac. Sci. Technol. B20, 924 (2002) Hiroshi Fukuda, Jpn. J. Appl. Phys. 42, 3748 (2003)Jonathan L. Cobb, et. al., Proc. SPIE 5037, 397 (2003)Gallatin, et. al., J. Vac. Sci. Technol. B21, 3172 (2003)William Hinsberg, et. al., Proc. SPIE 5039, 1 (2003) D. Fuard, et. al., Proc. SPIE 5040, 1536 (2003) Kozawa, et. al., J. Vac. Sci. Technol. 21 (2003)Lei Yuan and Andrew R. Neureuther, Proc. SPIE 5376, 312 (2004)William Hinsberg, et. al., Proc. SPIE 5376, 352 (2004)Robert L. Brainard, et. al., Proc. SPIE 5374, 74 (2004)Michael D. Shumway, et. al., Proc SPIE 5374, 454 (2004) Kruit, et. al., J. Vac. Sci. Technol. 22 (2004)Patrick P. Naulleau, Appl. Opt. 43, 788 (2004) Okoroanyanwu and Lammers, Future Fab. Intl. 17, Chapter 5, Section 5 (2004)Neureuther, et. al., J. Vac. Sci. Technol. B 24 (2006)Rydberg, et. al., J. Microlitho., Microfab., Microsys. 5 (2006)Kozawa, et. al., J. Vac. Sci. Technol. B. 25 (2007)
Refe
renc
es
… continued…
02/21/2010 Gallatin SPIE 77
Continued…LER and LER-Related Resist Modeling:
Gallatin, et. al., Proc. SPIE 6519 (2007)Bristol, Proc. SPIE 6519 (2007)Drygianakis, et. al., Proc. SPIE 6519 (2007)Gotkis, IEPBN Meeting, Portland Oregon, 2008Gotkis, IEUVI Resist TWG meeting, Feb 28, 2008 Saeki, et. al., Proc. SPIE 6923 (2008)Kozawa, et. al., Applied Physics Express 1 (2008)Chris Mack, LER Course, EUV Conference, Maui, (2008)
… and many others…
LER Effects on CD and Devices:2003P. Oldiges, et. al., SISPAD (2000)T. Linton, et. al., IEDM (2002)J. A. Croon, et. al., ESSDERC (2003)Asen Asenov, et. al., IEEE Trans. Electron Dev. 50, 1254 (2003)Goldfarb, et. al., J. Vac. Sci. Technol. B22, 647 (2004)Chandhok, Proc. SPIE 6519 (2007)Tsikrikas, et. al., Proc. SPIE 6518 (2007)Drygiannakis, et. al., Proc. SPIE 6518 (2007)Ma, et. al., Proc. SPIE 6518 (2007)
Refe
renc
es
… and many many many others…
02/21/2010 Gallatin SPIE 88
• What is Line Edge Roughness (LER)?
• How is it measured and quantified?• SEM vs AFM• s values• PSD, Autocorrelation, HHCF,• Resist Blur, Correlation Length, Slopes, Roughness Exponent
• How does it behave?• Dependence on Dose, ILS, Blur, Frequency, Base Loading, PAG loading, …
• The many causes of LER?
• Modeling LER… or at least the dominant contribution to LER
• Consequences? • The RLS tradeoff or Lithographic Uncertainty Principle
è “Resolution, LER, Sensitivity…Pick any two”
• How does it affect CD variation and device performance?
• Can it be fixed? Does it need to be fixed?
OUTLINE
02/21/2010 Gallatin SPIE 99
0 200 400 600 800 10000
200
400
600
800
Early EUV SEMSandia/Livermore
LER Examples
Recent EUV SEMImaged on MET at LBNLNaulleau, et. al. Resist: MET2D
We will use this as an example case for studying LER analysis. For the most part the data from this SEM has been processed using the SuMMIT software(www.euvl.com/summit) program for doing LER analysis.
02/21/2010 Gallatin SPIE 1010
0 100 200 300 4000
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dry_attPSM_7.tiff
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dry_attPSM_8.tiff
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dry_attPSM_9.tiff
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dry_attPSM_4.tiff
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dry_attPSM_5.tiff
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dry_attPSM_6.tiff
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dry_attPSM_1.tiff
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dry_attPSM_2.tiff
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dry_attPSM_3.tiff
193 LER Examples
02/21/2010 Gallatin SPIE 1111
Edge Finding Algorithms
1. Threshold2. Max slope3. Threshold a polynomial fit to the
image data in the region of the edge.
4. Max slope polynomial fit5. Sigmoidal fit….6. etc, etc, etc…
è Once the edge data is obtained subtract a best fit straightline from the edge data to remove• Average edge position• Edge “run-out”
• Removes SEM image rotation• Want just the roughness, not
the linear (“flat”) variation
0 200 400 600 800 1000 1200
50
100
150
200
250
02/21/2010 Gallatin SPIE 1212
Determining LER from a top-down CD SEM
1 2 3 4 5 6 7 8 9 10111213141516
2
4
6
8
10
Average 3s = 6.83 nm
Apply edge finding algorithm and determine best fit straight line for each edge
Subtract straight line fit to obtainroughness residual
1 5 10 50 100
10
50
100
500
1000
2_5h07.tif
Compute things… such as 3s per edge …and/or FFT and square to obtainFrequency content
Spatial frequency ~ cycles/micron
1. 2.
3.0 200 400 600 800 1000
0
200
400
600
800
NOTE: s values computed by standard algorithms are generally biased and can be systematically larger or smaller than the “real” values. (see discussion of PSD).
02/21/2010 Gallatin SPIE 1313
From the 2007 ITRS Roadmap
02/21/2010 Gallatin SPIE 1414
Semi-Spec
-2 micron long line è Sets Minimum Spatial Frequency = ½ cycle/micron
-10nm or less sample spacing è Sets Maximum Spatial Frequency = 100 cycles/micron
From the 2007 ITRS Roadmap
02/21/2010 Gallatin SPIE 1515
0 100 200 300 400 500- 4- 2024 3s LER = 4.71nm
0 100 200 300 400 500- 4- 2024 3s LER = 4.44nm
0 100 200 300 400 500- 6- 4- 2024 3s LER = 7.14nm
0 100 200 300 400 500- 4- 2
02
4 3s LER = 4.14nm
ExampleEdges
570nm862 points
nm
nm
nm
nm
nm
nm
nm
nm
02/21/2010 Gallatin SPIE 1616
( )
( ) ( ) ( ) ( )
( ) ( )
( )
NHHH
HN
HNL
LxHdx
Lrms
NLxdxdx
xHdxL
xHdxL
xHdxL
xHdxL
xhxH
xh
N
N
nn
N
nn
L
N
n
N
n
L L
L
L
L
L
L
L
L
222
21
1
2
1
2
0
2
110
2/
2/
2/
2/
2
0
22
2/
2/0
1111
11
110line)straight fit (best
data edge raw
+++=
====
=D==
==
==Þ-=
=
ååò
ååò ò
òò
òò
==
==
+
-
+
-
-
!
s
s
Computing s
LER is commonly quotedas the 3s value
Data is discrete not continuous
NOTE: s values computed this way are generally “biased”, i.e., they are systematically larger or smaller than the “real” values.
02/21/2010 Gallatin SPIE 1717
~6 nm Amplitude
~50nm
Low spatial frequency
è LER is long and slow compared to its amplitude
Implication: LER is apparently not “atomistic” in origin
è Not driven by molecular weight.
Cutler, et. al., SPIE 03
Brainard, et. al., SPIE 04
Chemical and “atomistic” effects must contribute
but apparently they are not the dominant cause.
02/21/2010 Gallatin SPIE 1818
( ) ( ) ( )
( ) ( )
( ) ( )( )
å
å
ò
åò
-
+
-
+
-
=
D-DD=
-=
-==
==
nmnn
n
L
L
n
L
L
HHN
xmnHxnHxL
sxHxHdxL
sxxxHxHxxACF
Ndx
L
1
1
1
''',
...1...1...
2/
2/
2/
2/
LER AutoCorrelation Function = ACF
Shift, multiply, sum and normalize
But the data has a finite length…Need to adjust for this
02/21/2010 Gallatin SPIE 1919
mNHHHHHHHH
mNACF mNNmm
mN
mnmnnm -
+++=
-= -++
-
+=-å !2211
1
1
1 Nm+1
1 N-mLop-off the ends
111
+-
++=
+-= --
=-å
startend
mnnmnnn
nnmnn
startendm nn
HHHHHH
nnACF endendstartstart
end
start
!
nstart nend
nstart - m nend - m
å=
-+ =Þ=N
nmnnmnNn HH
NACFHH
1
1
Take a fixed lengthout of the middle
Assume PeriodicityWorks well with FFT’s 1 N
1 N 1 N 1 N
02/21/2010 Gallatin SPIE 2020
- 100 - 50 0 50 100
- 1.0- 0.50.00.51.01.52.0
- 100 - 50 0 50 100
- 2
0
2
4
6
- 100 - 50 0 50 100- 0.5
0.0
0.5
1.0
1.5
2.0
- 100 - 50 0 50 100
- 0.5
0.0
0.5
1.0
1.5
570nm862 points
Use the middle401 pointsto compute ACF
nm2
nm
nm2
nm2
nm2
nm
nm
nm
02/21/2010 Gallatin SPIE 2121
- 100 - 50 0 50 100
- 0.5
0.0
0.5
1.0
1.5
2.0
- 100 - 50 0 50 100- 1
01
23
45
- 100 - 50 0 50 100
0.0
0.5
1.0
1.5
2.0
- 100 - 50 0 50 100
- 0.5
0.00.51.01.52.02.5
570nm862 points
Assume periodicityto compute ACF
nm2
nm
nm2
nm2
nm2
nm
nm
nm
02/21/2010 Gallatin SPIE 2222
- 100 - 50 0 50 100
- 0.5
0.0
0.5
1.0
1.5
2.0
- 100 - 50 0 50 100- 1
01
23
45
- 100 - 50 0 50 100
0.0
0.5
1.0
1.5
2.0
- 100 - 50 0 50 100
- 0.5
0.00.51.01.52.02.5
570nm862 points
Assume periodicityto compute ACF
nm2
nm
nm2
nm2
nm2
nm
nm
nm
02/21/2010 Gallatin SPIE 2323
( ) ( ) ( )
( ) ( ) ( ) ( ) ( )
( )
( ) ( )
( ) ( ) ( )'',
~2
~2
1'~~'1
'Let'',
...1...
'2
2
2/
2/
'2/
2/
2/
2/
xxACFsACFxxACF
eHdL
eHdL
edxL
eHHddsxHxHdxL
sxxxHxHxxACF
dxL
xxi
si
L
L
xisiL
L
L
L
-==Þ
=
=
=-=
-==
=
ò
ò
òòò
ò
-±
±
+
-
+-+
-
+
-
b
b
bbb
bbp
bbp
bbbb
( ) ( )ò -= xiexHdxH b
pb
21~Fourier transform
of the data
( ) ( )*~~ Real bb -=Þ HH
( ) squaredlength units ~ =Þ bH
( )!! "!! #$
'2 bbdp +@L
Acts like Dirac delta function
ACF = AutoCorrelation Function
02/21/2010 Gallatin SPIE 2424
( ) ( ) ( ) ( ) ( )bbpbbp b PSDHL
eHdL
xxACF xxi ~2~2'2'2=Þ=- ò -±
( ) ( ) ( ) ( )( ) ( ) ( )
( ) ( ) ( )
( ) ( ) ( ) ( )åååò
òò
D÷øö
çèæ=D=DD==
==÷øö
çèæ=
=-=Þ
===-=
nnnnH
LnH
LLnPSDPSDd
PSDdHL
dACF
fxxfxxACF
xHACFxxACFxxACF
22
22
22
2
22
~2~22
~20
10with'',
0,
bpbppbbbbs
sbbbpb
s
s
ACF = AutoCorrelation Function è PSD = Power Spectral Density
PSD is the square of the FFT of the data with a “normalization” factor 2p / L
NOTE: PSD units = length cubed
!!"!!#$
Frequencycontent of the LER
23 lengthlengthlength1
=´
è Area under PSD = s 2
02/21/2010 Gallatin SPIE 2525
0 100 200 300 400 500- 4- 2024 3s LER = 4.71nm
0 100 200 300 400 500- 4- 2024 3s LER = 4.44nm
0 100 200 300 400 500- 6- 4- 2024 3s LER = 7.14nm
0 100 200 300 400 500- 4- 2
02
4 3s LER = 4.14nm
ExampleEdges
570nm862 points
nm
nm
nm
nm
nm
nm
nm
nm
02/21/2010 Gallatin SPIE 2626
0 100 200 300 400 500 600 7000.000.020.040.060.080.100.120.14
cyclesêmicron
0 100 200 300 400 500 600 7000.00
0.05
0.10
0.15
cyclesêmicron 0 100 200 300 400 500 600 7000.00
0.05
0.10
0.15
0.20
0.25
cyclesêmicron
0 100 200 300 400 500 600 7000.00
0.05
0.10
0.15
0.20
cyclesêmicron
570nm862 points
Compute PSD’susing FFT(Careful different FFT algorithms have different normalization factors)
mnm µ2
mnm µ2
mnm µ2
mnm µ2
02/21/2010 Gallatin SPIE 2727
5 10 50 100 500
10-610-510-40.0010.010.1
cyclesêmicron
5 10 50 100 500
10-610-510-40.0010.010.1
cyclesêmicron 5 10 50 100 50010-710-610-510-40.0010.010.1
cyclesêmicron
5 10 50 100 500
10-610-510-40.0010.010.1
cyclesêmicron
570nm862 points
LogLog scale works much better for seeing PSD details
mnm µ2
mnm µ2
mnm µ2
mnm µ2
02/21/2010 Gallatin SPIE 2828
5 10 50 100 500
10-610-510-40.0010.010.1
cyclesêmicron
5 10 50 100 500
10-610-510-40.0010.010.1
cyclesêmicron 5 10 50 100 50010-710-610-510-40.0010.010.1
cyclesêmicron
5 10 50 100 500
10-610-510-40.0010.010.1
cyclesêmicron
570nm862 points
LogLog scale works much better for seeing PSD details
mnm µ2
mnm µ2
mnm µ2
mnm µ2
SEM Pixel-to PixelWhite Noise
02/21/2010 Gallatin SPIE 2929
5 10 50 100 500
10-610-510-40.0010.010.1
cyclesêmicron- 200 - 100 0 100 200- 0.4- 0.20.00.20.40.60.81.0
nm- 200 - 100 0 100 200
- 0.4- 0.20.00.20.40.60.81.0
nm
5 10 50 100 500
10-610-510-40.0010.010.1
cyclesêmicron- 200 - 100 0 100 200
0.0
0.2
0.4
0.6
0.8
1.0
nm- 200 - 100 0 100 200
0.0
0.2
0.4
0.6
0.8
1.0
nm
Spike in ACF comes from flat “white noise” background in the PSD
Subtract off the “white noise” background from the PSD to eliminate the spike
2/sACF
2/sACF
2/sACF
2/sACF
02/21/2010 Gallatin SPIE 3030
( ) ( ) ( )( )
( ) ( ) ( ) ( )( )( ) ( ) ( ) ( )
( )( )( )
( ) ( )( )
2
2 2
2 2
2 2
2
2
, ' '
' 2 '
' 2 '
2 '
2 1 '
, 2 1 0 0
HHCF x x H x H x
H x H x H x H x
H x H x H x H x
ACF x x
f x x
HHCF x x f
s s
s
s
= -
= + -
= + -
= + - -
= - -
= - =
“HHCF” = Height Height Correlation Function
( )xH
( )'xH
x 'x
( ) ( )'xHxH -
( ) ( )
( ) 10
2
=
=
f
xACFxfs
02/21/2010 Gallatin SPIE 3131
1 2 5 10 20 50100200
1.0000.500
0.1000.050
0.0100.005
nm
HHCF: Raw = RedBackground Subtracted = Black
1 2 5 10 20 50100200
1.000.500.200.100.050.020.01
nm
HHCF: Raw = RedBackground Subtracted = Black
- 200 - 100 0 100 200- 0.4- 0.20.00.20.40.60.81.0
nm- 200 - 100 0 100 200
- 0.4- 0.20.00.20.40.60.81.0
nm
- 200 - 100 0 100 200
0.0
0.2
0.4
0.6
0.8
1.0
nm- 200 - 100 0 100 200
0.0
0.2
0.4
0.6
0.8
1.0
nm
Raw ACFBackground subtracted ACF
2/sACF 2/sACF
2/sACF 2/sACF22/ sHHCF
22/ sHHCF
02/21/2010 Gallatin SPIE 3232
1 2 5 10 20 50100200
1.0000.500
0.1000.0500.0100.005
nm
HHCF: Raw = RedBackground Subtracted = Black
Beat down noise in PSD, ACF and HHCF by averaging the PSD’s from all the edges
5 10 50 100 5001¥ 10-4
5¥ 10-4
0.1000.050
0.0100.005
0.001
cyclesêmicron - 200 - 100 0 100 200
0.0
0.2
0.4
0.6
0.8
1.0
nm
2/sACFmnm µ2 22/ sHHCF
02/21/2010 Gallatin SPIE 3333
( ) ( ) ( )
( ) ( ) ( ) ( )
( )
( )
( ) ( )
( ) ( )( ) ( ) ( )222
2
4/22
2222
/224/22
/2222
22
263.011212
37.0length"n correlatio" 37.01
22~
1/
2~:SpectrumPower
2
~2
1/~2:PSD
22
222
ssxs
sxxx
pxs
pb
bxpxs
pb
spxsbp
ssbxpxsbp
bx
xbx
x
»÷øö
çèæ -==Þ-=
»=Þ=@==
÷ø
öçè
æ=
÷÷ø
öççè
æ+
=
==Þ=
==Þ+
=
-
--
-
exHHCFxfxHHCF
xACFe
xf
eLH
LH
exfσxACFeHL
exf xACFHL
x
x
NOTE Units
frequencyspatiallengthlength
23 =Þ
frequencyspatiallengthlength
23 =Þ
2
24
)( frequencyspatiallengthlength =Þ
2
24
)( frequencyspatiallengthlength =Þ
Standard shapes for the PSD and ACF
Lorentzian PSD Exponential ACF
Gaussian PSD Gaussian ACF
02/21/2010 Gallatin SPIE 3434
1.00.5 5.00.1 10.0 50.0 100.010-4
0.001
0.01
0.1
1
- 4 - 2 2 4
0.2
0.4
0.6
0.8
1.0
1.00.5 2.00.2 5.00.1
10-6
10-5
10-4
0.001
0.01
0.1
1
- 3 - 2 - 1 1 2 3
0.2
0.4
0.6
0.8
1.0
Lorentzian PSD Exponential ACF
Gaussian PSD Gaussian ACF
2 slope loglog -=
02/21/2010 Gallatin SPIE 3535
1.00.5 5.00.1 10.0 50.0 100.010-4
0.001
0.01
0.1
1
- 4 - 2 2 4
0.2
0.4
0.6
0.8
1.0
1.00.5 2.00.2 5.00.1
10-6
10-5
10-4
0.001
0.01
0.1
1
- 3 - 2 - 1 1 2 3
0.2
0.4
0.6
0.8
1.0
Lorentzian PSD Exponential ACF
Gaussian PSD Gaussian ACF
2 slope loglog -=
x1/ length n correlatio/1 = x x
x
02/21/2010 Gallatin SPIE 3636
( ) ( )( ) ( ) ( )( ) ( ) ( )
( )( )
( )( )( )
( )( )
( )
( )
1exponent critical 2 frequency high at slope loglog
12 Thus by defined exponent Critical
1For
lettingafter 1
1111
slope" loglog " ln
ln 1For 1
1~
1~22022
2
1
2
222
+´=
+=µ<<
µ<<Þ÷øö
çèæ»÷
øö
çèæ+Þ<<
=
÷øö
çèæ+
-=
+-
µ
=-=¶
¶>>Þ
+µ
-=-=-=
-
òò
ò
PSD
xxHHCF
xxHHCFqx
qx
x
xqqx
edqx
edxHHCF
PSDPSDH
eHdL
xACFACFxfxHHCF
iqxi
xi
agxa
xxxx
bxxb
b
gbbbx
xbb
bbpss
a
ggg
gg
b
g
b
PSD loglog slope g çè HHCF scaling at small x - x’
02/21/2010 Gallatin SPIE 3737
5 10 50 100 5001¥ 10-4
5¥ 10-4
0.1000.050
0.0100.005
0.001
cyclesêmicron
1 2 5 10 20 50 100 200
1.0000.500
0.1000.050
0.0100.005
nm
0 .63
x = 24 .1nm
0 5 10 15 20 250.00.20.40.60.81.01.21.4
nm
a as a function of fitting range
Loglog slope = -3 13 =Þ=Þ ag
PSD
22/ sHHCF
mnm µ2
02/21/2010 Gallatin SPIE 3838
SEM AFM
Probe ~ Gaussian e-beamRadius ~ 2 to 5nm
è Fundamental frequencycutoff ~ 1/2nm to1/5nm
~500/µm to 200/µm
Probe ~ “Mechanical” tipRadius ~ 10’s of nm
è Fundamental frequencycutoff ~ 1/10’s of nm
<< 100/µm
Cutoff frequency is much higher than the observed shoulder in LER PSD’sè SEM resolution is not significantly filtering the LER
Cutoff frequency is close to the observed shoulder in LER PSD’sè AFM tip is significantly filtering the LER
1 5 10 50 100 500
0.001
0.01
0.1
1SEM
AFMLERPSD
02/21/2010 Gallatin SPIE 3939
AFM tip has a finite radius
è Tip filters out high frequency content of the roughness
è Makes a smoothly varying surface look “grainy”
Amplitude at which tip filtering becomes significant
24
2
2
1
1
tip
tip
RAmplitude
RAmplitude
b
b
=
=
Large tip radius Small tip radius
è High frequency content of the PSD is filtered out. è Filtered PSD loglog-slope ~ -4
02/21/2010 Gallatin SPIE 4040
AFM measurement of LER Goldfarb, et. al., JVSTB 22 (2004)
Patterned wafer is cleaved and turned on edge
AFM
02/21/2010 Gallatin SPIE 4141
A note on the addition of a flat (constant) noise background to the “ideal” PSD
( )( ) ( )
BPSD ++
Þ+
= gg xbxbb
11
11
0.01 0.1 1 10 10010-4
0.001
0.01
0.1
10.01 0.1 1 10 100
10-4
0.001
0.01
0.1
1
0.01 0.1 1 10 10010-4
0.001
0.01
0.1
1
“Ideal”PSD
Might expecta sharpcorner
Get asmoothcorneras seen inreal data
SEM images contain “white” noise è Noise in each pixel is uncorrelated to noise in other pixelsè White Noise è Flat PSD
SEM WhiteNoise PSDIs added toData PSD
02/21/2010 Gallatin SPIE 4242
Bias in LER measurements:
0.01 0.1 1 10 10010-4
0.001
0.01
0.1
1
Minimum Freq= 1/Line Length
Maximum Freq= 1/Sample spacing
Missing lowFrequencycontributionto sTRUE
2
Area = sTRUE2
Area = sSEM Noise2
2Noise SEM
2TRUE sss +=measuredTotal Area è
Missing highFrequencycontributionto sTRUE
2
PSDunder Area=s
LER value is biased • Lower by missing frequency content • Higher by SEM noise.
See Villarubia and Bunday refs
02/21/2010 Gallatin SPIE 4343
SVL = Sigma Versus Length
( )
( ) ( ) ( )
( ) ( )
( ) ( ) ( ) ( )
( )
( )÷÷ø
öççè
æ--=
--=
-=
÷÷ø
öççè
æ-=
÷÷ø
öççè
æ-=
=
ò
ò
òò
òò
òò
ò
+
-
+
-
+
-
+
-
+
-
+
-
+
-
+
-
+
-
2/
2/2
2
2/
2/
22
2
2/
2/2
2/
2/
22
22/
2/2
2/
2/
2
22/
2/
2/
2/
2
2/
2/
22
''11
''1
''11
11
11
1
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
L
L
xxfdxdxl
xxfdxdxl
xHxHdxdxl
xHdxl
lSVL
xHdxl
xHdxl
xHdxl
xHdxl
lSVL
xHdxL
s
ss
sFull length s 2
Compute s 2over variable length l
Take average to determine mean behavior of SVL
02/21/2010 Gallatin SPIE 4444
( ) ( )
( )
( ) ( ) ÷÷ø
öççè
æ÷÷ø
öççè
æ-÷
øö
çèæ -+-=
=-
÷÷ø
öççè
æ--=
--
--
+
-ò
1121
get'For
''11
//22
/'
2/
2/2
22
xx
x
xxs
s
ll
xx
l
l
el
el
lSVL
exxf
xxfdxdxl
lSVL
0 1 2 3 4 5
0.2
0.4
0.6
0.8
1.0
x3l
Statistical Average behavior of SVL
Single Edge SVL Single Edge SVLSVL averaged over four edges
( )( )2/slSVL
x/l
0 20 40 60 80 100 1200.0
0.5
1.0
1.5
2.0
nm
nm2
0 20 40 60 80 100 1200.0
0.5
1.0
1.5
nm
nm2
0 20 40 60 80 100 1200.00.51.01.52.02.53.0
nm
nm2
02/21/2010 Gallatin SPIE 4545
Line Width “Roughness” (LWR) = Linewidth variation along a single line
Uncorrelated Edges “Correlated” Edges “Anticorrelated” Edges
LER
LWR rightleft
2
22
»
+= ss0=LWR LERLWR 2=
02/21/2010 Gallatin SPIE 4646
0 100 200 300 400 50046485052545658
0 100 200 300 400 500- 10- 50510 3s LWR = 7.11nm
Linear CD variation = 1.44nmLinear CD variation = 7.66nm
0 100 200 300 400 5004850525456586062
0 100 200 300 400 500- 10- 50510 3s LWR = 6.72nm
Line Width Roughness
02/21/2010 Gallatin SPIE 4747
0 100 200 300 4000
100
200
300
400
dry_attPSM_7.tiff
0 100 200 300 4000
100
200
300
400
dry_attPSM_8.tiff
0 100 200 300 4000
100
200
300
400
dry_attPSM_9.tiff
0 100 200 300 4000
100
200
300
400
dry_attPSM_4.tiff
0 100 200 300 4000
100
200
300
400
dry_attPSM_5.tiff
0 100 200 300 4000
100
200
300
400
dry_attPSM_6.tiff
0 100 200 300 4000
100
200
300
400
dry_attPSM_1.tiff
0 100 200 300 4000
100
200
300
400
dry_attPSM_2.tiff
0 100 200 300 4000
100
200
300
400
dry_attPSM_3.tiff
193 Example
02/21/2010 Gallatin SPIE 4848
2 3 4 5 65.5
6.5
7
7.5
8Average 3s LER = 6.72 nm
2 3 4 5 6
5.5
6
6.5
7
7.5Average 3s LER = 6.06 nm
2 3 4 5 6
6.5
7
7.5
8
Average 3s LER = 6.98 nm
2 3 4 5 65.5
6.5
7
7.5
Average 3s LER = 6.6 nm
2 3 4 5 6
6.5
7
7.5
8
Average 3s LER = 6.69 nm
2 3 4 5 65.5
6.5
7
7.5
8Average 3s LER = 6.42 nm
2 3 4 5 6
6.5
7
7.5
8Average 3s LER = 6.8 nm
2 3 4 5 6
5.56
6.57
7.58
8.5Average 3s LER = 6.54 nm
2 3 4 5 6
6.25
6.5
6.75
7
7.25
Average 3s LER = 6.51 nm
Edge by Edge 3s
02/21/2010 Gallatin SPIE 4949
5 10 50 100
0.0001
0.001
0.01
0.1
1
5 10 50 100
0.001
0.01
0.1
5 10 50 1000.0001
0.001
0.01
0.1
1
5 10 50 1000.0001
0.001
0.01
0.1
5 10 50 1000.0001
0.001
0.01
0.1
1
5 10 50 1000.0001
0.001
0.01
0.1
5 10 50 100
0.001
0.01
0.1
1
5 10 50 1000.0001
0.001
0.01
0.1
5 10 50 1000.0001
0.001
0.01
0.1
1
Edge by Edge PSD’s
02/21/2010 Gallatin SPIE 5050
193 data from Pawloski, et. al., JM3 2006
02/21/2010 Gallatin SPIE 5151
SEM noisefloor
SEM noisefloor
EUV Data from Cobb,et. al. SPIE 02.
02/21/2010 Gallatin SPIE 5252
….“known” LER Scaling Laws….
§ LER ~ 1 / Dose1/2
… Usually attributed to… and/or… called “shot noise”
§ LER ~ 1 / Image edge slope ~ 1 / Image Contrast ~ 1 / ILS
... Holds in the regime of low image contrast.
§ LER power spectra (PSD) ~ Generic Modified Lorentzian
Shape ~ 1 / (1 + (xb )g ) with g ≈ 3
… Dominated by low frequency content
è LER autocorrelation length is “large” ~ 20-30nm
… Determines how LER impacts CD variation
General Behavior of LER
02/21/2010 Gallatin SPIE 5353
LER ~ 1 / Dose1/2
Lots of references…..
For example: from Brainard, et. al., SPIE 2004
02/21/2010 Gallatin SPIE 5454
0 5 10 15 20 25 30 350246810
Dose
LER
Resist5435
0 10 20 30 40 50 600246810
Dose
LER
Resist5271
0 5 10 15 20 25 30 350246810
Dose
LER
Resist5496
0 10 20 30 400246810
Dose
LER
Resist6797
0 5 10 15 200246810
Dose
LER
ResistEH
LER versus Dose: Recent EUV data (“RLS” project supported by Sematech)
“5435” ~ EUV2D (High Ea Phenolic)“5271” ~ MET2D (High Ea Phenolic)“5496” ~ Low Ea Phenolic“6797” ~ Aliphatic 193nm resist“EH” ~ High Ea Phenolic
NOTE: LER “saturates” at high dose
(high dose ~ high baseloading)
Resists:
02/21/2010 Gallatin SPIE 5555
LER ~ 1/Image Log Slope =1 / ILS
Lots of references…..
For example: from Pawloski, JM3 2006
NOTESaturation at high ILS
( )( ) ( )( )xI
xxIxxIILS ln/
¶¶
=¶¶
=
02/21/2010 Gallatin SPIE 5656
( )( )
( ) Slope Image11~
ln1~
/1
µ÷øö
çèæ
¶¶
÷÷ø
öççè
æ ¶¶µ
ILSxI
xIxxI
LER
Image Intensity Image Intensity Image Intensity
Low ILS è Low slopeè Large Dxè High LER
Medium ILS è Medium slopeè Medium Dxè Medium LER
High ILS è High slopeè Low Dxè Low LER
ID
xD
xD
ID
xD
xD
xD
xD
ID
Implication: LER à0 as ILS à ∞…Data è LER saturates at high ILS
“Why the dependence on 1/ILS ??”
Given DI...
“Known”Scaling
Law
02/21/2010 Gallatin SPIE 5757
“Why is LER dominated by low spatial frequencies?”
Pawloski, et. al. JM3, 2006
Cobb, et. al. SPIE, 2002
The key question
Alex Liddle
LERFrequencyContent
02/21/2010 Gallatin SPIE 5858
Many contributors
• Quantum Mechanics
• Shot Noise
• Chemical Statistics
• Reaction Diffusion Statistics
• Speckle
• Mask Roughness
• Mesoscopic Structure (non-uniformity in resist properties)
• …
What causes LER?
02/21/2010 Gallatin SPIE 5959
Advantages Disadvantages
AnalyticalModels
Nominally straightforward to understand, use and interpret. Work on the macroscopic level. Approximations used are explicit, i.e., you know explicitly what is and is not included in the model.
Difficult to incorporate microscopic details of the chemistry, etc. …
NumericalModels
“Easily” incorporate details of the chemistry and physics on the molecular/atomic scale. Allow you to work up from the microscopic scale. Provide a direct connection of the fundamental chemistry and physics to the statistics of resist exposure and development
Detailed modeling of 3D resist over large volumes is prohibitive. Difficult/Impossible to get to the macroscopic scale of LER, i.e., the LER coherence length ~ many 10’s of nm or more.
Modeling LER?
02/21/2010 Gallatin SPIE 6060
Lots of models have been generated by lots of different people
Here we study a “3 step” analytical model that explains
• The various scaling laws
• The “saturation” of LER with Dose and ILS
• The low frequency content of the LER
• The shape of the PSD.
This model
• Is fundamentally analytic and linear or quasi-linear
• Covers the Quantum, Shot Noise, Chemical Statistics and Reaction-Diffusion contributors to LER
02/21/2010 Gallatin SPIE 6161
LER Model we will study here: Generated by tracking the process steps of a chemically amplified resist.
Model details: Gallatin SPIE 2005Model is very similar to Fukuda JPST 02, Fukuda JJAP 03, Brainard SPIE 04 and others.
Same approach used for CD evaluation: Fuard SPIE 03, Shumway SPIE 04, Naulleau AO 04, etc...
1. Exposure: Releases acid from “photo acid generator” (PAG) compound in the resist
LER Model: Probability of acid generation ~ Image intensity
è Sensitivity (“Dose-to-Size”)
2. Post Exposure Bake (PEB)….. “bake wafer at 90oC for 120seconds”
LER Model: Acid diffuses and “deprotects” resist polymer
è Resist Resolution (Intrinsic Resist “Blur”)
3. Development: Converts deprotection density into final resist profile
LER Model: Statistical Fluctuations in deprotection produce roughness
è LER (3s roughness)
02/21/2010 Gallatin SPIE 6262
Exposure according to Mr. Schrodinger
You control the image intensitybut not where interactions take placein the photoresist.
Consequences:
• Line Edge Roughness (LER)
• Contact Hole Size Variation• … etc…
Time
02/21/2010 Gallatin SPIE 6363
LER Model è RLS Model
Acids
ResolutionDiffusion/deprotection“blur” develops around each acid during PEB
Net DeprotectionDensity = Sum of“blurs” around each acid
Grayscale plot net deprotectiondensity
Resist edge position occurs at a fixed value of deprotection~Critical Ionization
Model
Resist edge with low spatial frequency content
= LER
PEB
SensitivityExposure dose releases acids.Image intensity at position x à Probability of acid release at x
Acid
2D Illustration
Burns,et.al., JVST B 2002
Intensity =1 Intensity =0
Development
Gallatin SPIE 2005
02/21/2010 Gallatin SPIE 6464
Exposure
( )
( ) ( ) ( )
( ) ( ) ( ) ( ) ( ) ( )( )
[ ]
( )
( ) ( ) ( )[ ]( ) ( ) ( )[ ]( )
( ) ( )( )eaphotons/ar# Dose Saturation 1/C photons)(area/# C Dill
ea)photons/ar(# Dose
exp10,exp10,, :Solution
time))reaphotons/(a (#intensity Image , n volumeinteractioPAG -photon
photon. absorbedgenerated/ acids # "Efficiency Quantum" ckness)resist thi intensity, ed transmitt exp (ty absorptiviresist
,0,,,
,0,,
at time position at density PAG ,
sat
PAGPAGAcid
AcidPAGPAGAcid
AcidPAGPAG
PAG
EvQtrIrE
rEvQrtrIvQrtr
trIvQ
TT
trrrIvQtrrIvQttr
trrtr
trtr
==Þ===
--=--=
´==
====-=
-==¶
¶
-=
=
a
ararr
aa
rrarar
rrr
r
!!
!!!!!
!
!!!!!!
!!!
!!
(Only PAGs within volume v surrounding the position of absorption can be affected)
02/21/2010 Gallatin SPIE 6565
Exposure StatisticsPrevious slide è Exposure is deterministic. IT IS NOT
Quantum Mechanics è Probability of photon absorption ~ Image Intensity
( )
( )( )( )
( ) ( )( ) ( )
( ) ( ) ( ) ( )NNacidacidacidNNnetacid
rCEa
rCEaacid
rCE
rCE
Acid
arParParParararP
eearPr
aa
erer
tr
,,,,,,,,,ondistributiy probabilitNet
1, at generated be toacidan for on distributiy Probabitit
released NOT acid 0released acid 1Let
position at acidan release not toPAG a ofy Probabilit1position at acidan release PAG to a ofy Probabilit
yprobabilit a as dinterprete be should ,
22112211
0,1,
!"
!!!"
!!
!
!
!
!
!
!!
!
!
=
+-=
Û=Û=
=
-=
--
-
-
dd
r
02/21/2010 Gallatin SPIE 6666
( )
( )
1Probability distribution for one PAG
Joint probability distribution for all PAG's
the total number of PAG molecules loaded into the resist volum
,0
NNPAG
PAG
V
N P V AT
N V ATN NrV AT
r
--
Þ =
Þ = = =
= =
Þ = =!
Combine
• Distribution of Released acids
• PAG distributionArea = A
Thickness = T
N PAGs uniformly distributed throughout volume V = AT
02/21/2010 Gallatin SPIE 6767
Poisson Statistics
Probability for releasing a fixed number of acids ( ) ( ) ( ) ( )NN rPrPrPrrrP !"!!!
"!!
2121 ,,, =
( ) PoissonAaPn ®<<
~1mm
~1mmExposure tool fixes exposure dose over mm2 areas
N is fixed in mm2 areas A
Any single feature lives in an area a ~ micron2
è a << A
Probability of getting n acids in area a << A
Quantum Mechanics è Image in resist builds up one absorption at a time
Fixed number of acids the macroscale è Poisson statistics on the microscale. “shot noise”
02/21/2010 Gallatin SPIE 6868
• Acids deprotect polymer during PEB• Assume acids act independently (deprotection is not saturated)• Solve chemical kinetics rate equations for the deprotection
generated by a single acid located at
PEB Reaction Diffusion “blur”
( ) ( ) ( )
( ) ( )trDttr
trtrkttr
AcidAcid
PAcidP
,,
sorder termhigher ,,,
2 !!!
!!!
rr
rrr
Ñ=¶
¶
+-=¶
¶
( )
( ) ( ) ( ) ( )
/time)volume"" (Unitsconstant rateon deprotecti
,,0, ,
,
0
==
-º-=
k
trtrrtr
tr
PPPPD
P
!!!!
!
rrrrr
r
0=r!
Rate at which polymer is deprotected
Rate at which acid diffuses around.
NOTE: The position dependence, i.e., image information, is encoded in the acid distribution
Density of Protected Polymer =
Deprotected Density + Protected Density = Initial Polymer Density
Density of Deprotected Polymer =
02/21/2010 Gallatin SPIE 6969
( ) ( )úû
ùêë
é--= ò Ñ
ttD
D xedtktx0
2
exp1, !! !
dr
( )
( )
( )úúû
ù
êêë
é÷÷ø
öççè
æ÷÷ø
öççè
æ÷øö
çèæ----=
úúû
ù
êêë
é÷÷ø
öççè
æ÷øö
çèæG--=
úû
ùêë
é÷÷ø
öççè
æ÷øö
çèæ---=
-
Rrerf
Rre
Rkttr
Rr
Rkttr
Rrerf
rRkttr
RrD
D
D
21
21exp1,
2,0
4exp1,
21
4exp1,
22/
2
2
2
22
pr
pr
pr
!
!
!
PEB Reaction-Diffusion Equations
DeprotectionDensity
DeprotectionRateUnits =
tDR =
Diffusion Range= Resist “Blur”
3D:
2D:
1D:
( ) Function Gamma Incomplete , =G ba
è
sec
dnm
Dimensions# =d
AcidDiffusion
02/21/2010 Gallatin SPIE 7070
0 50 100 150 200
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0 50 100 150 200
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
initialacid profile
Gaussian fit(w1/2 = 44.9 nm)
Lorentzian fit( w1/2 = 50.9 nm)
HOST profile
HO
ST F
ract
ion
Lateral Position (nm)
0.00
0.01
0.02
0.03
0.04
0.05
0.06
Numerical Chemical Kinetics Result1D Simulation
1D Analytic Form ~ Area integral of full 3D form
- 100 - 50 50 100
0.05
0.1
0.15
0.2
0.25
0.3
Lateral Position (nm)
Evaluate 1D result
§ Matches full numerical simulation Hinsberg, et. al, SPIE 03
§ And experimental shape Hoffnagle, Opt. Letts. 02
02/21/2010 Gallatin SPIE 7171
10 20 30 40 50 60
0.2
0.4
0.6
0.8
1.0
20 40 60 80
0.2
0.4
0.6
0.8
1.0
( )nmr
( )nmr
( )nmr
nmR 15=5 10 15 20 25 30
0.2
0.4
0.6
0.8
1.0
Dr3Dk Increasing
k Increasing
k Increasing
{ }1006.31101,316.01.0 ,,,,k =
Dr2D
Dr1D
Graphs of DeprotectionDensity
For all 3 Graphs
The value of k and the space dimensionality both have a very strong effect on the effective resist blur.
Kang, et. al., SPIE 6519 (2007)
02/21/2010 Gallatin SPIE 7272
Development
• Highly nonlinear process è Difficult to model in detail
• Algorithms• String algorithm (2D)• Surface algorithm (3D)• Ray algorithm (same idea works in any D)• Cell algorithm• ….
Here we use a naïve simplified version of the “critical ionization criteria”
Surface on which the net deprotection = constant è Resist surface
02/21/2010 Gallatin SPIE 7373
LER Model è RLS Model
Acids
ResolutionDiffusion/deprotection“blur” develops around each acid during PEB
Net DeprotectionDensity = Sum of“blurs” around each acid
Grayscale plot net deprotectiondensity
Resist edge position occurs at a fixed value of deprotection~Critical Ionization
Model
Resist edge with low spatial frequency content
= LER
PEB
SensitivityExposure dose releases acids.Image intensity at position x à Probability of acid release at x
Acid
2D Illustration
Burns,et.al., JVST B 2002
Intensity =1 Intensity =0
Development
Gallatin SPIE 2005
02/21/2010 Gallatin SPIE 7474
Surface depends on the particular values of and
Statistics given by
Average è Smooth resist surface (CD, edge placement, ….)
RMS Fluctuations è Edge roughness = LER
( )å -=n
nDn rra !!ronDeprotectiNet îíì
=
=
releasednot is acid if 0released is acid if 1
positionsPAG
nn
a
r
n
n!
( ) constant=-ån
nsurfaceDn rra !!rResist surface defined implicitly by
nr!
na
îíì
=
=
nnetacid
nPAG
aPrP
for theon distributiy Probabliti for theon distributiy Probabilit !
02/21/2010 Gallatin SPIE 7575
• Average or Mean resist surface is given implicitly by
( ) ( )[ ] ÷÷ø
öççè
æ----== ò
PAG
BaseV surfaceDPAG rEvQrrrd
rr
arrt !!! exp1 constant 3
surfacer!
• Resist edge roughness autocorrelation function
( )( ) ( ) ( )[ ]
( ) ( )( ) ( )[ ]2
3
32
exp
exp1'11',
÷øöç
èæ -¶-
÷÷ø
öççè
æ-----
÷÷ø
öççè
æ÷÷ø
öççè
æ=
^ò
ò
rEvQrErrrd
rEvQrrrrrd
vQrrACF
edgeDV
PAG
BaseedgeDedgeV D
PAGedgeedge
!!!!
!!!!!
!!
ar
rr
arr
ar
Total resist volume
…do the math…
Derivative in direction perpendicular to the edge
02/21/2010 Gallatin SPIE 7676
Model è Make Approximations è LER Scaling Laws
sizeEvQRars
PAG
1LER 1 »3
PAG
1LER 1REvQI
I
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Image
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Resist resolution is better than Image resolution
Image resolution is better than Resist resolution
The scaling laws are approximations to integrals in the full model prediction. Model predicts “bimodal” scaling depending on the relative sizes of the optics and resist blurs.
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ILS1
02/21/2010 Gallatin SPIE 7777
Scaling Laws è Resolution, LER and Sensitivity are tightly coupledModel mixes and hence couples the process steps to LER
1. Exposure: Image intensity ~ Probability distribution for acid release. Acid release positions are statistical è Sensitivity
2. PEB: Acids diffuse and deprotect the resistPEB diffusion range è Resolution (resist “blur”)
3. Development: Spatial distribution of deprotection determines final resist profileLine edge statistics è LER
Dose “Blur “LER
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ModelScalingLaw
02/21/2010 Gallatin SPIE 7878
Rearrange the scaling law
è “The Resolution, LER, Sensitivity (RLS) Tradeoff”
Constant~23 DoseLERBlur ´´
This type of behavior has been found by many researchers:
Lammers, et al., SPIE 2007, Bristol, et al., SPIE 2007, Brainard, et al., SPIE 2004, Gallatin SPIE 2005, ...
For a standard chemically amplified resist and process cannot have blur, LER and dose all small at the same time.
“You can’t always get what you want”… Mick Jagger
02/21/2010 Gallatin SPIE 7979
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LER Model à Analytical form of the PSD
Normalization factor ~ sLER2
Formula below is valid for small k. For large k, compute PSD perturbatively for an analytic solution or do the integral numerically.
PSD “shape”: Depends only on Rb = R2pn
n = Spatial Frequency (cycles/micron)0.1 1 10 100 1000
10- 4
0.001
0.01
0.1
1
R = 30nm
R = 20nm
R = 10nm
Can determine resist parameters from roughness data
• rms roughness à sLER à norm
• Intrinsic resist “blur” R is determined by fitting the analytic PSD “shape” to |FFT(data)|2 / norm
02/21/2010 Gallatin SPIE 8080
Model comparison to recent EUV LER data
• Combined effort of LBL, CNSE, and Rohm and Haas with SEMATECH funding
• Exposures were done on the 0.3 NA MET at Berkeley
• Four different resists with 4 or 5 different base loadings eachResist Names: “5435” “5271” “5496” “EH”
• Features imaged: 50 nm and 60 nm 1-to-1 lines/spaces
• CD and LER data through dose and focus at each base loading
• LER and PSDs computed from average of left and right edge data at each focus, dose, and base loading condition
• LER computed from both filtered and unfiltered PSD data • “Best Dose” is as indicated in the graphs and tables• “Best Focus” is set to 0, by definition
• Resist blur values, R, are fit using the analytical PSD formula: Resist “blur” R is the only fitting parameter
(EUV2D) (MET2D) (Open Source Resist)
02/21/2010 Gallatin SPIE 8181
BestFocus
BestFocus
BestDose
BestDose
LER(unfiltered) R (“blur”)Dose\Focus - 150 - 100 - 50 0 50 100 150
12.8 5.5 8.813.44 8.4 6. 5.2 5.514.11 11.7 4.4 5. 5.1 7.414.82 9.9 5. 4.6 4.6 5.3 8.215.56 6.8 6.3 5. 4. 5.1 5.7 15.816.34 8.4 4.9 4.3 5.2 5.1 14.217.15 10.7 5.2 4.7 4.9 8.218.01 7.3 6.5 6.8 10.7 16.5 23.18.91 14.7 8.6 8.8 11.5 25.
BestDose
Example Result: Resist “5435”, Base Loading G, 50 nm 1-1 lines/spaces
Dose\Focus - 150 - 100 - 50 0 50 100 15012.8 18 1613.44 25 22 20 1714.11 19 20 25 18 1714.82 20 20 18 20 21 2215.56 21 24 21 16 17 19 2516.34 22 17 16 22 18 3017.16 23 25 19 19 3818.01 20 18 29 21 21 2118.91 18 19 24 20 23
Average R = 21. nm
DR = 4. nm rms
BestDose
02/21/2010 Gallatin SPIE 8282
0 5 10 15 20 25 30 350
2
4
6
8
10
12
14
Dose
LER
5435
0 10 20 30 40 50 600
5
10
15
20
Dose
LER
5271
0 5 10 15 20 25 30 350
5
10
15
20
Dose
LER
5496
0 5 10 15 200
5
10
15
Dose
LER
EH
LER data compared to the scaling law
Red = 50 nm dense L/SBlack = 60 nm dense L/SDots = data, Curve = model using measuredvalues of ILS, PAG density, C, Dose, Blur,….
nm
nm
nm
nm
02/21/2010 Gallatin SPIE 8383
0 5 10 15 20 25 30 350
2
4
6
8
10
Dose
LER
5435
0 10 20 30 40 50 600
5
10
15
20
Dose
LER
5271
0 5 10 15 20 25 30 350
5
10
15
Dose
LER
5496
0 5 10 15 200
2
4
6
8
10
12
Dose
LER
EH
LER data compared to the scaling law with saturation effects included
nm
nm
nm
nm
02/21/2010 Gallatin SPIE 8484
0 5 10 15 20 25 30 35051015202530
Dose
Blur
Resist5435
0 10 20 30 40 50 60051015202530
Dose
Blur
Resist5271
0 5 10 15 20 25 30 35051015202530
Dose
Blur
Resist5496
0 5 10 15 20051015202530
Dose
Blur
ResistEH
Blur, R, determined from data PSD’s as a function of sizing dose
nm nm
nm nm
02/21/2010 Gallatin SPIE 8585
5 10 50 100 50010-5
10-4
0.001
0.01
0.1
1
cyclesêmicronR = 21 .3 nm5 10 50 100 500
10-5
10-4
0.001
0.01
0.1
1
cyclesêmicronR = 18 .7 nm
Highest Dose
5 10 50 100 50010-5
10-4
0.001
0.01
0.1
1
cyclesêmicronR = 22 .5 nm5 10 50 100 500
10-5
10-4
0.001
0.01
0.1
1
cyclesêmicronR = 20 .7 nm
5435EUV2D
60 nm
50 nm
Lowest Dose
02/21/2010 Gallatin SPIE 8686
5 10 50 100 50010-5
10-4
0.001
0.01
0.1
1
cyclesêmicronR = 15 .2 nm5 10 50 100 500
10-5
10-4
0.001
0.01
0.1
1
cyclesêmicronR = 16 .2 nm
5 10 50 100 50010-5
10-4
0.001
0.01
0.1
1
cyclesêmicronR = 16 .5 nm5 10 50 100 500
10-5
10-4
0.001
0.01
0.1
1
cyclesêmicronR = 17 .3 nm
60 nm
50 nm
Highest DoseLowest Dose 5271MET2D
02/21/2010 Gallatin SPIE 8787
5 10 50 100 50010-5
10-4
0.001
0.01
0.1
1
cyclesêmicronR = 15 .2 nm5 10 50 100 500
10-5
10-4
0.001
0.01
0.1
1
cyclesêmicronR = 15 .2 nm
5 10 50 100 50010-5
10-4
0.001
0.01
0.1
1
cyclesêmicronR = 16 .5 nm5 10 50 100 500
10-5
10-4
0.001
0.01
0.1
1
cyclesêmicronR = 17 .5 nm
60 nm
50 nm
Highest DoseLowest Dose 5496
02/21/2010 Gallatin SPIE 8888
60 nm
50 nm
5 10 50 100 50010-5
10-4
0.001
0.01
0.1
1
cyclesêmicronR = 19 .8 nm5 10 50 100 500
10-5
10-4
0.001
0.01
0.1
1
cyclesêmicronR = 18 .7 nm
5 10 50 100 50010-5
10-4
0.001
0.01
0.1
1
cyclesêmicronR = 19 .3 nm5 10 50 100 500
10-5
10-4
0.001
0.01
0.1
1
cyclesêmicronR = 20 .8 nm
Lowest Dose Highest DoseEH
02/21/2010 Gallatin SPIE 8989
There is no such thing as incoherent light
• All electromagnetic fields are perfectly coherent all the time.
• “Incoherence” is in the detection of the light not in the light itself
Consequence of the finite bandwidth of the detector.
Coherent è Incoherent è1BandwidthLight
BandwidthDetector >> 1
BandwidthLight BandwidthDetector
<<
SPECKLE
Well known in the speckle and statistical optics communitySee, for example: Goodman, “Statistical Optics”
Loudon, “Quantum Theory of Light”
Implications for Lithography are relatively recent:Rydberg, Bengtsson and Sandstrom, JM3, 2006, Gallatin, 2002, UnpublishedKritsun, et, al., 3Beams, 2008
02/21/2010 Gallatin SPIE 9090
Coherent incoming planewaves superpose to becomea focused spot
Difference between a coherent and an incoherent sum of plane waves.
Incoherent incoming planewaves superpose to become uniform intensity
02/21/2010 Gallatin SPIE 9191
2
Intensity å +-+=n
itiyixin
nnnynxea fwbb
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Intensity ååå +++-+-+ ===n
yixin
n
yixin
iti
n
itiyixin
nynxnynxnnnynx eaeaeea bbbbfwfwbb
222
Intensity ååå ++++-+-+ ===n
iyixin
n
iyixin
ti
n
itiyixin
nnynxnnynxnnnynx eaeaeea fbbfbbwfwbb
Frequencies and Phases the same
Intensity = TimeIndependent focused“spot”
Same frequencyDifferent (random) phases
Intensity = TimeDependent specklepattern
Different frequenciesDifferent (random) phases Þ
Intensity = TimeIndependent specklepattern
Þ
ÞSum of plane waves
02/21/2010 Gallatin SPIE 9292
0 50 100 150 2000
50
100
150
200
0 50 100 150 2000
50
100
150
200
0 50 100 150 2000
50
100
150
200
PupilNA = 1= 20pt radius
mµ4
mµ4
mµ4
mµ4
Grayscale coversall values.(full range)
Same data rescaled toshow details at low intensity
nm193=l
02/21/2010 Gallatin SPIE 9393
0 50 100 150 2000
50
100
150
200
0 50 100 150 2000
50
100
150
200
0 50 100 150 2000
50
100
150
200
0 50 100 150 2000
50
100
150
200
0.5 waveUniform distributionof random wavefronterror
Full Range Grayscale Low intensity grayscale
1.0 waveUniform distributionof random wavefronterror
Same data
Same data
02/21/2010 Gallatin SPIE 9494
0 50 100 150 2000
50
100
150
200
1 wave uniform phase distributionUniform amplitude distribution (0 to 1)
0 50 100 150 2000
50
100
150
200
50 100 150 200
0.01
0.02
0.03
0.04
0.05
0.06
Full Range Grayscale Low intensity grayscale
SameData
Single speckle pattern is 100% contrast
02/21/2010 Gallatin SPIE 959550 100 150 200
0.002
0.004
0.006
0.008
0.01
0.012
50 100 150 200
0.002
0.004
0.006
0.008
0.01
0.012
0 50 100 150 2000
50
100
150
200
0 50 100 150 2000
50
100
150
2000 50 100 150 200
0
50
100
150
200
20 patternaverage
0 50 100 150 2000
50
100
150
200
2040
6080
100
0.002
0.004
0.006
0.008
0.01
0.012
02/21/2010 Gallatin SPIE 9696
0 50 100 150 2000
50
100
150
200
0 50 100 150 2000
50
100
150
200
50 100 150 200
0.01
0.02
0.03
0.04
0 50 100 150 2000
50
100
150
200
0 50 100 150 2000
50
100
150
200
50 100 150 200
0.01
0.02
0.03
0.04
20 patternaverage
02/21/2010 Gallatin SPIE 9797
• Any single speckle pattern has 100% contrast è 100% intensity variation
• Sum of N independent speckle patterns has residual contrast (residual intensity variation)
• For time dependent speckle: N ~ Bandwidth of the Light X Detector Integration Time
Implication for Lithography:
Detector Integration Time = Excimer pulse length X Number of pulses
~ 20nsec X 50 pulses = 10-6 seconds
Illumination Bandwidth = Excimer bandwidth ~ 1pm = 10-3nm è ~1010Hz
410~NÞ
Illumination is not, and cannot be, perfectly uniform!Nonuniformity completely consumes Dose Uniformity Spec of < 1%
speckle"" Residual %1~%100=Þ
N
%1001´»
Ns
02/21/2010 Gallatin SPIE 9898
Chandhok, et. al., SPIE 2007
02/21/2010 Gallatin SPIE 9999
LER weightingfor CD variation
LER impact on Leakage Current
LER è LWR è Gate Length Roughness (GLR) x
( )xL( )( )
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I
xLLxL
dxxLJI
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W
W
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Croon IEDM 02Croon ESSDERC 03
Goldfarb EIPBN 04
Device Parameter
Gate Lengthfluctuates about average
Relativefluctuation
xs2/
~WLER
x
Note: The analysis here retains only the lowest order linear term. If J is highly nonlinear and/or dL/L is not small then can get highly nonlinear dependence of leakage current on LER
02/21/2010 Gallatin SPIE 100100
Can resist LER be fixed??
i.e.,
Can we “break” the RLS tradeoff and get what we want??
Two approaches considered here
1. Anisotropic resist blur
• Only a “What if” analysis…. Feasibility is not determined
2. Higher PAG loading and/or higher Q
02/21/2010 Gallatin SPIE 101101
Simplification…..Assume the following
• Ignore resist absorption è
• Resist line edge oriented along y è
• Image has much higher resolution than the resist
• Assume Gaussian deprotection blur
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relative to ( )rD!r
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Anisotropic resist “blur”
Image Intensity
Deprotection “blur” is NOT Gaussian. Gaussian form is used here only to simplify the analysis.
è The integrals can be done analytically for a Gaussian.
( ) ( ) ( )yxIzyxIrI ,,, ®=!
02/21/2010 Gallatin SPIE 102102
zyx RRR ==è Spherical Deprotection Blur:
zyx RRR~Volume
zyxzyx
zzy
yx
x
RRRRssR
sR~
RsRsR
RsRR
=
®®®
2
2
Volume
è Anisotropic Deprotection Blur:
Fixed Dose/1~Blur Horizontal
/1~
=s
sLER
1³s
z
y
x
s = Scaling Factor
Shrink in x and y Expand in z
Improved LER and resolution
Dose unchanged
Improved LER and resolution
…do the math…Anisotropic diffusion explicitly breaks the RLS tradeoff by improving resolution and LER at fixed Dose
02/21/2010 Gallatin SPIE 103103
1.2 1.4 1.6 1.8 2 2.2 2.4
0.2
0.4
0.6
0.8
1
Anisotropic resist “blur” Numerical results bracket the analytic prediction
s
( )( )1LERsLER
s/1
Surfaces = Resist sidewall topography variation as a function of sAll cases have the same starting distribution of acids in 3D
Upper and lower points indicate range of numerical results
AnalyticPrediction
02/21/2010 Gallatin SPIE 104104
Repeat the analysis for the regime where the resist has better resolution than the image
( )xI
( )xdr
x
Fixed Dose1~Blur Horizontal
Fixed ~
=/s
LERImproved resolution
LER unchanged
…do the math…Anisotropic diffusion breaks the RLS tradeoff by improving the resolution at fixed LER and Dose
Dose unchanged
02/21/2010 Gallatin SPIE 105105
248 nm and 193 nm photons release acids è
EUV photon has 92 eV of energy è
Energy required to release an acid is at most ~ 5 to 6 eV.
Each EUV photon has enough energy to release at least 92 eV/5 eV~18 acids
Using Quantum Yield Q to improve LER
Brainard, et al., SPIE 2004 2~
3/1~
EUV
DUV
QQ è 1 in 3 absorptions results in acid release
è EUV is not close to using its energy efficiently
“acid bottleneck” Neureuther, et al., JVST B 2006
DATA:
BUT Not all acids can be released in the same position è adds blur
• Assume acids are released along random walk path with steps spaced by r -1/3
Q released acids è Extra “exposure” blur r ~ (Q - 1)1/2 r -1/3
02/21/2010 Gallatin SPIE 106106
0.05 0.10 0.15 0.2015
16
17
18
19
20
( ) 3/2222 1~ --+=+ rQRrRRadiusBlurNet
R = Deprotection blur radius= FWHM/2 ~ 15nm
Q =16
Q = 8
Q = 4Q = 2
Clearly want “high” PAG density to avoid significantly increasing blur
Combine deprotection “blur” from each acid with the random walk distribution of released acids à “Net Blur Radius”
Net Blur Radius
(nm)
Photon
Acid
Acid
Acid
Acid
Spatial distribution of Q released acids
AddedBlur(nm)
0
1
2
3
Q = 1 ( )3/# nmPAGr
02/21/2010 Gallatin SPIE 107107
Mechanism for releasing multiple acids per photon:
Expect the dominant pathway for spreading energy out to multiple PAG molecules to be by secondary (Auger) electrons.
50 100 150 200 250
1
2
3
4
5IMFP(nm)
Electron Energy (eV)
Curve shows genericbehavior for PMMAPianetta, X-ray Data Booklet, Section 3.2
Han, et al., JVST B ‘02Drygiannakis, et al., Poster 6519-36
Electrons with energy less than ~25 eV can “travel” far enough to interact with multiplePAGs.
Inelastic Mean Free Path of electronsIn materials
02/21/2010 Gallatin SPIE 108108
Choi, et al., SPIE 2007Leunissen, et al., MNE 2005.
3PAG
11LER 1REvQILS sizear
s »
1. Increasing Q and/or with everything else fixed
LER decreases with Dose and blur fixed
è “breaks” RLS tradeoff
2. Dose E nominally decreases with increasing Q and
LER ~ constant but with decreasing Dose and fixed blur
è “breaks” RLS tradeoff
PAGr
PAGr
DATA è Case 1: Both LER and Dose decrease with increasing PAG loading
02/21/2010 Gallatin SPIE 109109
Question: “Does resist LER really matter???”
• Many process steps between resist patterning and the final device
• These process steps can smooth the edge roughness
See for example:
Palmateer, Sematech report, 1998Jang, et. al., JVSTB 2004Hwang, et. al., JVSTB 2004Goldfarb, et. al., SPIE 2004Prabhu, et. al., SPIE 2004Mahorowala, et. al., SPIE 2005
è So maybe we don’t need to worry about this afterall
02/21/2010 Gallatin SPIE 110110
Thanks for your attention
The End