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

http://nist.gov


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:


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.


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

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es


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…


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es


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

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es

… continued…


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)


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

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es

… and many many many others…


• 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


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.

http://www.euvl.com/summit


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 LER Examples


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


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).


From the 2007 ITRS Roadmap


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


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


( )

( ) ( ) ( ) ( )

( ) ( )

( )

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.


~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.


( ) ( ) ( )

( ) ( )

( ) ( )( )

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


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


- 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


- 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


( ) ( ) ( )

( ) ( ) ( ) ( ) ( )

( )

( ) ( )

( ) ( ) ( )'',

~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


( ) ( ) ( ) ( ) ( )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


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


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


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


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


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


( ) ( ) ( )( )

( ) ( ) ( ) ( )( )( ) ( ) ( ) ( )

( )( )( )

( ) ( )( )

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


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


- 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


1 2 5 10 20 50100200

1.0000.500

0.1000.0500.0100.005

nm


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


( ) ( ) ( )

( ) ( ) ( ) ( )

( )

( )

( ) ( )

( ) ( )( ) ( ) ( )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


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



2 slope loglog -=


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



2 slope loglog -=

x1/ length n correlatio/1 = x x

x


( ) ( )( ) ( ) ( )( ) ( ) ( )

( )( )

( )( )( )

( )( )

( )

( )

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’


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


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


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


AFM measurement of LER Goldfarb, et. al., JVSTB 22 (2004)

Patterned wafer is cleaved and turned on edge

AFM


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


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


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


( ) ( )

( )

( ) ( ) ÷÷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


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=


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


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


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


2 3 4 5 6

6.5

7

7.5

8


2 3 4 5 65.5

6.5

7

7.5


2 3 4 5 6

6.5

7

7.5


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


Edge by Edge 3s


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


193 data from Pawloski, et. al., JM3 2006


SEM noisefloor

SEM noisefloor

EUV Data from Cobb,et. al. SPIE 02.


….“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


LER ~ 1 / Dose1/2

Lots of references…..

For example: from Brainard, et. al., SPIE 2004


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:


LER ~ 1/Image Log Slope =1 / ILS

Lots of references…..

For example: from Pawloski, JM3 2006

NOTESaturation at high ILS

( )( ) ( )( )xI

xxIxxIILS ln/

¶¶

=¶¶

=


( )( )

( ) 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


“Why is LER dominated by low spatial frequencies?”

Pawloski, et. al. JM3, 2006

Cobb, et. al. SPIE, 2002

The key question

Alex Liddle

LERFrequencyContent


Many contributors

• Quantum Mechanics

• Shot Noise

• Chemical Statistics

• Reaction Diffusion Statistics

• Speckle

• Mask Roughness

• Mesoscopic Structure (non-uniformity in resist properties)

• …

What causes LER?


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?


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


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)


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


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


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)


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


( )

( )

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


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”


• 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 =


( ) ( )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


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


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)


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


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


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 !


• 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


Model è Make Approximations è LER Scaling Laws

sizeEvQRars

PAG

1LER 1 »3

PAG

1LER 1REvQI

I

sizeedge

edge

ars ÷

÷ø

öççè

æ

¶»

( )( ) ( )

( ) ( )3PAG

3

2

PAG/nm#density loadingPAG nm/1tyabsorptiviresist nm n volumeinteractioPAG -photon intensity Image

efficiency quantum photons/nm# Size-to-Dose (nm) cknessresist thi (nm) radius blur""on Deprotecti

==

==

==

==

ra

vxIQETR

size

Image

ResistBlur

ImageSlope

Image

ResistBlur

ImageSlope

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.

!"#

ILS1


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

3REvQT

II

sizePAGedgeLER ar

s ÷øö

çèæ¶

» ( )( )

)PAG/nm(# loadingPAG (nm) RangeDiffusion PEB

)(nm n volumeinteractioPAG -photon Efficiency Quantum

nmty Absorptivi nm ThicknessResist

)photons/nm(# Dose Sizing Intensity Image

3PAG

3

1

2

=

==

==

==

=

-

r

a

RvQ

TEI

size

ModelScalingLaw


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


( )( )

( ) ( ) ( )( )( )( ) ( )

( )( ) ( ) úúúú

û

ù

êêêê

ë

é

-+

-+

-

´=

-

bbp

bbp

ppb

bb

bb

RerfR

RerfR

eeR

RnormPSD

RR

214

212

2221

2

2

2

3

22

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


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)


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


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


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


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


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


10-5

10-4

0.001

0.01

0.1

1


5435EUV2D

60 nm

50 nm

Lowest Dose


5 10 50 100 50010-5

10-4

0.001

0.01

0.1

1


10-5

10-4

0.001

0.01

0.1

1


5 10 50 100 50010-5

10-4

0.001

0.01

0.1

1


10-5

10-4

0.001

0.01

0.1

1


60 nm

50 nm

Highest DoseLowest Dose 5271MET2D


5 10 50 100 50010-5

10-4

0.001

0.01

0.1

1


10-5

10-4

0.001

0.01

0.1

1


5 10 50 100 50010-5

10-4

0.001

0.01

0.1

1


10-5

10-4

0.001

0.01

0.1

1


60 nm

50 nm

Highest DoseLowest Dose 5496


60 nm

50 nm

5 10 50 100 50010-5

10-4

0.001

0.01

0.1

1


10-5

10-4

0.001

0.01

0.1

1


5 10 50 100 50010-5

10-4

0.001

0.01

0.1

1


10-5

10-4

0.001

0.01

0.1

1


Lowest Dose Highest DoseEH


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


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


2

Intensity å +-+=n

itiyixin

nnnynxea fwbb

222

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


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


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


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


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


• 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


Chandhok, et. al., SPIE 2007


LER weightingfor CD variation

LER impact on Leakage Current

LER è LWR è Gate Length Roughness (GLR) x

( )xL( )( )

( ) ( )

( ) ÷÷ø

öççè

æ÷÷ø

öççè

æ ¶¶

+=

= ò

xss

d

2//~

0

WLJLJ

I

xLLxL

dxxLJI

GLRI

W

W

Gate

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

( ) ( )xIyxI ®,

( ) ( )xxxI d »

¶¶

relative to ( )rD!r

( )xI( )xdr

x

( )úúû

ù

êêë

é

÷÷ø

öççè

æ++-» 2

2

2

2

2

2

222exp

zyxd

zyxrsss

r !

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

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