flare calculation on euv optics - sematech€¦ · · 2009-10-29flare calculation on euv optics...

Oct. 21, 2009 2009 EUVL Symposium @ Prague, Czech Republic

Flare Calculation on EUV Optics

Masayuki Shiraishi*Tetsuya Oshino*, Katsuhiko Murakami*, Hiroshi Chiba**

* 2nd Development Department** Optical Design DepartmentDevelopment HeadquartersPrecision Equipment Company

Precision Equipment Company

NIKON CORPORATION2nd Development department

Nikon Corporation Oct. 21, 2009 2009 International Symposium on Extreme Ultraviolet Lithography 2

OverviewOverview

Flare treatmentDefinition and notationConventional methodNew method

Multilayer extinct effectObscuration of scatterCombine PSFs not via system-PSDTwo PSFs, for flare and TIS

Results of flare evaluationPO #1 – Kirk flare test, flare correction (OPC)PO #2 – Kirk flare test



OverviewOverview






Definition and notationDefinition and notationImage Intensity

{ }

∫∫∞

′′′−+−=

⊗+−=

⊗+−=

xdxIxxPSFxITIS

xIxPSFxITIS

xIxPSFxTISxI

SC

SC

SC

rrrrr

rrr

rrrr

)()()()1(

)()()()1(

)()()()1()(

00

00

0δ PSFSC

(1–TIS)δ

PSFFlare

I(x): Flared image intensityI0(x): Original intensityTIS: Total integrated scatterPSFSC: PSF contributing flare; component reaching wafer

∫∫∫∞∞

⋅== drrPSFrxdxPSFTIS SCSC )(2)( 00 πrr

PSFSC0: PSF contributing flare; component as scattered, PSFSC≠

Uniform intensitydecrease Image blur

derived from PSDs

TIS

PDFxITIS ⋅+−= )()1( 0r

DC-flare modelF: DC flarePD: pattern density



Definition and notationDefinition and notationFlare

Kirk flare (KF)

∫∫ −=fieldbright

00 )()( xdxxPSFxF SC rrrr

ID(xD): Intensity at dark pad xDIB(xB): Intensity at bright area xB

⎪⎪⎩

⎪⎪⎨

⎧

−+−=

−=

=∫∫

∫∫

fieldbright

fieldbright

max

min

)()1()(

)()( ,

xdxxPSFTISxI

xdxxPSFxI

IIKF

BSC

BB

DSC

DD

B

Drrrr

rrrr

0

1

x

Inte

nsity

IDIBFlare effect on image can be expressed using TIS & PSFSC.

“Kirk flare”, which can be experimentally observed as an intensity ratio (= dimensionless), does not equal to “flare.”



OverviewOverview






Conventional methodConventional methodFlare calculation from power spectral density (PSD)

)(,),(),( 662211 fPSDfPSDfPSD L

∑=

=6

1

2 )()(i

iiii fPSDfSystemPSD αα

∫ ⋅= drrFrFlare )(2π

equivalent system PSD on pupil

PSF by scattering

Mirror PSDs

⎟⎠⎞

⎜⎝⎛

⎟⎠⎞

⎜⎝⎛=≡

zrSystemPSD

zrPSFrF SC

λλπ 2

24)()(

Problems:- No scatter extinction effect- No obscuration effect- Linear conversion twice(small angle approximation)

- PSF domain limited at afinite distance (not infinity)

- Same PSF for flare & TIS

zrf i

ii ≈≈θλ

∫∞

⋅= drrFrTIS )(2π

r in bright area

Not adequate at a larger scatter angle

Not adequate at alarger scatter angle

“Flare” componentshould be calculatedfrom another PSF,not as-scattered.

This infinite integrationcannot be carried outunder linear domainconversion.



OverviewOverview


Multilayer extinct effectObscuration of scatterCombine PSF not via system-PSDTwo PSFs, for flare and TIS




New method: TISNew method: TISTIS calculation from power spectral density (PSD)


⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

+′⎟

⎟⎠

⎞⎜⎜⎝

⎛′=

22

2

20 4)()(

rz

rDPSz

rrFi

ii

iiλλ

πβ

∫∞

⋅= drrPSFrTIS SC )(2 0π

Mirror PSFs

∑=

=6

1

00 )()(i

iSC rFrPSF

Mirror PSDs

PSF by scattering, component as scattered

Non-linear conversion,not via the SystemPSD.

)()()( iiiiii ExtfPSDfDPS θ⋅=′ Scatter extinction by ML

)sin( iif θλ =

Consideration:- Scatter extinction effect included- Approximation released partially(esp. between finite and infinite)

- Not via system PSD



New method: FlareNew method: FlareFlare calculation from power spectral density (PSD)


⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

+′′⎟

⎟⎠

⎞⎜⎜⎝

⎛′′=

22

2

24)()(

rz

rDPSz

rrFi

ii

iiλλ

πβ

∫ ⋅=areabright in

)(2r

SC drrPSFrFlare π

∑=

=6

1)()(

ii

SC rFrPSF

)()()()( iiiiiiii ObsExtfPSDfDPS

Mirror PSDs

Mirror PSFs

PSF by scattering, component reaching wafer

θθ ⋅⋅=′′

Scatter extinction by ML

Non-linear conversion

Obscuration

)sin( iif θλ =

Flare component on wafer

Consideration:- Obscuration effect included- Separate PSF for flare and TIS



Multilayer extinct effectMultilayer extinct effectScatter extinction by interference in multilayers (MLs) E.M.Gullikson, SPIE 3331

EUV scatter on MLEUV reflection on ML

spec

ular

scattered

substrate

multilayersincidence

incidence incidence

phase matched,peak reflectivity phase

mismatched,extinct

phase matched,peak reflectivity

spec

ular

specular

phase

mism

atched,

extinct

log (scatter), no ML ML extinct coeff.log (extinct * scatter)



Obscuration of scatterObscuration of scatterObscuration ratio (of component reaching wafer to as-scattered component)

Wafer

static field

Mirrorscattered light,not reaching wafer

scatter loss

scattered light,reaching wafer(within static field)

scattered light, reaching wafer(outside static field)

scatter ray tracing5,000,000 rays were thrown away

from the light source per condition.Internal obscuration was modeled.About 1,500,000 rays reached the

exposure field on the reticle plane.Each ray created scatter light on

each PO mirror in random direction at each scatter angle (including specular lights, of course 100% of them can reach wafer).

Total ~1 billion rays were thrown away. “Obscuration ratios”(how many scatter rays, out of rays leaving reticle, reach wafer) for each scatter angle for each PO mirror were obtained.

internalobscuration

Internal obscuration: apertures, mechanics, mirror coating areas and a flare stop.



Combine PSF not via system PSDCombine PSF not via system PSDConventional conversion

M1 PSDM2 PSDM3 PSDM4 PSDM5 PSDM6 PSD

SystemPSDon pupil Flare PSF

TISImage Calc.,Kirk Flare, ...

New conversionML extinct

M1 PSF’TIS

Image Calc.,Kirk flare, ...

Obscuration

M1 eq.PSD’

PSFSC

M1 PSF’’M1 eq.PSD’’

PSFSC0

M6 PSF’M6 eq.PSD’

M6 PSF’’M6 eq.PSD’’

......

......

linear linearsame PSF

non-linear

different PSF

equivalent PSD Mirror PSF Flare PSF

M1 PSDM2 PSDM3 PSDM4 PSDM5 PSDM6 PSD

not via systemPSD



Two PSFs, for flare and TISTwo PSFs, for flare and TISTIS and PSFSC are derived from PSFSC0

∫∫∞

≡ xdxPSFTIS SC rr)(0

Wafer

static field

Mirrorscattered light,not reaching wafer

scatter loss

scattered light,reaching wafer(within static field)

scattered light, reaching wafer(outside static field)

internalobscuration

0SCPSFPSF as scattered:created from mirror PSDs

TIS is obtained by integrationof this to infinity.

SCPSF

total integration(constant)ap

ply

all o

bscu

ratio

nsPSF as reaching wafer:applied all obscurations’effect to PSFSC0

convolution with I0(x). characteristic of PO



OverviewOverview






EUV1 PO #1 flare evaluationEUV1 PO #1 flare evaluationKirk-flare measurement By courtesy of Selete

Kirk flare measurement and calculation agree well with each other by ~1% error.

Kirk flare

0%

2%

4%

6%

8%

10%

12%

14%

16%

18%

20%

0.1 1 10dark pad's radius [um]

Kirk

Fla

re [%

]

Calculation (outer 26x2mm)Experiment (outer 26x2mm)Calculation (outer 200um dia.)Experiment (outer 200um dia.)

For the smallest pad, the apparent flare seems to be affected also by wavefront error. (~1%)



EUV1 PO #1 flare evaluationEUV1 PO #1 flare evaluationPrinted CD variation By courtesy of Selete

CD variation with flare canbe precisely predicted usingflare PSF and TIS.

H. Aoyama et al., Jpn. J. Appl. Phys., 48 (2009) 056510.on dark area

on clear area

calculation also including mask CD and resist blur effect



EUV1 PO #1 flare evaluationEUV1 PO #1 flare evaluationFVC evaluation on PL test site By courtesy of Selete/Toshiba

H. Aoyama et al., Proc. SPIE 7271 (2009) 72712D.

Flare variation compensation (FVC) based on flare PSF and TIS has +/– 2nm CD error in the range of 22%~65% pattern density.

hp 35nm

22% 36% 50% 65%Pattern density:

corn

erce

nter

Mask target size with FVC

FVC evaluation

Raw PSF and multi-fractal function

Top view of SEM images

full chip

flare mapping& mask resizingwith EDA



EUV1 PO #2 flare evaluationEUV1 PO #2 flare evaluationKirk-flare measurement By courtesy of Intel

Calculated Kirk-flare value is 7.4% at the center of field.

This variation includes mask contrast variation of ~1%and the illumination non-uniformity.

*Additional details are on Intel’s poster presented by Yashesh Shroff on EUV1 static imaging.(“Static Test Evaluation of EUV1 Full-Field Exposure Tools”)

2um pad in bright field



SummarySummary

New calculation method of flare PSF and TIS is developed.

Using flare PSF and TIS obtained by our new method,

actual flare behavior can be well predicted.

Parameters characteristic of PO are flare PSF and TIS,

which should be separately provided.

(TIS should not be obtained by integrating provided PSF.)

Acknowledgements

H. Aoyama, K. Tawarayama, Y. Tanaka and I. Mori (Selete), providingprecious flare evaluation data on Kirk-flare tests and on PL test site evaluation.Y. Nakajima and R. Inanami (Toshiba), PL test site design and evaluation.A. Myers, Y. Shroff (Intel), providing precious flare evaluation data.M. Nakajima (Nikon), throwing billions of scatter rays for months.



Thank you.

flare calculation on euv optics - sematech€¦ · · 2009-10-29flare calculation on euv optics...

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