“Shot Noise” - IEUVIieuvi.org/TWG/Resist/2008/022808/GMG-080228-ShotNoiseLER022808.pdfLER 5435 0...

02/28/08 Gallatin 1

“Shot Noise”

G. Gallatin

02/28/08 Gallatin 2

02/28/08 Gallatin 3

02/28/08 Gallatin 4

02/28/08 Gallatin 5

02/28/08 Gallatin 6

02/28/08 Gallatin 7

Probability distribution for absorbing a photon and releasing an acid ~ Image intensity

Probability for releasing a fixed number of acids ( ) ( ) ( ) ( )NN rPrPrPrrrPr

Lrrr

Lrr

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

� a << A

Probability of getting n acids in area a << A

“Shot noise for free”Consistent with quantum mechanics

� Interference patterns build up one absorption at a time

Even with the net number of acids fixed on the macr oscale get “shot noise”on the microscale.

02/28/08 Gallatin 8

LER Model � 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 � Probability of acid release at x

Acid

2D Illustration

Burns,et.al., JVST B 2002

Intensity =1 Intensity =0

Development

Gallatin SPIE 2005

02/28/08 Gallatin 9

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

EvQ

trIrE

rEvQrtrIvQrtr

trI

v

Q

TT

trrrIvQtrrIvQt

tr

trrtr

trtr

==⇒===

−−=−−=

×==

====−=

−==∂

∂

−=

=

α

αραρρ

αα

ρραραρ

ρρρ

ρ

rr

rrrrr

r

rrrrrr

rrr

rr

(Only PAGs within volume v surrounding the position of absorption can be affected)

02/28/08 Gallatin 10

Exposure Statistics

Previous slide � Exposure is deterministic. IT IS NOT

Quantum Mechanics � Probability of photon absorption ~ Image Intensity

( )

( )( )( )

( ) ( )( ) ( )

( ) ( ) ( ) ( )NNacidacidacidNN

net

acid

rCE

a

rCE

aacid

rCE

rCE

Acid

arParParParararP

eearP

r

a

a

er

er

tr

,,,,,,,,,

ondistributiy probabilitNet

1,

at generated be toacidan for on distributiy Probabitit

released NOT acid 0

released acid 1Let

position at acidan release not toPAG a ofy Probabilit

1position at acidan release PAG to a ofy Probabilit

yprobabilit a as dinterprete be should ,

22112211

0,1,

rL

rrrL

rr

r

r

r

r

r

rr

r

r

=

+−=

⇔=⇔=

=

−=

−−

−

−

δδ

ρ


( )

( ) 0,

umresist vol theinto loaded moleculesPAG ofnumber total the

sPAG' allfor on distributiy probabilitJoint

1 PAG onefor on distributiy Probabilit

me with voluanywhere becan PAG Each

umeresist vol t the throughouddistributeuniformly moleculesPAG Consider

ondistributiy probabilitlocation PAG eon with thdistributi release acid thecombine toNeed

AT

N

V

Nr

ATVN

ATVPN

V

V

N

PAG

NN

PAG

==⇒

==

===⇒

=⇒

−−

rρ


Constant Dose “Blur “LER

Also get…

• The explicit analytic form for the deprotection distribution around a released acid.

• The spatial frequency content (on average) of the roughness.

RLS TradeoffePAGs/volum#

volume

ninteractio Acid-Photon

RangeDiffusion PEB

Efficiency Quantum

tyAbsorptivi

Dose

Intensity Image

exposure

=

=

==

==

=×==

PAG

v

DtR

Q

tIE

I

ρ

α

LER Model

Result:

Put all the pieces together….do the math to get approximate scaling law……

3

1

REvQI

Ic

sizePAGedge

LER αρσ

∂≈

Intrinsic Resist “Blur”

( ) ( )[ ]( )( ) ( ) ( )[ ]( )2'3

232

'exp'

'exp111

rQvErErrrd

rQvErrrd

QvsDV

sDV

PAG

LERPAG

Base

rrrr

rrr

αρ

αραρ

σ ρρ

−∂−′∫

−−−−′∫

=

⊥′

′


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

Fra

ctio

n

Lateral Position (nm)

0.00

0.01

0.02

0.03

0.04

0.05

0.06

Numerical Chemical Kinetics Result

1D 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


( ) ( )

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

( )( ) ( )

−+

−+

−

×=

−

ββπββπ

ππβ

ββ

ββ

RerfR

RerfR

eeR

RnormPSD

RR

214

212

2221

2

2

2

3

22

LER Model � Analytical form of the PSD

Normalization factor ~ σLER2

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 Rβ = R2πν

ν = ν = ν = ν = 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 � σLER � norm

• Intrinsic resist “blur” R is determined by fitting the analytic PSD “shape” to |FFT(data)|2 / norm


5 10 50 100 50010- 5

10- 4

0.001

0.01

0.1

1

cycles�micronR =21.3 nm

5 10 50 100 50010- 5

10- 4

0.001

0.01

0.1

1


Highest Dose

5 10 50 100 50010- 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


5435EUV2D

5435EUV2D

60 nm

50 nm

Lowest Dose


5 10 50 100 50010- 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


5 10 50 100 50010- 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


60 nm

50 nm

Highest DoseLowest Dose 5271MET2D

5271MET2D


5 10 50 100 50010- 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


5 10 50 100 50010- 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


60 nm

50 nm

Highest DoseLowest Dose 54965496


60 nm

50 nm

5 10 50 100 50010- 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


5 10 50 100 50010- 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


Lowest Dose Highest DoseEHEH


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, Dill-C, Dose, Blur,….

nm

nm

nm

nm

3

11

REvQILSc

sizePAG

LER αρσ ≈

2≈c

EUV2DEUV2D MET2DMET2D

“A”“A” “B”“B”


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

sizeEvQ

sizePAGedge

LEReREvQI

Ic ααρ

σ −

∂≈

3

1

5.1≈c

“A”“A” “B”“B”

EUV2DEUV2D MET2DMET2D


0 1 2 3 4 5

2

4

6

8

10

“Shot Noise” - IEUVIieuvi.org/TWG/Resist/2008/022808/GMG-080228-ShotNoiseLER022808.pdfLER 5435 0...

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