Obtencion Del Coeficiente de Tension Optico

7/27/2019 Obtencion Del Coeficiente de Tension Optico

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Stress-Optical Coefficients of

157 nm Materials

John H. BurnettNational Institute of Standards and Technology

Gaithersburg, Maryland

Support from SEMATECH

SEMATECH 157nm Technical Data Review, 11 December 2001, Orlando, Florida


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Stress-Optical Coefficients at 157 nm

Need to determine effect of grown-in stress on optical properties Need to calculate the effect of external stress

Unknown for CaF2, BaF2, and any other material in the VUV

Effect of stress ij on optical properties given by:

1( )ij ijkl kl K q = ( 1( )i ij jK q = abbreviated notation)

ijklq piezo-optic tenser (4th rank)

For cubic crystals with fluorite structure Fm3m (classes 43m,432,m3m)

Crystal symmetry 36 components 3 independent components: 11 12 44, ,q q q

11 12 12

12 11 12

12 12 11

44

44

44

0 0 0

0 0 0

0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

ij

q q q

q q q

q q qq

q

q

q

=


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PE

q44 kE 111

q12 k 100E

P

q11

P

k

E

100

n||n | = (n /2) q44 P [111]_ 3

n | = (n /2) q12 P [100]3_

n|| = (n /2) q11 P [100]3

[100]

[010]

[001]

n

For uniaxial stress in direction $ " " "1 2 3sin cos sin sin cosn x x x = + +

1 2 2 2 2 2

1 11 12

1 2 2 2 2 22 11 12

1 2 2

3 11 12

1

4 44

1

5 44

1 2

6 44

( ) sin cos (sin sin cos )

( ) sin sin (sin cos cos )

( ) cos sin

( ) sin cos sin

( ) sin cos cos

( ) sin sin cos

K q q

K q q

K q q

K q

K q

K q

+ +

+ + +

=

But for stress along cube axes and cube diagonals, index uncouples coefficients:


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Uniaxial Stress Apparatus


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electrodelessdischage lamp

(Hg and Xe)

paralobicmirror

aperture

sample

stressapparatus

ground glassdiffuser plate

cameralens

CCD camera

video

detector

motor

filter

Rochon

linearpolarizer

aperture

Rochon

linearpolarizer

crossedpolarized

aperture beamsplitter

aperture

shutter

chopper

paralobic

mirror

lock-in amplifier

spherical

collectionmirror

to chopper

(q11 - q12) = (N/P)2/tn [100]

q44 = (N/P)2/tn [111]3

3

Stress-Induced Birefringence


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60 0 5 00 400 300 200 100

0.00 E+000

-1.00E-012

-2.00E-012

-3.00E-012

-4.00E-012

-5.00E-012

CaF2

MFS

BaF2

Stress-OpticalCoefficient(q11-q12

)(Pa

-1)

Wavelength (nm)

Stress Birefringence Constant q11-q12


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600 500 400 300 200 100

0.00E+000

2.00E-013

4.00E-013

6.00E-013

8.00E-013

1.00E-012

1.20E-012

1.40E-012

1.60E-012

CaF2

BaF2

Stress-OpticalC

oefficientq

44

(Pa

-1)

Wavelength (nm)

Absolute Stress-Optical Coefficient q44


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electrodelessdischage lamp

(Hg and Xe) shutter filterRochon

polarizer

flat mirror/reflection

filter

flat mirror

spherical

focusingmirror

aperture

sphericalcolumnatingmirror

beam

splitter

sample

stressapparatus interferometer

flat mirror

beam splittercompensator

sample

compensator

interferometer

flat mirror

beam splitter

phospher plate

or ground glassdiffuser

camera

lens

CCD camera

video

sphericalfocusing

mirror

detector

motor

Twyman-Green Interferometer

(N/P) = (2t/) [(n /2) q11{q12} - (n-1)s12]3

fringe shift per unit stress changeshutter

Absolute Stress-Optical Coefficients


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600 500 40 0 300 200 100

1.00E-012

1.20E-012

1.40E-012

1.60E-012

1.80E-012

2.00E-012

2.20E-012

2.40E-012

2.60E-012

2.80E-012

3.00E-012

BaF2

MFS

CaF2

Stress-OpticalCoefficientq12

(Pa

-1)

Wavelength (nm)



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600 500 400 300 200 100

-1 .60E-012

-1 .40E-012

-1 .20E-012

-1 .00E-012

-8 .00E-013

-6 .00E-013

-4 .00E-013

-2 .00E-013

0.00E+000

2 .00E-013

4 .00E-013

6 .00E-013

BaF2

CaF2

MFS

Stress-OpticalCoefficientq12

(Pa

-1)

Wavelength (nm)



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Stress-Birefringence Results

Coefficients

(10-12

Pa-1

)546.38 nm 435.96 nm 365.12 nm 253.73 nm 193.09 nm 156.10 nm

157.63 nm

(linear int.)

CaF2

q11-q12 1.530.02 1.550.02 1.570.02 1.660.02 1.770.02 1.910.05 1.90q11 0.380.06 0.400.06 0.350.05 0.320.05 extrap. 0.3 extrap. 0.3 extrap. 0.3q12 1.150.06 1.150.06 1.220.09 1.340.13 extrap. 1.5 extrap. 1.6 extrap. 1.6

q44 0.750.010 0.740.01 0.740.01 0.730.01 0.660.01 0.450.01 0.46

BaF2

q11-q12 3.100.03 3.150.03 3.210.03 3.440.03 3.710.04 4.420.04 4.39

q11 0.930.10 0.970.10 1.080.15 1.410.20 extrap. 1.7 extrap. 2.4 extrap. 2.4q12 2.170.10 2.180.10 2.130.15 2.030.20 extrap. 2.0 extrap. 2.0 extrap. 2.0

q44 0.990.02 1.010.02 1.010.02 1.040.02 1.080.02 1.310.02 1.30

mSiO2

q11-q12 2.340.022 2.370.02 2.410.02 2.550.02 2.760.03 3.040.03 3.03q11 0.330.10 0.220.10 0.110.15 0.200.15 extrap. 0.4 extrap. 0.8 extrap. 0.8q12 2.670.1.0 2.590.10 2.520.15 2.350.20 extrap. 2.3 extrap. 2.2 extrap. 2.2


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Summary

We have determined the complete set of stress-optical coefficients needed todetermine the effect of stress on the index of CaF2, BaF2, and a form of VUV

fused silica:

(q11

-q12

) and q44

from the visible through 156 nm

q11 and q12 from the visible through 254 nm

To obtain these we built a Twyman-Green interferometer that operates onatomic spectral lines from the visible through the fused silica beam splitter

cutoff near 200 nm.

Using our new CaF2beam splitter will allow measurements down to below157 nm ( by Jan. 2002.)

To Do: Measure the absolute coefficients q11 and q12 for CaF2, BaF2, and fused silicaat 157 nm (Jan. 2002)

Measure the stress-optical coefficients for other important VUV materials,

including SrF2, LiF, and possibly mixed crystals

Obtencion Del Coeficiente de Tension Optico

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