Post on 14-Apr-2018
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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)
Absolute Stress-Optical Coefficient q12
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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)
Absolute Stress-Optical Coefficient q11
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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