The authors are with Ecole Nationale Superieure de Physique de Marseille, Laboratoire d’Optique des Surfaces et des Couches Minces, U.A.1120, Domaine Universitaire de St Jerome, 13397 Marseille CEDEX 13, France.
The study of guided waves in a thin layer allows a precise characterization of refractive index and thickness. Optical anisotropy can also be measured. We show how this technique can be applied to the characterization of a multilayer structure.
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Measurement of Anisotropy: TiO2, ZnS, and Ta2O5 Layers Produced by Ion Assisted Depositiona
TiO2
ZnS
Ta2O5
Ta2O5 (IAD)
n1
2.320
2.349
2.119
2.151
n2
2.321
2.351
2.115
2.151
n3
2.357
2.356
2.127
2.155
d(nm)
422.4
506.9
429.9
269.4
Δ31
0.037
0.007
0.008
0.004
Δ32
0.036
0.005
0.012
0.004
Δ21
0.001
0.002
−0.004
0.000
The angle between the normal to the substrate and the direction of the material flux is 19°. Macleod and Horowitz model: values of the three principal indices n1, n2, and n3 (which corresponds to the columnar growth direction). The measured thickness is d and Δ31 = n3 − n1, Δ32 = n3 − n2, and Δ21 = n2 − n1.
Table II
Measurements of Anisotropy of Zinc Sulfide Layers Simultaneously Deposited on Four Different Substratesa
deposition angle (degrees)
0
19
25
32
n1
2.351
2.349
2.348
2.349
n2
2.351
2.351
2.349
2.351
n3
2.356
2.356
2.355
2.358
d (nm)
679.2
506.9
410.0
319.5
Δ31
0.005
0.007
0.007
0.009
Δ32
0.005
0.005
0.006
0.007
Δ21
0.000
0.002
0.001
0.002
For each of them, the angle of deposition is given with the measured values of n1, n2, n3, and thickness d.
Table III
Measurements of Anisotropy of Layers of Titanium Oxide Simultaneously Deposited on Three Different Substratesa
Deposition angle
3°
14°
19°
n1
2.241
2.197
2.147
n2
2.238
2.205
2.160
n3
2.292
2.264
2.223
d (nm)
802.0
490.0
476.0
Δ31
0.051
0.067
0.076
For each of them, the angle of deposition is given with the measured values of n1, n2, n3, and thickness d.
Table IV
Measurements of Anisotropy of Titanium Oxide Layersa
sample
C (3°)
B (14° − 24°)
A (19°)
n1
2.276
2.230
2.167
n2
2.258
2.210
2.169
n3
2.306
2.266
2.232
d (nm)
770.
467.
473.
Δ31
0.030
0.036
0.065
See Fig. 5. Substrates A and B rotate around the LN axis, C is in a fixed position. Δ31 strongly depends on deposition conditions; a noticeable reduction is obtained when the substrates rotate during deposition.
Table V
Determination of Anisotropy of a TiO2 Layer Sandwiched Between SiO2 Layers; The Angle of Incidence of the Vapor Flux is 19°
stack
indices and thicknesses
anisotropy
glass L 6H
n1 = 2.238
Δ31 = 0.062
n2 = 2.246
Δ32 = 0.054
n3 = 2.300
Δ21= 0.008
d = 444.4 nm
glass 6H
n1 = 2.233
Δ31 = 0.069
n2 = 2.245
Δ32 = 0.057
n3 = 2.302
Δ21 = 0.012
d = 448.7 nm
glass 6H L
n1 = 2.246
Δ31 = 0.055
n2 = 2.252
Δ32 = 0.049
n3 = 2.301
Δ21 = 0.006
d = 447.1 nm
glass L 6H L
n1 = 2.247
Δ31 = 0.055
n2 = 2.256
Δ32 = 0.046
n3 = 2.302
Δ21 = 0.009
d = 445.2 nm
Table VI
Triple Halfwave Filter Characterized by Guided Wavesa
Mode
Theoretical value (degrees)
Experimental result (degrees)
0
0.18
1
0.24
0.55
2
0.27
3
11.61
12.22
4
12.64
13.30
5
16.58
17.15
6
17.19
18.10
7
21.25
21.18
8
24.12
23.88
9
32.06
no detectable
10
35.05
35.78
11
38.6
39.13
Theoretical and measured values of the angles synchronous to the propagating TE modes. Perfect quarter-wave layers are assumed with nH = 2.37 and nL = 1.49.
Tables (6)
Table I
Measurement of Anisotropy: TiO2, ZnS, and Ta2O5 Layers Produced by Ion Assisted Depositiona
TiO2
ZnS
Ta2O5
Ta2O5 (IAD)
n1
2.320
2.349
2.119
2.151
n2
2.321
2.351
2.115
2.151
n3
2.357
2.356
2.127
2.155
d(nm)
422.4
506.9
429.9
269.4
Δ31
0.037
0.007
0.008
0.004
Δ32
0.036
0.005
0.012
0.004
Δ21
0.001
0.002
−0.004
0.000
The angle between the normal to the substrate and the direction of the material flux is 19°. Macleod and Horowitz model: values of the three principal indices n1, n2, and n3 (which corresponds to the columnar growth direction). The measured thickness is d and Δ31 = n3 − n1, Δ32 = n3 − n2, and Δ21 = n2 − n1.
Table II
Measurements of Anisotropy of Zinc Sulfide Layers Simultaneously Deposited on Four Different Substratesa
deposition angle (degrees)
0
19
25
32
n1
2.351
2.349
2.348
2.349
n2
2.351
2.351
2.349
2.351
n3
2.356
2.356
2.355
2.358
d (nm)
679.2
506.9
410.0
319.5
Δ31
0.005
0.007
0.007
0.009
Δ32
0.005
0.005
0.006
0.007
Δ21
0.000
0.002
0.001
0.002
For each of them, the angle of deposition is given with the measured values of n1, n2, n3, and thickness d.
Table III
Measurements of Anisotropy of Layers of Titanium Oxide Simultaneously Deposited on Three Different Substratesa
Deposition angle
3°
14°
19°
n1
2.241
2.197
2.147
n2
2.238
2.205
2.160
n3
2.292
2.264
2.223
d (nm)
802.0
490.0
476.0
Δ31
0.051
0.067
0.076
For each of them, the angle of deposition is given with the measured values of n1, n2, n3, and thickness d.
Table IV
Measurements of Anisotropy of Titanium Oxide Layersa
sample
C (3°)
B (14° − 24°)
A (19°)
n1
2.276
2.230
2.167
n2
2.258
2.210
2.169
n3
2.306
2.266
2.232
d (nm)
770.
467.
473.
Δ31
0.030
0.036
0.065
See Fig. 5. Substrates A and B rotate around the LN axis, C is in a fixed position. Δ31 strongly depends on deposition conditions; a noticeable reduction is obtained when the substrates rotate during deposition.
Table V
Determination of Anisotropy of a TiO2 Layer Sandwiched Between SiO2 Layers; The Angle of Incidence of the Vapor Flux is 19°
stack
indices and thicknesses
anisotropy
glass L 6H
n1 = 2.238
Δ31 = 0.062
n2 = 2.246
Δ32 = 0.054
n3 = 2.300
Δ21= 0.008
d = 444.4 nm
glass 6H
n1 = 2.233
Δ31 = 0.069
n2 = 2.245
Δ32 = 0.057
n3 = 2.302
Δ21 = 0.012
d = 448.7 nm
glass 6H L
n1 = 2.246
Δ31 = 0.055
n2 = 2.252
Δ32 = 0.049
n3 = 2.301
Δ21 = 0.006
d = 447.1 nm
glass L 6H L
n1 = 2.247
Δ31 = 0.055
n2 = 2.256
Δ32 = 0.046
n3 = 2.302
Δ21 = 0.009
d = 445.2 nm
Table VI
Triple Halfwave Filter Characterized by Guided Wavesa
Mode
Theoretical value (degrees)
Experimental result (degrees)
0
0.18
1
0.24
0.55
2
0.27
3
11.61
12.22
4
12.64
13.30
5
16.58
17.15
6
17.19
18.10
7
21.25
21.18
8
24.12
23.88
9
32.06
no detectable
10
35.05
35.78
11
38.6
39.13
Theoretical and measured values of the angles synchronous to the propagating TE modes. Perfect quarter-wave layers are assumed with nH = 2.37 and nL = 1.49.