A new wavelength-scanning two-channel polarization modulation ellipsometer is described, where a photo-elastic modulator is used and the analyzed light is separated into orthogonally polarized beams using a Wollaston prism. Both beams are detected using phototubes whose bias voltage is dynamically controlled for constant dc. The dc from each phototube is measured with a digital voltmeter, and the fundamental and second harmonic of the phototube current are measured using individual lock-in amplifiers. All three of the associated ellipsometric parameters (N = cos2ψ, S = sin2ψ sinΔ, and C = sin2ψ cosΔ) can be determined simultaneously in a single scan. The versatility of the instrument is demonstrated by the determination of the optical functions of Si from 238 to 652 nm (5.3–1.9 eV).
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Values of N, S, C, ψ, and Δ for the Straight through Configuration at Various Photon Energies and Azimuthal Angles of the Modulator and Analyzer; Polarizer–Modulator Azimuthal Angle Set to θb = 45°
E(eV)
θm
θa
N
S
C
ψ
Δ
5.3
22.5
45.0
.0057
.0021
.9920
44.83
0.12
−22.5
45.0
−.0058
.0013
1.0089
45.16
0.07
22.5
−45.0
−.0012
−.0014
.9969
45.03
−0.08
−22.5
−45.0
−.0026
−.0021
1.0003
45.07
−0.12
Zone Averaged
−.0010
.0000
.9995
45.02
0.00
5.0
22.5
45.0
−.0062
.0026
.9962
45.18
0.15
−22.5
45.0
.0025
.0018
1.0088
44.93
0.10
22.5
−45.0
.0036
−.0013
.9947
44.90
−0.07
−22.5
−45.0
.0011
−.0019
.9992
44.97
−0.11
Zone Averaged
.0000
.0000
.9997
44.99
0.02
4.0
22.5
45.0
−.0038
.0019
.9973
45.11
0.11
−22.5
45.0
.0010
.0014
1.0046
44.97
0.08
22.5
−45.0
−.0014
−.0009
.9980
45.04
−0.05
−22.5
−45.0
−.0026
−.0014
.9993
45.07
−0.08
Zone Averaged
−.0017
.0002
.9998
45.05
0.02
3.0
22.5
45.0
.0002
.0013
.9980
44.99
0.08
−22.5
45.0
−.0024
.0010
1.0053
45.07
0.06
22.5
−45.0
−.0013
−.0009
.9988
45.04
−0.05
−22.5
−45.0
−.0037
−.0011
1.0005
45.11
−0.06
Zone Averaged
−.0018
.0000
1.0010
45.05
0.01
1.9
22.5
45.0
−.0016
.0008
.9996
45.04
0.05
−22.5
45.0
−.0007
.0007
1.0075
45.02
0.04
22.5
−45.0
−.0033
−.0009
.9976
45.10
−0.05
−22.5
−45.0
−.0057
−.0009
.9998
45.16
−0.05
Zone Averaged
−.0028
−.0001
1.0011
45.08
0.00
Table II
Values of N, S, C, β, ψ, and Δ for Silicon Without Surface Treatment (BEFORE), Taken In the Measurement Configuration at Various Photon Energies and Azimuthal Angles of the Modulator and Analyzer; Polarizer–Modulator Azimuthal Angle set to θb = 45°
E(eV)
θm
θa
N
S
C
β
ψ
Δ
5.3
22.5
45.0
.3589
.8285
−.3523
0.9692
34.13
113.04
−22.5
45.0
.3599
.8291
−.3505
0.9695
34.10
112.60
22.5
−45.0
.3616
.8300
−.3451
0.9689
34.04
112.58
−22.5
−45.0
.3615
.8336
−.3505
0.9739
34.10
112.80
Zone Averaged
.3605
.8303
−.3496
0.9704
34.09
112.76
5.0
22.5
45.0
.3292
.8447
−.3908
0.9873
35.26
114.83
−22.5
45.0
.3294
.8559
−.3954
0.9987
35.15
113.91
22.5
−45.0
.3289
.8485
−.3813
0.9867
35.26
114.20
−22.5
−45.0
.3310
.8597
−.3930
1.0016
35.35
114.57
Zone Averaged
.3296
.8522
−.3901
0.9935
35.26
114.38
4.0
22.5
45.0
.5304
.4921
−.6876
0.9981
28.95
144.41
−22.5
45.0
.5369
.4948
−.6885
1.0036
28.83
144.29
22.5
−45.0
.5314
.4945
−.6811
0.9954
28.87
144.02
−22.5
−45.0
.5361
.4970
−.6884
1.0041
28.87
144.17
Zone Averaged
.5337
.4946
−.6864
1.0003
28.88
144.22
3.0
22.5
45.0
.7596
.1076
−.6398
0.9990
20.25
170.45
−22.5
45.0
.7662
.1074
−.6387
1.0033
20.10
170.45
22.5
−45.0
.7641
.1089
−.6334
0.9985
20.03
170.25
−22.5
−45.0
.7598
.1092
−.6370
0.9975
20.19
170.27
Zone Averaged
.7624
.1083
−.6372
0.9995
20.14
170.35
1.9
22.5
45.0
.9087
.0450
−.4147
0.9999
12.33
173.80
−22.5
45.0
.9135
.0447
−.4144
1.0041
12.26
173.84
22.5
−45.0
.9096
.0453
−.4104
0.9990
12.21
173.70
−22.5
−45.0
.9096
.0454
−.4124
0.9997
12.26
173.72
Zone Averaged
.9103
.0451
−.4130
1.0006
12.26
173.76
Table III
Resultant Angle of Incidence φ and Oxide Thickness (doxide) Determined from the Ellipsometric Angles ψ and Δ at λ = 652.4 nm; Also Shown are the Associated Ellipsometric Parameters N S, and C Defined in Eqs. (2).
N
C
S
ψ
Δ
φ
doxide
1) BEFORE
0.9098
−0.4126
0.0451
12.26°
173.76°
68.80°
2.44 nm
2) BRM
0.9098
−0.4136
0.0343
12.26°
175.26°
68.79°
1.79 nm
3) HF5
0.9108
−0.4125
0.0153
12.19°
177.88°
68.82°
0.67 nm
Table IV
Fractions of a-SIO2 and the Thicknesses of the Layers for the Various Calculations Discussed In the Test; the Real and Imaginary Parts of the Effective Dielectric Functions of the Oxide at λ = 652 nm are Shown, Resulting from the Effective Medium Calculation
Sample
Percent a-SiO2
Oxide Thickness (nm)
<ɛ1>
<ɛ2>
HF5 100
100.0
0.666
2.12
0.00
HF5 80
80.0
0.557
3.29
0.01
HF5 60
60.0
0.579
5.29
0.02
HF5 40
40.0
0.758
8.07
0.05
HF5 30
30.0
0.969
9.66
0.07
HF5 20
20.0
1.409
11.32
0.09
Table V
Resultant Dielectric Functions ∊ at Several Photon Energies of Interest Calculated from the Data Shown In Fig. 8, Corrected for the Oxide Overlayer in Various Ways (see Text)
Values of N, S, C, ψ, and Δ for the Straight through Configuration at Various Photon Energies and Azimuthal Angles of the Modulator and Analyzer; Polarizer–Modulator Azimuthal Angle Set to θb = 45°
E(eV)
θm
θa
N
S
C
ψ
Δ
5.3
22.5
45.0
.0057
.0021
.9920
44.83
0.12
−22.5
45.0
−.0058
.0013
1.0089
45.16
0.07
22.5
−45.0
−.0012
−.0014
.9969
45.03
−0.08
−22.5
−45.0
−.0026
−.0021
1.0003
45.07
−0.12
Zone Averaged
−.0010
.0000
.9995
45.02
0.00
5.0
22.5
45.0
−.0062
.0026
.9962
45.18
0.15
−22.5
45.0
.0025
.0018
1.0088
44.93
0.10
22.5
−45.0
.0036
−.0013
.9947
44.90
−0.07
−22.5
−45.0
.0011
−.0019
.9992
44.97
−0.11
Zone Averaged
.0000
.0000
.9997
44.99
0.02
4.0
22.5
45.0
−.0038
.0019
.9973
45.11
0.11
−22.5
45.0
.0010
.0014
1.0046
44.97
0.08
22.5
−45.0
−.0014
−.0009
.9980
45.04
−0.05
−22.5
−45.0
−.0026
−.0014
.9993
45.07
−0.08
Zone Averaged
−.0017
.0002
.9998
45.05
0.02
3.0
22.5
45.0
.0002
.0013
.9980
44.99
0.08
−22.5
45.0
−.0024
.0010
1.0053
45.07
0.06
22.5
−45.0
−.0013
−.0009
.9988
45.04
−0.05
−22.5
−45.0
−.0037
−.0011
1.0005
45.11
−0.06
Zone Averaged
−.0018
.0000
1.0010
45.05
0.01
1.9
22.5
45.0
−.0016
.0008
.9996
45.04
0.05
−22.5
45.0
−.0007
.0007
1.0075
45.02
0.04
22.5
−45.0
−.0033
−.0009
.9976
45.10
−0.05
−22.5
−45.0
−.0057
−.0009
.9998
45.16
−0.05
Zone Averaged
−.0028
−.0001
1.0011
45.08
0.00
Table II
Values of N, S, C, β, ψ, and Δ for Silicon Without Surface Treatment (BEFORE), Taken In the Measurement Configuration at Various Photon Energies and Azimuthal Angles of the Modulator and Analyzer; Polarizer–Modulator Azimuthal Angle set to θb = 45°
E(eV)
θm
θa
N
S
C
β
ψ
Δ
5.3
22.5
45.0
.3589
.8285
−.3523
0.9692
34.13
113.04
−22.5
45.0
.3599
.8291
−.3505
0.9695
34.10
112.60
22.5
−45.0
.3616
.8300
−.3451
0.9689
34.04
112.58
−22.5
−45.0
.3615
.8336
−.3505
0.9739
34.10
112.80
Zone Averaged
.3605
.8303
−.3496
0.9704
34.09
112.76
5.0
22.5
45.0
.3292
.8447
−.3908
0.9873
35.26
114.83
−22.5
45.0
.3294
.8559
−.3954
0.9987
35.15
113.91
22.5
−45.0
.3289
.8485
−.3813
0.9867
35.26
114.20
−22.5
−45.0
.3310
.8597
−.3930
1.0016
35.35
114.57
Zone Averaged
.3296
.8522
−.3901
0.9935
35.26
114.38
4.0
22.5
45.0
.5304
.4921
−.6876
0.9981
28.95
144.41
−22.5
45.0
.5369
.4948
−.6885
1.0036
28.83
144.29
22.5
−45.0
.5314
.4945
−.6811
0.9954
28.87
144.02
−22.5
−45.0
.5361
.4970
−.6884
1.0041
28.87
144.17
Zone Averaged
.5337
.4946
−.6864
1.0003
28.88
144.22
3.0
22.5
45.0
.7596
.1076
−.6398
0.9990
20.25
170.45
−22.5
45.0
.7662
.1074
−.6387
1.0033
20.10
170.45
22.5
−45.0
.7641
.1089
−.6334
0.9985
20.03
170.25
−22.5
−45.0
.7598
.1092
−.6370
0.9975
20.19
170.27
Zone Averaged
.7624
.1083
−.6372
0.9995
20.14
170.35
1.9
22.5
45.0
.9087
.0450
−.4147
0.9999
12.33
173.80
−22.5
45.0
.9135
.0447
−.4144
1.0041
12.26
173.84
22.5
−45.0
.9096
.0453
−.4104
0.9990
12.21
173.70
−22.5
−45.0
.9096
.0454
−.4124
0.9997
12.26
173.72
Zone Averaged
.9103
.0451
−.4130
1.0006
12.26
173.76
Table III
Resultant Angle of Incidence φ and Oxide Thickness (doxide) Determined from the Ellipsometric Angles ψ and Δ at λ = 652.4 nm; Also Shown are the Associated Ellipsometric Parameters N S, and C Defined in Eqs. (2).
N
C
S
ψ
Δ
φ
doxide
1) BEFORE
0.9098
−0.4126
0.0451
12.26°
173.76°
68.80°
2.44 nm
2) BRM
0.9098
−0.4136
0.0343
12.26°
175.26°
68.79°
1.79 nm
3) HF5
0.9108
−0.4125
0.0153
12.19°
177.88°
68.82°
0.67 nm
Table IV
Fractions of a-SIO2 and the Thicknesses of the Layers for the Various Calculations Discussed In the Test; the Real and Imaginary Parts of the Effective Dielectric Functions of the Oxide at λ = 652 nm are Shown, Resulting from the Effective Medium Calculation
Sample
Percent a-SiO2
Oxide Thickness (nm)
<ɛ1>
<ɛ2>
HF5 100
100.0
0.666
2.12
0.00
HF5 80
80.0
0.557
3.29
0.01
HF5 60
60.0
0.579
5.29
0.02
HF5 40
40.0
0.758
8.07
0.05
HF5 30
30.0
0.969
9.66
0.07
HF5 20
20.0
1.409
11.32
0.09
Table V
Resultant Dielectric Functions ∊ at Several Photon Energies of Interest Calculated from the Data Shown In Fig. 8, Corrected for the Oxide Overlayer in Various Ways (see Text)