Julio R. Blanco and Patrick J. McMarr, "Roughness measurements of Si and Al by variable angle spectroscopic ellipsometry," Appl. Opt. 30, 3210-3220 (1991)
Rough surfaces of silicon and aluminum have been studied by rotating analyzer spectroscopic ellipsometry (RASE). The roughness of a silicon sample similar to that used for the RASE measurements was also studied by cross-sectional transmission electron microscopy. Total integrated scattering was measured on the aluminum specimens to obtain numerical estimates of the rms roughness. The ellipsometry measurements on these specimens were carried out at a number of angles of incidence in the 30–80° range and at a number of discrete wavelengths in the 300–650-nm spectral range. The RASE results were then analyzed using the Bruggeman effective-medium theory for the Si sample and scalar diffraction theory for the Al samples. This study shows that 70° is the optimum angle of incidence for characterizing the roughness of these Al surfaces using RASE. It also demonstrates the self-consistency of the Bruggeman theory with angular variation for the Si sample. The need for a vector diffraction theory for the interpretation of the rms roughness using ellipsometric angles Δ and Ψ is discussed.
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Total Integrated Scattering and rms Roughness Calculated from TIS = 1 − exp[−(πσ/λ)2]a
Sample
TIS
rms Roughness (nm)
R-1B
1.20 ± 0.16 × 10−3
1.74 ± 0.12
R-2B
8.69 ± 0.61 × 10−4
1.49 ± 0.05
R-3B
1.37 ± 0.15 × 10−3
1.86 ± 0.10
R-4B
2.49 ± 0.66 × 10−3
2.52 ± 0.31
R-5B
7.60 ± 0.68 × 10−3
4.39 ± 0.20
R-6B
6.71 ± 0.47 × 10−3
4.13 ± 0.14
R-7B
1.43 ± 0.06 × 10−2
6.02 ± 0.15
R-8B
2.37 ± 0.07 × 10−2
7.76 ± 0.15
R-9B
5.74 ± 0.56 × 10−2
12.1 ± 0.7
R-1OB
1.53 ± 0.05 × 10−1
19.7 ± 1.2
R-11B
1.03 ± 0.03 × 10−1
16.2 ± 0.7
R-12B
3.02 ± 0.18 × 10−1
27.7 ± 3.6
R-13B
1.89 ± 0.28 × 10−1
21.9 ± 3.0
R-14B
3.12 ± 0.17 × 10−1
28.1 ± 3.7
R-15B
6.21 ± 0.11 × 10−1
39.7 ± 10.6
σ is the rms roughness and λ is the wavelength of light. The measurement was performed at a wavelength of 632.8 nm.
Table II
Ellipsometric Characterization of the Microroughness of the a-Si sample (Si Single Crystal Implanted with Si lonsa) Using the Bruggeman Effective-Medlum Theory
Angle of Incidence (degrees)
Effective Thickness of Surface Layer deff (nm)
Fraction of Voids fv
Unbiased Estimator ξ
80
4.9 ± 0.7
0.40 ± 0.06
0.011
70
5.4 ± 0.4
0.38 ± 0.02
0.007
60
4.4 ± 0.3
0.48 ± 0.04
0.004
50
5.1 ± 0.3
0.50 ± 0.04
0.003
40
6.4 ± 0.6
0.51 ± 0.06
0.005
30 (model I)
6.8 ± 2.4
0.50 ± 0.07
0.007
Average
5.5 ± 0.8
0.46 ± 0.05
30 (model II)
25.5 ± 1.6
0.85 ± 0.01
0.003
Ion energy 100 keV; implantation direction 〈100〉; ion current 6 μA/cm2; total dose 1 × 1016/cm2.
Table III
Root-Mean-Square Surface Slope (tan β) Derived from Spectroscopic Ellipsometry Measurements at 70° Angle of Incidencea
The values listed are the average over the 300–650-nm wavelength range. Autocovariance length T and factor πT/λ are also listed. T = (σ√2)/tan β; σ is given in Table I.
The average value of λ, 475 nm, was used.
Table IV
Angles Δ and Ψ (In Degrees) Measured by SE for Al Samples R-2B, R-4B, and R-8B as a Function of Wavelength and Angle of Incidence θ
Wavelength (nm)
θ = 30°
θ = 50°
θ = 70°
Δ
Ψ
Δ
Ψ
Δ
Ψ
Sample R-2B
300
165.669
44.480
142.821
43.821
93.039
43.234
330
168.638
44.557
146.118
43.902
99.154
43.202
360
170.155
44.557
149.146
43.908
104.297
43.096
390
171.307
44.572
151.773
43.892
109.128
42.958
420
172.176
44.572
153.844
43.878
113.236
42.830
450
172.947
44.575
155.750
43.862
117.116
42.691
480
173.349
44.565
157.245
43.833
120.348
42.551
510
173.611
44.569
158.622
43.807
123.473
42.411
540
173.836
44.569
159.787
43.782
126.140
42.279
570
173.885
44.569
160.864
43.758
128.699
42.125
600
173.818
44.559
161.752
43.717
130.880
41.962
630
173.899
44.552
162.570
43.671
133.018
41.794
Sample R-4B
300
164.550
44.676
141.216
43.939
92.187
43.232
330
167.201
44.712
145.421
43.984
98.320
43.196
360
168.566
44.699
148.453
43.974
103.499
43.087
390
169.591
44.683
151.074
43.955
108.369
42.952
420
170.328
44.680
153.142
43.936
112.498
42.826
450
170.949
44.677
155.063
43.911
116.413
42.687
480
171.369
44.653
156.530
43.873
119.675
42.546
510
171.509
44.643
157.902
43.840
122.829
42.403
540
171.665
44.622
159.026
43.806
125.526
42.276
570
171.608
44.606
160.100
43.759
128.138
42.122
600
171.516
44.592
160.917
43.705
130.328
41.964
630
171.407
44.571
161.712
43.654
132.472
41.781
Sample R-8B
300
165.094
44.523
141.440
43.599
92.318
42.917
330
167.632
44.579
145.540
43.709
98.329
42.856
360
169.039
44.580
148.510
43.727
103.402
42.756
390
169.981
44.572
151.096
43.725
108.201
42.639
420
170.709
44.579
153.154
43.732
112.290
42.523
450
171.322
44.580
155.024
43.728
116.150
42.391
480
171.726
44.566
156.509
43.707
119.375
42.272
510
171.953
44.569
157.888
43.696
122.495
42.144
540
172.119
44.561
159.029
43.670
125.168
42.016
570
172.205
44.557
160.109
43.658
127.723
41.893
600
172.204
44.539
160.992
43.611
129.917
41.746
630
172.108
44.533
161.784
43.573
132.078
41.564
Tables (4)
Table I
Total Integrated Scattering and rms Roughness Calculated from TIS = 1 − exp[−(πσ/λ)2]a
Sample
TIS
rms Roughness (nm)
R-1B
1.20 ± 0.16 × 10−3
1.74 ± 0.12
R-2B
8.69 ± 0.61 × 10−4
1.49 ± 0.05
R-3B
1.37 ± 0.15 × 10−3
1.86 ± 0.10
R-4B
2.49 ± 0.66 × 10−3
2.52 ± 0.31
R-5B
7.60 ± 0.68 × 10−3
4.39 ± 0.20
R-6B
6.71 ± 0.47 × 10−3
4.13 ± 0.14
R-7B
1.43 ± 0.06 × 10−2
6.02 ± 0.15
R-8B
2.37 ± 0.07 × 10−2
7.76 ± 0.15
R-9B
5.74 ± 0.56 × 10−2
12.1 ± 0.7
R-1OB
1.53 ± 0.05 × 10−1
19.7 ± 1.2
R-11B
1.03 ± 0.03 × 10−1
16.2 ± 0.7
R-12B
3.02 ± 0.18 × 10−1
27.7 ± 3.6
R-13B
1.89 ± 0.28 × 10−1
21.9 ± 3.0
R-14B
3.12 ± 0.17 × 10−1
28.1 ± 3.7
R-15B
6.21 ± 0.11 × 10−1
39.7 ± 10.6
σ is the rms roughness and λ is the wavelength of light. The measurement was performed at a wavelength of 632.8 nm.
Table II
Ellipsometric Characterization of the Microroughness of the a-Si sample (Si Single Crystal Implanted with Si lonsa) Using the Bruggeman Effective-Medlum Theory
Angle of Incidence (degrees)
Effective Thickness of Surface Layer deff (nm)
Fraction of Voids fv
Unbiased Estimator ξ
80
4.9 ± 0.7
0.40 ± 0.06
0.011
70
5.4 ± 0.4
0.38 ± 0.02
0.007
60
4.4 ± 0.3
0.48 ± 0.04
0.004
50
5.1 ± 0.3
0.50 ± 0.04
0.003
40
6.4 ± 0.6
0.51 ± 0.06
0.005
30 (model I)
6.8 ± 2.4
0.50 ± 0.07
0.007
Average
5.5 ± 0.8
0.46 ± 0.05
30 (model II)
25.5 ± 1.6
0.85 ± 0.01
0.003
Ion energy 100 keV; implantation direction 〈100〉; ion current 6 μA/cm2; total dose 1 × 1016/cm2.
Table III
Root-Mean-Square Surface Slope (tan β) Derived from Spectroscopic Ellipsometry Measurements at 70° Angle of Incidencea
The values listed are the average over the 300–650-nm wavelength range. Autocovariance length T and factor πT/λ are also listed. T = (σ√2)/tan β; σ is given in Table I.
The average value of λ, 475 nm, was used.
Table IV
Angles Δ and Ψ (In Degrees) Measured by SE for Al Samples R-2B, R-4B, and R-8B as a Function of Wavelength and Angle of Incidence θ