Giacomo Badano, Philippe Ballet, Jean-Paul Zanatta, Xavier Baudry, Alain Million, and James W. Garland, "Ellipsometry of rough CdTe(211)B-Ge(211) surfaces grown by molecular beam epitaxy," J. Opt. Soc. Am. B 23, 2089-2096 (2006)
The effect of surface roughness on the ellipsometric response of semiconductor surfaces is investigated. layers were grown on by molecular beam epitaxy using less than optimal growth conditions to enhance the formation of surface roughness. Their optical properties, measured by rotating-compensator ellipsometry, showed small but significant sample-to-sample differences not explainable in terms of nanometer-scale roughness. A critical-point analysis established that the critical-point structure of the dielectric function was the same for all samples. This result suggested that the observed sample-to-sample variations were due to macroscopic roughness, which scatters off-specular light into the detector, thereby causing errors. We introduced tentative corrections for off-specular reflection that fitted the observed differences and thus supported the idea that off-specular reflection was responsible for the observed differences. These results were obtained using but are easily extensible to other rough opaque materials.
P. S. Avdienko, I. V. Sedova, D. D. Firsov, O. S. Komkov, M. V. Rakhlin, A. I. Galimov, V. Yu. Davydov, and S. V. Sorokin J. Opt. Soc. Am. B 38(9) 2579-2586 (2021)
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Thickness (in Micrometers) and FHM of the x-Ray Rocking Curve and its Spreading across the Wafer, for the Layers Used for This Studya
Sample
Thickness
FWHM
Spreading
24350
6.1
98
12
24357
5.9
102
10
24358
6.5
92
8
24360
6.2
99
11
24364
6.6
91
16
24370
6.4
92
12
24377
5.9
103
14
24382
5.4
80
13
24388
6.5
91
13
24389
5.8
117
22
24391
6.3
93
12
24397
6.9
85
9
24399
6.8
87
10
24401
6.5
92
11
Sample 24357 was not fully characterized. Samples 24389 and 24399 had a milky surface morphology. All other samples showed some haziness under grazing light.
Table 2
Values of the CP Energies (in Electron Volts), Linewidths (in Mega-Electron-Volts), and Thickness of the Oxide Layer t (in Angstroms) Determined by a Fit to and Its Second Derivativea
Sample
t
24347
3.364
64
3.940
102
28
2.36
24350
3.364
64
3.941
102
26
2.47
24357
3.364
64
3.941
104
27
2.34
24358
3.364
64
3.941
103
25
2.30
24360
3.364
64
3.941
104
25
2.21
24364
3.364
65
3.942
105
25
2.38
24370
3.364
64
3.942
102
29
2.51
24377
3.364
65
3.941
104
25
2.30
24382
3.364
64
3.942
102
37
2.57
24388
3.364
66
3.940
105
25
1.67
24389
3.366
64
3.943
101
31
2.30
24391
3.364
65
3.941
104
26
2.49
24397
3.364
65
3.941
98
25
1.46
24399
3.367
64
3.943
100
35
1.53
24401
3.365
64
3.942
101
27
1.72
Variations in the reflect changes in the noise level rather than different degrees of verisimilitude of the model; as a matter of fact, the rms of the fit is of the order of for all fits, even for those samples that, like 24397, have a much lower .
Table 3
Average Values of the p and q Polynomial Coefficients Obtained from a Simultaneous Fit of and Its Second Derivative to All the 15 Spectra Measured, Which Are Multiplied by
Critical Point
2267.2
74.26
1209.44
-279.61
0.83
0
0
0
0
368.02
0
126.89
0
170.02
0
0.78
0
Table 4
Values of the CP Energies and Linewidths (given in Electron Volts) Found in the Literaturea
The first column shows where the values were found. The blanks indicate that the corresponding authors did not report the corresponding value.
Table 5
Results of the Fits to the Difference Spectra , Showing the Thickness of the Oxide Layer t, the Shifts in the CP Energies, the Changes in Linewidths, and the Three Parameters That Describe the Presence of Near-Specular Scattering and Cross Polarizationa
Sample
t
24350
1.46
44.699
0.0102
0.00644
24357
1.79
44.723
0.0132
0.00913
24358
1.78
44.635
0.0095
0.00488
24360
1.99
44.581
0.0151
0.00908
24364
1.61
44.272
0.0143
0.00851
24370
1.55
44.346
0.0198
0.01509
24377
1.33
44.963
0.0078
0.00288
24382
8.48
2.29
45.392
0.0098
0.00810
24388
1.80
44.268
0.0194
0.00932
24389
1.51
2.25
-2.43
44.234
0.0401
0.02901
24391
2.07
44.282
0.0197
0.01123
24397
2.68
44.252
0.0253
0.01646
24399
1.29
2.74
44.408
0.0433
0.04106
24401
3.07
44.365
0.0291
0.02088
All the parameters were reduced to constants to energy. For sample 24382, the oxide layer was replaced by an EMA roughness layer, to improve the quality of the fit. The surface is rougher because the sample was annealed up to for . This sample also showed a much lower FWHM of the x-ray rocking curve. However, neither this nor the CP analysis reveal any improvement in the values of the .
Tables (5)
Table 1
Thickness (in Micrometers) and FHM of the x-Ray Rocking Curve and its Spreading across the Wafer, for the Layers Used for This Studya
Sample
Thickness
FWHM
Spreading
24350
6.1
98
12
24357
5.9
102
10
24358
6.5
92
8
24360
6.2
99
11
24364
6.6
91
16
24370
6.4
92
12
24377
5.9
103
14
24382
5.4
80
13
24388
6.5
91
13
24389
5.8
117
22
24391
6.3
93
12
24397
6.9
85
9
24399
6.8
87
10
24401
6.5
92
11
Sample 24357 was not fully characterized. Samples 24389 and 24399 had a milky surface morphology. All other samples showed some haziness under grazing light.
Table 2
Values of the CP Energies (in Electron Volts), Linewidths (in Mega-Electron-Volts), and Thickness of the Oxide Layer t (in Angstroms) Determined by a Fit to and Its Second Derivativea
Sample
t
24347
3.364
64
3.940
102
28
2.36
24350
3.364
64
3.941
102
26
2.47
24357
3.364
64
3.941
104
27
2.34
24358
3.364
64
3.941
103
25
2.30
24360
3.364
64
3.941
104
25
2.21
24364
3.364
65
3.942
105
25
2.38
24370
3.364
64
3.942
102
29
2.51
24377
3.364
65
3.941
104
25
2.30
24382
3.364
64
3.942
102
37
2.57
24388
3.364
66
3.940
105
25
1.67
24389
3.366
64
3.943
101
31
2.30
24391
3.364
65
3.941
104
26
2.49
24397
3.364
65
3.941
98
25
1.46
24399
3.367
64
3.943
100
35
1.53
24401
3.365
64
3.942
101
27
1.72
Variations in the reflect changes in the noise level rather than different degrees of verisimilitude of the model; as a matter of fact, the rms of the fit is of the order of for all fits, even for those samples that, like 24397, have a much lower .
Table 3
Average Values of the p and q Polynomial Coefficients Obtained from a Simultaneous Fit of and Its Second Derivative to All the 15 Spectra Measured, Which Are Multiplied by
Critical Point
2267.2
74.26
1209.44
-279.61
0.83
0
0
0
0
368.02
0
126.89
0
170.02
0
0.78
0
Table 4
Values of the CP Energies and Linewidths (given in Electron Volts) Found in the Literaturea
The first column shows where the values were found. The blanks indicate that the corresponding authors did not report the corresponding value.
Table 5
Results of the Fits to the Difference Spectra , Showing the Thickness of the Oxide Layer t, the Shifts in the CP Energies, the Changes in Linewidths, and the Three Parameters That Describe the Presence of Near-Specular Scattering and Cross Polarizationa
Sample
t
24350
1.46
44.699
0.0102
0.00644
24357
1.79
44.723
0.0132
0.00913
24358
1.78
44.635
0.0095
0.00488
24360
1.99
44.581
0.0151
0.00908
24364
1.61
44.272
0.0143
0.00851
24370
1.55
44.346
0.0198
0.01509
24377
1.33
44.963
0.0078
0.00288
24382
8.48
2.29
45.392
0.0098
0.00810
24388
1.80
44.268
0.0194
0.00932
24389
1.51
2.25
-2.43
44.234
0.0401
0.02901
24391
2.07
44.282
0.0197
0.01123
24397
2.68
44.252
0.0253
0.01646
24399
1.29
2.74
44.408
0.0433
0.04106
24401
3.07
44.365
0.0291
0.02088
All the parameters were reduced to constants to energy. For sample 24382, the oxide layer was replaced by an EMA roughness layer, to improve the quality of the fit. The surface is rougher because the sample was annealed up to for . This sample also showed a much lower FWHM of the x-ray rocking curve. However, neither this nor the CP analysis reveal any improvement in the values of the .