R. Wolf, H.-G. Birken, C. Blessing, and C. Kunz, "Optical constants of gold in the soft-x-ray region from reflection and transmission measurements," Appl. Opt. 33, 2683-2694 (1994)
The optical constants of gold deposited on 300-nm-thick freestanding polyimide films have been measured in the energy range of 40–1350 eV. The optical constants of the polyimide films were known from a previous investigation. By performing both transmission measurements with Kramers–Kronig analysis and multiangle reflection measurements with analysis by fitting to a Fresnel multilayer model including roughness, one could carry out a detailed error analysis. In the energy range above 500 eV systematic deviations between the results obtained by both methods were found. For gold films the discrepancies can be attributed to deviations from Beckmann-type behavior at small grazing-incidence angles.
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Fit, error caused by the mean-square deviation of the fit; ΔN, error in the normalization signal obtained with the sample removed; Δϴ0, error in the angle of incidence; ΔP, error in the degree of polarization; Δσ(ϴ), error in the assumed vertical divergence of the beam; ΔE, error in the energy calibration of the monochromator; Δ∊2, error in ∊2 of the supporting polyimide film; (ΣΔ2)1/2, the result of the quadratic superposition of these first errors. The following error sources have their origin in contributions of wrong photon energies: R(E/2), contribution of long-wavelength light; R(2E), contribution of second harmonic light. One obtains Δtot by adding up all errors quadratically while R(2E) is taken into account linearly to stress the relative importance of this contribution.
Not included in Δtot since obviously overestimated.
Table 3
Results of the T(E) Measurements on Gold Film P87b over the Energy Range of 20–200 eV
E (eV)
1 − Re ∊ (×0.001)
Im ∊ (×0.001)
E (eV)
1 − Re ∊ (×0.001)
Im − ∊ (×0.001)
E (eV)
1 − Re ∊ (×0.001)
Im ∊ (×0.001)
20.00
−248.8
2664.0
43.00
472.0
527.2
94.25
204.3
91.83
44.00
464.0
509.6
96.00
195.3
84.59
45.00
457.7
486.8
97.71
188.3
79.08
21.00
187.2
2865.0
46.00
447.2
459.4
99.92
180.1
73.12
21.50
497.0
2845.0
47.00
431.5
434.1
101.8
174.1
67.43
22.00
763.8
2687.0
48.00
413.6
413.9
103.6
168.6
62.76
22.50
955.5
2468.0
49.00
396.3
397.9
105.9
160.9
55.28
23.00
1055.0
2218.0
50.00
379.4
384.5
107.8
153.6
51.18
23.50
1070.0
1988.0
109.8
147.0
47.94
24.00
1049.0
1806.0
52.00
352.8
365.7
112.2
140.6
43.99
114.0
135.8
40.57
54.00
331.6
349.6
116.6
128.6
35.80
25.00
938.2
1540.0
118.7
122.8
32.83
56.00
313.8
336.9
120.7
117.4
30.26
26.00
839.2
1395.0
123.4
110.3
27.42
58.00
301.1
329.0
125.5
105.3
25.55
27.00
757.9
1301.0
128.2
98.95
23.44
28.00
695.1
1248.0
60.00
297.6
323.6
130.4
93.89
22.13
62.00
299.5
310.8
133.4
87.88
20.80
29.00
678.7
1232.0
135.6
83.89
20.01
29.50
690.7
1225.0
64.00
300.4
292.2
138.7
78.58
18.83
30.00
716.9
1207.0
141.0
74.85
18.11
30.50
745.3
1172.0
66.00
299.7
272.6
144.0
70.27
17.20
31.00
771.2
1124.0
68.00
296.7
250.4
146.4
66.64
16.64
32.00
796.0
1009.0
149.9
61.82
16.04
70.00
289.4
227.5
152.5
58.24
15.83
33.00
754.2
880.1
72.00
276.8
206.8
155.3
54.78
15.85
34.00
702.8
807.3
158.7
51.24
16.00
74.00
264.0
195.0
161.3
48.79
15.95
35.00
656.9
754.4
76.00
255.0
185.5
165.1
45.09
15.76
36.00
621.4
716.0
78.00
248.9
175.6
168.1
42.29
15.99
171.1
39.75
16.37
37.00
593.1
680.8
80.69
239.6
159.7
174.7
37.14
16.91
38.00
567.4
648.0
82.20
234.0
152.0
177.6
35.31
17.28
83.82
226.4
142.4
181.3
33.08
17.71
39.00
546.2
619.8
85.25
221.7
146.1
185.0
31.05
18.23
40.00
526.9
590.8
86.98
224.1
135.9
188.7
29.36
18.96
41.00
504.8
563.2
88.86
221.1
127.2
192.6
27.93
19.43
42.00
485.6
544.0
90.51
218.6
115.7
196.1
26.81
19.79
92.21
213.7
104.3
199.9
25.71
20.00
Table 4
Results of the T(E) Measurements on Gold Film P87b over the Energy Range of 200–2000 eV
E (eV)
1 −Re ∊ (×0.001)
Im ∊ (×0.001)
E (eV)
1 − Re ∊ (×0.001)
Im ∊ (×0.001)
E (eV)
1 − Re ∊ (×0.001)
Im ∊ (×0.001)
199.9
25.71
20.00
434.4
11.26
12.35
941.6
4.663
2.328
203.4
24.70
20.18
442.3
11.12
11.98
959.8
4.526
2.205
208.2
23.50
20.32
450.3
10.97
11.63
977.8
4.392
2.088
211.6
22.65
20.37
459.9
10.81
11.20
996.6
4.256
1.974
216.2
21.47
20.48
468.6
10.66
10.80
1015.0
4.125
1.876
220.1
20.61
20.65
477.3
10.46
10.42
1034.0
4.004
1.778
224.6
19.70
20.94
487.0
10.23
10.03
1057.0
3.847
1.664
229.6
18.95
21.23
496.7
9.996
9.678
1076.0
3.727
1.578
233.8
18.47
21.40
506.3
9.778
9.364
1096.0
3.610
1.509
237.7
18.12
21.48
515.7
9.575
9.050
1122.0
3.477
1.401
242.8
17.72
21.49
525.4
9.323
8.740
1141.0
3.366
1.324
247.2
17.39
21.41
537.7
8.804
8.462
1162.0
3.257
1.254
252.6
16.99
21.25
547.5
8.767
8.316
1183.0
3.148
1.190
257.0
16.74
21.17
557.3
8.951
8.170
1212.0
3.013
1.111
261.9
16.46
20.99
569.8
8.734
7.763
1234.0
2.908
1.049
267.7
16.18
20.63
580.7
8.656
7.510
1258.0
2.807
0.9903
272.8
15.77
20.29
591.5
8.486
7.178
1283.0
2.703
0.9326
278.6
15.25
20.02
603.0
8.336
6.904
1306.0
2.611
0.8810
282.9
15.54
21.94
615.1
8.169
6.610
1331.0
2.518
0.8346
289.0
14.84
23.25
627.2
7.995
6.324
1358.0
2.422
0.7764
294.0
15.27
20.71
639.1
7.800
6.072
1392.0
2.301
0.7205
299.7
14.61
19.48
651.4
7.669
5.880
306.4
14.83
17.59
663.3
7.525
5.608
1426.0
2.190
0.6699
312.2
13.83
18.01
675.7
7.361
5.376
1460.0
2.087
0.6238
318.3
13.85
17.83
688.8
7.194
5.137
1496.0
1.984
0.5794
325.1
13.67
17.37
704.7
7.004
4.865
1533.0
1.885
0.5375
331.3
13.29
16.81
717.5
6.842
4.661
1570.0
1.791
0.4995
337.0
12.79
16.65
730.5
6.685
4.443
344.4
12.40
16.62
746.9
6.478
4.215
1609.0
1.698
0.4632
351.0
12.40
16.47
761.1
6.292
4.033
1648.0
1.610
0.4303
357.6
12.30
16.21
775.4
6.150
3.904
1688.0
1.526
0.3998
364.0
12.19
16.05
790.0
6.015
3.696
370.9
12.23
15.81
805.3
5.855
3.516
1730.0
1.441
0.3707
378.2
12.28
15.34
821.2
5.685
3.354
1772.0
1.362
0.3439
386.0
12.15
14.88
825.4
5.642
3.321
1815.0
1.284
0.3190
392.9
12.11
14.49
1860.0
1.205
0.2953
402.3
11.91
13.90
1905.0
1.130
0.2740
408.7
12.13
13.48
890.4
5.088
2.732
416.6
11.58
13.05
902.8
4.987
2.623
1952.0
1.052
0.2538
426.2
11.38
12.70
924.3
4.803
2.447
2000.0
0.9734
0.2351
Tables (4)
Table 1
Results of the R(ϴ) Measurements on Gold Film P87ba
E (eV)
1 −Re ∊ (×0.001)
Im ∊ (×0.001)
d (nm)
σ1 (nm)
σ2 (nm)
41.03 ± 0.21
348.4 ± 21.6
517.4 ± 29.5
1.201 ± 0.492
49.32
323.0
436.4
1.696
58.60
232.7
370.6
1.554
69.89
274.6
251.8
1.491
83.26
220.8
158.0
1.447
98.59 ± 0.49
176.9 ± 5.00
79.71 ± 1.83
47.97 ± 0.29
1.436 ± 0.022
0.475 ± 0.185
118.1
117.0
32.61
47.83
1.391
0.784
139.4
71.04
18.08
47.75
1.372
0.809
166.6
39.22
16.56
47.63
1.361
0.600
197.4
23.08
21.41
47.57
1.322
0.409
235.6 ± 1.2
15.84 ± 0.30
23.86 ± 0.38
47.42 ± 0.52
1.345 ± 0.019
0.010
269.6
14.10
23.26
47.29
1.361
0.001
333.4
12.08
19.53
47.41
1.332
0.020
397.7
11.91
16.82
1.341
470.2 ± 2.4
11.27 ± 0.158
12.87 ± 0.26
1.352 ± 0.015
560.4
9.851
9.597
1.345
668.8
8.410
6.060
1.301
794.5
6.753
3.732
1.266
950.4 ± 4.8
5.105 ± 0.077
2.172 ± 0.024
1.201 ± 0.026
1130.0
3.780
1.231
1.196
1345.0
2.723
0.7667
1.135
The significance of the blanks is that these parameters were held constant in the fit.
Table 2
Contributions to the Error Analysis for Five Selected Photon Energiesa
Fit, error caused by the mean-square deviation of the fit; ΔN, error in the normalization signal obtained with the sample removed; Δϴ0, error in the angle of incidence; ΔP, error in the degree of polarization; Δσ(ϴ), error in the assumed vertical divergence of the beam; ΔE, error in the energy calibration of the monochromator; Δ∊2, error in ∊2 of the supporting polyimide film; (ΣΔ2)1/2, the result of the quadratic superposition of these first errors. The following error sources have their origin in contributions of wrong photon energies: R(E/2), contribution of long-wavelength light; R(2E), contribution of second harmonic light. One obtains Δtot by adding up all errors quadratically while R(2E) is taken into account linearly to stress the relative importance of this contribution.
Not included in Δtot since obviously overestimated.
Table 3
Results of the T(E) Measurements on Gold Film P87b over the Energy Range of 20–200 eV
E (eV)
1 − Re ∊ (×0.001)
Im ∊ (×0.001)
E (eV)
1 − Re ∊ (×0.001)
Im − ∊ (×0.001)
E (eV)
1 − Re ∊ (×0.001)
Im ∊ (×0.001)
20.00
−248.8
2664.0
43.00
472.0
527.2
94.25
204.3
91.83
44.00
464.0
509.6
96.00
195.3
84.59
45.00
457.7
486.8
97.71
188.3
79.08
21.00
187.2
2865.0
46.00
447.2
459.4
99.92
180.1
73.12
21.50
497.0
2845.0
47.00
431.5
434.1
101.8
174.1
67.43
22.00
763.8
2687.0
48.00
413.6
413.9
103.6
168.6
62.76
22.50
955.5
2468.0
49.00
396.3
397.9
105.9
160.9
55.28
23.00
1055.0
2218.0
50.00
379.4
384.5
107.8
153.6
51.18
23.50
1070.0
1988.0
109.8
147.0
47.94
24.00
1049.0
1806.0
52.00
352.8
365.7
112.2
140.6
43.99
114.0
135.8
40.57
54.00
331.6
349.6
116.6
128.6
35.80
25.00
938.2
1540.0
118.7
122.8
32.83
56.00
313.8
336.9
120.7
117.4
30.26
26.00
839.2
1395.0
123.4
110.3
27.42
58.00
301.1
329.0
125.5
105.3
25.55
27.00
757.9
1301.0
128.2
98.95
23.44
28.00
695.1
1248.0
60.00
297.6
323.6
130.4
93.89
22.13
62.00
299.5
310.8
133.4
87.88
20.80
29.00
678.7
1232.0
135.6
83.89
20.01
29.50
690.7
1225.0
64.00
300.4
292.2
138.7
78.58
18.83
30.00
716.9
1207.0
141.0
74.85
18.11
30.50
745.3
1172.0
66.00
299.7
272.6
144.0
70.27
17.20
31.00
771.2
1124.0
68.00
296.7
250.4
146.4
66.64
16.64
32.00
796.0
1009.0
149.9
61.82
16.04
70.00
289.4
227.5
152.5
58.24
15.83
33.00
754.2
880.1
72.00
276.8
206.8
155.3
54.78
15.85
34.00
702.8
807.3
158.7
51.24
16.00
74.00
264.0
195.0
161.3
48.79
15.95
35.00
656.9
754.4
76.00
255.0
185.5
165.1
45.09
15.76
36.00
621.4
716.0
78.00
248.9
175.6
168.1
42.29
15.99
171.1
39.75
16.37
37.00
593.1
680.8
80.69
239.6
159.7
174.7
37.14
16.91
38.00
567.4
648.0
82.20
234.0
152.0
177.6
35.31
17.28
83.82
226.4
142.4
181.3
33.08
17.71
39.00
546.2
619.8
85.25
221.7
146.1
185.0
31.05
18.23
40.00
526.9
590.8
86.98
224.1
135.9
188.7
29.36
18.96
41.00
504.8
563.2
88.86
221.1
127.2
192.6
27.93
19.43
42.00
485.6
544.0
90.51
218.6
115.7
196.1
26.81
19.79
92.21
213.7
104.3
199.9
25.71
20.00
Table 4
Results of the T(E) Measurements on Gold Film P87b over the Energy Range of 200–2000 eV
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