Film-Thickness Measurement Method Combining Frequency-Domain White-Light Interference and Reflection Spectroscopy

Ruibo Gao; Hansheng Ye; Wei Fan; Lai Wei; Yuqiu Gu

doi:10.3788/LOP241352

Laser & Optoelectronics Progress, Volume. 62, Issue 3, 0312004(2025)

Film-Thickness Measurement Method Combining Frequency-Domain White-Light Interference and Reflection Spectroscopy

Ruibo Gao^1、*, Hansheng Ye^1,3, Wei Fan¹, Lai Wei¹, and Yuqiu Gu^1,2

Author Affiliations

¹Research Center of Laser Fusion, China Academy of Engineering Physics, Mianyang 621900, Sichuan , China

²Mianyang Sci-Tech City Institute of Photon Technology, Mianyang 621025, Sichuan ,China

³Department of Engineering Physics, Tsinghua University, Beijing 100084, China

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Figures & Tables(15)

Fig. 1. Schematic diagram of test system combining frequency domain white-light interference and reflection spectroscopy

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Fig. 2. Schematic diagram of single layer film reflection

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Fig. 3. Schematic diagram of multiple reflections between probe and film

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Fig. 4. Fourier analysis of frequency domain white light interference spectrum. (a) Interference fringes; (b) fringe pseudo-time domain distribution

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Fig. 5. Flow chart of film thickness measurement combined frequency domain white light interference and reflectance spectroscopy

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Fig. 6. Nonlinear phase retrieval process. (a) Frequency domain white light interference fringe $I_{m e a}$ and reference spectrum $I_{r e f}$ ; (b) fringe pseudo-time domain distribution; (c) phase retrieved from fringe; (d) nonlinear phase

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Fig. 7. Fitting results of reflection spectrum at different $α$ . (a) $α$ =0.02; (b) $α$ =0.10; (c) $α$ =0.20; (d) $α$ =0.40; (e) $α$ =0.60; (f) $α$ =0.80

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Fig. 8. Fourier transform of fringes at different $α$ . (a) $α$ =0.02; (b) $α$ =0.10; (c) $α$ =0.20; (d) $α$ =0.40; (e) $α$ =0.60; (f) $α$ =0.80

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Fig. 9. Fitting results of nonlinear phase at different $α$ . (a) $α$ =0.02; (b) $α$ =0.10; (c) $α$ =0.20; (d) $α$ =0.40; (e) $α$ =0.60; (f) $α$ =0.80

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Fig. 10. Reflection spectroscopy fitting process. (a) Reference spectrum $I_{r e f}$ ; (b) measured spectrum $I_{m e a}$ ; (c) pseudo-time domain of measured spectrum; (d) fitted curve of measured spectrum

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Fig. 11. Nonlinear phase fitting results. (a) 400 nm film; (b) 1000 nm film

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Table 1. Simulated measurement results of silicon dioxide film thickness

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Table 1. Simulated measurement results of silicon dioxide film thickness

Thickness /nm	Noiseless
Thickness /nm	Method of directly fitting /nm	Method of this article /nm	Method of directly fitting /nm	Method of this article /nm
400.00	575.55	400.00	691.00	400.80
600.00	410.71	600.00	1302.01	599.65
800.00	389.61	800.00	1273.93	800.33
1000.00	375.33	1000.00	1250.97	1000.26

Table 2. Fitting results of thickness at different $α$

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Table 2. Fitting results of thickness at different $α$

$α$	Fitting results
$α$	$α_{s r}$	$L_{s r}$ / $μ m$	$d_{s r}$ /nm	$d$ /nm
0.02	0.02	100.00000	400.00	398.36
0.10	0.10	100.00000	400.00	400.00
0.20	0.20	100.00000	400.00	400.00
0.40	0.40	100.00000	400.00	400.00
0.60	0.60	100.00000	400.00	400.00
0.80	0.80	100.00000	400.00	400.00

Table 3. Initial value fitting and measurement results of SiO₂ film thickness

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Table 3. Initial value fitting and measurement results of SiO₂ film thickness

Number of measurement	（400±10） nm film thickness
Number of measurement	$α_{s r}$	$L_{s r}$ / $μ m$	$d_{s r}$ /nm	$d$ /nm	$α_{s r}$	$L_{s r}$ / $μ m$	$d_{s r}$ /nm	$d$ /nm
1	0.39	72.70969	394.21	404.83	0.25	108.50626	1002.94	999.81
2	0.46	66.09508	397.70	404.64	0.29	100.46417	1002.12	999.91
3	0.46	63.66729	397.64	404.64	0.34	88.13583	1002.14	999.86
4	0.49	62.51479	398.30	405.83	0.40	78.21046	1002.21	1000.76
5	0.49	61.13563	398.24	405.70	0.42	74.96390	1001.91	1000.66
6	0.52	58.08964	398.77	405.23	0.49	63.67067	1001.55	1001.07
7	0.50	56.18262	397.48	404.38	0.55	55.96316	1001.04	1000.36
8	0.55	52.64338	398.70	404.43	0.60	50.62828	1001.44	1001.52
9	0.57	52.17568	398.01	404.48	0.63	48.00334	1001.45	1001.23

Table 4. Comparison of measurement results with different method
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Table 4. Comparison of measurement results with different method
Nominal thickness /nm Method Relative error /%
Reflection photometry /nm Method of this article /nm
400±10 403.02 404.91 0.469
1000±10 1001.10 1000.58 0.052

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Ruibo Gao, Hansheng Ye, Wei Fan, Lai Wei, Yuqiu Gu. Film-Thickness Measurement Method Combining Frequency-Domain White-Light Interference and Reflection Spectroscopy[J]. Laser & Optoelectronics Progress, 2025, 62(3): 0312004

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