Quantitative calculation of substrate bending caused by multilayer coating stresses

Muneo Sugiura; Koichi Tamura; Mitsunobu Kobiyama

doi:10.1364/AO.59.000A92

Applied Optics
Vol. 59,
Issue 5,
pp. A92-A98
(2020)
•https://doi.org/10.1364/AO.59.000A92

Quantitative calculation of substrate bending caused by multilayer coating stresses

Muneo Sugiura, Koichi Tamura, and Mitsunobu Kobiyama

Not Accessible

Your library or personal account may give you access

Get PDF
Email
Share
Get Citation
Copy Citation Text
Muneo Sugiura, Koichi Tamura, and Mitsunobu Kobiyama, "Quantitative calculation of substrate bending caused by multilayer coating stresses," Appl. Opt. 59, A92-A98 (2020)

Export Citation
- BibTex
- Endnote (RIS)
- HTML
- Plain Text
Citation alert
Save article

Check for updates

Abstract

A framework to quantitatively calculate substrate bending after coating has been proposed. By introducing fitting parameters to modified Stoney’s formula, the amount of bending has been calculated to accuracies of less than ${{\boldsymbol\lambda} / {10}}$ at 633 nm for ion-beam sputtering and ion-beam assisted deposition processes.

Full Article | PDF Article

More Like This

Optical and stress properties of ZrO₂/SiO₂ and TiO₂/SiO₂ anti-reflective coatings deposited by ion-beam-assisted deposition on a flexible substrate

Hsi-Chao Chen, Chun-Hao Chang, and Kun-Hong Chen
Appl. Opt. 63(31) 8280-8287 (2024)

Mechanical stress and thermal-elastic properties of oxide coatings for use in the deep-ultraviolet spectral region

Roland Thielsch, Alexandre Gatto, and Norbert Kaiser
Appl. Opt. 41(16) 3211-3217 (2002)

Ultra-low stress SiO₂ coatings by ion beam sputtering deposition

Aaron Davenport, Emmett Randel, and Carmen S. Menoni
Appl. Opt. 59(7) 1871-1875 (2020)

Previous Article Next Article

Cited By

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Figures (4)

You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Tables (3)

You do not have subscription access to this journal. Article tables are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Equations (5)

You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

No.	Substrate				Coating				Flatness After Coating (Wave)
	Glass	Diameter (mm)	Thickness (mm)	Flatness (Wave)	Layers	Thickness (µm)
	Glass	Diameter (mm)	Thickness (mm)	Flatness (Wave)		Total	$H$	$L$
		$2 l$	$b$	$δ_{0} / 633 n m$		$d$	$d_{H}$	$d_{L}$	$δ_{m} / 633 n m$
1	Quartz	30.0	3.09	−0.210	1	0.400	0.400	0.000	−0.316
2	Quartz	30.0	3.09	0.097	1	0.406	0.000	0.406	−0.205
3	Quartz	30.0	3.09	−0.130	27	2.803	0.994	1.809	−1.453
4	Quartz	30.0	5.03	0.095	28	4.478	1.785	2.693	−0.651
5	Quartz	30.0	5.03	0.021	28	4.478	1.785	2.693	−0.749
6	Quartz	50.8	12.04	−0.051	29	4.742	1.672	3.070	−0.456
7	Quartz	30.0	3.09	−0.191	49	4.887	1.835	3.052	−2.360
8	Quartz	30.0	3.08	0.049	49	4.887	1.835	3.052	−2.171
9	Quartz	30.0	3.09	0.098	36	6.343	2.332	4.011	−2.789
10	BK7	30.0	3.02	−0.121	1	0.400	0.400	0.000	−0.240
11	BK7	30.0	3.02	−0.112	1	0.406	0.000	0.406	−0.353
12	BK7	30.0	3.09	0.119	27	2.803	0.994	1.809	−1.208
13	BK7	30.0	3.09	−0.130	49	4.887	1.835	3.052	−2.238
14	BK7	30.0	3.08	0.031	49	4.887	1.835	3.052	−2.231
15	BK7	30.0	3.09	−0.176	36	6.343	2.332	4.011	−2.931

No.	Substrate				Coating				Flatness After Coating (Wave)
	Glass	Diameter (mm)	Thickness (mm)	Flatness (Wave)	Layers	Thickness (µm)
	Glass	Diameter (mm)	Thickness (mm)	Flatness (Wave)		Total	$H$	$L$
		$2 l$	$b$	$δ_{0} / 633 n m$		$d$	$d_{H}$	$d_{L}$	$δ_{m} / 633 n m$
1	Quartz	30.0	3.07	0.036	1	0.330	0.330	0.000	0.033
2	Quartz	30.0	3.08	0.110	1	0.330	0.000	0.330	0.110
3	Quartz	30.0	3.09	−0.095	14	0.960	0.388	0.573	−0.242
4	Quartz	30.0	3.09	−0.071	43	4.929	1.878	3.051	−0.755
5	Quartz	30.0	3.08	0.085	14	3.154	1.273	1.881	−0.376
6	Quartz	30.0	3.09	0.099	34	5.995	1.404	4.591	−0.876
7	Quartz	50.8	12.03	0.074	34	5.995	1.404	4.591	−0.186
8	Quartz	30.0	3.10	−0.195	66	8.227	2.712	5.514	−1.338
9	BK7	30.0	3.09	−0.127	1	0.330	0.330	0.000	−0.219
10	BK7	30.0	3.09	0.125	1	0.330	0.000	0.330	0.045
11	BK7	30.0	3.06	−0.083	14	0.960	0.388	0.573	−0.370
12	BK7	30.0	3.06	−0.042	43	4.929	1.878	3.051	−1.468
13	BK7	30.0	3.08	0.061	14	3.154	1.273	1.881	−0.912
14	BK7	30.0	3.10	−0.195	34	5.995	1.404	4.591	−1.945
15	BK7	30.0	3.10	−0.173	66	8.227	2.712	5.514	−2.584

No.	Substrate				Coating				Flatness After Coating (Wave)
	Glass	Diameter (mm)	Thickness (mm)	Flatness (Wave)	Layers	Thickness (µm)
	Glass	Diameter (mm)	Thickness (mm)	Flatness (Wave)		Total	$H$	$L$
		$2 l$	$b$	$δ_{0} / 633 n m$		$d$	$d_{H}$	$d_{L}$	$δ_{m} / 633 n m$
1	Quartz	30.0	3.08	0.075	1	0.335	0.335	0.000	0.021
2	Quartz	30.0	3.08	0.080	1	0.338	0.000	0.338	−0.060
3	Quartz	30.0	3.09	−0.084	30	3.970	1.500	2.470	−0.657
4	Quartz	30.0	3.08	0.063	18	2.554	0.959	1.596	−0.337
5	Quartz	30.0	3.08	0.066	18	2.554	0.959	1.596	−0.349
6	Quartz	30.0	3.10	−0.085	77	9.236	3.358	5.878	−1.497
7	Quartz	30.0	3.10	−0.074	77	9.236	3.358	5.878	−1.484
8	Quartz	30.0	3.10	−0.074	79	9.704	3.729	5.974	−1.496
9	Quartz	30.0	3.08	0.062	46	5.171	1.701	3.470	−0.753
10	Quartz	25.4	5.00	0.044	46	5.171	1.701	3.470	−0.210
11	Quartz	30.0	5.00	0.071	46	5.171	1.701	3.470	−0.244
12	Quartz	50.0	4.96	0.043	46	5.171	1.701	3.470	−0.823
13	Quartz	30.0	3.08	0.078	33	2.697	1.100	1.597	−0.351
14	Quartz	30.0	3.08	0.109	52	5.140	1.350	3.790	−0.704
15	BK7	30.0	3.09	−0.164	1	0.335	0.335	0.000	−0.260
16	BK7	30.0	3.09	−0.178	1	0.338	0.000	0.338	−0.304
17	BK7	30.0	3.06	0.049	30	3.970	1.500	2.470	−1.017
18	BK7	30.0	3.05	−0.079	18	2.554	0.959	1.596	−0.725
19	BK7	30.0	3.05	−0.078	18	2.554	0.959	1.596	−0.734
20	BK7	30.0	3.07	−0.105	77	9.236	3.358	5.878	−2.460
21	BK7	30.0	3.06	0.068	77	9.236	3.358	5.878	−2.365
22	BK7	30.0	3.07	0.085	79	9.704	3.729	5.974	−2.406
23	BK7	30.0	3.06	0.051	46	5.171	1.701	3.470	−1.265
24	BK7	30.0	3.08	−0.067	33	2.697	1.100	1.597	−0.706
25	BK7	30.0	3.08	0.046	52	5.140	1.350	3.790	−1.268

No.	Substrate				Coating				Flatness After Coating (Wave)
	Glass	Diameter (mm)	Thickness (mm)	Flatness (Wave)	Layers	Thickness (µm)
	Glass	Diameter (mm)	Thickness (mm)	Flatness (Wave)		Total	$H$	$L$
		$2 l$	$b$	$δ_{0} / 633 n m$		$d$	$d_{H}$	$d_{L}$	$δ_{m} / 633 n m$
1	Quartz	30.0	3.09	−0.210	1	0.400	0.400	0.000	−0.316
2	Quartz	30.0	3.09	0.097	1	0.406	0.000	0.406	−0.205
3	Quartz	30.0	3.09	−0.130	27	2.803	0.994	1.809	−1.453
4	Quartz	30.0	5.03	0.095	28	4.478	1.785	2.693	−0.651
5	Quartz	30.0	5.03	0.021	28	4.478	1.785	2.693	−0.749
6	Quartz	50.8	12.04	−0.051	29	4.742	1.672	3.070	−0.456
7	Quartz	30.0	3.09	−0.191	49	4.887	1.835	3.052	−2.360
8	Quartz	30.0	3.08	0.049	49	4.887	1.835	3.052	−2.171
9	Quartz	30.0	3.09	0.098	36	6.343	2.332	4.011	−2.789
10	BK7	30.0	3.02	−0.121	1	0.400	0.400	0.000	−0.240
11	BK7	30.0	3.02	−0.112	1	0.406	0.000	0.406	−0.353
12	BK7	30.0	3.09	0.119	27	2.803	0.994	1.809	−1.208
13	BK7	30.0	3.09	−0.130	49	4.887	1.835	3.052	−2.238
14	BK7	30.0	3.08	0.031	49	4.887	1.835	3.052	−2.231
15	BK7	30.0	3.09	−0.176	36	6.343	2.332	4.011	−2.931

No.	Substrate				Coating				Flatness After Coating (Wave)
	Glass	Diameter (mm)	Thickness (mm)	Flatness (Wave)	Layers	Thickness (µm)
	Glass	Diameter (mm)	Thickness (mm)	Flatness (Wave)		Total	$H$	$L$
		$2 l$	$b$	$δ_{0} / 633 n m$		$d$	$d_{H}$	$d_{L}$	$δ_{m} / 633 n m$
1	Quartz	30.0	3.07	0.036	1	0.330	0.330	0.000	0.033
2	Quartz	30.0	3.08	0.110	1	0.330	0.000	0.330	0.110
3	Quartz	30.0	3.09	−0.095	14	0.960	0.388	0.573	−0.242
4	Quartz	30.0	3.09	−0.071	43	4.929	1.878	3.051	−0.755
5	Quartz	30.0	3.08	0.085	14	3.154	1.273	1.881	−0.376
6	Quartz	30.0	3.09	0.099	34	5.995	1.404	4.591	−0.876
7	Quartz	50.8	12.03	0.074	34	5.995	1.404	4.591	−0.186
8	Quartz	30.0	3.10	−0.195	66	8.227	2.712	5.514	−1.338
9	BK7	30.0	3.09	−0.127	1	0.330	0.330	0.000	−0.219
10	BK7	30.0	3.09	0.125	1	0.330	0.000	0.330	0.045
11	BK7	30.0	3.06	−0.083	14	0.960	0.388	0.573	−0.370
12	BK7	30.0	3.06	−0.042	43	4.929	1.878	3.051	−1.468
13	BK7	30.0	3.08	0.061	14	3.154	1.273	1.881	−0.912
14	BK7	30.0	3.10	−0.195	34	5.995	1.404	4.591	−1.945
15	BK7	30.0	3.10	−0.173	66	8.227	2.712	5.514	−2.584

Quantitative calculation of substrate bending caused by multilayer coating stresses

Author Affiliations

ORCID

Abstract

Cited By

Figures (4)

Tables (3)

Equations (5)

Applied Optics