Fracture mechanics of delamination defects in multilayer dielectric coatings

H. P. H. Liddell; K. Mehrotra; J. C. Lambropoulos; S. D. Jacobs

doi:10.1364/AO.52.007689

Applied Optics
Vol. 52,
Issue 32,
pp. 7689-7698
(2013)
•https://doi.org/10.1364/AO.52.007689

Fracture mechanics of delamination defects in multilayer dielectric coatings

H. P. H. Liddell, K. Mehrotra, J. C. Lambropoulos, and S. D. Jacobs

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H. P. H. Liddell, K. Mehrotra, J. C. Lambropoulos, and S. D. Jacobs, "Fracture mechanics of delamination defects in multilayer dielectric coatings," Appl. Opt. 52, 7689-7698 (2013)

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Abstract

During the fabrication of multilayer-dielectric (MLD) thin-film-coated optics, such as the diffraction gratings used in OMEGA EP’s pulse compressors, acid piranha cleaning can lead to the formation of chemically induced delamination defects. We investigate the causes of these defects and describe a mechanism for the deformation and failure of the MLD coating in response to hydrogen peroxide in the cleaning solution. A fracture mechanics model is developed and used to calculate the crack path that maximizes the energy-release rate, which is found to be consistent with the characteristic fracture pattern observed in MLD coating delamination defects.

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Factor	Level	Mean Defect Density ( $defects / {cm}^{2}$ )	Sum of Squares	Mean Square	Degrees of Freedom	$F$ Ratio	$Prob > F$ ( $p$ Value)
Coating age	2 weeks	1.92	9.57	4.78	2	0.96	0.39
	6 weeks	1.47
	12 weeks	0.95
Piranha ratio ( $H_{2} {SO}_{4} : H_{2} O_{2}$ )	$5 : 1$	0.24	68.57	68.57	1	13.74	0.001^***
Piranha ratio ( $H_{2} {SO}_{4} : H_{2} O_{2}$ )	$2 : 1$	2.76	68.57	68.57	1	13.74	0.001^***
Soak temperature	50°C	1.18	2.09	1.05	2	0.21	0.81
	70°C	1.44
	90°C	1.69
Soak time	0 min	0.98	13.31	6.66	2	1.33	0.28
	30 min	1.23
	60 min	2.12
Heat shock	Shocked	1.06	7.56	7.56	1	1.52	0.23
Heat shock	Not shocked	1.82	7.56	7.56	1	1.52	0.23
Error estimate	—	—	154.59	4.99	31	—	—

Material	Young’s Modulus $E (GPa)$	Poisson Ratio $ν$	Shear Modulus $μ (GPa)$	Bulk Modulus $B (GPa)$
BK7 (bulk)	82	0.21	33.9	47.1
${SiO}_{2}$ (thin film)	95	0.17	40.6	48.0
${HfO}_{2}$ (thin film)	130	0.25	52.0	86.7
MLD coating	108	0.20	44.7	60.6

Material 1	Material 2	$α$	$β$	$ε$
BK7	MLD coating	$- 0.13$	$- 0.04$	0.01
BK7	${HfO}_{2}$	$- 0.23$	$- 0.09$	0.03
${HfO}_{2}$	${SiO}_{2}$	0.17	0.10	$- 0.03$
${SiO}_{2}$	${HfO}_{2}$	$- 0.17$	$- 0.10$	0.03

Factor	Level	Mean Defect Density ( $defects / {cm}^{2}$ )	Sum of Squares	Mean Square	Degrees of Freedom	$F$ Ratio	$Prob > F$ ( $p$ Value)
Coating age	2 weeks	1.92	9.57	4.78	2	0.96	0.39
	6 weeks	1.47
	12 weeks	0.95
Piranha ratio ( $H_{2} {SO}_{4} : H_{2} O_{2}$ )	$5 : 1$	0.24	68.57	68.57	1	13.74	0.001^***
Piranha ratio ( $H_{2} {SO}_{4} : H_{2} O_{2}$ )	$2 : 1$	2.76	68.57	68.57	1	13.74	0.001^***
Soak temperature	50°C	1.18	2.09	1.05	2	0.21	0.81
	70°C	1.44
	90°C	1.69
Soak time	0 min	0.98	13.31	6.66	2	1.33	0.28
	30 min	1.23
	60 min	2.12
Heat shock	Shocked	1.06	7.56	7.56	1	1.52	0.23
Heat shock	Not shocked	1.82	7.56	7.56	1	1.52	0.23
Error estimate	—	—	154.59	4.99	31	—	—

Material	Young’s Modulus $E (GPa)$	Poisson Ratio $ν$	Shear Modulus $μ (GPa)$	Bulk Modulus $B (GPa)$
BK7 (bulk)	82	0.21	33.9	47.1
${SiO}_{2}$ (thin film)	95	0.17	40.6	48.0
${HfO}_{2}$ (thin film)	130	0.25	52.0	86.7
MLD coating	108	0.20	44.7	60.6

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Tables (3)

Equations (10)

Applied Optics