Computational manufacturing of optical interference coatings: method, simulation results, and comparison with experiment

Karen Friedrich; Steffen Wilbrandt; Olaf Stenzel; Norbert Kaiser; Karl Heinz Hoffmann

doi:10.1364/AO.49.003150

Applied Optics
Vol. 49,
Issue 16,
pp. 3150-3162
(2010)
•https://doi.org/10.1364/AO.49.003150

Computational manufacturing of optical interference coatings: method, simulation results, and comparison with experiment

Karen Friedrich, Steffen Wilbrandt, Olaf Stenzel, Norbert Kaiser, and Karl Heinz Hoffmann

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Karen Friedrich, Steffen Wilbrandt, Olaf Stenzel, Norbert Kaiser, and Karl Heinz Hoffmann, "Computational manufacturing of optical interference coatings: method, simulation results, and comparison with experiment," Appl. Opt. 49, 3150-3162 (2010)

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Abstract

Virtual deposition runs have been performed to estimate the production yield of selected oxide optical interference coatings when plasma ion-assisted deposition with an advanced plasma source is applied. Thereby, deposition of each layer can be terminated either by broadband optical monitoring or quartz crystal monitoring. Numerous deposition runs of single-layer coatings have been performed to investigate the reproducibility of coating properties and to quantify deposition errors for the simulation. Variations of the following parameters are considered in the simulation: refractive index, extinction coefficient, and film thickness. The refractive index and the extinction coefficient are simulated in terms of the oscillator model. The parameters are varied using an apodized normal distribution with known mean value and standard deviation. Simulation of variations in the film thickness is performed specific to the selected monitoring strategy. Several deposition runs of the selected oxide interference coatings have been performed to verify the simulation results by experimental data.

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Effect	Possible Origin	Model	Data Acquisition	Described in Subsection
variation of optical constants	fluctuations of the process parameters	oscillator model with randomly distributed parameters	reproducibility experiments + analysis of the optical constants according to the oscillator model	2B
variation of film thicknesses by quartz crystal monitoring	rate variations, shutter reaction time	linear superposition of random offset and rate effects in terms of Eq. (1)	reproducibility experiments for different required film thicknesses	2A1
variation of film thicknesses by broadband optical monitoring	fluctuations in intensity spectra cause errors in transmission spectra	transmittance = ratio of intensities with random noise in terms of Eqs. (2, 3, 4)	multiple measurements of dark and lamp intensity spectra	2A2

Material	Substrate	Required Film Thickness (nm)	$U_{Bias}$ (V)	$O_{2}$ flow (sccm)	$I_{Em}$ (mA)	Rate (nm/s)
$Si O_{2}$	SF10, SQ1	30, 200, 300	140	15	95	0.2
${Nb}_{2} O_{5}$	SQ1, BK7, B270	200, 300	110	30	230	0.2
${Ta}_{2} O_{5}$		20, 200, 500	140	15	220	0.2
$Ti O_{2}$		50, 100, 200	100	30	210	0.2

Material	Quartz Crystal Monitoring		Broadband Optical Monitoring
Material	$Δ B$	$Δ A$ (nm)	$Δ d$ (nm)
$Si O_{2}$	0.011	2.8	0.50
${Nb}_{2} O_{5}$	0.000	1.8	0.16
${Ta}_{2} O_{5}$	0.004	1.2	0.15
$Ti O_{2}$	0.008	0.7	0.16

Material	$Si O_{2}$		${Nb}_{2} O_{5}$		${Ta}_{2} O_{5}$		$Ti O_{2}$
Spectral range in ${cm}^{- 1}$	8500–27,700		8500–27,700		10,000–30,000		8500–29,000
Oscillator	Osz ( ${cm}^{- 1}$ )	$Δ Osz$ (%)	Osz ( ${cm}^{- 1}$ )	$Δ Osz$ (%)	Osz ( ${cm}^{- 1}$ )	$Δ Osz$ (%)	Osz ( ${cm}^{- 1}$ )	$Δ Osz$ (%)
$v_{01}$	94,000	9.6	30,250	0.1	35,810	0.4	29,000	0.4
$J_{1}$	172,000	9.3	5430	1.7	4950	3.2	1080	4.7
$Γ_{1}$	0	0	54	11.1	227	2.2	810	2.0
$v_{02}$	—	—	51,080	0.2	58,730	0.2	30,400	0.7
$J_{2}$	—	—	288,300	0.2	28,9700	0.1	2330	8.5
$Γ_{2}$	—	—	0	0	0	0	0	0
$v_{03}$	—	—	—	—	—	—	33,430	0.5
$J_{3}$	—	—	—	—	—	—	33,310	0.6
$Γ_{3}$	—	—	—	—	—	—	0	0
$v_{04}$	—	—	—	—	—	—	55,400	0.9
$J_{4}$	—	—	—	—	—	—	28,1000	0.5
$Γ_{4}$	—	—	—	—	—	—	0	0

Wavelength		$Si O_{2}$	${Ta}_{2} O_{5}$	${Nb}_{2} O_{5}$	$Ti O_{2}$
$350 nm$	n	—	$2.315 \pm 0.002$	—	$2.877 \pm 0.006$
$350 nm$	k	—	$(4.8 \pm 0.4) 10^{- 4}$	—	$(5.1 \pm 0.1) 10^{- 2}$
$400 nm$	n	$1.500 \pm 0.003$	$2.238 \pm 0.002$	$2.473 \pm 0.002$	$2.582 \pm 0.004$
$400 nm$	k	—	$(2.2 \pm 0.2) 10^{- 4}$	$(6.1 \pm 0.7) 10^{- 4}$	$(3.0 \pm 0.2) 10^{- 3}$
$600 nm$	n	$1.483 \pm 0.001$	$2.128 \pm 0.002$	$2.283 \pm 0.002$	$2.337 \pm 0.003$
$600 nm$	k	—	$(6.8 \pm 0.5) 10^{- 5}$	$(1.4 \pm 0.2) 10^{- 4}$	$(3.5 \pm 0.2) 10^{- 4}$
$1000 nm$	n	$1.474 \pm 0.002$	$2.080 \pm 0.002$	$2.213 \pm 0.002$	$2.255 \pm 0.003$
	k	—	$(3.0 \pm 0.3) 10^{- 5}$	$(5.6 \pm 0.6) 10^{- 5}$	$(1.3 \pm 0.1) 10^{- 4}$

Abstract

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Applied Optics