Estimation of the composition of coelectron-beam-evaporated thin-mixture films by making use of the Wiener bounds

C. Franke; O. Stenzel; S. Wilbrandt; J. Wolf; N. Kaiser; A. Tünnermann

doi:10.1364/AO.54.002362

Applied Optics
Vol. 54,
Issue 9,
pp. 2362-2370
(2015)
•https://doi.org/10.1364/AO.54.002362

Estimation of the composition of coelectron-beam-evaporated thin-mixture films by making use of the Wiener bounds

C. Franke, O. Stenzel, S. Wilbrandt, J. Wolf, N. Kaiser, and A. Tünnermann

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C. Franke, O. Stenzel, S. Wilbrandt, J. Wolf, N. Kaiser, and A. Tünnermann, "Estimation of the composition of coelectron-beam-evaporated thin-mixture films by making use of the Wiener bounds," Appl. Opt. 54, 2362-2370 (2015)

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Abstract

Material mixtures offer prospective possibilities for synthesizing coating materials with tailored optical constants. We present experimental results for mixture coatings of alumina/aluminum fluoride and alumina/hafnia deposited by electron beam evaporation. Thereby, the volume filling factors of the components are commonly estimated on the basis of deposition rates measured by quartz crystal microbalance. The interplay between the vapor fluxes from the two evaporation sources, the crosstalk between quartz crystal microbalances, and the influence of the plasma source on the tooling factors limit the accuracy of this estimation, and this has motivated us to develop an alternative approach. The general idea of our approach is based on the commonly high accuracy in thin-film optical constant determination using spectrophotometry. Therefore, these optical constants serve as a reliable input for a rather simple but robust evaluation procedure based on the concept of Wiener bounds. The consistency of the obtained results is illustrated by opposing the data to the elementary film composition estimated from energy-dispersive x-ray spectroscopy.

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Element	${Al}_{2} O_{3} / {AlF}_{3}$	${Al}_{2} O_{3} / {HfO}_{2}$
Al	$N_{at} (p_{a}) = \frac{1}{4} + \frac{3}{20} χ_{a}$	$N_{at} (p_{a}) = \frac{2}{5} χ_{a}$
Hf	—	$N_{at} (p_{a}) = \frac{1}{3} - \frac{1}{3} χ_{a}$
O	$N_{at} (p_{a}) = \frac{3}{5} χ_{a}$	$N_{at} (p_{a}) = \frac{2}{3} - \frac{1}{15} χ_{a}$
F	$N_{at} (p_{a}) = \frac{3}{4} (1 - χ_{a})$	—
With	$χ_{a} (p_{a}) = \frac{M_{mol, b} ρ_{a} p_{a}}{M_{mol, b} ρ_{a} p_{a} + M_{mol, a} ρ_{b} (1 - p_{a})}$ $M_{mol, {Al}_{2} O_{3}} = M_{mol, a} = 102.0$ $ρ_{{Al}_{2} O_{3}} = ρ_{a} = 3.97 \frac{g}{{cm}^{3}}$ $M_{mol, {HfO}_{2}} = M_{mol, b} = 210.5$ $ρ_{{HfO}_{2}} = ρ_{b} = 9.68 \frac{g}{{cm}^{3}}$ $M_{mol, {AlF}_{3}} = M_{mol, b} = 84.0$ $ρ_{{AlF}_{3}} = ρ_{b} = 2.90 \frac{g}{{cm}^{3}}$

Type of Mixture	${Al}_{2} O_{3} / {HfO}_{2}$		${AlF}_{3} / {Al}_{2} O_{3}$
Electron Beam Gun	HPE6	HPE10	HPE6	HPE10
Material	${Al}_{2} O_{3}$	${HfO}_{2}$	${AlF}_{3}$	${Al}_{2} O_{3}$
Inert Gas	—		Series 3: 12 sccm Ar
Inert Gas	—		Series 4: 4 sccm Xe
Reactive Gas	15 sccm $O_{2}$		Series 1: 0 sccm $O_{2}$
			Series 2–4: 10 sccm $O_{2}$
Temperature	200°C		100°C
Deposition Rates in nm/s	0.3	0.1	0	2.25
	0.57	0.1	0.25	2.25
	0	0.4	0.75	1.75
	0.07		1.25	1.25
	0.13		1.75	0.75
	0.22		2.25	0.25
	0.33		2.25	0
	0.49
	0.75
	1	0

Mixture Series	Sample	1	2	3	4	5	6	7	8
${Al}_{2} O_{3} - {AlF}_{3}$	$r_{H} / (r_{H} + r_{L})$	0	0.1	0.3	0.5	0.7	0.9	1	—
Without $O_{2}$	$p_{Alumina, ar}$	0	0.042	0.088	0.515	0.683	0.863	1	—
${Al}_{2} O_{3} - {AlF}_{3}$	$r_{H} / (r_{H} + r_{L})$	0	0.1	0.3	0.5	0.7	0.9	1	—
With $O_{2}$	$p_{Alumina, ar}$	0	0.084	0.195	0.231	0.45	0.76	1	—
${Al}_{2} O_{3} - {AlF}_{3}$	$r_{H} / (r_{H} + r_{L})$	0	0.1	0.3	0.5	0.7	0.9	1	—
With PIAD $Ar / O_{2}$	$p_{Alumina, ar}$	0	0.057	0.17	0.303	0.483	0.71	1	—
${Al}_{2} O_{3} - {AlF}_{3}$	$r_{H} / (r_{H} + r_{L})$	0	0.1	0.3	0.5	0.7	0.9	1	—
With PIAD $Xe / O_{2}$	$p_{Alumina, ar}$	0	0.035	0.165	0.31	0.46	0.742	1	—
${Al}_{2} O_{3} - {HfO}_{2}$	$r_{H} / (r_{H} + r_{L})$	0.149	0.25	0.348	0.449	0.548	0.645	0.755	0.851
With $O_{2}$	$p_{Alumina, ar}$	0.118	0.222	0.319	0.531	0.602	0.695	0.775	0.915

Element	${Al}_{2} O_{3} / {AlF}_{3}$	${Al}_{2} O_{3} / {HfO}_{2}$
Al	$N_{at} (p_{a}) = \frac{1}{4} + \frac{3}{20} χ_{a}$	$N_{at} (p_{a}) = \frac{2}{5} χ_{a}$
Hf	—	$N_{at} (p_{a}) = \frac{1}{3} - \frac{1}{3} χ_{a}$
O	$N_{at} (p_{a}) = \frac{3}{5} χ_{a}$	$N_{at} (p_{a}) = \frac{2}{3} - \frac{1}{15} χ_{a}$
F	$N_{at} (p_{a}) = \frac{3}{4} (1 - χ_{a})$	—
With	$χ_{a} (p_{a}) = \frac{M_{mol, b} ρ_{a} p_{a}}{M_{mol, b} ρ_{a} p_{a} + M_{mol, a} ρ_{b} (1 - p_{a})}$ $M_{mol, {Al}_{2} O_{3}} = M_{mol, a} = 102.0$ $ρ_{{Al}_{2} O_{3}} = ρ_{a} = 3.97 \frac{g}{{cm}^{3}}$ $M_{mol, {HfO}_{2}} = M_{mol, b} = 210.5$ $ρ_{{HfO}_{2}} = ρ_{b} = 9.68 \frac{g}{{cm}^{3}}$ $M_{mol, {AlF}_{3}} = M_{mol, b} = 84.0$ $ρ_{{AlF}_{3}} = ρ_{b} = 2.90 \frac{g}{{cm}^{3}}$

Type of Mixture	${Al}_{2} O_{3} / {HfO}_{2}$		${AlF}_{3} / {Al}_{2} O_{3}$
Electron Beam Gun	HPE6	HPE10	HPE6	HPE10
Material	${Al}_{2} O_{3}$	${HfO}_{2}$	${AlF}_{3}$	${Al}_{2} O_{3}$
Inert Gas	—		Series 3: 12 sccm Ar
Inert Gas	—		Series 4: 4 sccm Xe
Reactive Gas	15 sccm $O_{2}$		Series 1: 0 sccm $O_{2}$
			Series 2–4: 10 sccm $O_{2}$
Temperature	200°C		100°C
Deposition Rates in nm/s	0.3	0.1	0	2.25
	0.57	0.1	0.25	2.25
	0	0.4	0.75	1.75
	0.07		1.25	1.25
	0.13		1.75	0.75
	0.22		2.25	0.25
	0.33		2.25	0
	0.49
	0.75
	1	0

Abstract

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Tables (3)

Equations (11)

Applied Optics