Photometric methods for determining the optical constants and the thicknesses of thin absorbing films: criteria for precise and unambiguous determination of n, k, and d in a wide spectral range

Tzwetanka Babeva; Snejana Kitova; Ivan Konstantinov

doi:10.1364/AO.40.002682

Photometric methods for determining the optical constants and the thicknesses of thin absorbing films: criteria for precise and unambiguous determination of n, k, and d in a wide spectral range

Tzwetanka Babeva, Snejana Kitova, and Ivan Konstantinov

Applied Optics
Vol. 40,
Issue 16,
pp. 2682-2686
(2001)
•https://doi.org/10.1364/AO.40.002682

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Tzwetanka Babeva, Snejana Kitova, and Ivan Konstantinov, "Photometric methods for determining the optical constants and the thicknesses of thin absorbing films: criteria for precise and unambiguous determination of n, k, and d in a wide spectral range," Appl. Opt. 40, 2682-2686 (2001)

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Optics & Photonics Topics
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The topics in this list come from the OSA Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- Instrumentation, measurement, and metrology (120.0120)
- Optical constants (120.4530)
- Spectrometers and spectroscopic instrumentation (120.6200)
- Thin films (310.0310)
- Thin films, optical properties (310.6860)

About this Article
History
- Original Manuscript: August 9, 2000
- Revised Manuscript: February 15, 2001
- Published: June 1, 2001

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Abstract

The application of error analysis within a certain algorithm for the most accurate and unambiguous determination of refractive index n, absorption coefficient k, and thickness d of thin absorbing films in a wide spectral range is illustrated with three examples. Thin films of a dye, Ag, and Au are selected because their optical constants (small n for Ag and Au and considerable variations of n and k for the dye films) along with their thinness make investigating these thin films difficult. The important steps of the algorithm that ensure reliable isolation of the physically correct solutions and maximum accuracy of n and k in the spectral range investigated are also demonstrated.

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λ (nm)	Dye					Ag					Au
λ (nm)	T a	R a	R _m	$R_{p}^{70}$	$R_{mp}^{70}$	T a	R a	R _m	$R_{p}^{70}$	$R_{mp}^{70}$	T a	R a	R _m	$R_{p}^{70}$	$R_{mp}^{70}$
400	80.2	6.4	18.2	5.6	34.6	26.7	67.5	80.2	63.8	74.1	12.2	38.8	46.2	17.6	23.9
425	86.5	6.0	16.6	6.1	33.2	21.3	73.9	81.3	66.5	73.6	13.9	38.1	47.4	17.3	24.1
450	90.8	5.0	18.3	6.4	30.5	17.5	78.4	82.5	68.6	73.6	16.4	36.6	48.3	17.2	24.6
475	93.4	4.1	23.8	6.1	24.8	14.7	81.6	83.7	70.4	73.6	20.6	34.6	49.7	18.2	26.1
500	88.8	4.9	30.9	5.0	11.3	12.5	84.0	84.7	72.0	73.8	25.2	36.0	54.4	25.4	33.4
525	70.7	11.0	38.7	15.1	4.3	10.8	85.9	85.5	73.4	74.2	24.8	45.2	61.8	36.6	44.4
550	36.7	20.6	39.5	33.5	30.2	9.5	87.3	86.4	74.7	74.5	21.8	55.5	67.9	45.6	51.5
575	18.7	26.7	38.6	30.0	30.8	8.4	88.6	87.2	75.9	75.1	18.4	64.0	72.5	52.6	56.6
600	10.7	30.0	37.4	25.2	27.3	7.5	89.5	87.9	77.1	75.6	15.5	70.4	76.2	58.2	60.2
625	5.9	32.8	36.6	20.4	22.5	6.8	90.4	88.5	77.8	76.2	13.1	75.3	79.0	62.7	63.3
650	5.0	31.0	32.1	13.8	15.5	6.2	91.1	89.1	78.7	76.7	11.2	79.0	81.4	66.4	65.9
675	4.8	31.7	32.1	12.4	13.8	5.6	91.8	89.7	79.4	77.2	9.6	81.8	83.4	69.4	68.0
700	2.9	35.1	34.8	10.1	10.1	5.1	92.3	90.3	80.2	77.9	8.3	83.8	85.0	71.8	69.8
725	6.3	30.9	32.2	4.8	3.9	4.7	92.9	90.7	81.1	78.5	7.3	85.4	86.2	73.8	71.3
750	52.1	20.8	25.7	5.4	0.4	4.4	93.3	91.2	81.8	79.1	6.4	86.5	87.2	75.4	72.6
775	64.7	34.2	11.8	3.7	3.1	4.1	93.7	91.6	82.3	79.6	5.8	87.4	88.1	76.5	73.6
800	66.0	33.8	5.2	1.8	6.8	3.4	94.0	91.9	83.6	80.9	4.9	88.2	88.7	75.9	72.4

Thin Film	n		k
Thin Film	λ (nm)	Method	λ (nm)	Method
Dye (d = 102 ± 1.4 nm)	400–440	(TR)	400–440	(TR)
	440–470	(TR _m $R_{mp}^{70}$ )	440–470	(TR _m $R_{mp}^{70}$ )
	470–630	(TR _m)	470–750	(TR _m)
	630–715	( ${TRR}_{mp}^{70}$ )	750–800	(TR)
	715–760	(TR _m)
	760–800	( ${TRR}_{mp}^{70}$ )
			400–490	( ${TRR}_{mp}^{70}$ )
Ag (d = 31 ± 1.5 nm)	400–800	( ${TR}_{p}^{70}$ )	490–660	(TR)
			660–800	(TR _m)
Au (d = 37 ± 2 nm)	400–700	( ${TRR}_{p}^{70}$ )	400–800	(TR)
	700–800	( ${TR}_{p}^{70}$ )

λ (nm)	Dye					Ag					Au
λ (nm)	T a	R a	R _m	$R_{p}^{70}$	$R_{mp}^{70}$	T a	R a	R _m	$R_{p}^{70}$	$R_{mp}^{70}$	T a	R a	R _m	$R_{p}^{70}$	$R_{mp}^{70}$
400	80.2	6.4	18.2	5.6	34.6	26.7	67.5	80.2	63.8	74.1	12.2	38.8	46.2	17.6	23.9
425	86.5	6.0	16.6	6.1	33.2	21.3	73.9	81.3	66.5	73.6	13.9	38.1	47.4	17.3	24.1
450	90.8	5.0	18.3	6.4	30.5	17.5	78.4	82.5	68.6	73.6	16.4	36.6	48.3	17.2	24.6
475	93.4	4.1	23.8	6.1	24.8	14.7	81.6	83.7	70.4	73.6	20.6	34.6	49.7	18.2	26.1
500	88.8	4.9	30.9	5.0	11.3	12.5	84.0	84.7	72.0	73.8	25.2	36.0	54.4	25.4	33.4
525	70.7	11.0	38.7	15.1	4.3	10.8	85.9	85.5	73.4	74.2	24.8	45.2	61.8	36.6	44.4
550	36.7	20.6	39.5	33.5	30.2	9.5	87.3	86.4	74.7	74.5	21.8	55.5	67.9	45.6	51.5
575	18.7	26.7	38.6	30.0	30.8	8.4	88.6	87.2	75.9	75.1	18.4	64.0	72.5	52.6	56.6
600	10.7	30.0	37.4	25.2	27.3	7.5	89.5	87.9	77.1	75.6	15.5	70.4	76.2	58.2	60.2
625	5.9	32.8	36.6	20.4	22.5	6.8	90.4	88.5	77.8	76.2	13.1	75.3	79.0	62.7	63.3
650	5.0	31.0	32.1	13.8	15.5	6.2	91.1	89.1	78.7	76.7	11.2	79.0	81.4	66.4	65.9
675	4.8	31.7	32.1	12.4	13.8	5.6	91.8	89.7	79.4	77.2	9.6	81.8	83.4	69.4	68.0
700	2.9	35.1	34.8	10.1	10.1	5.1	92.3	90.3	80.2	77.9	8.3	83.8	85.0	71.8	69.8
725	6.3	30.9	32.2	4.8	3.9	4.7	92.9	90.7	81.1	78.5	7.3	85.4	86.2	73.8	71.3
750	52.1	20.8	25.7	5.4	0.4	4.4	93.3	91.2	81.8	79.1	6.4	86.5	87.2	75.4	72.6
775	64.7	34.2	11.8	3.7	3.1	4.1	93.7	91.6	82.3	79.6	5.8	87.4	88.1	76.5	73.6
800	66.0	33.8	5.2	1.8	6.8	3.4	94.0	91.9	83.6	80.9	4.9	88.2	88.7	75.9	72.4

Thin Film	n		k
Thin Film	λ (nm)	Method	λ (nm)	Method
Dye (d = 102 ± 1.4 nm)	400–440	(TR)	400–440	(TR)
	440–470	(TR _m $R_{mp}^{70}$ )	440–470	(TR _m $R_{mp}^{70}$ )
	470–630	(TR _m)	470–750	(TR _m)
	630–715	( ${TRR}_{mp}^{70}$ )	750–800	(TR)
	715–760	(TR _m)
	760–800	( ${TRR}_{mp}^{70}$ )
			400–490	( ${TRR}_{mp}^{70}$ )
Ag (d = 31 ± 1.5 nm)	400–800	( ${TR}_{p}^{70}$ )	490–660	(TR)
			660–800	(TR _m)
Au (d = 37 ± 2 nm)	400–700	( ${TRR}_{p}^{70}$ )	400–800	(TR)
	700–800	( ${TR}_{p}^{70}$ )

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