Infrared optical constants and roughness factor functions determination: the HTHRTR method

Marta Klanjšek Gunde; Boris Aleksandrov

doi:10.1364/AO.30.003186

Applied Optics
Vol. 30,
Issue 22,
pp. 3186-3196
(1991)
•https://doi.org/10.1364/AO.30.003186

Infrared optical constants and roughness factor functions determination: the H_TH_RTR method

Marta Klanjšek Gunde and Boris Aleksandrov

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Marta Klanjšek Gunde and Boris Aleksandrov, "Infrared optical constants and roughness factor functions determination: the HTHRTR method," Appl. Opt. 30, 3186-3196 (1991)

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Abstract

This method was developed to determine the complex infrared optical constant of a single free-standing partially absorbing plate as well as a thin solid film deposited on it. The method is based on exact formulas normal transmittance T and near-normal reflectance R of the substrate as well as the film–substrate double layer. Coherent multiple reflections throughout the film and incoherent multiple reflections in the substrate as well as the intensity losses on the rough surface are taken into account. The influence of various data on solution of the inverse problem is discussed by a contour map study. The method is explained using examples of both- and single-side-polished silicon wafers where the transmission and reflection roughness factor functions H_T,H_R are determined for the rough surface. The thin-film example has been the silicon oxide formed on the single-side-polished silicon substrate by chemical vapor deposition.

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Equations (21)

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(d/λ)	n₁	(n₁d/λ)	m	m/16
0.4	1.06	0.424	7	0.4375
0.4	1.28	0.512	8	0.5
0.4	1.85	0.740	12	0.75
0.4	2.54	1.016	16	1.
0.4	2.92	1.168	19	1.1875
0.4	4.48	1.792	29	1.8125
0.4	4.99	1.996	32	2.
0.4	5.68	2.272	36	2.25
0.4	6.24	2.496	40	2.5
0.4	6.91	2.764	44	2.75
0.4	7.49	2.996	48	3.
0.3	1.19	0.357	6	0.375
0.3	1.71	0.513	8	0.5
0.3	2.36	0.708	11	0.6875
0.3	4.37	1.311	21	1.3125
0.3	4.97	1.491	24	1.5
0.3	5.92	1.776	28	1.75
0.3	6.65	1.995	32	2.
0.3	7.55	2.265	36	2.25
0.2	1.44	0.288	5	0.3125
0.2	4.26	0.852	14	0.875
0.2	4.94	0.988	16	1.
0.2	6.40	1.28	20	1.25
0.2	7.18	1.496	24	1.5
0.1	1.92	0.192	3	0.1875

Initial Reticle	Following Reticle	Magnifying Steps	n₂	k₂(×10⁻⁶)
100 × 100	10 × 10	0	3.410946	3.7942
100 × 100	10 × 10	1	3.411403	3.5632
100 × 100	10 × 10	2	3.411406	3.5618
50 × 50	10 × 10	0	3.410440	4.0663
50 × 50	10 × 10	1	3.411350	3.5897
50 × 50	10 × 10	2	3.411406	3.5620

	ν(cm⁻¹)	λ(μm)	n₁	(n₁d/λ)	m	m/16
A	3480	2.87	1.11	0.429	7	0.4375
B	3209	3.12	1.41	0.501	8	0.5
C	3200	3.12	2.82	1.002	16	1
D	3000	3.33	3.20	1.066	17	1.0625
E	2291	4.36	2.72	0.692	11	0.6875
F	2150	4.65	1.34	0.319	5	0.3125
G	1060	9.43	2.68	0.315	5	0.3125
H	950	10.53	2.25	0.237	4	0.25

(d/λ)	n₁	(n₁d/λ)	m	m/16
0.4	1.06	0.424	7	0.4375
0.4	1.28	0.512	8	0.5
0.4	1.85	0.740	12	0.75
0.4	2.54	1.016	16	1.
0.4	2.92	1.168	19	1.1875
0.4	4.48	1.792	29	1.8125
0.4	4.99	1.996	32	2.
0.4	5.68	2.272	36	2.25
0.4	6.24	2.496	40	2.5
0.4	6.91	2.764	44	2.75
0.4	7.49	2.996	48	3.
0.3	1.19	0.357	6	0.375
0.3	1.71	0.513	8	0.5
0.3	2.36	0.708	11	0.6875
0.3	4.37	1.311	21	1.3125
0.3	4.97	1.491	24	1.5
0.3	5.92	1.776	28	1.75
0.3	6.65	1.995	32	2.
0.3	7.55	2.265	36	2.25
0.2	1.44	0.288	5	0.3125
0.2	4.26	0.852	14	0.875
0.2	4.94	0.988	16	1.
0.2	6.40	1.28	20	1.25
0.2	7.18	1.496	24	1.5
0.1	1.92	0.192	3	0.1875

Initial Reticle	Following Reticle	Magnifying Steps	n₂	k₂(×10⁻⁶)
100 × 100	10 × 10	0	3.410946	3.7942
100 × 100	10 × 10	1	3.411403	3.5632
100 × 100	10 × 10	2	3.411406	3.5618
50 × 50	10 × 10	0	3.410440	4.0663
50 × 50	10 × 10	1	3.411350	3.5897
50 × 50	10 × 10	2	3.411406	3.5620

Abstract

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Figures (14)

Tables (3)

Equations (21)

Applied Optics