Structure analysis and models for optical constants of discontinuous metallic silver films

R. R. Singer; A. Leitner; F. R. Aussenegg

doi:10.1364/JOSAB.12.000220

Journal of the Optical Society of America B
Vol. 12,
Issue 2,
pp. 220-228
(1995)
•https://doi.org/10.1364/JOSAB.12.000220

Structure analysis and models for optical constants of discontinuous metallic silver films

R. R. Singer, A. Leitner, and F. R. Aussenegg

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R. R. Singer, A. Leitner, and F. R. Aussenegg, "Structure analysis and models for optical constants of discontinuous metallic silver films," J. Opt. Soc. Am. B 12, 220-228 (1995)

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Abstract

Existing models for optical properties of metallic particle films differ in their treatment of the mechanisms for particle interaction. For model comparison and improvement we fit the calculated optical spectra to obtained ones experimentally by variation of several structural parameters. The deviation of the model’s structure parameters from those obtained experimentally (by analysis of transmission electron microscope pictures) permits comparison of models. We find that for thermally treated silver island films in the mass thickness range 1–6 nm the particle interaction is described best by a quasi-static dipole–dipole interaction, neglecting retardation effects and mirror dipole effects.

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	d_w (nm)	Oblate Spheroid			Prolate Spheroid			Exp. Results

		M1	M2	M3	M1	M2	M3
ā (nm)	1	3.8	3.8	4.1	4.0	4.0	4.0
	2	6.0	6.0	5.7	6.0	6.0	6.0	5.3	±0.6
	3	7.9	7.9	8.0	8.0	8.0	8.0	8.3	±0.6
	4	10.1	10.1	10.2	10.0	10.0	10.5	10.4	±0.6
	5	10.6	10.7	11.3	10.6	10.6	10.5	10.7	±0.6
	6	19.5	19.8	19.9	19.0	19.2	19.7	20.7	±0.7
q	1	0.30	0.53	0.48	0.25	0.31	0.32
	2	0.39	0.55	0.55	0.31	0.36	0.37	0.33	±0.03
	3	0.42	0.66	0.71	0.35	0.44	0.44	0.39	±0.04
	4	0.45	0.73	0.73	0.36	0.48	0.44	0.40	±0.04
	5	0.49	0.77	0.80	0.41	0.53	0.52	0.44	±0.04
	6	0.41	0.62	0.70	0.32	0.42	0.45	0.39	±0.04
d_eff (nm)	1	1.0	1.2	1.0	1.0	0.9	1.0	1.0	±0.1
	2	2.0	1.6	1.4	2.0	1.6	1.6	2.0	±0.1
	3	3.0	2.8	2.8	3.0	2.7	2.6	3.0	±0.1
	4	4.0	4.1	3.7	4.0	3.9	3.4	4.0	±0.1
	5	5.0	5.0	4.9	5.0	4.7	4.2	5.0	±0.1
	6	6.1	6.0	5.6	5.9	6.1	6.0	6.0	±0.1
σ_γ (nm)	1	1.42	1.45	1.34	1.22	1.21	1.19
	2	1.46	1.32	1.22	1.23	1.21	1.16	1.56	±0.08
	3	1.49	1.33	1.18	1.22	1.21	1.13	1.51	±0.07
	4	1.45	1.32	1.18	1.20	1.21	1.07	1.59	±0.08
	5	1.45	1.41	1.16	1.25	1.25	1.11	1.56	±0.12
	6	1.45	1.42	1.08	1.28	1.27	1.04	1.77	±0.29
b (nm)	1				3.0	2.3	2.3
	2				4.8	3.4	3.3	5.3	±0.6
	3				6.5	4.6	4.5	7.4	±0.6
	4				8.3	6.0	5.8	9.3	±0.6
	5				9.2	6.7	6.1	9.8	±0.6
	6				13.8	10.9	9.9	16.4	±0.7
∊_m (nm)	1	1.48			1.49			1.58
	2	1.46			1.50			1.58
	3	1.49			1.46			1.58
	4	1.45			1.55			1.58
	5	1.45			1.56			1.58
	6	1.45			1.38			1.58
σ_fit	1	0.001	0.002	0.002	0.001	0.001	0.001
	2	0.001	0.002	0.002	0.002	0.002	0.002
	3	0.002	0.003	0.012	0.002	0.003	0.008
	4	0.006	0.005	0.027	0.005	0.005	0.021
	5	0.009	0.009	0.036	0.009	0.009	0.019
	6	0.016	0.016	0.006	0.017	0.016	0.006

	d_w (nm)	Oblate Spheroid		Prolate Spheroid

		M1	M2	M1	M2
ā (nm)	1	3.0	3.0	3.0	3.0
	2	7.0	7.0	5.9	6.0
	3	10.0	10.0	9.5	9.4
q	1	0.48	0.76	0.36	0.48
	2	0.55	0.83	0.39	0.53
	3	0.62	0.91	0.39	0.53
d_eff (nm)	1	1.0	1.0	1.0	1.0
	2	2.1	2.1	2.1	2.1
	3	3.0	3.2	2.9	3.1
σ_γ (nm)	1	1.48	1.48	1.30	1.29
	2	1.55	1.52	1.35	1.36
	3	1.83	1.80	1.53	1.52
$\bar{b} (nm)$	1			2.1	1.6
	2			3.8	2.9
	3			5.6	4.4
∊_m (nm)	1	1.49		1.50
	2	1.47		1.55
	3	1.38		1.46
σ_fit	1	0.001	0.001	0.001	0.001
	2	0.004	0.004	0.004	0.004
	3	0.025	0.026	0.025	0.027

	d_w (nm)	Oblate Spheroid			Prolate Spheroid			Exp. Results

		M1	M2	M3	M1	M2	M3
ā (nm)	1	3.8	3.8	4.1	4.0	4.0	4.0
	2	6.0	6.0	5.7	6.0	6.0	6.0	5.3	±0.6
	3	7.9	7.9	8.0	8.0	8.0	8.0	8.3	±0.6
	4	10.1	10.1	10.2	10.0	10.0	10.5	10.4	±0.6
	5	10.6	10.7	11.3	10.6	10.6	10.5	10.7	±0.6
	6	19.5	19.8	19.9	19.0	19.2	19.7	20.7	±0.7
q	1	0.30	0.53	0.48	0.25	0.31	0.32
	2	0.39	0.55	0.55	0.31	0.36	0.37	0.33	±0.03
	3	0.42	0.66	0.71	0.35	0.44	0.44	0.39	±0.04
	4	0.45	0.73	0.73	0.36	0.48	0.44	0.40	±0.04
	5	0.49	0.77	0.80	0.41	0.53	0.52	0.44	±0.04
	6	0.41	0.62	0.70	0.32	0.42	0.45	0.39	±0.04
d_eff (nm)	1	1.0	1.2	1.0	1.0	0.9	1.0	1.0	±0.1
	2	2.0	1.6	1.4	2.0	1.6	1.6	2.0	±0.1
	3	3.0	2.8	2.8	3.0	2.7	2.6	3.0	±0.1
	4	4.0	4.1	3.7	4.0	3.9	3.4	4.0	±0.1
	5	5.0	5.0	4.9	5.0	4.7	4.2	5.0	±0.1
	6	6.1	6.0	5.6	5.9	6.1	6.0	6.0	±0.1
σ_γ (nm)	1	1.42	1.45	1.34	1.22	1.21	1.19
	2	1.46	1.32	1.22	1.23	1.21	1.16	1.56	±0.08
	3	1.49	1.33	1.18	1.22	1.21	1.13	1.51	±0.07
	4	1.45	1.32	1.18	1.20	1.21	1.07	1.59	±0.08
	5	1.45	1.41	1.16	1.25	1.25	1.11	1.56	±0.12
	6	1.45	1.42	1.08	1.28	1.27	1.04	1.77	±0.29
b (nm)	1				3.0	2.3	2.3
	2				4.8	3.4	3.3	5.3	±0.6
	3				6.5	4.6	4.5	7.4	±0.6
	4				8.3	6.0	5.8	9.3	±0.6
	5				9.2	6.7	6.1	9.8	±0.6
	6				13.8	10.9	9.9	16.4	±0.7
∊_m (nm)	1	1.48			1.49			1.58
	2	1.46			1.50			1.58
	3	1.49			1.46			1.58
	4	1.45			1.55			1.58
	5	1.45			1.56			1.58
	6	1.45			1.38			1.58
σ_fit	1	0.001	0.002	0.002	0.001	0.001	0.001
	2	0.001	0.002	0.002	0.002	0.002	0.002
	3	0.002	0.003	0.012	0.002	0.003	0.008
	4	0.006	0.005	0.027	0.005	0.005	0.021
	5	0.009	0.009	0.036	0.009	0.009	0.019
	6	0.016	0.016	0.006	0.017	0.016	0.006

	d_w (nm)	Oblate Spheroid		Prolate Spheroid

		M1	M2	M1	M2
ā (nm)	1	3.0	3.0	3.0	3.0
	2	7.0	7.0	5.9	6.0
	3	10.0	10.0	9.5	9.4
q	1	0.48	0.76	0.36	0.48
	2	0.55	0.83	0.39	0.53
	3	0.62	0.91	0.39	0.53
d_eff (nm)	1	1.0	1.0	1.0	1.0
	2	2.1	2.1	2.1	2.1
	3	3.0	3.2	2.9	3.1
σ_γ (nm)	1	1.48	1.48	1.30	1.29
	2	1.55	1.52	1.35	1.36
	3	1.83	1.80	1.53	1.52
$\bar{b} (nm)$	1			2.1	1.6
	2			3.8	2.9
	3			5.6	4.4
∊_m (nm)	1	1.49		1.50
	2	1.47		1.55
	3	1.38		1.46
σ_fit	1	0.001	0.001	0.001	0.001
	2	0.004	0.004	0.004	0.004
	3	0.025	0.026	0.025	0.027

Abstract

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Figures (7)

Tables (2)

Equations (27)

Journal of the Optical Society of America B