Optical properties of metallic films for vertical-cavity optoelectronic devices

Aleksandar D. Rakić; Aleksandra B. Djurišić; Jovan M. Elazar; Marian L. Majewski

doi:10.1364/AO.37.005271

Optical properties of metallic films for vertical-cavity optoelectronic devices

Aleksandar D. Rakić, Aleksandra B. Djurišić, Jovan M. Elazar, and Marian L. Majewski

Applied Optics
Vol. 37,
Issue 22,
pp. 5271-5283
(1998)
•https://doi.org/10.1364/AO.37.005271

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Aleksandar D. Rakić, Aleksandra B. Djurišić, Jovan M. Elazar, and Marian L. Majewski, "Optical properties of metallic films for vertical-cavity optoelectronic devices," Appl. Opt. 37, 5271-5283 (1998)

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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
- Laser materials (160.3380)
- Optical properties (160.4760)
- Vertical cavity surface emitting lasers (250.7260)
- Thin films, optical properties (310.6860)

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History
- Original Manuscript: December 22, 1997
- Published: August 1, 1998

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Abstract

We present models for the optical functions of 11 metals used as mirrors and contacts in optoelectronic and optical devices: noble metals (Ag, Au, Cu), aluminum, beryllium, and transition metals (Cr, Ni, Pd, Pt, Ti, W). We used two simple phenomenological models, the Lorentz–Drude (LD) and the Brendel–Bormann (BB), to interpret both the free-electron and the interband parts of the dielectric response of metals in a wide spectral range from 0.1 to 6 eV. Our results show that the BB model was needed to describe appropriately the interband absorption in noble metals, while for Al, Be, and the transition metals both models exhibit good agreement with the experimental data. A comparison with measurements on surface normal structures confirmed that the reflectance and the phase change on reflection from semiconductor–metal interfaces (including the case of metallic multilayers) can be accurately described by use of the proposed models for the optical functions of metallic films and the matrix method for multilayer calculations.

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Metal	ℏω_p
Ag	9.01
Au	9.03
Cu	10.83
Al	14.98
Be	18.51
Cr	10.75
Ni	15.92
Pd	9.72
Pt	9.59
Ti	7.29
W	13.22

	Metal
Parameters	Ag	Au	Cu	Al	Be	Cr	Ni	Pd	Pt	Ti	W
f ₀	0.845	0.760	0.575	0.523	0.084	0.168	0.096	0.330	0.333	0.148	0.206
Γ₀	0.048	0.053	0.030	0.047	0.035	0.047	0.048	0.008	0.080	0.082	0.064
f ₁	0.065	0.024	0.061	0.227	0.031	0.151	0.100	0.649	0.191	0.899	0.054
Γ₁ a	3.886	0.241	0.378	0.333	1.664	3.175	4.511	2.950	0.517	2.276	0.530
ω₁ a	0.816	0.415	0.291	0.162	0.100	0.121	0.174	0.336	0.780	0.777	1.004
f ₂	0.124	0.010	0.104	0.050	0.140	0.150	0.135	0.121	0.659	0.393	0.166
Γ₂	0.452	0.345	1.056	0.312	3.395	1.305	1.334	0.555	1.838	2.518	1.281
ω₂	4.481	0.830	2.957	1.544	1.032	0.543	0.582	0.501	1.314	1.545	1.917
f ₃	0.011	0.071	0.723	0.166	0.530	1.149	0.106	0.638	0.547	0.187	0.706
Γ₃	0.065	0.870	3.213	1.351	4.454	2.676	2.178	4.621	3.668	1.663	3.332
ω₃	8.185	2.969	5.300	1.808	3.183	1.970	1.597	1.659	3.141	2.509	3.580
f ₄	0.840	0.601	0.638	0.030	0.130	0.825	0.729	0.453	3.576	0.001	2.590
Γ₄	0.916	2.494	4.305	3.382	1.802	1.335	6.292	3.236	8.517	1.762	5.836
ω₄	9.083	4.304	11.18	3.473	4.604	8.775	6.089	5.715	9.249	19.43	7.498
f ₅	5.646	4.384	—	—	—	—	—	—	—	—	—
Γ₅	2.419	2.214	—	—	—	—	—	—	—	—	—
ω₅	20.29	13.32	—	—	—	—	—	—	—	—	—

	Metal
Parameter	Ag	Au	Cu	Al	Be	Cr	Ni	Pd	Pt	Ti	W
f ₀	0.821	0.770	0.562	0.526	0.081	0.154	0.083	0.330	0.333	0.126	0.197
Γ₀	0.049	0.050	0.030	0.047	0.035	0.048	0.022	0.009	0.080	0.067	0.057
f ₁	0.050	0.054	0.076	0.213	0.066	0.338	0.357	0.769	0.186	0.427	0.006
Γ₁ a	0.189	0.074	0.056	0.312	2.956	4.256	2.820	2.343	0.498	1.877	3.689
ω₁ a	2.025	0.218	0.416	0.163	0.131	0.281	0.317	0.066	0.782	1.459	0.481
σ₁ a	1.894	0.742	0.562	0.013	0.277	0.115	0.606	0.694	0.031	0.463	3.754
f ₂	0.133	0.050	0.081	0.060	0.067	0.261	0.039	0.093	0.665	0.218	0.022
Γ₂	0.067	0.035	0.047	0.315	3.962	3.957	0.120	0.497	1.851	0.100	0.277
ω₂	5.185	2.885	2.849	1.561	0.469	0.584	1.059	0.502	1.317	2.661	0.985
σ₂	0.665	0.349	0.469	0.042	3.167	0.252	1.454	0.027	0.096	0.506	0.059
f ₃	0.051	0.312	0.324	0.182	0.346	0.817	0.127	0.309	0.551	0.513	0.136
Γ₃	0.019	0.083	0.113	1.587	2.398	2.218	1.822	2.022	2.604	0.615	1.433
ω₃	4.343	4.069	4.819	1.827	2.827	1.919	4.583	2.432	3.189	0.805	1.962
σ₃	0.189	0.830	1.131	0.256	1.446	0.225	0.379	1.167	0.766	0.799	0.273
f ₄	0.467	0.719	0.726	0.014	0.311	0.105	0.654	0.409	2.214	0.0002	2.648
Γ₄	0.117	0.125	0.172	2.145	3.904	6.983	6.637	0.119	2.891	4.109	4.555
ω₄	9.809	6.137	8.136	4.495	4.318	6.997	8.825	5.987	8.236	19.86	5.442
σ₄	1.170	1.246	1.719	1.735	0.893	4.903	0.510	1.331	1.146	2.854	1.912
f ₅	4.000	1.648	—	—	—	—	—	—	—	—	—
Γ₅	0.052	0.179	—	—	—	—	—	—	—	—	—
ω₅	18.56	27.97	—	—	—	—	—	—	—	—	—
σ₅	0.516	1.795	—	—	—	—	—	—	—	—	—

Metal	ℏω_p
Ag	9.01
Au	9.03
Cu	10.83
Al	14.98
Be	18.51
Cr	10.75
Ni	15.92
Pd	9.72
Pt	9.59
Ti	7.29
W	13.22

	Metal
Parameters	Ag	Au	Cu	Al	Be	Cr	Ni	Pd	Pt	Ti	W
f ₀	0.845	0.760	0.575	0.523	0.084	0.168	0.096	0.330	0.333	0.148	0.206
Γ₀	0.048	0.053	0.030	0.047	0.035	0.047	0.048	0.008	0.080	0.082	0.064
f ₁	0.065	0.024	0.061	0.227	0.031	0.151	0.100	0.649	0.191	0.899	0.054
Γ₁ a	3.886	0.241	0.378	0.333	1.664	3.175	4.511	2.950	0.517	2.276	0.530
ω₁ a	0.816	0.415	0.291	0.162	0.100	0.121	0.174	0.336	0.780	0.777	1.004
f ₂	0.124	0.010	0.104	0.050	0.140	0.150	0.135	0.121	0.659	0.393	0.166
Γ₂	0.452	0.345	1.056	0.312	3.395	1.305	1.334	0.555	1.838	2.518	1.281
ω₂	4.481	0.830	2.957	1.544	1.032	0.543	0.582	0.501	1.314	1.545	1.917
f ₃	0.011	0.071	0.723	0.166	0.530	1.149	0.106	0.638	0.547	0.187	0.706
Γ₃	0.065	0.870	3.213	1.351	4.454	2.676	2.178	4.621	3.668	1.663	3.332
ω₃	8.185	2.969	5.300	1.808	3.183	1.970	1.597	1.659	3.141	2.509	3.580
f ₄	0.840	0.601	0.638	0.030	0.130	0.825	0.729	0.453	3.576	0.001	2.590
Γ₄	0.916	2.494	4.305	3.382	1.802	1.335	6.292	3.236	8.517	1.762	5.836
ω₄	9.083	4.304	11.18	3.473	4.604	8.775	6.089	5.715	9.249	19.43	7.498
f ₅	5.646	4.384	—	—	—	—	—	—	—	—	—
Γ₅	2.419	2.214	—	—	—	—	—	—	—	—	—
ω₅	20.29	13.32	—	—	—	—	—	—	—	—	—

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