Revisiting the Fabry–Perot reflectivity method for mid-infrared optical index measurement: case study of InGaAs, AlInAs, and InP

G. Quinchard; T. Poletti; R. Zakhama; J. Pereira; A. Larrue; G. Badano; C. Licitra; R. Espiau de Lamaestre; J. L. Reverchon; A. Delga

doi:10.1364/AO.456827

Applied Optics
Vol. 61,
Issue 14,
pp. 4079-4086
(2022)
•https://doi.org/10.1364/AO.456827

Revisiting the Fabry–Perot reflectivity method for mid-infrared optical index measurement: case study of InGaAs, AlInAs, and InP

G. Quinchard, T. Poletti, R. Zakhama, J. Pereira, A. Larrue, G. Badano, C. Licitra, R. Espiau de Lamaestre, J. L. Reverchon, and A. Delga

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G. Quinchard, T. Poletti, R. Zakhama, J. Pereira, A. Larrue, G. Badano, C. Licitra, R. Espiau de Lamaestre, J. L. Reverchon, and A. Delga, "Revisiting the Fabry–Perot reflectivity method for mid-infrared optical index measurement: case study of InGaAs, AlInAs, and InP," Appl. Opt. 61, 4079-4086 (2022)

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About this Article
History
- Original Manuscript: February 22, 2022
- Revised Manuscript: April 13, 2022
- Manuscript Accepted: April 19, 2022
- Published: May 2, 2022

Abstract

We revisit the Fabry–Perot (FP) reflectivity method to measure optical indices in the mid-infrared spectrum. This simple approach can be readily implemented using a standard Fourier transform infrared spectrometer. Measuring samples with multiple heights allows for enhanced precision of the measurement, making the FP method consistent in values and uncertainties with more advanced ellipsometric measurements. An extensive discussion about experimental errors is carried out. Results between 4 and 12 µm for AlInAs, n-doped InGaAs, and InP, which are the most standard materials for quantum cascade lasers, are given.

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Material	Hall Doping ( ${c m}^{- 3}$ )	Thickness (nm)
InGaAs	nid	5389	5283	5192
InGaAs	4e17	5014	4923	4724
InGaAs	6e18	4775	4547	4055
InGaAs	2e19	3770	3502	2919
AlInAs	nid	3868	–	–
InP	nid	4807	4544	4047
InP	1e17	4995	4493	3973
InP	1e18	4891	4314	3275

Sample	$ϵ_{\infty}$	$ω_{F C A}$	$γ_{F C A}$	–
InGaAs nid	11.23(11.23)	–	–	–
InGaAs 4e17	11.25(11.23)	89(89)	0.01(0.01)	–
InGaAs 6e18	11.22(11.23)	252(251)	4.45(4.30)	–
InGaAs 2e19	11.23(11.23)	428(434)	6.72(6.10)	–
AlInAs	9.15(9.15)	–	–	–
	$ω_{gap}$	$γ_{gap}$	$E_{gap}$	–
InGaAs nid	544(538)	67(70)	748(750)	–
InGaAs 4e17	510	73	772	–
InGaAs 6e18	510	73	841	–
InGaAs 2e19	510	73	965	–
AlInAs	1453(9.15)	60(434)	1455(1430)	–
Sample	$ϵ_{\infty}$	$ω_{FCA}$	$γ_{FCA}$	–
InP nid	10.14	–	–	–
InP 1e17	10.14	60.65	0.01	–
InP 1e18	10.14	193.80	9.28	–
	$ω_{LO}$	$γ_{LO}$	$ω_{TO}$	$γ_{TO}$
InP nid	48.40	0.67	43.82	0.47
InP 1e17	48.40	0.67	43.82	0.47
InP 1e18	48.40	0.67	43.82	0.47

Sample	$Δ ϵ_{\infty}$	$Δ ω_{F C A}$	$Δ γ_{F C A}$	–
InGaAs nid	0.042(0.37%)	–	–	–
InGaAs 4e17	0.018(0.16%)	0.326 (0.37%)	0.0003(3%)	–
InGaAs 6e18	0.007(0.06%)	0.098 (0.04%)	0.004 (0.09%)	–
InGaAs 2e19	0.006(0.053%)	0.13(0.03%)	0.005 (0.07%)	–
AlInAs	0.237(2.59%)	–	–	–
	$Δ ω_{gap}$	$Δ γ_{gap}$	$Δ E_{gap}$	–
InGaAs nid	25(4.6%)	1(1.5%)	14(1.9%)	–
InGaAs 4e17	–	–	–	–
InGaAs 6e18	–	–	–	–
InGaAs 2e19	–	–	–	–
AlInAs	271(18.7%)	7(11.7%)	118(8.11%)	–
Sample	$Δ ϵ_{\infty}$	$Δ ω_{FCA}$	$Δ γ_{FCA}$	–
InP nid	–	–	–	–
InP 1e17	–	0.171 (0.28%)	0.0003(3%)	–
InP 1e18	–	0.114 (0.06%)	0.020 (0.002%)	–
	$Δ ω_{LO}$	$Δ γ_{LO}$	$Δ ω_{TO}$	$Δ γ_{TO}$
InP nid	2.41(4.98%)	0.154 (23.0%)	2.96(6.75%)	0.147 (31.3%)
InP 1e17	–	–	–	–
InP 1e18	–	–	–	–

Material	Hall Doping ( ${c m}^{- 3}$ )	Thickness (nm)
InGaAs	nid	5389	5283	5192
InGaAs	4e17	5014	4923	4724
InGaAs	6e18	4775	4547	4055
InGaAs	2e19	3770	3502	2919
AlInAs	nid	3868	–	–
InP	nid	4807	4544	4047
InP	1e17	4995	4493	3973
InP	1e18	4891	4314	3275

Sample	$ϵ_{\infty}$	$ω_{F C A}$	$γ_{F C A}$	–
InGaAs nid	11.23(11.23)	–	–	–
InGaAs 4e17	11.25(11.23)	89(89)	0.01(0.01)	–
InGaAs 6e18	11.22(11.23)	252(251)	4.45(4.30)	–
InGaAs 2e19	11.23(11.23)	428(434)	6.72(6.10)	–
AlInAs	9.15(9.15)	–	–	–
	$ω_{gap}$	$γ_{gap}$	$E_{gap}$	–
InGaAs nid	544(538)	67(70)	748(750)	–
InGaAs 4e17	510	73	772	–
InGaAs 6e18	510	73	841	–
InGaAs 2e19	510	73	965	–
AlInAs	1453(9.15)	60(434)	1455(1430)	–
Sample	$ϵ_{\infty}$	$ω_{FCA}$	$γ_{FCA}$	–
InP nid	10.14	–	–	–
InP 1e17	10.14	60.65	0.01	–
InP 1e18	10.14	193.80	9.28	–
	$ω_{LO}$	$γ_{LO}$	$ω_{TO}$	$γ_{TO}$
InP nid	48.40	0.67	43.82	0.47
InP 1e17	48.40	0.67	43.82	0.47
InP 1e18	48.40	0.67	43.82	0.47

Abstract

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Equations (10)

Applied Optics