Parameterized optical properties of In<sub>x</sub>Al<sub>1-x</sub>P alloys

Hoang Tung Nguyen; Hoang Tung Nguyen; Tae Jung Kim; Tae Jung Kim; Tae Jung Kim; Han Gyeol Park; Van Long Le; Van Long Le; Xuan Au Nguyen; Xuan Au Nguyen; Young Dong Kim; Young Dong Kim

doi:10.1364/AO.387891

Applied Optics
Vol. 59,
Issue 9,
pp. 2924-2928
(2020)
•https://doi.org/10.1364/AO.387891

Parameterized optical properties of In_xAl_1-xP alloys

Hoang Tung Nguyen, Tae Jung Kim, Han Gyeol Park, Van Long Le, Xuan Au Nguyen, and Young Dong Kim

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Hoang Tung Nguyen, Tae Jung Kim, Han Gyeol Park, Van Long Le, Xuan Au Nguyen, and Young Dong Kim, "Parameterized optical properties of In_xAl_1-xP alloys," Appl. Opt. 59, 2924-2928 (2020)

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Abstract

We report values of parametric-model (PM) parameters that can be used to obtain dielectric functions (refractive indices) from 1.5 to 6.0 eV for ${{\rm In}_x}{{\rm Al}_{1 - x}}{\rm P}$ alloys of arbitrary compositions $x$. Using reported pseudo-dielectric data for several In compositions, we extract their dielectric functions by multilayer calculations, then parameterize them with PM lineshapes that well describe the asymmetric nature of their critical point (CP) contributions. We follow the ${E_0}$ fundamental bandgap as a function of $x$, and determine the composition of the indirect-to-direct crossover.

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CP	No.	$C_{L}$	$C_{U}$	A	B (meV)	$E_{C} (e V)$	$E_{L M}$	$A_{L M}$	$E_{U M}$	$A_{U M}$
$E_{0}$ (direct)	0	8	2	0.8392	13.438*	1.34	0.5*	0.5*	0.5*	0.41*
$A$	1	0	2	0	0	1.4534	0.98*	0.366*	0.068*	0.001*
$E_{1}$	2	0	4	13.581	42.494	3.1554	0.378*	0.1437	0.76*	0.2525
$E_{1} + Δ_{1}$	3	0	4	10.703	44.61	3.272	0.65*	0.01*	0.02*	0.01*
$E_{0}^{'}$	4	3	6	15.585	82.164	4.72	0.6136	0.3*	0.8314*	0.1334
$E_{2}$	5	3	6	20.997	140.08	4.9457	0.166*	0.031	0.827*	0.3034
$E_{1}^{'}$	6	5	7	8.7141	228.16*	6.3331*	0.635*	0.246*	0.3*	0.01*
	7					12*
$E_{0}$ (indirect)	8					1.34
Pole position (eV)				20*
Pole amplitude				221.3

	$a$	$b$	$c$	$d$
$E_{0}$ (indirect) ( $x \leq 0.609$ )	2.4312	−0.1284	0	0
$E_{0}$ (indirect) ( $x > 0.609$ )	3.5401	−1.6108	−0.5533	0
$E_{0}$ (direct)	3.5401	−1.6108	−0.5533	0
$A$	4.2007	−1.2782	−5.2495	0
$E_{1}$	4.6813	−2.7027	1.8782	−0.701
$E_{1} + Δ_{1}$	4.6813	−1.7126	0.3033	0
$E_{0}^{'}$	4.7657	0.1651	−0.2105	0
$E_{2}$	5.0817	0.0363	-0.1692	0
$A$ ( $E_{0}$ (direct))	0.2459	0.3466	−0.7926	1.0405
$A (A) (x \leq 0.310)$	1	−4.4023	4.8357	0
$A (A) (x > 0.310)$	0	0	0	0
$A (E_{1}) (x \leq 0.186)$	35.0278	−87.2001	146.7052	0
$A (E_{1}) (x > 0.186)$	26.7877	−11.263	−23.1271	21.2149
$A (E_{1} + Δ_{1}) (x \leq 0.186)$	0	39.8375	−104.1153	−10.6644
$A (E_{1} + Δ_{1}) (x > 0.186)$	7.1446	−30.922	67.6282	−33.2868
$A (E_{0}^{'}) (x \leq 0.186)$	32.1072	−98.973	211.3042	0
$A (E_{0}^{'}) (x > 0.186)$	20.9184	−5.0879	36.4877	−36.7451
$A (E_{2}) (x \leq 0.186)$	82.1644	−310.6837	488.9889	0
$A (E_{2}) (x > 0.186)$	63.3292	−150.304	190.0016	−81.946
$A (E_{1}^{'})$	12.6039	−3.7114	3.1043	−3.1956
$B (A) (x \leq 0.310)$	39.3189	−31.7754	−98.5278	0
$B (A) (x > 0.310)$	0	0	0	0
$B (E_{1}) (x \leq 0.186)$	75.0019	1006.6174	−2195.998	0
$B (E_{1}) (x > 0.186)$	153.5349	280.9878	−704.9152	310.1909
$B (E_{1} + Δ_{1})$	0.01	827.9176	−1466.8608	681.8892
$B (E_{0}^{'})$	70.1204	149.4588	134.9545	−273.1497
$B (E_{2})$	372.9092	−460.5347	524.3955	−297.7224
$A_{L M} (E_{1})$	0.0223	0.6899	−1.2381	0.6677
$A_{U M} (E_{1})$	0.5808	−0.2515	0.3218	−0.3972
$E_{L M} (E_{0}^{'})$	0.9222	−0.2495	0.1726	−0.2317
$A_{U M} (E_{0}^{'})$	0.3377	−0.5708	0.7077	−0.3458
$A_{L M} (E_{2})$	0.0849	0.1667	−0.4248	0.2047
$A_{U M} (E_{2})$	0.1048	0.5318	−0.2233	−0.1059
Pole	72.3142	187.8433	−36.4595	−2.4189

CP	No.	$C_{L}$	$C_{U}$	A	B (meV)	$E_{C} (e V)$	$E_{L M}$	$A_{L M}$	$E_{U M}$	$A_{U M}$
$E_{0}$ (direct)	0	8	2	0.8392	13.438*	1.34	0.5*	0.5*	0.5*	0.41*
$A$	1	0	2	0	0	1.4534	0.98*	0.366*	0.068*	0.001*
$E_{1}$	2	0	4	13.581	42.494	3.1554	0.378*	0.1437	0.76*	0.2525
$E_{1} + Δ_{1}$	3	0	4	10.703	44.61	3.272	0.65*	0.01*	0.02*	0.01*
$E_{0}^{'}$	4	3	6	15.585	82.164	4.72	0.6136	0.3*	0.8314*	0.1334
$E_{2}$	5	3	6	20.997	140.08	4.9457	0.166*	0.031	0.827*	0.3034
$E_{1}^{'}$	6	5	7	8.7141	228.16*	6.3331*	0.635*	0.246*	0.3*	0.01*
	7					12*
$E_{0}$ (indirect)	8					1.34
Pole position (eV)				20*
Pole amplitude				221.3

	$a$	$b$	$c$	$d$
$E_{0}$ (indirect) ( $x \leq 0.609$ )	2.4312	−0.1284	0	0
$E_{0}$ (indirect) ( $x > 0.609$ )	3.5401	−1.6108	−0.5533	0
$E_{0}$ (direct)	3.5401	−1.6108	−0.5533	0
$A$	4.2007	−1.2782	−5.2495	0
$E_{1}$	4.6813	−2.7027	1.8782	−0.701
$E_{1} + Δ_{1}$	4.6813	−1.7126	0.3033	0
$E_{0}^{'}$	4.7657	0.1651	−0.2105	0
$E_{2}$	5.0817	0.0363	-0.1692	0
$A$ ( $E_{0}$ (direct))	0.2459	0.3466	−0.7926	1.0405
$A (A) (x \leq 0.310)$	1	−4.4023	4.8357	0
$A (A) (x > 0.310)$	0	0	0	0
$A (E_{1}) (x \leq 0.186)$	35.0278	−87.2001	146.7052	0
$A (E_{1}) (x > 0.186)$	26.7877	−11.263	−23.1271	21.2149
$A (E_{1} + Δ_{1}) (x \leq 0.186)$	0	39.8375	−104.1153	−10.6644
$A (E_{1} + Δ_{1}) (x > 0.186)$	7.1446	−30.922	67.6282	−33.2868
$A (E_{0}^{'}) (x \leq 0.186)$	32.1072	−98.973	211.3042	0
$A (E_{0}^{'}) (x > 0.186)$	20.9184	−5.0879	36.4877	−36.7451
$A (E_{2}) (x \leq 0.186)$	82.1644	−310.6837	488.9889	0
$A (E_{2}) (x > 0.186)$	63.3292	−150.304	190.0016	−81.946
$A (E_{1}^{'})$	12.6039	−3.7114	3.1043	−3.1956
$B (A) (x \leq 0.310)$	39.3189	−31.7754	−98.5278	0
$B (A) (x > 0.310)$	0	0	0	0
$B (E_{1}) (x \leq 0.186)$	75.0019	1006.6174	−2195.998	0
$B (E_{1}) (x > 0.186)$	153.5349	280.9878	−704.9152	310.1909
$B (E_{1} + Δ_{1})$	0.01	827.9176	−1466.8608	681.8892
$B (E_{0}^{'})$	70.1204	149.4588	134.9545	−273.1497
$B (E_{2})$	372.9092	−460.5347	524.3955	−297.7224
$A_{L M} (E_{1})$	0.0223	0.6899	−1.2381	0.6677
$A_{U M} (E_{1})$	0.5808	−0.2515	0.3218	−0.3972
$E_{L M} (E_{0}^{'})$	0.9222	−0.2495	0.1726	−0.2317
$A_{U M} (E_{0}^{'})$	0.3377	−0.5708	0.7077	−0.3458
$A_{L M} (E_{2})$	0.0849	0.1667	−0.4248	0.2047
$A_{U M} (E_{2})$	0.1048	0.5318	−0.2233	−0.1059
Pole	72.3142	187.8433	−36.4595	−2.4189

Abstract

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Equations (4)

Applied Optics