First-principles study of structure, elasticity, and electronic properties of ternary semiconductor Al4In2N6 under high pressure

CHEN Meijuan; GUO Jiaxin; WU Hao; ZHENG Xiaoran; MIN Nan; TIAN Hui; LI Quanjun; DU Shiyu; SHEN Longhai

doi:10.7498/aps.74.20250287

Abstract
The effects of pressure on the crystal structure, elastic properties, and electronic characteristics of Al₄In₂N₆ are systematically studied using first-principles density functional theory. The lattice constants of Al₄In₂N₆ decrease with the increase of pressure, exhibiting anisotropic compression with greater compressibility along the c-axis. In terms of mechanical properties, the bulk modulus increases with the increase of pressure, indicating enhanced compressive resistance. Notably, the Vickers hardness decreases with the increase of pressure, indicating that high pressure can induce plastic deformation in Al₄In₂N₆. The calculations of elastic constants and phonon spectra confirm that Al₄In₂N₆ retains mechanical and dynamical stability in the pressure range of 0–30 GPa. Electronic structure calculations reveal that Al₄In₂N₆ possesses a direct band gap, and non-overlapping conduction and valence bands at the Fermi level. The conduction band has a higher carrier mobility than the valence band. The band gap increases almost linearly with pressure rising from 3.35 eV at 0 GPa to 4.24 eV at 30 GPa, demonstrating significant pressure-induced modulation of the electronic structure. Furthermore, the analysis of differential charge densities reveals that increasing pressure can strengthen the Al-N and In-N bonds in Al₄In₂N₆ through shortened interatomic distances and stronger atomic interactions, increasing its compression resistance. In summary, this study not only deepens our understanding of the high-pressure properties of Al₄In₂N₆ but also provides theoretical guidance for its application in UV optoelectronics. Pressure-driven modulation of its mechanical and electronic characteristics highlights its potential in efficient high-pressure optoelectronic devices and materials.

Keywords:
ternary semiconductor /

high pressure /

first-principles /

band gap
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图 1 Al₄In₂N₆的晶体结构

Figure 1. Crystal structure of Al₄In₂N₆.

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图 2 Al₄In₂N₆的相对晶格参数和相对体积随压力的变化

Figure 2. Pressure dependence of relative lattice parameters and relative unit cell volume for Al₄In₂N₆.

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图 3 不同压力下Al₄In₂N₆的差分电荷密度　(a) 0 GPa; (b) 15 GPa; (c) 30 GPa

Figure 3. Differential charge density of Al₄In₂N₆ under different pressures: (a) 0 GPa; (b) 15 GPa; (c) 30 GPa.

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图 4 不同压力下Al₄In₂N₆的声子色散曲线　(a) 0 GPa; (b) 10 GPa; (c) 20 GPa; (d) 30 GPa

Figure 4. Phonon dispersion curves for Al₄In₂N₆ at different pressures: (a) 0 GPa; (b) 10 GPa; (c) 20 GPa; (d) 30 GPa.

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图 5 Al₄In₂N₆的弹性常数(a)和弹性模量(b)随压力的变化

Figure 5. The elastic constants (a) and elastic modulus (b) of Al₄In₂N₆ change with pressure.

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图 6 在0, 10, 20, 30 GPa压力下Al₄In₂N₆的三维体积模量((a)—(d))、剪切模量((e)—(h))、杨氏模量((i)—(l))

Figure 6. The 3D plot of bulk modulus ((a)–(d)), shear modulus ((e)–(h)), and Young’s modulus ((i)–(l)) of Al₄In₂N₆ under pressures of 0, 10, 20, and 30 GPa.

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图 7 Al₄In₂N₆在(a) 0 GPa、(b) 5 GPa、(c) 10 GPa、(d) 15 GPa、(e) 20 GPa、(f) 25 GPa、(g) 30 GPa下的能带结构和(h)带隙随压强的变化趋势

Figure 7. The band structures of Al₄In₂N₆ at (a) 0 GPa, (b) 5 GPa, (c) 10 GPa, (d) 15 GPa, (e) 20 GPa, (f) 25 GPa, (g) 30 GPa, and (h) the variation trend of the band gap with pressure.

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图 8 Al₄In₂N₆在(a) 0, (b) 20和(c) 30 GPa下的总态密度和分波态密度

Figure 8. The total density of states and partial density of states of Al₄In₂N₆ at (a) 0, (b) 20, and (c) 30 GPa.

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表 1 Al₄In₂N₆在不同压力下的晶格参数

Table 1. Lattice parameters of Al₄In₂N₆ under different pressures.

Pressure/GPa	a/Å	b/Å	c/Å
0	9.832	5.654	5.250
5	9.749	5.603	5.195
10	9.669	5.557	5.149
15	9.600	5.516	5.107
20	9.535	5.478	5.068
25	9.477	5.445	5.032
30	9.422	5.413	4.999

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表 2 在0—30 GPa 压力 Al₄In₂N₆的弹性常数

Table 2. Elastic constant of Al₄In₂N₆ under 0–30 GPa pressures.

Pressure/GPa	C₁₁/GPa	C₁₂/GPa	C₁₃/GPa	C₂₂/GPa	C₂₃/GPa	C₃₃/GPa	C₄₄/GPa	C₅₅/GPa	C₆₆/GPa
0	318.606	113.886	89.017	305.200	92.444	311.408	84.739	84.903	95.602
5	330.169	126.317	103.218	327.053	105.181	326.999	86.887	88.385	96.321
10	340.077	143.266	118.822	337.579	124.623	338.138	85.186	87.028	94.397
15	359.171	163.187	130.986	352.270	135.623	357.799	88.682	87.873	95.539
20	375.952	175.971	146.621	363.912	151.179	361.684	89.566	86.445	93.548
25	389.382	192.252	161.374	370.366	171.460	363.533	88.451	87.052	91.683
30	402.037	207.158	171.490	379.130	181.476	381.927	86.653	84.002	90.021

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表 3 0—30 GPa 压力下Al₄In₂N₆的弹性模量(B, G, E, B/G)、硬度H_v和泊松比$\mu $

Table 3. The elastic modulus (B, G, E, B/G), hardness (H_v), and Poisson’s ratio ($\mu $) of Al₄In₂N₆ under pressures of 0–30 GPa.

Pressure/GPa	B/GPa	E/GPa	G/GPa	(B/G)	$\mu $	H_V/GPa
0	169.443	240.336	95.099	1.782	0.264	11.998
5	183.649	247.651	97.099	1.891	0.275	11.377
10	198.718	245.38	94.800	2.096	0.294	9.952
15	214.192	251.75	96.522	2.219	0.304	9.447
20	227.465	250.967	95.344	2.386	0.316	8.625
25	241.177	247.277	93.023	2.593	0.329	7.711
30	253.426	245.888	91.866	2.759	0.338	7.123

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First-principles study of structure, elasticity, and electronic properties of ternary semiconductor Al₄In₂N₆ under high pressure

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