First-principles study of anisotropic physical properties of layered nitride BaMN2 (M = Ti, Zr, Hf)

YU Jianxiang; LIANG Hualin; YANG Yijun; MING Xing

doi:10.7498/aps.74.20241665

Abstract

Ternary layered nitrides have received widespread attention due to their unique electrical, optical and optoelectronic properties, which are promising for the fabrication of low-cost and high-efficiency optoelectronic materials, solar cell materials and photocatalysts. Although there is a lack of experimental reports on BaTiN₂ so far, BaZrN₂ and BaHfN₂ have been synthesized experimentally by solid state methods. However, their optical and electrical transport properties have not been investigated systematically. This work is to systematically investigates the mechanical, electronic, optical absorption, carrier transport, and dielectric response properties of BaMN₂ (M = Ti, Zr, Hf) nitrides through first-principles calculations based on density functional theory. Due to the quasi-two-dimensional layered arrangement of [MN₂]^2– slabs, the ionic bonds between Ba²⁺ and N^3–, and the weak interactions between the slabs, the deformation along this direction is most likely to occur under the action of external stress. BaMN₂ nitrides exhibit significant anisotropic physical properties. Firstly, the mechanical properties of BaMN₂, such as bulk modulus, shear modulus, Young’s modulus, and Poisson’s ratio, show prominent anisotropy. The lower modulus, higher Poisson’s ratios and Pugh’s modulus ratios indicate good flexibility of the BaMN₂ nitrides. In addition, BaMN₂ has indirect bandgap values (1.75–2.25 eV) within the visible-light energy range, which meets the basic requirement for the band gap of a photocatalyst for water splitting (greater than 1.23 eV). Moreover, BaMN₂ has suitable band-edge positions. The appropriate bandgap values and band-edge positions indicate their broad application prospects in the absorber layer of solar cells and photocatalytic water decomposition. Due to the significant difference in the effective mass of its charge carriers between different directions, BaMN₂ exhibits ultrahigh anisotropic carrier mobility (on the order of 10³ cm²⋅s^–1⋅v^–1) and lower exciton binding energy. At the same time, there are significant differences in atomic arrangement and bonding interactions between the in-plane direction and out of plane direction, resulting in high anisotropic visible-light absorption coefficient (on the order of 10⁵ cm^–1) in the low energy region. In contrast, the increase of the opportunity for electrons to transition from occupied to unoccupied states leads to more complex light absorption and relatively reduced anisotropy in higher energy region. Furthermore, the special layered structure has lower polarizability and higher vibration frequency along the vertical direction perpendicular to the [MN₂]^2– layers, rendering BaMN₂ nitrides show high dielectric constants. These excellent anisotropic mechanical, optoelectronic, and transport properties allow BaMN₂ layered nitrides to be used as promising semiconductor materials in the fields of optoelectronics, photovoltaics, and photocatalysis.

Keywords:

Authors and contacts

1.
College of Materials Science and Engineering, Guilin University of Technology, Guilin 541004, China
2.
College of Physics and Electronic Information Engineering, Guilin University of Technology, Guilin 541004, China

Corresponding author: MING Xing, mingxing@glut.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 12264011) and the China Undergraduate Innovation Research Program (Grant No. 202410596471).

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References

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Cited By

图 1 BaMN₂的晶体结构模型, 蓝色、粉色和青色的球分别表示Ba, M和N原子

Figure 1. Crystal structures of BaMN₂, the blue, pink and azure balls denote Ba, M and N atoms.

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图 2 (a) BaTiN₂, (b) BaZrN₂和(c) BaHfN₂的ELF切片图, 上图和下图分别是(001)平面和(100)平面

Figure 2. Slices of the electron localization function (ELF) for (a) BaTiN₂, (b) BaZrN₂ and (c) BaHfN₂, top and bottom planes are the (001) and (100) planes, respectively.

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图 3 BaMN₂的体模量、剪切模量、杨氏模量和泊松比ν　(a) BaTiN₂; (b) BaZrN₂; (c) BaHfN₂

Figure 3. Bulk modulus, shear modulus, Young’s modulus and Poisson’s ratio ν of BaMN₂: (a) BaTiN₂; (b) BaZrN₂; (c) BaHfN₂.

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图 4 (a) BaTiN₂, (b) BaZrN₂和(c) BaHfN₂的电子能带结构和态密度以及(d)带边位置

Figure 4. Electronic band structures and density of states (DOS) of (a) BaTiN₂, (b) BaZrN₂, and (c) BaHfN₂ as well as (d) band edge positions.

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图 5 CBM和VBM在实空间中的波函数　(a) BaTiN₂; (b) BaZrN₂; (c) BaHfN₂

Figure 5. Wave function of CBM and VBM in real space: (a) BaTiN₂; (b) BaZrN₂; (c) BaHfN₂.

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图 6 BaMN₂的可见光吸收系数　(a) BaTiN₂; (b) BaZrN₂; (c) BaHfN₂

Figure 6. Optical absorption coefficient of BaMN₂: (a) BaTiN₂; (b) BaZrN₂; (c) BaHfN₂.

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表 1 BaMN₂的晶格常数, 晶格体积和M—N键长的理论计算值与实验(括号中数据)对比

Table 1. Comparison of theoretically calculated and experimental measured (in parenthesis) lattice constants, lattice volumes and the M—N bond lengths of BaMN₂.

	a/Å	b/Å	c/Å	V/Å³	l_M-N1/Å	l_M-N2/Å
BaTiN₂	4.011	4.011	8.107	130.454	1.806	2.105
BaZrN₂	4.188 (4.161^[26])	4.188 (4.161^[26])	8.478 (8.392^[26])	148.725	2.022 (2.06^[28])	2.213 (2.208^[28])
BaHfN₂	4.149 (4.128^[27])	4.149 (4.128^[27])	8.481 (8.382^[27])	145.971	1.991 (2.05^[28])	2.196 (2.186^[28])

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表 2 BaMN₂的弹性常数C_ij、体模量B、剪切模量G、杨氏模量Y、泊松比ν、Pugh模量比(B/G). 模量下标V和R分别表示Voigt-Reuss-Hill模型近似中Voigt和Reuss模型的结果, 没有下标的B和G定义为Voigt和Reuss值的平均值

Table 2. Elastic constants C_ij, bulk modulus B, shear modulus G, Young’s modulus Y, Poisson’s ratio ν, Pugh’s ratio (B/G) of BaMN₂. The subscripts V and R of the moduli denote results from the Voigt and Reuss models, while B and G moduli without subscripts are defined as the average of the Reuss and Voight values from the Voigt-Reuss-Hill approximations.

Materials	C₁₁/GPa	C₁₂/GPa	C₁₃/GPa	C₂₂/GPa	C₂₃/GPa	C₃₃/GPa	C₄₄/GPa	C₅₅/GPa	C₆₆/GPa
BaTiN₂	180.639	126.136	56.702	180.639	56.702	121.448	38.493	38.493	118.834
BaZrN₂	151.829	110.797	66.919	151.829	66.919	129.396	37.723	37.723	95.162
BaHfN₂	163.876	118.407	69.072	163.876	69.072	130.419	37.811	37.811	103.077
Materials	B_V/GPa	B_R/GPa	B	G_V	G_R	G/GPa	Y/GPa	ν	B/G
BaTiN₂	106.870	95.480	101.175	55.380	42.420	48.900	126.253	0.294	2.070
BaZrN₂	102.480	98.630	100.555	46.680	36.539	41.610	109.580	0.318	2.420
BaHfN₂	107.920	102.211	105.066	49.180	38.366	43.773	115.194	0.317	2.400

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表 3 BaMN₂的有效质量m^*、形变势常数E_i和载流子迁移率μ

Table 3. Effective mass m^*, deformation potential constants E_i, and carrier mobility μ of BaMN₂.

Material	Carrier	m^*/m₀		E_i/eV		μ/(cm²·s^–1·V^–1)
Material	Carrier	x/y	z	x/y	z	x/y	z
BaTiN₂	Electron	0.237	29.929	–7.366	–4.159	7439.406	0.088
BaTiN₂	Hole	0.536	2.560	–8.141	–5.514	791.781	23.277
BaZrN₂	Electron	0.229	32.657	–7.652	–2.399	6313.601	0.225
BaZrN₂	Hole	0.400	5.435	–8.017	–4.669	1426.402	5.267
BaHfN₂	Electron	0.223	30.268	–7.650	–0.679	7286.037	3.429
BaHfN₂	Hole	0.415	3.608	–7.870	–3.731	1457.158	23.152

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表 4 介电张量的对角线分量的电子和离子贡献和介电常数

Table 4. Diagonal components of the dielectric tensor from the electronic and ionic contributions and dielectric permittivity.

Material	$ {\varepsilon }_{{\mathrm{e}}{\mathrm{l}}{\mathrm{e}}} $		$ {\varepsilon }_{{\mathrm{i}}{\mathrm{o}}{\mathrm{n}}} $		$ {\varepsilon }_{{\mathrm{r}}} $
Material	x/y	z	x/y	z	$ {\varepsilon }_{{\mathrm{r}}} $
BaTiN₂	10.59	7.48	35.70	18.40	39.48
BaZrN₂	8.30	7.88	39.08	18.61	40.42
BaHfN₂	7.71	7.46	34.37	16.32	35.98

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表 5 BaMN₂的波恩有效电荷张量及平均值($ {Z}^{*} $)

Table 5. Born effective charges tensors along three directions (x, y and z) and the average value ($ {Z}^{*} $) of BaMN₂.

	BaTiN₂			BaZrN₂			BaHfN₂
	x/y	z	$ {Z}^{*} $	x/y	z	$ {Z}^{*} $	x/y	z	$ {Z}^{*} $
Ba	2.884	3.094	2.954	2.687	3.233	2.869	2.751	3.130	2.877
M	5.355	2.689	4.466	4.811	3.362	4.328	4.617	3.098	4.111
N1	–2.611	–4.357	–3.193	–2.582	–4.839	–3.334	–2.613	–4.552	–3.259
N2	–5.650	–1.433	–4.244	–4.926	–1.764	–3.872	–4.763	–1.672	–3.733

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表 6 声子模及其频率$ {\omega }_{\lambda } $(以cm^–1为单位)和有效电荷$ \widetilde{{Z}_{\lambda }^{*}} $(以|e|表示)

Table 6. The mode, mode frequencies $ {\omega }_{\lambda } $ (in cm^–1) and effective charges $ \widetilde{{Z}_{\lambda }^{*}} $ (in |e|).

Mode	Symmetry	Active	Polarization	BaTiN₂		BaZrN₂		BaHfN₂
Mode	Symmetry	Active	Polarization	$ {\omega }_{\lambda } $	$ \widetilde{{Z}_{\lambda }^{*}} $	$ {\omega }_{\lambda } $	$ \widetilde{{Z}_{\lambda }^{*}} $	$ {\omega }_{\lambda } $	$ \widetilde{{Z}_{\lambda }^{*}} $
1-2	E_u	IR	x-y	119	0.52	67	0.34	62	0.24
3-4	E_g	Raman	x-y	80	0	73	0	76	0
5	A_2u	IR	z	110	0.52	99	0.43	89	0.30
6	A_1g	Raman	z	115	0	109	0	109	0
7-8	E_g	Raman	x-y	225	0	157	0	139	0
9	A_1g	Raman	z	285	0	222	0	166	0
10-11	E_u	IR	x-y	286	0.23	204	0.31	213	0.48
12-13	E_g	Raman	x-y	336	0	262	0	234	0
14	B_1g	Raman	z	300	0	311	0	325	0
15-16	E_u	IR	x-y	332	6.10	359	4.38	363	3.84
17	A_2u	IR	z	496	0.04	462	0.69	452	0.78
18-19	E_g	Raman	x-y	560	0	541	0	572	0
20	A_2u	IR	z	682	2.90	588	3.07	605	2.53
21	A_1g	Raman	z	769	0	679	0	683	0

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[1]	Ahmed S, Yi J B 2017 Nano-Micro Lett. 9 106313 Google Scholar
[2]	Liao L, Lin Y C, Bao M Q, Cheng R, Bai J W, Liu Y, Qu Y Q, Wang K L, Huang Y, Duan X F 2010 Nature 467 305 Google Scholar
[3]	Mitta S B, Choi M S, Nipane A, Ali F, Kim C, Teherani J T, Hone J, Yoo W J 2021 2D Mater. 8 012002 Google Scholar
[4]	Lu C C, Lin Y C, Yeh C H, Huang J C, Chiu P W J A N 2012 Nanscale 6 4469 Google Scholar
[5]	Allain A, Kang J, Banerjee K, Kis A J N M 2015 Nat. Mater. 14 1195 Google Scholar
[6]	张冷, 张鹏展, 刘飞, 李方政, 罗毅, 侯纪伟, 吴孔平 2024 物理学报 73 047101 Google Scholar Zhang L, Zhang P Z, Liu F, Li F Z, Luo Y, Hou J W, Wu K P 2024 Acta Phys. Sin. 73 047101 Google Scholar
[7]	Ling X, Wang H, Huang S X, Xia F N, Dresselhaus M S 2015 PNAS 112 4523 Google Scholar
[8]	Qiao J S, Kong X H, Hu Z X, Yang F, Ji W 2014 Nat. Commun. 5 4475 Google Scholar
[9]	程秋振, 黄引, 李玉辉, 张凯, 冼国裕, 刘鹤元, 车冰玉, 潘禄禄, 韩烨超, 祝轲, 齐琦, 谢耀锋, 潘金波, 陈海龙, 李永峰, 郭辉, 杨海涛, 高鸿钧 2023 物理学报 72 218102 Google Scholar Cheng Q Z, Huang Y, Li Y H, Zhang K, Xian G Y, Liu H Y, Che B Y, Pan L L, Han Y C, Zhu K, Qi Q, Xie Y F, Pan J B, Chen H L, Li Y F, Guo H, Yang H T, Gao H J 2023 Acta Phys. Sin. 72 218102 Google Scholar
[10]	Xue P Y, Chu D D, Xie C W, Tikhonov E, Butler K T 2022 J. Phys. Chem. C 126 17398 Google Scholar
[11]	Greenaway A L, Ke S, Culman T, Talley K R, Mangum J S, Heinselman K N, Kingsbury R S, Smaha R W, Gish M K, Miller E M, Persson K A, Gregoire J M, Bauers S R, Neaton J B, Tamboli A C, Zakutayev A 2022 J. Am. Chem. Soc. 144 13673 Google Scholar
[12]	Szymanski N J, Walters L N, Hellman O, Gall D, Khare S V 2018 J. Mater. Chem. A 6 20852 Google Scholar
[13]	Arca E, Perkins J D, Lany S, Mis A, Chen B R, Dippo P, Partridge J L, Sun W, Holder A, Tamboli A C, Toney M F, Schelhas L T, Ceder G, Tumas W, Teeter G, Zakutayev A 2019 Mater. Horiz. 6 1669 Google Scholar
[14]	Bauers S R, Holder A, Sun W, Melamed C L, Woods-Robinson R, Mangum J, Perkins J, Tumas W, Gorman B, Tamboli A, Ceder G, Lany S, Zakutayev A 2019 PNAS 116 14829 Google Scholar
[15]	Hinuma Y, Hatakeyama T, Kumagai Y, Burton L A, Sato H, Muraba Y, Iimura S, Hiramatsu H, Tanaka I, Hosono H J N C 2016 Nat. Commun. 7 11962 Google Scholar
[16]	Kangsabanik J, Alam A 2019 Phys. Rev. Mater. 3 105405 Google Scholar
[17]	Shiraishi A, Kimura S, He X, Watanabe N, Katase T, Ide K, Minohara M, Matsuzaki K, Hiramatsu H, Kumigashira H, Hosono H, Kamiya T 2022 Inorg. Chem. 61 6650 Google Scholar
[18]	Zakutayev A, Jankousky M, Wolf L, Feng Y, Rom C L, Bauers S R, Borkiewicz O, LaVan D A, Smaha R W, Stevanovic V 2024 Nat. Synth 3 1471 Google Scholar
[19]	Ming X, Kuang X J 2024 Nat. Synth. 3 1444 Google Scholar
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First-principles study of anisotropic physical properties of layered nitride BaMN₂ (M = Ti, Zr, Hf)

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Corresponding author: MING Xing, mingxing@glut.edu.cn

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