-
三元层状氮化物因其独特的电学、光学和光电性质而受到广泛关注, 有希望用于制造低成本、高效率的光电材料、太阳能电池材料和光催化剂. 三元层状氮化物BaZrN2和BaHfN2已经被固态实验合成, 但其光学性质和电输运性质尚未被系统地研究. 本文采用基于密度泛函理论的第一性原理计算系统地研究了BaMN2(M = Ti, Zr, Hf)氮化物的力学、电子、光吸收、载流子传输和介电响应性质. 由于BaMN2氮化物由准二维[MN2]2–板层排列组成独特的层状晶体结构, 且板层内的电子云重叠较多形成强共价键, 板层之间的成键作用较弱, 使得其物理性质表现出显著的各向异性. 首先, BaMN2的体模量、剪切模量、杨氏模量和泊松比等力学性质表现出各向异性, 具有较低的模量、较高的泊松比和Pugh模量比, 表明其具有良好的塑性. 此外, BaMN2具有处于可见光能量范围内的间接带隙值(1.75—2.25 eV), 适宜用于太阳能电池吸收层, 且带边位置满足水分解光催化剂的要求. 由于其载流子在不同方向上的有效质量存在巨大差异, 使得它们还具有超高各向异性的载流子迁移率(103 cm2/(s·v)数量级)和较低的激子结合能. 同时, 沿平面内方向和面外方向的原子排列和成键作用存在显著差异, 导致在低能量区域沿平面内具有非常强的光吸收能力和较高的各向异性可见光吸收系数(105 cm–1数量级); 而在较高的能量区域中, 电子从占据态到非占据态的跃迁概率增大, 导致对光的吸收情况变得更复杂, 各向异性相对减弱. 此外, 特殊的层状结构沿垂直于板层的方向具有较低极化率和较高振动频率, 使得BaMN2有较高的介电常数. 这些优异的各向异性的力学、光电和输运性质使得BaMN2层状氮化物可以作为光电子、光伏和光催化领域的有前景的半导体材料.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 N3–, 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:
- nitrides /
- carrier mobility /
- anisotropy /
- first-principles study
-
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
Fig. 1. Crystal structures of BaMN2, the blue, pink and azure balls denote Ba, M and N atoms.
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
Fig. 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.
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
Fig. 3. Bulk modulus, shear modulus, Young’s modulus and Poisson’s ratio ν of BaMN2: (a) BaTiN2; (b) BaZrN2; (c) BaHfN2.
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
Fig. 4. Electronic band structures and density of states (DOS) of (a) BaTiN2, (b) BaZrN2, and (c) BaHfN2 as well as (d) band edge positions.
图 5 CBM和VBM在实空间中的波函数 (a) BaTiN2; (b) BaZrN2; (c) BaHfN2
Fig. 5. Wave function of CBM and VBM in real space: (a) BaTiN2; (b) BaZrN2; (c) BaHfN2.
图 6 BaMN2的可见光吸收系数 (a) BaTiN2; (b) BaZrN2; (c) BaHfN2
Fig. 6. Optical absorption coefficient of BaMN2: (a) BaTiN2; (b) BaZrN2; (c) BaHfN2.
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.
下载: 导出CSV
表 2 BaMN2的弹性常数Cij、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 Cij, 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 BV/GPa BR/GPa B GV GR 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
下载: 导出CSV
表 3 BaMN2的有效质量m*、形变势常数Ei和载流子迁移率μ
Table 3. Effective mass m*, deformation potential constants Ei, and carrier mobility μ of BaMN2.
Material Carrier m*/m0 Ei/eV μ/(cm2·s–1·v–1) x/y z x/y z x/y z BaTiN2 Electron 0.237 29.929 –7.366 –4.159 7439.406 0.088 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 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 Hole 0.415 3.608 –7.870 –3.731 1457.158 23.152
下载: 导出CSV
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}}} $ x/y z x/y z 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
下载: 导出CSV
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
下载: 导出CSV
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 $ {\omega }_{\lambda } $ $ \widetilde{{Z}_{\lambda }^{*}} $ $ {\omega }_{\lambda } $ $ \widetilde{{Z}_{\lambda }^{*}} $ $ {\omega }_{\lambda } $ $ \widetilde{{Z}_{\lambda }^{*}} $ 1-2 Eu IR x-y 119 0.52 67 0.34 62 0.24 3-4 Eg Raman x-y 80 0 73 0 76 0 5 A2u IR z 110 0.52 99 0.43 89 0.30 6 A1g Raman z 115 0 109 0 109 0 7-8 Eg Raman x-y 225 0 157 0 139 0 9 A1g Raman z 285 0 222 0 166 0 10-11 Eu IR x-y 286 0.23 204 0.31 213 0.48 12-13 Eg Raman x-y 336 0 262 0 234 0 14 B1g Raman z 300 0 311 0 325 0 15-16 Eu IR x-y 332 6.10 359 4.38 363 3.84 17 A2u IR z 496 0.04 462 0.69 452 0.78 18-19 Eg Raman x-y 560 0 541 0 572 0 20 A2u IR z 682 2.90 588 3.07 605 2.53 21 A1g Raman z 769 0 679 0 683 0
下载: 导出CSV
-
[1] Ahmed S, Yi J B 2017 Nano-Micro Lett. 9 106313
[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
[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 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 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
[20] Liu J W, Lu S L, Wang Y H, Li C, Ming X, Kuang X J 2022 Chem. Mater. 34 4505
[21] Gregory D H, Barker M G, Edwards P P, Siddons D J 1996 Inorg. Chem. 35 7608
Google Scholar
[22] Seeger O, Strähle J 1994 Z. Naturforsch. B 49 1169
Google Scholar
[23] Li X H, Wang X M, Han Y F, Jing X P, Huang Q Z, Kuang X J, Gao Q L, Chen J, Xing X R 2017 Chem. Mater. 29 1989
Google Scholar
[24] Farault G, Gautier R, Baker C F, Bowman A, Gregory D H 2003 Chem. Mater. 15 3922
Google Scholar
[25] Gregory D H, Barker M G, Edwards P P, Siddons D J 1998 Inorg. Chem. 37 3775
Google Scholar
[26] Seeger O, Hofmann M, Strähle J, Laval J P, Frit B 2004 Z Anorg. Allg. Chem. 620 2008
[27] Gregory D H, Barker M G, Edwards P P, Slaski M, Siddons D J 1998 J. Solid. State. Chem. 137 62
Google Scholar
[28] Gregory D H, O’Meara P M, Gordon A G, Siddons D J, Blake A J, Barker M G, Hamor T A, 2001 J. Alloys Compd 317-318 237
Google Scholar
[29] Yao M, Zhang Y Y, Ban J M, Hou J J, Zhang B W, Liu J W, Ming X, Kuang X J 2023 PCCP 25 19158
Google Scholar
[30] Ohkubo I, Mori T 2015 Chem. Mater. 27 7265
Google Scholar
[31] Ohkubo I, Mori T 2016 APL Mater. 4 104808
Google Scholar
[32] Liang H L, Lu J, Zhang W Y, Ming X 2025 Mater. Sci. Semicond. Process. 185 108955
Google Scholar
[33] Luo H M, Wang H Y, Bi Z X, Zou G F, McCleskey T M, Burrell A K, Bauer E, Hawley M E, Wang Y Q, Jia Q X 2009 Angew. Chem. Int. Ed. 48 1490
Google Scholar
[34] Kaur A, Ylvisaker E R, Li Y, Galli G, Pickett W E 2010 Phys. Rev. B 82 155125
Google Scholar
[35] Yao M L, Li M, Zhang L, Wang H 2024 Phys. Rev. B 110 115202
Google Scholar
[36] Yang X F, Wang Z Q, Fu H H 2024 Phys. Rev. B 109 155414
Google Scholar
[37] Blöchl P E 1994 Phys. Rev. B 50 17953
Google Scholar
[38] Kresse G, Joubert D 1999 Phys. Rev. B 59 1758
[39] Kresse G, Furthmüller J 1996 P Phys. Rev. B 54 11169
Google Scholar
[40] Kresse G, Furthmüller J 1996 Comput. Mater. Sci. 6 15
Google Scholar
[41] Monkhorst H J, Pack J D 1976 Phys. Rev. B 13 5188
Google Scholar
[42] Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865
Google Scholar
[43] Heyd J, Scuseria G E, Ernzerhof M 2003 J. Chem. Phys. 118 8207
Google Scholar
[44] Yim K, Yong Y, Lee J, Lee K, Nahm H H, Yoo J, Lee C, Seong Hwang C, Han S 2015 NPG Asia Mater. 7 e190
Google Scholar
[45] Gonze X, Lee C 1997 Phys. Rev. B 55 10355
Google Scholar
[46] Giannozzi P, de Gironcoli S, Pavone P, Baroni S 1991 Phys. Rev. B 43 7231
Google Scholar
[47] Ceperley D M, Alder B J 1980 Phys. Rev. Lett. 45 566
Google Scholar
[48] Bokdam M, Sander T, Stroppa A, Picozzi S, Sarma D D, Franchini C, Kresse G 2016 Sci. Rep. 6 28618
Google Scholar
[49] Gajdoš M, Hummer K, Kresse G, Furthmüller J, Bechstedt F 2006 Phys. Rev. B 73 045112
Google Scholar
[50] Zhao X, Vanderbilt D 2002 Phys. Rev. B 65 075105
Google Scholar
[51] Cockayne E, Burton B P 2000 Phys. Rev. B 62 3735
Google Scholar
[52] Bardeen J, Shockley W 1950 Phys. Rev. 80 72
Google Scholar
[53] Mouhat F, Coudert F X 2014 Phys. Rev. B 90 224104
Google Scholar
[54] Wu Z J, Zhao E J, Xiang H P, Hao X F, Liu X J, Meng J 2007 Phys. Rev. B 76 054115
Google Scholar
[55] Wang V, Xu N, Liu J C, Tang G, Geng W T 2021 Comput. Phys. Commun. 267 108033
Google Scholar
[56] Yu R, Xiao F, Lei W, Wang W, Ma Y P, Gong X J, Ming X 2023 PCCP 25 30066
Google Scholar
[57] Pugh S F 2009 Lond. Edinb. Phil. Mag. 45 823
[58] Liao M Q, Liu Y, Min L J, Lai Z H, Han T Y, Yang D N, Zhu J C 2018 Intermetallics 101 152
Google Scholar
[59] Xu Y, Schoonen M A A 2000 Am. Mineral. 85 543
Google Scholar
[60] Zhang H, Guégan F, Wang J, Frapper G 2024 PCCP 26 14675
Google Scholar
[61] Heying B, Smorchkova I, Poblenz C, Elsass C, Fini P, Den Baars S, Mishra U, Speck J S 2000 Appl. Phys. Lett. 77 2885
Google Scholar
[62] Lang H F, Zhang S Q, Liu Z R 2016 Phys. Rev. B 94 235306
Google Scholar
[63] Kosarev I, Kistanov A 2024 Nanoscale 16 10030
Google Scholar
[64] Zhang H, Wang J J, Guégan F, Frapper G 2023 Nanoscale 15 7472
Google Scholar
[65] Dvorak M, Wei S H, Wu Z 2013 Phys. Rev. Lett. 110 016402
Google Scholar
[66] Muth J F, Lee J H, Shmagin I K, Kolbas R M, Casey H C, Keller B P, Mishra U K, DenBaars S P 1997 Appl. Phys. Lett. 71 2572
Google Scholar
下载:
计量
- 文章访问数: 275
- PDF下载量: 3
- 被引次数: 0
