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基于形变势理论的掺杂计算Sb2Se3空穴迁移率

张冷 张鹏展 刘飞 李方政 罗毅 侯纪伟 吴孔平

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基于形变势理论的掺杂计算Sb2Se3空穴迁移率

张冷, 张鹏展, 刘飞, 李方政, 罗毅, 侯纪伟, 吴孔平

Carrier mobility in doped Sb2Se3 based on deformation potential theory

Zhang Leng, Zhang Peng-Zhan, Liu Fei, Li Fang-Zheng, Luo Yi, Hou Ji-Wei, Wu Kong-Ping
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  • 硒化锑(Sb2Se3)是一种元素丰富、经济且无毒的太阳电池吸收层材料. 太阳电池的性能在很大程度上取决于载流子的传输特性, 然而在Sb2Se3中, 这些特性尚未得到很好的理解. 通过密度泛函理论和形变势理论, 本文对纯Sb2Se3以及掺杂了As, Bi的Sb2Se3的空穴传输特性进行研究, 计算并分析了影响迁移率的3个关键参数: 有效质量、形变势和弹性常数. 结果显示, 有效质量对迁移率具有最大影响, 掺杂Bi的Sb2Se3表现出最高的平均迁移率. 同时发现, Sb2Se3的空穴迁移率呈现出明显的各向异性, 其中x方向的迁移率远高于y, z方向, 这应该与x方向的原子主要以较强的共价键连接, 而y, z方向以较弱的范德瓦耳斯力连接有关. 载流子传输能力强的方向有助于有效传输和收集光生载流子, 本研究从理论上强调了控制Sb2Se3沿特定方向生长的重要性.
    Antimony selenide (Sb2Se3) is an element-rich, cost-effective, and non-toxic material used as an absorber layer in solar cells. The performance of solar cells is significantly influenced by the transport characteristics of charge carriers. However, these characteristics in Sb2Se3 have not been well understood. In this work, through density functional theory and deformation potential theory, we investigate the hole transport properties of pure Sb2Se3 and As-, Bi-doped Sb2Se3. The incorporation of as element and Bi element does not introduce additional impurity levels within the band gap. However, the band gaps are reduced in both As-Sb2Se3 and Bi-Sb2Se3 due to the band shifts of energy levels. This phenomenon is primarily attributed to the interactions between the unoccupied 4p and 6p states of the doping atoms and the unoccupied 4p states of Se atoms, as well as the unoccupied 5p states of Sb atoms. In this study, we calculate and analyze three key parameters affecting mobility: effective mass, deformation potential, and elastic constants. The results indicate that effective mass has the greatest influence on mobility, with Bi-Sb2Se3 exhibiting the highest average mobility. The average effective mass is highest in As-Sb2Se3 and lowest in Bi-Sb2Se3. The elastic constants of the As- and Bi-doped Sb2Se3 structures show minimal differences compared with that of the intrinsic Sb2Se3 structure. By comparing the intrinsic, As-doped, and Bi-doped Sb2Se3, it is evident that doping has a minor influence on deformation potential energy along various directions. The study reveals that the hole mobility in Sb2Se3 displays significant anisotropy, with higher mobilities observed in the x-direction and the y-direction than in the z-direction. This discrepancy is attributed to stronger covalent bonding primarily in the x- and y-direction, while in the z-direction weaker van der Waals forces is dominant. The directions with enhanced charge carrier transport capability contribute to efficient transfer and collection of photo-generated charge carriers. Therefore, our research theoretically underscores the significance of controlling the growth of antimony selenide along specific directions.
      通信作者: 吴孔平, kpwu@jit.edu.cn
    • 基金项目: 国家自然科学基金(批准号: 61904071, 52002170)、江苏省高校青蓝工程和金陵科技学院高层次人才科研启动金(批准号: jit-rcyj-202001)资助的课题.
      Corresponding author: Wu Kong-Ping, kpwu@jit.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 61904071, 52002170), the Qing Lan Project of Jiangsu Provincial University of China, and the Jinling Institute of Technology High-level Talent Research Startup Fund (Grant No. jit-rcyj-202001).
    [1]

    Chen C, Li K H, Tang J 2022 Sol. RRL 6 2200094Google Scholar

    [2]

    Zhang X, Li C, Sun K, Zhou J, Zhang Z 2021 Adv. Energy Mater. 11 2002614Google Scholar

    [3]

    薛丁江, 石杭杰, 唐江 2015 物理学报 64 038406Google Scholar

    Xue D J, Shi H J, Tang J 2015 Acta Phys. Sin. 64 038406Google Scholar

    [4]

    Zhao Y, Wang S, Li C, Che B, Chen X, Chen H, Tang R, Wang X, Chen G, Wang T, Gong J, Chen T, Xiao X 2022 Energy Environ. Sci. 15 5118Google Scholar

    [5]

    Li Z, Liang X, Li G, Liu H, Zhang H, Guo J, Chen J, Shen K, San X, Yu W, Schropp R, Mai Y 2019 Nat. Commun. 10 125Google Scholar

    [6]

    Wang X, Ganose A M, Kavanagh S R, Walsh A 2022 ACS Energy Lett. 7 2954Google Scholar

    [7]

    Spaggiari G, Bersani D, Calestani D, Gilioli E, Gombia E, Mezzadri F, Casappa M, Pattini F, Trevisi G, Rampino S 2022 Int. J. Mol. Sci. 23 15529Google Scholar

    [8]

    Huang M, Lu S, Li K, Lu Y, Chen C, Tang J, Chen S 2022 Sol. RRL 6 2100730Google Scholar

    [9]

    Liang G, Chen X, Ren D, Jiang X, Tang R, Zheng Z, Su Z, Fan P, Zhang X, Zhang Y, Chen S 2021 J. Materiomics 7 1324Google Scholar

    [10]

    Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865Google Scholar

    [11]

    Vadapoo R, Krishnan S, Yilmaz H, Marin C 2011 Phys. Status Solidi B 248 700Google Scholar

    [12]

    Bardekn J, Shockley W 1950 Phys. Rev. 80 72Google Scholar

    [13]

    Xi J, Long M, Tang L, Wang D, Shuai Z 2012 Nanoscale 4 4348Google Scholar

    [14]

    El-Sayad E A, Moustafa A M, Marzouk S Y 2009 Physica B 404 1119Google Scholar

    [15]

    Zheng X, Xie Y, Zhu L, Jiang X, Jia Y, Song W, Sun Y 2002 Inorg. Chem. 41 455Google Scholar

    [16]

    Effective Mass Calculator for Semiconductors, Fonari A, Sutton C https://github.com/afonari/emc [2013-3-18

    [17]

    Zhang B, Qian X 2022 ACS Appl. Energy Mater. 5 492Google Scholar

    [18]

    Wang X, Li Z, Kavanagh S R, Ganose A M, Walsh A 2022 Phys. Chem. Chem. Phys. 24 7195Google Scholar

    [19]

    Wang V, Xu N, Liu J C, Tang G, Geng W T 2021 Comput. Phys. Commun. 267 108033Google Scholar

    [20]

    Silva E Lora da, Skelton J M, Rodríguez-Hernández P, Muõz A, Santo M C, Martínez-García D, Vilaplana R, Manjón F J 2022 J. Mater. Chem. C 10 15061Google Scholar

    [21]

    Zhou Y, Leng M, Xia Z, Zhong J, Song H, Liu X, Yang B, Zhang J, Chen J, Zhou K 2014 Adv. Energy Mater. 4 1301846Google Scholar

    [22]

    Madelung O 1996 Semiconductor: Data Handbook (2rd Ed.) (New York: Springer-Verlag Berlin Heidelbergy) p204

    [23]

    Black J, Conwell E, Seigle L, Spencer C 1957 J. Phys. Chem. Solids 2 240Google Scholar

    [24]

    Cheng L, Liu Y 2018 J. Am. Chem. Soc. 140 17895Google Scholar

  • 图 1  Sb2Se3的晶胞

    Fig. 1.  Crystal structure of Sb2Se3 computational model.

    图 2  纯Sb2Se3 (a), As-Sb2Se3 (b), Bi-Sb2Se3 (c)的能带结构及分态密度图. 虚线处是费米能级, 蓝圈处是价带顶(VBM)

    Fig. 2.  Band structures and partial density of states of pure Sb2Se3 (a), As-Sb2Se3 (b), and Bi-Sb2Se3 (c). Dashed line represents the Fermi level and the blue circle represents the valence band maximum (VBM).

    图 3  (a)本征Sb2Se3总能量与形变的抛物线拟合, 其决定了弹性常数; (b)不同结构的弹性常数

    Fig. 3.  (a) Parabolic fitting of the intrinsic Sb2Se3 total energy and deformations, determining the elastic constants; (b) calculated elastic constants of different structures.

    图 4  (a)本征Sb2Se3在3个不同方向应变下的价带边缘位置, 实线是线性拟合, 其决定了形变势; (b)不同结构的形变势能

    Fig. 4.  (a) Valence band edge positions of intrinsic Sb2Se3 under strain along three different directions, solid lines represent linear fitting, determining the deformation potential; (b) calculated deformation potential energies of different structures.

    表 1  优化后的晶格参数

    Table 1.  Optimized lattice parameters.

    文献[14] 文献[15] Sb2Se3 AsSb2Se3 BiSb2Se3
    a 3.98 3.99 3.99 3.97 4.00
    b 11.64 11.63 11.35 11.35 11.36
    c 11.79 11.78 11.65 11.63 11.65
    v3 547.1 546.6 527.3 524.7 528.9
    下载: 导出CSV

    表 2  不同Sb2Se3结构的空穴有效质量

    Table 2.  Effective mass of holes for different structures of Sb2Se3.

    m*/m0Sb2Se3As-Sb2Se3Bi-Sb2Se3
    $ {m}_{xx}^{*} $0.430.450.42
    $ {m}_{yy}^{*} $0.880.890.67
    $ {m}_{zz}^{*} $1.081.221.61
    $ {\stackrel{-}{m}}^{*} $0.680.720.67
    下载: 导出CSV

    表 3  三种结构的空穴迁移率

    Table 3.  Hole mobility of Sb2Se3, As-Sb2Se3 and Bi-Sb2Se3 along three principle directions.

    迁移率/(cm2·V–1·s–1)Sb2Se3As-Sb2Se3Bi-Sb2Se3
    μx232.62221.59240.66
    μy32.7831.2066.71
    μz20.0215.118.04
    μavg95.1489.30105.13
    下载: 导出CSV
  • [1]

    Chen C, Li K H, Tang J 2022 Sol. RRL 6 2200094Google Scholar

    [2]

    Zhang X, Li C, Sun K, Zhou J, Zhang Z 2021 Adv. Energy Mater. 11 2002614Google Scholar

    [3]

    薛丁江, 石杭杰, 唐江 2015 物理学报 64 038406Google Scholar

    Xue D J, Shi H J, Tang J 2015 Acta Phys. Sin. 64 038406Google Scholar

    [4]

    Zhao Y, Wang S, Li C, Che B, Chen X, Chen H, Tang R, Wang X, Chen G, Wang T, Gong J, Chen T, Xiao X 2022 Energy Environ. Sci. 15 5118Google Scholar

    [5]

    Li Z, Liang X, Li G, Liu H, Zhang H, Guo J, Chen J, Shen K, San X, Yu W, Schropp R, Mai Y 2019 Nat. Commun. 10 125Google Scholar

    [6]

    Wang X, Ganose A M, Kavanagh S R, Walsh A 2022 ACS Energy Lett. 7 2954Google Scholar

    [7]

    Spaggiari G, Bersani D, Calestani D, Gilioli E, Gombia E, Mezzadri F, Casappa M, Pattini F, Trevisi G, Rampino S 2022 Int. J. Mol. Sci. 23 15529Google Scholar

    [8]

    Huang M, Lu S, Li K, Lu Y, Chen C, Tang J, Chen S 2022 Sol. RRL 6 2100730Google Scholar

    [9]

    Liang G, Chen X, Ren D, Jiang X, Tang R, Zheng Z, Su Z, Fan P, Zhang X, Zhang Y, Chen S 2021 J. Materiomics 7 1324Google Scholar

    [10]

    Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865Google Scholar

    [11]

    Vadapoo R, Krishnan S, Yilmaz H, Marin C 2011 Phys. Status Solidi B 248 700Google Scholar

    [12]

    Bardekn J, Shockley W 1950 Phys. Rev. 80 72Google Scholar

    [13]

    Xi J, Long M, Tang L, Wang D, Shuai Z 2012 Nanoscale 4 4348Google Scholar

    [14]

    El-Sayad E A, Moustafa A M, Marzouk S Y 2009 Physica B 404 1119Google Scholar

    [15]

    Zheng X, Xie Y, Zhu L, Jiang X, Jia Y, Song W, Sun Y 2002 Inorg. Chem. 41 455Google Scholar

    [16]

    Effective Mass Calculator for Semiconductors, Fonari A, Sutton C https://github.com/afonari/emc [2013-3-18

    [17]

    Zhang B, Qian X 2022 ACS Appl. Energy Mater. 5 492Google Scholar

    [18]

    Wang X, Li Z, Kavanagh S R, Ganose A M, Walsh A 2022 Phys. Chem. Chem. Phys. 24 7195Google Scholar

    [19]

    Wang V, Xu N, Liu J C, Tang G, Geng W T 2021 Comput. Phys. Commun. 267 108033Google Scholar

    [20]

    Silva E Lora da, Skelton J M, Rodríguez-Hernández P, Muõz A, Santo M C, Martínez-García D, Vilaplana R, Manjón F J 2022 J. Mater. Chem. C 10 15061Google Scholar

    [21]

    Zhou Y, Leng M, Xia Z, Zhong J, Song H, Liu X, Yang B, Zhang J, Chen J, Zhou K 2014 Adv. Energy Mater. 4 1301846Google Scholar

    [22]

    Madelung O 1996 Semiconductor: Data Handbook (2rd Ed.) (New York: Springer-Verlag Berlin Heidelbergy) p204

    [23]

    Black J, Conwell E, Seigle L, Spencer C 1957 J. Phys. Chem. Solids 2 240Google Scholar

    [24]

    Cheng L, Liu Y 2018 J. Am. Chem. Soc. 140 17895Google Scholar

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出版历程
  • 收稿日期:  2023-08-31
  • 修回日期:  2023-11-20
  • 上网日期:  2023-11-24
  • 刊出日期:  2024-02-20

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