六方氮化硼单层中一种(CN)3VB缺陷的第一性原理计算

孙志海; 黄强; 张颖; 黄鹏儒; 植慧茵; 邹勇进; 徐芬; 孙立贤

doi:10.7498/aps.70.20201364

摘要

二维六方氮化硼(hBN)的点缺陷最近被发现可以实现室温下的单光子发射, 而成为近年的研究热点. 尽管其具有重要的基础和应用研究意义, hBN中发光缺陷的原子结构起源仍然存在争议. 本文采用基于密度泛函理论的第一性原理计算, 研究hBN单层中一种B空位附近3个N原子被C替代的缺陷(C_N)₃V_B. 在hBN的B空位处, 3个N原子各自带一个在平面内的悬挂键及相应的未配对电子, 而通过C替换可以消除未配对的电子. 系统研究了(C_N)₃V_B缺陷的几何结构、电子结构以及光学性质, 结果表明, 缺陷可以由一个对称的亚稳态经过原子结构弛豫变成1个非对称的、3个C原子连在一起的基态结构. 缺陷的形成在hBN中引入了一些由缺陷悬挂σ键及重构的π键贡献的局域缺陷态. 这些缺陷态可以导致能量阈值在2.58 eV附近的可见光内部跃迁. 本文的工作有助于进一步理解hBN中点缺陷的构成及光学性质, 为实验上探讨发光点缺陷的原子结构起源及其性质提供理论依据.

关键词:

Abstract

The point defect of two-dimensional hexagonal boron nitride (hBN) has recently been discovered to achieve single photon emission at room temperature, and it has become a research hotspot. Despite its important fundamental and applied research significance, the origin of the atomic structure of luminescence defects in hBN is still controversial. In this paper, first-principle calculations based on density functional theory are used to study a defect (C_N)₃V_B in the hexagonal boron nitride monolayer (hBN) where three N atoms near the B vacancy are replaced by C atoms. At the B vacancy of hBN, the three N atoms each carry an in-plane dangling bond and the corresponding unpaired electron, and the unpaired electron can be eliminated by C substitution. We systematically study the geometric structure, electronic structure and optical properties of (C_N)₃V_B defects, analyze the thermodynamic stability of defects through the calculation of the atomic structure, formation energy, and charge state of the defect, and analyze the position in the band gap and its atomic orbital contribution of defect state through energy band structure and wave function. We also analyze its optical properties through dielectric function and absorption coefficient, and predict its luminous photon energy. The results show that the defect can change from a symmetric metastable state to an asymmetric ground state structure with three C atoms connected together through atomic structure relaxation. The formation energy of asymmetric (C_N)₃V_B is 7.94 eV, which is 3.72 eV lower than that of symmetric one. The formation of defects introduces some local defect states contributed by defect dangling σ bonds and reconstructed π bonds in hBN. The defects have valence states between –2 and +2, and the thermodynamic transition energy level of asymmetric (C_N)₃V_B is higher than that of symmetric (C_N)₃V_B. In the transition from the metastable state to the ground state, these defect states can redshift the light absorption boundary of hBN, enhance the absorption intensity of visible light by hBN, and cause internal optical transitions. Among them, there is a visible light transition with an energy threshold around 2.58 eV in the asymmetry (C_N)₃V_B defect. Single boron atom vacancy defect and (C_N)₃V_B have optical transitions near infrared and ultraviolet energy, respectively. The present work will help to further understand the composition and optical properties of point defects in hBN, and provide a theoretical basis for experimentally exploring the origin and properties of the atomic structure of light-emitting point defects.

Keywords:

作者及机构信息

1.
桂林电子科技大学材料科学与工程学院, 广西信息材料重点实验室, 广西新能源材料结构与性能协同创新中心, 桂林　541004

2.
广西师范大学物理科学与技术学院, 桂林　541004

通信作者: 黄鹏儒, pengruhuang@guet.edu.cn ; 孙立贤, sunlx@guet.edu.cn

基金项目: 国家重点研发计划(批准号: 2018YFB1502103, 2018YFB1502105)、国家自然科学基金(批准号: 51801041, 551671062, 5187011196, 51971068)、广西自然科学基金(批准号: 2017JJB150085)和广西科技计划(批准号: 2018AD19052, AA19182014, AD17195073, AA17202030-1)资助的课题

Authors and contacts

1.
Guangxi Collaborative Innovation Center of Structure and Property for New Energy and Materials, Guangxi Key Laboratory of Information Materials, School of Material Science and Engineering, Guilin University of Electronic Technology, Guilin 541004, China

2.
School of Physics and Technology, Guangxi Normal University, Guilin 541004, China

Corresponding author: Huang Peng-Ru, pengruhuang@guet.edu.cn ; Sun Li-Xian, sunlx@guet.edu.cn

Funds: Project supported by the National Key R&D Program of China (Grant Nos. 2018YFB1502103, 2018YFB1502105), the National Natural Science Foundation of China (Grant Nos. 51801041, 551671062, 5187011196, 51971068), the Natural Science Foundation of Guangxi, China (Grant No. 2017JJB150085), and the Science and Technology Project of Guangxi, China (Grant Nos. 2018AD19052, AA19182014, AD17195073, AA17202030-1)

文章全文

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施引文献

图 1 本征hBN单层　(a) hBN的俯视图和侧视图; (b) 模拟的hBN单层表面STM形貌, 加载电压为–2 V, 探针与原子表面的距离为0.479564 nm; (c) hBN的能带投影图

Fig. 1. Intrinsic hBN monolayer: (a) Top view and side view of hBN; (b) the simulated hBN single-layer surface STM morphology, loading voltage is –2 V, the distance between probe and atomic surface is 0.479564 nm; (c) energy band projection view of hBN.

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图 2 V_B和as-V_B的电子结构　(a), (c)分别为V_B和as-V_B优化后的局部结构俯视图; (b), (d)分别为V_B和as-V_B的能带投影图; (e), (f)分别为V_B和as-V_B的缺陷能级在Γ点处波函数的俯视图和自旋电荷密度图

Fig. 2. Electronic structure of V_B and as-V_B: (a), (c) The top views of the optimized partial structure of V_B and as-V_B, respectively; (b), (d) the energy band projection diagrams of V_B and as-V_B, respectively; (e), (f) the top view of the Γ-point wave functions of the defect levels and spin charge density of V_B and as-V_B, respectively.

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图 3 V_B在不同价态的电子结构图　(a)−(c)分别为$ {\rm{V}}_{\rm{B}}^{-1} $, $ {\rm{V}}_{\rm{B}}^{-2} $, $ {\rm{V}}_{\rm{B}}^{-3} $优化后的局部结构俯视图; (d)−(f)分别为$ {\rm{V}}_{\rm{B}}^{-1} $, $ {\rm{V}}_{\rm{B}}^{-2} $, ${\rm{V}}_{\rm{B}}^{-3}$的能带投影图

Fig. 3. Electronic structure diagrams of V_B in different valence states: (a)−(c) The top views of the optimized partial structure diagrams of $ {\rm{V}}_{\rm{B}}^{-1} $, $ {\rm{V}}_{\rm{B}}^{-2} $, and $ {\rm{V}}_{\rm{B}}^{-3} $, respectively; (d)−(f) the energy band projection diagrams of $ {\rm{V}}_{\rm{B}}^{-1} $, $ {\rm{V}}_{\rm{B}}^{-2} $, and $ {\rm{V}}_{\rm{B}}^{-3} $, respectively.

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图 4 在富氮和贫氮条件下, 不同价态的V_B形成能为费米能级的函数

Fig. 4. Formation energies of V_B with different valences as a function of Fermi level under the nitrogen-rich and nitrogen-poor conditions.

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图 5 (C_N)₃V_B和as-(C_N)₃V_B的电子结构　(a), (c)分别为(C_N)₃V_B, as-(C_N)₃V_B优化后局部结构的俯视图; (b), (d)分别为(C_N)₃V_B, as-(C_N)₃V_B的能带投影图; (e) (C_N)₃V_B缺陷能级在Γ点处的波函数图和自旋电荷密度图; (f) as-(C_N)₃V_B缺陷能级在Γ点处的波函数图

Fig. 5. Electronic structure of (C_N)₃V_B and as-(C_N)₃V_B: (a), (c) The top views of the optimized partial structure of (C_N)₃V_B and as-(C_N)₃V_B; (b), (d) the energy band projection diagrams of (C_N)₃V_B and as-(C_N)₃V_B; (e) the top view of the Γ-point wave functions of the defect levels and spin charge density of (C_N)₃V_B; (f) the top view of the Γ-point wave functions of the defect levels of as-(C_N)₃V_B.

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图 6 (C_N)₃V_B不同价态优化后的局部结构和能带投影图　(a)−(d)分别为(C_N)₃$ {\rm{V}}_{\rm{B}}^{-1} $, (C_N)₃$ {\rm{V}}_{\rm{B}}^{-2} $, (C_N)₃$ {\rm{V}}_{\rm{B}}^{+1} $, (C_N)₃$ {\rm{V}}_{\rm{B}}^{+2} $优化后的局部结构图; (e)−(h)分别为(C_N)₃$ {\rm{V}}_{\rm{B}}^{-1} $, (C_N)₃$ {\rm{V}}_{\rm{B}}^{-2} $, (C_N)₃$ {\rm{V}}_{\rm{B}}^{+1} $, (C_N)₃$ {\rm{V}}_{\rm{B}}^{+2} $的能带投影图

Fig. 6. Local structure and energy band projection diagram of (C_N)₃V_B after optimization of different valence states: (a)−(d) The top views of the optimized partial structure diagrams of (C_N)₃$ {\rm{V}}_{\rm{B}}^{-1} $, (C_N)₃$ {\rm{V}}_{\rm{B}}^{-2} $, (C_N)₃$ {\rm{V}}_{\rm{B}}^{+1} $, (C_N)₃$ {\rm{V}}_{\rm{B}}^{+2} $; (e)−(h) the energy band projection diagrams of (C_N)₃$ {\rm{V}}_{\rm{B}}^{-1} $, (C_N)₃$ {\rm{V}}_{\rm{B}}^{-2} $, (C_N)₃$ {\rm{V}}_{\rm{B}}^{+1} $, (C_N)₃$ {\rm{V}}_{\rm{B}}^{+2} $.

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图 7 as-(C_N)₃V_B不同价态优化后的局部结构和能带投影图　(a)−(d)分别为as-(C_N)₃$ {\rm{V}}_{\rm{B}}^{-1} $, as-(C_N)₃$ {\rm{V}}_{\rm{B}}^{-2} $, as-(C_N)₃$ {\rm{V}}_{\rm{B}}^{+1} $, as-(C_N)₃$ {\rm{V}}_{\rm{B}}^{+2} $优化后的局部结构图; (e)−(h)分别为as-(C_N)₃$ {\rm{V}}_{\rm{B}}^{-1} $, as-(C_N)₃$ {\rm{V}}_{\rm{B}}^{-2} $, as-(C_N)₃$ {\rm{V}}_{\rm{B}}^{+1} $, as-(C_N)₃$ {\rm{V}}_{\rm{B}}^{+2} $的能带投影图

Fig. 7. Electronic structure diagrams of as-(C_N)₃V_B in different valence states: (a)−(d) The top views of the optimized partial structure diagrams of as-(C_N)₃$ {\rm{V}}_{\rm{B}}^{-1} $, as-(C_N)₃$ {\rm{V}}_{\rm{B}}^{-2} $, as-(C_N)₃$ {\rm{V}}_{\rm{B}}^{+1} $, as-(C_N)₃$ {\rm{V}}_{\rm{B}}^{+2} $; (e)−(h) the energy band projection diagrams of as-(C_N)₃$ {\rm{V}}_{\rm{B}}^{-1} $, as-(C_N)₃$ {\rm{V}}_{\rm{B}}^{-2} $, as-(C_N)₃$ {\rm{V}}_{\rm{B}}^{+1} $, as-(C_N)₃$ {\rm{V}}_{\rm{B}}^{+2} $.

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图 8 在富氮和贫氮条件下, 不同价态的(C_N)₃V_B形成能为费米能级的函数

Fig. 8. Formation energies of (C_N)₃V_B with different valences as a function of Fermi level under the nitrogen-rich and nitrogen-poor conditions.

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图 9 在富氮和贫氮条件下, 不同价态的as-(C_N)₃V_B形成能为费米能级的函数

Fig. 9. Formation energies of as-(C_N)₃V_B with different valences as a function of Fermi level under the nitrogen-rich and nitrogen-poor conditions.

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图 10 0 K和0 GPa时hBN, V_B, as-V_B, (C_N)₃V_B, as-(C_N)₃V_B的复介电函数

Fig. 10. Complex dielectric functions of hBN, V_B, as-V_B, (C_N)₃V_B, as-(C_N)₃V_B at 0 K and 0 GPa.

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图 11 0 K和0 GPa时hBN, V_B, as-V_B, (C_N)₃V_B, as-(C_N)₃V_B的吸收系数

Fig. 11. Absorption coefficients of hBN, V_B, as-V_B, (C_N)₃V_B, as-(C_N)₃V_B at 0 K and 0 GPa.

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图 12 0 K和0 GPa时hBN, V_B, as-V_B, (C_N)₃V_B, as-(C_N)₃V_B的损失函数

Fig. 12. Loss function of hBN, V_B, as-V_B, (C_N)₃V_B, as-(C_N)₃V_B at 0 K and 0 GPa.

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图 13 hBN单层硼原子空位的模型图　(a), (d)分别为V_B和as-V_B优化后的局部结构图; (b), (e)分别为V_B和as-V_B的电子结构模拟图, 黑色箭头和灰色箭头分别代表占据态和未占据态; (c), (f)分别为V_B和as-V_B的介电虚部在X和Y方向张量

Fig. 13. Model diagram of boron vacancies in hBN monolayer: (a), (d) The optimized local structure diagrams of V_B and as-V_B; (b), (e) simulated electronic structures diagrams of V_B and as-V_B, where black and grey arrows indicate occupied and unoccupied states; (c), (f) the tensors of the dielectric imaginary part of V_B and as-V_B in the X and Y directions.

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图 14 hBN单层碳掺杂的模型图　(a), (d) (C_N)₃V_B和as-(C_N)₃V_B优化后的局部结构图; (b), (e) (C_N)₃V_B和as-(C_N)₃V_B的电子结构模拟图, 黑色箭头和灰色箭头分别代表占据态和未占据态; (c), (f) (C_N)₃V_B和as-(C_N)₃V_B的介电虚部在X和Y方向张量

Fig. 14. Model diagram of carbon doping in hBN monolayer: (a), (d) The optimized local structure diagrams of (C_N)₃V_B and as-(C_N)₃V_B; (b), (e) simulated electronic structures diagrams of (C_N)₃V_B and as-(C_N)₃V_B, where black and grey arrows indicate occupied and unoccupied states; (c), (f) the tensors of the dielectric imaginary part of (C_N)₃V_B and as-(C_N)₃V_B in the X and Y directions.

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[2]	Abderrahmane A, Ko P J, Thu T V, Ishizawa S, Takamura T, Sandhu A 2014 Nanotechnology 25 365202 Google Scholar
[3]	Li X, Yin J, Zhou J, Wang Q, Guo W 2014 Nanotechnology 25 105701 Google Scholar
[4]	Abdi M, Degenfeld-Schonburg P, Sameti M, Navarrete-Benlloch C, Hartmann M J 2016 Phys. Rev. Lett. 116 233604 Google Scholar
[5]	Xia F, Wang H, Xiao D, Dubey M, Ramasubramaniam A 2014 Nat. Photonics 8 899 Google Scholar
[6]	Clark G, Schaibley J R, Ross J, Taniguchi T, Watanabe K, Hendrickson J R, Mou S, Yao W, Xu X 2016 Nano Lett. 16 3944 Google Scholar
[7]	Shiue R J, Efetov D K, Grosso G, Peng C, Fong K C, Englund D 2017 Nanophotonics 6 1329 Google Scholar
[8]	Koenderink A F, Alu A, Polman A 2015 Science 348 516 Google Scholar
[9]	Caldwell J D, Aharonovich I, Cassabois G, Edgar J H, Gil B, Basov D 2019 Nat. Rev. Mater. 4 552 Google Scholar
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六方氮化硼单层中一种(C_N)₃V_B缺陷的第一性原理计算