摘要
基于第一性原理计算方法研究空位点缺陷对单层六角氮化硼材料的非线性二次谐波产生系数的影响。结合线性单光子吸收光谱,详细分析了二次谐波产生系数增强的微观机制,并利用态求和跟踪技术准确定位缺陷态对二次谐波产生系数的贡献。结果表明,缺陷态总体导致含缺陷结构的二次谐波产生系数相比于原生结构的系数明显增大,与实验结果一致,部分二次谐波产生系数增强峰几乎完全由缺陷态决定。缺陷态把单层六角氮化硼材料的光学应用从深紫外区扩展到紫外可见光区。
Objective For two-dimensional layered hexagonal boron nitride(2D-hBN)materials,various defects are inevitably generated during experimental synthesis.Defects directly affect the electronic structure of the material and thus influence the optical properties of the material.The defect-related electronic states cause the red-shift of the linear absorption spectrum from the deep ultraviolet region of pristine 2D-hBN to the ultraviolet-visible region of defective 2D-hBN.Meanwhile,defects also have a significant effect on the nonlinear optical properties of the material.Recent experiments have shown that defects increase the nonlinear second-harmonic generation(SHG)coefficient of 2D-hBN by an order of magnitude.These findings suggest that defects can be used to tune the nonlinear optical properties of materials.To use defects to tail the optical properties of materials,it is of great significance to reveal their influence on optical properties from a microscopic view.In this study,we attempt to study the influence of point defects on the SHG coefficient of monolayer 2D-hBN(ML-BN).The sum-over-states method is used to study the microscopic mechanism of the enhancement of SHG coefficients and to reveal the relationship between the enhanced SHG coefficients and defect states.Methods We create three vacancy-related defective structures in the 5×5 supercell of ML-BN(Fig.1).The PBE functional of generalized gradient approximation(PBE-GGA)combined with the norm-conserving pseudopotential planewave method is used to optimize all defective structures.We use a 3×3×1 k grid,a force threshold of 0.01 eV/Å,and a pressure threshold of 0.02 GPa for optimization.The relaxation of the unit cell is included during the optimization process and a vacuum spacing greater than 15Åis used to ensure negligible interlayer interactions.The PBE-GGA combined with the norm-conserving pseudopotential plane-wave method is used to calculate the energy band structure of three defective structures.A k-grid of 24×24×1 and a kinetic energy cutoff of 60 Ry are used in the calculations.The linear and nonlinear optical properties are calculated within the independent particle approximation(IPA).The linear one-photon absorption(OPA)ɛ_(2)(ω)and the SHG coefficientχ_(zyx)(-2ω;ω,ω)are calculated by the sum-over-states expressions Eqs.(1)-(3).A 24×24×1 k grid and 200 IPA empty states(300 states in total)are used to obtain the converged SHG spectra within 4 eV.Hybrid GGA-HSE06 calculations are performed to correct the energy band structure used in optical calculations.Results and Discussions The OPA of V_(N) almost overlaps with that of ML-BN in the input photon energy range from 6 eV to 8 eV and shows a characteristic absorption peak at about 3.3 eV(Fig.4).The reason for the overlap is that the absorption peaks after 6 eV are mainly transitions between intrinsic states.The defects result in a characteristic absorption peak at about 3.3 eV.This characteristic absorption peak mainly originates from the electronic transition from the defect band 98 to the intrinsic conduction band(101,102,and 103).The B-atom vacancy defect leads to three OPA characteristic absorption peaks(Fig.5).These three characteristic absorption peaks are mainly formed by the transition of electrons from the valence band to three defect states.V_(BN) has two characteristic absorption peaks at the same position in two directions.The transition of electrons from the intrinsic valence band and the defect state at the valence band edge to the defect state 97 produces these two characteristic absorption peaks(Fig.6).For both the real part Re[χ_(xxx)^(2)(ω)]and the imaginary part Im[χ_(xxx)^(2)(ω)]of V_(N),pure interband transitions and intraband transitions have similar contributions with opposite signs,which leads to relatively small SHG coefficients in the entire 4.0 eV range except for the near-resonance peak(Fig.7).The SHG enhancement peaks within 4 eV are caused by single-photon or two-photon resonance,or both.The two-photon resonance process related to the defect bands plays a major role in the enhancement of the SHG coefficient.For VB and V_(BN),contributions of defect bands to the enhancement of the SHG coefficient are also observed and the defect bands are located by tracing the sum-over-states process(Figs.8 and 9).In the range of 1.0 to 4.0 eV,the defective structure has a significant enhancement in SHG coefficient relative to native ML-BN(Fig.10).Although it is difficult to directly compare the theoretical and experimental results quantitatively,the enhancement in the SHG coefficient caused by the defect state is consistent qualitatively between the theory and the experiment.Conclusions The defect unit leads to the defect states in the energy band gap of native ML-BN,which causes a red shift of the OPA spectrum from the deep ultraviolet region to the ultraviolet-visible region.Tracing the sum-over-states process confirms the main contribution of defect states to the absorption peak in the UV-visible region.In the visible light region,the enhancement of the SHG coefficient is caused by single-photon or two-photon resonance,or both.Compared with the SHG of native ML-BN,the SHG of the defective structure has an obvious enhancement trend,in good agreement with recent experimental results.Our results are applicable to other defective structures such as doping and surface defects not discussed here because these defects have similar effects on the OPA and ultimately on the SHG.
作者
蓝尤钊
Lan Youzhao(Key Laboratory of Ministry of Education for Advanced Catalysis Materials,College of Chemistry and Materials Science,Zhejiang Normal University,Jinhua 321004,Zhejiang,China)
出处
《光学学报》
北大核心
2025年第2期231-242,共12页
Acta Optica Sinica
关键词
材料
态求和
二次谐波产生
缺陷
单层六角氮化硼
第一性原理
material
sum-over-state
second harmonic generation
defect
monolayer hexagonal boron nitride
first principles
