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基于第一性原理和蒙特卡罗模拟方法, 系统地研究了氧化铝晶体内部O空位缺陷和Al空位缺陷对二次电子发射特性的影响. 密度泛函计算结果表明, 空位缺陷会导致能带结构发生改变, 其中Al空位缺陷的存在使得禁带宽度变窄, 费米能级降低至价带内部. 在此基础之上, 获得了不同晶体结构下的弹性和非弹性平均自由程. 氧化铝中存在Al空位缺陷时的弹性平均自由程最大, 而存在O空位缺陷时的非弹性平均自由程最大. 为了分析不同缺陷浓度下的二次电子发射特性, 对已有蒙特卡罗模拟算法进一步优化. 模拟结果表明, 随着O空位和Al空位缺陷占比的增加, 最大二次电子发射系数随之而下降. 相比于Al空位缺陷, 相同缺陷占比下O空位缺陷导致二次电子发射系数降低更多.Based on the combination of the first-principles and Monte Carlo method, the effect of vacancy defect on secondary electron characteristic of Al2O3 is studied in this work. The density functional theory (DFT) calculation results show that the band structure changes when the vacancy defects exist. The existence of Al vacancy defects results in a decrease in band gap from 5.88 to 5.28 eV, and in Fermi level below the energy of the valence band maximum as well. Besides, the elastic mean free paths and inelastic mean free paths of electrons in different crystal structures are also obtained. The comparison shows that the inelastic mean free path of electrons in Al2O3 with O vacancy defects is much larger than those of Al2O3 without defects and Al2O3 with Al vacancy defects. When the energy of electrons is smaller than 50 eV, the inelastic mean free path of electrons in Al2O3 without defects is longer than that in Al2O3 with Al vacancy defects. The elastic mean free path of electrons slightly increases when the vacancy defects exist, and the elastic mean free path of electrons in Al2O3 with Al vacancy defects is the largest. In order to investigate the secondary electron emission characteristics under different vacancy defect ratios, an optimized Monte Carlo algorithm is proposed. When the ratio between O vacancy defect and Al vacancy defect increases, the simulation results show that the maximum value of secondary electron yield decreases with the ratio of vacancy defect increasing. The existence of O vacancy defects increases the probability of inelastic scattering of electrons, so electrons are difficult to emit from the surface. As a result, comparing with Al vacancy defect, the SEY of Al2O3 decreases greatly under the same ratio of O vacancy defect.
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Keywords:
- secondary electron /
- vacancy defects /
- Monte Carlo /
- density functional theory
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图 1 Al2O3内部产生缺陷和无缺陷的晶体结构 (a) O空位缺陷; (b) Al空位缺陷; (c) 无缺陷 (灰色原子为Al3+ , 红色原子为O2–, 蓝色圆圈为缺陷原子位置)
Fig. 1. Crystal structure of Al2O3 with ideal state and defects: (a) O vacancy defect; (b) Al vacancy defect; (c) ideal state (the gray atoms are Al3+, the red atoms are O2– and the blue circles are the defective atom positions).
图 2 Al2O3内部存在缺陷和无缺陷时的能带分布
Fig. 2. Energy band profile in Al2O3 with and without internal defects.
图 3 Al2O3存在Al空位缺陷和O空位缺陷情况时, 基于不同方向下动量转移的ELFs (a), (b), (c) O空位缺陷的ELF, 依次为x, y, z方向; (d), (e), (f) Al空位缺陷的ELF, 依次为x, y, z方向. $\left| {\boldsymbol{q}} \right|$的取值为: 0—0.1区间内, 间隔增量为0.005; 0.1—1.5区间内, 间隔增量为0.02; 1.5—5.25区间内, 间隔增量为0.05; 5.25—6.95区间内, 间隔增量为0.1; 7.45—10.95区间内, 间隔增量为0.5. $\left| {\boldsymbol{q}} \right|$以$2\pi /a$为单位, a为晶格常数. 从$\left| {\boldsymbol{q}} \right|$=0开始, 每四个连续$\left| {\boldsymbol{q}} \right|$取一行, 偏移量是–0.01
Fig. 3. ELFs based on momentum transfer in different directions when Al2O3 has Al vacancy defect and O vacancy defect: (a), (b), (c) The ELFs of O vacancy defect in x, y, and z directions; (d), (e), (f) the ELFs of Al vacancy defect in x, y, and z directions. The increments of $\left| {\boldsymbol{q}} \right|$ are 0.005 between 0 and 0.1, 0.02 between 0.1 and 1.5, 0.05 between 1.5 and 5.25, 0.1 between 5.25 and 6.95, and 0.5 between 7.45 and 10.95. $\left| {\boldsymbol{q}} \right|$ takes the unit of 2π/a, and a is the lattice parameter. Lines are taken in the order of one for every four successive $\left| {\boldsymbol{q}} \right|$ from $\left| {\boldsymbol{q}} \right|$ = 0 and offset by –0.01.
图 4 Al2O3在无缺陷、存在O空位缺陷和Al空位缺陷时, 基于不同方向动量转移的电子非弹性平均自由程 (a) x方向; (b) y方向; (c) z方向
Fig. 4. Inelastic mean free paths of electrons in Al2O3 in the ideal state, Al vacancy defect and O vacancy defect with momentum transfer in different direction: (a) x-direction; (b) y-direction; (c) z-direction.
图 5 Al2O3在无缺陷、O空位缺陷和Al空位缺陷情况下的弹性平均自由程
Fig. 5. Elastic mean free paths of electrons in Al2O3 under conditions of ideal state, Al vacancy defect and O vacancy defect.
图 7 空位缺陷概率对Al2O3的二次电子发射系数的影响 (a) O空位缺陷; (b)Al空位缺陷
Fig. 7. Effect of vacancy defect probability on the secondary electron emission coefficient of Al2O3: (a) O vacancy defect; (b) Al vacancy defect.
表 1 不同空位缺陷概率对二次电子发射系数的影响
Table 1. Effect of different vacancy defect probabilities on the coefficients of secondary electron emission.
缺陷概率/% O空位缺陷 Al空位缺陷 W/eV SEY W/eV SEY 1 440 4.08 460 4.14 4 460 4.06 460 4.06 7 440 4.02 460 4.08 10 440 3.96 420 4.06 
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[1] Seiler H 1983 J. Appl. Phys. 54 R1
Google Scholar
[2] Joe H E, Lee W S, Jun M B G, Park N C, Min B K 2018 Ultramicroscopy 184 37
Google Scholar
[3] Chai K, Lu Q, Song Y, Gong X, Li A, Zhang Z 2024 Vacuum 221 112869
Google Scholar
[4] Tao S X, Chan H W, Van Der Graaf H 2016 Materials 9 1017
Google Scholar
[5] 常超 2018 科学通报 63 1390
Google Scholar
Chang C 2018 Chin. Sci. Bull. 63 1390
Google Scholar
[6] Hu T C, Zhu S K, Zhao Y N, Sun X, Yang J, He Y, Wang X B, Bai C J, Bai H, Wei H, Cao M, Hu Z Q, Liu M, Cui W Z 2022 Chin. Phys. B 31 047901
Google Scholar
[7] Kirby R E, King F K 2001 Nucl. Instrum. Methods Phys. Res. , Sect. A 469 1
Google Scholar
[8] 林舒, 闫杨娇, 李永东, 刘纯亮 2014 63 147902
Google Scholar
Lin S, Yan Y J, Li Y D, Liu C L 2014 Acta Phys. Sin. 63 147902
Google Scholar
[9] 李爽, 常超, 王建国, 刘彦升, 朱梦, 郭乐田, 谢佳玲 2015 64 137701
Google Scholar
Li S, Chang C, Wang J G, Liu Y S, Zhu M, Guo L T, Xie J L 2015 Acta Phys. Sin. 64 137701
Google Scholar
[10] 周前红, 董烨, 董志伟, 周海京 2015 64 085201
Google Scholar
Zhou Q H, Dong Y, Dong Z W, Zhou H J 2015 Acta Phys. Sin. 64 085201
Google Scholar
[11] He J, Yang J, Zhao W, Long J, Lan C, Liu E, Chen X, Li J, Yang Z, Dong P, Wang T, Shi J 2020 Appl. Surf. Sci. 515 145990
Google Scholar
[12] González L A, Larciprete R, Cimino R 2016 AIP Adv. 6 095117
Google Scholar
[13] Brillson L J, Foster G M, Cox J, Ruane W T, Jarjour A B, Gao, H, Von Wenckstern H, Grundmann M, Wang B, Look D C, Hyland A, Allen M W 2018 J. Electron. Mater. 47 4980
Google Scholar
[14] Sun X L, Goss S H, Brillson L J, Look D C, Molnar R J 2002 J. Appl. Phys. 91 6729
Google Scholar
[15] Taha M, Abdelhay R A, Khedr M H 2022 Optik 271 170125
Google Scholar
[16] Heo S, Cho E, Lee H I, Park G S, Kang H J, Nagatomi T, Choi P, Choi B D 2015 AIP Adv. 5 077167
Google Scholar
[17] Hussain A, Mian S A, Ahmed E, Jang J 2023 J. Mol. Model 29 393
Google Scholar
[18] Nguyen H K A, Sanati M, Joshi R P 2019 J. Appl. Phys. 126 123301
Google Scholar
[19] 李盛涛, 聂永杰, 闵道敏, 潘绍明 2017 电工技术学报 32 1
Li S T, Nie Y J, Min D M, Pan S M 2017 Trans. Chin. Electrotech. Soc. 32 1
[20] Zhang G J, Su G Q, Song B P, Mu H B 2018 IEEE Trans. Dielectr. Electr. Insul. 25 2321
Google Scholar
[21] Wang Y L, Craven M, Yu X T, Ding J, Bryant P, Huang J, Tu X 2019 ACS Catal. 9 10780
Google Scholar
[22] Diao Y, Wang H, Chen B, Zhang X, Shi C 2023 Appl. Catal., B 330 122573
Google Scholar
[23] Quantum ESPRESSO https://www.quantum-espresso.org/ (accessed 8 March 2023
[24] Vanderbilt D 1990 Phys. Rev. B 41 7892
Google Scholar
[25] Monkhorst H J, Pack J D 1976 Phys. Rev. B 13 5188
Google Scholar
[26] Hussain A, Yang L H, Zou Y B, Mao S F, Da B, Li H M, Ding Z J 2020 J. Appl. Phys. 128 015305
Google Scholar
[27] Yater J E 2023 J. Appl. Phys. 133 050901
Google Scholar
[28] Zhang J, Niu Y, Yan R Q, Zhang R Q, Cao M, Li Y D, Liu C L, Zhang J W, Luo W 2024 J. Appl. Phys. 135 013301
Google Scholar
[29] Waidmann S, Knupfer M, Arnold B, Fink J, Fleszar A, Hanke W 2000 Phys. Rev. B 61 10149
Google Scholar
[30] Polak M P, Morgan D 2021 Comput. Mater. Sci. 193 110281
Google Scholar
[31] Drouin D, Hovington P, Gauvin R 1997 Scanning 19 20
Google Scholar
[32] Czyżewski Z, MacCallum D O N, Romig A, Joy D C 1990 J. Appl. Phys. 68 3066
Google Scholar
[33] Tho T H, Nguyen-Truong H T 2019 J. Phys. Condens. Matter. 31 415901
Google Scholar
[34] 张朝民, 江勇, 尹登峰, 陶辉锦, 孙顺平, 姚建刚 2016 65 076101
Google Scholar
Zhang C M, Jiang Y, Yin D F, Tao H J, Sun S P, Yao J G 2016 Acta Phys. Sin. 65 076101
Google Scholar
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