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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), (c), (e) O空位缺陷的ELF, 从上往下依次为x, y, z方向; (b), (d), (f) Al空位缺陷的ELF, 从上往下依次为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), (c), (e) The ELFs of O vacancy defect in x, y, and z directions from top to bottom; (b), (d), (f) the ELFs of Al vacancy defect in x, y, and z directions from top to bottom. 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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