Processing math: 100%

Search

Article

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

Analysis of effect of bulk vacancy defect on secondary electron emission characteristics of Al2O3

Zhang Jian-Wei Niu Ying Yan Run-Qi Zhang Rong-Qi Cao Meng Li Yong-Dong Liu Chun-Liang Zhang Jia-Wei

Analysis of effect of bulk vacancy defect on secondary electron emission characteristics of Al2O3

Zhang Jian-Wei, Niu Ying, Yan Run-Qi, Zhang Rong-Qi, Cao Meng, Li Yong-Dong, Liu Chun-Liang, Zhang Jia-Wei
Article Text (iFLYTEK Translation)
PDF
HTML
Get Citation
  • 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.
      PACS:
      79.20.Hx(Electron impact: secondary emission)

    Erratum: Analysis of effect of bulk vacancy defect on secondary electron emission characteristics of Al2O3 [Acta Phys. Sin. 2024, 73(21): 219901]

    Zhang Jian-Wei, Niu Ying, Yan Run-Qi, Zhang Rong-Qi, Cao Meng, Li Yong-Dong, Liu Chun-Liang, Zhang Jia-WeiActa Phys. Sin., 2024, 73(21): 219901. doi: 10.7498/aps.73.219901
    Erratum: Analysis of effect of bulk vacancy defect on secondary electron emission characteristics of Al2O3
      Corresponding author: Zhang Jian-Wei, zhangjianwei@xaut.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 52307186), the Natural Science Basic Research Program of Shaanxi Province, China (Grant No. 2023-JC-QN-0585), and the Youth Innovation Scientific Research Program of the Education Department of Shaanxi Province, China (Grant No. 23JP104).

    由电子辐照激发的二次电子发射现象是物理学中一个重要的研究分支, 在诸多领域都有着广泛的应用. 由于二次电子对材料表面状态敏感, 常被用于材料的表征和探测, 如扫描电子显微镜成像[1]、离子束加工聚焦检测[2]、碳污染检测[3]等. 此外, 采用高二次电子产额(secondary emission yield, SEY)的材料还可以实现光电倍增管中电子的倍增和信号的放大[4]. 但是在大功率微波器件[5,6]和加速器[7]中, 二次电子倍增将会导致击穿的发生[810], 损害器件的性能, 因此是需要遏制和规避的.

    为了分析材料缺陷对二次电子发射特性的影响, 已经开展了大量的相关研究. He等[11]通过测量无氧铜和不锈钢经过Ti离子辐照后的二次电子产额, 结果表明辐照损伤缺陷对二次电子发射有抑制的效果. Gonzalez等[12]采用Ar+轰击高定向热解石墨样品, 得到了相似的结论. Brillson等[13]与Sun等[14] 通过阴极荧光谱技术证明了材料体内部点缺陷对二次电子发射特性会产生相应的影响. 此外, Taha等[15]与Heo等[16]分别从第一性原理计算和实验诊断研究发现, 点空位缺陷的存在会使材料的带隙变窄. Hussain等[17]的计算结果表明, 空位缺陷的存在不仅减小了带隙, 还可以获得较低的光学能量损失函数, 从而影响二次电子发射特性. 而在数值模拟方面, Nguyen等[18]采用密度泛函理论(density functional theory, DFT)和蒙特卡罗(Monte Carlo, MC)模拟研究了晶向和表面空位对铜二次电子产额的影响, 结果表明在晶向为[111]时, 有空位的铜材料比无空位时的SEY值略高.

    氧化铝以其优异的物理性质(低电导率、高硬度、高熔点)和稳定的化学性质, 被广泛用于电气绝缘设备[19,20]及等离子催化[21,22]中. Al2O3的二次电子发射特性是影响相关电学性能的重要因素, 然而目前尚缺乏材料缺陷对Al2O3二次电子发射特性影响的相关研究. 电子在材料中的散射轨迹与平均自由程密切相关, 因此, 本文首先利用密度泛函理论计算得到含有Al空位缺陷和O空位缺陷时Al2O3的弹性和非弹性平均自由程. 当发生非弹性散射时, 电子损失能量并有一定概率产生内二次电子; 而在弹性散射过程中, 电子只改变散射的角度, 不损失能量. 在此基础之上, 对已有蒙特卡罗模拟算法进行优化, 分析了空位缺陷对氧化铝二次电子发射特性的影响.

    图1为Al2O3材料存在氧空位、铝空位以及无空位时的晶体结构. Al2O3为刚玉结构(¯R3c空间群), 如图1(c)所示, 无缺陷的Al2O3晶胞中包含12个Al3+原子和18个O2–原子. 在本文中, 所有关于空位缺陷的计算都是基于在一个Al2O3晶胞中引入单个空位缺陷的结构进行的, 此时Al2O3晶胞的缺陷浓度为3.33%, 空位缺陷原子的位置由图1可见. 本文中的第一性原理计算均是采用Quantum ESPRESSO 7.1[23]完成的. 计算中采用了广义梯度近似(generalized gradient approximation, GGA)的Perdew-Burke-Ernzerhof (PBE)方法来考虑电子之间相互作用中的交换关联势, 电子波函数经平面波基矢组进行扩展, 并采用了超软赝势[24]描述离子实与价电子间的相互作用. 布里渊区域K点网格[25]的设置采用12×12×12. Al2O3的晶格常数为9.09 Bohr, 为了保证存在缺陷时晶体结构的稳定性, 对原子位置进行了弛豫计算.

    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)\r\nFig. 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 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).

    内二次电子的初始能量为其未发生碰撞时的能量与碰撞过程中入射电子能量损失的总和. 而未发生碰撞时的能量即取决于材料的能带分布. 在本文中, 假定材料内电子满足自由电子气模型, 价电子被激发为内二次电子的概率与自由电子的联合态密度E0(E0+EF)成正比[26], 其中EF为费米能级, E0为自由电子的初始能量. 同时, 能带分布决定了材料的表面势垒高度, 对于导体和非导体材料, 界面势垒高度不同. 对于导体材料, 势垒高度为功函数; 而非导体材料, 势垒高度为电子亲和势[27]. 在二次电子发射中, 基于不同方向下动量转移的能量损失函数决定了电子在材料中损失的能量及非弹性平均自由程, 从而影响内二次电子的产生及穿过势垒出射的概率.

    图2为Al2O3内部存在缺陷和无缺陷时的能带分布. 由图2可以看出, 当存在O空位缺陷时, 导带底(conduction band minimum, CBM)与价带顶(valance band maximum, VBM)能量均有所降低, 分别从13.23 eV和7.35 eV降低到13.20 eV和7.14 eV. 相比于无缺陷时, 禁带宽度变化不大, 但费米能级EF较无缺陷时从12.55 eV降低到10.92 eV. 而Al空位缺陷的存在使CBM, VBM和EF都有所下降, 分别为12.58 eV, 7.30 eV和6.81 eV. 因此, Al空位缺陷的存在使禁带宽度由5.88 eV下降至5.28 eV, 同时EF进入价带内部.

    图 2 Al2O3内部存在缺陷和无缺陷时的能带分布\r\nFig. 2. Energy band profile in Al2O3 with and without internal defects.
    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为存在空位缺陷时, 基于不同方向下动量转移的能量损失函数(energy loss function, ELF). ELF为材料介电函数ε(q,ω)虚部的倒数. 其中动量|q|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. |q|2π/a为单位, a为晶格常数. 由于各向异性的晶体结构, Al2O3在三个方向上的ELF略有不同[28]. 如图3所示, 当Al2O3内部存在Al空位缺陷和O空位缺陷时, z方向上的ELF在W = 28.25—31.15 eV内和W = 40.50—44.35 eV内的下降速度比在xy方向更慢, 可归因于带间跃迁; 在W = 31.15—40.50 eV内的下降速度比在xy方向更快, 这是由等离子体激发所致. 当|q|=0时, 存在Al空位缺陷和O空位缺陷时不同方向的ELF峰值均在24.65 eV附近, 这是由等离子体共振引起的[29]. 当Al空位缺陷存在且|q|增大到0.39 Bohr–1, 以及O空位缺陷存在且|q|增大到0.55 Bohr–1时, x, y, z方向的ELF在30.25 eV处均出现一个峰值. 当Al空位缺陷存在且|q|增大到0.77 Bohr–1, 以及O空位缺陷存在且|q|增大到0.88 Bohr–1时, z方向的ELF在44.35 eV处出现另一个峰值.

    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\r\nFig. 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 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. |q|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. |q|2π/a为单位, a为晶格常数. 从|q|=0开始, 每四个连续|q|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 |q| 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. |q| takes the unit of 2π/a, and a is the lattice parameter. Lines are taken in the order of one for every four successive |q| from |q| = 0 and offset by –0.01.

    基于DFT计算所得的介电常数ε(q,ω), 可以得到固体材料中电子的非弹性平均自由程λin[30]:

    λ1indω=1πa0Wq+q1qIm[1ε(q,ω)]dq, (1)
    q±=2m2[W±Wω], (2)

    其中ω为能量损失, a0=5.29177×1011m为Bohr半径, q为动量转移, 为约化普朗克常数, W为电子能量, m为电子质量.

    当电子在材料中运动时, 电子的能量损失可以用阻止本领来表达:

    dWds=πWa0W/0ωdωq+qdqqIm[1ε(ω,q)]. (3)

    其中s为电子在材料中的运动距离.

    在非弹性散射中, 入射电子的能量会传递给材料, 并在材料内部激发出次级电子, 当电子遇到界面势垒时, 一些电子会被反射回材料内部, 而另一些电子则会跨越界面势垒U0. 次级电子在向材料表面运动的过程中与材料中其他电子发生碰撞, 导致自身能量转移或损失, 以至于没有足够的能量越过界面势垒. 由Drouin等[31]的研究结果可知, 当入射能量较高时, 入射电子的能量损失很小, 此时次级电子越过界面势垒的概率增大. 电子越过势垒出射的概率为

    T(W,β)={41U0/Wcos2β[1+1U0/cos2β]2,Wcos2β>U0,0,Wcos2βU0. (4)

    由(4)式可知, 当满足Wcos2β>U0时电子才能跨过势垒, 其中β为次级电子到达表面时与表面法线的夹角.

    图4为Al2O3在无缺陷、存在O空位缺陷和Al空位缺陷三种情况下, 基于不同方向下动量转移的ELF计算得到的电子的非弹性平均自由程. 不同晶体结构中电子的非弹性平均自由程略有不同. 当W < 110 eV时, 电子的非弹性平均自由程较大, 但总体趋势是随着入射电子能量的增加而快速减小的, 在W >110 eV时, 非弹性平均自由程又随着入射电子能量的增加而逐渐增大. 同一种晶体结构下不同方向动量转移的电子非弹性平均自由程存在一定的差异. 当动量转移在z方向时, 电子的非弹性平均自由程最大; 当动量转移在y方向时, 电子的非弹性平均自由程最小. 这是由Al2O3晶体的各向异性引起的, 由于各向异性的晶体结构, Al2O3在三个方向上的ELF不同, 由(1)式和(2)式可得, 当z方向上的能量损失率最小时, 导致非弹性平均自由程最大, 当y方向上的能量损失率最大时, 导致非弹性平均自由程最小. 如图4所示, 当W < 50 eV时, 无缺陷氧化铝的非弹性平均自由程比存在Al空位缺陷氧化铝的非弹性平均自由程大; 当W > 50 eV时, 则完全相反. 而存在O空位缺陷氧化铝的非弹性平均自由程在整个能量区间内总是大于存在Al空位缺陷和无空位缺陷氧化铝的非弹性平均自由程.

    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\r\nFig. 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 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.

    10 keV入射能量以下的电子在发生弹性碰撞时, 其总微分弹性截面是各单元微分弹性截面比例的总和, 总弹性截面可由Mott微分散射截面[32]来表达:

    σel=2ππ0dσeldΩsinθdθ, (5)

    其中dσeldΩ为微分弹性截面. 电子的弹性平均自由程为

    λel=ANAρσel, (6)

    其中A是原子的相对质量, NA是阿伏伽德罗常数, ρ是物质密度.

    在发生弹性碰撞时, 化合物中的原子比例对弹性平均自由程也具有一定的影响[33], 此时弹性微分截面为

    dσeldΩ=nCn(dσeldΩ)n, (7)

    其中Cn为第n种原子的权重分数. 因此当Al2O3内部产生空位缺陷的情况下, Al原子和O原子的比例将发生变化, 从而影响到弹性平均自由程的大小.

    图5为Al2O3在无缺陷、存在O空位缺陷和Al空位缺陷情况下电子的弹性平均自由程. 结果表明Al空位缺陷和O空位缺陷的存在使得弹性平均自由程增大. 其中存在Al空位缺陷时的弹性平均自由程最大, 而无缺陷的弹性平均自由程最小. 当Al2O3内部产生Al空位缺陷时, Al原子的权重分数最小, 所以此时的弹性微分截面最小, 根据(5)式和(6)式可知, 相对应的弹性平均自由程最大. 同理可得, 由于此时Al原子的权重分数最大, 因此在无缺陷情况下的弹性平均自由程最小.

    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\r\nFig. 5. Elastic mean free paths of electrons in Al2O3 under conditions of ideal state, Al vacancy defect and O vacancy defect.
    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.

    由于材料内的缺陷分布存在一定的随机性, 为了简化起见, 本文通过O空位缺陷和Al空位缺陷的缺陷概率来表征体空位缺陷对二次电子发射系数的影响. 实际中材料的缺陷浓度最高为10%[34], 因此本文对空位缺陷概率的取值范围为1%—10%, 此时Al2O3晶体中的空位缺陷浓度为Al2O3晶胞的空位缺陷浓度与空位缺陷概率的乘积, 即空位缺陷浓度最大为0.33%, 最小为0.033%. 因此, 对已有考虑各向异性的蒙特卡罗模拟算法[28]进一步优化, 当电子发生碰撞之前, 先确定所在区域是否存在缺陷及其缺陷的类型. 图6为本文所采用的蒙特卡罗方法模拟流程图. 在碰撞发生前, 先生成一个0—1之间的随机数, 当空位缺陷的概率On1和Aln2确定时, 根据生成的随机数来判断碰撞所采用的弹性及非弹性截面. 若随机数在0—On1之间, 则缺陷类型为O空位缺陷; 若随机数在On1— On1 + Aln2之间, 则缺陷类型为Al空位缺陷; 若随机数在On1 + Aln2—1之间, 则无缺陷. 当发生碰撞时, 需要确定碰撞的类型. 若为弹性碰撞, 则只改变电子的运动方向, 无能量损失; 若为非弹性碰撞, 则求得电子的能量损失和非弹性平均自由程, 并更新电子的能量及速度位置信息. 如果产生内次级电子, 则二次电子的产生取决于电子越过表面势垒的概率[26]. 当电子运动至材料表面时, 如果能够越过势垒, 则成为真正的二次电子.

    图 6 蒙特卡罗模拟流程图\r\nFig. 6. A flow chart of Monte Carlo simulation.
    图 6  蒙特卡罗模拟流程图
    Fig. 6.  A flow chart of Monte Carlo simulation.

    本文利用蒙特卡罗模拟方法获得了Al2O3晶体中存在Al空位缺陷和O空位缺陷时的二次电子发射系数. 如图7所示, 研究了O空位缺陷概率和Al空位缺陷概率在1%—10%范围内对氧化铝SEY的影响. 当两种空位缺陷概率分别为1%, 4%, 7%, 10%时对二次电子发射系数的影响结果如表1所列, 当O空位缺陷和Al空位缺陷概率从1%增加到10%时, Al2O3 SEY的最大值所对应的入射电子能量在420—460 eV之间; Al2O3 SEY峰值随着O空位缺陷概率的增加而下降; 当Al空位缺陷的概率大于1%时, Al2O3 SEY峰值在4.06—4.08之间波动. 结果表明, Al2O3的SEY值是随着两种空位缺陷概率的增加而下降, 其中O空位缺陷概率的变化对SEY的影响比Al空位缺陷概率变化对其影响更为明显. 这种现象是由于O空位缺陷概率越高, 碰撞就更加接近于Al的情况. 而Al2O3的非弹性截面小于Al[28,30], 因此O空位缺陷的存在使非弹性散射的概率增大, 发生非弹性散射后的偏转角较小, 电子不容易出射.

    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\r\nFig. 7. Effect of vacancy defect probability on the secondary electron emission coefficient of Al2O3: (a) O vacancy defect; (b) Al 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
    下载: 导出CSV 
    | 显示表格

    本文采用第一性原理与蒙特卡罗模拟相结合的方法, 对Al2O3材料内部产生Al空位缺陷和O空位缺陷时的二次电子发射特性进行了研究. 根据密度泛函的计算结果得到了空位缺陷对能带分布的影响. 其中Al空位缺陷的存在使得禁带宽度变窄, 同时费米能级与无缺陷时相比明显下降, 进入了价带内部. 此外, 还获得了不同晶体结构中的电子非弹性和弹性平均自由程, 当Al2O3中存在Al空位缺陷时的弹性平均自由程最大, 存在O空位缺陷时的非弹性平均自由程最大. 基于优化后的蒙特卡罗模拟算法, 研究了空位缺陷概率对SEY的影响. 结果表明, 当O空位缺陷和Al空位缺陷概率从1%增加到10%时, 入射电子能量大于100 eV时, 二次电子发射系数随之降低. 相同缺陷概率下, O空位缺陷对二次电子发射特性的影响比Al空位缺陷更为显著.

    [1]

    Seiler H 1983 J. Appl. Phys. 54 R1Google Scholar

    [2]

    Joe H E, Lee W S, Jun M B G, Park N C, Min B K 2018 Ultramicroscopy 184 37Google Scholar

    [3]

    Chai K, Lu Q, Song Y, Gong X, Li A, Zhang Z 2024 Vacuum 221 112869Google Scholar

    [4]

    Tao S X, Chan H W, Van Der Graaf H 2016 Materials 9 1017Google Scholar

    [5]

    常超 2018 科学通报 63 1390Google Scholar

    Chang C 2018 Chin. Sci. Bull. 63 1390Google 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 047901Google Scholar

    [7]

    Kirby R E, King F K 2001 Nucl. Instrum. Methods Phys. Res. , Sect. A 469 1Google Scholar

    [8]

    林舒, 闫杨娇, 李永东, 刘纯亮 2014 物理学报 63 147902Google Scholar

    Lin S, Yan Y J, Li Y D, Liu C L 2014 Acta Phys. Sin. 63 147902Google Scholar

    [9]

    李爽, 常超, 王建国, 刘彦升, 朱梦, 郭乐田, 谢佳玲 2015 物理学报 64 137701Google Scholar

    Li S, Chang C, Wang J G, Liu Y S, Zhu M, Guo L T, Xie J L 2015 Acta Phys. Sin. 64 137701Google Scholar

    [10]

    周前红, 董烨, 董志伟, 周海京 2015 物理学报 64 085201Google Scholar

    Zhou Q H, Dong Y, Dong Z W, Zhou H J 2015 Acta Phys. Sin. 64 085201Google 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 145990Google Scholar

    [12]

    González L A, Larciprete R, Cimino R 2016 AIP Adv. 6 095117Google 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 4980Google Scholar

    [14]

    Sun X L, Goss S H, Brillson L J, Look D C, Molnar R J 2002 J. Appl. Phys. 91 6729Google Scholar

    [15]

    Taha M, Abdelhay R A, Khedr M H 2022 Optik 271 170125Google 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 077167Google Scholar

    [17]

    Hussain A, Mian S A, Ahmed E, Jang J 2023 J. Mol. Model 29 393Google Scholar

    [18]

    Nguyen H K A, Sanati M, Joshi R P 2019 J. Appl. Phys. 126 123301Google 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 2321Google Scholar

    [21]

    Wang Y L, Craven M, Yu X T, Ding J, Bryant P, Huang J, Tu X 2019 ACS Catal. 9 10780Google Scholar

    [22]

    Diao Y, Wang H, Chen B, Zhang X, Shi C 2023 Appl. Catal., B 330 122573Google Scholar

    [23]

    Quantum ESPRESSO https://www.quantum-espresso.org/ (accessed 8 March 2023

    [24]

    Vanderbilt D 1990 Phys. Rev. B 41 7892Google Scholar

    [25]

    Monkhorst H J, Pack J D 1976 Phys. Rev. B 13 5188Google 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 015305Google Scholar

    [27]

    Yater J E 2023 J. Appl. Phys. 133 050901Google 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 013301Google Scholar

    [29]

    Waidmann S, Knupfer M, Arnold B, Fink J, Fleszar A, Hanke W 2000 Phys. Rev. B 61 10149Google Scholar

    [30]

    Polak M P, Morgan D 2021 Comput. Mater. Sci. 193 110281Google Scholar

    [31]

    Drouin D, Hovington P, Gauvin R 1997 Scanning 19 20Google Scholar

    [32]

    Czyżewski Z, MacCallum D O N, Romig A, Joy D C 1990 J. Appl. Phys. 68 3066Google Scholar

    [33]

    Tho T H, Nguyen-Truong H T 2019 J. Phys. Condens. Matter. 31 415901Google Scholar

    [34]

    张朝民, 江勇, 尹登峰, 陶辉锦, 孙顺平, 姚建刚 2016 物理学报 65 076101Google Scholar

    Zhang C M, Jiang Y, Yin D F, Tao H J, Sun S P, Yao J G 2016 Acta Phys. Sin. 65 076101Google Scholar

  • 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)

    Figure 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

    Figure 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. |q|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. |q|2π/a为单位, a为晶格常数. 从|q|=0开始, 每四个连续|q|取一行, 偏移量是–0.01

    Figure 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 |q| 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. |q| takes the unit of 2π/a, and a is the lattice parameter. Lines are taken in the order of one for every four successive |q| from |q| = 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

    Figure 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

    Figure 5.  Elastic mean free paths of electrons in Al2O3 under conditions of ideal state, Al vacancy defect and O vacancy defect.

    图 6  蒙特卡罗模拟流程图

    Figure 6.  A flow chart of Monte Carlo simulation.

    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

    Figure 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
    DownLoad: CSV
  • [1]

    Seiler H 1983 J. Appl. Phys. 54 R1Google Scholar

    [2]

    Joe H E, Lee W S, Jun M B G, Park N C, Min B K 2018 Ultramicroscopy 184 37Google Scholar

    [3]

    Chai K, Lu Q, Song Y, Gong X, Li A, Zhang Z 2024 Vacuum 221 112869Google Scholar

    [4]

    Tao S X, Chan H W, Van Der Graaf H 2016 Materials 9 1017Google Scholar

    [5]

    常超 2018 科学通报 63 1390Google Scholar

    Chang C 2018 Chin. Sci. Bull. 63 1390Google 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 047901Google Scholar

    [7]

    Kirby R E, King F K 2001 Nucl. Instrum. Methods Phys. Res. , Sect. A 469 1Google Scholar

    [8]

    林舒, 闫杨娇, 李永东, 刘纯亮 2014 物理学报 63 147902Google Scholar

    Lin S, Yan Y J, Li Y D, Liu C L 2014 Acta Phys. Sin. 63 147902Google Scholar

    [9]

    李爽, 常超, 王建国, 刘彦升, 朱梦, 郭乐田, 谢佳玲 2015 物理学报 64 137701Google Scholar

    Li S, Chang C, Wang J G, Liu Y S, Zhu M, Guo L T, Xie J L 2015 Acta Phys. Sin. 64 137701Google Scholar

    [10]

    周前红, 董烨, 董志伟, 周海京 2015 物理学报 64 085201Google Scholar

    Zhou Q H, Dong Y, Dong Z W, Zhou H J 2015 Acta Phys. Sin. 64 085201Google 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 145990Google Scholar

    [12]

    González L A, Larciprete R, Cimino R 2016 AIP Adv. 6 095117Google 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 4980Google Scholar

    [14]

    Sun X L, Goss S H, Brillson L J, Look D C, Molnar R J 2002 J. Appl. Phys. 91 6729Google Scholar

    [15]

    Taha M, Abdelhay R A, Khedr M H 2022 Optik 271 170125Google 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 077167Google Scholar

    [17]

    Hussain A, Mian S A, Ahmed E, Jang J 2023 J. Mol. Model 29 393Google Scholar

    [18]

    Nguyen H K A, Sanati M, Joshi R P 2019 J. Appl. Phys. 126 123301Google 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 2321Google Scholar

    [21]

    Wang Y L, Craven M, Yu X T, Ding J, Bryant P, Huang J, Tu X 2019 ACS Catal. 9 10780Google Scholar

    [22]

    Diao Y, Wang H, Chen B, Zhang X, Shi C 2023 Appl. Catal., B 330 122573Google Scholar

    [23]

    Quantum ESPRESSO https://www.quantum-espresso.org/ (accessed 8 March 2023

    [24]

    Vanderbilt D 1990 Phys. Rev. B 41 7892Google Scholar

    [25]

    Monkhorst H J, Pack J D 1976 Phys. Rev. B 13 5188Google 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 015305Google Scholar

    [27]

    Yater J E 2023 J. Appl. Phys. 133 050901Google 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 013301Google Scholar

    [29]

    Waidmann S, Knupfer M, Arnold B, Fink J, Fleszar A, Hanke W 2000 Phys. Rev. B 61 10149Google Scholar

    [30]

    Polak M P, Morgan D 2021 Comput. Mater. Sci. 193 110281Google Scholar

    [31]

    Drouin D, Hovington P, Gauvin R 1997 Scanning 19 20Google Scholar

    [32]

    Czyżewski Z, MacCallum D O N, Romig A, Joy D C 1990 J. Appl. Phys. 68 3066Google Scholar

    [33]

    Tho T H, Nguyen-Truong H T 2019 J. Phys. Condens. Matter. 31 415901Google Scholar

    [34]

    张朝民, 江勇, 尹登峰, 陶辉锦, 孙顺平, 姚建刚 2016 物理学报 65 076101Google Scholar

    Zhang C M, Jiang Y, Yin D F, Tao H J, Sun S P, Yao J G 2016 Acta Phys. Sin. 65 076101Google Scholar

  • [1] Jiang Yuan-Qi, Peng Ping. Electronic structures of stable Cu-centered Cu-Zr icosahedral clusters studied by density functional theory. Acta Physica Sinica, 2018, 67(13): 132101. doi: 10.7498/aps.67.20180296
    [2] Li Ping, Xu Yu-Tang. Monte Carlo simulation of time-dependent dielectric breakdown of oxide caused by migration of oxygen vacancies. Acta Physica Sinica, 2017, 66(21): 217701. doi: 10.7498/aps.66.217701
    [3] Sun Xian-Ming, Xiao Sai, Wang Hai-Hua, Wan Long, Shen Jin. Transportation of Gaussian light beam in two-layer clouds by Monte Carlo simulation. Acta Physica Sinica, 2015, 64(18): 184204. doi: 10.7498/aps.64.184204
    [4] Li Shu, Lan Ke, Lai Dong-Xian, Liu Jie. Monte Carlo simulation of the radiation transport of spherical holhraum. Acta Physica Sinica, 2015, 64(14): 145203. doi: 10.7498/aps.64.145203
    [5] Chen Kun, Deng You-Jin. Higgs mode near superfluid-to-Mott-insulatortransition studied by the quantum Monte Carlo method. Acta Physica Sinica, 2015, 64(18): 180201. doi: 10.7498/aps.64.180201
    [6] Peng Ya-Jing, Jiang Yan-Xue. Analyses of the influences of molecular vacancy defect on the geometrical structure, electronic structure and vibration characteristics of Hexogeon energetic material. Acta Physica Sinica, 2015, 64(24): 243102. doi: 10.7498/aps.64.243102
    [7] Song Qing-Qing, Wang Xin-Bo, Cui Wan-Zhao, Wang Zhi-Yu, Ran Li-Xin. Probabilistic analysis of the lateral diffusion of secondary electrons in multicarrier multipactor. Acta Physica Sinica, 2014, 63(22): 220205. doi: 10.7498/aps.63.220205
    [8] Chang Tian-Hai, Zheng Jun-Rong. Monte-Carlo simulation of secondary electron emission from solid metal. Acta Physica Sinica, 2012, 61(24): 241401. doi: 10.7498/aps.61.241401
    [9] Song Jian, Li Feng, Deng Kai-Ming, Xiao Chuan-Yun, Kan Er-Jun, Lu Rui-Feng, Wu Hai-Ping. Density functional study on the stability and electronic structure of single layer Si6H4Ph2. Acta Physica Sinica, 2012, 61(24): 246801. doi: 10.7498/aps.61.246801
    [10] Duan Ping, Li Xi, E Peng, Qing Shao-Wei. Effect of magnetized secondary electron on the characteristics of sheath in Hall thruster. Acta Physica Sinica, 2011, 60(12): 125203. doi: 10.7498/aps.60.125203
    [11] Yuan Jian-Hui, Cheng Yu-Min, Zhang Zhen-Hua. Effects of vacancy structural defects on the elastic properties of carbon nanotubes. Acta Physica Sinica, 2009, 58(4): 2578-2584. doi: 10.7498/aps.58.2578
    [12] Fu Fang-Zheng, Li Ming. Calculating the threshold of random laser by using Monte Carlo method. Acta Physica Sinica, 2009, 58(9): 6258-6263. doi: 10.7498/aps.58.6258
    [13] Qi Kai-Tian, Yang Chuan-Lu, Li Bing, Zhang Yan, Sheng Yong. Density functional theory study on TinLa(n=1—7) clusters. Acta Physica Sinica, 2009, 58(10): 6956-6961. doi: 10.7498/aps.58.6956
    [14] Tang Chun-Mei, Chen Xuan, Deng Kai-Ming, Hu Feng-Lan, Huang De-Cai, Xia Hai-Yan. The evolution of the structure and electronic properties of the fullerene derivatives C60(CF3)n(n=2, 4, 6, 10): A density functional calculation. Acta Physica Sinica, 2009, 58(4): 2675-2679. doi: 10.7498/aps.58.2675
    [15] Cao Qing-Song, Deng Kai-Ming, Chen Xuan, Tang Chun-Mei, Huang De-Cai. Density functional study on the geometric and electronic properties of MC20F20 (M=Li, Na, Be, Mg). Acta Physica Sinica, 2009, 58(3): 1863-1869. doi: 10.7498/aps.58.1863
    [16] Ouyang Fang-Ping, Xu Hui, Wei Chen. First-principles study of electronic structure and transport properties of zigzag graphene nanoribbons. Acta Physica Sinica, 2008, 57(2): 1073-1077. doi: 10.7498/aps.57.1073
    [17] Jiang Yan-Ling, Fu Shi-You, Deng Kai-Ming, Tang Chun-Mei, Tan Wei-Shi, Huang De-Cai, Liu Yu-Zhen, Wu Hai-Ping. Density functional study on the structural and electronic properties of fullerene-barbituric acid and its dimmer. Acta Physica Sinica, 2008, 57(6): 3690-3697. doi: 10.7498/aps.57.3690
    [18] Bai Yu-Jie, Fu Shi-You, Deng Kai-Ming, Tang Chun-Mei, Chen Xuan, Tan Wei-Shi, Liu Yu-Zhen, Huang De-Cai. Density functional calculations on the geometric and electronic structures of the endohedral fullerene H2@C60 and its dimmer. Acta Physica Sinica, 2008, 57(6): 3684-3689. doi: 10.7498/aps.57.3684
    [19] Yao Ming-Zhen, Liang Ling, Gu Mu, Duan Yong, Ma Xiao-Hui. . Acta Physica Sinica, 2002, 51(1): 125-128. doi: 10.7498/aps.51.125
    [20] TONG HONG-YONG, GU MU, TANG XUE-FENG, LIANG LING, YAO MING-ZHEN. ELECTRONIC STRUCTURES OF PbWO4 CRYSTAL CALCULATED IN TERMS OF DENSITY FUNCTIONAL THEORY. Acta Physica Sinica, 2000, 49(8): 1545-1549. doi: 10.7498/aps.49.1545
Metrics
  • Abstract views:  2588
  • PDF Downloads:  56
Publishing process
  • Received Date:  26 April 2024
  • Accepted Date:  06 June 2024
  • Available Online:  26 June 2024
  • Published Online:  05 August 2024

/

返回文章
返回