扫描电子显微学中二次电子产生的Monte Carlo模拟
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摘要
二次电子是扫描电子显微镜中最为基础和常用的信号。同时,实验中所测得的二次电子信号的产生也是最为复杂的。由理论计算来得到二次电子的产额以及能谱,并与实验进行对比分析有助于加深对二次电子产生的理解,进而对实验中如何更有效的得到和利用二次电子有着重要的意义。本文首先简单介绍扫描电子显微镜的原理及目前的发展情况,概述了电子与固体相互作用研究的发展,以及实验中二次电子相关的现象及其原理。(第1章)
二次电子产生的与电子在固体中复杂的输运过程紧密相关。理论上,很难通过解析公式得到二次电子的产额以及能谱,因此我们使用Monte Carlo模拟来得到所需要的结果。电子在固体中的输运过程一般可以简化为电子与固体之间一系列的弹性或者非弹性碰撞以及在连续两次碰撞之间电子自由飞行的过程。这两种不同的碰撞可以通过相应的理论来进行描述。弹性碰撞已经有了较为透彻的研究,人们发现Mott弹性散射截面可以较为准确的描述电子在固体中的弹性散射。而对于非弹性散射,Penn提出的基于外推光学实验数据的介电函数模型相对来说更加合理。先前的研究中由于计算条件的限制,对Penn的模型一般采用了一种被称为单极近似的手段来简化计算。而最新的研究进展表明,放弃单极近似,采用我们称之为full Penn方法的完整的模型能够更加准确的描述电子的非弹性散射过程,尤其对于近自由电子金属。文中将详细介绍full Penn方法,并给出由此得到的非弹性平均自由程以及阻止本领。在此基础上,将简要介绍下Monte Carlo模拟的具体过程以及并行计算的相关处理。(第2章)
我们首先研究了二次电子的产额和能谱。二次电子的产额是反映材料性质的重要参数。实验上对不同材料不同入射能量下的二次电子产额有着广泛的研究。模拟得到的结果与实验数据有着很好的符合,同时二次电子的能谱也与实验有着较好的符合,这说明现在的模型是合理的。在此基础上,我们研究了二次电子的空间分布。二次电子所携带信息的空间分辨率可以从二次电子的空间分布得到,而这是实验无法测量的。(第3章)
在验证了理论模拟的有效性的基础上,研究了如下与二次电子的相关的几种现象:
1、形貌衬度:这是扫描电子显微图像的基本衬度。与该衬度相关的一个基本问题是扫描电镜分辨率的测量。目前扫描电镜显微镜的分辨率测量有着多种方法,但最为准确的方法难以确定。为了检测这些方法,需要各种情况下的实验图像,但这是非常困难的。一个替代的方法就是利用Monte Carlo模拟得到的图像。我们引入了理论产生的复杂表面构型,模拟实验的扫描过程得到了需要的图像。模拟得到的图像还可以给出不考虑实验参数影响时理想的分辨率极限。同时通过图像看到的样品尺寸与真实尺寸之间的差异也可以通过比较模拟得到的图像与模拟中采用的样品构型得到。(第4章)
2、半导体掺杂衬度:由于半导体各个区域的掺杂浓度不同,将导致二次电子产额的变化并形成衬度,并且衬度与掺杂浓度有着很好的线性关系。这个现象对半导体器件的评估有着极高的应用价值。我们认为这种衬度主要来源于表面态所导致的功函数变化。模拟的结果与实验有着很好的一致性。(第5章)
3、自旋极化:一束无自旋极化的电子在Fe、Ni之类的物质中所产生的二次电子有着显著的自旋极化率(超过材料本身的磁化)。通常认为这种现象主要是由于自旋相关的非弹性平均自由程非对称性所导致。模拟的结果表明,Stoner激发,即自旋反转的非弹性散射过程,有着重要的影响。(第6章)
为了能够直观的了解等离子体激元激发与二次电子产生之间的关系,可以通过双电子符合实验来测量由一个电子入射所导致的两个反射电子之间的符合谱。对于Al这样典型的近自由电子金属,我们根据实验的设置模拟得到了相应的符合谱,结果反映了二次电子产生与等离子体激元的激发之间有着紧密的关联。(第7章)
Secondary electron is the most basic and useful signal in Scanning Electron Mi-croscopy, while the generation process of detected secondary electrons is most com-plex. It is helpful for making a deep understanding of the generation of the secondaryelectrons by comparing the yields and spectrums obtained by the theoretical calcula-tion and experiment. Furthermore, it is also meaningful for generation and applying thesecondary electrons more effectively. In this thesis, the principle and the state-of-the-art development of the Scanning Electron Microscopy would be firstly introduced, thenthe development of the research on electron-solid interaction is summarized, togetherwith some experimental phenomenons related to secondary electrons and correspond-ing mechanism. (1st chapter)
The generation of secondary electrons is closely related to the complex transportprocess of the electrons in solid. Theoretically, it is hardly to obtain the yields and spec-trums of secondary electron by using analytical formulas. Therefore, the Monte Carlosimulation is adapted to obtain the results needed. The transport process of the electronscan be simplified to a combination of a series of elastic and/or inelastic collisions be-tween the moving electron and the solid and the free movement of the electron betweentwo sequential collisions. These two types of collisions can be described by corre-sponding theory. Numerous of researches have been done on the elastic collision, andMott elastic cross section is considered as the most accurate description. On the otherhand, the dielectric function model proposed by Penn, which is based on the extrapola-tion of optical data, is reasonable for the description of inelastic collision. Because ofthe restriction of computation ability in the past, an approximation named single-poleapproximation is adopted to simplify the calculation based on Penn model. Accordingto our recent research, the original model named full Penn algorithm is more accuratethan the single-pole approximation for description of the inelastic collision, especiallyfor near-free-electron metal. In this thesis, the full-Penn algorithm would be introducedin detail, and the inelastic mean free path and the stopping power obtained by this al-gorithm would be also given. Based on the above theory, the detailed process of theMonte Carlo simulation would be introduced together with corresponding treatment onparalleled calculation. (2nd chapeter)
The yields, spectrums and the space distribution of the secondary electron are firstly calculated. The secondary yield is an important parameter related to the ma-terial. It has been widely researched experimentally for various materials and incidentenergies. The simulated results and the experiment results are in good agreement, whilethe spectrums of the secondary electrons are also in good consistency, which indicatesthe present model is reasonable. Furthermore, the space distribution of the secondaryelectrons is also studied. The space resolution of the information carried by secondaryelectron can be obtained from the space distribution, which is unable to be measuredexperimentally. (3rd chapeter)
As the efficiency of the theoretical simulation has been proved, the following phe-nomenons related to secondary electrons are studied:
1. Topographic contrast. The topographic contrast is a basic phenomenon in Scan-ning Electron Microscopy. A basic subject corresponding to this contrast is the mea-surement of the resolution of the Scanning Electron Microscopy. There are severalmethods to do the measurement; however, an objective method is still not decided. Forassessing these methods, the experiment images under various condition are needed,which is difficult to realize. An alternative way is to use the simulation images. Thecomplex surface structure generated by a series of formulas is introduced to the MonteCarlo simulation and the images need are obtained through simulation the scanningprocess as in experiment. The simulated image can also give the idea limit resolutionwithout the infection of the experimental parameter. Nevertheless, the difference be-tween the sample size measured from the image and the actual size can be obtainedthrough comparison of the simulated image and the sample topograph used in simula-tion. (4th charpter)
2. Dopant contrast. The contrast would be induced by the different secondaryyields in different regions where the dopant concentrations are different, and is pro-portion to the dopant concentration. This phenomenon is valuable for assessing thesemiconductor device. The change of the work function induced by the surface state isconsidered as a main mechanism. The simulated results are in good agreement to theexperimental results. (5th chapter)
3. Spin polarization. The unpolarized electron beam would generates secondaryelectrons of great polarization (much more than the bulk magnetization of the mate-rial) in the material like Fe and Ni. a spin-dependent asymmetry of mean free path isusually considered as the main reason. The simulation results indicated that the Stonerexcitation, the spin-?ip inelastic collision, affects the results significantly. (6th chapter)
For understanding the relation between plasmon excitation and secondary electron generation intuitionisticly, the coincident spectrum of two emitting electrons generatedby one incident electron is measured through coincident experiment. For the typicalnear-free-electron metal Al, the corresponding coincident spectrum is simulated ac-cording to the actual setting of experiment. The results indicates that the secondaryelectron excitation is closely related to the plasmon excitation. (7th chapter)
二次电子产生的与电子在固体中复杂的输运过程紧密相关。理论上,很难通过解析公式得到二次电子的产额以及能谱,因此我们使用Monte Carlo模拟来得到所需要的结果。电子在固体中的输运过程一般可以简化为电子与固体之间一系列的弹性或者非弹性碰撞以及在连续两次碰撞之间电子自由飞行的过程。这两种不同的碰撞可以通过相应的理论来进行描述。弹性碰撞已经有了较为透彻的研究,人们发现Mott弹性散射截面可以较为准确的描述电子在固体中的弹性散射。而对于非弹性散射,Penn提出的基于外推光学实验数据的介电函数模型相对来说更加合理。先前的研究中由于计算条件的限制,对Penn的模型一般采用了一种被称为单极近似的手段来简化计算。而最新的研究进展表明,放弃单极近似,采用我们称之为full Penn方法的完整的模型能够更加准确的描述电子的非弹性散射过程,尤其对于近自由电子金属。文中将详细介绍full Penn方法,并给出由此得到的非弹性平均自由程以及阻止本领。在此基础上,将简要介绍下Monte Carlo模拟的具体过程以及并行计算的相关处理。(第2章)
我们首先研究了二次电子的产额和能谱。二次电子的产额是反映材料性质的重要参数。实验上对不同材料不同入射能量下的二次电子产额有着广泛的研究。模拟得到的结果与实验数据有着很好的符合,同时二次电子的能谱也与实验有着较好的符合,这说明现在的模型是合理的。在此基础上,我们研究了二次电子的空间分布。二次电子所携带信息的空间分辨率可以从二次电子的空间分布得到,而这是实验无法测量的。(第3章)
在验证了理论模拟的有效性的基础上,研究了如下与二次电子的相关的几种现象:
1、形貌衬度:这是扫描电子显微图像的基本衬度。与该衬度相关的一个基本问题是扫描电镜分辨率的测量。目前扫描电镜显微镜的分辨率测量有着多种方法,但最为准确的方法难以确定。为了检测这些方法,需要各种情况下的实验图像,但这是非常困难的。一个替代的方法就是利用Monte Carlo模拟得到的图像。我们引入了理论产生的复杂表面构型,模拟实验的扫描过程得到了需要的图像。模拟得到的图像还可以给出不考虑实验参数影响时理想的分辨率极限。同时通过图像看到的样品尺寸与真实尺寸之间的差异也可以通过比较模拟得到的图像与模拟中采用的样品构型得到。(第4章)
2、半导体掺杂衬度:由于半导体各个区域的掺杂浓度不同,将导致二次电子产额的变化并形成衬度,并且衬度与掺杂浓度有着很好的线性关系。这个现象对半导体器件的评估有着极高的应用价值。我们认为这种衬度主要来源于表面态所导致的功函数变化。模拟的结果与实验有着很好的一致性。(第5章)
3、自旋极化:一束无自旋极化的电子在Fe、Ni之类的物质中所产生的二次电子有着显著的自旋极化率(超过材料本身的磁化)。通常认为这种现象主要是由于自旋相关的非弹性平均自由程非对称性所导致。模拟的结果表明,Stoner激发,即自旋反转的非弹性散射过程,有着重要的影响。(第6章)
为了能够直观的了解等离子体激元激发与二次电子产生之间的关系,可以通过双电子符合实验来测量由一个电子入射所导致的两个反射电子之间的符合谱。对于Al这样典型的近自由电子金属,我们根据实验的设置模拟得到了相应的符合谱,结果反映了二次电子产生与等离子体激元的激发之间有着紧密的关联。(第7章)
Secondary electron is the most basic and useful signal in Scanning Electron Mi-croscopy, while the generation process of detected secondary electrons is most com-plex. It is helpful for making a deep understanding of the generation of the secondaryelectrons by comparing the yields and spectrums obtained by the theoretical calcula-tion and experiment. Furthermore, it is also meaningful for generation and applying thesecondary electrons more effectively. In this thesis, the principle and the state-of-the-art development of the Scanning Electron Microscopy would be firstly introduced, thenthe development of the research on electron-solid interaction is summarized, togetherwith some experimental phenomenons related to secondary electrons and correspond-ing mechanism. (1st chapter)
The generation of secondary electrons is closely related to the complex transportprocess of the electrons in solid. Theoretically, it is hardly to obtain the yields and spec-trums of secondary electron by using analytical formulas. Therefore, the Monte Carlosimulation is adapted to obtain the results needed. The transport process of the electronscan be simplified to a combination of a series of elastic and/or inelastic collisions be-tween the moving electron and the solid and the free movement of the electron betweentwo sequential collisions. These two types of collisions can be described by corre-sponding theory. Numerous of researches have been done on the elastic collision, andMott elastic cross section is considered as the most accurate description. On the otherhand, the dielectric function model proposed by Penn, which is based on the extrapola-tion of optical data, is reasonable for the description of inelastic collision. Because ofthe restriction of computation ability in the past, an approximation named single-poleapproximation is adopted to simplify the calculation based on Penn model. Accordingto our recent research, the original model named full Penn algorithm is more accuratethan the single-pole approximation for description of the inelastic collision, especiallyfor near-free-electron metal. In this thesis, the full-Penn algorithm would be introducedin detail, and the inelastic mean free path and the stopping power obtained by this al-gorithm would be also given. Based on the above theory, the detailed process of theMonte Carlo simulation would be introduced together with corresponding treatment onparalleled calculation. (2nd chapeter)
The yields, spectrums and the space distribution of the secondary electron are firstly calculated. The secondary yield is an important parameter related to the ma-terial. It has been widely researched experimentally for various materials and incidentenergies. The simulated results and the experiment results are in good agreement, whilethe spectrums of the secondary electrons are also in good consistency, which indicatesthe present model is reasonable. Furthermore, the space distribution of the secondaryelectrons is also studied. The space resolution of the information carried by secondaryelectron can be obtained from the space distribution, which is unable to be measuredexperimentally. (3rd chapeter)
As the efficiency of the theoretical simulation has been proved, the following phe-nomenons related to secondary electrons are studied:
1. Topographic contrast. The topographic contrast is a basic phenomenon in Scan-ning Electron Microscopy. A basic subject corresponding to this contrast is the mea-surement of the resolution of the Scanning Electron Microscopy. There are severalmethods to do the measurement; however, an objective method is still not decided. Forassessing these methods, the experiment images under various condition are needed,which is difficult to realize. An alternative way is to use the simulation images. Thecomplex surface structure generated by a series of formulas is introduced to the MonteCarlo simulation and the images need are obtained through simulation the scanningprocess as in experiment. The simulated image can also give the idea limit resolutionwithout the infection of the experimental parameter. Nevertheless, the difference be-tween the sample size measured from the image and the actual size can be obtainedthrough comparison of the simulated image and the sample topograph used in simula-tion. (4th charpter)
2. Dopant contrast. The contrast would be induced by the different secondaryyields in different regions where the dopant concentrations are different, and is pro-portion to the dopant concentration. This phenomenon is valuable for assessing thesemiconductor device. The change of the work function induced by the surface state isconsidered as a main mechanism. The simulated results are in good agreement to theexperimental results. (5th chapter)
3. Spin polarization. The unpolarized electron beam would generates secondaryelectrons of great polarization (much more than the bulk magnetization of the mate-rial) in the material like Fe and Ni. a spin-dependent asymmetry of mean free path isusually considered as the main reason. The simulation results indicated that the Stonerexcitation, the spin-?ip inelastic collision, affects the results significantly. (6th chapter)
For understanding the relation between plasmon excitation and secondary electron generation intuitionisticly, the coincident spectrum of two emitting electrons generatedby one incident electron is measured through coincident experiment. For the typicalnear-free-electron metal Al, the corresponding coincident spectrum is simulated ac-cording to the actual setting of experiment. The results indicates that the secondaryelectron excitation is closely related to the plasmon excitation. (7th chapter)
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