反射电子能量损失能谱学中的Monte Carlo方法和其应用研究
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摘要
最近几十年随着纳米材料研究的兴起与发展,材料表面与其所处的环境相互作用所导致的表面性质越来越吸引研究者的目光。一大批专门表征材料表面的分析手段被发明,而对这些表面分析手段的进一步研究,逐渐成为物理领域中的一个重要分支-表面分析科学。在表面分析领域的种种表征手段中,表面电子能谱分析技术应用相当广泛。表面电子能谱分析技术的迅速发展和广泛利用,需要理论方面的研究支持。电子在固体表面的输运与散射过程是表面电子能谱分析技术的物理基础,因此对电子在材料表面附近的散射过程及相应的截面的准确描述是表面电子能谱理论研究的关键。通过仔细分析,电子在固体表面附近的散射过程可以简化为能量不发生任何损失的弹性散射以及能量发生损失的非弹性散射。电子与原子的弹性碰撞已经有了较为透彻的研究,而Mott的弹性散射截面是最为准确的描述。另一方面,Ritchie在1957年提出一个处理电子材料表面相互作用时的表面激发的理论模型,随后很多研究都计算了空间位置相关的非弹性散射截面。结合这两个截面,蒙特卡洛方法被广泛的应用在表面电子能谱的理论研究中。近年来实验样品制备方法越来越完善,表面电子能谱的实验测量也越来越精确,然而相应的理论研究并没有跟上实验发展的脚步。目前的研究中,还没有形成一套能够有效的研究真实样品表面形貌对表面电子能谱造成影响的定量分析方法。
在上述的研究背景下,本博士论文工作主要围绕着以下两点展开：首先,我们研究了真实样品形貌、表面碳污染层以及非弹性散射截面中负值部分对表面电子能谱的影响,建立了理想表面与粗糙表面的材料表面激发参数数据库；其次,我们发展出了一套全新的反射电子能量损失谱的解谱方法,逆蒙特卡洛方法,可从实验能谱出发提取出相应材料的光学常数。最后我们通过离散偶极子近似研究了任意纳米结构的局域表面等离子体激发,并模拟出相应的电子能量损失谱。本文共包含以下五章：
第一章介绍了表面电子能谱技术的基本原理与发展趋势,概述了电子与固体及表面的相互作用理论、蒙特卡洛模拟方法在表面电子能谱领域的应用。其次,概述了马尔可夫链蒙特卡洛方法和模拟退火法,阐明了研究目的和待完成的工作。
第二章首先介绍了表面等离激元与体等离激元的定义与研究背景,而表面激发参数是用来描述一个电子经过材料表面时发生表面等离激元激发的概率,用于评估实验能谱中表面激发的贡献。通过比较半经典框架和量子框架下材料表面附近的非弹性散射截面值,我们讨论了半经典模型计算表面激发参数的准确性。结合各方法对所需计算量的考量,使用半经典模型建立了多种材料的表面激发参数数据库。另外,大多数的实际样品表面形貌并不是理想平面,而有一定的粗糙度,我们采用有限三角形网格法通过真实样品的原子力显微镜图像来构建出样品真实的表面形貌。基于这些构建出的粗糙表面,我们也建立了粗糙样品的表面激发参数数据库。
第三章中研究了真实样品表面形貌对反射电子能量损失谱的影响。由于样品表面形貌很难在数学上给予一般性描述,因此很少有对此的计算研究。本文中,我们不讨论一般性的粗糙面的数学模型,而是直接使用有限三角形网格法来构建真实的全三维粗糙表面形貌,并在蒙特卡洛模拟中考虑了表面激发效应,从而能够定量的分析表面粗糙度与表面激发效应协同对反射电子能量损失谱造成的影响。对于薄膜样品,膜厚与衬底材料都会对反射电子能量损失谱造成影响。为此我们建立了电子与多层结构样品的相互作用模型,在此基础上计算了相应的依赖于深度的电子非弹性散射截面,利用蒙特卡洛方法对硅衬底上铁膜的反射电子能量损失谱进行了模拟,以该例分析了表面激发与界面激发。我们进一步研究了样品表面碳污染层对反射电子能量损失谱的影响,给出了避免碳污染层信号出现在能谱中的阈值入射电子能量。最后研究了在量子框架下理论计算非弹性微分散射截面时出现的负值问题,发展出一种对负值概率进行抽样的方法。对硅的计算结果表明,考虑了负微分截面后,模拟的反射电子能量损失谱更加符合实验结果。
第四章介绍了我们最近发展出的一种用于分析反射电子能量损失谱的新型蒙特卡洛计算技术-逆蒙特卡洛方法,阐述了发展该方法的出发点和主要思想,详细地描述了如何通过逆蒙特卡洛方法从实验反射电子能量损失谱中提取出材料的光学常数。其他解谱方法大多使用反卷积数学手段来从实验能谱中提取出光学数据,其中为了数学方便都要采取极大的近似,而真实的能谱形成过程远比卷积复杂的多。因此,我们抛弃传统的反卷积手段,直接采用蒙特卡洛方法模拟的电子能谱,将其与实验能谱比较,结合模拟退火法来不断的调整作为蒙特卡洛模拟输入参数的材料光学常数。通过不断地迭代能谱模拟步骤,最终得到使模拟能谱与实验能谱一致的光学常数最佳拟合数据。逆蒙特卡洛方法最大的优点采用已经发展非常完善的蒙特卡洛方法来处理复杂的电子与固体相互作用,算得的数据更加准确。我们将该方法成功运用到银和二氧化硅材料的研究中,分析结果显示,该方法可以得到非常准确的光学数据。
第五章中研究改进离散偶极子近似法,以使其能够模拟任意纳米结构的电子能量损失谱。事实上离散偶极子近似法在计算电磁场散射问题以及纳米颗粒等离激元激发问题中发挥了显著的作用,然而现有的采用离散偶极子近似方法来进行电磁特性分析的软件都只能计算外光场激发,并不能直接拓展到电子束激发情形。为了解决这一问题,我们发展出一套基于离散偶极子近似方法计算任意纳米机构材料的电子能量损失谱的程序。我们模拟了在单个银纳米颗粒附近不同入射位置下的电子能量损失谱,其计算结果与实验能谱非常吻合。虽然离散偶极子近似法早在很多年前就已经被应用到处理外加光场激发的情形,但正是我们这套方法提供了一个研究电子束诱导金属纳米颗粒局域表面等离激元激发的计算工具。
第六章对前面的几章内容进行了系统的总结。
In recent decades with the raid development of the nano material science, the surface properties induced by the interaction of material with external environment in-creasingly attracts the attention of researchers. Many specialized surface analysis tools are developed, and further study of these surface analysis techniques gradually be-comes an important branch field of physics study, the surface analysis science. Among various characterization means in surface analysis science, electron spectroscopy tech-niques have been widely applied. Theoretical investigation is necessary to accommo-date the fast development and wide application of the electron spectroscopic analysis techniques. The transport and scattering processes of electrons in the vicinity of solid surface forms the physics basis for electron spectroscopy analysis techniques. Thus, it is crucial to describe correctly the electron scattering processes and the corresponding cross sections for the study of electron spectroscopy. By careful analysis, the transport process of electrons near solid surface can be simplified to a series of electron scattering events for elastic scattering without energy loss and inelastic scattering with amount of energy loss. Numerous researches have been done on the electron-atom elastic colli-sion, and Mott's elastic cross section is considered as the most accurate description. On the other hand, a theoretical modeling of the surface excitation effect in electron inelastic interaction with a surface has been built by Ritchie in1957. Many works have then been done to calculate the spatially varying differential inelastic scattering cross section. Combining these two sections, Monte Carlo method has been widely used in the theoretical study of electron spectroscopy. As the rapid development in sample preparation techniques and measurement accuracy, however, theoretical research has not kept up with the development of experiment. There has been no yet a quantita-tive analysis method for investigating the influence to the surface electron spectroscopy spectra by the surface topography of a realistic sample.
This thesis thus concerns mainly the two aspects:first of all, we study the influence of surface topography of real sample, carbon surface contamination and the calculated negative inelastic cross section on electron spectroscopy spectrum, which enable us to build a database of surface excitation parameter for both ideal planar surface and rough surface. Second, a reverse Monte Carlo (RMC) method is developed to obtain the op-tical constants of solids from a measured reflection electron energy loss spectroscopy (REELS) spectrum. Finally, a discrete dipole approximation (DDA) method is em-ployed to study the localized surface plasmon excitation in arbitrary nano-structure and to simulate electron energy loss spectrum. The thesis consists of following five chap-ters.
Chapter One introduces the basic principles and development of the surface elec-tron spectroscopy technique. A brief introduction to theories of electron interaction with solids and surfaces and application of Monte Carlo simulation method in sur-face electron spectroscopies is given. Then an overview of Markov chain Monte Carlo method and the simulated annealing method is presented. It has been pointed out the research aim and the urgent works that to be carried out.
Chapter Two firstly introduces the definition of the surface plasmon and bulk plas-mon and research background. The excitation probability of surface plasmons is char-acterized by the surface excitation parameter (SEP) for an electron moving across a solid surface. It is used to estimate the contribution of surface plasmon excitation in a surface electron spectroscopy spectrum. By a comparison made on the calculated dif-ferential inverse inelastic mean free paths between semi-classical framework and quan-tum mechanical framework, we have discussed the accuracy of SEP calculation with a semi-classical model. Based on consideration of calculation efficiency, we have built a SEP database for many metals and cmpuounds based on the semi-classical model. In addition, most sample surface is not ideal smooth but with roughness; we have then used a finite element triangle mesh modeling of a realistic rough surface based on the surface topography profiles measured by atomic force microscopy. Then SEP database has also been built by using these rough surfaces.
Chapter Three investigates the influence of a realistic sample surface topography to reflection electron energy loss spectroscopy (REELS) spectrum. Because it is hard to mathematically describe the surface topography in a general form, little computa-tional work has been done in this aspect. Instead of providing a general mathematical modeling of rough surface, here we directly use a finite element triangle mesh model-ing of a full3D rough surface. Furthermore, we have included surface excitation in the Monte Carlo simulation, enabling us to study simultaneously the surface roughness and surface excitation effects on REELS spectra. For thin film on substrate samples both the film thickness and substrate material will affect the REELS spectrum. Therefore, a theoretical model for studying the interaction of electrons with a multilayered structure material is established; the depth-dependent electron inelastic scattering cross sections are calculated. We have erformed a Monte Carlo simulation of REELS spectrum for Fe film on Si substrate as an example study of the influence of surface excitation and interface excitation. Furthermore, the influence of carbon surface contamination on REELS spectrum is also studied, leading to derive the threshold energy that the car-bon contamination signal can be detected to appear in an energy spectrum. Finally, we have considered the problem of negative value in the inelastic differential cross sec-tion calculated in quantum-mechanical framework and developed a negative probability sampling method. Calculation result for Si has shown that by taking into account of this negative differential cross section, the simulated RRELS spectrum agrees better with an experimental result.
Chapter Four introduces our newly developed reverse Monte Carlo (RMC) method, a new type Monte Carlo technique for analysis of REELS spectrum. We describe in de-tail the idea for developing the technique and the RMC procedure to extract optical constants from a measured REELS spectrum. Most of other analysis methods rely on deconvolution of experimental spectrum in order to obtain optical constants, and ap-proximations have to be used for sake of mathematical convenience. The formation of a measured spectrum is much complex than the way of a simple convolution process. Therefore, instead of improving deconvolution formalism, we directly use the simu-lated RRELS spectrum to compare with an experimental spectrum. Combined with simulated annealing for improving oscillator parameters of optical constants, which is an input to Monte Carlo simulation, the difference on the REELS spectra between experiment and simulation is minimized by an iterative process. The best fitted data of optical constants are then obtained when the agreement is found. The key advan-tage of this RMC method is that the complicated electron-solid interaction process is approached by a well developed Monte Carlo simulation method, the obtained data should be better in accuracy. We have successfully applied the method to Ag and SiO2; the results show that very accurate optical data can obtained with the method.
Chapter Five studies the modification to a discrete dipole approximation (DDA) in order to be used for the simulation of electron energy loss spectroscopy (EELS) spec-trum for arbitrary nano-structures. The DDA method has played a significant role in computation of electromagnetic wave scattering and plasmon excitation in nanoparti-cles. However, the existing DDA softwares for analysis of electromagnetic properties only deals with the optical excitation and can not be extended directly to excitation by an electron beam. For this reason, we have developed a code for calculation of EELS spectra for arbitrary nano-structure based on DDA method. We have simulated EELS spectra at different beam positions nearby a single Ag nanoparticle; an excellent agreement has been found between our simulated and experimental spectra. Although DDA has been employed long ago to optical excitation problems, but it is this method provides a computation tool for study of the surface plasmon excitation of metallic nanoparticles by an electron beam.
Chapter Six summarizes the contents of previous chapters.
在上述的研究背景下,本博士论文工作主要围绕着以下两点展开：首先,我们研究了真实样品形貌、表面碳污染层以及非弹性散射截面中负值部分对表面电子能谱的影响,建立了理想表面与粗糙表面的材料表面激发参数数据库；其次,我们发展出了一套全新的反射电子能量损失谱的解谱方法,逆蒙特卡洛方法,可从实验能谱出发提取出相应材料的光学常数。最后我们通过离散偶极子近似研究了任意纳米结构的局域表面等离子体激发,并模拟出相应的电子能量损失谱。本文共包含以下五章：
第一章介绍了表面电子能谱技术的基本原理与发展趋势,概述了电子与固体及表面的相互作用理论、蒙特卡洛模拟方法在表面电子能谱领域的应用。其次,概述了马尔可夫链蒙特卡洛方法和模拟退火法,阐明了研究目的和待完成的工作。
第二章首先介绍了表面等离激元与体等离激元的定义与研究背景,而表面激发参数是用来描述一个电子经过材料表面时发生表面等离激元激发的概率,用于评估实验能谱中表面激发的贡献。通过比较半经典框架和量子框架下材料表面附近的非弹性散射截面值,我们讨论了半经典模型计算表面激发参数的准确性。结合各方法对所需计算量的考量,使用半经典模型建立了多种材料的表面激发参数数据库。另外,大多数的实际样品表面形貌并不是理想平面,而有一定的粗糙度,我们采用有限三角形网格法通过真实样品的原子力显微镜图像来构建出样品真实的表面形貌。基于这些构建出的粗糙表面,我们也建立了粗糙样品的表面激发参数数据库。
第三章中研究了真实样品表面形貌对反射电子能量损失谱的影响。由于样品表面形貌很难在数学上给予一般性描述,因此很少有对此的计算研究。本文中,我们不讨论一般性的粗糙面的数学模型,而是直接使用有限三角形网格法来构建真实的全三维粗糙表面形貌,并在蒙特卡洛模拟中考虑了表面激发效应,从而能够定量的分析表面粗糙度与表面激发效应协同对反射电子能量损失谱造成的影响。对于薄膜样品,膜厚与衬底材料都会对反射电子能量损失谱造成影响。为此我们建立了电子与多层结构样品的相互作用模型,在此基础上计算了相应的依赖于深度的电子非弹性散射截面,利用蒙特卡洛方法对硅衬底上铁膜的反射电子能量损失谱进行了模拟,以该例分析了表面激发与界面激发。我们进一步研究了样品表面碳污染层对反射电子能量损失谱的影响,给出了避免碳污染层信号出现在能谱中的阈值入射电子能量。最后研究了在量子框架下理论计算非弹性微分散射截面时出现的负值问题,发展出一种对负值概率进行抽样的方法。对硅的计算结果表明,考虑了负微分截面后,模拟的反射电子能量损失谱更加符合实验结果。
第四章介绍了我们最近发展出的一种用于分析反射电子能量损失谱的新型蒙特卡洛计算技术-逆蒙特卡洛方法,阐述了发展该方法的出发点和主要思想,详细地描述了如何通过逆蒙特卡洛方法从实验反射电子能量损失谱中提取出材料的光学常数。其他解谱方法大多使用反卷积数学手段来从实验能谱中提取出光学数据,其中为了数学方便都要采取极大的近似,而真实的能谱形成过程远比卷积复杂的多。因此,我们抛弃传统的反卷积手段,直接采用蒙特卡洛方法模拟的电子能谱,将其与实验能谱比较,结合模拟退火法来不断的调整作为蒙特卡洛模拟输入参数的材料光学常数。通过不断地迭代能谱模拟步骤,最终得到使模拟能谱与实验能谱一致的光学常数最佳拟合数据。逆蒙特卡洛方法最大的优点采用已经发展非常完善的蒙特卡洛方法来处理复杂的电子与固体相互作用,算得的数据更加准确。我们将该方法成功运用到银和二氧化硅材料的研究中,分析结果显示,该方法可以得到非常准确的光学数据。
第五章中研究改进离散偶极子近似法,以使其能够模拟任意纳米结构的电子能量损失谱。事实上离散偶极子近似法在计算电磁场散射问题以及纳米颗粒等离激元激发问题中发挥了显著的作用,然而现有的采用离散偶极子近似方法来进行电磁特性分析的软件都只能计算外光场激发,并不能直接拓展到电子束激发情形。为了解决这一问题,我们发展出一套基于离散偶极子近似方法计算任意纳米机构材料的电子能量损失谱的程序。我们模拟了在单个银纳米颗粒附近不同入射位置下的电子能量损失谱,其计算结果与实验能谱非常吻合。虽然离散偶极子近似法早在很多年前就已经被应用到处理外加光场激发的情形,但正是我们这套方法提供了一个研究电子束诱导金属纳米颗粒局域表面等离激元激发的计算工具。
第六章对前面的几章内容进行了系统的总结。
In recent decades with the raid development of the nano material science, the surface properties induced by the interaction of material with external environment in-creasingly attracts the attention of researchers. Many specialized surface analysis tools are developed, and further study of these surface analysis techniques gradually be-comes an important branch field of physics study, the surface analysis science. Among various characterization means in surface analysis science, electron spectroscopy tech-niques have been widely applied. Theoretical investigation is necessary to accommo-date the fast development and wide application of the electron spectroscopic analysis techniques. The transport and scattering processes of electrons in the vicinity of solid surface forms the physics basis for electron spectroscopy analysis techniques. Thus, it is crucial to describe correctly the electron scattering processes and the corresponding cross sections for the study of electron spectroscopy. By careful analysis, the transport process of electrons near solid surface can be simplified to a series of electron scattering events for elastic scattering without energy loss and inelastic scattering with amount of energy loss. Numerous researches have been done on the electron-atom elastic colli-sion, and Mott's elastic cross section is considered as the most accurate description. On the other hand, a theoretical modeling of the surface excitation effect in electron inelastic interaction with a surface has been built by Ritchie in1957. Many works have then been done to calculate the spatially varying differential inelastic scattering cross section. Combining these two sections, Monte Carlo method has been widely used in the theoretical study of electron spectroscopy. As the rapid development in sample preparation techniques and measurement accuracy, however, theoretical research has not kept up with the development of experiment. There has been no yet a quantita-tive analysis method for investigating the influence to the surface electron spectroscopy spectra by the surface topography of a realistic sample.
This thesis thus concerns mainly the two aspects:first of all, we study the influence of surface topography of real sample, carbon surface contamination and the calculated negative inelastic cross section on electron spectroscopy spectrum, which enable us to build a database of surface excitation parameter for both ideal planar surface and rough surface. Second, a reverse Monte Carlo (RMC) method is developed to obtain the op-tical constants of solids from a measured reflection electron energy loss spectroscopy (REELS) spectrum. Finally, a discrete dipole approximation (DDA) method is em-ployed to study the localized surface plasmon excitation in arbitrary nano-structure and to simulate electron energy loss spectrum. The thesis consists of following five chap-ters.
Chapter One introduces the basic principles and development of the surface elec-tron spectroscopy technique. A brief introduction to theories of electron interaction with solids and surfaces and application of Monte Carlo simulation method in sur-face electron spectroscopies is given. Then an overview of Markov chain Monte Carlo method and the simulated annealing method is presented. It has been pointed out the research aim and the urgent works that to be carried out.
Chapter Two firstly introduces the definition of the surface plasmon and bulk plas-mon and research background. The excitation probability of surface plasmons is char-acterized by the surface excitation parameter (SEP) for an electron moving across a solid surface. It is used to estimate the contribution of surface plasmon excitation in a surface electron spectroscopy spectrum. By a comparison made on the calculated dif-ferential inverse inelastic mean free paths between semi-classical framework and quan-tum mechanical framework, we have discussed the accuracy of SEP calculation with a semi-classical model. Based on consideration of calculation efficiency, we have built a SEP database for many metals and cmpuounds based on the semi-classical model. In addition, most sample surface is not ideal smooth but with roughness; we have then used a finite element triangle mesh modeling of a realistic rough surface based on the surface topography profiles measured by atomic force microscopy. Then SEP database has also been built by using these rough surfaces.
Chapter Three investigates the influence of a realistic sample surface topography to reflection electron energy loss spectroscopy (REELS) spectrum. Because it is hard to mathematically describe the surface topography in a general form, little computa-tional work has been done in this aspect. Instead of providing a general mathematical modeling of rough surface, here we directly use a finite element triangle mesh model-ing of a full3D rough surface. Furthermore, we have included surface excitation in the Monte Carlo simulation, enabling us to study simultaneously the surface roughness and surface excitation effects on REELS spectra. For thin film on substrate samples both the film thickness and substrate material will affect the REELS spectrum. Therefore, a theoretical model for studying the interaction of electrons with a multilayered structure material is established; the depth-dependent electron inelastic scattering cross sections are calculated. We have erformed a Monte Carlo simulation of REELS spectrum for Fe film on Si substrate as an example study of the influence of surface excitation and interface excitation. Furthermore, the influence of carbon surface contamination on REELS spectrum is also studied, leading to derive the threshold energy that the car-bon contamination signal can be detected to appear in an energy spectrum. Finally, we have considered the problem of negative value in the inelastic differential cross sec-tion calculated in quantum-mechanical framework and developed a negative probability sampling method. Calculation result for Si has shown that by taking into account of this negative differential cross section, the simulated RRELS spectrum agrees better with an experimental result.
Chapter Four introduces our newly developed reverse Monte Carlo (RMC) method, a new type Monte Carlo technique for analysis of REELS spectrum. We describe in de-tail the idea for developing the technique and the RMC procedure to extract optical constants from a measured REELS spectrum. Most of other analysis methods rely on deconvolution of experimental spectrum in order to obtain optical constants, and ap-proximations have to be used for sake of mathematical convenience. The formation of a measured spectrum is much complex than the way of a simple convolution process. Therefore, instead of improving deconvolution formalism, we directly use the simu-lated RRELS spectrum to compare with an experimental spectrum. Combined with simulated annealing for improving oscillator parameters of optical constants, which is an input to Monte Carlo simulation, the difference on the REELS spectra between experiment and simulation is minimized by an iterative process. The best fitted data of optical constants are then obtained when the agreement is found. The key advan-tage of this RMC method is that the complicated electron-solid interaction process is approached by a well developed Monte Carlo simulation method, the obtained data should be better in accuracy. We have successfully applied the method to Ag and SiO2; the results show that very accurate optical data can obtained with the method.
Chapter Five studies the modification to a discrete dipole approximation (DDA) in order to be used for the simulation of electron energy loss spectroscopy (EELS) spec-trum for arbitrary nano-structures. The DDA method has played a significant role in computation of electromagnetic wave scattering and plasmon excitation in nanoparti-cles. However, the existing DDA softwares for analysis of electromagnetic properties only deals with the optical excitation and can not be extended directly to excitation by an electron beam. For this reason, we have developed a code for calculation of EELS spectra for arbitrary nano-structure based on DDA method. We have simulated EELS spectra at different beam positions nearby a single Ag nanoparticle; an excellent agreement has been found between our simulated and experimental spectra. Although DDA has been employed long ago to optical excitation problems, but it is this method provides a computation tool for study of the surface plasmon excitation of metallic nanoparticles by an electron beam.
Chapter Six summarizes the contents of previous chapters.
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