Study Of Monte Carlo Methods And Their Applications To Reflection Electron Energy Loss Spectroscopy

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.