S. F. Mao

Electron inelastic scattering and secondary electron emission calculated without the single pole approximation

In this work, aimed primarily at providing more accurate electron inelastic mean free paths (IMFPs) and stopping powers (SPs) at low energies than are provided by the single pole approximation, the “full Penn” algorithm has been employed to derive the electron inelastic scattering energy loss function in solids. IMFPs and SPs have thus been calculated in the energy range from 1 eV to 10 keV and are in good agreement with the experimental data. This treatment of electron inelastic scattering combined with a consistent model for the cascade secondary electron generation has enabled more elaborate Monte Carlo simulations of secondary electron emission from metals. The calculated results of the energy distributions and the secondary electron emission yields for Al and Cu agree reasonably with experimental results.

Validity of the semi-classical approach for calculation of the surface excitation parameter

The problem of surface plasmon excitation by moving charges has been elaborated by several different approaches, mainly based on dielectric response theory within either semi-classical or quantum mechanical frameworks. In this work, a comparison of the surface excitation effect between two different frameworks is made by calculation of the differential inverse inelastic mean free path (DIIMFP) and a Monte Carlo simulation of reflection electron energy loss spectroscopy (REELS) spectra. A semi-classical modeling of the interaction between electrons and a solid surface is based on analyzing the work done by moving electrons; the stopping power and inelastic cross section are derived with the induced potential. On the other hand, a quantum mechanical approach is based on derivation of the complex inhomogeneous self-energy of the electrons. The numerical calculation shows that the semi-classical model presents almost the same values of DIIMFP as by the quantum model except at the glancing condition. The simulation of REELS spectra for Ag and SiO(2) as well as a comparison with experimental spectra also confirms that a good agreement with the spectral shape is found among the two simulation results and the experimental data.

Monte Carlo simulation study of scanning electron microscopy images of rough surfaces

In this paper, we have developed a Monte Carlo (MC) simulation method for calculation of scanning electron microscopy (SEM) images of rough surfaces. The roughness structure is constructed in a finite element triangulated mesh by using a Gaussian function to describe the distribution of amplitude of the random rough peaks. Further spatial subdividing can accelerate the calculation and improves MC simulation efficiency. The MC model is based on the using of the Mott cross section for description of the electron elastic scattering and the using of the full Penn algorithm in a dielectric functional approach to the electron inelastic scattering. This simulation relates directly a defined rough surface structure modeling described by exact values of roughness parameters to the contrast observed in a SEM image, enabling the investigation of the influence of line edge roughness to the critical dimension (CD) metrology of a metal-oxide-semiconductor device by SEM. Example calculation of line images with sidewall ...

Monte Carlo modeling of surface excitation in reflection electron energy loss spectroscopy spectrum for rough surfaces

It has been experimentally found that the surface roughness influences strongly the surface and bulk plasmon excitation by glancing-angle reflection electron energy loss spectroscopy (REELS). However, there is still little theoretical work dealing with the surface roughness effect in REELS. Such a work is required to predict REELS spectra accurately, providing an understanding of the experimental phenomena observed. In this study, we use a finite element triangle mesh method build in a fully 3D rough surface model based on the surface topography measured by atomic force microscopy. Then REELS spectra for these rough surfaces are theoretically simulated by using Monte Carlo simulation including surface plasmon excitation and bulk plasmon excitation. The simulation results for Al sample with different surface roughnesses agree well with experimental data. Based on the analysis of the maximum depth of backscattered electrons and the depth distribution of surface bulk excitation under different conditions of ...

A reverse Monte Carlo method for deriving optical constants of solids from reflection electron energy-loss spectroscopy spectra

A reverse Monte Carlo (RMC) method is developed to obtain the energy loss function (ELF) and optical constants from a measured reflection electron energy-loss spectroscopy (REELS) spectrum by an iterative Monte Carlo (MC) simulation procedure. The method combines the simulated annealing method, i.e., a Markov chain Monte Carlo (MCMC) sampling of oscillator parameters, surface and bulk excitation weighting factors, and band gap energy, with a conventional MC simulation of electron interaction with solids, which acts as a single step of MCMC sampling in this RMC method. To examine the reliability of this method, we have verified that the output data of the dielectric function are essentially independent of the initial values of the trial parameters, which is a basic property of a MCMC method. The optical constants derived for SiO2 in the energy loss range of 8-90 eV are in good agreement with other available data, and relevant bulk ELFs are checked by oscillator strength-sum and perfect-screening-sum rules....

A calculation of backscattering factor database for quantitative analysis by Auger electron spectroscopy

A systematic calculation of the backscattering factor in quantitative analysis by Auger electron spectroscopy has been performed for the primary electron beam of energy from the threshold energy of inner-shell ionization to 30 keV at the incident angle of 0°–89° and for principal Auger transition and Auger electrons emitted from over 28 pure elements at an emission angle of 0°–89° by using a Monte Carlo simulation method. The calculation employs a general definition of backscattering factor, Casnati’s ionization cross section, up-to-date Monte Carlo model of electron scattering, and a large number of electron trajectories to ensure less statistical error. Both the configuration geometry of concentric hemispherical analyzer and the cylindrical mirror analyzer for Auger electron detection are considered in the calculation. The calculated backscattering factors are found to describe very well an experimental dependence of Auger electron intensity on primary energy and on incident angle for Si, Cu, Ag, and W ...

Monte Carlo Study of the Influence of Electron Beam Focusing to SEM Linewidth Measurement

Based on a Monte Carlo simulation method we have analyzed the influence of electron beam focusing to linewidth measurement for Si trapezoid lines by scanning electron microscopy (SEM) image. The electron probe focusing with finite probe width due to aberration is considered by two different models for simulating incident electron trajectories. The simulation result shows that on the specimen surface the electron beam profile is deviated from the Gaussian probe shape because of the surface topography; the measured linewidth then depends on the focus position and aperture angle.

Monte Carlo Simulation of Realistic Beam-Sample Interaction in SEM: Application to Evaluation of Sharpness Measurement Methods

Monte Carlo simulated SEM images for realistic instrumental conditions are used to evaluate measurement methods for SEM image sharpness. The Monte Carlo simulation of the SEM image is based on a well-developed physical model of electron-solid interaction, which employs Mott’s cross section for elastic electron scattering and dielectric functional approach to electron inelastic scattering with cascade secondary electron production included, a finite element mesh modeling of complex sample topography and a modeling of SEM instrumental conditions (i.e. focus, astigmatism, drift and vibration). A series of simulated SEM images of a realistic sample, gold particles on a carbon substrate, for different instrumental parameters are generated to represent practical images where all instrumental conditions are precisely known and controlled. An estimation of three measurement methods of SEM image sharpness, i.e. FT, CG and DR methods, has then been performed with these simulated images. The responses of image sharpness measurement methods to various instrumental conditions are studied. The calculation shows that all the three methods present similar and reasonable response to focus parameter; their dependences of the measured sharpness on astigmatism coefficient are complicated and CG method presents reasonable sharpness value. For drift and vibration, the situation is more complex because CG/DR methods can be less or more sensitive to vibration coefficient than FT method. Because of the different response behaviors of the three sharpness measurement methods to experimental parameters, we propose to use a mean, simple average or weighted average, of three sharpness values as a proper measure of sharpness.

Monte Carlo study of depth distribution function of secondary electrons (Extended abstracts book of the International Workshop for Surface Analysis and Standardization '09 (iSAS-09))

As fundamental importance to SEM observation of specimen surface, secondary electron generation and emission processes have been studied by a Monte Carlo method. The simulation is based on a discrete description of cascade secondary electron production. The Monte Carlo model combines the use of Mott’s cross section for electron elastic scattering and of Penn’s dielectric function for electron inelastic scattering. Two models of dielectric function, i.e. the single pole approximation and the full Penn algorithm, are shown to give energy distribution and yield of secondary electrons in agreement with experimental results for non-free electron materials and free electron metals, respectively. We use a constructive solid geometry modeling to describe sample 3D geometry and a Gaussian function to describe random surface roughness. The technique is efficient and powerful in a simulation of SEM images of secondary electrons and backscattered electrons for a quite complex geometry of nanostructures. Finally we present the depth distribution functions for secondary electron generation and emission. Their dependences on primary energy and atomic numbers are analyzed. Furthermore, we shall also discuss a general issue of depth distribution function for rough surfaces.

Surface sensitivity of secondary electrons emitted from amorphous solids: Calculation of mean escape depth by a Monte Carlo method

A Monte Carlo simulation method for study of electron-solid interaction based on modeling of cascade secondary electron (SE) production and transportation has been used to determine the escape depth of emitted SE signals from amorphous solid specimens. The excitation depth distribution function and emission depth distribution function for, respectively, excited and emitted SEs are obtained at first based on the continuous medium approximation, whose product yields the secondary electron depth distribution function from which the mean escape depth (MED) of SEs is calculated. In this work, we study systematically the dependence of the MED on the atomic number of the specimen, primary energy, and incident angle of the incident electron beam. The derived MEDs of SEs for C, Ni, Cu, Ag, Pt, and Au specimens are found surprisingly to fall into a shallow sub-nanometer region, i.e., 0.4–0.9 nm, while Al and Si present larger values, due to elastic scattering effects. Furthermore, SE energy-depth distributions indi...