Electron Trajectories In Solids Research Articles

Angular distribution of elastic electron backscattering from surfaces: determination of the electron inelastic mean free path

The development of analytical techniques based on measurements of electron elastic-backscattering probabilities stimulated an interest in the theoretical description of such phenomena. The most accurate and reliable theoretical models involve Monte Carlo (MC) simulations of electron trajectories in solids; however, this approach generally requires considerable computer effort. It has been shown that the performance of a modified analytical theory originally proposed by Oswald et al (1993 J. Electron Spectrosc. Relat. Phenom. 61 251), designated with the acronym OKGM, compares reasonably well with MC calculations. The MC data are usually underestimated by the OKGM model, and the mean percentage deviation, averaged over nine elements and five energies up to 5 keV, is equal to 8.8% for typical experimental configurations. However, the agreement between ratios of backscattering probabilities from MC simulations and the OKGM model agree much better due to the fact that underestimation of backscattering probability by the OMGM theory is partially cancelled. The percentage deviation between ratios from these theoretical models decreases to 3.14%. The OKGM model should then be useful for determining inelastic mean free paths (IMFPs) from measured elastic-peak intensities. The accuracy of the obtained IMFPs is comparable with IMFPs from MC simulations.

Experimental verification of the shape of the excitation depth distribution function for AES

In the common formalism of AES, it is assumed that the in-depth distribution of ionizations is uniform. There are experimental indications that this assumption may not be true for certain primary electron energies and solids. The term “excitation depth distribution function” (EXDDF) has been introduced to describe the distribution of ionizations at energies used in AES. This function is conceptually equivalent to the Phi-rho-z function of electron microprobe analysis (EPMA). There are, however, experimental difficulties to determine this function in particular for energies below ∼ 10 keV. In the present paper, we investigate the possibility of determining the shape of the EXDDF from the background of inelastically scattered electrons on the low energy side of the Auger electron features in the electron energy spectra. The experimentally determined EXDDFs are compared with the EXDDFs determined from Monte Carlo simulations of electron trajectories in solids. It is found that this technique is useful for the experimental determination of the EXDDF function.

Design of a conversion electron Mössbauer spectrometer based on an electron multiplier. Evaluation of the mean-escape-depth of the detected signals

A Conversion Electron Mossbauer Spectrometer to be used for the characterization of Fe-containing metal surfaces was designed and installed in an Ultra High Vacuum chamber. The design is based in the use of a Channeltron electron multiplier for the detection of electrons emerging from the sample after an incident γ-Ray is absorbed by resonant nuclear excitation. Using a Monte Carlo simulation for electron trajectories in solids the mean-escape-depth of the detected Mossbauer signal from a metallic iron sample was estimated to be 80 nm, assuming that the main signals being detected correspond to the Fe(M), Fe(L) and Fe(K) conversion electrons as well as the Fe(KLM), Fe(KLL) and Fe(LMM) Auger electrons. The sensitivity to the surface region was also estimated experimentally by acquiring Mossbauer spectra from a series of Fe films of different thickness deposited by magnetron sputtering on 304 stainless steel substrates.

The Inelastic Mean Free Path οf Electrons. Research in Budapest, Warsaw, Wrocław and Clermont-Ferrand. Brief History and New Results

The inelastic mean free path of electrons (IMFP) is an important material parameter for description of electron transport processes in solids. This parameter is particularly useful for quantifying the electron spectroscopies, in particular Auger electron spectroscopy, X-ray photoelectron spectroscopy, electron energy loss spectroscopy and elastic peak electron spectroscopy. In this work, a brief overview of the IMFP determination is presented. Generally, there are two groups of methods to determine the IMFP: (i) calculations using the theoretical model based on the experimental optical data, and (ii) calculations using theory relating the IMFP and the measured probability elastic electron backscattering from solids. Major advances in the development of the second group of methods were made in three laboratories; these advances are reviewed here. The elastic backscattering probability, in absolute or relative units, can be conveniently evaluated from the elastic peak intensity. However, much effort is needed to develop the theory for calculating the IMFP, which typically involves the Monte Carlo simulations of electron trajectories in solids. Presently, this theory and typical procedures of the spectra processing are implemented in the software package EPESWIN developed by Jablonski. In recent years, much attention is devoted to the phenomenon of the electron energy losses in the surface region of solids. Reliability of the theory of elastic backscattering is distinctly improved if this effect is taken into account.

Modified predictive formula for the electron stopping power

We report an improved predictive formula for the electron stopping power (SP) based on an analysis and fit of SPs and electron inelastic mean free paths (IMFPs) calculated from optical data for 37 elemental solids and energies between 200eV and 30keV. The formula is a function of energy, density, and IMFP, and is recommended for solids with atomic numbers larger than 6. While the mean deviation between predicted and calculated SPs was 7.25%, larger deviations were found for four additional materials, Li (22.2%), Be (17.9%), graphite (15.3%), and diamond (15.7%). The predictive SP formula can be applied to multicomponent materials. Test comparisons for two compounds, guanine and InSb, showed average deviations of 16.0% and 19.1%, respectively. The improved SP formula is expected to be useful in simulations of electron trajectories in solids with the continuous slowing-down approximation (e.g., in Auger-electron spectroscopy and electron microprobe analysis).

Angle-resolved elastic-peak electron spectroscopy: Solid-state effects

It has been frequently reported that characteristics of electrons elastically backscattered from solid surfaces (e.g., the angular distribution) are well described by Monte Carlo simulations of electron trajectories in solids. The theoretical model implemented in these simulations requires knowledge of accurate differential elastic-scattering cross sections (DCSs). In computational practice, the DCSs for isolated neutral atoms constituting the solid are used to simplify the calculations. In reality, the interaction potential between an electron and an atom inside a solid is different from the interaction between an electron and an isolated atom. In the present work, we study changes of the DCSs due to agglomeration of atoms. The interaction between an atom and an electron in the solid is approximated by the muffin-tin potential. It has been found that the DCSs are considerably influenced by the agglomeration of atoms for small scattering angles. The difference for silicon reaches 500% for silicon at 200 eV. On the other hand, electron elastic-backscattering probabilities calculated using DCSs from two potentials were only slightly affected. Calculations and measurements of elastically backscattered intensity were compared for 10 elemental solids, a number of emission angles from 35° to 74°, and three energies (200 eV, 500 eV, and 1000 eV). The experimental angular distributions compare very well with the calculated distributions; the mean percentage deviation between them was about 10% at 200 eV, and decreased to about 5% at 1000 eV. Agreement between theory and experiment was not improved when DCSs determined from muffin-tin potentials were used in the calculations. This result justifies the use of DCSs for isolated atoms in theoretical description of elastic-electron backscattering from surfaces.

Monte Carlo strategies for simulations of electron backscattering from surfaces

AbstractReliable algorithms for simulation of electron trajectories in solids are needed for quantification of Auger‐electron spectroscopy, particularly for the determination of the backscattering factor (BF). The computational schemes for this purpose should be universal, i.e. applicable to any solid for energies down to 50 eV. In addition, the algorithms should ideally require simple input parameters, e.g. the stoichiometry of the solid and the experimental configuration. Previous Monte Carlo simulations have often been based on the continuous slowing down approximation (CSDA), a relatively simple and convenient approach. However, this approach requires information on the electron stopping power for a given solid. General expressions for the stopping power are briefly reviewed and discussed. We report results of BF calculations for Cu M3VV, Ag M5VV, and Au N67VV Auger transitions from Monte Carlo simulations based on the CSDA in which stopping powers from optical data and from Tougaard's two‐parameter universal inelastic‐scattering cross section were employed. The resulting BFs, for primary energies between 500 eV and 10 keV, differed by up to 12% (at an energy of 10 keV). BFs from the Monte Carlo algorithm based on the CSDA were compared with similar results from a more sophisticated code involving simulations of individual elastic‐ and inelastic‐scattering events. Both algorithms yielded equivalent BFs for the same Auger transitions with primary energies exceeding 1000 eV; at lower energies, deviations up to 10% occurred because of an approximation in the evaluation of an integral. Copyright © 2005 John Wiley & Sons, Ltd.

Some applications of elastic peak electron spectroscopy for semiconductor surface studies

The usefulness of elastic peak electron spectroscopy (EPES) has been demonstrated by application to a semiconductor study of indium phosphide or InAsP. In this paper, we present some results obtained with EPES. The inelastic mean free paths of indium phosphide have been calculated using EPES and the Monte-Carlo simulation or electron trajectories in solids. The second part of this work deals with the determination of the concentration of elements in heterostructures such as Au/InSb/InP(100) and InAs x P 1-x , and the results are compared to those obtained using AES.

X-Ray Emission of Porous Materials In The Scanning Electron Microscope Computed Using Monte Carlo Simulations

Conventional quantitative X-ray microanalysis in the scanning electron microscope or in the electron microprobe is valid for specimens of bulk homogeneous composition and with flat and polished surfaces. Quantitative methods, using X-ray microanalysis and Monte Carlo simulations of electron trajectories in solids, have been developed for the chemical analysis of spherical inclusions embedded in a matrix and for multilayered specimens. In this paper, the effect of porosity and of the size of the pores are investigated concerning their effect on X-ray emission using Monte Carlo simulation of electron trajectories in solids since porous materials are of great technological importance.This new Monte Carlo program uses elastic Mott cross-sections to compute electron trajectories and the Joy & Luo modification of the continuous Bethe law of energy loss and the details are given elsewhere. This program assumes that all the pores are spherical and have the same size.

The determination of the thickness and composition of multilayered thin films in the SEM by x-ray microanalysis with Monte Carlo simulations

X-Ray microanalysis is now a well established technique to determine the composition and the thickness of multilayer structures of different materials. The most popular software used to quantify such system are based on analytical φ(ρz) curves which are approximation of the x-Ray generation process. The computed φ(ρz) curves of multilayered samples are based on mixtures rules and weight functions which are not always accurate. In this paper, Monte Carlo simulations of electron trajectories in solids are used to compute φ(ρz) curves in multilayered specimens directly and then used to computed the K ratios.To validate this procedure, a TiN(100 nm)/Ti(10 nm) multilayer metallization structure deposited on SiO2(100 nm)/Si substrate was used in conjonction with a TiN(400 nm)/Si standard sample. This system is a very active field of research and development in the microelectronics industry. The thicknesses, composition and microstructure of both systems were fully characterized by Elastic Recoil Detection (ERD), X-ray diffraction (XRD) and Transmission Electron Microscopy (TEM).

MULTIFRACTAL DESCRIPTION OF ELECTRON SCATTERING IN SOLIDS

The fundamental understanding of electron scattering is of critical importance concerning Scanning Electron Microscopy and for electron beam lithography. In these process of great technological importance, it is important to know the volume of diffusion of electrons to define the resolution. Also, it is important to know the rate of energy loss, the number of backscattered and secondary electrons created, their angular distribution, …. All these quantities depend on the shape of the trajectories of the electrons in the solid when they diffuse into it. The use of fractal geometry to describe such trajectories have been previously studied by Gauvin and Drouin1,2 from trajectories computed by Monte Carlo simulations. In these studies, the multifractal behavior of the shape of electron trajectories in solids have also been reported but no explanations have been given to describe the shape of the corresponding f(α) curves. In this paper, we present such explanation for the f(α) curves computed from the electron trajectories simulated in C and in Au with an initial energy of 30 keV (see Gauvin and Drouin2).

Quantitation of SEM EBIC and CL signals using Monte Carlo electron‐trajectory simulations

AbstractA microcomputer Monte Carlo program simulates electron trajectories in solids and describes the distribution of energy deposited throughout the energy‐dissipation (electron‐hole pair generation) volume. From this distribution, the electron‐beam‐induced current or cathodoluminescence signal that will be generated can be calculated for the chosen beam conditions in a multilayer specimen of any geometry and compositions. The use of this program is illustrated by applications (1) to simulate curves of cathodoluminescence intensity versus beam energy for fitting to experimental data to evaluate materials and device parameters, (2) to calculate the energy deposited in each layer of a HEMT structure in which electron‐beam‐induced current studies are in progress, and (3) to the simulation of defect contrast linescan profiles which are compared to experimental observations.

The attenuation and backscattering of electron beams by thin films

A description is given of a Monte Carlo method for the computation of electron trajectories in solids. The calculations are based on the Bethe energy loss law and the Rutherford scattering equation. By assembling a large number of these trajectories, predictions are made on the transmission, backscattering, angular distribution and energy spectrum of electrons passing through thin films. The results are in good agreement with experimental data on the passage of electrons, initially of energy from 5 to 30 keV, through aluminium, aluminium oxide, copper and gold.