Monte Carlo simulation study of reflection electron energy loss spectroscopy of an Fe/Si overlayer sample

Reflection electron energy loss spectroscopy (REELS) has been used to study the optical and electronic properties of semi-infinite solid samples, aided by a theoretical model of the interaction between electrons and a solid. However, REELS has not been used to its full capacity in studying nanomaterial samples because of the difficulty in modeling the electron interaction with a layered nanostructure. In this study, we present a numerical calculation result on the spatially varying inelastic mean free path for a sample comprising an Fe layer of varying thickness on an Si substrate. Furthermore, a Monte Carlo model for electron interaction with this Fe-Si layered structure sample is built based on this inelastic scattering cross section and used to reproduce the REELS spectra of Fe-Si layered structures. The simulated spectra of the sample with varying Fe layer thickness on top of a Si substrate were compared with the experimental spectra. This comparison clearly identifies that the Fe layer remaining on top of the experimental Si substrate after Ar⁺ beam sputtering is in the form of a homogeneous mixed layer, where the Fe/Si interface excitation is absent in the experimental spectra owing to pulverization of the Fe/Si interface during the Ar⁺ sputtering process.     

Inelastic scattering and energy loss of swift electron beams in biologically relevant materials

The inelastic mean free path and the stopping power of swift electrons in relevant biomaterials, such as liquid water, DNA, protein, lipid, carotene, sugar, and ice are calculated in the framework of the dielectric formalism. The Mermin Energy Loss Function – Generalized Oscillator Strength model is used to determine the energy loss function of these materials for arbitrary energy and momentum transfer using electron energy‐loss spectroscopy data as input. To ensure the consistency of the model, efforts are made so that both the Kramers–Kronig and f‐sum rules are fulfilled to better than 2%. Our findings indicate sizeable differences in the inelastic mean free path and stopping power among these biomaterials for low‐energy electrons. For example, at 100‐eV electron energy, the inelastic mean free path in protein is 25% smaller than for water and around 10% smaller than for the other biomaterials. The stopping power values of protein, DNA, and sugar are rather similar but 20% larger than for water. Taking into account these results, we conclude that electron interactions with living tissues at the nanometric scale cannot be reliably described using only liquid water as the surrogate of the biological target. Copyright © 2016 John Wiley & Sons, Ltd.     

Local inverse inelastic mean free path at interface

We calculated a local inverse inelastic mean free path (local-IIMFP) for electrons crossing a medium–medium interface, considering various incident electron energies, crossing angles and combinations of materials. We used an extension of a classical dielectric model developed by Li and co-workers for an electron crossing a surface (interface vacuum-medium). Moreover, the integration over the distance of the local-IIMFP allows to obtain the interface excitation parameter (or IEP) characterizing the change in excitation probability for an electron crossing an interface once caused by the presence of the interface in comparison with an electron for which only volume excitations are considered. We perform these calculations for angles between 0° and 80°, for electron energies between 500 and 2500 eV and for various pairs of materials, as Al/In for its academic interest or Au/Si and SiO₂/Si for their technological importance. Small but not negligible variations of the local-IIMFP and the IEP were observed for metal–metal or metal–semiconductor interfaces, while quite significant variations are obtained when one of the materials is a insulator.     

Theoretical study toward rationalizing inelastic background analysis of buried layers in XPS and HAXPES

The approach of inelastic background analysis was previously demonstrated to be a useful tool for retrieving the depth distribution of buried layers with an accuracy, which is better than 5% even for some complex samples. This paper presents a study that attempt at rationalizing the approach by exploring how to make the best choice of the inelastic mean free path and the inelastic scattering cross section, which are the two main input parameters needed in the analysis. To this end, spectra from buried layers were created with Quases-Generate software. The layers consisted of Si 1s recorded at 6099 eV and Au 4d recorded at 1150 eV kinetic energy buried under overlayers of Si, Au, Al, polymer, or Ta. Spectra from samples with a wide range of buried layer thickness and overlayer thickness were created. Subsequently, these spectra were analyzed with Quases-Analyze software and for each case the analysis was done with different combinations of the input parameters. Among these, the best choice for all cases was to use an effective IMFP and effective inelastic scattering cross section with relative weights being half the thickness of the buried layer and the full thickness of the overlayer. This general formula together with a new version of the software makes the inelastic background analysis of buried layers faster and easier to apply even for nonspecialists.     

Monte Carlo Simulation of Electron Transport and X-Ray Generation. I. Electron Elastic and Inelastic Scattering

We present different theoretical approaches to determine differential cross sections for elastic and inelastic interactions of electrons. These cross sections are the basic ingredients for accurate Monte Carlo simulation of electron transport in matter. The considered models range from simple analytical approximations employed in early calculations to purely numerical differential cross sections described by large databases calculated with state-of-the-art theory.     

Improved depth information from routine analysis of the inelastic background of XPS and HAXPES spectra using optimized two- and three-parameter cross-sections

Determination of the depth distribution of complex nanostructures by X-ray photoelectron spectroscopy (XPS) inelastic background analysis may be complicated if the sample materials have widely different inelastic scattering cross-sections. It was recently demonstrated that this may be solved by using a mixture of cross-sections. This permits retrieval of depth distributions of complex stacks and deeply buried layers with a typical 5% accuracy. This requires however that the cross-sections of the individual sample materials are known which is often not the case and this can complicate practical use for routine analysis. In this paper, we explore to what extent a suitable two- or three-parameter cross-section can be defined independent of prior knowledge of the cross-sections involved but simply defined by fitting the cross-section parameters to the spectrum being analyzed. This paper presents a theoretical study following our recent paper that explored how to make the best choice of inelastic mean free path and inelastic scattering cross-section for the inelastic background analysis with the Quases-Tougaard software. It was previously shown that a rough analysis of the inelastic background could give a good idea of the depth distribution. Here, we demonstrate with model spectra from buried layers created with Quases-Tougaard Generate software that a rather accurate analysis can be performed for very different cases with an average ~5% error. This analysis is easy to apply as it only needs the two- or three-parameter cross-sections generated with the Quases-Tougaard software. This study is aimed to improve routine analysis of the inelastic background of XPS and hard X-ray photoelectron spectroscopy (HAXPES) spectra.     

Semi‐empirical inelastic mean free paths for positrons

Previously, we developed a semi‐empirical method for determining the inelastic mean free paths of positrons in a wide variety of materials. This work is heavily based on the earlier work of Tanuma, Powell and Penn on the inelastic mean free paths of electrons in the 50–2000 eV energy range. One of the remaining questions still to be answered was the validity of ignoring terms of the order of the inverse energy squared in the denominator of our final expression. In this paper, we investigate this question in some detail by comparing our approximations with calculated values of the positron inelastic mean free paths based on experimental optical data. We conclude that the exclusion of the higher order terms is consistent with the other approximations in this methodology. Copyright © 2005 John Wiley & Sons, Ltd.     

Improved Tougaard background calculation by introduction of fittable parameters for the inelastic electron scattering cross‐section in the peak fit of photoelectron spectra with UNIFIT 2011

The shape of the background in x‐ray photoemission spectra is strongly affected by scattered electrons from inelastic energy loss processes. A polynomial of low order has very often been applied to model the secondary‐electron background, giving satisfying results in some cases. An improved analysis employing the Tougaard background model has been successfully used to characterize the inelastic loss processes. However, the correct usage of the Tougaard background needs a well defined inelastic electron scattering cross‐section function λ(E) · K(E, T) (λ = inelastic mean free path, E = kinetic energy, T = energy loss). This paper presents a four‐parameter loss function λ(E) · K(E, T) = B · T/(C + C′ · T²)² + D · T² with the fitting parameters B, C, C′ and D implemented in the background function allowing the improved estimation of the λ(E) · K(E, T) function for homogenous materials. The fit of the background parameters is carried out parallel to the peak fit. The results will be compared with the parameters recommended by Tougaard. The calculation of inelastic electron scattering cross‐sections of clean surfaces from different materials using UNIFIT 2011 will be demonstrated. Copyright © 2011 John Wiley & Sons, Ltd.     

Report on the 42nd IUVSTA workshop ‘Electron scattering in solids: from fundamental concepts to practical applications’

A summary is given of the workshop entitled ‘Electron Scattering in Solids: from fundamental concepts to practical applications,’ which was held in Debrecen, Hungary, on July 4–8, 2004, under the sponsorship of the International Union of Vacuum Science, Technique, and Applications (IUVSTA). This workshop was held to review the present status and level of understanding of electron‐scattering processes in solids, to identify issues of key importance (hot topics) in the light of the most recent scientific results, and to stimulate discussions leading to a deeper understanding and new solutions of current problems. This report contains summaries of presentations and discussions in sessions on elastic scattering of electrons by atoms and solids, inelastic scattering of electrons in solids, modeling of electron transport in solids and applications, and software. The principal areas of application include Auger‐electron spectroscopy (AES), X‐ray photoelectron spectroscopy, elastic‐peak electron spectroscopy (EPES), reflection electron energy‐loss spectroscopy (REELS), secondary‐electron microscopy, electron‐probe microanalysis (EPMA), and the use of coincidence techniques in electron‐scattering experiments. A major focus of the workshop was determination of the inelastic mean free path of electrons for various surface spectroscopies, particularly corrections for surface and core‐hole effects. Published in 2005 by John Wiley & Sons, Ltd.     

Morphology,surface roughness,electron inelastic and quasielastic scattering in elastic peak electron spectroscopy of polymers

In elastic peak electron spectroscopy (EPES), the nearest vicinity of elastic peak in the low kinetic energy region reflects electron inelastic and quasielastic processes. Incident electrons produce surface excitations, inducing surface plasmons, with the corresponding loss peaks separated by 1–20 eV energy from the elastic peak. In this work, X‐ray photoelectron spectroscopy (XPS) and helium pycnometry are applied for determining surface atomic composition and bulk density, whereas atomic force microscopy (AFM) is applied for determining surface morphology and roughness. The component due to electron recoil on hydrogen atoms can be observed in EPES spectra for selected primary electron energies. Simulations of EPES predict a larger contribution of the hydrogen component than observed experimentally, where hydrogen deficiency is observed. Elastic peak intensity is influenced more strongly by surface morphology (roughness and porosity) than by surface excitations and quasielastic scattering of electrons by hydrogen atoms. Copyright © 2007 John Wiley & Sons, Ltd.     

Memory effect on the inelastic interaction of electrons moving parallel to a solid surface

It is generally assumed that two successive inelastic interactions between an electron and a solid are independent of each other. In other words, the electron has no memory of its previous interaction. However, the previous interaction of the electron generates a potential that should influence its succeeding inelastic interaction. The aim of this work is to establish a model to account for the memory effect of an electron between two successive inelastic interactions. On the basis of the dielectric response theory, formulae for differential inverse inelastic mean free paths (DIIMFPs) and inelastic mean free paths (IMFPs) considering the memory effect were derived for electrons moving parallel to a solid surface by solving the Poisson equation and applying suitable boundary conditions. These mean free paths were then calculated with the extended Drude dielectric function for a Cu surface. It was found that the DIIMFP and the IMFP with the memory effect for electron energy E lay between the corresponding values without the memory effect for electron energy E and previous energy E₀. The memory effect increased with increasing electron energy loss, E₀ ? E, in the previous inelastic interaction. Copyright © 2005 John Wiley & Sons, Ltd.     

Surface excitations in electron spectroscopy. Part I: dielectric formalism and Monte Carlo algorithm

The theory describing energy losses of charged non‐relativistic projectiles crossing a planar interface is derived on the basis of the Maxwell equations, outlining the physical assumptions of the model in great detail. The employed approach is very general in that various common models for surface excitations (such as the specular reflection model) can be obtained by an appropriate choice of parameter values. The dynamics of charged projectiles near surfaces is examined by calculations of the induced surface charge and the depth‐ and direction‐dependent differential inelastic inverse mean free path (DIIMFP) and stopping power. The effect of several simplifications frequently encountered in the literature is investigated: differences of up to 100% are found in heights, widths, and positions of peaks in the DIIMFP. The presented model is implemented in a Monte Carlo algorithm for the simulation of the electron transport relevant for surface electron spectroscopy. Simulated reflection electron energy loss spectra are in good agreement with experiment on an absolute scale. Copyright © 2012 John Wiley & Sons, Ltd.     

Inelastic mean free path of low‐energy electrons in condensed media: beyond the standard models

The most established approach for ‘practical’ calculations of the inelastic mean free path (IMFP) of low‐energy electrons (~10 eV to ~10 keV) is based on optical‐data models of the dielectric function. Despite nearly four decades of efforts, the IMFP of low‐energy electrons is often not known with the desired accuracy. A universal conclusion is that the predictions of the most popular models are in rather fair agreement above a few hundred electron volts but exhibit considerable differences at lower energies. However, this is the energy range where their two main approximations, namely, the random‐phase approximation (RPA) and the Born approximation, may be invalid. After a short overview of the most popular optical‐data models, we present an approach to include exchange and correlation (XC) effects in IMFP calculations, thus going beyond the RPA and Born approximation. The key element is the so‐called many‐body local‐field correction (LFC). XC effects among the screening electrons are included using a time‐dependent local‐density approximation for the LFC. Additional XC effects related to the incident and struck electrons are included through the vertex correction calculated using a screened‐Hubbard formula for the LFC. The results presented for liquid water reveal that XC may increase the IMFP by 15–45% from its Born–RPA value, yielding much better agreement with available experimental data. The present work provides a manageable, yet rigorous, approach to improve upon the standard models for IMFP calculations, through the inclusion of XC effects at both the level of screening and the level of interaction. Copyright © 2015 John Wiley & Sons, Ltd.     

Inelastic electron tunneling spectroscopy by STM of phonons at solid surfaces and interfaces

Inelastic electron tunneling spectroscopy (IETS) combined with scanning tunneling microscopy (STM) allows the acquisition of vibrational signals at surfaces. In STM-IETS, a tunneling electron may excite a vibration, and opens an inelastic channel in parallel with the elastic one, giving rise to a change in conductivity of the STM junction. Until recently, the application of STM-IETS was limited to the localized vibrations of single atoms and molecules adsorbed on surfaces. The theory of the STM-IETS spectrum in such cases has been established. For the collective lattice dynamics, i.e., phonons, however, features of STM-IETS spectrum have not been understood well, though in principle STM-IETS should also be capable of detecting phonons. In this review, we present STM-IETS investigations for surface and interface phonons and provide a theoretical analysis. We take surface phonons on Cu(1?1?0) and interfacial phonons relevant to graphene on SiC substrate as illustrative examples. In the former, we provide a theoretical formalism about the inelastic phonon excitations by tunneling electrons based on the nonequilibrium Green’s function (NEGF) technique applied to a model Hamiltonian constructed in momentum space for both electrons and phonons. In the latter case, we discuss the experimentally observed spatial dependence of the STM-IETS spectrum and link it to local excitations of interfacial phonons based on ab-initio STM-IETS simulation.     

Calculations of electron inelastic mean free paths

We report calculations of electron inelastic mean free paths (IMFPs) for 50–2000 eV electrons in 14 elemental solids (Li, Be, diamond, graphite, Na, K, Sc, Ge, In, Sn, Cs, Gd, Tb, and Dy) and for one solid (Al) using better optical data than in our previous work. The new IMFPs have also been used to test our TPP‐2M equation for estimating IMFPs in these materials. We found surprisingly large root‐mean‐square (RMS) deviations (39.3–71.8%) between IMFPs calculated from TPP‐2M and those calculated here from optical data for diamond, graphite and cesium; previously we had found an average RMS deviation of 10.2% for a group of 27 elemental solids. An analysis showed that the large deviations occurred for relatively small computed values of the parameter β in the TPP‐2M equation (β ～ 0.01 for diamond and graphite) and also for relatively large values of β (β ～ 0.25 for Cs). Although such extreme values of β are unlikely to be encountered for many other materials, the present results indicate an additional limitation in the reliability of the TPP‐2M equation. We also show that the parameter N_v in the TPP‐2M equation should be computed for the rare‐earth elements from the number of valence electrons and the six 5p electrons. Copyright © 2004 John Wiley & Sons, Ltd.     

无脂链磺化酞菁铜多层膜体系：电子非弹性平均自由程的研究

磺化酞菁铜多层膜体系是利用Langmuir-Blodgett技术制备的有序有机分子膜,它对于XPS测试有很好的稳定性,本文在固定电子出射角的条件下利用XPS方法研究了不同厚度的膜样品中Cu_((2(?))_(3/2))、Ni_(1(?))、S_(2p)峰强度的变化规律,讨论了膜内分子有序排列引起的散射效应对电子平均自由程的影响。     

Obtaining quantitative information on surface excitations from reflection electron energy‐loss spectroscopy (REELS)

A new analysis of reflection electron energy‐loss spectroscopy (REELS) spectra is presented. Assuming inelastic scattering in the bulk to be quantitatively understood, this method provides the distribution of energy losses in a single surface excitation in absolute units without the use of any fitting parameters. For this purpose, REELS spectra are decomposed into contributions corresponding to surface and volume excitations in two steps: first the contribution of multiple volume excitations is eliminated from the spectra and subsequently the distribution of energy losses in a single surface scattering event is retrieved. This decomposition is possible if surface and bulk excitations are uncorrelated, a condition that is fulfilled for medium‐energy electrons because the thickness of the surface scattering layer is small compared with the electron elastic mean free path. The developed method is successfully applied to REELS spectra of several materials. The resulting distributions of energy losses in an individual surface excitation are in good agreement with theory. In particular, the so‐called begrenzungs effect, i.e. the reduction of the intensity of bulk losses due to coupling with surface excitations near the boundary of a solid‐state plasma, becomes clearly observable in this way. Copyright © 2003 John Wiley & Sons, Ltd.     

Insight to Dynamics of Molecules with Nuclear Inelastic Scattering

We discuss an application of nuclear inelastic scattering to molecular dynamics. The basis of the technique, the experimental setup, and the introduction to data treatment are illustrated with examples of hexacyanoferrate (II) and ferrocene. The application of nuclear inelastic scattering to more complicated systems is demonstrated by the spin–crossover Fe(II) complex [Fe(bpp)₂][BF₄]₂.