Search

This study systematically underlines the significance of comparing theoretical differential inelastic inverse mean free paths (DIIMFPs) for various quantum oscillator models of incident electrons with kinetic energies of up to 1 keV in poly(methyl methacrylate) with an energy transfer range of ħω = 0 to 120 eV. The energy loss function (ELF) was described employing three alternative dielectric function models: the Mermin–Belkacem-Sigmund (MBS) model, the plasmon pole approximation (PPA) model, and the Belkacem-Sigmund (BS) model. The ELFs for momentum transfer ħk up to 10 Å−1 display important features in maximum ELF, line width, plasmon lifetime τp and peak position. Recent MBS-type ELF demonstrates a minor shift toward low energy transfer compared to previous models and tends to more effectively reflect the actual plasmon lifetime behavior found in real materials. Thus, improvements in the ELF profile, namely broadening, peak shift, and damping extending all across Bethe surface, were realized. When the energy is more than 40 eV, our DIIMFP models agree with the Monte Carlo algorithm approach based on the Mermin model. The root-mean-square deviations of theoretical estimations of inelastic mean free paths compared to experimental values for electron kinetic energy of T = 1196 and 1328 eV were 3.1 Å for MBS, 3.9 Å for PPA, 4.1 Å for Mermin, 9 Å for Tanuma–Powell–Penn (TPP), and 11.4 Å for BS. The MBS dielectric function exhibits a reliable relaxation time and describes the realistic behaviour of materials over the Bethe surface to give a deeper understanding and a better correlation between experimental and theoretical data for insulator applications. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Elastic peak electron spectroscopy (EPES) was employed to measure the inelastic mean free path (IMFP) for energies between 500 and 1600 eV for five insulating organic compounds: Kapton, polyethylene (PE), poly(methyl methacrylate) (PMMA), polystyrene (PS) and polytetrafluoroethylene (PTFE). A Ni and a Si sample were used as reference materials to avoid measurement of the elastic reflection coefficient in absolute units. Correction of experimental elastic peak intensities for surface excitations was performed which turned out to be essential. The results are compared with recent evaluations of optical constants to yield the IMFP in the literature giving satisfactory agreement, with deviations generally below 20%. Investigation of the kinematics in an electron reflection experiment shows that the dispersion coefficient used in REELS data analysis cannot be identified with the true plasmon dispersion. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In recent years, highly accurate measurements of photoelectron holograms have become possible through the development of electron energy analyzers with an energy range of 300–1000 eV. Effects of the inelastic mean free path (IMFP) and thermal vibration became apparent in the hologram pattern. For example, the quasi‐Kikuchi band is clearly observed, which cannot be explained by conventional multiple scattering theories. Herein, the theory of photoelectron holograms is summarized, considering the inelastic scattering (IES) and thermal vibration effects. Furthermore, the simulated hologram is compared with a diamond hologram measured at a kinetic energy of 563.4 eV. It is also shown that the formation mechanism of the quasi‐Kikuchi band differs from that of the normal Kikuchi band. [ABSTRACT FROM AUTHOR]

The TPP-2M formula is the most popular empirical formula for the estimation of the electron inelastic mean free paths (IMFPs) in solids from several simple material parameters. The TPP-2M formula, however, poorly describes several materials because it relies heavily on the traditional least-squares analysis. Herein, we propose a new framework based on machine learning to overcome the weakness. This framework allows a selection from an enormous number of combined terms (descriptors) to build a new formula that describes the electron IMFPs. The resulting framework not only provides higher average accuracy and stability but also reveals the physics meanings of several newly found descriptors. Using the identified principle descriptors, a complete physics picture of electron IMFPs is obtained, including both single and collective electron behaviors of inelastic scattering. Our findings suggest that machine learning is robust and efficient to predict the IMFP and has great potential in building a regression framework for data-driven problems. Furthermore, this method could be applicable to find empirical formula for given experimental data using a series of parameters given a priori, holds potential to find a deeper connection between experimental data and a priori parameters. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

A Fourier transform (FT) algorithm is proposed to retrieve the energy loss function (ELF) of solid surfaces from experimental X-ray photoelectron spectra. The intensity measured over a broad energy range towards lower kinetic energies results from convolution of four spectral distributions: photoemission line shape, multiple plasmon loss probability, X-ray source line structure and Gaussian broadening of the photoelectron analyzer. The FT of the measured XPS spectrum, including the zero-loss peak and all inelastic scattering mechanisms, being a mathematical function of the respective FT of X-ray source, photoemission line shape, multiple plasmon loss function, and Gaussian broadening of the photoelectron analyzer, the proposed algorithm gives straightforward access to the bulk ELF and effective dielectric function of the solid, assuming identical ELF for intrinsic and extrinsic plasmon excitations. This method is applied to aluminum single crystal Al(002) where the photoemission line shape has been computed accurately beyond the Doniach-Sunjic approximation using the Mahan-Wertheim-Citrin approach which takes into account the density of states near the Fermi level; the only adjustable parameters are the singularity index and the broadening energy Г (inverse hole lifetime). After correction for surface plasmon excitations, the q-averaged bulk loss function, ε(E, q)]>q, of Al(002) differs from the optical value Im[− 1 / ε(E, q = 0)] and is well described by the Lindhard-Mermin dispersion relation. A quality criterion of the inversion algorithm is given by the capability of observing weak interband transitions close to the zero-loss peak, namely at 0.65 and 1.65 eV in ε(E, q) as found in optical spectra and ab initio calculations of aluminum. [ABSTRACT FROM AUTHOR]

Electron energy loss and photoelectron spectra are obtained on the basis of transfer equation solution. The boundary problem is solved using invariant imbedding approach. The partial intensity method is used to calculate electron energy loss and photoelectron spectra. Differential inelastic electron scattering cross sections in bulk aluminium and in a surface layer are extracted by fitting procedure in an energy range 0.5-120 keV. The method of spectra computation is tested by comparison of results with the experimental data of five foreign scientific laboratories. The physical meaning of the surface-excitation parameter is discussed. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The presented Monte Carlo model simulates excitation of the electron subsystem of semiconductors by a penetrating swift heavy ion (SHI). The cross sections of interaction of an ion with the electron subsystem of a target are calculated via the complex dielectric function formalism, which accounts for all the collective modes of the electron ensemble of the target. The predicted electron inelastic mean free paths are in a very good agreement with those from the NIST database. The calculated SHI energy losses coincide well with SRIM and CasP codes. The model is used to calculate the spectra of electrons emitted from germanium and silicon targets during SHI irradiation. These spectra agree well with the experimental data. [ABSTRACT FROM AUTHOR]

An analysis is presented for a simple, universal equation for the computation of attenuation lengths ( L) for any material, necessary for quantifying layer thicknesses in Auger electron spectroscopy (AES) and X-ray photoelectron spectroscopy (XPS). Attenuation lengths for selected materials may be computed from the inelastic mean free path ( λOpt) computed, in turn, from optical data. The computation of L involves the transport mean free path and gives good L values where values of λOpt are available. However, λOpt values are not available for all materials. Instead, λ may be calculated from the TPP-2M relation, but this requires the accurate estimation of a number of materials parameters that vary over a wide range. Although these procedures are all soundly based, they are impractical in many analytical situations. L is therefore simply reexpressed, here, in terms of the average Z of the layer which may be deduced from the AES or XPS analysis, the average atomic size a (varies in a small range) and the kinetic energy E of the emitted electron. For strongly bonded materials, such as oxides and alkali halides, a small extra term is included for the heat of formation. A new equation, S3, is established with a root mean square (RMS) deviation of 8% compared with the values of attenuation length calculated from λOpt available for elements, inorganic compounds, and organic compounds. This excellent result is suitable for practical analysis. In many films, an average value of a of 0.25 nm is appropriate, and then L may be expressed only in terms of the average Z and E. Then, L expressed in monolayers, equation S4, exhibits an RMS deviation of 9% for many elements. These results are valid for the energy range 100 to 30 000 eV and for angles of emission up to 65°. Copyright © 2012 Crown copyright. [ABSTRACT FROM AUTHOR]

Transmission electron microscopy specimens in the form of elongated, conical needles were made using a dual-beam focused ion beam system, allowing the specimen thickness to be geometrically determined for a range of thickness values. From the same samples electron energy loss maps were acquired and the plasmon mean free path (λ) for inelastic scattering was determined experimentally from the measured values of specimen thickness. To test the method λ was determined for Ni (174 ± 17 nm), α-Al2O3 (143 ± 14 nm), Si (199 ± 20 nm) and amorphous SiO2 (238 ± 12 nm), and compared both to experimental values of λ taken from the literature and to calculated values. The calculated values of λ significantly underestimate the true sample thickness for high accelerating voltages (300 kV) and large collection angles. A linear dependence of λ on thickness was confirmed for t/λ < 0.5–0.6, but this method also provides an approach for calibrating λ at sample thicknesses for which multiple scattering occurs, thus expanding the thickness range over which electron energy loss spectroscopy can be used to determine the absolute sample thickness ( t/λ > 0.6). The experimental method proposed in this contribution offers a means to calibrate λ for any type of material or phase that can be milled using a focused ion beam system. [ABSTRACT FROM AUTHOR]

Inelastic mean free paths (IMFPs) of electrons with energies between 100 eV and 5,000 eV have been frequently obtained from measurements of elastic-backscattering probabilities for different specimen materials. A calculation of these probabilities is also required to determine IMFPs. We report calculations of elastic-backscattering probabilities for gold at energies of 100 eV and 500 eV with differential elastic-scattering cross sections obtained from the Thomas-Fermi-Dirac potential and the more reliable Dirac-Hartree-Fock potential. For two representative experimental configurations, the average deviation between IMFPs obtained with cross sections from the two potentials was 11.4%. [ABSTRACT FROM AUTHOR]

The detailed examination of electron scattering in solids is of crucial importance for the theory of solid-state physics, as well as for the development and diagnostics of novel materials, particularly those for micro- and nanoelectronics. Among others, an important parameter of electron scattering is the inelastic mean free path (IMFP) of electrons both in bulk materials and in thin films, including 2D crystals. The amount of IMFP data available is still not sufficient, especially for very slow electrons and for 2D crystals. This situation motivated the present study, which summarizes pilot experiments for graphene on a new device intended to acquire electron energy-loss spectra (EELS) for low landing energies. Thanks to its unique properties, such as electrical conductivity and transparency, graphene is an ideal candidate for study at very low energies in the transmission mode of an electron microscope. The EELS are acquired by means of the very low-energy electron microspectroscopy of 2D crystals, using a dedicated ultra-high vacuum scanning low-energy electron microscope equipped with a time-of-flight (ToF) velocity analyzer. In order to verify our pilot results, we also simulate the EELS by means of density functional theory (DFT) and the many-body perturbation theory. Additional DFT calculations, providing both the total density of states and the band structure, illustrate the graphene loss features. We utilize the experimental EELS data to derive IMFP values using the so-called log-ratio method. [ABSTRACT FROM AUTHOR]

The inelastic mean free path of 120 keV electrons in vitrified ice layers has been determined in an energy-filtering TEM. From the ratio of the unfiltered and zero-loss-filtered image intensities recorded with a slow-scan CCD camera, the relative sample thickness t/ Λ can be calculated. For calibration, the geometric ice thickness was measured by imaging a tilted view of a cylindrical hole which had been burnt into the ice layer. The total inelastic mean free path was found to be 161 nm, and the partial inelastic mean free path for an acceptance angle of 4.2 mrad was 232 nm. These results were built into a standard protocol for use in cryo-electron microscopy allowing on-line measurements of local ice-layer thicknesses by zero-loss-filtered/unfiltered imaging. [ABSTRACT FROM AUTHOR]