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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]

To gain a mechanistic understanding of the phase stability of M 23 C 6 upon irradiation, the bulk W-doped M 23 C 6 (Cr-W-C system) in the range of 0–12 at.% W concentration was prepared and subjected to helium beam irradiation, following with a thorough electron energy loss spectroscopy (EELS) analysis. Radiation-induced amorphization (RIA) was observed only at the 4 W sample with a W concentration of ∼12 at.%. Analysis of the low-loss spectrum showed that the inelastic mean free path (λ) could be applied an effective indicator of the presence of an amorphous phase. The white line ratio of the carbon K -edge spectrum showed that the chemical bonding state in the crystalline state is mainly 2 p3/2 bonding, and it changes to dominantly 2 p1/2 bonding accompanying with the crystal-to-amorphous (c-a) transition. Discussion on the relationship between the change in λ (Δλ) and the lattice parameter (Δa) due to irradiation reveals that Δa is not dependent on Δλ , indicating that Δλ is mainly caused by the volume expansion due to the c-a transition. In addition, a crystalline state is remained even after a lattice parameter change of ∼1.5 % in 0 W and 1W-samples, whereas, a lattice expansion of ∼0.2 % would trigger the occurrence of crystal-to-amorphous transition in the 4W-sample. The detailed EELS analysis demonstrated that the constitutional W atoms play an important role in facilitating the occurrence of RIA in M 23 C 6 , that is, the phase instability accompanying the lattice expansion due to irradiation was emphasized by the addition of W in M 23 C 6. The insights obtained here suggest that a higher W concentration in M 23 C 6 is more susceptible to RIA, and therefore the resistance to amorphization is achievable by decreasing the W concentration in the steels. [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]

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.

Electron driven chemistry of biomolecules in aqueous phase presents the realistic picture to study molecular processes. In this study we have investigated the interactions of electrons with the DNA constituents in their aqueous phase in order to obtain the quantities useful for DNA damage assessment. We have computed the inelastic mean free path (IMFP), mass stopping power (MSP) and absorbed dose (D) for the DNA constituents (Adenine, Cytosine, Guanine, Thymine and Uracil) in the aqueous medium from ionisation threshold to 5000 eV. We have modified complex optical potential formalism to include band gap of the systems to calculate inelastic cross sections which are used to estimate these entities. This is the maiden attempt to report these important quantities for the aqueous DNA constituents. We have compared our results with available data in gas and other phase and have observed explicable accord for IMFP and MSP. Since these are the first results of absorbed dose (D) for these compounds, we have explored present results vis-a-vis dose absorption in water., (© 2024 Wiley‐VCH GmbH.)

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 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.

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]

Highlights • Mean-inner-potential of single crystal α-Al 2 O 3 sapphire measured at 16.90 ± 0.36 V using off-axis electron holography. • Measurement method, based on mechanically polished wedge sample, is discussed. • Density-Functional-Theory calculations of the mean-inner-potential based on VASP. • The plasmon mean free path for inelastic scattering of sapphire is measured. Abstract The mean inner potential (MIP) of a single crystal α-Al 2 O 3 sapphire was measured using off-axis electron holography. To measure the MIP, we use mechanically polished wedge specimens for transmission electron microscopy (TEM). This approach also enabled us to measure the plasmon mean free path for inelastic scattering (IMFP). The wedge specimen, chosen here at an angle of approximately 45°, allows to determine the MIP by measuring the gradient of phase variations of the reconstructed electron wave over extended regions across the sample. The angle of the wedge was measured to an accuracy of better than 1° by two methods: first, perpendicular sectioning in a focused ion beam for direct measurement by TEM and second, by a non-destructive approach of confocal optical microscopy. The validity of this methodology was examined on a single crystal Si(001) sample showing that the mechanically polished wedge approach can be applied to a wide range of materials. Our measurements concluded that the MIP of sapphire is V 0 = 16.90 ± 0.36 V. Furthermore, the IMFP of sapphire was measured at 136 ± 2 nm for 197 keV electrons with a collection angle of 18mrad. The measured MIP of sapphire reflects its degree of ionicity, which lies between theoretical calculations based on electron scattering factors of charged and neutral isolated atoms obtained by Dirac–Fock calculations. Our MIP measurements tend to the expected value for this predominantly ionic material. To account for chemical bonding and the role of the crystallographic plane at the surface of the sample, we compared the experimental measurements to density-functional-theory calculations of the MIP. Calculations of α-Al 2 O 3 slabs cut along (0001) and (1–100) planes obtained MIP values of 15.7 V and 16.7 V, respectively. [ABSTRACT FROM AUTHOR]

Low-energy electrons (20 – 300 eV) hold the promise for low-dose, non-destructive, high-resolution imaging, but at the price of challenging data analysis. This study provides theoretical considerations and models for the quantitative analysis of experimental data observed in low-energy electron transmission microscopy and in-line holography. The scattering of low-energy electrons and the imaging parameters, such as the inelastic mean free path, point spread function, depth of focus, and resolution, are quantitatively described. It is shown that unlike high-energy electrons (20 – 300 keV), low-energy electrons (20 – 300 eV) introduce a large phase shift into the probing electron waves. Using the projected potentials formalism, the maximal phase shift acquired by a 120 eV electron wave scattered by a carbon atom is theoretically estimated to be 5. 03 radian and experimentally measured to be between 3 and 7. 5 radian. The point spread function evaluated for low-energy electrons shows that they diffract much stronger than high-energy electrons, and that only very thin objects of up to 3 Å in thickness can be imaged in focus. Thus, when imaging an object of finite thickness, such as a macromolecule, the obtained image will always be blurred due to the out-of-focus signal. This can provide an explanation for a long-standing problem of limited resolution in low-energy electron holography of macromolecules. As for imaging of a macromolecule's structure, it is shown that the amplitude of the wavefront reconstructed from the sample's hologram provides the best match to the projected potential distribution of the macromolecule. To evaluate the absorption properties, the inelastic mean free path (IMFP) is considered. The IMFP values calculated from theoretical models agree with the measured values. The IMFP of about 5 Å was measured by transmission through graphene of 50 – 200 eV electrons. This result implies that the internal structure of only very thin samples can be imaged in transmission mode. A simple method to quantitatively evaluate the absorption of a specimen from its in-line hologram without the need to reconstruct the hologram is presented. • Extracting parameters of scattering amplitudes from experimental in-line holograms • Evaluation of object's absorption directly from its in-line hologram • Intrinsic resolution limit of low-energy electrons due to their point-spread function • Inelastic mean free path (IMFP), theoretical and measured in graphene values • Multislice simulation via projected potentials of 3D macromolecules. [ABSTRACT FROM AUTHOR]

We present the combined experimental and theoretical investigations of optical properties and excitation energies of metallic iridium. The reflected energy loss spectroscopy (REELS) spectra of polycrystalline Ir were measured with a cylindrical mirror analyzer in UHV conditions at primary energies of 500, 1000 and 2000 eV. The energy loss function (ELF) and thereby the refractive index n and the extinction coefficient k were calculated from these REELS spectra in the loss energy range of 2–200 eV by applying our reverse Monte Carlo method. The high accuracy of the obtained results is justified with the ps- and f -sum rules. Using the derived ELF the inelastic mean free paths of Ir were calculated from 1 eV up to 10 keV. Moreover, we identified for the first time in the optical data the 5p 3/2 , 4f 5/2 and 4f 7/2 shell excitations of the solid Ir sample. [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]

It is investigated how the model used to describe a dielectric function (i.e. a Mermin, Drude, Drude–Lindhard, Levine–Louie with relaxation time dielectric function) affects the interpretation of a REELS experiment, the calculation of the electron inelastic mean free path as well proton stopping and straggling. Three dielectric functions are constructed that are based on different models describing a metal, but have identical loss functions in the optical limit. A loss function with the same shape, but half the amplitude, is used to derive four different model dielectric functions for an insulator. From these dielectric functions we calculate the differential inverse mean free path, the mean free path itself, as well as the stopping force and straggling for protons. The similarity of the underlying physics between proton stopping, straggling and the electron inelastic mean free path is stressed by describing all three in terms of the differential inverse inelastic mean free path. To further highlight the reason why observed quantities depend on the model dielectric function used we study partial differential inverse inelastic mean free paths, i.e. those obtained by integrating over only a limited range of momentum transfers. In this way it becomes quite transparent why the observable quantities depend on the choice of model dielectric function. [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 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 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]

Photoelectron Energy Loss Spectroscopy (PEELS) is a highly valuable non destructive tool in applied surface science because it gives access to both chemical composition and electronic properties of surfaces, including the near-surface dielectric function. An algorithm is proposed for real materials to make full use of experimental X-ray photoelectron spectra (XPS). To illustrate the capabilities and limitations of this algorithm, the near-surface dielectric function ε ( ℏ ω) of a wide range of amorphous carbon (a-C) thin films is derived from energy losses measured in XPS, using a dielectric response theory which relates ε ( ℏ ω) and the bulk plasmon (BP) loss distribution. Self-consistent separation of bulk vs surface plasmon excitations, deconvolution of multiple BP losses and evaluation of Bethe-Born sensitivity factors for bulk and surface loss distributions are crucial to obtain several material parameters: (1) energy loss function for BP excitation, (2) dielectric function of the near-surface material (3–5 nm depth sensitivity), (3) inelastic mean free path, λ P ( E 0 ), for plasmon excitation, (4) surface excitation parameter, (5) effective number N EFF of valence electrons participating in the plasma oscillation. This photoelectron energy loss spectra analysis has been applied to a-C and a-C:H films grown by physical and chemical methods with a wide range of (sp 3 /sp 2 + sp 3 ) hybridization, optical gap and average plasmon energy values. Different methods are assessed to accurately remove the photoemission peak tail at low loss energy (0–10 eV) due to many-body interactions during the photo-ionization process. The σ + π plasmon excitation represents the main energy-loss channel in a-C; as the C atom density decreases, λ P (970 eV) increases from 1.22 nm to 1.6 nm, assuming a cutoff plasmon wavenumber given by a free electron model. The π-π* and σ-σ* transitions observed in the retrieved dielectric function are discussed as a function of the average (sp 3 /sp 2 + sp 3 ) C hybridization and compared with literature results. [ABSTRACT FROM AUTHOR]

New theoretical model describing the sampling depth of elastic peak electron spectroscopy (EPES) has been proposed. Surface sensitivity of this technique can be generally identified with the maximum depth reached by trajectories of elastically backscattered electrons. A parameter called the penetration depth distribution function (PDDF) has been proposed for this description. Two further parameters are descendant from this definition: the mean penetration depth (MPD) and the information depth (ID). From the proposed theory, relatively simple analytical expressions describing the above parameters can be derived. Although the Monte Carlo simulations can be effectively used to estimate the sampling depth of EPES, this approach may require a considerable amount of computations. In contrast, the analytical model proposed here (AN) is very fast and provides the parameters PDDF, MPD and ID that very well compare with results of MC simulations. As follows from detailed comparisons performed for four elements (Al, Ni, Pd and Au), the AN model practically reproduced complicated emission angle dependences of the MPDs and the IDs, correctly indicating numerous maximum and minimum positions. In the energy range from 200 eV to 5 keV, the averaged percentage differences between MPDs obtained from the MC and the AN models were close to 4%. An important conclusion resulting from the present studies refers to the procedure of determination of the inelastic mean free path (IMFP) from EPES. Frequently, the analyzed sample is deposited as a thin overlayer on a smooth substrate. From an analysis of the presently obtained IDs, is follows that 99% of trajectories in analyzed experimental configurations reaches depth not exceeding 2.39 in units of IMFP. Thus, one can postulate that a safe minimum thickness of an overlayer should be larger than about 3 IMFPs. For example, the minimum thickness of an Al overlayer shoud be about 8 nm at 5000 eV. [ABSTRACT FROM AUTHOR]

Probability of elastic electron backscattering from surfaces is typically calculated from theoretical models implemented in Monte Carlo simulation strategies since this approach is considered to be the most accurate. However, an analytical model proposed by Oswald et al. [J. Electron Spectrosc. Relat. Phenom. 61 (1993) 251], after later modifications, has been found to be of similar accuracy. The relevant analysis was performed for selected elemental solids. In the present work, a possibility to use the analytical formalism in elastic peak electron spectroscopy for determination of the IMFP has been presently studied. For this purpose, two further modifications of the analytical theory were made: (i) creation of a database of parameters facilitating calculations of the angular distribution of electrons after multiple collisions, and (ii) extension of the formalism to solids constituted of different atomic species, i.e. alloys and compounds. Comparison of experimental data (angular distribution of backscattered electrons, ratios of elastic peak intensities) with predictions of both theoretical models proves that these models are of similar accuracy. The IMFPs for elemental solids derived from experimentally measured ratios using the analytical formalism and the Monte Carlo simulations are practically identical. On analysis of IMFPs obtained for 13 elemental solids in the energy range from 200 eV to 5000 eV, it has been estimated that the IMFPs obtained from the analytical formalism deviate on average from IMFPs from Monte Carlo calculations by 3.09%. Similar agreement was found for an alloy (Al 0.48 Ni 0.52 ) and compounds (GaSb, InSb, GaN and SiC) considered here. [ABSTRACT FROM AUTHOR]