Inelastic Mean Free Path Research Articles

A study of the effect of inelastic absorption on the validity of trajectory simulation of elastic scattering

The effect of inelastic events on the elastic scattering of particles in a scattering medium may be described in terms of inelastic absorption (depletion of the elastic scattering channel), which may be implemented either by means of a complex phaseshift or by means of an optical potential. Using both methods, inelastic absorption is introduced in the exact quantum calculation of multiple elastic s-wave scattering of a particle in a cluster of point scatterers. The average solution of the quantum calculation for a large number of simulated clusters with identical boundaries but with scatterers in randomly varying positions is compared with the result of a corresponding trajectory simulation, where an inelastic mean free path has been introduced. In the trajectory simulation an inelastic event results in the absorption of the particle, i.e. termination of the trajectory. It has previously been shown that trajectory simulation of purely elastic scattering is a valid approximation of the average quantum solution if the incident particle wavelength is at most about equal to the average distance between neighbour scatterers. It is found that this condition still holds in the presence of inelastic absorption, although quantum and trajectory calculations of the scattering event distribution inside the cluster give increasingly similar results for decreasing inelastic mean free path.

Molar concentration–depth profiles at the solution surface of a cationic surfactant reconstructed with angle resolved X-ray photoelectron spectroscopy

In the current work, we first reconstructed the molar fraction–depth profiles of cation and anion near the surface of tetrabutylammonium iodide dissolved in formamide by a refined calculation procedure, based on angle resolved X-ray photoelectron spectroscopy experiments. In this calculation procedure, both the transmission functions of the core levels and the inelastic mean free paths of the photoelectrons have been taken into account. We have evaluated the partial molar volumes of surfactant and solvent by the densities of such solutions with different bulk concentrations. With those partial molar volumes, the molar concentration–depth profiles of tetrabutylammonium ion and iodide ion were determined. The surface excesses of both surfactant ions were then achieved directly by integrating these depth profiles. The anionic molar concentration–depth profiles and surface excesses have been compared with their counterparts determined by neutral impact ion scattering spectroscopy. The comparisons exhibit good agreements. Being capable of determining molar concentration–depth profiles of surfactant ions by core levels with different kinetic energies may extend the applicable range of ARXPS in investigating solution surfaces.

Absolutely determined inelastic mean free paths for 300–3000 eV electrons in 10 elemental solids

AbstractThe inelastic mean free path (IMFP), surface excitation parameter (SEP), and differential SEP (DSEP) were determined for 10 elemental solids by the absolute analysis of reflection electron energy loss spectra (REELS). The obtained IMFPs were compared with values calculated using predictive equations for the IMFP, and it is found that the obtained IMFPs show a fairly good agreement with those calculated by the TPP‐2M predictive equation. The obtained IMFPs were analyzed by the Fano plot and fitted to the Bethe equation, revealing that the obtained IMFPs are well described by the Bethe equation. The obtained DSEPs were compared with the theoretically calculated DSEPs, and the reasonable agreement between the present and theoretical DSEPs was confirmed. The dependence of the present SEPs on the electron energy is found to be described well by predictive equations for the SEP, and material parameters in the predictive equations were determined. Copyright © 2010 John Wiley & Sons, Ltd.

Quasiparticle dynamics in ferromagnetic compounds of the Co–Fe and Ni–Fe systems

We report a theoretical study of the quasiparticle lifetime and the quasiparticle mean free path caused by inelastic electron-electron scattering in ferromagnetic compounds of the Co–Fe and Ni–Fe systems. The study is based on spin-polarized calculations, which are performed within the G 0 W 0 approximation for equiatomic and Co(Ni)-rich compounds, as well as for their constituents. We mainly focus on the spin asymmetry of the quasiparticle properties, which leads to the spin-filtering effect experimentally observed in spin-dependent transport of hot electrons and holes in the systems under study. By comparing with available experimental data on the attenuation length, we estimate the contribution of the inelastic mean free path to this length.

Ion-induced kinetic electron emission from 6LiF, 7LiF and MgF2 thin films

Secondary electron yields for Ar+ impact on 6LiF, 7LiF and MgF2 thin films grown on aluminum substrates are measured each as a function of target temperature and projectile energy. Remarkably different behaviours of the electron yields for LiF and MgF2 films are observed in a temperature range from 25 °C to 300 °C. The electron yield of LiF is found to sharply increase with target temperature and to be saturated at about 175 °C. But the target temperature has no effect on the electron yield of MgF2. It is also found that for the ion energies greater than 4 keV, the electron yield of 6LiF is consistently high as compared with that of 7LiF that may be due to the enhanced contribution of recoiling 6Li atoms to the secondary electron generation. A comparison between the electron yields of MgF2 and LiF reveales that above a certain ion energy the electron yield of MgF2 is considerably low as compared with that of LiF. We suggest that the short inelastic mean free path of electrons in MgF2 can be one of the reasons for its low electron yield.

X-ray Spectroscopic Measurement of Photoelectron Inelastic Mean Free Paths in Molybdenum

The electron inelastic mean free path (IMFP) of molybdenum is determined experimentally over an energy range of 1−120 eV using analysis of X-ray absorption fine structure (XAFS). This new approach enables accurate measurements of IMFPs in this energy range where direct measurements are often difficult and highly uncertain, and provides a means for studying materials inaccessible through current alternate techniques. This approach can also be used to determine localized IMFPs within complex molecular systems, enabling detailed study of surfaces and nanoenvironments. This information is important for diverse applications in physical chemistry including electron microscopy, spectroscopy, and diffraction (low-energy electron diffraction (LEED) and electron energy loss spectroscopy (EELS) in particular). Here we reveal the accuracy achievable using experimental data of high statistical precision, and critically evaluate the form of the IMFP in the asymptotic region in the low energy limit.

Proton inelastic mean free path in amino acids and protein over the energy range of 0.05–10 MeV

The inelastic mean free paths (MFP) of 0.05–10 MeV protons in a group of 15 amino acids and a protein have been systematically calculated. The calculations are based on the method newly derived from the Ashley’s optical-data model and from the higher-order correction terms in stopping power calculations. Especially, in this method the new and empirical Bloch correction for the inelastic MFP was given. An evaluation for the optical energy loss function is incorporated into the present calculations because of the lack of available experimental optical data for the bioorganic compounds under consideration. The proton inelastic MFPs for these 15 amino acids and the protein in the energy range from 0.05 to 10 MeV are presented here for the first time, and the combination of these inelastic MFP data and our previous data of the SP calculations for these bioorganic compounds may form a useful database for Monte Carlo track-structure studies of various radiation effects in these materials.

Measurements of Electron Inelastic Mean Free Paths in Materials

We present a method for determining inelastic mean free paths (IMFPs) in materials using high-accuracy measurements of x-ray absorption fine structure (XAFS). For electron energies below 100 eV, theoretical predictions have large variability and alternate measurement techniques exhibit significant uncertainties. In this regime, the short IMFP makes photoelectrons ideal for structural determination of surfaces and nanostructures, and measurements are valuable for studies of diverse fields such as low-energy electron diffraction and ballistic electron emission microscopy. Our approach, here applied to solid copper, is unique and exhibits enhanced sensitivity at electron energies below 100 eV. Furthermore, it is readily applicable to any material for which sufficiently high accuracy XAFS data can be obtained.

Measurement of optical constants of Si and SiO2 from reflection electron energy loss spectra using factor analysis method

The energy loss functions (ELFs) and optical constants of Si and SiO2 were obtained from quantitative analysis of reflection electron energy loss spectroscopy (REELS) by a new approach. In order to obtain the ELF, which is directly related to the optical constants, we measured series of angular and energy dependent REELS spectra for Si and SiO2. The λ(E)K(ΔE) spectra, which are the product of the inelastic mean free path (IMFP) and the differential inverse IMFP, were obtained from the measured REELS spectra. We used the factor analysis (FA) method to analyze series of λ(E)K(ΔE) spectra for various emission angles at fixed primary beam energy to separate the surface-loss and bulk-loss components. The extracted bulk-loss components enable to obtain the ELFs of Si and SiO2, which are checked by oscillator strength-sum and perfect-screening-sum rules. The real part of the reciprocal of the complex dielectric function was determined by Kramers–Kronig analysis of the ELFs. Subsequently, the optical constants of Si and SiO2 were calculated. The resulting optical constants in terms of the refractive index and the extinction coefficient for Si and SiO2 are in good agreement with Palik’s reference data. The results demonstrate the general applicability of FA as an efficient method to obtain the bulk ELF and to determine the optical properties from REELS measurements.

Proton inelastic mean free path in a group of bioorganic compounds and water in 0.05–10 MeV range – Including higher-order corrections

The systematic calculations of the inelastic mean free paths (MFP) of 0.05–10 MeV protons in a group of eleven important bioorganic compounds, i.e. DNA, five bases, three fatty acids, cellulose and β -carotene, have been performed. The expressions for the calculations are derived from the Ashley’s optical-data model and from the higher-order correction terms in stopping power calculations. Especially, the Bloch correction for the inelastic MFP is proposed empirically in this work. The inelastic MFPs for energetic protons in water are also evaluated and compared with other theoretical calculations. The proton inelastic MFPs for these 11 bioorganic compounds in the energy range from 0.05 to 10 MeV are presented here for the first time, and might be useful for studies of various radiation effects in these materials.

Auger Electron Spectroscopy: A Rational Method for Determining Thickness of Graphene Films

We report the determination of the thickness of graphene layers by Auger electron spectroscopy (AES). We measure AES spectra of graphenes with different numbers of layers. The AES spectroscopy shows distinct spectrum shape, intensity, and energy characteristics with an increasing number of graphene layers. We also calculate electron inelastic mean free paths for graphene layers directly from these measurements. The method allows unambiguous and high-throughput determination of thickness up to six graphene layers and detection of defect and dopant in graphene films on almost any substrate. The availability of this reliable method will permit direct probing of graphene growth mechanisms and exploration of novel properties of graphenes with different thicknesses on diverse substrates.

Effect of gap opening on the quasiparticle properties of doped graphene sheets

We present numerical calculations of the effect of gap opening on the quasiparticle properties of a doped graphene sheet within G0W -RPA approximation. We present results of the renormalized Fermi velocity suppression and the renormalization constant over a broad range of the energy gap values. We find that the renormalized velocity is density independent at large density values which is in agreement with recent experimental observations. We also show that the inelastic quasiparticle lifetime decreases by increasing the gap value. Finally, we show that the inelastic mean free path reduces by increasing the gap values but in the range of the typical gap values it is large enough and transport remains in the semi-ballistic regime.

Study of Charge Trap Sites in SiN Films by Hard X-ray Photoelectron Spectroscopy

Hard X-ray photoelectron spectroscopy (HAX-PES) was performed at SPring-8, and has enabled us to study the bulk properties of SiN films deposited by microwave plasma-enhanced chemical vapor deposition and deeply buried SiN/SiO2 interfaces, owing to the large inelastic mean free path of a photoelectron with a high kinetic energy. The defect states in the SiN films were examined by HAX-PES in order to verify the charge-trapping mechanism in a silicon–oxide–nitride–oxide–silicon flash memory device. X-ray reflectometry (XRR) was also performed at SPring-8. There is a complementary relationship between photoelectron spectroscopy and XRR. This methodology is proposed in this paper as a powerful tool for examining material properties. The detailed depth profile analysis of the chemical states in the SiN films obtained by angle-resolved HAX-PES also helped us to examine the charge-trapping mechanism.

Energy loss function for Si determined from reflection electron energy loss spectra with factor analysis method

AbstractThe Si energy loss function (ELF) for energy loss ΔE less than 30 eV was obtained from experimental λ(E)K(ΔE) distributions using a factor analysis method. λ(E)K(ΔE), which are the products of the inelastic mean free path (IMFP) [λ(E)] and the differential inverse IMFPs or inelastic scattering cross sections [K(ΔE)], were obtained from angle‐resolved REELS at various primary beam energies with QUASES‐XS‐REELS software. The application of the factor analysis method to determine the ELF is described in detail. We performed factor analysis on the data matrix formed by λ(E)K(ΔE) spectra to separate surface‐ and bulk‐loss components. Finally, the ELF for Si was derived from extracted bulk‐loss component by an iterative calculation. The resulting ELF is in good agreement with the ELF from Palik's optical data. The suggested approach should be applicable as a general method to determine ELF from REELS. Copyright © 2010 John Wiley & Sons, Ltd.

A comparative X‐ray photoelectron spectroscopy and medium‐energy ion‐scattering study of ultra‐thin, Hf‐based high‐k films

AbstractUltra‐thin high‐k layers based on HfO2, or Hf‐silicates in combination with sub‐nanometer SiO2, show much promise in their use as Si‐compatible gate dielectrics. XPS has been applied on a range of HfO2/SiO2 and HfSiOx(60%Hf)/SiO2 films on Si(100), before and after decoupled plasma nitridation (DPN) at 1073 K. The treatment of the data was optimized in order to determine individual layer thicknesses of the multilayer stack taking into account the measured nitrogen content of the nitrided films. The procedure adhered to the prescriptions of ISO18118:2004(E) for the calculations of inelastic mean free paths (IMFP) and elastic corrections thereof, using film material properties, like densities and band gaps. Effective attenuation lengths (EAL) were taken throughout as 90% of the respective IMFP, whereas an appropriate set of empirical relative sensitivity factors (RSF) was used. The XPS‐derived thicknesses were compared with corresponding values obtained from medium‐energy ion scattering (MEIS) measurements on the same series of specimens in combination with energy spectrum simulation to provide quantitative layer information with sub‐nanometer resolution. The XPS and MEIS results exhibit very good agreement on the deduced layer structures within the respective experimental uncertainty, and both sets are consistent with the grown nominal layer parameters of the high‐k nanofilms. Copyright © 2010 John Wiley & Sons, Ltd.

Optical properties of silver thin films, derived from REELS

AbstractThe differential surface excitation probabilities (DSEPs) for medium‐energy electrons traveling in Ag are extracted from reflection electron energy loss spectroscopy (REELS) spectra by using the Werner's elimination‐retrieved algorithm. Based on a surface Kramers–Kronig dispersion relationship, the electronic structure and optical properties of Ag thin film are determined. The results show that the optical property curves between surface thin layer and bulk are similar in shape, whereas they deviate quantitatively for energies below 40 eV, which may be caused by the different electronic structures at surface and in bulk. The present data would be an appropriate approximation to the optical properties of thin film, whose thickness is characterized by the inelastic mean free path of the electrons in a REELS experiment. Copyright © 2010 John Wiley & Sons, Ltd.

Effective medium theory for REELS analysis of amorphous carbon films

AbstractWe use effective medium theory (EMT) as a framework to describe reflection electron energy loss spectra (REELS) from polycrystalline graphite and amorphous carbon (a‐C), the latter obtained by ion irradiation of the former. Such materials, isotropic at a macroscopic scale, are anisotropic at the micro‐ or nano‐scale. For them, we prove the value of the concept of effective isotropic energy loss function to describe EELS in the plasmon region. Based on this function, we calculate a differential inverse inelastic mean free path (DIIMFP) which, compared to experimental spectra from pristine and ion‐irradiated polycrystalline graphite, is able to reproduce their main features. Copyright © 2010 John Wiley & Sons, Ltd.

Determination of Structural Parameters by EXAFS Analysis of Some Co Complexes

In this paper we deal with a relatively simpler method for the Fourier analysis of EXAFS data and illustrate this by a detailed analysis of the data for cobalt metal foil and cobalt complexes of isoxezol series. The Fourier analysis is useful in extracting distances and information about the phase shifts, the amplitudes, the Debye–Waller factors and the mean free paths. Here we have determined interatomic distances, mean square deviation and inelastic mean free path from the Fourier transform of EXAFS data for cobalt metal foil and cobalt complexes of isoxezol series by MathCAD programming.

Remarks on Some Reference Materials for Applications in Elastic Peak Electron Spectroscopy

The quantification of results of electron spectroscopies, AES and XPS, requires knowledge of the inelastic mean free path (IMFP) of signal electrons in solids. This parameter determines the surface sensitivity of both techniques. There are two methods of determining the IMFPs that provide these parameters in agreement with the definition: (i) calculations based on the experimental optical data, and (ii) calculations based on measurements of the electron elastic backscattering intensity. The latter method requires the use of some reference material for which the IMFP is known. In 1999, an extensive analysis of the published IMFPs has been performed; the results indicated that there is a very good agreement between the calculated and measured IMFPs for four elemental solids: Ni, Cu, Ag and Au. The averaged IMFPs for these elements are known under the name of the recommended IMFPs. However, no preference among these four elements has been established. In the present work, an attempt is made to select an element for which the recommended IMFPs result in the best agreement between the calculated and measured intensities of elastic electron backscattering. For this purpose, the elastic backscattering intensity has been measured at eight electron energies varying from 200 to 1500 eV. At each energy, the intensity was measured over a wide range of emission angles from 35 degrees to 74 degrees . The experiments were accompanied with Monte Carlo calculations of the elastic backscattering probability for the same energies and experimental configurations. It has been found, from comparison, that the best agreement is observed for Au, and this element is thus recommended as the reference material. It has been shown that the shape of the emission angle dependence of the elastic backscattering intensity is noticeably influenced by the surface energy losses.

Surface Excitations in Surface Electron Spectroscopies Studied by Reflection Electron Energy-Loss Spectroscopy and Elastic Peak Electron Spectroscopy

Surface excitations, in addition to bulk excitation, undergone by signal electrons in surface electron spectroscopies, such as Auger electron spectroscopy, and X-ray photoelectron spectroscopy, play an important role in the formation of electron spectra. Those inelastic scattering processes not only induce decay in the peak intensity, but also form background appearing in the lower kinetic energy side of relevant peaks. Information on surface excitation is essential in addition to bulk excitations for the quantification of material surfaces by surface electron spectroscopies, and extensive studies have been devoted to it. In this report, we introduce the basics of the study of surface excitations by reflection electron energy loss spectroscopy (REELS) and elastic peak electron spectroscopy (EPES). The application of several approaches within the schemes of EPES analysis and REELS analysis to the experimental determination of inelastic scattering parameters, such as the surface excitation parameter (SEP), differential SEP (DSEP), inelastic mean free path (IMFP), and dielectric function, are also introduced. Information useful to calculate the values of the IMFP and SEP using predictive equations is provided in Supporting Information as well.