Electron Inelastic Mean Free Paths Research Articles

Effect of atomic structure on excitation of the electronic subsystem of a solid by a swift heavy ion

An effect of different phase states of a solid on excitation of its electronic subsystem due to penetration of a swift heavy ion (SHI) is examined on example of silicon dioxide (crystalline quartz vs. amorphous glass). The complex dielectric function formalism describing collective response of the electronic and ionic subsystems of a condensed target to excitation is used to calculate scattering cross sections of a penetrating ion and electrons generated due to target ionizations. A Monte Carlo model based on these cross sections is applied for tracing electron kinetics in the nanometric vicinity of the trajectory of a swift heavy ion. It is demonstrated that differences of the maximal values of the SHI energy losses and the electron inelastic mean free paths calculated for two phase states of SiO2 do not exceed 10–15%, whereas the elastic mean free paths differ more significantly.

Electron emission from silicon and germanium after swift heavy ion impact

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.

Extended Mermin method for calculating the electron inelastic mean free path.

We propose an improved method for calculating electron inelastic mean free paths (IMFPs) in solids from experimental energy-loss functions based on the Mermin dielectric function. The "extended Mermin" method employs a nonlimited number of Mermin oscillators and allows negative oscillators to take into account not only electronic transitions, as is common in the traditional approaches, but also infrared transitions and inner shell electron excitations. The use of only Mermin oscillators naturally preserves two important sum rules when extending to infinite momentum transfer. Excellent agreement is found between calculated IMFPs for Cu and experimental measurements from elastic peak electron spectroscopy. Notably improved fits to the IMFPs derived from analyses of x-ray absorption fine structure measurements for Cu and Mo illustrate the importance of the contribution of infrared transitions in IMFP calculations at low energies.

Quantification of surface roughness effect on elastically backscattered electrons

Electron inelastic mean free path can be obtained from a measured elastic peak electron spectroscopy spectrum combined with a Monte Carlo simulation. It is thus necessary to know the influence of various experimental factors to the measured and calculated results. This work investigates the effect of the surface roughness or the surface topography on the intensity of the elastic peak. A Monte Carlo simulation, by taking into account of realistic surface roughness for both Gaussian and non‐Gaussian type rough surfaces experimentally prepared, has been employed to study the surface topography effect. The simulations of elastic peak electron spectroscopy were performed for both planar and rough Al and Cu surfaces and for varied primary energies ranging from 200 to 2000 eV. To quantify the surface roughness effect, the surface roughness parameter is introduced according to the ratio of elastic peak intensities between a rough surface and an ideal planar surface. Simulation results have shown that surface roughness parameter is important in a certain range of emission angle and particularly for large emission angles. For grazing emission, the elastic peak intensity can be largely enhanced by roughness even at nanometer scale. Copyright © 2014 John Wiley & Sons, Ltd.

Uncertainty Evaluation in Measurement of Thickness of SiO<sub>2</sub>/Si Using X-Ray Photoelectron Spectroscopy

Ultra-thin films of SiO2 (nominally 2, 4, 6, 8 and 10nm thick) on silicon, prepared by thermal oxidation, were investigated using x-ray photoelectron spectroscopy (XPS). The thickness of these thin films was obtained from a measurement of the photoelectron intensities originating from the substrate and the oxide layers by applying an appropriate quantitative model. The uncertainty budget of that thickness measurement method is given. The effective attenuation lengths or the corresponding electron inelastic mean free paths are of the most importance in the contribution of the uncertainties. For the SiO2 ultra-thin film with the nominal thickness of 2nm, it could generate 20% of the uncertainty.

Full-potential theoretical investigations of electron inelastic mean free paths and extended x-ray absorption fine structure in molybdenum

X-ray absorption fine structure (XAFS) spectroscopy is one of the most robust, adaptable, and widely used structural analysis tools available for a range of material classes from bulk solids to aqueous solutions and active catalytic structures. Recent developments in XAFS theory have enabled high-accuracy calculations of spectra over an extended energy range using full-potential cluster modelling, and have demonstrated particular sensitivity in XAFS to a fundamental electron transport property—the electron inelastic mean free path (IMFP). We develop electron IMFP theory using a unique hybrid model that simultaneously incorporates second-order excitation losses, while precisely accounting for optical transitions dictated by the complex band structure of the solid. These advances are coupled with improved XAFS modelling to determine wide energy-range absorption spectra for molybdenum. This represents a critical test case of the theory, as measurements of molybdenum K-edge XAFS represent the most accurate determinations of XAFS spectra for any material. We find that we are able to reproduce an extended range of oscillatory structure in the absorption spectrum, and demonstrate a first-time theoretical determination of the absorption coefficient of molybdenum over the entire extended XAFS range utilizing a full-potential cluster model.

Energy-loss function including damping and prediction of plasmon lifetime

An approach to include plasmon damping in the energy-loss function is described within the dielectric theory. Use of the energy-loss function included damping for calculating the electron inelastic mean free path yields results in good agreement with the experimental data and other theoretical results at medium–high energies. At a few eV above the Fermi energy, the present results are entirely consistent with those obtained from other measurements for Au. Also, a simple way to predict the values of damping and lifetime at low energies is described. Two values of lifetime for an electron with energy (above the Fermi energy) of 5eV in Al and 6eV in Au are predicted to be 2.18fs and 1.70fs, respectively. These predicted values are in reasonable agreement with those estimated from other measurements at the corresponding energies: 2.16 ± 0.22fs in Al, and 1.91 ± 0.32fs in Au.

Low-energy electron energy losses and inelastic mean free paths in zinc, selenium, and zinc selenide

We compute low-energy optical energy loss spectra for the elemental solids zinc and selenium, and for the binary compound zinc selenide. The optical data are transformed via a constrained partial-pole algorithm to produce momentum-dependent electron energy loss spectra and electron inelastic mean free paths. This enables a comparison between the electron scattering behaviour in a compound solid and its constituent elements. Results cannot be explained by aggregation methods or commonly used universal curves, and prove that new approaches are required. Our work demonstrates new capabilities for the determination of fundamental material properties for a range of structures previously inaccessible to established theoretical models, and at energy levels inaccessible to most experimental techniques.

Inelastic electron scattering cross-section spectroscopy of Ge x Si1 − x nanoheterostructures

Two-component GexSi1 − x (0 ≤ x ≤ 1) structures are studied by electron spectroscopy. The atomic composition of the structures is determined from X-ray photoelectron spectroscopy data. The reflection electron-energy-loss spectra for a series of samples with different x at primary-electron energies from 200 to 3000 eV are recorded. Using the experimental spectra, the electron energy loss dependences of the product of the electron inelastic mean free path and the differential inelastic electron scattering cross section are calculated. It is shown that the quantitative characteristics of these dependences can be used to determine the atomic concentrations of elements in the investigated system.

Electron Inelastic Mean Free Path Theory and Density Functional Theory Resolving Discrepancies for Low-Energy Electrons in Copper

We develop the many-pole dielectric theory of UV plasmon interactions and electron energy losses, and couple our advances with recent developments of Kohn-Sham density functional theory to address observed discrepancies between high-precision measurements and tabulated data for electron inelastic mean free paths (IMFPs). Recent publications have demonstrated that a five standard error difference exists between longstanding theoretical calculations and measurements of electron IMFPs for elemental solids at energies below 120 eV, a critical region for analysis of electron energy loss spectroscopy (EELS), X-ray absorption spectroscopy (XAS), and related technologies. Our implementation of improved optical loss spectra and a physical treatment of second-order excitation lifetimes resolves this problem in copper for the first time for energies in excess of 80 eV and substantially improves agreement for lower energy electrons.

Monte-Carlo modeling of excitation of the electron subsystem of Al2O3 and polyethylene after swift heavy ion impact

The Monte-Carlo (MC) model simulating the femto-second kinetics of the electron subsystem in a track of a swift heavy ion decelerated in the electronic stopping regime is developed. The complex dielectric function (CDF) formalism is used to calculate the cross sections of interactions of an ion and fast electrons with the electron subsystem of a target. It accounts for all collective modes in the electron ensemble. The applied method of CDF reconstruction from the experimental optical data provided a very good agreement of the calculated electron inelastic mean free paths with the NIST database as well as of the calculated SHI energy loss with those from SRIM and CasP codes. The MC model was applied to determine the radial distributions of delocalized electrons and their energy density in tracks of Au (2187MeV) ions in insulators (Al2O3 and polyethylene) at different times. The femtosecond electron kinetics reveals two fronts of the spatial propagation: the primary fast delta-electrons form the front of excitations while electrons appearing due to decay of plasmons generated in a track form the second slow front following behind.

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

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

Calculations of mean escape depths of photoelectrons in elemental solids excited by linearly polarized X-rays for high-energy photoelectron spectroscopy

We have calculated mean escape depths (MEDs, D) of photoelectrons from Si, Cu, and Au excited by linearly polarized X-rays over the 50–10,000eV energy range for high-energy photoelectron spectroscopy. These calculations were done with Monte Carlo methods using the values of electron inelastic mean free paths λ that were calculated by the relativistic full Penn algorithm and the Dirac–Hartree–Fock atomic potential for elastic scattering of electrons. In order to know the dependence of MED on the asymmetry parameter β and the emission angle θ, we calculated MEDs for β=−1 to β=2 (by 0.5 steps) and θ=0° to θ=80° (with respect to the surface normal). The resulting MED values increase as the β values decrease over the 50–10,000eV energy range. We also found that the values of D/λcosθ are approximately constant to within 10% for a given value of θ and for energies over 1000eV (except for the condition of β=−1) over a range of emission angles (typically 0–40° or 60°). We also found that the energy dependence of the ratios D/λcosθ at emission angle θ=0° can be expressed by the Jablonski–Powell predictive equation over the 50–10,000eV energy range.Finally, we have obtained a predictive MED equation that could be applied to the wide range of experimental conditions that are used in high-energy XPS with synchrotron radiation.

Complex dielectric function formalism for description of the electron kinetics in swift heavy ion tracks in LiF and Y2O3

Complex dielectric function formalism is applied to obtain the cross-sections, mean free path of electrons, and energy losses of swift heavy ions (SHI) in solid LiF and Y2O3 out of the experimentally known loss function. The calculated electron inelastic mean free paths in these materials agree very well with the NIST database; the inelastic energy losses of swift Pb and Au ions agree well with those calculated with the widely used SRIM and CasP codes. The obtained cross-sections are used in Monte Carlo simulations of the electronic kinetics after SHI impacts. The radial distributions of the electron and valence hole densities as well as their energy densities were calculated.

Insight into the Compositional and Structural Nano Features of AlN/GaN DBRs by EELS-HAADF

III-V nitride (AlGa)N distributed Bragg reflector devices are characterized by combined high-angle annular dark-field (HAADF) and electron energy loss spectroscopy (EELS) in the scanning transmission electron microscope. Besides the complete structural characterization of the AlN and GaN layers, the formation of AlGaN transient layers is revealed using Vegard law on profiles of the position of the bulk plasmon peak maximum. This result is confirmed by comparison of experimental and simulated HAADF intensities. In addition, we present an advantageous method for the characterization of nano-feature structures using low-loss EELS spectrum image (EEL-SI) analysis. Information from the materials in the sample is extracted from these EEL-SI at high spatial resolution.The log-ratio formula is used to calculate the relative thickness, related to the electron inelastic mean free path. Fitting of the bulk plasmon is performed using a damped plasmon model (DPM) equation. The maximum of this peak is related to the chemical composition variation using the previous Vegard law analysis. In addition, within the context of the DPM, information regarding the structural properties of the material can be obtained from the lifetime of the oscillation. Three anomalous segregation regions are characterized, revealing formation of metallic Al islands.

Reflection electron energy loss spectroscopy in Mn x Si1 − x composite structures

The dependences of the product of the electron inelastic mean free path λ and the differential cross section for inelastic electron scattering K on energy loss are determined from the experimental energy-loss spectra of the reflected electrons of MnxSi1 − x (0 ≤ x ≤ 1) composite structures. It is shown that the minimum values for the dependences of the product λK on the electron-energy loss can be used for the quantitative determination of element concentrations in this composite structure.

Validity of automated x-ray photoelectron spectroscopy algorithm to determine the amount of substance and the depth distribution of atoms

The author reports a systematic study of the range of validity of a previously developed algorithm for automated x-ray photoelectron spectroscopy analysis, which takes into account the variation in both peak intensity and the intensity in the background of inelastically scattered electrons. This test was done by first simulating spectra for the Au4d peak with gold atoms distributed in the form of a wide range of nanostructures, which includes overlayers with varying thickness, a 5 Å layer of atoms buried at varying depths and a substrate covered with an overlayer of varying thickness. Next, the algorithm was applied to analyze these spectra. The algorithm determines the number of atoms within the outermost 3 λ of the surface. This amount of substance is denoted AOS3λ (where λ is the electron inelastic mean free path). In general the determined AOS3λ is found to be accurate to within ∼10–20% depending on the depth distribution of the atoms. The algorithm also determines a characteristic length L, which was found to give unambiguous information on the depth distribution of the atoms for practically all studied cases. A set of rules for this parameter, which relates the value of L to the depths where the atoms are distributed, was tested, and these rules were found to be generally valid with only a few exceptions. The results were found to be rather independent of the spectral energy range (from 20 to 40 eV below the peak energy) used in the analysis.

Stopping Powers and Inelastic Mean Free Path of 100 eV to 30 keV Electrons in Zirconium Silicates

We have determined the electron stopping power (SP) and inelastic mean free path (IMFP) of (ZrO 2 ) x (SiO 2 ) 1-x (x=1, 0.75, 0.5, 0.25, 0) for electron energies from 100 eV to 30 keV by means of modified Born–Ochkur equations. The energy loss function (ELF) is required in the calculation of SP and IMFP. We used the electron energy losses from 0 to 80 eV obtained by quantitative analysis of reflection electron energy-loss spectroscopy (REELS) spectra. The values of SP and IMFP for high contents of ZrO 2 (x=50% and x=75%) in Zr-silicates are similar to those of ZrO 2 , and similar to those of SiO 2 for low contents of ZrO 2 (x=25%) in Zr-silicates. There are small differences in the values of SP and IMFP for ZrO 2 and SiO 2 .We found that the SP decreases while the IMFP increases with increasing electron energy. We have demonstrated that the ELF obtained from the quantitative analysis of REELS spectra provide us with a straightforward way to determine SP and IMFP for alloy materials by using modified Born-Ochkur equations. Received: 04 December 2012; Revised: 18 December 2012; Accepted: 19 December 2012

Theoretical and experimental developments in the determination of electron energy loss functions and inelastic mean free paths in elemental solids and binary compounds

We present a new theoretical representation of the electron energy loss function in terms of partial plasmon poles. This representation allows the determination of electron inelastic mean free paths from a known optical spectrum without empirical fitting, and for the first time, with consistent fulfilment of optical sum rules. We compare the new theory to recent experimental determinations of the inelastic mean free path and demonstrate improved agreement.

The X-ray Extended Range Technique a model for investigating X-ray and electron collision processes at a synchrotron

New techniques at synchrotrons can not only drive higher accuracy, structural information and insight in photoabsorption and inelastic scattering of the photon, but also inelastic scattering of the electron. This is important for fields such as XAFS, XANES and powder diffraction, but has also initiated new fields of nanoroughness measurement, measurement of electron inelastic mean free paths, bonding information at an accuracy of crystallographic determination, and similar advances for fluorescence and scattering investigations. We summarise and present some key opportunities for research and development.