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

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

Stopping powers and inelastic mean free path from quantitative analysis of experimental REELS spectra for electrons in Ti,Fe, Ni,and Pd

Stopping power (SP) and inelastic mean free path (IMFP) of electrons in Ti, Fe, Ni, and Pd have been determined by using dielectric models. We have used energy loss function (ELF) determined from quantitative analysis of experimental reflection electron energy loss spectroscopy (REELS) spectra as the input parameter for this model. ELF in this study was determined from the previously published quantitative analysis of REELS spectra. The SP of Fe, Ni, Pd, and Ti was compared with several calculation methods for energies from 100 eV to 10 keV and shows SP in this study, which are in best agreement for medium to high energies (greater than or equal to 300 eV). The IMFP obtained in this study shows the best agreement with online database TPP2M and NIST and also calculation by Tanuma with a root mean square (rms ) less than 12%. The present approach shows ELF from quantitative analysis of REELS spectra has a high potential for the experimental determination of SP and IMFP of metals.     

Calculations of electron inelastic mean free paths. XI. Data for liquid water for energies from 50 eV to 30 keV

We calculated electron inelastic mean free paths (IMFPs) for liquid water from its optical energy‐loss function (ELF) for electron energies from 50 eV to 30 keV. These calculations were made with the relativistic full Penn algorithm that has been used for previous IMFP and electron stopping‐power calculations for many elemental solids. We also calculated IMFPs of water with three additional algorithms: the relativistic single‐pole approximation, the relativistic simplified single‐pole approximation, and the relativistic extended Mermin method. These calculations were made by using the same optical ELF in order to assess any differences of the IMFPs arising from choice of the algorithm. We found good agreement among the IMFPs from the four algorithms for energies over 300 eV. For energies less than 100 eV, however, large differences became apparent. IMFPs from the relativistic TPP‐2M equation for predicting IMFPs were in good agreement with IMFPs from the four algorithms for energies between 300 eV and 30 keV, but there was poorer agreement for lower energies. We calculated values of the static structure factor as a function of momentum transfer from the full Penn algorithm. The resulting values were in good agreement with results from first‐principle calculations and with inelastic X‐ray scattering spectroscopy experiments. We made comparisons of our IMFPs with earlier calculations from authors who had used different algorithms and different ELF data sets. IMFP differences could then be analyzed in terms of the algorithms and the data sets. Finally, we compared our IMFPs with measurements of IMFPs and of a related quantity, the effective attenuation length. There were large variations in the measured IMFPs and effective attenuation lengths (as well as their dependence on electron energy). Further measurements are therefore required to establish consistent data sets and for more detailed comparisons with calculated IMFPs. Copyright © 2016 John Wiley & Sons, Ltd.     

Summary of ISO/TC 201 Standard XI. ISO 17974:2002—Surface chemical analysis—High‐resolution Auger electron spectrometers—Calibration of energy scales for elemental and chemical‐state analysis

This International Standard specifies a method for calibrating the kinetic energy scales of Auger electron spectrometers for elemental and chemical‐state analysis at surfaces. It is only applicable to instruments that incorporate an ion gun for sputter cleaning. This International Standard further specifies a method to establish a calibration schedule, to test for the kinetic energy scale linearity at one intermediate energy, to confirm the uncertainty of the scale calibration at one low and one high kinetic energy value, to correct for small drifts of that scale and to define the expanded uncertainty of the calibration of the kinetic energy scale for a confidence level of 95%. This uncertainty includes contributions for behaviours observed in interlaboratory studies but does not cover all of the defects that could occur. This International Standard is not applicable to instruments with kinetic energy scale errors that are significantly non‐linear with energy, to instruments operated at relative resolutions poorer than 0.2% in the constant ΔE/E mode or poorer than 1.5 eV in the constant ΔE mode, to instruments requiring tolerance limits of ±0.05 eV or less or to instruments equipped with an electron gun that cannot be operated in the energy range 5–10 keV. This standard does not provide a full calibration check, which would confirm the energy measured at each addressable point on the energy scale and should be performed according to the manufacturer's recommended procedures. Crown Copyright © 2003. Published by John Wiley & Sons, Ltd.     

Monte Carlo simulation of full energy spectrum of electrons emitted from silicon in Auger electron spectroscopy

A Monte Carlo simulation including surface excitation, Auger electron‐ and secondary electron production has been performed to calculate the energy spectrum of electrons emitted from silicon in Auger electron spectroscopy (AES), covering the full energy range from the elastic peak down to the true‐secondary‐electron peak. The work aims to provide a more comprehensive understanding of the experimental AES spectrum by integrating the up‐to‐date knowledge of electron scattering and electronic excitation near the solid surface region. The Monte Carlo simulation model of beam–sample interaction includes the atomic ionization and relaxation for Auger electron production with Casnati's ionization cross section, surface plasmon excitation and bulk plasmon excitation as well as other bulk electronic excitation for inelastic scattering of electrons (including primary electrons, Auger electrons and secondary electrons) through a dielectric functional approach, cascade secondary electron production in electron inelastic scattering events, and electron elastic scattering with use of Mott's cross section. The simulated energy spectrum for Si sample describes very well the experimental AES EN(E) spectrum measured with a cylindrical mirror analyzer for primary energies ranging from 500 eV to 3000 eV. Surface excitation is found to affect strongly the loss peak shape and the intensities of the elastic peak and Auger peak, and weakly the low energy backscattering background, but it has less effect to high energy backscattering background and the Auger electron peak shape. Copyright © 2014 John Wiley & Sons, Ltd.     

Experimental determination of the effective attenuation length of palladium 3d 5/2 photoelectrons in a magnetron sputtered Pd nanolayer

An electron effective attenuation length (EAL) of 1.68 nm for Al Kα excited Pd 3d 5/2 photoelectrons with a kinetic energy of 1.152 keV has been determined experimentally using a sputtered Pd film deposited on an ultra flat fused quartz substrate. The film thickness was reduced by Ar ion sputtering several times in order to obtain different Pd film thicknesses which are used to determine experimental EAL values. These results are compared to data generated by using a Simulation of Electron Spectra for Surface Analysis (SESSA) simulation using an inelastic mean free path (IMFP) calculated with the Tanuma–Powell–Penn (TPP)‐2M formula and with ‘elastic scattering on and off’. Contributions to the uncertainty budget related to the experimental approach are discussed in detail. Proposals on how to further improve the approach are suggested. Copyright © 2016 John Wiley & Sons, Ltd.     

Total scattering cross sections for ethylene by electron impact for incident electron energies from 1 to 2000 eV

We report total scattering cross sections for C₂H₄ molecule by electron impact. Calculations are performed by using two different quantum mechanical methods and they cover the energy range from 1 to 2000 eV. For low energy calculations up to 15 eV, UK molecular R‐matrix code through QUANTEMOL‐N software is used, while intermediate to high energy (15–2000 eV) calculations were carried out by applying spherical complex optical potential formalism. Comparison is made with earlier measurements and theoretical data wherever available. A shape resonance is detected around 2 eV due to the ²B_2g symmetry of an electronic state that corresponds to the temporary negative ion formation of ethylene. The differential cross sections are also calculated for the energy range from 1 to15 eV for the scattering angles between 0º and 180º. © 2013 Wiley Periodicals, Inc.     

Variation of the electron inelastic mean free path during depth profiling of the Fe/Si interface as determined by quantitative REELS

The aim of this work is to determine the dependence of the electron inelastic mean free path (IMFP) at the Fe/Si interface during depth profiling by sputtering with 3 keV Ar⁺ ions. In order to estimate the variation of the IMFP at the interface, reflection electron energy‐loss spectroscopy (REELS) measurements were performed after different sputtering times at the Fe/Si interface with three different primary electron energies (i.e. 0.5, 1 and 1.5 keV). Even though it is highly likely that a compound (i.e. Fe_xSi) is formed at the interface, all the experimental REELS spectra could be analysed as a linear combination of those corresponding to pure Si and Fe. Using the model developed by Yubero and Tougaard for quantitative analysis of these REELS spectra we could estimate the IMFP values along the depth profile at the interface. The resulting IMFPs are observed to vary linearly with the average composition (as determined by REELS) at the Fe/Si interface as it is sputter depth profiled. The energy dependence of the IMFP for different compositions is presented and discussed. For completeness, we have determined the energy‐loss functions as well as the IMFPs of the pure elements (i.e. Fe and Si). Copyright © 2004 John Wiley & Sons, Ltd.     

Calculations of electron inelastic mean free paths. XIII. Data for 14 organic compounds and water over the 50 eV to 200 keV range with the relativistic full Penn algorithm

We have calculated inelastic mean free paths (IMFPs) for 14 organic compounds (26-n-paraffin, adenine, β-carotene, diphenyl-hexatriene, guanine, Kapton, polyacetylene, poly (butene-1-sulfone), polyethylene, polymethylmethacrylate, polystyrene, poly(2-vinylpyridine), thymine, and uracil) and liquid water for electron energies from 50 eV to 200 keV with the relativistic full Penn algorithm including the correction of the bandgap effect in insulators. These calculations were made with energy-loss functions (ELFs) obtained from measured optical constants and from calculated atomic scattering factors for X-ray energies. Our calculated IMFPs could be fitted to a modified form of the relativistic Bethe equation for inelastic scattering of electrons in matter from 50 eV to 200 keV. The average root-mean-square (RMS) deviation in these fits was 0.17%. The IMFPs were also compared with a relativistic version of our predictive Tanuma–Powell–Penn (TPP-2M) equation. The average RMS deviation in these comparisons was 7.2% for energies between 50 eV and 200 keV. This average RMS deviation is smaller than that found in a similar comparison for our group of 41 elemental solids (11.9%) and for our group of 42 inorganic compounds (10.7%) for the same energy range. We found generally satisfactory agreement between our calculated IMFPs and values from other calculations for energies between 200 eV and 10 keV. We also found reasonable agreement between our IMFPs for organic compounds and measured IMFPs for energies between 50 eV and 200 keV. Substantial progress for IMFP measurements for liquid water has been made in recent years through the invention of liquid water microjet photoelectron spectroscopy and droplet photoelectron imaging. We found that the IMFPs from these experiments and the associated analyses were larger than our IMFPs by factors between two and four for energies between about 30 eV and 1000 eV. The energy dependences of the measured IMFPs are, however, similar to that of our IMFPs in the same energy range. Since IMFPs calculated from the same algorithm for a number of inorganic compounds agree reasonably well with measured IMFPs for energies between 100 eV and 200 keV, the large differences between IMFPs for water from recent experiments and our results are surprising and need to be resolved with additional experiments.     

Polymer Electron Acceptors Based on Fluorinated Isoindigo Unit for Polymer Solar Cells

Most of efficient polymer electron acceptors for polymer solar cells (PSCs) are based on naphthalene diimide or perylene diimide as the electron deficient building block. In this paper, for the first time, we report polymer electron acceptors based on fluorinated isoindigo (F‐IID) as the electron deficient building block. We synthesized two polymer electron acceptors consisting of alternating F‐IID unit and thiophene/selenophen unit. They show low‐lying LUMO/HOMO energy levels of –3.69/–5.69 eV, high electron mobilities of 1.31×10^–5 cm²·V^–1·s^–1 and broad absorption spectra with the optical bandgap of 1.61 eV. PSC devices using the two F‐IID‐based polymers as polymer electron acceptors show encouraging power conversion efficiencies (PCEs) of up to 1.50% with an open‐circuit voltage (V_OC) of 0.97 V, a short‐circuit current density (J_SC) of 2.91 mA·cm^–2, and a fill factor (FF) of 53.2%. This work suggests a new kind of polymer electron acceptors based on F‐IID unit.     

Conjugated polymers based on 1,8‐naphthalene monoimide with high electron mobility

1,4,8,9‐Naphthalene diimides (NDIs) with strong electron accepting ability and high stability are excellent building blocks for semiconductor polymers. However, 1,8‐naphthalene monoimide (NMI) with similar structure and energy levels as that of NDI has never been used to construct conjugated polymers because of synthetic difficulty. Herein, 3,6‐dibromo‐NMI (DBNMI) with bulky alkyl groups was obtained effectively in a four‐step synthesis, and three donor‐acceptor (D‐A) type conjugated polymers based on NMI were firstly prepared. These polymers have strong absorption in the range of 300–600 nm, low LUMO level of 3.68 eV, and moderate bandgaps of 2.18 eV. Space charge limiting current measurements indicate these polymers are typical electron transporting materials, and the highest electron mobility is up to 5.8 × 10⁻³ cm² V⁻¹ s⁻¹, which is close to the star acceptor based on NDI (N2200, 5.0 × 10⁻³ cm² V⁻¹ s⁻¹). © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2018 , 56, 276–281     

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

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

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

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

Calculations of electron inelastic mean free paths. X. Data for 41 elemental solids over the 50 eV to 200 keV range with the relativistic full Penn algorithm

We have calculated inelastic mean free paths (IMFPs) for 41 elemental solids (Li, Be, graphite, diamond, glassy C, Na, Mg, Al, Si, K, Sc, Ti, V, Cr, Fe, Co, Ni, Cu, Ge, Y, Nb, Mo, Ru, Rh, Pd, Ag, In, Sn, Cs, Gd, Tb, Dy, Hf, Ta, W, Re, Os, Ir, Pt, Au, and Bi) for electron energies from 50 eV to 200 keV. The IMFPs were calculated from measured energy loss functions for each solid with a relativistic version of the full Penn algorithm. The calculated IMFPs could be fitted to a modified form of the relativistic Bethe equation for inelastic scattering of electrons in matter for energies from 50 eV to 200 keV. The average root‐mean‐square (RMS) deviation in these fits was 0.68%. The IMFPs were also compared with IMFPs from a relativistic version of our predictive Tanuma, and Powell and Penn (TPP‐2M) equation that was developed from a modified form of the relativistic Bethe equation. In these comparisons, the average RMS deviation was 11.9% for energies between 50 eV and 200 keV. This RMS deviation is almost the same as that found previously in a similar comparison for the 50 eV to 30 keV range (12.3%). Relatively large RMS deviations were found for diamond, graphite, and cesium as in our previous comparisons. If these three elements were excluded in the comparisons, the average RMS deviation was 8.9% between 50 eV and 200 keV. The relativistic TPP‐2M equation can thus be used to estimate IMFPs in solid materials for energies between 50 eV and 200 keV. We found satisfactory agreement between our calculated IMFPs and those from recent calculations and from measurements at energies of 100 and 200 keV. Copyright © 2015 John Wiley & Sons, Ltd.     

Partitioning of atomization energy

The present work provides a technique for partitioning the atomization energy of a molecule into diatomic contributions. The method is largely based on the redistribution of the kinetic energy term in Mayer's energy partitioning and uses free‐atom energies as a reference. The comparison of Mayer's original method, the alternative Ichikawa–Yoshida approach, and the new atomization energy partitioning (AEP) shows that the new approach has advantages in describing trends in diatomic energies in molecules with triple bonds, as well as for hydrogen bonds. The proposed AEP is a viable alternative to Mayer's energy partitioning method. © 2007 Wiley Periodicals, Inc. Int. J. Quantum Chem, 2008     

Relation between Kinetic and Exchange Energies in a Relativistic Inhomogeneous Electron Liquid

Abstract

The relativistic kinetic energy of a weakly inhomogeneous electron liquid can be calculated from Dirac's equation, as recently shown by Baltin and March. Here this result is combined with the relativistic exchange energy as given by MacDonald and Vosko to yield the exchange energy density in terms of kinetic energy and electron densities.