Comparison of energy‐loss functions from REELS spectra with surface and bulk energy loss functions for Ag

Effective energy‐loss functions were derived from the reflection electron energy‐loss spectroscopy (REELS) spectra of Ag by an extended Landau approach. The effective energy‐loss functions obtained are close to the surface energy‐loss function in the low‐energy‐loss region, but tend to be closer to the bulk energy‐loss function in the higher energy‐loss region for higher primary energy. The REELS spectra incorporating the effective energy‐loss function are also reproduced in a Monte‐Carlo simulation model and confirm that the simulation reproduces the experimental REELS spectra with considerable success. Copyright © 2003 John Wiley & Sons, Ltd.     

Construction of database of effective energy‐loss functions

Effective energy‐loss functions for Al, Cu, Ag and Au were derived from the reflection electron energy‐loss spectroscopy (REELS) spectra for 1 keV electrons using extended Landau theory. Features of the obtained effective energy‐loss functions are close to those of optical surface energy‐loss functions, revealing the significant contribution of the low energy loss below a few tens of electron‐volts in the REELS spectrum for Cu, Ag and Au. The REELS spectra were reproduced using the newly derived effective energy‐loss functions, leading to the confirmation that this type of database of the effective energy‐loss function is very useful not only for more comprehensive understanding of the measured spectrum of surface electron spectroscopies but also for practical background subtraction in surface electron spectroscopy. Copyright © 2003 John Wiley & Sons, Ltd.     

Evaluation of robustness to surface conditions of the target factor analysis method for determining the dielectric function from reflection electron energy loss spectra: Application to GaAs

Target factor analysis (TFA) of a series of angle‐resolved reflection electron energy loss spectra (REELS) was recently demonstrated to be a useful method to determine bulk energy loss functions (ELFs), which by the TFA are separated from the surface‐loss structures of REELS. The dielectric function is then readily derived by Kramers–Kronig analysis of the ELF. The advantage of the method compared with other methods, which are also based on the analysis of REELS, is that the condition of the outermost surface region is unimportant because the excitations that occur there are removed by the TFA and ideally a pure bulk component is determined. Our method is thus particularly useful for determining the ELF from compound materials that are hard to clean without modifying the outermost atomic layers. In this paper, the robustness of the method was studied by applying it to three GaAs samples with different surface compositions caused by different surface cleaning methods. The results showed that when electrons of energy 3000–4500 eV were used, the resulting bulk ELFs were essentially identical except for small differences for the sample that had the largest thickness of the modified surface layer. It is concluded that this is a useful method, provided that the thickness of the modified layer is kept to a minimum by using shallow angle sputtering and by using REELS electrons at a sufficiently high energy that a major part of the electron trajectories are at a depth larger than the thickness of the modified surface layer. Copyright © 2013 John Wiley & Sons, Ltd.     

Memory effect on the inelastic interaction of electrons moving parallel to a solid surface

It is generally assumed that two successive inelastic interactions between an electron and a solid are independent of each other. In other words, the electron has no memory of its previous interaction. However, the previous interaction of the electron generates a potential that should influence its succeeding inelastic interaction. The aim of this work is to establish a model to account for the memory effect of an electron between two successive inelastic interactions. On the basis of the dielectric response theory, formulae for differential inverse inelastic mean free paths (DIIMFPs) and inelastic mean free paths (IMFPs) considering the memory effect were derived for electrons moving parallel to a solid surface by solving the Poisson equation and applying suitable boundary conditions. These mean free paths were then calculated with the extended Drude dielectric function for a Cu surface. It was found that the DIIMFP and the IMFP with the memory effect for electron energy E lay between the corresponding values without the memory effect for electron energy E and previous energy E₀. The memory effect increased with increasing electron energy loss, E₀ ? E, in the previous inelastic interaction. Copyright © 2005 John Wiley & Sons, Ltd.     

Theoretical study of the surface excitation parameter from reflection‐electron‐energy‐loss spectra

A theoretical method to determine the so‐called surface excitation parameter (SEP) is presented. This method is based on the modelling of reflection‐electron‐energy‐loss spectroscopy and more particularly on the analysis of energy‐differential inelastic electron scattering cross sections calculated within the model. The SEP is extracted from theoretical cross‐section spectrum by calculating the ratio between the surface loss component of the spectrum and the elastic peak intensity. The calculations have been performed entirely with the dielectric function, using the software QUEELS (Quantitative analysis of Electron Energy Losses at Surfaces) recently developed by Yubero and Tougaard [Surf. Interface Anal. 2004; 36 : 824]. The angular distribution of SEP is calculated for angles between 10° and about 70° for aluminium and silicon. We propose also an extension of the method for materials (e.g. copper) that do not present clear surface and volume plasmons. Copyright © 2005 John Wiley & Sons, Ltd.     

Surface excitation parameter for 12 semiconductors and determination of a general predictive formula

The surface excitation parameter (SEP) is theoretically calculated for 12 semiconductors (GaN, GaP, GaSb, GaAs, InSb, InAs, InP, SiC, ZnSe, ZnS, Si and Ge) and for Ni (which is usually used as a reference in experiments) for electron energies between 300 eV and 3400 eV, and for angles between 0° and 70° to the surface normal. We use our previous definition of SEP, as the change in excitation probability, for an electron, caused by the presence of the surface in comparison with an electron moving the same distance in an infinite medium. The calculations are performed within the dielectric response theory by means of the QUEELS‐ε(k, ω)‐REELS software determining the energy‐differential inelastic electron scattering cross‐sections for reflection‐electron‐energy‐loss spectroscopy (REELS), and for which the only input is the dielectric function of the medium. By fitting to these SEP values as well as our previous ones, i.e. from 27 materials, including metals, oxides, polymers and semiconductors, we also establish a simple equation depending on the generalized plasmon energy and the energy band gap of the material which allows to estimate the SEP when the dielectric function is not available. Copyright © 2009 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.     

Optical constants of organic insulators in the UV range extracted from reflection electron energy loss spectra

Reflection electron energy loss spectroscopy (REELS) spectra were measured for seven insulating organic compounds (DNA, Irganox 1010, Kapton, polyethylene [PE], poly(methyl methacrylate) [PMMA], polystyrene [PS] and polytetrafluoroethylene [PTFE]). Optical constants and energy band gaps were extracted from the measured REELS spectra after elimination of multiple electron scattering via a deconvolution and fitting the normalised single scattering energy loss spectra to Drude and Drude–Lindhard model dielectric functions, constrained by the Kramers–Kronig sum and f-sum rules. Satisfactory agreement is found for those optical constants for which literature data exists. For PTFE, the observed features in the optical data correspond to its electronic structure.     

Surface excitations in electron spectroscopy. Part I: dielectric formalism and Monte Carlo algorithm

The theory describing energy losses of charged non‐relativistic projectiles crossing a planar interface is derived on the basis of the Maxwell equations, outlining the physical assumptions of the model in great detail. The employed approach is very general in that various common models for surface excitations (such as the specular reflection model) can be obtained by an appropriate choice of parameter values. The dynamics of charged projectiles near surfaces is examined by calculations of the induced surface charge and the depth‐ and direction‐dependent differential inelastic inverse mean free path (DIIMFP) and stopping power. The effect of several simplifications frequently encountered in the literature is investigated: differences of up to 100% are found in heights, widths, and positions of peaks in the DIIMFP. The presented model is implemented in a Monte Carlo algorithm for the simulation of the electron transport relevant for surface electron spectroscopy. Simulated reflection electron energy loss spectra are in good agreement with experiment on an absolute scale. Copyright © 2012 John Wiley & Sons, Ltd.     

Monte‐Carlo simulation of x‐ray photoelectron emission from silver

Silver 3d x‐ray photoelectron spectroscopy (XPS) spectra were simulated with the Monte‐Carlo method using an effective energy‐loss function that was derived from a reflected electron energy‐loss spectroscopy (REELS) analysis based on an extended Landau approach. After confirming that Monte‐Carlo simulation based on the use of the effective energy‐loss function can successfully describe the experimental REELS spectrum and Ag 3d XPS spectrum, we applied Monte‐Carlo simulation to predict the angular distribution of Ag 3d x‐ray photoelectrons for different x‐ray incidence angles and different photoelectron take‐off angles. The experimental photoelectron emission microscope that we are constructing was confirmed as being close to the optimum configuration, in which the x‐ray incident angle as measured from the surface normal direction is 74° and the photoelectron take‐off angle is set normal to the surface. The depth distribution functions of the Ag 3d X‐ray photoelectrons for different energy windows suggest that the photoelectron emission microscope will exhibit greater surface sensitivity for narrower photoelectron energy windows. Copyright © 2003 John Wiley & Sons, Ltd.     

Dynamic Determination of Some Optical and Electrical Properties of Galena Natural Mineral: Potassium Ethyl Xanthate Solution Interface

This paper presents results concerning optical and electrical properties of galena natural mineral and of the interface layer formed between it and the potassium ethyl xanthate solution. The applied experimental method was differential optical reflectance spectroscopy over the UV–Vis/NIR spectral domain. Computations were made using the Kramers–Kronig formalism. Spectral dependencies of the electron loss functions, determined from the reflectance data obtained from the polished mineral surface, display van Hove singularities, leading to the determination of its valence band gap and electron plasma energy. Time dependent measurement of the spectral dispersion of the relative reflectance of the film formed at the interface, using the same computational formalism, leads to the dynamical determination of the spectral variation of its optical and electrical properties. We computed behaviors of the dielectric constant (dielectric permittivity), the dielectric loss function, refractive index and extinction coefficient, effective valence number and of the electron loss functions. The measurements tend to stabilize when the dynamic adsorption-desorption equilibrium is reached at the interface level.     

Calculations of Energy-Loss Function for 26 Materials

We present a fitting calculation of energy-loss function for 26 bulk materials, including 18 pure elements (Ag, Al, Au, C, Co, Cs, Cu, Er, Fe, Ge, Mg, Mo, Nb, Ni, Pd, Pt, Si, Te) and 8 compounds (AgCl, Al₂O₃, AlAs, CdS, SiO₂, ZnS, ZnSe, ZnTe) for application to surface electron spectroscopy analysis. The experimental energy-loss function, which is derived from measured optical data, is fitted into a finite sum of formula based on the Drude-Lindhard dielectric model. By checking the oscillator strength-sum and perfectscreening-sum rules, we have validated the high accuracy of the fitting results. Furthermore, based on the fitted parameters, the simulated reflection electron energy-loss spectroscopy (REELS) spectrum shows a good agreement with experiment. The calculated fitting parameters of energy loss function are stored in an open and online database at http://micro.ustc.edu.cn/ELF/ELF.html.     

Influence of Nonlocal Effects on Kinetic Parameters of Heterogeneous Charge Transfer Reactions

The influence of the spatial dispersion of the solvent and of the effect of the electrical field penetration into a metal on the free energy of the solvent reorganization and the activation free energy for heterogeneous charge transfer reactions is studied. The calculations are based on the exactly solved model of a sharp metal/electrolyte interface, the model of a Born sphere for the ion, and the three-mode approximation for the dielectric function of the solvent. In the sharp-interface model, in the case of a mirror reflection, a relationship for the dielectric tensor of a heterogeneous system comprising two contacting media with a plane interface is obtained, along with an expression for the potential created by a point charge. This expression formally coincides with the expression derived earlier by Vorotyntsev and Kornyshev, but it contains true bulk dielectric functions of contacting media. In the model of the Born sphere for the ion and the three-mode approximation for the dielectric function of the solvent, an expression for the potential of image forces, which determines the dependence of the solvent reorganization energy on the distance from the reacting ion to the electrode, is obtained. It is shown that both the reorganization energy and the activation free energy decrease with decreasing distance from the ion to the electrode. The calculation results are compared with estimates of the reorganization energy obtained from experimental data for the reaction Fe³⁺/Fe²⁺ and the reaction of the hydronium ion discharge.     

Polarizable empirical force field for alkanes based on the classical Drude oscillator model

Recent extensions of potential energy functions used in empirical force field calculations have involved the inclusion of electronic polarizability. To properly include this extension into a potential energy function it is necessary to systematically and rigorously optimize the associated parameters based on model compounds for which extensive experimental data are available. In the present work, optimization of parameters for alkanes in a polarizable empirical force field based on a classical Drude oscillator is presented. Emphasis is placed on the development of parameters for CH3, CH2, and CH moieties that are directly transferable to long chain alkanes, as required for lipids and other biomolecules. It is shown that a variety of quantum mechanical and experimental target data are reproduced by the polarizable model. Notable is the proper treatment of the dielectric constant of pure alkanes by the polarizable force field, a property essential for the accurate treatment of, for example, hydrophobic solvation in lipid bilayers. The present alkane force field will act as the basis for the aliphatic moieties in an extensive empirical force field for biomolecules that includes the explicit treatment of electronic polarizability.     

Momentum transfer effects in near surface electron energy loss

We examine two formulations for the differential surface excitation parameter (DSEP): one provided by Tung et al. and the other given by the Chen–Kwei position‐dependent differential inverse inelastic mean free path integrated over the electron trajectory. We demonstrate that the latter converges to the former provided that the dielectric function of the solid does not depend on the momentum transfer or it depends on just the momentum transfer component parallel to the surface. Tung's DSEP represents therefore an approximation to the Chen–Kwei DSEP calculated for a dielectric function with no restrictions on the momentum dependence. The approximation is shown to work in the limit of small momentum transfer and to imply an error of 4%–5% for electrons traveling through the solid with energy E = 1 keV. Copyright © 2015 John Wiley & Sons, Ltd.     

Surface excitation parameter for selected polymers

The surface excitation parameter (SEP) is theoretically determined for different polymers, namely, polyethylene (PE), polystyrene (PS), polyacetylene (PA) and polymethyl methacrylate (PMMA), for electron energies between 300 and 5000 eV and for angles between 0 and 70^o to the surface normal. We use our previous definition of SEP as the change in excitation probability of an electron caused by the presence of the surface in comparison with an electron moving in an infinite medium. The calculations are performed within the dielectric response theory by means of the QUEELS‐ε(k, ω)‐ REELS software determining the energy‐differential inelastic electron scattering cross‐sections for reflection‐electron‐energy‐loss spectroscopy (REELS). More precisely, the volume component for an infinite medium is subtracted from the calculated REELS cross‐section and in this way the surface excitation component of the cross‐section is determined and the SEP calculated. We find that the presence of an energy band gap reduces the SEP values compared to those for metals, and this decrease is larger for polymers with larger gaps. Copyright © 2008 John Wiley & Sons, Ltd.     

Effective depths for surface excitation derived by reflection electron energy‐loss spectroscopy analysis

A method of estimation is proposed for determining the effective depth of surface excitation. For this, the effective differential inverse inelastic mean free path (DIIMFP) is presumed to be represented as a linear combination of theoretical DIIMFPs for surface and bulk excitation, which are derived by the use of optical dielectric constants. The effective DIIMFP in the approach is derived by a reflected electron energy‐loss spectroscopy analysis based on the extended Landau approach. The present analysis for 1 kV electrons has led to a simple estimation of the effective depth for surface excitations (～14.5 Å for Al and ～21 Å for Ag), agreeing well with an estimation given by υ/ω _s, where υ and ω _s are the velocity of the primary electrons and the average surface plasmon frequency, respectively. Copyright © 2004 John Wiley & Sons, Ltd.     

Effective dielectric functions of samples obtained by evaporation of alkali halides

This paper investigates the dielectric properties of inhomogeneous samples consisting of small alkali halide particles (NaCl, KBr) on gold-coated substrates. Our reflection measurements in the far infrared can be simulated as a thin layer of the powder with an effective dielectric function on a perfectly reflecting substrate. Scanning electron micrographs provide useful information about sample topology. Several mixing formulas (e.g. the Maxwell-Garnett, the Bruggeman- and the Looyenga-formula) lead to effective dielectric functions neglecting the individual arrangement of the particles. The essence of our work is that, in contrast, the general ansatz of the Bergman spectral representation has to be employed in order to take into account topology effects on the dielectric function based on the so-called spectral densityg adjustable to the specific situation.