Electronic and optical properties of Cu, CuO and Cu2O studied by electron spectroscopy

The electronic and optical properties of Cu, CuO and Cu(2)O were studied by x-ray photoelectron spectroscopy (XPS) and reflection electron energy-loss spectroscopy (REELS). We report detailed Cu 2p, Cu LVV, O 1s and O KLL spectra which are in good agreement with previous results. REELS spectra, recorded for primary energies in the range from 150 to 2000 eV, were corrected for multiple inelastically scattered electrons to determine the effective inelastic scattering cross section. The dielectric functions and optical properties were determined by comparing the experimental inelastic electron scattering cross section with a simulated cross section calculated within the semi-classical dielectric response model in which the only input is Im(-1/ε) by using the QUEELS-ε(k,ω)-REELS software package. By Kramers-Kronig transformation of the determined Im(-1/ε), the real and imaginary parts (ε(1) and ε(2)) of the dielectric function, and the refractive index n and extinction coefficient k were determined for Cu, CuO, and Cu(2)O in the 0-100 eV energy range. Observed differences between Cu, CuO and Cu(2)O are mainly due to modifications of the 3d and O 2p electron configurations.     

Accuracy of the Tougaard method for quantitative surface analysis. Comparison of the Universal and REELS inelastic cross sections

Three tests have been performed to investigate whether cross sections determined experimentally from reflection electron energy loss spectroscopy (REELS) are more accurate than the Universal cross section for background correction of electron spectra. In the first test, the shape of background corrected spectra from a thin layer and from an infinitely thick layer of the same element were compared for the Ag3d, Au4d, and Yb4d peaks. It was found that the Universal cross section is more accurate than the experimentally determined REELS cross sections to determine consistently the peak shape of background corrected spectra. In the second test, the intensity ratio of the two components in the Au4d, Cu2p, Zn2p, and Yb4d doublets were compared to theoretical photoionization cross sections. For both the Universal and the REELS inelastic cross sections, the obtained intensity ratios agree well with theory. In the third test, we compare with theory the peak intensity ratios to Au4d of major peaks from Si, Cu, Ag, Yb, and Au obtained by using the Universal and the REELS cross sections for background correction. For the metals, the two cross sections give peak intensity ratios that are equally close to theory to within the expected uncertainties in the theoretical peak intensity ratios. However, for Ag with application of the Universal cross section the deviation from theory is slightly larger. For Si the REELS cross section is clearly most accurate.     

Comparative analysis of characteristic electron energy loss spectra and inelastic scattering cross-section spectra of Fe

The inelastic electron scattering cross section spectra of Fe have been calculated based on experimental spectra of characteristic reflection electron energy loss as dependences of the product of the inelastic mean free path by the differential inelastic electron scattering cross section on the electron energy loss. It has been shown that the inelastic electron scattering cross-section spectra have certain advantages over the electron energy loss spectra in the analysis of the interaction of electrons with substance. The peaks of energy loss in the spectra of characteristic electron energy loss and inelastic electron scattering cross sections have been determined from the integral and differential spectra. It has been shown that the energy of the bulk plasmon is practically independent of the energy of primary electrons in the characteristic electron energy loss spectra and monotonically increases with increasing energy of primary electrons in the inelastic electron scattering cross-section spectra. The variation in the maximum energy of the inelastic electron scattering cross-section spectra is caused by the redistribution of intensities over the peaks of losses due to various excitations. The inelastic electron scattering cross-section spectra have been analyzed using the decomposition of the spectra into peaks of the energy loss. This method has been used for the quantitative estimation of the contributions from different energy loss processes to the inelastic electron scattering cross-section spectra of Fe and for the determination of the nature of the energy loss peaks.     

Studies of EPES REELS spectra of polyethylenes aided by line shape analysis—Effect of electron irradiation

Polyethylenes of different density, branching structure, crystallographic order, and their degradation due to electron beam were studied using elastic peak electron spectroscopy (EPES) and reflection electron energy loss spectroscopy (REELS) aided with line shape analysis by the pattern recognition (PR) method. This approach offers an algorithm of classification derived from a reference set, i.e. set of spectra recorded from standards exposed to low electron dose (about few C m⁻²), i.e. polyethylene (100% of C sp³ bonds) and polystyrene (75% of C sp² bonds). Then, the obtained classifier is applied for identification of spectra recorded from polyethylenes exposed to electron beam (doses from 40 to 60 C m⁻²). The EPES REELS spectra are analyzed in the vicinity of electron quasi-elastic and inelastic losses. Due to electrons undergoing a quasi-elastic scattering from atoms of different atomic numbers, i.e. carbon and hydrogen, for undamaged polymers the surface hydrogen content can be evaluated.Changes due to electron irradiation in polyethylenes are indicated by decreasing content of hydrogen, increasing C sp² content and changes in the π loss peak in the REELS spectra. Results of PR method are consistent with results obtained from the C 1s XPS spectra fitting and the width of C KLL XAES spectra (parameter D). Highest stability under electron irradiation was shown by polyethylene of largest molecular weight and most linear branching structure. Application of the PR method to EPES REELS spectra allows to distinguish different polyethylenes and quantify the C sp² content.     

Deconvolution of inelastic background signal from XPS spectra of homogeneous solids

For noble and transition metals, the product of the inelastic electron mean free path and the differential inelastic scattering cross section is a weak function of both the particular metal and the electron energy. It is demonstrated that this property can be useful in the removal of inelastically scattered electrons from XPS spectra of homogeneous solids.     

New opportunities for quantitative analysis as applied to reflected electron energy loss spectroscopy of Fe/Si structures

The feasibility of determining the elemental composition, chemical state, and element distribution across the depth in a subsurface region using the computer simulation of the electron inelastic scattering cross section is demonstrated with iron layers on silicon substrates. Analysis is carried out based on the dielectric theory and on the experimental determination of the product of the electron inelastic mean free path by the inelastic scattering cross section from reflected electron energy loss spectra.     

Simple algorithm for quantitative analysis of reflection electron energy loss spectra (REELS)

A detailed comparison of two different physical approaches for quantitative analysis of reflection electron energy loss spectra (REELS) is presented. The Tougaard–Chorkendorff (TC) algorithm [S. Tougaard, I. Chorkendorff, Phys. Rev. B35 (1987) 6570] is analyzed theoretically and applied to experimental spectra of four elemental solids (Si, Cu, Ag, and Au). A closed expression is derived for the quantity retrieved by the TC-algorithm, the so-called “effective” cross section, which was originally only given as a recursive procedure. Single scattering loss distributions are derived from the experimental spectra using the bivariate reversal method [W.S.M. Werner, Phys. Rev. B74 (2006) 075421]. The latter agree satisfactorily with density functional theory (DFT) calculations and other data found in the literature. Using these single scattering loss distributions, the TC “effective” cross section can be perfectly reproduced if the fact is taken into account that the effective cross section is not a single scattering loss distribution and is governed to a significant extent by elastic scattering. On the basis of the above results, a dramatically simplified deconvolution scheme for quantitative analysis of REELS is developed.     

Analysis of reflection electron energy loss spectra (REELS) for determination of the dielectric function of solids: Fe, Co, Ni

A simple procedure is developed to simultaneously eliminate multiple scattering contributions from two reflection electron energy-loss spectra (REELS) measured at different energies or for different experimental geometrical configurations. The procedure provides the differential inverse inelastic mean free path (DIIMFP) and the differential surface excitation probability (DSEP). The only required input parameters are the differential cross section for elastic scattering and a reasonable estimate for the inelastic mean free path (IMFP). No prior information on surface excitations is required for the deconvolution. The retrieved DIIMFP and DSEP can be used to determine the dielectric function of a solid by fitting the DSEP and DIIMFP to theory. Eventually, the optical data can be used to calculate the (differential and total) inelastic mean free path and the surface excitation probability. The procedure is applied to Fe, Co and Ni and the retrieved optical data as well as the inelastic mean free paths and surface excitation parameters derived from it are compared to values reported earlier in the literature. In all cases, reasonable agreement is found between the present data and the earlier results, supporting the validity of the procedure.     

Validity of the semi-classical approach for calculation of the surface excitation parameter

The problem of surface plasmon excitation by moving charges has been elaborated by several different approaches, mainly based on dielectric response theory within either semi-classical or quantum mechanical frameworks. In this work, a comparison of the surface excitation effect between two different frameworks is made by calculation of the differential inverse inelastic mean free path (DIIMFP) and a Monte Carlo simulation of reflection electron energy loss spectroscopy (REELS) spectra. A semi-classical modeling of the interaction between electrons and a solid surface is based on analyzing the work done by moving electrons; the stopping power and inelastic cross section are derived with the induced potential. On the other hand, a quantum mechanical approach is based on derivation of the complex inhomogeneous self-energy of the electrons. The numerical calculation shows that the semi-classical model presents almost the same values of DIIMFP as by the quantum model except at the glancing condition. The simulation of REELS spectra for Ag and SiO(2) as well as a comparison with experimental spectra also confirms that a good agreement with the spectral shape is found among the two simulation results and the experimental data.     

Reflection electron energy loss spectroscopy of aluminum

Reflection electron energy loss spectra (REELS) of Al(111) single crystal and of the aluminum polycrystalline (poly Al) film were measured at 200 eV and 1000 eV electron energies for a variety of experimental geometries and were mutually compared. No anisotropy was found for the poly Al, as expected. Polar intensity plots evaluated from the elastic (no loss) and inelastic first surface plasmon- and first bulk plasmon-loss intensities of the Al(111) surface show clearly discernable peaks for both considered electron energies. Their positions on the angular axis are the same for the elastic as well as for the inelastic, surface and bulk plasmon-loss peaks. The polar plots of intensities of the elastically and inelastically reflected electrons were compared to calculated intensities of photoelectrons emitted from the Al 2s core level to the same kinetic energy. Peak positions in the theoretically determined polar plots of electron intensities agree with those obtained experimentally in REELS.     

Deconvolution of loss features from electron spectra

The problem of deconvoluting loss features from energy spectra of electrons emitted from solids is investigated. A new formula is found for the case of an exponentially decreasing intensity from the solid surface of electron emitters. This as well as a formula for the case of a homogeneous distribution of electron emitters is studied in detail. Central in the formulas is the cross section for inelastic scattering. Under the assumption that angular deflection of electrons can be ignored the formulas are exact, i.e. the effect of all multiple scattering events is included. Through numerical calculations on Al spectra the effect of deconvolution is tested, and it is demonstrated that a small deviation from the exact procedure can result in spurious structure in the deconvoluted spectrum.     

Electron spectroscopy of iron disilicide

We have reported on the results of a complex investigation of iron disilicide FeSi₂ using characteristic electron energy loss spectroscopy, inelastic electron scattering cross section spectroscopy, and X-ray photoelectron spectroscopy. It has been shown that the main peak in the spectra of inelastic electron scattering for FeSi₂ is a superposition of two unresolved peaks, viz., surface and bulk plasmons. An analysis of the fine structure of the spectra of inelastic electron scattering cross section by their decomposition into Lorentzlike Tougaard peaks has made it possible to quantitatively estimate the contributions of individual energy loss processes to the resulting spectrum and determine their origin and energy.     

Excitation of electron-hole pairs in low-energy electron scattering from surfaces

We calculate the Distorted Wave Born Aprroximation differential cross section for the inelastic scattering of low-energy electrons reflected from metallic surfaces via the dynamically screened Coulomb potential, and in particular the excitation of low-energy electron-hole pairs. We discuss the angular and energy dependence of the loss spectra, and the application of this method to study the spectrum of the electron-hole excitations at surfaces.     

Reflected electron-energy-loss spectra,differential inverse inelastic mean free paths,and angular resolved X-ray photoelectron spectra of a niobium sample

A technique for recovering the differential inverse inelastic mean free paths (DIIMFP) of electrons in Nb from the reflected electron energy loss spectra (REELS) at initial energies of 5 to 40 keV using a threelayer model of the sample surface is presented. The recovered DIIMFP are used for analyzing X-ray photoelectron spectra measured at different viewing angles. Comparison with experimental data is carried out.     

Quantitative interpretation of EELS and REELS spectra

A critical analysis of the present day Electron Energy Loss Spectroscopy (EELS) data interpretation methods has been done. The necessity for the consideration of a target as a multilayered structure with different inelastic energy loss cross sections in the surface and the bulk layers has been shown to be a reality both for the transmission EELS and the reflection EELS (REELS). A method to reconstruct inelastic energy loss cross sections in various target layers from the experimental data has been presented. Essential qualitative and quantitative dependence of the path length distribution function for reflected electrons as a function of scattering angle has been revealed. The tested method for extraction of the information from REELS experiments with angular resolution has been presented.Received: 9 October 2003, Published online: 19 February 2004PACS: 34.80.-i Electron scattering - 34.50.Bw Energy loss and stopping power - 25.30.Fj Inelastic electron scattering to continuum     

Inelastic electron tunnelling from a metal tip

A simple model for inelastic electron tunnelling between a metal probe tip and a surface is presented. The inelastic tunnelling cross section resulting from vibrational or electronic excitation of an adsorbed molecule is estimated. The role thermal and, more important, non-thermal processes have on the measurement process is also discussed.     

Quantitative AES and XPS: convergence between theory and experimental databases

Experimental spectral databases have been recorded for AES and XPS using fully calibrated instruments. These instruments have been calibrated so that the spectra have the true shape and peak area intensities may be integrated to give absolute yields for AES and relative yields for XPS. Removal of all the backgrounds requires care but may be completed by using information from both databases. The resultant yields may be compared with theory. The correlations for AES are the more complex and involve the total intensities for all transitions originating in each shell. The correlations are excellent using significant changes to the traditional approach. These involve the use of the Casnati et al. ionisation cross section and the restriction of the number of electrons for use in the inelastic mean free path calculations to electrons of 14 eV or less binding energy in the s, p or d sub-shells. The average ratio of experiment to theory is 1.04 with a standard uncertainty of the mean of 4%. Results for XPS are excellent using Scofield’s ionisation cross section together with the above rules for the inelastic mean free path calculations. Improvements for certain elements are still needed for removing the inelastically scattered Auger and photoelectrons in both databases. To assist analysts in using such databases a simpler measure of Auger electron intensity is developed involving differential spectra broadened with a Gaussian function of 15–20 eV width. The peak-to-peak intensities from these broadened spectra are reasonably closely related to the peak area of the direct spectra except in a few exceptional cases. The unbroadened differential spectra show strong contributions from the spectrometer resolution and changes in the chemical state which are avoided by the spectral broadening. To simplify calculations for the analyst when studying homogeneous materials by AES and XPS, the relative sensitivity factors are re-defined to be for an average matrix instead of the pure element. This leads to a matrix-less equation for calculating compositions from the spectra.     

Quantitative analysis of reflection electron energy loss spectra of aluminum

Reflection electron energy loss spectra of aluminium were studied for primary energies in the 500–2000 eV and loss energies in the 0–80 eV range. The absolute intensity observed could be well explained by using an electron-gas model for the inelastic electron scattering cross section and by assuming that the distribution of the path lengths travelled in the solid is exponentially decreasing. The attenuation length in this distribution is found to be on the order of the transport mean free path for elastic electron scattering.     

Direct numerical reconstruction of inelastic cross sections from REELS and ISS spectra

The reconstruction of inelastic scattering cross sections faces two problems: the measured signal (energy spectrum) is a multiple scattering signal; the inelastic energy loss is nonuniform over the target depth. In this paper, we present a method for numerical reconstruction of cross sections from characteristic energy loss spectra, which efficiently solves both problems within a multilayer model. It is shown that the inverse problem of cross section extraction in the three-layer model is ill-conditioned, and the method is practically inapplicable to the three-layer model. The direct numerical reconstruction method yields a strongly “noised” result and can be applied only to obtain a priori information on the inelastic cross section form for further fitting. Using a combination of two methods, inelastic scattering cross sections were reconstructed for aluminum from characteristic energy loss spectra at probe beam energies of 5 and 40 keV. It is shown that ionization in solids should be described as a local process and as a collective one using the dispersion formula similarly to the case of excitation plasmons.     

Coupling to the elastic channel in electron impact spectroscopy: A simple second born model and its application to excitation of the 61P1 state of mercury and to the excitation of molecules

The matrix element in the infinite channel close coupling approximation responsible for coupling to the elastic channel in electron impact inelastic encounters is investigated. The contribution from the imaginary part of the energy denominator in the elastic coupling matrix element for dipole allowed transitions is shown to yield large angle differential cross sections in good agreement with experiment. This coupling mechanism predicts that the shape of the inelastic differential cross section will be dominated by the shape of the elastic cross section in the large angle high energy limit. In fact the coupling matrix element exhibits a dependence on incident energy, k², and momentum transfer, K, of the form 1/kK² which is in agreement with the theoretical predictions of Huo and means that in the limit of high incident energy the non-first-Born elastic coupling will dominate the angular dependence of the inelastic differential cross section at large scattering angles. In the case of molecular electron impact spectra it is shown that the analog of the Massey—Moore coherence features depending on the symmetry of the states involved in the excitation process will also occur in the coupling contribution. It is suggested that this new mechanism for producing coherent features in inelastic differential cross sections may be the explanation of the coherent features observed experimentally by Karle and Swick.It can be concluded on the basis of the results obtained here that the coupling to the elastic cross section provided by the imaginary contribution from the second Born energy denominator is sufficient to explain presently available experimental data on the large angle differential cross section and spin polarization. The simple coupling model was found to be inadequate to explain the small angle differential cross section in the range 10° < θ < 30° even at incident energies as high as 400 eV. The calculations also showed significant differences between first and second Born calculations at zero scattering angle. No conclusion can be drawn about this observation as all the omitted terms should make significant contributions in the small angle region. It is important to again emphasize that the large angle scattering even in the limit of high incident electron energy will be completely dominated by the coupling to the elastic channel^{7, 11}. On the basis of this work it appears that the coherent structure in the large angle inelastic differential cross section observed by Swick and Karle^{12, 13} at incident electron energies in the keV region may well be due to coupling to the elastic channel.