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The method based on the elastic peak electron spectroscopy was used to determine the energy dependence of the IMFP for different carbon samples and selected metals. This method provides the values of the IMFP corresponding to the definition of the E-42 Committee of the ASTM. The measurements were made with respect to the aluminium standard. The main features of the method were extensively discussed: the choice of the aluminium standard, quantification of the elastic peak intensity, and the validity of the theoretical model relating the elastic peak intensity to the IMFP. The values of the IMFP were obtained for energies ranging from 270 to 2350 eV. The results are in good agreement with the theoretical data available in the literature. Attention is drawn to the fact that the density of the sample should be known, since this parameter influences greatly the resulting values of the IMFP.

The parameters describing scattering of electrons by atoms, which usually involve multiple integration of the atomic potentials, may be severely affected by the accuracy of these potentials. In the present work an iterative procedure is proposed providing a sequence of solutions of the Thomas-Fermi equation with increasing accuracy. Such a sequence makes it possible to establish the sensitivity of a given parameter to the accuracy of the atomic potential, and consequently to determine the accurate value of this parameter. Based on the present solutions, the differential scattering cross-sections for the Thomas-Fermi atom are calculated, and are found to deviate from the literature data.

The energy dependence of the ionization cross-section and the backscattering factor resulting from the experimental method of Gallon are shown to be affected by simplifying the definition of the backscattering factor. In the case of Auger transitions following the ionization of the L 3 shell the errors in the ionization cross-section and the backscattering factor reach 10% and 4%, respectively. Larger deviations are probable for Auger transitions involving higher shells.

The values of the screening parameter mu infinity have been recalculated on the basis of accurate solutions of the Thomas-Fermi equation. The values of mu infinity calculated in the present work are larger by 10-20% than the values published in the literature.

In Parts I and II the inelastic mean free path of electrons has been determined from their elastic scattering measured by elastic peak electron spectroscopy. The simple theoretical model based on the Thomas-Fermi-Dirac (TFD) atomic potential has been extended to higher kinetic energies. Theσ eff effective andσ τ total elastic scattering cross sections have been calculated forZ=2–50 atomic number andE=5–40 keV kinetic energy range. Theσ eff values deduced from Riley’s results are similar and agree within a factor of 2. The elastic differential cross sections determining also the angular distribution of elastic scattering are discussed for the TFD, screened Rutherford, Fink and Riley models. The application of elastic scattering is promising for scanning electron and Auger microscopy and for thin film in depth analysis using REELS and EPES. Some possibilities are briefly treated.

The elastic backscattering probability Pe of electrons is proportional to the product of the inelastic mean free path (IMFP), effective backscattering cross section (σeff), and atomic density (N). Thus, experimental evaluation of Pe, e.g. from the elastic peak intensity measurements, enables the determination of the IMFP. σeff can be calculated by integrating the differential elastic scattering cross sections using a simplified model based on the first Born approximation and the Thomas–Fermi–Dirac atomic potential. No significant difference in the values of σeff was found using the Thomas–Fermi, the Thomas–Fermi–Dirac and the Hartree–Fock atomic potentials or integrating the scattering cross sections tabulated by Fink et al. From the experimental values of Pe reported by Schmid et al. and by Gergely the IMFP was determined for a number of elements. A good agreement was found with the data on the IMFP published in the literature. Comparing the elastic peak of two samples and using the data of Ashley and Tung as reference values, the IMFP has been determined for GaP, GaSb, InP, InSb and Si3N4 samples. Good agreement with the data of Ashley and Tung was obtained for Si, Ge, SiO2 and GaAs.

In the standard equation for the strength of photoelectron signals the angular dependence of emitted photoelectrons is represented by the asymmetry parameter. As the geometry has a number of characteristic angles, γ, for example due to a finite solid angle of electron detection, one expects an effective asymmetry parameter β* instead of the theoretical β. But elastic electron scattering causes much more of a spread from the characteristic angle γ to a spectrum of possible γ-values. This paper aims to obtain quantitative results allowing a quantification of the influence of elastic scattering on the theoretical asymmetry parameter β. For photoelectrons with kinetic energies within 1–1.5 keV and elements up to Z = 46 the result is β* = (1.0688 −0.0235Z+0.000188Z2)β

It is shown that calculations of electron attenuation lengths and escape depths would require modification of definitions proposed in the literature, since these definition are not universally applicable. Exemplary experimental arrangements are indicated for which more general definitions are necessary, and such definitions are proposed. A Monte Carlo program has been developed with which it is possible to estimate attenuation lengths and escape depths. A comparison of these parameters is made for photoelectrons arising from s levels.

A fast Monte Carlo algorithm calculating the effects of elastic photoelectron collisions is presented. The algorithm is applicable to analyzer geometries with axial symmetry and with axis perpendicular to the surface (e.g. the CMA). The calculations were performed for four photoelectron lines: carbon 1s, aluminium 2s, cobalt 3p, and palladium 3d5/2. The following photoelectron characteristics were considered. (i) The angular distribution of photoelectrons leaving the surface. The distribution was found to follow the cosine distribution in practically all considered cases. Taking into account the elastic collisions did not change the shape of the distribution but decreased the photoelectron current leaving the surface, the difference increasing with atomic number of element. (ii) The distribution of emission depths of photoelectrons entering the analyzer. As a result of elastic collisions, more photoelectrons originate from the layer at the surface and less from the deeper layers. Thus, the actual depth of analysis is decreased. (iii) The total photoelectron current entering the analyzer. This current was also decreased by the elastic collisions. The difference reaches 1.6% for carbon 1s line, but increases to 16–19% for palladium 3d5/2 line. An elastic scattering correction in formalism of quantitative XPS is suggested. (iv) The average depth of analysis. This parameter was found to be most significantly affected by elastic scattering of photoelectrons. The depth of analysis was decreased by elastic collisions from 3–5% for carbon 1s line to 60–80% for palladium 3d5/2 line.

The single scattering Monte Carlo algorithm of Murata, Matsukawa and Shimizu and the Gryzinski ionization cross-section were used in calculations of the backscattering factor r. The calculations were based on two definitions of r. Generally, the backscattering factor was defined as the ratio of the Auger electron current recorded by the analyser to the current that would be recorded in the ideal case of no backscattering and no energy loss. The usual definition, involving the energy distribution of backscattered electrons, was also used. The calculations were performed for L3MM Auger transitions of elements with atomic numbers between 23 and 32. The primary energy ranged from 3 to 10 keV. The difference in backscattering factors resulting from both definitions varied from 0.1% to 10%, decreasing with the primary energy increase. The single scattering Monte Carlo algorithm can also be used in simulation of electron scattering in binary alloys. This makes possible the calculation of the backscattering factor as a function of the solid composition. The calculations were performed for L3MM Auger transitions of Cr, Cu, Fe and Ni in Au/Ni, Cr/Fe, Cr/Pd, Cu/Ni and Ni/Pd binary alloys. It was found that the backscattering factor varies almost linearly with mass fraction. The dependence on concentration is more pronounced when the difference in atomic numbers of alloy components is larger. The relative sensitivity factors, calculated for Cu/Ni and Cr/Fe binary alloys, are practically independent of composition, but depend on the primary energy.

In principle, one expects from a method for the determination of thicknesses of thin overlayers no angular dependence (take-off angle ϵ) of the results, which means d /λ = const. Earlier investigations, however, gave evidence for such a constant response of d /λ versus ϵ only up to about ϵ = 40 to 70° (depending on the value of d /λ) followed by a drop. This drop is explained by the finite solid angle of detection and elastic scattering of photoelectrons. As a concentration gradient exists in the interface, a horizontal portion ( d /λ = const.) is only obtained for thick overlayers on thin interfaces. Surface roughness causes a restriction of the horizontal portion and in addition systematic errors.

Coexisting two‐dimensional (2D) gas and 2D solid phases of Xe adsorbed on Ag(111), Cu(111), and Ru(001) can be distinguished by means of their Xe(5p) photoemission. The relative equilibrium concentrations (at a given temperature) are substrate dependent and correlate with the xenon–metal interaction strength. Namely, the maximum gas concentration just before 2D phase separation grows with increasing Xe adsorption energy as well as adsorption induced xenon dipole moment in the order Ag(111)

In the mathematical formalism of quantitative AES and XPS, the elastic electron collisions are not taken into account. However, recent calculations have shown that the neglect of the elastic collisions may result in considerable errors. Theoretical analysis of the actual electron transport in a solid requires two major problems to be considered. (i) calculation of the differential elastic scattering cross-sections for a given potential and electron energy and (ii) description of the multiple electron scattering. Both problems are extensively reviewed. The Monte Carlo method is usually used to describe the electron trajectories in a solid at energies of surface-sensitive electron spectroscopies. Such simulations have indicated that the elastic collisions of photoelectrons affect considerably the angular distribution of the measured intensity and the photoelectron escape depth. The latter parameter may be diminished by > 30%. Elastic collisions of Auger electrons decrease the current recorded by the typical analysers and also considerably decrease the escape depth. Thus, the actual electron transport in a solid should be considered in calculations associated with determining the inelastic mean free path using the overlayer method or overlayer thickness measurements. The usual formalism of quantitative AES and XPS can be extended easily to account for the elastic electron collisions. The values of the corresponding correcting factors are extensively compiled. To check the validity of the Monte Carlo calculations, the results of simulations of forward electron scattering and electron back-scattering are compared with the available experimental data. Excellent agreement between experimental and theoretical angular distributions of photoelectrons has been found. A very good agreement was also observed in the case of elastic electron back-scattering from surfaces.

The Thomas-Fermi-Dirac differential equation for the neutral atom was proved to be equivalent to the variational problem with movable boundary. The functional corresponding to the TFD equation can be used to determine the analytical solution with controlled accuracy, or can be a criterion to compare the accuracy of different solutions. The function published by Bonham and Strand is found to be the most accurate analytical solution available at present.

A new method for determining the inelastic mean free path was applied to the ordered polycrystalline AlNi alloy. The results obtained agree well with the literature data.

The difficulties of boron detection by AES in catalysts containing low concentration of boron can be partially associated with elastic scattering of Auger electrons. In the present work the Monte Carlo approach was used to estimate the effects of Auger electron collisions in different matrices. Elastic scattering events were described within the partial wave expansion method. The scattering centres were approximated by the Thomas-Fermi-Dirac potentials. It was found that elastic collisions decrease by up to 10% the boron KLL Auger electron signal. In addition, the sampling depth of AES was strongly decreased. This decrease reached 35% for medium atomic number elements. The values of parameters correcting for elastic scattering effects were determined for boron embedded in 14 elements. An attempt was also made to interpolate the correcting parameters for matrices not considered in the present work.

Publisher Summary In this chapter, the Monte Carlo method has been used in calculations of angular distribution of photoelectrons. Although all details of the corresponding algorithm is of current interest, only the main features of this algorithm are briefly sketched in the chapter. Creation of the photoelectron trajectory requires generating the three parameters—namely, photoelectron emission angle, elastic scattering angles, and the length of the linear step among elastic collisions. Angular resolved experiments have been carried out in VG ADES 400. The 2 pm thin foil of poly-AI was used as a sample after Xe ion sputtering of surface contaminations and the oxide layer. The intensity ratios I2s/I2p are estimated using the Monte Carlo algorithm, which takes into account photoelectron trajectories. These calculations were made only for the angle a = 0—that is, assuming normal incidence of X-rays. In such a case, the studied system has axial symmetry, which greatly facilitates calculations. As it is evident from the discussion presented, the anisotropy observed experimentally is much less pronounced than anisotropy resulting from the formalism. The experimental data are in much better agreement with Monte Carlo results. This fact indicates that main part of observed discrepancies is because of the neglect of photoelectron elastic scattering. In effect, the angular distribution of photoelectrons is somewhat flattened. The difference between experimental results and the Monte Carlo data may be because of other effects, which may further randomize the photoelectron trajectories, for example, surface roughness and analyzer acceptance angle. The discrepancy may also be because of inaccuracies in published values of λ and σ, where λ is inelastic mean free path, and σ is the total photoelectric cross-section.

X-ray photoelectron spectroscopy (XPS) and atomic absorption spectroscopy (AAS) have been used to determine the composition of volatile reaction products generated from Pt-Rh and Pt-Pd-Rh alloys and the pure alloy components platinum, rhodium and palladium. The changes in surface morphology induced by the reaction environment were monitored by means of electron probe microanalysis and scanning electron microscopy. The materials were oxidized with molecular oxygen (0.094 MPa, 1163 K) or with r.f. oxygen plasma. XPS studies proved the formation of RhO2, α-PtO2, PdO and probably PtO3 in the losses generated with oxygen plasma, whereas RhO2, α-PtO2, PdO and PtO were found in oxide deposits obtained during molecular oxygen interaction with materials studied. The oxide content of platinum-containing reaction products was found to be dependent on the platinum content in the oxidized samples. AAS showed that oxides generated by plasma from Pt-Pd-Rh alloys were enriched with palladium and, to smaller extent, with rhodium. No enrichment was detected in the case of oxides formed during plasma etching of Pt-Rh alloys. The oxides obtained in molecular oxygen were distinctly enriched with platinum. The rate of oxide formation decreased with increase in rhodium or palladium content in the alloys. A possible mechanism for oxide production under the experimental conditions studied is proposed.

Elastic electron backscattering from solid surfaces has been studied experimentally and theoretically. It has been shown that the recently published ${P}_{1}$ approximation gives an inadequate description. Much more realistic results are obtained from the Monte Carlo algorithm based on differential cross sections calculated within the partial-wave expansion method. Excellent agreement has been found between the calculated results and the experimental data obtained in the present work or taken from the literature. The present calculations seem to be valid for electron energies exceeding 200 eV and for low- and medium-atomic-number elements. The possibility of measuring the inelastic mean free path of electrons from the elastically backscattered intensity is discussed.

Palladium-based alloys and bimetallic systems are of importance in heterogeneous catalysis. Recently, attention was devoted to studies of the catalytic properties of the Co-Pd binary system. An important issue to consider is the surface composition of this alloy. The aim of the present work was to determine the surface composition of the polycrystalline CoPd alloys in a wide range of constituent concentrations (Co30Pd70 at.%, Co50Pd50 at.% and Co70Pd30 at.%) at temperatures up to 900°C. Quantitative AES and XPS analyses were used for this purpose. To determine the surface composition, the values of the inelastic mean free path (IMFP) for the studied alloys are necessary. These were derived from the elastic peak intensity. The reported values of the IMFP for Pd are in agreement with the data available in the literature. Reasonable consistency of the IMFP values for CoPd alloys and Co was also observed. The surface compositions of the CoPd alloys at room temperature determined by AES and XPS are in good agreement. It has been found that Pd segregates to surfaces of the Co30Pd70 and Co50Pd50 alloys at temperatures above 300 °C.

An analytical expression for the escape probability of signal pbotoelectrons as a function of the depth of origin, energy and direction of emission from a solid has been found by solving a kinetic equation. The solution is expressed by a series of partial escape probabilities corresponding to contributions of electrons that have suffered a certain number of inelastic collisions before leaving a target. The universal relationship between the probability for an electron to escape from a certain depth after being scattered inelastically n times (n = 0, 1, 2, ...) and the pathlength distribution has been derived. The photoelectron spectra from an Si(Au) tracer located at different depths in an Au(Si) matrix has been calculated analytically and by means of the Monte Carlo technique for different XPS configurations. The peak and the background regions have been found to be strongly affected by elastic scattering of electrons in the sample. The neglect of the elastic collisions has been shown to over- or underestimate the photoelectron current (up to 100% in the case of the Au sample and the Si tracer located at a depth of the order of several inelastic mean free paths). The analytical theory predictions are compared with the corresponding Monte Carlo data and good agreement in absolute units is observed. The obtained results indicate that the assumption of a simple exponential attenuation of electrons made in non-destructive depth-profile reconstructions seems to be less valid in the case of materials in which elastic scattering is significant.

The IMFP of electrons is a fundamental material parameter of surface analysis by AES, XPS, EPES and EELS. In surface analysis calculated IMFP values are used. Their experimental determination is rather difficult. The IMFP of amorphous Ge and polycrystalline Si was determined by comparing the elastic peak intensity ratios with electrolytic Ni reference sample of 1 nm surface roughness, achieved by dedicated Ar+ ion bombardment cleaning and examined by STM. Experimental results obtained with a hemispherical analyser type ESA 31 developed by ATOMKI Debrecen have been evaluated by Monte Carlo analysis, based on Jablonski's differential elastic scattering cross sections and elaborated for the HSA analyser angular window. Due to the 5 × 10−5 energy resolution of the ESA 31 no spectrometer correction was needed. The ratio of the background to the elastic peak was

The inelastic mean free path (IMFP) of electrons is an important material parameter needed for quantitative AES, EELS and non-destructive depth profiling. The distinction between the terms for IMFP and the attenuation length (AL) has been established by ASTM standards. A practical experimental method for determining values of the IMFP is elastic peak electron spectroscopy (EPES). In this method, experimentally determined ratios of elastically backscattered electrons from test surfaces and from a Ni reference standard are compared with the values evaluated theoretically. The present paper reports systematic measurements of the IMFP by EPES for GaAs and InP. They are carried out in two laboratories using two different electron spectrometers: a CMA in Budapest and DCMA in Warsaw. Prior to measurements, the samples were amorphized by high-energy Ar + ions (100–400 keV), and the surface composition was determined by quantitative XPS. Argon cleaning produces enrichment of samples in the surface layer in Ga (80%) and In (70%), respectively. The experiments refer to a such modified sample surface that was considered in Monte Carlo calculations. The experimental data were analyzed using calibration curves from Monte Carlo calculations which account for multiple elastic scattering events. This approach has been used previously for elemental solids and is now extended to amorphized binary compounds. The experimental values of IMFP obtained in both laboratories exhibited a reasonable agreement with the available literature data in the 0.1–3.0 keV energy range. With respect to the information depth of EPES, the experimental results refer to the bulk composition within a reasonable extent.

A general differential equation has been derived which describes the concentration of atoms diffusing and recombining in a cylindrical tube. It is shown that the previously published equations are particular cases of that equation. The boundary conditions have also been generalized. In the case of the Smith–Linnett method the simplifications of the general equation, leading to the one-dimensional linear equation, are the cause of a systematic error in calculation of the recombination coefficient. This error is considerable for very active and slightly active surfaces. In the case of recombination of atomic hydrogen, the error due to omission of the homogeneous reaction in the analysis of experimental data is negligibly small when the pressure is lower than 0.1 Torr and the concentration of atoms is lower than 10 %.The atomic hydrogen recombination coefficient γ has been calculated for nickel films and for Pyrex on the basis of the one-dimensional linear equation and on the basis of the model proposed in the present work. It was found that the two methods of calculation differ by 3–6 % in the case of surfaces having the high activity (γ over 10–2) and by 30–40 % in the case of surfaces having low activity (γ below 10–4). Both methods give approximately the same fit to the experimental data.

The formulas defining the backscattering factor met with in the literature are derived from the general definition. These formulas are shown to depend on the simplifying assumptions made in the derivation. The Monte Carlo algorithm is used to calculate the dependence of the backscattering factor on the primary electron incidence angle for different defining formulas. Considerable differences were found between values of the backscattering factor resulting from these definitions at grazing incidence of primary electrons.