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The attenuation length approach for determination of an overlayer thickness is analyzed in the case of overlayer/substrate systems in which both materials distinctly differ; in particular, they exhibit considerably different electron transport properties. Typical measurement conditions for overlayer-thickness determination were simulated for numerous systems using an advanced Monte Carlo strategy. Three experimental procedures were considered: (i) measurement of only one signal intensity from an overlayer; (ii) only one signal intensity from a substrate; and (iii) measurement of two signal intensities from an overlayer and a substrate. It turned out that differences in electron transport properties of the overlayer and substrate materials (elastic scattering cross sections, the inelastic mean free path) can generally be ignored. One can safely assume that the overlayer and substrate materials are identical, and the effective attenuation length (EAL) values needed in calculations should correspond to the overlayer material only. Furthermore, one can use for that purpose the EALs estimated for the overlayer material from available predictive formulas. However, care must be taken to estimate correctly the needed albedo values. In that case, the overlayer thicknesses assumed in Monte Carlo simulations are reproduced from calculated signal intensities within 2 – 3%.

We analyzed the experiments of Rubio-Zuazo and Castro [J. Electron Spectrosc. Relat. Phenom. 184 (2011) 384] who reported measurements of effective attenuation lengths (EALs) of gold for electron energies between 1 keV and 15 keV. They deposited thin films of gold on a copper substrate and measured the intensities of various Cu and Au photoelectron lines excited by synchrotron X-rays. Their derived EALs were based on the assumption that their films were of uniform thickness (i.e., layer-by-layer film growth). We considered two other forms of film growth: island formation (Volmer-Weber film growth) and island growth on a continuous monatomic wetting layer (Stranski-Krastanov film growth). We utilized the National Institute of Standards and Technology Database for the Simulation of Electron Spectra for Surface Analysis (SESSA) to determine the fractional Au island areas for each Au film thickness that would give the same intensity changes of Cu and Au photoelectron lines that were observed in the experiments. These results showed that growth of the Au film as islands provided a better description of the experimental results than uniform film growth. We could also distinguish Stranski-Krastanov film growth from Volmer-Weber growth and believe that the former is more likely.

A very simple method for determining the photoelectron partial intensities and reduced partial intensities for HAXPES photoelectrons is proposed. For these calculations, it is sufficient to know a formalism expressing the photoelectron signal intensity as a function of the inelastic mean free path. The only computational problem is due to required procedure of multiple numerical differentiation, although one can use published programs for that purpose. The proposed method was designed to photoemission emitted by unpolarized X-rays and for planar samples. A wide range of photoelectron energies was considered: from 500 eV to 4000 eV. Evaluation of accuracy was performed by comparison with partial intensities obtained from accompanying Monte Carlo simulations of photoelectron trajectories in the same analytical conditions. The proposed method was found to provide up to eight partial intensities with reasonable accuracy. Depending on element, photoelectron line, and kinetic energy, the mean percentage deviation varied in the range from 0.95% to 3.11%. Similar agreement was observed in comparisons with published partial intensities obtained from Monte Carlo simulations, and with partial intensities obtained from the database SESSA (NIST Database for the Simulation of Electron Spectra for Surface Analysis, Version 2.1.1).

Mo disulfide overlayers with the thickness exceeding 1.77 nm were obtained on Si substrates through mechanical exfoliation. The resulting Mo disulfide flakes were then analyzed ex situ using combination of Auger electron spectroscopy (AES), elastic-peak electron spectroscopy (EPES) and scanning electron microscopy (SEM) in order to characterize their surface chemical composition, electron transport phenomena and surface morphology. Prior to EPES measurements, the Mo disulfide surface was sputter-cleaned and amorphized by 3 kV argon ions, and the resulting S/Mo atomic ratio varied in the range 1.80–1.88, as found from AES measurements. The SEM images revealed single crystalline small-area (up to 15 μm in lateral size) Mo disulfide flakes having polygonal or near-triangular shapes. Such irregular-edged flakes exhibited high crystal quality and thickness uniformity. The inelastic mean free path (IMFP), characterizing electron transport, was evaluated from the relative EPES using Au reference material for electron energies E = 0.5–2 keV. Experimental IMFPs, λ, determined for the AES-measured surface compositions were approximated by the simple function λ = kEp, where k = 0.0289 and p = 0.946 were fitted parameters. Additionally, these IMFPs were compared with IMFPs resulting from the two methods: (i) present calculations based on the formalism of the Oswald et al. model; (ii) the predictive equation of Tanuma et al. (TPP-2M) for the measured Mo0.293S0.551C0.156 surface composition (S/Mo = 1.88), and also for stoichiometric MoS2 composition. The fitted function was found to be reasonably consistent with the measured, calculated and predicted IMFPs. We concluded that the measured IMFP value at 0.5 keV was only slightly affected by residual carbon contamination at the Mo disulfide surface.

The step-by-step growth of yttrium oxide layer was controlled in situ using X-ray photoelectron spectroscopy (XPS). The O/Y atomic concentration (AC) ratio in the surface layer of finally oxidized Y substrate was found to be equal to 1.48. The as-grown yttrium oxide layers were then analyzed ex situ using combination of Auger electron spectroscopy (AES), elastic-peak electron spectroscopy (EPES) and scanning electron microscopy (SEM) in order to characterize their surface chemical composition, electron transport phenomena and surface morphology. Prior to EPES measurements, the Y oxide surface was pre-sputtered by 3 kV argon ions, and the resulting AES-derived composition was found to be Y0.383O0.465C0.152 (O/Y AC ratio of 1.21). The SEM images revealed different surface morphology of sample before and after Ar sputtering. The oxide precipitates were observed on the top of un-sputtered Y oxide layer, whereas the oxide growth at the Ar ion-sputtered surface proceeded along defects lines normal to the layer plane. The inelastic mean free path (IMFP) characterizing electron transport was evaluated as a function of energy in the range of 0.5–2 keV from the EPES method. Two reference materials (Ni and Au) were used in these measurements. Experimental IMFPs determined for the Y0.383O0.465C0.152 and Y2O3 surface compositions, λ, were uncorrected for surface excitations and approximated by the simple function λ = kEp at electron energies E between 500 eV and 2000 eV, where k and p were fitted parameters. These values were also compared with IMFPs resulting from the TPP–2 M predictive equation for both oxide compositions. The fitted functions were found to be reasonably consistent with the measured and predicted IMFPs. In both cases, the average value of the mean percentage deviation from the fits varied between 5% and 37%. The IMFPs measured for Y0.383O0.465C0.152 surface composition were found to be similar to the IMFPs for Y2O3.

Growing availability of synchrotron facilities stimulates an interest in quantitative applications of hard X-ray photoemission spectroscopy (HAXPES) using linearly polarized radiation. An advantage of this approach is the possibility of continuous variation of radiation energy that makes it possible to control the sampling depth for a measurement. Quantitative applications are based on accurate and reliable theory relating the measured spectral features to needed characteristics of the surface region of solids. A major complication in the case of polarized radiation is an involved structure of the photoemission cross-section for hard X-rays. In the present work, details of the relevant formalism are described and algorithms implementing this formalism for different experimental configurations are proposed. The photoelectron signal intensity may be considerably affected by variation in the positioning of the polarization vector with respect to the surface plane. This information is critical for any quantitative application of HAXPES by polarized X-rays. Different quantitative applications based on photoelectrons with energies up to 10 keV are considered here: (i) determination of surface composition, (ii) estimation of sampling depth, and (iii) measurements of an overlayer thickness. Parameters facilitating these applications (mean escape depths, information depths, effective attenuation lengths) were calculated for a number of photoelectron lines in four elemental solids (Si, Cu, Ag and Au) in different experimental configurations and locations of the polarization vector. One of the considered configurations, with polarization vector located in a plane perpendicular to the surface, was recommended for quantitative applications of HAXPES. In this configurations, it was found that the considered parameters vary weakly in the range of photoelectron emission angles from normal emission to about 50° with respect to the surface normal. The averaged values of the mean escape depth and effective attenuation length were approximated with accurate predictive formulas. The predicted effective attenuation lengths were compared with published values; major discrepancies observed can be ascribed to a possibility of discontinuous structure of the deposited overlayer.

Numerous parameters needed for quantification of X-ray photoelectron spectroscopy can be derived from the emission depth distribution function (EMDDF) known for a given photoelectron line, an experimental configuration, and a solid. This function describes the probability that a photoelectron emitted at a certain depth enters an analyzer without energy loss. The EMDDF turns out to be distinctly affected by photoelectron elastic scattering effects. A useful measure of influence of elastic scattering is a closely related function named the correction factor (CF). This function is a useful tool for correcting the in-depth concentration profiles obtained from the procedure of non-destructive depth profiling. Due of complexity of the theoretical models describing transport of photoelectrons emitted by unpolarized X-rays in the surface region of solids, a typical computational approach involves Monte Carlo algorithms with different simulation strategies. However, convenient sources of EMDDFs (and CF functions) are analytical formulas that can be implemented in the software dedicated for practical surface analysis. The present report evaluates accuracy of different analytical formulae. A new expression is proposed which can be considered as a predictive formula, i.e., a simple analytical expression of reasonable accuracy for typical measurement conditions. This formula is applicable to photoelectrons emitted by unpolarized or circularly polarized X-rays. Furthermore, stress is put on the influence of non-dipolar parameters that define a high-energy photoemission cross section on the EMDDF for photoelectrons with kinetic energies exceeding 1500 eV. Eventually, a photoelectron kinetic energy of 5 keV was established as an upper limit of applicability of the presented formalism. Finally, applicability of the analytical formalism, derived for unpolarized X-rays, to photoelectrons emitted by linearly polarized radiation is analyzed. Due to the considerable influence of the position of the polarization vector on the photoelectron signal, the analytical formalism developed for unpolarized radiation cannot be recommended for use if the of X-ray beam is linearly polarized or has partial polarization.

Electron transport properties in praseodymium (Pr) foil samples were studied by elastic-peak electron spectroscopy (EPES). Prior to EPES measurements, the Pr sample surface was pre-sputtered by Ar ions with ion energy of 2–3 keV. After such treatment, the Pr sample still contained about 10 at.% of residual oxygen in the surface region, as detected by X-ray photoelectron spectroscopy (XPS) and Auger electron spectroscopy (AES) analyses. The inelastic mean free path (IMFP), characterizing electron transport within this region (4 nm-thick), was evaluated from EPES using both Ni and Au standards as a function of energy in the range of 0.5–2 keV. Experimental IMFPs, λ , were approximated by the simple function λ = kE p , where E is energy (in eV), and k = 0.1549 and p = 0.7047 were the fitted parameters. These values were compared with IMFPs for the praseodymium surface in which the presence of oxygen was tentatively neglected, and also with IMFPs resulting from the TPP-2M predictive equation for bulk praseodymium. We found that the measured IMFP values to be only slightly affected by neglect of oxygen in calculations. The fitted function applied here was consistent with the energy dependence of the EPES-measured IMFPs. Additionally, the measured IMFPs were found to be from 2% to 4.2% larger than the predicted IMFPs for praseodymium in the energy range of 500–1000 eV. For electron energies of 1500 eV and 2000 eV, there was an inverse correlation between these values, and then the resulting deviations of −0.4% and −2.7%, respectively, were calculated.

Zinc oxide films single, double and triple doped with arsenic, arsenic and nitrogen, arsenic, nitrogen and antimony, were grown by plasma assisted molecular beam epitaxy. Differently doped ZnO samples were post-growth annealed in oxygen or argon atmospheres. Incorporation of impurities into ZnO layers was confirmed by the results of secondary ion mass spectrometry measurements. The high resolution X-ray photoelectron spectroscopy (XPS) studies of arsenic 3d state revealed three arsenic states at the binding energy of ∼41 eV, 44.2 and 45.6 eV which we attribute to As deep acceptor, As Zn -2V Zn shallow acceptor, and to As Zn donor, respectively. Concentration of the As O species was found to be low in all samples. The relative fractions of arsenic chemical states in As-doped ZnO layers, were altered as a result of doping by antimony and/or nitrogen and post grown annealing in argon and oxygen atmosphere.

In the present study, two kind of samples were used: (i) a monolayer graphene film with a thickness of 0.345 nm deposited by the CVD method on Cu foil, (ii) graphene flakes obtained by modified Hummers method and followed by reduction of graphene oxide. The inelastic mean free path (IMFP), characterizing electron transport in graphene/Cu sample and reduced graphene oxide material, which determines the sampling depth of XPS and AES were evaluated from relative Elastic Peak Electron Spectroscopy (EPES) measurements with the Au standard in the energy range 0.5–2 keV. The measured IMFPs were compared with IMFPs resulting from experimental optical data published in the literature for the graphite sample. The EPES IMFP values at 0.5 and 1.5 keV was practically identical to that calculated from optical data for graphite (less than 4% deviation). For energies 1 and 2 keV, the EPES IMFPs for rGO were deviated up to 14% from IMFPs calculated using the optical data by Tanuma et al. [1] . Before EPES measurements all samples were characterized by various techniques like: FE-SEM, AFM, XPS, AES and REELS to visualize the surface morphology/topography and identify the chemical composition.

New theoretical model describing the sampling depth of elastic peak electron spectroscopy (EPES) has been proposed. Surface sensitivity of this technique can be generally identified with the maximum depth reached by trajectories of elastically backscattered electrons. A parameter called the penetration depth distribution function (PDDF) has been proposed for this description. Two further parameters are descendant from this definition: the mean penetration depth (MPD) and the information depth (ID). From the proposed theory, relatively simple analytical expressions describing the above parameters can be derived. Although the Monte Carlo simulations can be effectively used to estimate the sampling depth of EPES, this approach may require a considerable amount of computations. In contrast, the analytical model proposed here (AN) is very fast and provides the parameters PDDF, MPD and ID that very well compare with results of MC simulations. As follows from detailed comparisons performed for four elements (Al, Ni, Pd and Au), the AN model practically reproduced complicated emission angle dependences of the MPDs and the IDs, correctly indicating numerous maximum and minimum positions. In the energy range from 200 eV to 5 keV, the averaged percentage differences between MPDs obtained from the MC and the AN models were close to 4%. An important conclusion resulting from the present studies refers to the procedure of determination of the inelastic mean free path (IMFP) from EPES. Frequently, the analyzed sample is deposited as a thin overlayer on a smooth substrate. From an analysis of the presently obtained IDs, is follows that 99% of trajectories in analyzed experimental configurations reaches depth not exceeding 2.39 in units of IMFP. Thus, one can postulate that a safe minimum thickness of an overlayer should be larger than about 3 IMFPs. For example, the minimum thickness of an Al overlayer shoud be about 8 nm at 5000 eV.

Arsenic doped ZnO films were grown by plasma assisted molecular beam epitaxy and post-growth annealed at 700 °C in oxygen, nitrogen or argon atmosphere. The high resolution X-ray photoelectron spectroscopy (XPS) studies of the ZnO:As films revealed that the As3d core level spectra is formed by three components located at about 41 eV, 44.5 eV and 45.5 eV below the Fermi level which we ascribe to As O , As Zn ‐2V Zn and As Zn, respectively. The relative intensity of the three XPS contributions strongly depends on an annealing atmosphere, but in any case none of the contributions clearly dominates, which is a fingerprint of complicated nature of arsenic states in ZnO. This conclusion is also confirmed by the temperature dependent photoluminescence (PL) studies. Differences in the dominant PL peak positions and in their relative intensities are present and suggest different acceptor states in the examined samples.

The effective attenuation length (EAL) is a useful parameter in quantitative applications of x-ray photoelectron spectroscopy (XPS). This parameter is used in place of the inelastic mean free path (IMFP) in expressions for different XPS applications to correct those expressions for elastic scattering of the photoelectrons. We consider expressions used to determine (i) the thickness of an overlayer film on a planar substrate, (ii) the surface composition, (iii) the depth of a thin marker or delta layer, and (iv) the shell thickness of a core–shell nanoparticle. An EAL can be used for each of these applications. In general, the EAL depends on the particular defining equation as well as on the XPS configuration. Many attempts were made in the 1970s and 1980s to measure EALs for the determination of overlayer-film thicknesses, but there were often wide scatters in the reported results due to the difficulty in preparing uniform films with known thicknesses. We have therefore been motivated to calculate EALs for each application. The SRD 82 database from the National Institute of Standards and Technology (NIST) provides EALs for the measurement of overlayer-film thicknesses and of marker-layer depths. These EALs can be determined for photoelectron energies between 50 eV and 2 keV and for user-specified XPS configurations. We review EAL predictive equations for the determination of overlayer-film thicknesses on a planar substrate for XPS with unpolarized x rays and with linearly polarized x rays as well as an EAL predictive equation for quantitative analysis by XPS. These equations are simple analytical expressions that are valid for well-defined ranges of experimental conditions and for useful ranges of electron energies. We also point out that EALs for the determination of overlayer-film thicknesses can be derived from the simulated photoelectron intensities obtained from the NIST Database for the Simulation of Electron Spectra for Surface Analysis (SRD 100). Where possible, we make comparisons of the calculated EALs with illustrative experimental results. A key parameter in the EAL predictive equations is the so-called albedo, a useful measure of the strength of elastic-scattering effects in a material. The albedo is a simple function of the IMFP and the transport mean free path (TRMFP). We provide a tabulation of albedo and TRMFP values in the supplementary material for 41 elemental solids and 42 inorganic compounds for photoelectron energies between 50 eV and 30 keV. For other materials, albedo values can be determined from IMFP and TRMFP data available in the NIST SRD 82 and SRD 100 databases.

Mo disulfide overlayers with the thickness exceeding 1.77 nm were obtained on Si substrates through mechanical exfoliation. The resulting Mo disulfide flakes were then analyzed ex situ using combination of Auger electron spectroscopy (AES), elastic-peak electron spectroscopy (EPES) and scanning electron microscopy (SEM) in order to characterize their surface chemical composition, electron transport phenomena and surface morphology. Prior to EPES measurements, the Mo disulfide surface was sputter-cleaned and amorphized by 3 kV argon ions, and the resulting S/Mo atomic ratio varied in the range 1.80&ndash, 1.88, as found from AES measurements. The SEM images revealed single crystalline small-area (up to 15 &mu, m in lateral size) Mo disulfide flakes having polygonal or near-triangular shapes. Such irregular-edged flakes exhibited high crystal quality and thickness uniformity. The inelastic mean free path (IMFP), characterizing electron transport, was evaluated from the relative EPES using Au reference material for electron energies E = 0.5&ndash, 2 keV. Experimental IMFPs, &lambda, determined for the AES-measured surface compositions were approximated by the simple function &lambda, = kEp, where k = 0.0289 and p = 0.946 were fitted parameters. Additionally, these IMFPs were compared with IMFPs resulting from the two methods: (i) present calculations based on the formalism of the Oswald et al. model, (ii) the predictive equation of Tanuma et al. (TPP-2M) for the measured Mo0.293S0.551C0.156 surface composition (S/Mo = 1.88), and also for stoichiometric MoS2 composition. The fitted function was found to be reasonably consistent with the measured, calculated and predicted IMFPs. We concluded that the measured IMFP value at 0.5 keV was only slightly affected by residual carbon contamination at the Mo disulfide surface.

Probability of elastic electron backscattering from surfaces is typically calculated from theoretical models implemented in Monte Carlo simulation strategies since this approach is considered to be the most accurate. However, an analytical model proposed by Oswald et al. [J. Electron Spectrosc. Relat. Phenom. 61 (1993) 251], after later modifications, has been found to be of similar accuracy. The relevant analysis was performed for selected elemental solids. In the present work, a possibility to use the analytical formalism in elastic peak electron spectroscopy for determination of the IMFP has been presently studied. For this purpose, two further modifications of the analytical theory were made: (i) creation of a database of parameters facilitating calculations of the angular distribution of electrons after multiple collisions, and (ii) extension of the formalism to solids constituted of different atomic species, i.e. alloys and compounds. Comparison of experimental data (angular distribution of backscattered electrons, ratios of elastic peak intensities) with predictions of both theoretical models proves that these models are of similar accuracy. The IMFPs for elemental solids derived from experimentally measured ratios using the analytical formalism and the Monte Carlo simulations are practically identical. On analysis of IMFPs obtained for 13 elemental solids in the energy range from 200 eV to 5000 eV, it has been estimated that the IMFPs obtained from the analytical formalism deviate on average from IMFPs from Monte Carlo calculations by 3.09%. Similar agreement was found for an alloy (Al0.48Ni0.52) and compounds (GaSb, InSb, GaN and SiC) considered here.

An algorithm for modeling transport of photoelectrons with kinetic energies up to 10 keV has been developed. Calculations were performed for photoelectrons emitted by the unpolarized (or circularly polarized) X-ray radiation. In the theoretical model used, different approximations for the photoemission cross section were used: the cross sections derived within the dipole approximation or the cross sections corrected for the nondipolar effects. It turned out that the photoelectron signal intensity can be considerably affected in the high energy range by the neglect of the first order correction. The percentage deviations may reach 40%. On the other hand, the influence of the second order correction is less pronounced; the difference between both corrections is below 6%. On the other hand, the parameters needed for quantification of XPS (or HAXPES), the mean escape depth and the effective attenuation length, were found to be practically independent of the photoelectron cross section used in calculations in wide range of the experimental configurations. An attempt has been made to elucidate this unexpected result. A criterion has been proposed that allows prediction of systems and experimental geometries in which the above parameters are insensitive to the photoemission cross sections.

Electron transport properties in CeO2 powder samples were studied by elastic-peak electron spectroscopy (EPES). Prior to EPES measurements, the CeO2 sample surface was pre-sputtered by 0.5 keV Ar ion etching. As a result, an altered layer with thickness of 1.3 nm was created. X-ray photoelectron spectroscopy (XPS) analysis revealed two chemical states of cerium Ce4+ (68%) and Ce3+ (32%) at the surface region of CeO2 sample after such treatment. The inelastic mean free path (IMFP), characterizing electron transport, was evaluated as a function of energy within the 0.5–2 keV range. Experimental IMFPs were corrected for surface excitations and approximated by the simple function λ = kEp, where λ was the IMFP, E denoted the energy (in eV), and k = 0.207 and p = 0.6343 were the fitted parameters. The IMFPs measured here were compared with IMFPs resulting from the TPP-2M predictive equation for the measured composition of oxide surface. The measured IMFPs were found to be from 3.1% to 20.3% smaller than the IMFPs obtained from the predictive formula in the energy range of 0.5–2 keV. The EPES IMFP value at 500 eV was related to the altered layer of sputtered CeO2 samples.

We report calculations of effective attenuation lengths (EALs) for Si 2s1/2, Cu 2p3/2, Ag 3d5/2, and Au 4f7/2 photoelectrons excited by Mg Kα, Al Kα, Zr Lα, and Ti Kα X-rays, where the photoelectron energies ranged from 321 eV to 4.426 keV. These EALs, appropriate for determining overlayer-film thicknesses, were calculated from the transport-approximation formalism and from Monte Carlo simulations using photoionization cross sections from the dipole and non-dipole approximations. Satisfactory consistency was found between EALs determined from the TA formalism and from MC simulations, while differences between EALs for Au 4f7/2 photoelectrons from the dipole and non-dipole approximations were between 1% (for Mg and Al Kα X-rays) and 2.5% (for Ti Kα X-rays) for photoelectron emission angles less than 50°. As in past work for electron energies less than 2 keV, we found a simple linear relation between the ratio of the average EAL (for emission angles less than 50°) to the inelastic mean free path (IMFP) and the single-scattering albedo, a function of the IMFP and the transport mean free path. The root-mean-square difference between our average EALs and those from the linear expression was 1.44%. This expression should be useful in determinations of film thicknesses by XPS with unpolarized X-rays for photoelectron energies up to about 5 keV.

The effective attenuation length (EAL) is normally used in place of the inelastic mean free path (IMFP) to account for elastic-scattering effects when describing the attenuation of Auger electrons and photoelectrons from a planar substrate by an overlayer film. An EAL for quantitative determination of surface composition by Auger-electron spectroscopy (AES) or X-ray photoelectron spectroscopy (XPS) is similarly useful to account for elastic-scattering effects on the signal intensities. We calculated these EALs for four elemental solids (Si, Cu, Ag, and Au) and for energies between 160 eV and 1.4 keV. The XPS calculations were made for two instrumental configurations while the AES calculations were made from the XPS formalism after “switching off” the XPS anisotropy. The EALs for quantitative determination of surface composition by AES and XPS were weak functions of emission angle for emission angles between 0 and 50°. The ratios of the average values of these EALs to the corresponding IMFPs could be fitted to a second-order function of the single-scattering albedo, a convenient measure of the strength of elastic-scattering effects. EALs for quantitative determination of surface composition by AES and XPS for other materials can be simply found from this relationship.

Formalism of quantitative X-ray photoelectron spectroscopy is based on a function describing the probability that a photoelectron emitted at a certain depth leaves the solid without energy loss. Determination of this function called the emission depth distribution function (EMDDF) requires knowledge of the photoemission cross section for analyzed photoelectrons. Typically, this cross section estimated within the so-called dipole approximation (DA) is used in the relevant formalism. It is well known now that the DA approach is applicable to photoelectrons with kinetic energy below 2 keV. An attempt is made here to extend the analytical expression for the EMDDF to higher energies by taking into account the non-dipolar contributions to the photoemission cross section, i.e. the non-dipole approximation (NDA). Accuracy of the derived formalism has been analyzed by extensive comparisons with Monte Carlo simulations. It has been found that the EMDDFs derived from both theoretical models compare very well. This analysis has been performed for Si 2s1/2, Cu 2p3/2, Ag 3d5/2 and Au 4f7/2 photoelectrons emitted by Ti Kα radiation (4510 eV). It has been found that the photoelectron signal intensity was considerably affected by the NDA effects, by up to 30% depending on the experimental configuration. The EMDDFs derived for high energy photoelectrons were used in calculations of parameters describing the photoelectron transport, i.e. the information depth (ID) and the mean escape depth (MED). It has been found that both parameters are practically not affected by the NDA model. This is an unexpected result indicating that the IDs and MEDs determined in the past using the DA model are also valid for high kinetic energy photoelectrons.

The XPS technique combined with low energy Ar + ion sputter depth profiling was used to obtain information about chemical composition and reproducibility of the growth procedure by the MOVPE method of the InGaN multi quantum wells (MQWs). A good in-depth resolution of the XPS depth profiling technique, allows observation of InGaN quantum wells with thickness down to 2 nm. However quantitative characterization of very narrow QWs is limited by the elemental detection range of the XPS analysis. Both the InGaN QWs and GaN barriers parameters were well characterized using the model MQWs samples with various QW thickness. Inter-diffusion of indium within the GaN barrier layers, induced by high-temperature annealing, has been detected. This work evidences the successful application of the XPS depth profiling analysis as a very useful tool to optimize the growth parameters and thermal stability of InGaN/GaN MQWs.

Electron transport in both ZnO(0 0 0 1)–Zn and ZnO(0 0 0–1)–O bulk single crystals was studied using the elastic-peak electron spectroscopy (EPES) measurements. The inelastic mean free path (IMFP) was evaluated from EPES using both Ni and Au standards in the energy range 200–2000 eV, and compared with IMFPs calculated from the predictive TPP-2 M formula for the measured composition of both single crystal surfaces. In the electron energy range from 1 to 2 keV, the IMFPs were found to be 34% larger for the ZnO(0 0 0 1)–Zn crystal surface than for the ZnO(0 0 0–1)–O crystal surface, and considerably larger than the IMFPs obtained from the TPP-2 M predictive formula. At energies lower than 1 keV, a good agreement between the corresponding IMFPs values was found. However, the electron transport at larger energies seems to be affected by different bulk structure of both crystals.

The in-depth profiles obtained from Auger electron spectroscopy or X-ray photoelectron spectroscopy (XPS) experiments are known to differ from an actual concentration profiles due to limitations of surface-sensitive techniques, e.g. finite sampling depth, or atomic mixing during sputtering. However, the monitored signal intensities are also affected by elastic scattering of signal electrons. Calculations performed for idealized multilayer structures indicate that elastic scattering of photoelectrons may significantly influence the in-depth signal intensity. In the present work, an attempt is made to evaluate the contribution of elastic photoelectron scattering to measured signal intensity profile for samples with diffused interfaces. The in-depth profile measured for the 5x(Au/Ni)/Si multilayer structure has been submitted to this analysis. A relatively simple procedure to evaluate the contribution of elastic scattering to the profile shape has been proposed. The effect of elastic scattering is found to be a reduction of the XPS intensity by 5–10% in the investigated cases. Copyright © 2014 John Wiley & Sons, Ltd.

Arsenic-doped ZnO films were formed by thermal annealing of epitaxial ZnO films grown by Atomic Layer Deposition (ALD) in arsenic atmosphere at temperature 850–950 °C. X-ray photoelectron spectroscopy (XPS) studies of the ZnO:As films revealed the complex As3d core level spectra formed by three components located at about 41 eV, 45 eV and 47.5 eV below the Fermi level. The As3d component at binding energy (BE) of 45 eV was found to be correlated with the acceptor bound A°X exciton state observed in low temperature photoluminescence. This observation strongly supports the previously postulated assumption that the origin of the 45 eV component of the As3d spectra can be ascribed to arsenic atoms in As Zn –2V Zn complexes formed as a result of high temperature annealing. This assumption is also supported by the evident valence band shift towards the Fermi level in the ZnO:As film annealed at 950 °C.

Aluminum-doped zinc magnesium oxide (Zn1−xMgxO:Al) films with the Mg content from x = 0 to 0.48 were obtained using atomic layer deposition (ALD). Together with the thorough studies of the properties of the deposited films, the ALD growth parameters conditioning possible applications of Zn1−xMgxO:Al films as transparent electrodes are investigated. Very low film resistivities (≤~10−3 Ω cm) and the metallic-type conductivity behavior at room temperature for Zn1−xMgxO:Al films are observed for Mg content x < 0.19. The Mg content of x = 0.19 results in the optical absorption edge of Zn1−xMgxO:Al films at 3.81 eV (325 nm). Other film parameters like work function or sheet resistance can be easily modified by variation of growth parameters.

XPS spectrometers are typically equipped with the Mg Kα radiation and/or Al Kα radiation sources. However, for some analyses, it is convenient to use the laboratory sources emitting high energy X-rays, e.g. to avoid coincidence of peaks due to photoelectrons and Auger electrons, or to increase the information depth. On the other hand, the mathematical formalism of quantitative XPS analysis is based on the theoretical photoemission cross section that is valid for photoelectrons emitted with a relatively low kinetic energy (the so-called dipole approximation – DA). For high kinetic energy photoelectrons, the photoemission cross section needs to be modified with nondipolar parameters. An important issue for an analyst is the correction of the formalism of quantitative analysis for the photoelectron elastic scattering effects. The Monte Carlo program has been developed for simulation of transport of photoelectrons emitted from polycrystalline or amorphous solids by four X-ray radiation sources: Mg Kα, Al Kα, Zr Lα and Ti Kα. Calculations were performed for photoelectrons emitted in elemental solids with a wide range of atomic numbers: Al, Cu, Ag and Au. The photoelectron emission event was described within the DA and the model modified with the multipole correction (non-dipole approximation – NDA). It has been found that, in a typical XPS configuration, the dipole approximation is of sufficient accuracy for the Mg Kα and Al Kα radiation sources. The difference between photoelectron signal intensities calculated within the DA and NDA did not exceed 8% when elastic photoelectron elastic scattering is neglected. For high-energy radiation sources, Zr Lα and Ti Kα, the difference may reach 25% in this geometry, and thus the NDA model is recommended for calculations. The photoelectron elastic collisions are found to decrease the difference between the DA and NDA models. An important result of the present analysis is the observation that the NDA formalism can be corrected for elastic scattering effects in the same way as the DA formalism, i.e. with two parameters, Q x and β x . Furthermore, the expressions for calculating these parameters derived for the DA model and for the Mg Kα and Al Kα sources are found to be also applicable to photoelectron emitted by the Zr Lα and Ti Kα sources. However, new expressions valid for all four radiation sources have been tentatively derived in the present work.

We analyzed chemical composition and electron transport phenomena in surface and sub-surface region of hot-pressed TiN specimens using a combination of X-ray photoelectron spectroscopy (XPS) and elastic-peak electron spectroscopy (EPES) techniques. Both the surface chemical composition and the elements distribution in the bulk of TiN specimens were determined using XPS and XPS depth profiling analysis. In addition to TiN, a mixture of Ti oxynitride (TiOxNy) and TiO2 compounds as well as carbon contaminants have been detected in the surface region of the TiN specimens. The elemental depth-profiles disclosed uniform chemical bulk composition formed mainly by titanium and nitrogen as well as carbon and oxygen contaminants. Surface enrichment of Ti was evidenced as result of Ar ion-induced preferential sputtering of nitrogen. The inelastic mean free path (IMFP) data evaluated from the relative EPES for electron energies 0.5–2 keV were uncorrected for surface excitations and compared with those calculated from the predictive TPP-2M formula for the measured surface composition. Except to the electron energy of 0.5 keV, a good agreement was found between the measured and predicted IMFPs in the TiN specimen. The higher discrepancies in the measured IMFPs at the lowest energy can be explained by the surface excitation effect. The smallest root-mean-square-deviation and the mean percentage deviation of 2.8 A and 14.8%, respectively, were found between EPES IMFP data and those predicted for TiN with respect to the Ni standard.

Photoelectron signal intensities calculated for a thin overlayer from theoretical models taking elastic photoelectron collisions into account are shown to be very weakly dependent on the substrate material. This result has been obtained for photoelectrons analyzed in XPS spectrometers equipped with typical X-ray sources, i.e. sources of Mg Kα and Al Kα radiation. Low sensitivity to the substrate material is due to the fact that trajectories of photoelectrons emitted in the overlayer and entering the substrate have a low probability to reach the analyzer without energy loss. On the other hand, the signal intensity of photoelectrons emitted in the overlayer is found to be distinctly affected by elastic photoelectron scattering. Consequently, a theoretical model that can accurately describe the photoelectron intensity from an overlayer deposited on any material (e.g. on a substrate of the same material as the overlayer) can be a useful basis for a universal and convenient method for determination of the overlayer thickness. It is shown that the formalism derived from the kinetic Boltzmann equation within the so-called transport approximation satisfies these requirements. This formalism is postulated for use in overlayer-thickness measurements to avoid time-consuming Monte Carlo simulations of photoelectron transport, and also to circumvent problems with determining the effective attenuation lengths for overlayer/substrate systems.

We present improved formulae for the correction parameters Q x and β eff that are used to account for elastic scattering of photoelectrons in quantitative X-ray photoelectron spectroscopy (XPS). The new formulae are based on new Monte Carlo simulations for 584 photoelectrons in 39 elemental solids that could be excited by Mg Kα and Al Kα X-rays in 315 different XPS configurations. The new simulations differed from similar earlier calculations in that differential elastic-scattering cross sections calculated from the Dirac–Hartree–Fock potential were utilized rather than those from the Thomas–Fermi–Dirac potential, a smaller analyzer acceptance angle was chosen, and the number of trajectories in each simulation was an order of magnitude larger. New values of Q x and β eff were obtained for each photoelectron line, each X-ray source, and each XPS configuration. These Q x and β eff values could be fitted to simple two-parameter expressions, each a function of the single-scattering albedo and the photoelectron emission angle. Values of Q x from the new predictive formula differed from the previous expression by less than 1%. Larger deviations in the values of β eff , up to 2.5%, were found from the new fit to the β eff parameter. The new expressions for Q x and β eff provide a convenient means for correction of elastic-scattering effects in XPS.

InGaN layers with multiple quantum wells are widely used as active layers in advanced optoelectronic devices. In the present work, surface properties of some InGaN layers grown on GaN/sapphire substrates by plasma-assisted molecular beam epitaxy were examined. The total indium content incorporated in the crystalline lattice of In0.165Ga0.835N and In0.353Ga0.647N layers grown with a thickness of 70–200 nm was controlled by the growth temperature, and was determined from X-ray diffraction. Auger electron spectroscopy and X-ray photoelectron spectroscopy analysis reveal relatively smaller concentration of In within the surface area than in the bulk of the InGaN layers. The Ar+ XPS depth profile analysis shows the thick InGaN layers to be chemically homogeneous within an analytical area. To determine the electron inelastic mean free path in the layers within the 500–2000 eV range, relative elastic-peak electron spectroscopy measurements with Ni and Au standards were performed. The measured IMFPs were considerably larger than those predicted from the TPP-2M formula. The smallest root-mean-square-deviation and the mean percentage deviation of 9.9 A and 44.5%, respectively, were found between EPES IMFP data and those predicted for the In0.353Ga0.647N layer with respect to the Au standard. This work provided the detailed compositional and chemical changes of InGaN thick layers, and could be useful in solving key issues associated with the growth of high-quality layer with much higher In content.

There is currently renewed interest in the backscattering correction for Auger electron spectroscopy (AES). There are several reasons for this interest. First, the energy of the primary-beam energy reaches 25 keV in modern AES instruments and Shimizu’s predictive formulae based on calculations for primary energies between 3 keV and 10 keV are of uncertain validity at higher energies. Second, it has been shown recently that the present definition of the backscattering factor is based on a simplified model of electron transport that breaks down for low primary energies and/or more grazing-incidence angles. A new term, the backscattering correction factor (BCF) has therefore been introduced that is based on an advanced model of electron transport. Third, much progress has been recently made in the theory of electron transport and the data for electron-scattering parameters which should improve the reliability of calculated backscattering correction factors. Finally, the BCF from the advanced theoretical model has been found to depend on numerous parameters defining the solid, the selected Auger transition, and the experimental configuration. Since the derivation of a simple predictive formula for the BCF does not seem to be feasible, a computer-controlled database has been developed to provide BCFs for a user-specified material and experimental configuration. Examples are given of BCFs from the advanced and simplified models for Ag M4N45N45 Auger electrons from silver.

Electron spectra are generally presented in arbitrary units. The experimental elastic peak intensity Iespec(E) is determined by the elastic backscattering probability Ie(E) of electrons backscattered elastically within the solid angle of the spectrometer. The experimental elastic peak Iespec(E) is converted to Ie(E) backscattering probability using our new procedure based on the Goto ie(E) elastic backscattering current database. The elastic backscattering probability Ic(E) was calculated applying the EPESWIN software of Jablonski. Ie(E) < Ic(E) due to the surface losses of electrons, characterized by the surface excitation parameter Pse (SEP). Pse(E) was determined experimentally using the Goto database and the relationship of Tanuma. Our new procedure is applied to angular-resolved (AREPES) spectra of Jablonski and Zemek presented in arbitrary units. In their AREPES experiments, the experimental elastic peak intensity Iespec = Ie(E, αd, ΔΩ) was measured at αd angle of detection (35–74°) with a small HSA, with ΔΩ solid angle. The experimental value at 42° was converted to probability with the Goto database. It was corrected with a SEP parameter Pse, determined by trial and error method for Si, Ni, Cu and Ag for E = 0.5 and 1 keV primary energies. Copyright © 2010 John Wiley & Sons, Ltd.

We give a survey of information needed for quantitative surface analyses by X-ray photoelectron spectroscopy (XPS). We describe four terms (the inelastic mean free path, the effective attenuation length, the mean escape depth, and the information depth) that are commonly used as descriptors of the surface sensitivity of an XPS experiment. Due to the complicating effects of elastic scattering, numerical values for each measure are generally different. Analytical formulae are given for each quantity. We describe procedures for determination of surface composition (with an emphasis on three types of relative sensitivity factors), measurements of overlayer-film thickness, and determination of composition-versus-depth information from angle-resolved XPS. Information is given on measurements of photoelectron intensities and the effects of sample morphology and sample roughness. Sources of data are given for all parameters needed for quantitative XPS. We discuss some major remaining uncertainties in quantitative XPS analyses and describe expected future areas of growth in XPS applications.