Relationships between electron inelastic mean free paths, effective attenuation lengths, and mean escape depths

The terms inelastic mean free path (IMFP), effective attenuation length (EAL), and mean escape depth (MED) are frequently used to specify the surface sensitivity of Auger-electron spectroscopy (AES) and X-ray photoelectron spectroscopy (XPS). These terms are different conceptually because of the effects of elastic-electron scattering, and generally have different numerical values for a specified material and electron energy. In addition, values of the EAL and MED depend on the instrumental configuration. We give an historical overview of efforts to measure EALs by the overlayer method and of work to investigate elastic-scattering effects in AES and XPS. We then apply an analytical formalism developed from a solution of the kinetic Boltzmann equation within the transport approximation to demonstrate the relationships between the IMFP, EAL, and MED for selected elemental solids and for common measurement conditions. Examples are given to show the magnitude of elastic-scattering effects on MED values for angle-resolved XPS and AES. If XPS or AES data are acquired for emission angles between zero and 60°, the ratio of the MED to that found with elastic scattering neglected is approximately constant (to within 10%), and this ratio can be used to determine an average value for the EAL. This EAL value can then be used to establish the depth scale in the data analysis. Finally, we show ratios of the EAL to the IMFP for XPS from the Au 4s subshell with Mg K X-rays as a function of emission angle and depth; this ratio has a weak dependence on emission angle from zero to 40° but a more pronounced dependence for larger emission angles.     

Determination of the inelastic mean free paths (IMFPs) in Ti by elastic peak electron spectroscopy (EPES): Effect of impurities and surface excitations

Surface excitations are important in surface sensitive electron spectroscopes, especially in elastic peak electron spectroscopy (EPES) since they may distort quantitative information. This phenomenon is more pronounced at low electron energy and glancing emission angles and should be appropriately corrected.In the present work we investigate quantitatively the role of contaminations, density and surface excitations on electron inelastic mean free paths (IMFPs) in Ti determined by elastic peak electron spectroscopy (EPES) using Cu standard. In the Monte Carlo algorithm the new NIST 3.1 database of electron elastic scattering cross sections was applied. It has been also shown that accounting for surface excitations, as well as for appropriate input parameters (surface composition, density, hydrogen) in the EPES method, is important for accuracy of evaluated IMFPs. Due to high reactivity of Ti, the IMFPs for contaminated Ti may be of interest. The authors indicate the magnitude of various corrections on the IMFPs derived by EPES.     

Electron IMFPs in bulk Cd0.88Mn0.12Te crystals determined by EPES

The inelastic mean free path (IMFP) of electrons is a basic parameter for surface-sensitive electron spectroscopies (AES, XPS, EELS) in quantitative analyses.Cd_1−xMn_xTe mixed crystals are currently of great interest due to their magnetic and magneto-optical properties. Since information on electron transport processes in these semimagnetic compounds is scarce, their systematic studies are highly desirable.In the present work, the IMFPs in Cd_0.88Mn_0.12Te (1 1 0) crystal samples were obtained from EPES with use of the Ni standard in the electron energy range 500-2000 eV. In addition, we also explored the effect of bulk Mn content in the determination of the IMFP. Relative EPES measurements were carried out using the MICROLAB 350 spectrometer. The sample surface was sputter cleaned and amorphized by Ar⁺ ions. Surface composition of the samples was monitored in situ by XPS and AES. The measured IMFPs were uncorrected for surface excitations and compared with those predicted from the TPP-2M and G-1 formulae. Also, the values of the IMFPs determined here were compared with those evaluated from the expression of Sekine et al. However, accuracy of this expression is rather poor except the case of pure CdTe (x = 0). In general, good agreement was found between the measured IMFPs in Cd_0.88Mn_0.12Te and the corresponding predicted IMFPs. The root-mean-square deviation from IMFP values predicted from the TPP-2M formula was 1.2 Å. The mean percentage deviation from the TPP-2M IMFPs was 9.3%.     

蒙特卡洛方法计算材料表面激发参数

电子非弹性散射平均自由程（IMFP）是用表面电子能谱进行表面化学定量分析时极为重要的一个参数,它可以用测量的弹性峰电子能谱分析以及蒙特卡洛模拟来确定.为了更加精确地确定电子非弹性散射平均自由程,必须对弹性峰电子能谱中的表面激发效应进行修正,通常使用介电响应理论方法计算得到的表面激发参数.然而,通过理论计算得到的表面激发参数不能包含电子在材料内部输运过程中弹性散射的影响,进而影响所测的电子非弹性散射平均自由程的准确度.在这个工作中,我们采用蒙特卡洛方法来确定包含弹性散射效应时的表面激发参数.所得到的表面激发参数在不同能量、角度情况下,尤其是在弹性散射效应显著的60°以上的大角度入射、出射情况下,都与实验测量值符合得非常好.基于这些新确定的表面激发参数,可以在弹性峰电子能谱测量中获得更为准确的电子非弹性散射平均自由程数据.     

Evaluation of the inelastic mean free path (IMFP) of electrons in polyaniline and polyacetylene samples obtained from elastic peak electron spectroscopy (EPES)

The inelastic mean free path (IMFP) of electrons was determined experimentally for selected polyaniline and polyacetylene samples with Ag and Ni references using elastic peak electron spectroscopy (EPES). The surface composition was determined by XPS and density by helium pycnometry. The high resolution hemispherical ESA-31 and ADES-400 spectrometers were used for measurements in the energy range E = 0.5–3.0 keV and E =0.4 − 1.6 keV, respectively. The integrated elastic peak intensity ratios for sample and reference were calculated using the Monte Carlo (MC) algorithm based on the electron elastic scattering cross-sections database NIST SRD64 version 3.1 and applying TPP-2M IMFPs for polymers. Surface excitation parameters (SEP) and material parameters ( _ach ) for polymers were determined, using the model of Chen, from comparison of measured and MC calculated elastic peak intensity ratios. These corrections proved to be efficient in decreasing the percentage deviations between the obtained IMFPs and the TPP-2M formula IMFPs. The elastic peak of hydrogen was observed in the EPES spectra of polymers. The experimental contribution of the hydrogen to the total elastic peak was 0.58%, while this value obtained from the MC simulations was 1.98%.      

Determination of the inelastic mean free path of electrons in GaAs and InP after surface cleaning by ion bombardment using elastic peak electron spectroscopy

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 practical depth distribution function for angle-resolved Auger/photoelectron spectroscopy

It is shown that, to a good approximation, over the range of energies (single scattering albedo, ω 0.5) and angles (take-off angle >30°) used in angle-resolved AES and XPS spectroscopy, the depth distribution function (DDF) is approximately exponential with decay length Λ = λ_i(1 + λ_i/λ_tr)^−1/2, for inelastic mean free path (IMFP) λ_i, and transport mean free path λ_tr.

As Λ is also the length measured for the attenuation length experimentally (with either the overlayer technique or from backscatter spectra, equivalent to λ_i, using an interpretation which neglects elastic effects), the CDP may be obtained by straightforward Laplace inversion using experimentally determined attenuation lengths. That is, the correct composition depth profile may be obtained from systematically ignoring elastic scattering.     

Studies of iron and iron oxide layers by electron spectroscopes

Thin iron oxide layers prepared “in situ” in the ultra high vacuum on polycrystalline iron substrate were investigated by electron spectroscopy methods—X-ray photoelectron spectroscopy (XPS) and elastic peak electron spectroscopy (EPES), using spectrometer ADES-400. The texture and the average grain size of the iron substrate foil have been examined by glancing angle X-ray diffraction (XRD). Qualitative and quantitative estimation of investigated oxide layers was made using (i) the relative sensitivity factor XPS method, (ii) comparison of binding energy shifts of Fe 2p photoelectron line and (iii) non-linear fitting procedure of Fe 2p photoelectron lines.Both, sputter-clean polycrystalline iron substrate and finally grown Fe_2.2O₃ layer, were investigated by the EPES method to measure the electron transport parameters used for quantitative electron spectroscopy, such as the electron inelastic mean free path (IMFP) values. The IMFPs were measured in the electron kinetic energy range 200-1000 eV with the Cu standard. The surface excitation parameters using Chen and Werner et al. approaches were evaluated and applied for correcting these IMFPs. The discrepancies between the evaluated parameters obtained using the above quantitative and qualitative approaches for characterising the iron oxide layers were discussed.     

Characterization of thin films on the nanometer scale by Auger electron spectroscopy and X-ray photoelectron spectroscopy

We describe two NIST databases that can be used to characterize thin films from Auger electron spectroscopy (AES) and X-ray photoelectron spectroscopy (XPS) measurements. First, the NIST Electron Effective-Attenuation-Length Database provides values of effective attenuation lengths (EALs) for user-specified materials and measurement conditions. The EALs differ from the corresponding inelastic mean free paths on account of elastic-scattering of the signal electrons. The database supplies “practical” EALs that can be used to determine overlayer-film thicknesses. Practical EALs are plotted as a function of film thickness, and an average value is shown for a user-selected thickness. The average practical EAL can be utilized as the “lambda parameter” to obtain film thicknesses from simple equations in which the effects of elastic-scattering are neglected. A single average practical EAL can generally be employed for a useful range of film thicknesses and for electron emission angles of up to about 60°. For larger emission angles, the practical EAL should be found for the particular conditions. Second, we describe a new NIST database for the Simulation of Electron Spectra for Surface Analysis (SESSA) to be released in 2004. This database provides data for many parameters needed in quantitative AES and XPS (e.g., excitation cross-sections, electron-scattering cross-sections, lineshapes, fluorescence yields, and backscattering factors). Relevant data for a user-specified experiment are automatically retrieved by a small expert system. In addition, Auger electron and photoelectron spectra can be simulated for layered samples. The simulated spectra, for layer compositions and thicknesses specified by the user, can be compared with measured spectra. The layer compositions and thicknesses can then be adjusted to find maximum consistency between simulated and measured spectra, and thus, provide more detailed characterizations of multilayer thin-film materials. SESSA can also provide practical EALs, and we compare values provided by the NIST EAL database and SESSA for hafnium dioxide. Differences of up to 10% were found for film thicknesses less than 20 Å due to the use of different physical models in each database.     

Surface excitation correction of the inelastic mean free path in selected conducting polymers

In earlier works, the inelastic mean free path (IMFP) of electrons was determined by elastic peak electron spectroscopy (EPES) using Ni and Ag reference standard samples, but fully neglecting surface excitation. Surface excitation that is characterized by the surface excitation parameter (SEP), and may affect considerably the elastic peak for the sample and the reference material. The SEP parameters of selected conducting polymers (polythiophenes, polyaniline and polyethylene) were determined by EPES using Si and Ge reference samples. Experiments were made with a hemispherical analyzer of energy resolution 100-200 meV in the E = 0.2-2.0 keV energy range. The composition of the sample surfaces was determined by in situ XPS, their surface roughness by AFM. The experimental SEP parameter data of eight polymer samples were determined by our new procedure, using the formulae of Chen and Werner et al. in the E = 0.2-2.0 keV energy range. The trial and error procedure is based on the best approach between the experimental and calculated IMFPs, corrected on surface excitation. The improvement in the SEP correction appears in the difference between the corrected and Monte Carlo calculated IMFPs, assuming Gries and Tanuma et al. IMFPs for polymers and standard, respectively. The term describing the improvement by SEP resulted in 50-72% (good correction for five polymers) 24% (poor correction for one polymer), 1-6% (no correction for two polymers). The 100% correction was not achieved, indicating that the difference between experimental and calculated IMFP cannot be entirely explained by surface excitation. Using the SEP data of Si and Ge reference samples based on Chen's and Werner's material parameter values resulted in similar SEP corrections for the polymer samples.     

Inelastic mean free path, surface excitation parameter, and differential surface excitation parameter in Au for 300-3000 eV electrons

An analytical approach for simultaneously determining an inelastic mean free path (IMFP), a surface excitation parameter (SEP) and a differential SEP (DSEP) with absolute units was applied for the analysis of absolutely measured reflection electron energy loss spectra for Au. The IMFP, SEP and DSEP in Au for 300-3000 eV electrons are successfully obtained. The obtained DSEPs show a reasonable agreement with those theoretically calculated. The present SEPs were compared with those calculated by several empirical equations, revealing that the present SEPs are close to those calculated using the Oswald's equation. The IMFPs for Au determined by the present analysis were compared with those calculated by the TPP-2M predictive equation, revealing that the present IMFPs are in fairly good agreement with those calculated by the TPP-2M equation. The results confirmed that the present approach is effective for experimentally determining the SEP, DSEP, and IMFP for electrons in solids.     

Background subtraction in electron spectroscopy by use of reflection electron energy loss spectra

The use of reflected electron energy loss spectra (REELS) in deconvoluting the inelastic background signal from XPS and AES spectra from homogeneous samples is studied. It is demonstrated that under certain assumptions, the cross section for inelastic electron scattering can be extracted from a REELS spectrum. This cross section is applied to deconvolute an experimental XPS spectrum of aluminium. The method, its limitations and its relation to other methods are discussed.     

Surface and core hole effects in X-ray photoelectron spectroscopy

In XPS analysis, two effects, which significantly reduce the measured peak intensity, are usually neglected: the core hole left behind in an XPS process which causes “intrinsic” excitations and excitations as the photoelectron pass through the surface region. We have calculated these effects quantitatively for various energies, geometries, and materials. Instead of considering the two effects separately, we introduce a new parameter, namely the correction parameter for XPS or CP_XPS, which takes into account both effects. We define this CP_XPS as the change in probability for emission of a photoelectron caused by the presence of the surface and the core hole in comparison with the situation where the core hole is neglected and the electron travels the same distance in an infinite medium. The calculations are performed within the dielectric response theory by means of the QUEELS–XPS software determining the energy-differential inelastic electron scattering cross-sections for X-ray photoelectron spectroscopy (XPS) including surface and core hole effects. This study has been carried out for electron energies between 300 eV and 3400 eV, for angles to the surface normal between 0° and 60° and for various materials. We find that the absolute effect is a reduction by 35–45% in peak intensities but that the variation in CP_XPS with material, angle and energy are < ± 10% for emission angle ≤ 60° and photoelectron energy ≤ 1500 eV. This implies that when XPS analysis is done using relative intensities, the combined effect of the surface and of the core hole is typically less than ≈ ± 10% for geometries and energies normally used in XPS. In practice, it is however difficult to determine the bare peak intensity without the intrinsic electrons because the two overlap in energy.     

Spin dependent mean-free path of low-energy electrons in ferromagnetic materials

Spin resolved attenuation measurements of electrons transmitted through overlayers of Fe and Co show that the electron inelastic mean free path (IMFP) in these materials is spin-dependent at low energies. The spin-up IMFP is larger than the spin-down IMFP. The values from different studies are in reasonable agreement. The data suggest that the origin of the spin dependence is mainly due to inelastic processes. Effects from spin dependent elastic scattering have not been identified directly in these experiments. The spin filter effect based on preferential attenuation of spin-down electrons can be used as a basis of spin polarization detectors.     

Angular and energy dependences of the surface excitation parameter for semiconducting III-V compounds

Sum-rule-constrained extended Drude dielectric functions were used to study surface excitations generated by energetic electrons moving across surfaces of semiconducting III-V compounds. Parameters in the dielectric functions were determined from fits to experimental optical data and electron energy-loss spectra. Electron inelastic mean free paths (IMFPs) in GaN, GaP, GaAs, GaSb, InAs and InSb were calculated for electron energies between 200 and 2000 eV, and the results were found to follow the simple formula, i.e., λ = kE^p, where λ is the IMFP and E is the electron energy. Surface excitation parameters (SEPs), which describe the total probability of surface excitations by electrons crossing the surface and travelling in vacuum, were also calculated for different electron energies and crossing angles. The SEP was found to follow the simple formula, i.e., , where P_s is the SEP and α is the crossing angle relative to the surface normal.     

Relative electron inelastic mean free paths for diamond and graphite at 8 keV and intrinsic contributions to the energy-loss

We used hard X-ray photoelectron spectroscopy (HAXPES) with 8 keV X-rays to investigate the 1s emission of carbon. We recorded spectra extending from the peak of the C 1s electrons (“elastic” line) to electrons with up to 110 eV energy-loss. Using two samples side by side, we could compare the inelastic mean free paths (IMFPs) of the electrons of almost 8 keV in diamond and graphite and find them to be practically identical despite about 50% difference in densities. Published extrapolations of their IMFP calculations at lower energies are in good agreement with this result. We show that information from the almost structureless region of overlapping multiple extrinsic energy-losses can be used to quantify the fraction of photoelectrons experiencing intrinsic energy-losses (those due to the sudden creation of the hole). We find that this fraction is 58% of the primary excited C 1s electrons for diamond and is practically the same for graphite. This is at first sight an unexpected result since hole-screening should differ in a semimetal from that in an insulator. The observation can be accounted for by dynamic screening in contrast to static screening.     

Universal quantification of elastic scattering effects in AES and XPS

Elastic scattering of photoelectrons in a solid can be accounted for in the common formalism of XPS by introducing two correction factors, β_eff and Q_x. In the case of AES, only one correction factor, Q_A, is required. As recently shown, relatively simple analytical expressions for the correction factors can be derived from the kinetic Boltzmann equation within the so-called “transport approximation”. The corrections are expressed here in terms of the ratio of the transport mean free path (TRMFP) to the inelastic mean free path (IMFP). Since the available data for the TRMFP are rather limited, it was decided to complete an extensive database of these values. They were calculated in the present work for the same elements and energies as in the IMFP tabulation published by Tanuma et al. An attempt has been made to derive a predictive formula providing the ratios of the TRMFP to the IMFP. Consequently, a very simple and accurate algorithm for calculating the correction factors β_eff, Q_x and Q_A has been developed. This algorithm can easily be generalized to multicomponent solids. The resulting values of the correction factors were found to compare very well with published values resulting from Monte Carlo calculations.     

On line shape analysis in X-ray photoelectron spectroscopy

Any solid state X-ray photoelectron spectrum (XPS) contains contributions due to multiple inelastic scattering in the bulk, surface excitations, energy losses originating from the screening of the final state hole (intrinsic losses), and, for non-monochromatized incident radiation, ghost lines originating from the X-ray satellites. In the present paper it is shown how all these contributions can be consecutively removed from an experimental spectrum employing a single general deconvolution procedure. Application of this method is possible whenever the contributions mentioned above are uncorrelated. It is shown that this is usually true in XPS to a good approximation. The method is illustrated on experimental non-monochromatized MgK spectra of Au acquired at different detection angles but for the same angle of incidence of the X-rays.     

Surface excitation effects in elastic peak electron spectroscopy

Surface electron inelastic excitations, a consequence of electron-surface interaction, effect the measured intensities in surface-sensitive electron spectroscopic methods and distort the quantitative information. This phenomenon is more pronounced at low electron energy and glancing emission angles. In this work we investigate quantitatively the influence of the surface excitation effects on the measured electron elastic backscattering probability. As a model system we used Si, Cu and Al, i.e. materials with different surface excitation properties. Results obtained show that properly corrected measured elastic electron backscattering probabilities lead to inelastic mean free path values which compare well with the theory.