Inelastic Mean Free Path Length Research Articles

Accuracy limitations for composition analysis by XPS using relative peak intensities: LiF as an example

Although precision in XPS can be excellent, allowing small changes to be easily observed, obtaining an accurate absolute elemental composition of a solid material from relative peak intensities is generally much more problematical, involving many factors such as background removal, differing analysis depths at different photoelectron kinetic energies, possible angular distribution effects, calibration of the instrument transmission function, and variations in the distribution of photoelectron intensity between “main” peaks (those usually used for analysis) and associated substructure following the main peak, as a function of the chemical bonding of the elements concerned. The last item, coupled with the use of photoionization cross sections and/or relative sensitivity factors (RSFs), is the major subject of this paper, though it is necessary to consider the other items also, using LiF as a test case. The results show that the above issues, which are relevant to differing degrees in most XPS analyses, present significant challenges to highly accurate XPS quantification. LiF, using the Li1s and F1s XPS peaks, appears, at first sight, to be an ideal case for high accuracy. Only 1s core levels are involved, removing any possible angular effects, and it is a wide bandgap material, resulting in the main Li1s and F1s peaks being well separated from the following scattered electron backgrounds. There are, however, two serious complications: (1) the main F1s and F2s levels have a major loss of intensity diverted into satellite substructure spread over ∼100 eV KE from the main line, whereas the Li1s level has very much less diversion of intensity; (2) there is serious overlap of the substructure from F2s (∼30 eV BE) with the main line of Li1s at ∼56 eV. We report here a detailed analysis of the LiF XPS, plus a supporting theory analysis of losses of intensity from Li1s and F1s to satellite structure, based on the cluster models of LiF. We conclude that, if the overlap from the F2s substructure is correctly subtracted from Li1s, and the intensity from satellites for F1s and Li1s properly estimated, the atomic composition of the single crystal LIF may be recovered to within 5%, using the photoionization cross sections of Scofield, inelastic mean free path lengths based on Tanuma, Powell, and Penn, and the calibrated instrument transmission function. This refutes the claim by Wagner et al., based on their empirical determination of RSFs, (which applied only to the instruments and the analysis procedure they used, in 1981) that Scofield values are too low in general and, for Li1s in particular, are low by a factor of ∼2. This is important because Wagner-based RSFs (sometimes modified and sometimes not) are still embedded in quantification software on modern commercial instruments, and so analysts need to be aware of how those RSFs were obtained/modified. Incorrect use can lead to large quantification errors.

Nanoscale three-dimensional reconstruction of elastic and inelastic mean free path lengths by electron holographic tomography

Electron holography at medium resolution simultaneously probes projected electrostatic and magnetostatic potentials as well as elastic and inelastic attenuation coefficients with a spatial resolution of a few nanometers. In this work, we derive how the elastic and inelastic attenuation can be disentangled. Using that result, we perform the first three dimensional tomographic reconstruction of potential and (in)elastic attenuation in parallel. The technique can be applied to distinguish between functional potentials and composition changes in nanostructures, as demonstrated using the example of a GaAs—Al0.33Ga0.67As core-shell nanowire.

Resolving power of lens‐less low energy electron point source microscopy

Simulations show the resolving power of lens-less low energy electron point source microscopy to be approximately 15 A for electron energies of between 14 and 105 eV. This resolution can be improved to 10 A by employing a composite hologram method. However, these values fall short of predictions of at least 3 A resolution for electron energies in this range because the limited divergence angle of the electron beam had not previously been taken into account. Also shown is that electron coherence from field emitting tips that terminate in a single atom will not limit the resolving power as much as the beam divergence angle. The penetration depth of electrons with energies of between 50 and 100 eV, into biological molecules, was estimated from the inelastic mean free path length to be 25 A . This places an upper limit on the size of biological molecules for which internal structural information can be obtained using low energy electrons.

Growth of Fe on Ge(1 1 1) at room temperature studied by X-ray photoelectron diffraction

The growth of ultrathin Fe films of various coverages on Ge(1 1 1) at room temperature using molecular beam epitaxy (MBE) was studied via X-ray photoelectron diffraction (XPD or XPED) together with low energy electron diffraction (LEED) and X-ray photoelectron spectroscopy (XPS). All experimentally observed XPD patterns suggested local order structures of the Fe layers for all thicknesses studied. The short-range order of the resulting structures was found to be enhanced for thinner layers whereas the long-range order was gradually lost with increasing Fe thicknesses. At a very low coverage of 0.8 Å Fe and Ge tend to react to the partly ordered structure in which Fe atoms were located in local environments similar to those for higher Fe coverages. Comparison of theoretical and experimental XPD patterns, along with XPS results, showed that intermixing between Fe and Ge occurred during the pseudomorphic growth with a stacking fault near the interface for all Fe coverages under study. Nevertheless, small percentage of domains without the stacking fault was also found to coexist with those with the stacking fault by performing a quantitative analysis of a reliability factor R of the Fe2p pattern for 5.4 Å. The orientation changes of the Ge2p and Ge3d XPD patterns with Fe thickness were unambiguously explained in terms of their different dependencies on the overlayer thickness due to the different inelastic mean free path lengths used in the simulations. Also, Fe got increasingly enriched in the grown layers with increased Fe coverage. The resulting structures and intermixing are discussed in detail.

A Universal Predictive Equation for the Inelastic Mean Free Pathlengths of X-ray Photoelectrons and Auger Electrons

A new universal inelastic mean free pathlength (IMFP)-predictive equation (the G1 equation) has been formulated for use in the analytical electron spectroscopies XPS and AES which essentially states that the IMFP of an electron traversing matter is inversely proportional to the atomic density. The equation is based on a concept of matter in which the latter consists of clusters of interaction-prone regions (identified with the orbitals of an atom) in an otherwise interaction-free space. The energy dependence and best values for two fitting parameters were obtained from a large set of IMFPs, derived by Tanuma, Powell and Penn (TPP) from published optical data. The G1 equation has been developed to allow the IMFPs to be predicted not only for regular phases of elements and compounds (a common restriction on existing IMFP-predictive equations), but also for any sub- and non-stoichiometric arrangement of atoms found at technological surfaces. Evidence is presented which substantiates the claim of universal applicability of the G1 equation.

A Universal Predictive Equation for the Inelastic Mean Free Pathlengths of Xray Photoelectrons and Auger Electrons

A new universal inelastic mean free pathlength (IMFP)-predictive equation (the G1 equation) has been formulated for use in the analytical electron spectroscopies XPS and AES which essentially states that the IMFP of an electron traversing matter is inversely proportional to the atomic density. The equation is based on a concept of matter in which the latter consists of clusters of interaction-prone regions (identified with the orbitals of an atom) in an otherwise interaction-free space. The energy dependence and best values for two fitting parameters were obtained from a large set of IMFPs, derived by Tanuma, Powell and Penn (TPP) from published optical data. The G1 equation has been developed to allow the IMFPs to be predicted not only for regular phases of elements and compounds (a common restriction on existing IMFP-predictive equations), but also for any sub- and non-stoichiometric arrangement of atoms found at technological surfaces. Evidence is presented which substantiates the claim of universal applicability of the G1 equation.

Inelastic mean free pathlengths of electrons for quantitative investigations of ultrathin technological surface layers by angle-resolved x-ray photoelectron spectrometry

Angle-resolved self-ratio x-ray photoelectron spectrometry is shown to yield quantitative information on the depth composition of technological surfaces. The inelastic mean free pathlengths (IMFP) of x-ray photoelectrons required for quantification of the experimental data are obtained from a new universal formula (documented here for the first time). For the energy range 200–2000 eV, the two fitting parameters of the formula were deduced from the optical-data-derived IMFP of Tanuma, Powell, and Penn. These ‘‘optical’’ IMFP are presently being checked against IMFP derived from stopping data of high-energy protons and from mean-energy-loss-per-collision data (obtained from electron energy loss spectra). These latter IMFP are found to be significantly shorter than the optical IMFP. Equations are presented for conversion of proton-stopping powers to electron-stopping powers, and thence to IMFP.

Imaging of Metal/Semiconductor Interface by Ballistic-Electron-Emission Microscopy (Beem)

AbstractStudies in ballistic-electron-emission spectroscopy (BEES) have enabled precise energy measurements of Schottky barrier heights with excellent spatial resolution and, more recently, it was shown that even scattering at the metal/semiconductor interface affects the BEES spectrum [1]. Monte Carlo simulations have been done to predict the spatial resolution of ballistic-electron-emission microscopy (BEEM) [2]. In this paper, we will discuss the experimental spatial resolution of BEEM, and we will also give some of our BEES results for Au/Si and for Au/PtSi/Si. Our experimental BEEM studies indicate that, for Au/Si, hot electron transport is diffusive rather than ballistic, because the inelastic mean free path length (∼100 nm) is much larger than the elastic mean free path length (∼10 nm). This is in agreement with existing theories and with the literature on the internal photoemission method of studying the transport. Even in this diffusive regime, the spatial resolution of BEEM is still expected to be very good, being on the order of 10 nm [2]. Our preliminary work on PtSi shows that it has an attenuation length of 4 nm, which differs significantly from that of Au.

Quantitative Auger electron spectroscopy of silicides by extended matrix correction using dN(E)/dE spectra

AbstractAn extended matrix correction procedure is proposed which considers effects created by different atomic densities, electron backscattering, electron attenuation and peak shapes. Asymmetry factors are introduced that reflect line shape changes of signals in compounds or alloys very well. From asymmetry factors a peak shape correction factor is determined. To overcome the uncertainties in correction for changing electron attenuation, a new method for calculation of λ is presented. The results are compared with experimental values and tested in matrix correction. The concentration ratios obtained are compared with results using inelastic mean free path lengths or attenuation depths determined by the methods of Penn. Tanuma et al., Tokutaka et al. and Seah and Dench in matrix correction. For the determination of concentration ratios from samples of unknown composition, an iteration procedure is introduced. The extended matrix correction is applied on silicides such as VSi2, V5Si3, V3Si, CrSi2, Cr3Si, MoSi2, Pd2Si and PtSi, yielding results which are accurate to 7%. The weight of the individual correction factors in the extended matrix correction procedure is discussed, dependent on experimental conditions and sample constituents. Without correction for matrix effects, erroneous results up to 30% can occur.

Angular-Resolved ESCA Studies of Cadmium Arachidate Monolayers on Si (100): Inelastic Mean-Free Path and Depth Profile Analysis

AbstractAngular-resolved ESCA was used to study single cadmium arachidate monolayers transferred to Si (100) wafers by the Langmuir-Blodgett technique. We find the monolayers to be of high integrity with respect to those defects which enhance the escape probability of substrate photoelectrons through the overlayer. The inelastic mean-free pathlengths of Si (2p) and C (1s) electrons were calculated to be 49±6 Å and 45±6 Å for the kinetic energies of 1388 eV and 1202 eV, respectively. The overall ordering of the hydrocarbon chains is less than for alkane thiols assembled on noble metals. We find that the precision of the Tyler algorithm to deconvolute angular-resolved ESCA data into depth profiles is accurate within 10% for predicting the thickness of the hydrocarbon overlayer but less precise for intermediate layers.

Analytical Calculation of Complex Lattice Potentials for Electron Diffraction

For the quantitative interpretation of electron microscopical diffraction patterns it is often indispensable to perform simulations to get insight into the contrast mechanisms. If the inelastic mean free path length is not small compared with the crystal thickness the diffraction patterns are affected by absorption phenomena. In this case a realistic calculation must include these effects. Within the dynamical theory this can be done by adding an absorptive part to the Fourier coefficients Vg of the lattice potential .Because there are only few experimental data available the absorptive part must be computed. In the most cases the dominant contribution to arises from the thermal diffuse scattering since plasmon excitations and electron excitations contribute in good approximation only to the mean absorption potential . Then all branches of the dispersion surface are similiar attenuated.Extensive numerical calculations have been performed by Radi for many crystals. Nevertheless it is impossible to tabulate the for all crystals even for only few temperatures and acceleration voltages.

Electron mean-free pathlengths through monolayers of cadmium arachidate

The inelastic mean-free pathlengths λ, of 1042–1402 eV electrons through cadmium arachidate (C19H39COO)2Cd, monolayers have been determined from attenuation measurements of the core level photoemission (XPS) signals from gold, silver and indium substrates. Both fixed angle-variable overlayer thickness experiments and variable angle-fixed overlayer thickness experiments were performed. We derive a preferred value of 3.6 nm at 1117 eV and an E0.5 energy dependence over the narrow energy range considered. Values determined for bulk cadmium arachidate and arachidic acid from absolute intensity comparisons with gold and silver are close to the monolayer values. The results are discussed in the light of the controversy existing concerning other values of λ’s determined for organic and polymeric materials.

Quantitative electron spectroscopy of surfaces: A standard data base for electron inelastic mean free paths in solids

AbstractA compilation is presented of all published measurements of electron inelastic mean free path lengths in solids for energies in the range 0–10 000 eV above the Fermi level. For analysis, the materials are grouped under one of the headings: element, inorganic compound, organic compound and adsorbed gas, with the path lengths each time expressed in nanometers, monolayers and milligrams per square metre. The path lengths are vary high at low energies, fall to 0.1–0.8 nm for energies in the range 30–100 eV and then rise again as the energy increases further. For elements and inorganic compounds the scatter about a ‘universal curve’ is least when the path lengths are expressed in monolayers, λm. Analysis of the inter‐element and inter‐compound effects shows that λm is related to atom size and the most accuratae relations are λm = 538E−2+0.41(aE)1/2 for elements and λm=2170E−2+0.72(aE)1/2 for inorganic compounds, where a is the monolayer thickness (nm) and E is the electron energy above the Fermi level in eV. For organic compounds λd=49E−2+0.11E1/2 mgm−2. Published general theoretical predictions for λ, valid above 150 eV, do not show as good correlations with the experimental data as the above relations.

On the behavior of nuclear energy losses of electrons in alkali halides

The energy loss spectra of 50 keV-electrons passing through alkali halides consist of a steplike broad background with superposed characteristic maxima. All measured losses show an angular distribution of their intensity like ϑ 2. Some losses are so sharp that the measurement of a dispersion of less than 1 eV is possible. The inelastic mean free path length is very long, and amount to about 5 × 10 4 Å for the 13.6 eV- loss in LiF.