Inelastic Mean Free Path Research Articles

Factor analysis of inelastic electron scattering cross section spectra of Si, Fe and iron silicides FeSi2, Fe5Si3

The inelastic electron scattering cross-section spectra of Si, Fe and iron silicides FeSi2, Fe5Si3 were calculated from the experimental reflected electron energy loss spectra as the product of the average inelastic mean free path and the differential cross section of the inelastic electron scattering. The inelastic electron scattering cross-section spectra were studied using factor analysis. This method allowed us to quantitatively separate the surface and volume contributions to the spectra, and determine the energy of the bulk plasmon more accurately than it is possible using traditional methods.

GaP/Si(0 0 1) interface study by XPS in combination with Ar gas cluster ion beam sputtering

The study of the chemical composition of buried interfaces by X-ray photoelectron spectroscopy (XPS) is limited by the inelastic mean free path of emitted photoelectrons (PE). Soft X-ray sources (AlKα) are generally suitable for careful probing of surfaces or very thin films. Here we applied gas cluster ion beam sputtering in combination with in-situ XPS (GCIB-XPS) to analyze buried GaP/Si(0 0 1) heterointerfaces. The GCIB method was used to dig a crater into the 20 nm thick GaP(0 0 1) film. We found optimal parameters for GCIB sputtering and achieved interface layers without severe damage. Destructive effects, i.e. broadening of core level peaks, could not be completely avoided, however, and the formation of metallic Ga on the GaP surface was observed. PE spectra of the sputtered heterostructures were compared with corresponding reference spectra of sputtered bulk crystals. Interface contributions to the intensity of phosphorus and sillicon core level peaks were revealed: interface components are shifted to high binding energies of P 2p Si 2p core levels. Similar results were obtained on 4 nm thick GaP/Si(0 0 1) by XPS. Finally, a top-to-bottom concept for buried semiconductor interfaces studies by GCIB-XPS is demonstrated.

Practical guide for inelastic mean free paths, effective attenuation lengths, mean escape depths, and information depths in x-ray photoelectron spectroscopy

Information is provided on four terms that are used for different purposes in x-ray photoelectron spectroscopy (XPS): the inelastic mean free path (IMFP), the effective attenuation length (EAL), the mean escape depth (MED), and the information depth (ID). While the IMFP is a parameter that depends on both the material and electron energy, the other three terms depend on the IMFP, the instrumental configuration, and the magnitude of elastic-scattering effects in the sample material. In addition, different EALs can be defined for different XPS applications, and the numerical values for each application can differ. Guidance is given on sources of IMFP and EAL data and on predictive equations for IMFPs, EALs, MEDs, and IDs. This guide is one of a series intended to highlight best practices in the use of XPS.

Electron Inelastic Mean Free Paths for LiF, CaF2, Al2O3, and Liquid Water from 433 keV down to the Energy Gap.

We report new calculations, which include the influence of the band gap and exciton states, of the electron inelastic mean free path (IMFP) for liquid water, LiF, CaF2, and Al2O3 from the band gap to 433 keV. Among compounds, liquid water is the most studied due to its role in radiobiological research, whereas LiF and CaF2 are the most widely used thermoluminescent dosimeters in environmental monitoring and medical and space dosimetry. Due to its sensitivity, the optically stimulated luminescent dosimeter, Al2O3, has recently begun to be used for personnel monitoring. Previous treatments have modified the integration domain to consider the indistinguishability between the incident electron and the ejected one or the bandgap energy for nonconductors but not to accommodate exciton states within the band gap, and no published IMFP data are available for CaF2. Our calculation was carried out using an electron-beam–solid-state interaction model through the relativistic full Penn algorithm. Integration limits that consider the band gap, the valence band width, and exciton interactions have been used. The results suggest that, at electron energies below 100 eV, the different choices of models for integration limits and the exciton interaction can affect the IMFP by 9–29%. At higher energies, the differences associated with the choice of energy-loss function and other input parameters are around 2.5–7.5%.

Inelastic mean free path measurement by STEM-EELS technique using needle-shaped specimen

Inelastic mean free path (IMFP) was determined by electron energy loss spectroscopy (EELS) to estimate the accurate thickness of TEM thin foil using needle-shaped specimen. From EELS measurements performed for 99.99% Al, Si wafer and 99.99% Fe, linear relationships were confirmed between the thickness of the TEM thin foil and the ratio of the total intensity of EELS spectrum to the total intensity of zero-loss spectrum for all samples. By weighted least-square fitting, the IMFP was estimated to be 143−150 nm for Al, 159−165 nm for Si with amorphous layer, and 92−94 nm for Fe with the collection semi-angle β = 11.9 − 35.7 mrad, and accelerated voltage of 200 kV. Thus, the dependence of IMFP on β is not dominant. The accuracy depends on the roundness of the cross-section of the needle-shaped specimen, and is observed to be low in terms of percentage in this work.

Raw-to-repository characterization data conversion for repeatable, replicable, and reproducible measurements

The National Institute for Materials Science, Japan, has been developing a materials data platform linked with a materials data repository system for rapid new material searching using materials informatics. Data conversion from raw data to a human-legible/machine-readable data file is one of the key preparation techniques prior to data analysis, where the converted data file should include metainformation. The tools developed by the authors can convert raw data to a structured data package that consists of mandatory and measurement-characterization metadata, primary and raw parameters, and formatted numerical data (FND). The FND are expressed as a matrix type with robust flexibility. This flexibility is achieved by applying the data analysis architecture of schema-on-read, not schema-on-write based on de jure standards, such as ISO documents. The primary parameters are carefully selected from raw parameters, and their vocabularies are transformed from instrument-dependent terms to general terms that everyone can readily understand. The converted data are linked with, for example, specimen information, process information, specimen handling records, and the electronic laboratory notebook. Using this raw-to-repository (R2R) conversion flow, the authors demonstrated that they can generate and store interoperable data files of x-ray photoelectron spectroscopy (XPS) spectra and depth profiles, powder x-ray diffraction patterns, (scanning) transmission electron microscope images, transmission electron diffraction patterns, electron energy-loss spectroscopy spectra, and calculated electron inelastic mean free path data. Linking measurement data to other required information ensures experimentally repeatable, replicable, and reproducible results. The mandatory and characterization metadata are used for quick electronic searching, and primary and raw parameters are convenient for setting up measurement conditions and useful for reproducibility/replicability and replicability/repeatability, respectively. The FND are human legible and machine readable using parser software, leading to a long lifetime of data utilization. The authors also developed a system to allow the semiautomatic data transfer from an instrument-controlling personal computer (PC) isolated from the communication network by adopting a Wi-Fi-capable secure digital card’s scripting capability while keeping the PC offline. They are developing further software for on-demand data manipulation after R2R data conversion. To date, it has been possible to perform XPS peak separation using an automated information compression technique without any a priori assumption. By combining R2R conversion with a high-throughput data collection system and automated data analysis routine, highly reproducible data acquisition and data analysis could be achieved, where human interaction is minimized. At this early stage, the authors demonstrate automated peak separation processing for XPS C 1s and O 1s narrow spectra of polyethylene terephthalate with very high reproducibility.

Alternative Approach for the Determination of Mean Free Paths of Electron Scattering in Liquid Water Based on Experimental Data.

Mean free paths of low-energy electrons in liquid water are of importance for modeling many physicochemical processes, but neither theoretical predictions nor experimental results have converged for these parameters. We therefore introduce an approach to determine elastic and inelastic mean free paths (EMFP, IMFP) based on experimental data. We show that ab initio calculations of electron scattering with water clusters converge with cluster size, thus providing access to condensed-phase scattering. The results are used in Monte Carlo simulations to extract EMFP and IMFP from recent liquid-microjet experiments that determined the effective attenuation length (EAL) and the photoelectron angular distribution (PAD) following oxygen 1s-ionization of liquid water. For electron kinetic energies from 10 to 300 eV, we find that the IMFP is noticeably larger than the EAL. The EMFP is longer than that of gas-phase water and the IMFP is longer compared to latest theoretical estimations, but both EMFP and IMFP are much shorter than suggested by experimental measurements of integral cross sections for amorphous ice.

Electron inelastic mean free path in water.

Liquid phase transmission electron microscopy (LPTEM) is rapidly developing as a powerful tool for probing processes in liquid environments with close to atomic resolution. Knowledge of the water thickness is needed for reliable interpretation and modelling of analytical studies in LPTEM, and is particularly essential when using thin liquid layers, required for achieving the highest spatial resolutions. The log-ratio method in electron energy-loss spectroscopy (EELS) is often applied in TEM to quantify the sample thickness, which is measured relative to the inelastic mean free path (λIMFP). However, λIMFP itself is dependent on sample material, the electron energy, and the convergence and divergence angles of the microscope electronoptics. Here, we present a detailed quantitative analysis of the λIMFP of water as functions of the EELS collection angle (β) at 120 keV and 300 keV in a novel nanochannel liquid cell. We observe good agreement with earlier studies conducted on ice, but find that the most widely used theoretical models significantly underestimate λIMFP of water. We determine an adjusted average energy-loss term Em, water, and characteristic scattering angle θE, water that improve the accuracy. The results provide a comprehensive knowledge of the λIMFP of water (or ice) for reliable interpretation and quantification of observations in LPTEM and cryo-TEM studies.

Optical properties of silicon and germanium determined by high-precision analysis of reflection electron energy loss spectroscopy spectra

We present a detailed analysis and comparison of four models describing the extension of the electron-energy loss function from the optical limit of q\ensuremath{\rightarrow}0 into the (q,\ensuremath{\omega}) plane to obtain the bulk and surface terms of differential inverse inelastic mean free paths. We found that the best model that describes accurately and times efficiently the calculation of the energy loss function of free-electron-like materials is the combination of the Penn algorithm [Phys. Rev. B 35, 482 (1987)] with the Ritchie-Howie method [Philos. Mag. 36, 463 (1977)]. Applying this model in our reverse Monte Carlo method, we determined, with high-precision, electron-energy loss functions of silicon and germanium based on the theoretical analysis of the high-energy resolution reflected electron energy loss spectroscopy (REELS) spectra, measured at 3, 4, and 5 keV incident electron energies. The refractive index $n$, the extinction coefficient $k$, and the complex dielectric function ($\ensuremath{\varepsilon}={\ensuremath{\varepsilon}}_{1}+i{\ensuremath{\varepsilon}}_{2}$) were calculated from the obtained energy loss function in a wide energy loss range of 0--200 eV. The accuracy of the obtained results is justified with various sum rules. We found that the calculated optical data of Si and Ge fulfill the sum rules with an average accuracy of 0.11% or even better. Therefore, the use of these optical data in materials science and surface analysis is highly recommended for further applications.

Stopping powers and inelastic mean free path from quantitative analysis of experimental REELS spectra for electrons in Ti, Fe, Ni, and Pd

Stopping power (SP) and inelastic mean free path (IMFP) of electrons in Ti, Fe, Ni, and Pd have been determined by using dielectric models. We have used energy loss function (ELF) determined from quantitative analysis of experimental reflection electron energy loss spectroscopy (REELS) spectra as the input parameter for this model. ELF in this study was determined from the previously published quantitative analysis of REELS spectra. The SP of Fe, Ni, Pd, and Ti was compared with several calculation methods for energies from 100 eV to 10 keV and shows SP in this study, which are in best agreement for medium to high energies (greater than or equal to 300 eV). The IMFP obtained in this study shows the best agreement with online database TPP2M and NIST and also calculation by Tanuma with a root mean square (rms) less than 12%. The present approach shows ELF from quantitative analysis of REELS spectra has a high potential for the experimental determination of SP and IMFP of metals.

Unveiling the principle descriptor for predicting the electron inelastic mean free path based on a machine learning framework

ABSTRACT The TPP-2M formula is the most popular empirical formula for the estimation of the electron inelastic mean free paths (IMFPs) in solids from several simple material parameters. The TPP-2M formula, however, poorly describes several materials because it relies heavily on the traditional least-squares analysis. Herein, we propose a new framework based on machine learning to overcome the weakness. This framework allows a selection from an enormous number of combined terms (descriptors) to build a new formula that describes the electron IMFPs. The resulting framework not only provides higher average accuracy and stability but also reveals the physics meanings of several newly found descriptors. Using the identified principle descriptors, a complete physics picture of electron IMFPs is obtained, including both single and collective electron behaviors of inelastic scattering. Our findings suggest that machine learning is robust and efficient to predict the IMFP and has great potential in building a regression framework for data-driven problems. Furthermore, this method could be applicable to find empirical formula for given experimental data using a series of parameters given a priori, holds potential to find a deeper connection between experimental data and a priori parameters.

Velocity map imaging of inelastic and elastic low energy electron scattering in organic nanoparticles.

Electron transport is of fundamental importance and has application in a variety of fields. Different scattering mechanisms affect electron transport in the condensed phase; hence, it is important to comprehensively understand these mechanisms and their scattering cross sections to predict electron transport properties. Whereas electron transport is well understood for high kinetic energy (KE) electrons, there is a discrepancy in the experimental and theoretical values for the Inelastic Mean Free Path (IMFP) in the low KE regime. In this work, velocity map imaging soft X-ray photoelectron spectroscopy is applied to unsupported organic nanoparticles (squalene) to extract experimental values of inelastic and elastic mean free paths (EMFPs). The obtained data are used to calculate corresponding scattering cross sections. The data demonstrate a decrease in the IMFP and increase in the EMFP with increasing electron KE between 10 and 50 eV.

Principles of High-Resolution Dopant Profiling in the Scanning Helium Ion Microscope, Image Widths, and Surface Band Bending

Dopant mapping using secondary electrons (SEs) in the scanning helium ion microscope is correlated with the surface charge distributions and electron inelastic mean free path. Numerical results show that the doping contrast is mainly a function of bulk built-in voltages modified by surface band-bending effects within a 3-nm-thick surface layer. The strong surface work function sensitivity of the SE yield and highly suppressed SE2/SE1 ratio militate the higher specificity to acceptors (donors), with surface charging constraining the threshold sensitivity to around 1017 cm−3 in thicker p-layers, compared to ~1015 cm−3 commonly attainable in the scanning electron microscope.

Analysis of XPS and REELS spectra of beryllium

The differential inverse inelastic mean free paths (DIIMFP) of beryllium were derived from energy spectra acquired using X-ray photoelectron spectroscopy and electron energy loss spectroscopy techniques by means of the fitting of calculated spectra to experimental data. The calculation of the energy spectra is performed employing the partial intensity approach (PIA). The EELS and XPS spectra were acquired in different laboratories using different Be samples. The comparison of the obtained DIIMFPs with literature data is presented.

The interplay of work function and polarization state at the Schottky barriers height for Cu/BaTiO3 interface

The emerging field of electronics based on ferro-functional materials relies on driving effectively and predictably a ferroelectric system between different polarization states through bias applied to metallic contacts. This requires detailed understanding of the growth mechanisms and electronic properties of the interface, including ferroelectric and material – dependent band alignment and Schottky barrier heights. Whether the major contribution at the interface band alignment comes from the work function difference or from the ferroelectric state is still under debate. Here, using X-ray photoemsion and ab-initio calculations, we derive the complex microscopic picture of metal/ferroelectric interface formation, including growth mechanism, valence alteration, ferroelectric-dependent electrostatic potential and thickness – dependent compensation mechanisms of ferroelectricity, starting from the ultrathin growth of Cu up to 100Å on BaTiO3. One establishes the evolution of the band bending and of the build-in potential from the initial probed thickness of the ferroelectric in the range of 3λ (λ – the inelastic mean free path) while gradually approaching the contact region with the metal at higher thickness of the top layer. We find that the well-defined orientation of the ferroelectric polarization lead to a band bending at the interface, which add at the bending expected from the work function difference of the two joining materials.

Local atomic structure analysis of GaN surfaces via X-ray absorption spectroscopy by detecting Auger electrons with low energies.

GaN is a promising material for power semiconductor devices used in next-generation vehicles. Its electrical properties such as carrier mobility and threshold voltage are affected by the interface between the oxide and the semiconductor, and identifying the interface states is important to improve these properties. A surface-sensitive measurement of Ga K-edge extended X-ray absorption fine structure (EXAFS) by detecting Ga LMM Auger electrons that originate from Ga K-shell absorption is proposed for GaN. LMM Auger electrons with low energies were detected and the EXAFS oscillation was confirmed, providing information on the Ga atoms at the surface. Investigation of thermally oxidized GaN with an oxide film of defined thickness showed that the analysis depth was less than 10 nm, which is consistent with the inelastic mean free path of 2.3 nm estimated for LMM Auger electrons in GaN.

Stopping power and inelastic mean free path of 300 eV–50 keV electrons for lanthanum aluminate

SP (Stopping Power) and IMFP (Inelastic Mean Free Path) of lanthanum alumínate (La2O3)x (Al2O3)1–x was varied with x = 0.25, 0.34, and 0.5. for electron energy from 300 eV to 50 keV have been determined by using composite Simpson from the equation of Born Ochkur correction. The main parameter in determining the SP and IMFP is Energy Loss Function (ELF) which was obtained from the experimental reflection electron energy loss (REELS) spectra. The method in this study is convenient methods for determining SP for binary compound lanthanum aluminate.

Determination of the Relative Concentration of Deuterium Implanted into Beryllium by Elastic Peak Electron Spectroscopy

The relative concentration of deuterium implanted into a beryllium sample is determined by elastic peak electron spectroscopy (EPES). The method of partial intensities based on solution of the boundary value problem for the transport equation by the invariant embedding method is used for subsequent determination of the energy spectra of reflected electrons. The differential inverse inelastic mean free paths (DIIMFPs) and the differential surface excitation probability (DSEP) are retrieved using a fitting procedure based on numerous solutions of the direct problem with fitting parameters. The high efficiency of the fitting procedure is based on the technique of numerical solution of equations for the partial intensities, which combines precision and a record-high calculation speed. In the work DIIMFP and DSEP are obtained for both the surface region and for a homogeneous array in the bulk. Calculations of DIIMFP and DSEP are carried out for pure beryllium and for beryllium samples implanted with deuterium. The relative concentrations of deuterium into beryllium were determined at a different fluence. The obtained values of the relative deuterium concentrations are nD/nBe = 0.12 ± 0.02 and 0.15 ± 0.03 for an irradiation dose of 5.5 × 1021 and 20.1 × 1021 m–2, respectively. The results indicate that, in comparison with the methods used earlier, the developed method allows an order of magnitude in of the sensitivity of determining the relative hydrogen-isotope concentration in compounds to be attained.

Energy-Dependent Relative Cross Sections in Carbon 1s Photoionization: Separation of Direct Shake and Inelastic Scattering Effects in Single Molecules.

We demonstrate that the possibility of monitoring relative photoionization cross sections over a large photon energy range allows us to study and disentangle shake processes and intramolecular inelastic scattering effects. In this gas-phase study, relative intensities of the carbon 1s photoelectron lines from chemically inequivalent carbon atoms in the same molecule have been measured as a function of the incident photon energy in the range of 300-6000 eV. We present relative cross sections for the chemically shifted carbon 1s lines in the photoelectron spectra of ethyl trifluoroacetate (the "ESCA" molecule). The results are compared with those of methyl trifluoroacetate and S-ethyl trifluorothioacetate as well as a series of chloro-substituted ethanes and 2-butyne. In the soft X-ray energy range, the cross sections show an extended X-ray absorption fine structure type of wiggles, as was previously observed for a series of chloroethanes. The oscillations are damped in the hard X-ray energy range, but deviations of cross-section ratios from stoichiometry persist, even at high energies. The current findings are supported by theoretical calculations based on a multiple scattering model. The use of soft and tender X-rays provides a more complete picture of the dominant processes accompanying photoionization. Such processes reduce the main photoelectron line intensities by 20-60%. Using both energy ranges enabled us to discern the process of intramolecular inelastic scattering of the outgoing electron, whose significance is otherwise difficult to assess for isolated molecules. This effect relates to the notion of the inelastic mean free path commonly used in photoemission studies of clusters and condensed matter.

Scattering of e∓ from ytterbium atoms

The differential, total, momentum transfer and viscosity cross sections for the elastic scattering of electrons and positrons by ytterbium atoms have been calculated. We have also calculated the total inelastic and ionization cross sections. In addition, the Sherman function S(θ) and the inelastic mean free paths have been determined for the scattering of both projectiles. The critical minima in the elastic differential cross sections (DCS) were determined from the analysis of the DCS and S(θ). These investigations have been carried out within the framework of two different theoretical approaches at the impact energies 1 eV–0.5 GeV for both projectiles. In the atomic domain the solution involves a complex projectile-atom optical potential while in the nuclear domain only the nuclear potential has been employed. Both approaches employ the Dirac partial wave analysis. Our results are in reasonable agreement with available experimental data and other theoretical findings. To the best of our knowledge, for positron scattering, there are no experimental data available in the literature.