Inelastic Mean Free Path Research Articles

How the choice of model dielectric function affects the calculated observables

It is investigated how the model used to describe a dielectric function (i.e. a Mermin, Drude, Drude–Lindhard, Levine–Louie with relaxation time dielectric function) affects the interpretation of a REELS experiment, the calculation of the electron inelastic mean free path as well proton stopping and straggling. Three dielectric functions are constructed that are based on different models describing a metal, but have identical loss functions in the optical limit. A loss function with the same shape, but half the amplitude, is used to derive four different model dielectric functions for an insulator. From these dielectric functions we calculate the differential inverse mean free path, the mean free path itself, as well as the stopping force and straggling for protons. The similarity of the underlying physics between proton stopping, straggling and the electron inelastic mean free path is stressed by describing all three in terms of the differential inverse inelastic mean free path. To further highlight the reason why observed quantities depend on the model dielectric function used we study partial differential inverse inelastic mean free paths, i.e. those obtained by integrating over only a limited range of momentum transfers. In this way it becomes quite transparent why the observable quantities depend on the choice of model dielectric function.

Thickness and structure of thin films determined by background analysis in hard X-ray photoelectron spectroscopy

We report on the analysis of inelastic backgrounds associated with photoelectron peaks from thin films of Ru on Si using hard X-ray photoelectron spectroscopy (HAXPES) with an X-ray energy of 7939 eV. To extract information on the thickness and morphology of the Ru films, the Tougaard-background-analysis method was used. Consistent results from the analysis of the Si 1s peaks as well as the Ru 2p, 2s peaks to the thicknesses determined with X-ray reflectivity were found. Good agreement was also found for surface topography (the Ru forms islands on the Si surface for film thicknesses <12 nm and covers the complete surface for larger thicknesses) determined by our fitting results and scanning electron microscopy. It is demonstrated that with this method it is possible to obtain information on films up to 150 nm thickness, which corresponds to ∼20 times the inelastic mean free paths (IMFPs). This is larger than the previously reported ∼10 times the IMFP for X-ray photoelectron spectroscopy with conventional X-ray sources owing to the fact that the spectrum can be followed over a larger range of energy-loss. The method can also be used to determine the IMFP if the film thickness is known by another technique and it was applied to determine the IMFP for Ru at 4900 eV (4.3 nm) and 6050 eV (5.3 nm). In addition, some possible applications of the methods are described.

Determination of the input parameters for inelastic background analysis combined with HAXPES using a reference sample

The recent progress in HAXPES combined with Inelastic Background Analysis makes this method a powerful, non-destructive solution to get quantitative information on deeply buried layers and interfaces at depths up to 70nm. However, we recently highlighted the need for carefully choosing the scattering cross-sections in order to accurately describe the transport of photoelectrons through a complex overlayer structure with layers presenting very different scattering properties. It is found that the transport through such thick bi-layer structures can be described with an effective inelastic scattering cross-section in the form of a weighted sum of individual cross-sections of the pure layers. In this study, we have experimentally investigated this by analyzing Al/Ta/AlGaN stacks on a GaN substrate. We present a refined analytical method, based on the use of a reference spectrum, for determining the required input parameters, i.e. the inelastic mean free path and the effective inelastic scattering cross-section. The use of a reference sample gives extra constraints which make the analysis faster to converge towards a more accurate result. Based on comparisons with TEM, the improved method provides results determined with a deviation typically better than 5% instead of around 10% without reference. The case of much thicker overlayers up to 66nm is also discussed, notably in terms of accounting for elastic scattering in the analysis.

Outrunning damage: Electrons vs X-rays—timescales and mechanisms

Toward the end of his career, Zewail developed strong interest in fast electron spectroscopy and imaging, a field to which he made important contributions toward his aim of making molecular movies free of radiation damage. We therefore compare here the atomistic mechanisms leading to destruction of protein samples in diffract-and-destroy experiments for the cases of high-energy electron beam irradiation and X-ray laser pulses. The damage processes and their time-scales are compared and relevant elastic, inelastic, and photoelectron cross sections are given. Inelastic mean-free paths for ejected electrons at very low energies in insulators are compared with the bioparticle size. The dose rate and structural damage rate for electrons are found to be much lower, allowing longer pulses, reduced beam current, and Coulomb interactions for the formation of smaller probes. High-angle electron scattering from the nucleus, which has no parallel in the X-ray case, tracks the slowly moving nuclei during the explosion, just as the gain of the XFEL (X-ray free-electron laser) has no parallel in the electron case. Despite reduced damage and much larger elastic scattering cross sections in the electron case, leading to not dissimilar elastic scattering rates (when account is taken of the greatly increased incident XFEL fluence), progress for single-particle electron diffraction is seen to depend on the effort to reduce emittance growth due to Coulomb interactions, and so allow formation of intense sub-micron beams no larger than a virus.

Attosecond chronoscopy of electron scattering in dielectric nanoparticles

Attosecond streaking is used to study the dynamics of electron scattering in dielectric nanoparticles in real time. Revealing the mechanisms involved is the first step towards understanding electron scattering in more complex dielectrics. The scattering of electrons in dielectric materials is central to laser nanomachining1, light-driven electronics2 and radiation damage3,4,5. Here, we demonstrate real-time access to electron scattering by implementing attosecond streaking spectroscopy on dielectric nanoparticles: photoelectrons are generated inside the nanoparticles and both their transport through the material and photoemission are tracked on an attosecond timescale. We develop a theoretical framework for attosecond streaking spectroscopy in dielectrics and identify that the presence of the internal field inside the material cancels the influence of elastic scattering, enabling the selective characterization of the inelastic scattering time. The approach is demonstrated on silica nanoparticles, where an inelastic mean-free path is extracted for 20–30 eV. Our approach enables the characterization of inelastic scattering in various dielectric solids and liquids, including water, which can be studied in the form of droplets.

Triggering surface ferroelectric order in Pb(Zr,Ti)O3(001) by deposition of platinum

By platinum deposition on a 150nm thick film of lead zirco-titanate oriented PZT(001), grown on strontium titanate (001) single crystals with a strontium ruthenate buffer layer, which did not show initial preferential out-of-plane orientation of its ferroelectric polarization, a band bending near the interface towards lower energies is observed using photoelectron spectroscopy, by following all core levels from the substrate (Pb 4f, Zr 3d, Ti 2p, O 1s). This is unexpected given the fact that platinum has a larger work function than PZT and a rectifying contact for electrons is expected to be built at the interface. This observation may have two explanations: (i) platinum forms an alloy with elements from PZT yielding a metal with considerable lower work function; (ii) platinum provides electrons to the substrate which are able to compensate the depolarization field generated by the outwards polarization state. Several arguments are brought in favor of the second hypothesis, especially the attenuation of core levels from the substrate which is well described by exponential functions with reasonable values of the photoelectron inelastic mean free path, suggesting the formation of a sharp interface. High resolution transmission electron microscopy confirmed the sharpness of the interface.

Effective attenuation lengths for quantitative determination of surface composition by Auger-electron spectroscopy and X-ray photoelectron spectroscopy

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 160eV 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.

Electron inelastic mean free path at energies below 100 eV

Knowledge of electron inelastic mean free paths (IMFPs) is important for electron spectroscopy and microscopy studies. Here, we determine the IMFPs at energies below 100 eV for 10 elemental solids (V, Fe, Ni, Mo, Pd, Ag, Ta, W, Pt, and Au) within the dielectric formalism, using the energy-loss function calculated in the adiabatic local-density approximation of time-dependent density-functional theory. The resulting IMFPs at a few eV above the Fermi energy are comparable to those from ab initio calculations in the GW approximation of many-body theory. The present approach provides an alternative to evaluate hot-electron inelastic lifetimes.

Determination of the mean inner potential of cadmium telluride via electron holography

Mean inner potential is a fundamental material parameter in solid state physics and electron microscopy and has been experimentally measured in CdTe, a technologically important semiconductor. As a first step, the inelastic mean free path for electron scattering in CdTe was determined, using electron energy loss spectroscopy, to enable precise thickness mapping of thin CdTe lamellae. The obtained value was λi(CdTe, 300 kV) = 192 ± 10 nm. This value is relatively large, given the high density of the material, and is discussed in the text. Next, electron diffraction and specimen tilting were employed to identify weakly diffracting lattice orientations, to enable the straightforward measurement of the electron phase shift. Finally, electron holography was utilized to quantitatively map the phase shift experienced by electron waves passing through a CdTe crystal, with several different propagation vectors. Utilization of both thickness and phase data allowed computation of mean inner potential as V0 (CdTe) = 14.0 ± 0.9 V, within the range of previous theoretical estimates.

Numerical analysis of electronic conductivity in graphene with resonant adsorbates: comparison of monolayer and Bernal bilayer

We describe the electronic conductivity, as a function of the Fermi energy, in the Bernal bilayer graphene (BLG) in presence of a random distribution of vacancies that simulate resonant adsorbates. We compare it to monolayer (MLG) with the same defect concentrations. These transport properties are related to the values of fundamental length scales such as the elastic mean free path $L_{e}$, the localization length $\xi$ and the inelastic mean free path $L_{i}$. Usually the later, which reflect the effect of inelastic scattering by phonons, strongly depends on temperature $T$. In BLG an additional characteristic distance $l_1$ exists which is the typical traveling distance between two interlayer hopping events. We find that when the concentration of defects is smaller than 1\%--2\%, one has $l_1 \le L_e \ll \xi$ and the BLG has transport properties that differ from those of the MLG independently of $L_{i}(T)$. Whereas for larger concentration of defects $L_{e} < l_1 \ll \xi $, and depending on $L_{i}(T)$, the transport in the BLG can be equivalent (or not) to that of two decoupled MLG. We compare two tight-binding model Hamiltonians with and without hopping beyond the nearest neighbors.

In situ X-ray photoelectron spectroscopy of electrochemically active solid-gas and solid-liquid interfaces

In this account the application of synchrotron radiation based X-ray photoelectron spectroscopy (XPS) for the investigation of electrochemically active gas-solid and liquid-solid interfaces will be discussed. The potential of Near Ambient Pressure XPS (NAP-XPS) for the estimation of the surface electronic structure of electrochemically active interfaces will be described by two examples. Thereto the oxygen evolution reaction (OER) over Pt and IrOx anodes will be introduced. In particular the analysis of XP core level spectra of IrOx requires the development of an appropriate fit model. Furthermore the design of reaction cells based on proton exchange membranes (PEM) and on electron transparent graphene membranes, which enables the investigation of liquid-gas and liquid-solid interfaces under electrochemical relevant conditions will be discussed. In the last part of this article a perspective to the EMIL project at the synchrotron radiation facility BESSY will be given. The purpose of this project is the implementation of two new beamlines enabling X-ray photoelectron spectroscopy in the X-ray regime from 80eV–8keV under reaction conditions. The extension to the so called tender X-ray regime will allow the release of higher kinetic energy photoelectrons which have a higher inelastic mean free path compared to photoelectrons excited by soft X-ray radiation and therefore will enable the investigation of solid-liquid interfaces under electrochemical reaction conditions.

Monte Carlo simulations of measured electron energy-loss spectra of diamond and graphite: Role of dielectric-response models

In this work we compare Monte Carlo (MC) simulations of electron-transport properties with reflection electron energy-loss measurements in diamond and graphite films. We assess the impact of different approximations of the dielectric response on the observables of interest for the characterization of carbon-based materials. We calculate the frequency-dependent dielectric response and energy-loss functions of these materials in two ways: a full ab initio approach, in which we carry out time-dependent density functional simulations in linear response for different momentum transfers, and a semi-classical model, based on the Drude–Lorentz extension to finite momenta of the optical dielectric function. Ab initio calculated dielectric functions lead to better agreement with measured energy-loss spectra compared to the widely used Drude–Lorentz model. This discrepancy is particularly evident for insulators and semiconductors beyond the optical limit (q≠0), where single-particle excitations become relevant. Furthermore, we show that the behaviour of the energy-loss function obtained at different accuracy levels has a dramatic effect on other physical observables, such as the inelastic mean free path and the stopping power in the low energy (<100 eV) regime and thus on the accuracy of MC simulations.

Calculation of Surface Excitation Parameters by a Monte Carlo Method

Electron inelastic mean free path (IMFP) is an important parameter for surface chemical quantification by surface electron spectroscopy techniques. It can be obtained from analysis of elastic peak electron spectroscopy (EPES) spectra measured on samples and a Monte Carlo simulation method. To obtain IMFP parameters with high accuracy, the surface excitation effect on the measured EPES spectra has to be quantified as a surface excitation parameter (SEP), which can be calculated via a dielectric response theory. However, such calculated SEP does not include influence of elastic scattering of electrons inside samples during their incidence and emission processes, which should not be neglected simply in determining IMFP by an EPES method. In this work a Monte Carlo simulation method is employed to determine surface excitation parameter by taking account of the elastic scattering effect. The simulated SEPs for different primary energies are found to be in good agreement with the experiments particularly for larger incident or emission angles above 60° where the elastic scattering effect plays a more important role than those in smaller incident or emission angles. Based on these new SEPs, the IMFP measurement by EPES technique can provide more accurate data.

Surface EXAFS via differential electron yield.

Surface-sensitive analysis via extended X-ray absorption fine-structure (EXAFS) spectroscopy is demonstrated using a thickness-defined SiO2 (12.4 nm)/Si sample. The proposed method exploits the differential electron yield (DEY) method wherein Auger electrons escaping from a sample surface are detected by an electron analyzer. The DEY method removes local intensity changes in the EXAFS spectra caused by photoelectrons crossing the Auger peak during X-ray energy sweeps, enabling EXAFS analysis through Fourier transformation of wide-energy-range spectral oscillations. The Si K-edge DEY X-ray absorption near-edge structure (XANES) spectrum appears to comprise high amounts of SiO2 and low Si content, suggesting an analysis depth, as expressed using the inelastic mean free path of electrons in general electron spectroscopy, of approximately 4.2 nm. The first nearest neighbor (Si-O) distance derived from the Fourier transform of the Si K-edge DEY-EXAFS oscillation is 1.63 Å. This value is within the reported values of bulk SiO2, showing that DEY can be used to detect a surface layer of 12.4 nm thickness with an analysis depth of approximately 4.2 nm and enable `surface EXAFS' analysis using Fourier transformation.

A comparative study of inelastic scattering models at energy levels ranging from 0.5 keV to 10 keV

Six models, including a single-scattering model, four hybrid models, and one dielectric function model, were evaluated using Monte Carlo simulations for aluminum and copper at incident beam energies ranging from 0.5keV to 10keV. The inelastic mean free path, mean energy loss per unit path length, and backscattering coefficients obtained by these models are compared and discussed to understand the merits of the various models. ANOVA (analysis of variance) statistical models were used to quantify the effects of inelastic cross section and energy loss models on the basis of the simulated results deviation from the experimental data for the inelastic mean free path, the mean energy loss per unit path length, and the backscattering coefficient, as well as their correlations. This work in this study is believed to be the first application of ANOVA models towards evaluating inelastic electron beam scattering models. This approach is an improvement over the traditional approach which involves only visual estimation of the difference between the experimental data and simulated results. The data suggests that the optimization of the effective electron number per atom, binding energy, and cut-off energy of an inelastic model for different materials at different beam energies is more important than the selection of inelastic models for Monte Carlo electron scattering simulation. During the simulations, parameters in the equations should be tuned according to different materials for different beam energies rather than merely employing default parameters for an arbitrary material. Energy loss models and cross-section formulas are not the main factors influencing energy loss. Comparison of the deviation of the simulated results from the experimental data shows a significant correlation (p<0.05) between the backscattering coefficient and energy loss per unit path length. The inclusion of backscattering electrons generated by both primary and secondary electrons for backscattering coefficient simulation is recommended for elements with high atomic numbers. In hybrid models, introducing the inner shell ionization model improves the accuracy of simulated results.

An almost knowledge-free approach to XPS intensity evaluation where use of atomic photoemission cross sections suffices for yielding material-specific inelastic background

A general procedure for peak intensity evaluation on the inelastic background of X-ray photoelectron spectra (XPS) has been developed, which is made up of tasks in three nested levels, level I, II and III. The task in level I is a simple background optimization for the case when the inelastic mean free path (IMFP, denoted λ(E)) and other constraints are given in advance [M. Jo, Surf. Interface Anal., 2003, 35, 729–737]. In order to find appropriate constraints, a batch job, which is a series of single jobs with systematically varied constraints, is constructed and iteratively solved in level II by improving the constraints from the viewpoint of how successfully the background is subtracted. It is found that, by the task in level II, for polycrystal Cu metal, the spectrum after inelastic background subtraction still contains a baseline component proportional to E−k, where E (>50eV) is the electron kinetic energy and the exponent k around 2.4. This baseline is attributed to the high-energy tail of primary excitation spectrum of true secondary electron emission. The relative core intensities thus determined are in good agreement with the Scofield’s photoexcitation cross sections. The relation of core and Auger peak intensities is consistent as demonstrated by the fact that the sum of Cu 2p and 2s equals that of all Cu LMM peaks. The level III calculation is designed for the general case where λ is not available before the analysis. The relative energy dependence of λ except for the absolute value can be estimated by iterating the level II tasks with updated λ(E), based on the assumption that the peak intensities should be proportional to Scofield’s values. The relative deviation of thus determined λ(E) in level III from those by the well-known calculation (Tanuma, Powell, and Penn, TPP) is less than 1.7% between E=600 and 2000eV if their values at 800eV are assumed to coincide. The normalized peak shapes and relative intensities after background subtraction in this level are also very similar to those obtained in level II starting with λ(E) by TPP that is currently known to be reliable. These findings indicate that an almost knowledge-free analysis, which is free from the detail of the solid’s properties such as chemical composition and nevertheless retains the material-dependent results, became possible for the first time, as long as one keeps away from the discussion of absolute intensity.

Graphene nanobubbles on TiO2 for in-operando electron spectroscopy of liquid-phase chemistry.

X-Ray Photoelectron Spectroscopy (XPS) and X-Ray Absorption Spectroscopy (XAS) provide unique knowledge on the electronic structure and chemical properties of materials. Unfortunately this information is scarce when investigating solid/liquid interfaces and chemical or photochemical reactions under ambient conditions because of the short electron inelastic mean free path (IMFP) that requires a vacuum environment, which poses serious limitation on the application of XPS and XAS to samples present in the atmosphere or in the presence of a solvent. One promising approach is the use of graphene (Gr) windows transparent to both photons and electrons. This paper proposes an innovative system based on sealed Gr nanobubbles (GNBs) on a titanium dioxide TiO2 (100) rutile single crystal filled with the solution of interest during the fabrication stage. The GNBs were successfully employed to follow in-operando the thermal-induced reduction of FeCl3 to FeCl2 in aqueous solution. The electronic states of chlorine, iron and oxygen were obtained through a combination of electron spectroscopy methods (XPS and XAS) in different phases of the process. The interaction of various components in solution with solid surfaces constituting the cell was obtained, also highlighting the formation of a covalent C-Cl bond in the Gr structure. For the easiness of GNB fabrication and straightforward extension to a large variety of solutions, we envisage a broad application of the proposed approach to investigate in detail electronic mechanisms that regulate liquid/solid electron transfer in catalytic and energy conversion related applications.

Proton Impact of Bimolecular Targets

For a better control and understanding of the effects of radiation damage in living tissues by using the irradiation of biological systems by energetic ion beams have multiple applications in medical physics and space radiation health, such as hadron therapy for cancer treatment and it is necessary to advance an accurate description of the energy loss from the ion beam to the target. In the present work the dielectric formalism like Drude has been used to calculate the probability for an energetic proton and to produce electronic excitations in five targets of high biological interest, namely, liquid water, DNA, PMMA, Adenine and Guanine. Also, the effects of ionization fraction on the mean excitation energy, average energy and Inelastic mean free path studied taking in to consideration electronic excitation in the target. Good agreement achieved with previous work.

水における電子の非弾性平均自由行程。I. 運動量移送依存性

水における電子の非弾性平均自由行程。I. 運動量移送依存性

Fabrication of thin TEM sample of ionic liquid for high-resolution ELNES measurements

Investigation of the local structure, ionic and molecular behavior, and chemical reactions at high spatial resolutions in liquids has become increasingly important. Improvements in these areas help to develop efficient batteries and improve organic syntheses. Transmission electron microscopy (TEM) and scanning-TEM (STEM) have excellent spatial resolution, and the electron energy-loss near edge structure (ELNES) measured by the accompanied electron energy-loss spectroscopy (EELS) is effective to analyze the liquid local structure owing to reflecting the electronic density of states. In this study, we fabricate a liquid-layer-only sample with thickness of single to tens nanometers using an ionic liquid. Because the liquid film has a thickness much less than the inelastic mean free path (IMFP) of the electron beam, the fine structure of the C-K edge electron energy loss near edge structure (ELNES) can be measured with sufficient resolution to allow meaningful analysis. The ELNES spectrum from the thin liquid film has been interpreted using first principles ELNES calculations.