Inelastic Mean Free Path Research Articles

Low-energy electron inelastic mean free path in materials

We show that the dielectric approach can determine electron inelastic mean free paths in materials with an accuracy equivalent to those from first-principle calculations in the GW approximation of many-body theory. The present approach is an alternative for calculating the hot-electron lifetime, which is an important quantity in ultrafast electron dynamics. This approach, applied here to solid copper for electron energies below 100 eV, yields results in agreement with experimental data from time-resolved two-photon photoemission, angle-resolved photoelectron spectroscopy, and X-ray absorption fine structure measurements in the energy ranges 2–3.5, 10–15, and 60–100 eV, respectively.

Quantitative interpretation of molecular dynamics simulations for X-ray photoelectron spectroscopy of aqueous solutions.

Over the past decade, energy-dependent ambient pressure X-ray photoelectron spectroscopy(XPS) has emerged as a powerful analytical probe of the ion spatial distributions at the vapor (vacuum)-aqueous electrolyteinterface. These experiments are often paired with complementary molecular dynamics (MD) simulations in an attempt to provide a complete description of the liquidinterface. There is, however, no systematic protocol that permits a straightforward comparison of the two sets of results. XPS is an integrated technique that averages signals from multiple layers in a solution even at the lowest photoelectron kinetic energies routinely employed, whereas MD simulations provide a microscopic layer-by-layer description of the solution composition near the interface. Here, we use the National Institute of Standards and Technology database for the Simulation of Electron Spectra for Surface Analysis (SESSA) to quantitatively interpret atom-density profiles from MD simulations for XPS signal intensities using sodium and potassium iodide solutions as examples. We show that electron inelastic mean free paths calculated from a semi-empirical formula depend strongly on solution composition, varying by up to 30% between pure water and concentrated NaI. The XPS signal thus arises from different information depths in different solutions for a fixed photoelectron kinetic energy. XPS signal intensities are calculated using SESSA as a function of photoelectron kinetic energy (probe depth) and compared with a widely employed ad hoc method. SESSA simulations illustrate the importance of accounting for elastic-scattering events at low photoelectron kinetic energies (<300 eV) where the ad hoc method systematically underestimates the preferential enhancement of anions over cations. Finally, some technical aspects of applying SESSA to liquidinterfaces are discussed.

Surface sensitivity of elastic peak electron spectroscopy

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

Inelastic scattering and energy loss of swift electron beams in biologically relevant materials

The inelastic mean free path and the stopping power of swift electrons in relevant biomaterials, such as liquid water, DNA, protein, lipid, carotene, sugar, and ice are calculated in the framework of the dielectric formalism. The Mermin Energy Loss Function – Generalized Oscillator Strength model is used to determine the energy loss function of these materials for arbitrary energy and momentum transfer using electron energy‐loss spectroscopy data as input. To ensure the consistency of the model, efforts are made so that both the Kramers–Kronig and f‐sum rules are fulfilled to better than 2%. Our findings indicate sizeable differences in the inelastic mean free path and stopping power among these biomaterials for low‐energy electrons. For example, at 100‐eV electron energy, the inelastic mean free path in protein is 25% smaller than for water and around 10% smaller than for the other biomaterials. The stopping power values of protein, DNA, and sugar are rather similar but 20% larger than for water. Taking into account these results, we conclude that electron interactions with living tissues at the nanometric scale cannot be reliably described using only liquid water as the surrogate of the biological target. Copyright © 2016 John Wiley &amp; Sons, Ltd.

Determination of electronic properties of nanostructures using reflection electron energy loss spectroscopy: Nano-metalized polymer as case study

In this work, Au was deposited with nominal effective thickness of 0.8nm on polystyrene (PS) at room temperature. According to previous study, using XPS peak shape analysis [S. Hajati, V. Zaporojtchenko, F. Faupel, S. Tougaard, Surf. Sci. 601 (2007) 3261–3267], Au nanoparticles (Au-NPs) of sizes 5.5nm were formed corresponding to such effective thickness (0.8nm). Then the sample was annealed to 200°C, which is far above the glass transition of PS. At this temperature, the Au-NPs were diffused within the depth 0.5nm–6.5nm as found using nondestructive XPS peak shape analysis. Electrons with primary energy 500eV were used because the electronic properties will then be probed in utmost surface (∼1 IMFP range of depths that is 1.8nm for PS). By using QUEELS software, theoretical and experimental electron inelastic cross section, energy loss function, electron inelastic mean free path and surface excitation parameters were obtained for the sample. The information obtained here, does not rely on any previously known information on the sample. This means that the method, applied here, is suitable for the determination of the electronic properties of new and unknown composite nanostructures.

Surface characterization of graphene based materials

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

Surface studies of praseodymium by electron spectroscopies

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

Reflected electron-energy-loss spectra, differential inverse inelastic mean free paths, and angular resolved X-ray photoelectron spectra of a niobium sample

A technique for recovering the differential inverse inelastic mean free paths (DIIMFP) of electrons in Nb from the reflected electron energy loss spectra (REELS) at initial energies of 5 to 40 keV using a threelayer model of the sample surface is presented. The recovered DIIMFP are used for analyzing X-ray photoelectron spectra measured at different viewing angles. Comparison with experimental data is carried out.

Inelastic mean free path of low‐energy electrons in condensed media: beyond the standard models

The most established approach for ‘practical’ calculations of the inelastic mean free path (IMFP) of low‐energy electrons (~10 eV to ~10 keV) is based on optical‐data models of the dielectric function. Despite nearly four decades of efforts, the IMFP of low‐energy electrons is often not known with the desired accuracy. A universal conclusion is that the predictions of the most popular models are in rather fair agreement above a few hundred electron volts but exhibit considerable differences at lower energies. However, this is the energy range where their two main approximations, namely, the random‐phase approximation (RPA) and the Born approximation, may be invalid. After a short overview of the most popular optical‐data models, we present an approach to include exchange and correlation (XC) effects in IMFP calculations, thus going beyond the RPA and Born approximation. The key element is the so‐called many‐body local‐field correction (LFC). XC effects among the screening electrons are included using a time‐dependent local‐density approximation for the LFC. Additional XC effects related to the incident and struck electrons are included through the vertex correction calculated using a screened‐Hubbard formula for the LFC. The results presented for liquid water reveal that XC may increase the IMFP by 15–45% from its Born–RPA value, yielding much better agreement with available experimental data. The present work provides a manageable, yet rigorous, approach to improve upon the standard models for IMFP calculations, through the inclusion of XC effects at both the level of screening and the level of interaction. Copyright © 2015 John Wiley &amp; Sons, Ltd.

Determination of Mean Inner Potential and Inelastic Mean Free Path of ZnTe Using Off-Axis Electron Holography and Dynamical Effects Affecting Phase Determination.

The mean inner potential (MIP) and inelastic mean free path (IMFP) of undoped ZnTe are determined using a combination of off-axis electron holography and convergent beam electron diffraction. The ZnTe MIP is measured to be 13.7±0.6 V, agreeing with previously reported simulations, and the IMFP at 200 keV is determined to be 46±2 nm for a collection angle of 0.75 mrad. Dynamical effects affecting holographic phase imaging as a function of incident beam direction for several common semiconductors are systematically studied and compared using Bloch wave simulations. These simulation results emphasize the need for careful choice of specimen orientation when carrying out quantitative electron holography studies in order to avoid erroneous phase measurements.

The spatial extent of surface effects on electron inelastic scattering

We calculate the thickness of the surface scattering layer, defined as the region where electron inelastic scattering is affected by the surface, using the semi‐classical treatment of electron energy loss provided by the Chen–Kwei theory. To this end, we consider the depth‐dependent, surface‐related contributions to the inverse inelastic mean free path, namely, the excitation of surface plasmons and the reduction in bulk plasmon excitation (Begrenzung effect). We find that surface effects extend further after electrons cross the surface than before they cross it. The ‘pre‐surface thickness’ is given by the ratio of the electron velocity to the plasma frequency, the characteristic decay length for surface effects. All thickness estimates increase linearly with the electron velocity and decrease as (cosα)x with the angle α between the electron trajectory and the surface normal. Copyright © 2015 John Wiley &amp; Sons, Ltd.

Surface analysis of zeolites: An XPS, variable kinetic energy XPS, and low energy ion scattering study

The surface Si/Al ratio in a series of zeolite Y samples has been obtained using laboratory XPS, synchrotron (variable kinetic energy) XPS, and low energy ion scattering (LEIS) spectroscopy. The non-destructive depth profile obtained using variable kinetic energy XPS is compared to that from the destructive argon ion bombardment depth profile from the lab XPS instrument. All of the data indicate that the near surface region of both the ammonium form and steamed Y zeolites is strongly enriched in aluminum. It is shown that when the inelastic mean free path of the photoelectrons is taken into account the laboratory XPS of aluminosilicates zeolites does not provide a true measurement of the surface stoichiometry, while variable kinetic energy XPS results in a more surface sensitive measurement. A comprehensive Si/Al concentration profile as a function of depth is developed by combining the data from the three surface characterization techniques. The LEIS spectroscopy reveals that the topmost atomic layer is further enriched in Al compared to subsequent layers.

New constraints for low-momentum electronic excitations in condensed matter: fundamental consequences from classical and quantum dielectric theory

We present new constraints for the transportation behaviour of low-momentum electronic excitations in condensed matter systems, and demonstrate that these have both a fundamental physical interpretation and a significant impact on the description of low-energy inelastic electron scattering. The dispersion behaviour and characteristic lifetime properties of plasmon and single-electron excitations are investigated using popular classical, semi-classical and quantum dielectric models. We find that, irrespective of constrained agreement to the well known high-momentum and high-energy Bethe ridge limit, standard descriptions of low-momentum electron excitations are inconsistent and unphysical. These observations have direct impact on calculations of transport properties such as inelastic mean free paths, stopping powers and escape depths of charged particles in condensed matter systems.

Simultaneous determination of sample thickness, tilt, and electron mean free path using tomographic tilt images based on Beer-Lambert law.

Cryo-electron tomography (cryo-ET) is an emerging technique that can elucidate the architecture of macromolecular complexes and cellular ultrastructure in a near-native state. Some important sample parameters, such as thickness and tilt, are needed for 3-D reconstruction. However, these parameters can currently only be determined using trial 3-D reconstructions. Accurate electron mean free path plays a significant role in modeling image formation process essential for simulation of electron microscopy images and model-based iterative 3-D reconstruction methods; however, their values are voltage and sample dependent and have only been experimentally measured for a limited number of sample conditions. Here, we report a computational method, tomoThickness, based on the Beer-Lambert law, to simultaneously determine the sample thickness, tilt and electron inelastic mean free path by solving an overdetermined nonlinear least square optimization problem utilizing the strong constraints of tilt relationships. The method has been extensively tested with both stained and cryo datasets. The fitted electron mean free paths are consistent with reported experimental measurements. The accurate thickness estimation eliminates the need for a generous assignment of Z-dimension size of the tomogram. Interestingly, we have also found that nearly all samples are a few degrees tilted relative to the electron beam. Compensation of the intrinsic sample tilt can result in horizontal structure and reduced Z-dimension of tomograms. Our fast, pre-reconstruction method can thus provide important sample parameters that can help improve performance of tomographic reconstruction of a wide range of samples.

Calculations of electron inelastic mean free paths. X. Data for 41 elemental solids over the 50 eV to 200 keV range with the relativistic full Penn algorithm

Our inelastic mean free paths were calculated correctly.

Measurement of mean inner potential and inelastic mean free path of ZnO nanowires and nanosheet

ZnO nanowires (NWs) and ZnO nano-sheets were grown using the chemical vapor deposition method. The NW structure was characterized using transmission electron microscopy, while the mean inner potential and inelastic mean free path for 200 keV electrons were measured using off-axis electron holography to be 15.3 ± 0.2 V and 55 ± 3 nm, respectively. These values were then used to characterize the thickness of a ZnO nano-sheet, and gave consistent results. This study demonstrates that electron holography can provide useful information about nanostructured ZnO materials and devices.

Analytical Formula for High-Energy Electron Inelastic Mean Free Path

We derive an analytical formula for the electron inelastic mean free path (IMFP) from its definition within the dielectric formalism. The parameters in this formula are determined solely by the optical energy-loss function of the material of interest. This formula is valid for electrons of energy larger than 500 eV, including relativistic electrons.

Momentum transfer effects in near surface electron energy loss

We examine two formulations for the differential surface excitation parameter (DSEP): one provided by Tung et al. and the other given by the Chen–Kwei position‐dependent differential inverse inelastic mean free path integrated over the electron trajectory. We demonstrate that the latter converges to the former provided that the dielectric function of the solid does not depend on the momentum transfer or it depends on just the momentum transfer component parallel to the surface. Tung's DSEP represents therefore an approximation to the Chen–Kwei DSEP calculated for a dielectric function with no restrictions on the momentum dependence. The approximation is shown to work in the limit of small momentum transfer and to imply an error of 4%–5% for electrons traveling through the solid with energy E = 1 keV. Copyright © 2015 John Wiley &amp; Sons, Ltd.

Energy Loss Function of Solids Assessed by Ion Beam Energy-Loss Measurements: Practical Application to Ta2O5

We present a study where the energy loss function of Ta2O5, initially derived in the optical limit for a limited region of excitation energies from reflection electron energy loss spectroscopy (REELS) measurements, was improved and extended to the whole momentum and energy excitation region through a suitable theoretical analysis using the Mermin dielectric function and requiring the fulfillment of physically motivated restrictions, such as the f- and KK-sum rules. The material stopping cross section (SCS) and energy-loss straggling measured for 300–2000 keV proton and 200–6000 keV helium ion beams by means of Rutherford backscattering spectrometry (RBS) were compared to the same quantities calculated in the dielectric framework, showing an excellent agreement, which is used to judge the reliability of the Ta2O5 energy loss function. Based on this assessment, we have also predicted the inelastic mean free path and the SCS of energetic electrons in Ta2O5.

Monte-Carlo modeling of excitation of the electron subsystem of ZnO and MgO in tracks of swift heavy ions

Monte Carlo code TREKIS is applied to trace kinetics of excitation of the electron subsystem of ZnO and MgO after an impact of a swift heavy ion (SHI). The event-by-event simulations describe excitation of the electron subsystems by a penetrating SHI, spatial spreading of generated electrons and secondary electron cascades. Application of the complex dielectric function (CDF) formalism for calculation of the cross sections of charged particle interaction with a solid target allows to consider collective response of the target to perturbation, which arises from the spatial and temporal correlations in the target electrons ensemble. The method of CDF reconstruction from the experimental optical data is applied. Electron inelastic mean free paths calculated within the CDF formalism are in very good agreement with NIST database. SHI energy losses agree well with those from SRIM and CasP codes. The radial distributions of valence holes, core holes and delocalized electrons as well as their energy densities in SHI tracks are calculated. The analysis of these distributions is presented.