Inelastic Mean Free Path Values Research Articles

Investigating the structure of the oxide on Ni‐Cr‐Mo alloys while presenting a method for analysis of complex oxides using QUASES

X‐ray photoelectron spectroscopy (XPS) is a technique that is widely used to study thin oxide films because of its extremely high surface sensitivity. Utilizing the QUASES (Quantitative Analysis of Surfaces by Electron Spectroscopy) software package developed by Sven Tougaard (University of Southern Denmark), a user can obtain additional information that is not extracted in conventional XPS analysis, specifically the composition as a function of depth. Presented here is the QUASES analysis of four Ni‐Cr‐Mo alloys performed while testing various inelastic mean free path (IMFP) determination methods in the context of providing a framework for the analysis of complex oxides in QUASES. Ni‐Cr‐Mo alloys are often used to replace conventional materials under aggressive conditions, because of their exceptional corrosion resistance. Their corrosion resistance is conferred by the formation of an inert surface oxide film that protects the underlying metal. Using the QUASES software, the thickness of the air‐formed oxide on four Ni‐Cr‐Mo alloys was found to lie within the range of 2.5–3.6 nm. They were found to be composed of an inner Cr2O3 layer and an outer Cr (OH)3 layer, with a transition zone where the two coexisted. Oxidized Mo species, MoO2 and MoO3, were found in trace amounts at the boundary between the Cr2O3‐only and mixed Cr2O3/Cr (OH)3 regions of the oxide. We also determined that using 20% reduced IMFP values gave results similar to those obtained using electron effective attenuation length (EAL) values. Auger depth profiles showed comparable trends to the QUASES models.

Coherent imaging with low-energy electrons, quantitative analysis

Low-energy electrons (20–300eV) hold the promise for low-dose, non-destructive, high-resolution imaging, but at the price of challenging data analysis. This study provides theoretical considerations and models for the quantitative analysis of experimental data observed in low-energy electron transmission microscopy and in-line holography. The scattering of low-energy electrons and the imaging parameters, such as the inelastic mean free path, point spread function, depth of focus, and resolution, are quantitatively described. It is shown that unlike high-energy electrons (20–300 keV), low-energy electrons (20–300eV) introduce a large phase shift into the probing electron waves. Using the projected potentials formalism, the maximal phase shift acquired by a 120eV electron wave scattered by a carbon atom is theoretically estimated to be 5.03 radian and experimentally measured to be between 3 and 7.5 radian. The point spread function evaluated for low-energy electrons shows that they diffract much stronger than high-energy electrons, and that only very thin objects of up to 3Å in thickness can be imaged in focus. Thus, when imaging an object of finite thickness, such as a macromolecule, the obtained image will always be blurred due to the out-of-focus signal. This can provide an explanation for a long-standing problem of limited resolution in low-energy electron holography of macromolecules. As for imaging of a macromolecule’s structure, it is shown that the amplitude of the wavefront reconstructed from the sample’s hologram provides the best match to the projected potential distribution of the macromolecule. To evaluate the absorption properties, the inelastic mean free path (IMFP) is considered. The IMFP values calculated from theoretical models agree with the measured values. The IMFP of about 5Å was measured by transmission through graphene of 50–200eV electrons. This result implies that the internal structure of only very thin samples can be imaged in transmission mode. A simple method to quantitatively evaluate the absorption of a specimen from its in-line hologram without the need to reconstruct the hologram is presented.

Electron inelastic mean free path in UO2 and (U, Pu)O2 fuels

Inelastic mean free path (IMFP) of UO2 and (U, Pu)O2 fuels at 0, 20, 50 and 95 at.% of Pu were determined for the first time using a combination of convergent beam electron diffraction (CBED) and electron energy loss spectroscopy (EELS) on TEM FIB lamellae. Non-linear least squares fit was performed on the CBED intensity profiles to only obtain the crystalline thickness of the sample with a precision of up to 0.2% [1] while EELS spectra were used to calculate the relative thickness of the sample: crystalline and amorphous contribution. The IMFP were determined to be 119 – 129 nm for UO2, 107 – 117 nm for (U, Pu)O2 at 20 at.% of Pu, 116 – 125 nm for (U, Pu)O2 at 50 at.% of Pu and 123 – 137 nm for (U, Pu)O2 at 95 at.% of Pu using collection semi-angles β = 23.4 – 11.6 mrad, convergence semi-angle α = 8 mrad and accelerated voltage of 200 keV on a Thermofischer TALOS F200X TEM in the LECA STAR hot laboratory (CEA Cadarache). A comparison with the most relevant models in the literature shows that for compounds with a comparable quantity of light and heavy elements it is better to use a mean atomic number instead of an effective one as proposed by different authors. The importance of accurate density determination is also emphasized if the IMFP values are to be predicted by the existed models. As a second part, a strategy is developed to calculate the effective refractive index at the nanometer scale for the fuels allowing to easily find the IMFP under different measurement parameters such as those in energy filtered transmission electron microscopy (EFTEM) maps.

Multiple elastic scattering of electrons in condensed matter (new version announcement)

Multiple elastic scattering of electrons in condensed matter (new version announcement)

Low-Energy Electron Inelastic Mean Free Path of Graphene Measured by a Time-of-Flight Spectrometer.

The detailed examination of electron scattering in solids is of crucial importance for the theory of solid-state physics, as well as for the development and diagnostics of novel materials, particularly those for micro- and nanoelectronics. Among others, an important parameter of electron scattering is the inelastic mean free path (IMFP) of electrons both in bulk materials and in thin films, including 2D crystals. The amount of IMFP data available is still not sufficient, especially for very slow electrons and for 2D crystals. This situation motivated the present study, which summarizes pilot experiments for graphene on a new device intended to acquire electron energy-loss spectra (EELS) for low landing energies. Thanks to its unique properties, such as electrical conductivity and transparency, graphene is an ideal candidate for study at very low energies in the transmission mode of an electron microscope. The EELS are acquired by means of the very low-energy electron microspectroscopy of 2D crystals, using a dedicated ultra-high vacuum scanning low-energy electron microscope equipped with a time-of-flight (ToF) velocity analyzer. In order to verify our pilot results, we also simulate the EELS by means of density functional theory (DFT) and the many-body perturbation theory. Additional DFT calculations, providing both the total density of states and the band structure, illustrate the graphene loss features. We utilize the experimental EELS data to derive IMFP values using the so-called log-ratio method.

Low-energy electron properties: Electron inelastic mean free path, energy loss function and the dielectric function. Recent measurements, applications, and the plasmon-coupling theory

We review new self-consistent models of inelastic electron scattering in condensed matter systems for accurate calculations of low-energy electron inelastic mean free paths (IMFPs) for XAFS and low energy diffraction. The accuracy of theoretical determinations of the electron IMFP at low energies is one of the key limiting factors in current XAFS modeling and Monte Carlo transport. Recent breakthroughs in XAFS analysis show that there exist significant discrepancies between theoretical and experimental IMFP values, and that this can significantly impact upon extraction of other key structural parameters from both XANES and XAFS. Resolution of these discrepancies is required to validate experimental studies of material structures, and is particularly relevant to the characterization of small molecules and organometallic systems for which tabulated electron scattering data is often sparse or highly uncertain.Novel models implement plasmon coupling mechanisms for the first time, in addition to causally-constrained lifetime broadening and high-precision density functional theory, and enables dramatic improvements in the agreement with recent high profile IMFP measurements. We discuss a theoretical approach for IMFP determination linking the optical dielectric function and energy loss spectrum of a material with its electron scattering properties and characteristic plasmon excitations. We review models inclusive of plasmon coupling, allowing us to move beyond the longstanding statistical approximation and explicitly demonstrate the effects of band structure on the detailed behaviour of bulk electron excitations in a solid or small molecule. This interrogates the optical response of the material, which we obtain using density functional theory. We find that new developments dramatically improve agreement with experimental electron scattering results in the low-energy region (30 eV → 200 eV) where plasmon excitations are dominant. Corresponding improvements are therefore made in Low Energy Electron Transport, LEEM, theoretical XAFS spectra and detector modelling.

Low energy (1–100 eV) electron inelastic mean free path (IMFP) values determined from analysis of secondary electron yields (SEY) in the incident energy range of 0.1–10 keV

Since the emission of secondary electrons for any incident energy always involves the formation and emission of a cascade of slow electrons (<50 eV) the secondary electron yield (SEY) for arbitrary energies depends sensitively on the inelastic mean free path (IMFP) values at low energies (below 100 eV). This makes it possible to retrieve the information about the low energy IMFP from high energy SEY experiments. A Monte Carlo (MC) code has been developed to simulate SEY values and was employed to determine the IMFP at low energies (<100 eV). This is done by varying the energy dependence of the IMFP at low energies (<100 eV) during the MC simulation of the SEY between two extremes, calculated on the basis of the Mermin dielectric function and the Penn algorithm within the simplified single-pole approximation (SSPA). Those IMFP values that give the best χ2 fit of the simulated SEY values with experimental results are considered to be the most reliable. The described algorithm was employed for the investigation of Be, Al, Si, Ti, V, Fe, Ni, Cu, Ge, Nb, Mo, Pd, Ag, Ta, W, Pt, Au. For most materials these optimum IMFP values are found to be close to IMFP values based on the Mermin dielectric function.

Electron inelastic mean free path in carbon and polycarbonate using a newly developed wide spectrum measurement method

The electron inelastic mean free path (IMFP) is commonly used in surface analysis techniques such as X-ray photoelectron spectroscopy. Though numerous studies have been conducted in the quest to define the IMFP value, it is still substantiated mainly on the basis of calculations and extrapolations. Experimental methods such as elastic peak electron spectroscopy tend to rely on indirect measurements. The main disadvantage of current methods is that the signal to noise ratio decreases with the increase in layer thickness or as the electron energy decreases.The newly developed wide energy spectrum (WES) method previously published by our group allows the IMFP to be directly evaluated for different electron energies. It exploits the attenuated electron multiple inelastic collisions (MIC) peak counts to calculate mean electron energy loss, rather than use the signal-electron peaks.In contrast, currently accepted methods focus on the signal electron in the spectrum and disregard the information contained in the lower-energy electrons. In understanding how to exploit this information, WES enhanced the relevant data collection by using a wide energy region upper bounded by the signal electron energy and lower bounded by the peak MIC energy in the spectrum.In this work, we have markedly expanded the validity of the WES method by assessing the IMFP values of a low Z polymer and by using a different substrate to produce the photoelectrons. The experiment was performed at the Spanish CRG Beamline (SpLine) at the European Synchrotron Radiation Facility (ESRF). Herein we present our initial results. In addition, we improved both the raw-data analysis and the background reduction processes used in WES to obtain enhanced and more accurate results.The IMFP values of carbon and polycarbonate were evaluated and compared with those predicted by the NIST. Small differences notwithstanding, the reported IMFP were shown to be well within the uncertainty boundaries.This work shows that the electron IMFP can be evaluated in solids by directly measuring the electrons that pass-through samples of the solids of interest. For the first time, there is an orderly path to experimentally evaluate electron IMFP by using the WES method. The new method was established to address the lack of experimental IMFP values for low energy electrons in solid materials.

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.

Elastic-peak electron spectroscopy (EPES) studies of ZnO single crystals

Electron transport in both ZnO(0001)–Zn and ZnO(000–1)–O bulk single crystals was studied using the elastic-peak electron spectroscopy (EPES) measurements. The inelastic mean free path (IMFP) was evaluated from EPES using both Ni and Au standards in the energy range 200–2000eV, and compared with IMFPs calculated from the predictive TPP-2M formula for the measured composition of both single crystal surfaces. In the electron energy range from 1 to 2keV, the IMFPs were found to be 34% larger for the ZnO(0001)–Zn crystal surface than for the ZnO(000–1)–O crystal surface, and considerably larger than the IMFPs obtained from the TPP-2M predictive formula. At energies lower than 1keV, a good agreement between the corresponding IMFPs values was found. However, the electron transport at larger energies seems to be affected by different bulk structure of both crystals.

Spin-resolved inelastic mean free path of slow electrons in Fe

The spin-dependent reflectivity of slow electrons from ultrathin Fe films on W(110) has been measured with spin polarized low energy electron microscopy. From the amplitude of the quantum size oscillations observed in the reflectivity curves the spin-dependent inelastic mean free path (IMFP) of electrons in Fe has been determined in the energy range from 5 to 16 eV above the vacuum level. The resulting IMFP values for the spin-up electrons are clearly larger than those for the spin-down electrons and the difference between the two values decreases with increasing electron energy in agreement with theoretical predictions.

Stopping Powers and Inelastic Mean Free Path of 100 eV to 30 keV Electrons in Zirconium Silicates

We have determined the electron stopping power (SP) and inelastic mean free path (IMFP) of (ZrO 2 ) x (SiO 2 ) 1-x (x=1, 0.75, 0.5, 0.25, 0) for electron energies from 100 eV to 30 keV by means of modified Born–Ochkur equations. The energy loss function (ELF) is required in the calculation of SP and IMFP. We used the electron energy losses from 0 to 80 eV obtained by quantitative analysis of reflection electron energy-loss spectroscopy (REELS) spectra. The values of SP and IMFP for high contents of ZrO 2 (x=50% and x=75%) in Zr-silicates are similar to those of ZrO 2 , and similar to those of SiO 2 for low contents of ZrO 2 (x=25%) in Zr-silicates. There are small differences in the values of SP and IMFP for ZrO 2 and SiO 2 .We found that the SP decreases while the IMFP increases with increasing electron energy. We have demonstrated that the ELF obtained from the quantitative analysis of REELS spectra provide us with a straightforward way to determine SP and IMFP for alloy materials by using modified Born-Ochkur equations. Received: 04 December 2012; Revised: 18 December 2012; Accepted: 19 December 2012

Experimental Determination of Effective Attenuation Length for SiO2 Thin Film with Synchrotron Radiation Photoemission Spectroscopy

The effective attenuation length (EAL) is a necessary parameter to estimate the thickness of SiO2 overlayer by X-ray photoemission spectroscopy (XPS). Inelastic mean free path (IMFP) is often used instead of EAL because EAL is scarcely known. EAL values were determined experimentally in the photon energy region from 480 eV to 800 eV using synchrotron radiation photoemission spectroscopy. EALs estimated are different from calculated IMFPs. Average values of theoretically-calculated IMFPs are close to the estimated EALs.

Nondestructive Surface Depth Profiles from Angle-Resolved X-ray Photoelectron Spectroscopy Data Using the Maximum Entropy Method. I. A New Protocol

The knowledge of the depth concentration profile of thin-layered surfaces a few nanometers thick is very important for research and applications in microelectronics, corrosion, wear, and tribology. In-depth profiling methods reported in the literature are either destructive (ion sputtering), based on severe approximations (concentration gradients are not taken into account, and electron inelastic mean free paths (IMFPs) are calculated for electrons traveling throughout pure elemental materials) or limited to relatively simple profiles (less than three components and constant IMFPs). A reconstructed depth profile should be consistent with the angle-resolved X-ray photoelectron spectroscopy (ARXPS) data acquired, but transformation of XPS signal intensities vs emission angle into chemical species concentrations vs depth is an ill-posed mathematical problem which requires inversion of a Laplace transform. The main goal of this work was thus to develop a new, iterative protocol based on the maximum entropy method (MEM) that allows obtaining in-depth concentration profiles of layered surfaces from nondestructive ARXPS measurements. Numerical experiments were performed on a large series of computer generated, ideal, and error-containing ARXPS data from model depthprofiles with up to four layers and up to eight components. The new algorithm enabled us to reconstruct these depth profiles with a maximum uncertainty of ±20% for layer thickness and of ±30% for composition of the individual layers. Moreover, the new protocol involves an iterative procedure for calculating the IMFP values of the different components, taking into account the actual depth concentration profile of the sample surface under investigation. The new protocol proved to be more powerful than any of the existing algorithms since it has been successfully applied for reconstructing depth profiles with up to eight components.

Determination of electron inelastic mean free paths for poly[methyl(phenyl)silylene] films

The inelastic mean free paths (IMFPs) of electrons at a poly[methyl(phenyl)silylene] thin film surface were determined using elastic peak electron spectroscopy (EPES) and Monte Carlo calculations for a wide electron energy range, 200–1600 eV. We considered the surface composition determined from X-ray induced photoelectron spectra (XPS), the hydrogen concentration evaluated by EPES, and a correction for surface excitations. The results compare well to those calculated from the predictive TPP-2M and G1, formulae. Calculations carried out with the quantitative structure–property relationship of Cumpson and the formula of Ashley and Williams provide larger IMFP values, and can be useful only for a rough estimation.

Estimation of Inelastic Mean Free Paths in Au and Cu from Their Elastic Peak Intensity Ratios without IMFP Values of Reference Material in The 200 – 5000 eV Energy Range

We have determined electron inelastic mean free paths (IMFPs) and surface-electronic excitation parameters (SEPs) of Au and Cu in the 200 – 5000 eV from their elastic peak intensity ratios without reference IMFP values. This proposed method does not require the IMFP values of the reference material. The measurements of elastic peak intensities of these elements were done with noble CMA system. The elastic peak intensities were also calculated from two parameter sets (IMFPs and SEPs for both elements) with Monte Carlo method. By comparison of these two EPI ratios as changing the parameter sets, we have estimated their IMFPs and SEPs in the 200 – 5000 eV energy range. The resulting IMFPs of Au and Cu were in good agreement with optical IMFPs over 1000 eV energy range.

Angular and energy distribution of backscattered electrons simulated by Monte-Carlo—Assessment by experiment I

The angular and energy distributions of backscattered electrons for the primary energies of 0.2, 0.5 and 1 keV and for Cu and Au were calculated by Monte-Carlo method and compared to measurement. The elastic differential cross-sections were calculated by ELSEPA code. For inelastic scattering a modified Tougaard's model of universal cross-section was used. We fit inelastic mean free path (IMFP) obtained from energy loss distribution, given by the modified Tougaard's model, in order they agreed with the value of IMFP from the TPP-2 formula. By this way we obtained an energy-dependent correction of the constants in Tougaard's formula. A very good agreement was found for the calculated and measured values of angular distribution of elastically reflected electrons. For the energy distribution of backscattered electrons some differences between experiment and calculation appeared, which were probably caused mainly by very low energy losses, e.g. losses at exiting of bremsstrahlung radiation.

Elastic electron backscattering from flat and rough Si surfaces

In earlier studies, it has been found that the surface roughness influences only weakly the inelastic mean free path values resulting from elastic peak electron spectroscopy. To address this issue, in the present work, the elastic electron backscattering intensity has been systematically studied in numerous experimental configurations. Measurements were made for the flat Si sample, and for the Si sample with well-defined roughness in the form of long trapezoidal channels. Such structure is a good representation for one-dimensional models used in theoretical description of the surface roughness effects in XPS. It has been found that there is a pronounced influence of the surface roughness on the electron backscattered intensity at the primary beam incidence different from normal. These results were observed at energies of interest for surface sensitive electron spectroscopies, i.e. 200, 500 and 1000 eV. Additionally, the elastic backscattering probability for a flat surface was found to agree well with the theoretical predictions. Correction for the surface energy losses further improved the agreement between theory and experiment.

Electron IMFPs in bulk Cd 0.88Mn 0.12Te crystals determined by EPES

The inelastic mean free path (IMFP) of electrons is a basic parameter for surface-sensitive electron spectroscopies (AES, XPS, EELS) in quantitative analyses. Cd 1− x Mn x Te mixed crystals are currently of great interest due to their magnetic and magneto-optical properties. Since information on electron transport processes in these semimagnetic compounds is scarce, their systematic studies are highly desirable. In the present work, the IMFPs in Cd 0.88Mn 0.12Te (1 1 0) crystal samples were obtained from EPES with use of the Ni standard in the electron energy range 500–2000 eV. In addition, we also explored the effect of bulk Mn content in the determination of the IMFP. Relative EPES measurements were carried out using the MICROLAB 350 spectrometer. The sample surface was sputter cleaned and amorphized by Ar + ions. Surface composition of the samples was monitored in situ by XPS and AES. The measured IMFPs were uncorrected for surface excitations and compared with those predicted from the TPP-2M and G-1 formulae. Also, the values of the IMFPs determined here were compared with those evaluated from the expression of Sekine et al. However, accuracy of this expression is rather poor except the case of pure CdTe ( x = 0). In general, good agreement was found between the measured IMFPs in Cd 0.88Mn 0.12Te and the corresponding predicted IMFPs. The root-mean-square deviation from IMFP values predicted from the TPP-2M formula was 1.2 Å. The mean percentage deviation from the TPP-2M IMFPs was 9.3%.