Inelastic Mean Free Path Research Articles

TEM-EELS analysis reveals the W-atom mediated radiation-induced amorphization in M23C6

To gain a mechanistic understanding of the phase stability of M23C6 upon irradiation, the bulk W-doped M23C6 (Cr-W-C system) in the range of 0–12 at.% W concentration was prepared and subjected to helium beam irradiation, following with a thorough electron energy loss spectroscopy (EELS) analysis. Radiation-induced amorphization (RIA) was observed only at the 4 W sample with a W concentration of ∼12 at.%. Analysis of the low-loss spectrum showed that the inelastic mean free path (λ) could be applied an effective indicator of the presence of an amorphous phase. The white line ratio of the carbon K-edge spectrum showed that the chemical bonding state in the crystalline state is mainly 2p3/2 bonding, and it changes to dominantly 2p1/2 bonding accompanying with the crystal-to-amorphous (c-a) transition. Discussion on the relationship between the change in λ (Δλ) and the lattice parameter (Δa) due to irradiation reveals that Δa is not dependent on Δλ, indicating that Δλ is mainly caused by the volume expansion due to the c-a transition. In addition, a crystalline state is remained even after a lattice parameter change of ∼1.5 % in 0 W and 1W-samples, whereas, a lattice expansion of ∼0.2 % would trigger the occurrence of crystal-to-amorphous transition in the 4W-sample. The detailed EELS analysis demonstrated that the constitutional W atoms play an important role in facilitating the occurrence of RIA in M23C6, that is, the phase instability accompanying the lattice expansion due to irradiation was emphasized by the addition of W in M23C6. The insights obtained here suggest that a higher W concentration in M23C6 is more susceptible to RIA, and therefore the resistance to amorphization is achievable by decreasing the W concentration in the steels.

XPS depth profiling of nano-layers by a novel trial-and-error evaluation procedure

In spite of its superior chemical sensitivity, XPS depth profiling is rarely used because of the alteration introduced by the sputter removal process and the resulting inhomogeneous in-depth concentration distribution. Moreover, the application of XPS becomes increasingly challenging in the case of the analysis of thin layers, if the thickness is in the range of 2–3 inelastic mean free paths (IMFP) of the photoelectrons. In this paper we will show that even in these unfavorable cases the XPS depth profiling is applicable. Herein the XPS depth profiling of a model system tungsten-carbide-rich nano-layer of high hardness and corrosion resistance is presented. We will show that the problems arising because of the relatively high IMFP can be corrected by introducing a layer model for the calculation of the observed XPS intensities, while the alteration, e.g. ion mixing, compound formation and similar artefact, introduced by the sputter removal process can be handled by TRIDYN simulation. The method presented here overcomes the limitation of XPS depth profiling.

Electron backscattering coefficients for Cr, Co, and Pd solids: A Monte Carlo simulation study

We have calculated electron backscattering coefficients, η(Ep), at primary electron energies Ep of 0.1–100 keV for three elemental and intermediate atomic number solids, Cr, Co and Pd, with an up-to-date Monte Carlo simulation model. A relativistic dielectric functional approach is adopted for the calculation of the electron inelastic cross section, where several different datasets of optical energy loss function (ELF) are adopted. The calculated backscattering coefficient is found to be substantially affected by the ELF, where the influence can be seen to follow the f- and ps-sum rules and the resultant energy dependence of electron inelastic mean free path. To understand the uncertainties involved in a comparison with experimental data both the theoretical uncertainty due to the elastic cross-section model and the experimental systematic error for the contaminated surfaces are investigated. A total of 192 different scattering potentials are employed for the calculation of Mott's electron elastic cross section and this theoretical uncertainty is confirmed to be small. On the other hand, the simulation of contaminated Co and Pd surfaces with several carbonaceous atomic layers can well explain the experimental data. The present results indicate that accurate backscattering coefficient data should be either measured from fully cleaned surfaces or obtained from modern Monte Carlo theoretical calculations involving reliable optical constants data. With the recent progress in the accurate measurement of optical constants by reflection electron energy loss spectroscopy technique, constructing a reliable theoretical database of electron backscattering coefficients for clean surfaces of elemental solids is highly hopeful.

Energy Dissipation of Fast Electrons in Polymethylmethacrylate: Toward a Universal Curve for Electron-Beam Attenuation in Solids between ∼0 eV and Relativistic Energies.

Spectroscopy of correlated electron pairs was employed to investigate the energy dissipation process, as well as the transport and the emission of low-energy electrons on a polymethylmethacrylate surface, providing secondary electron spectra causally related to the energy loss of the primary. Two groups are identified in the cascade of slow electrons, corresponding to different stages in the energy dissipation process. The characteristic lengths for attenuation due to collective excitations and momentum relaxation are quantified for both groups and are found to be distinctly different: λ_{1}=(12±2) Å and λ_{2}=(62±11) Å. The results strongly contradict the commonly employed model of exponential attenuation with the electron inelastic mean free path as characteristic length, but they essentially agree with a theory used for decades in astrophysics and neutron transport, albeit with characteristic lengths expressed in units of angstroms rather than light-years.

Depth profiling of microwave nitrogen-terminated polycrystalline diamond surfaces by energy-dependent X-ray photoelectron spectroscopy

Nitrogen-terminated diamonds hold promise for stabilizing near-surface NV− centers, which is essential for reliable quantum sensing. Among various surface preparation methods, microwave (MW) nitrogen plasma, known for its minimal surface damage, appears as the most effective choice. In this investigation, we explore the nature of nitrogen bonding of polycrystalline diamond (PCD) surfaces exposed to MW nitrogen plasma using X-ray Photoelectron Spectroscopy (XPS) depth profiling and Near-Edge X-ray Absorption Fine Structure (NEXAFS) spectroscopy at the C K- and N K-edges. XPS depth profiling with atomic resolution, achieved by varying the probing photon energy using synchrotron radiation and supported by a physical model considering the associated inelastic mean free path, suggests a surface of almost fully saturated nitrogen in two main bonding configurations of similar contribution and a low coverage of ∼5 % of graphene-like islands residing atop the nitrogen-terminated diamond surface. The thermal stability of these surface groups is monitored by in situ annealing up to 700 °C. The depth profiles reveal that nitrogen atoms do not diffuse in the diamond crystal, resulting in excellent diamond crystallinity in the first atomic planes below the surface. C K-edge NEXAFS analysis reveals the position of unoccupied surface states within the diamond bandgap, opening new perspective on the stabilization of near-surface NV− centers.

Empirical test of the Kelvin relation in thermoelectric nanostructures

Thermoelectric (TE) nanostructures with dimensions of ∼100 nm can show substantially better TE properties compared to the same material in the bulk form due to charge and heat transport effects specific to the nanometer scale. However, TE physics in nanostructures is still described using the Kelvin relation (KR) Π = αT, where Π is the Peltier coefficient, α the thermopower, and T the absolute temperature, even though derivation of the KR uses a local equilibrium assumption (LEA) applicable to macroscopic systems. It is unclear whether nanostructures with nanostructures with dimensions on the order of an inelastic mean free path satisfy a LEA under any nonzero temperature gradient. Here, we present an experimental test of the KR on a TE system consisting of doped silicon-based nanostructures with dimensions comparable to the phonon–phonon and electron–phonon mean-free-paths. Such nanostructures are small enough that true local thermodynamic equilibrium may not exist when a thermal gradient is applied. The KR is tested by measuring the ratio Π/α under various applied temperature differences and comparing it to the average T. Results show relative deviations from the KR of |(Π/α)/T − 1| ≤ 2.2%, within measurement uncertainty. This suggests that a complete local equilibrium among all degrees of freedom may be unnecessary for the KR to be valid but could be replaced by a weaker condition of local equilibrium among only charge carriers.

Electron interaction with DNA constituents in aqueous phase.

Electron driven chemistry of biomolecules in aqueous phase presents the realistic picture to study molecular processes. In this study we have investigated the interactions of electrons with the DNA constituents in their aqueous phase in order to obtain the quantities useful for DNA damage assessment. We have computed the inelastic mean free path (IMFP), mass stopping power (MSP) and absorbed dose (D) for the DNA constituents (Adenine, Cytosine, Guanine, Thymine and Uracil) in the aqueous medium from ionisation threshold to 5000 eV. We have modified complex optical potential formalism to include band gap of the systems to calculate inelastic cross sections which are used to estimate these entities. This is the maiden attempt to report these important quantities for the aqueous DNA constituents. We have compared our results with available data in gas and other phase and have observed explicable accord for IMFP and MSP. Since these are the first results of absorbed dose (D) for these compounds, we have explored present results vis-a-vis dose absorption in water.

An extension of first principle combined Monte Carlo method to simulate secondary electron yield of anisotropic crystal Al2O3

An extension of a first-principle combined Monte Carlo method is proposed in this work to obtain the secondary electron emission characteristics of anisotropic crystal Al2O3. Unlike isotropic crystal Cu, density functional theory calculations reveal that the q-dependent energy loss function of Al2O3 in all directions is different. Therefore, an interpolation algorithm is introduced in the Monte Carlo method to determine the loss of energy and inelastic mean free path of electrons. The simulation results are in good agreement with experimental data. This method can be further used to simulate the secondary emission yield of other anisotropic crystal materials.

Analysis of effect of bulk vacancy defect on secondary electron emission characteristics of Al<sub>2</sub>O<sub>3</sub>

Based on the combination of the first-principles and Monte Carlo method, the effect of vacancy defect on secondary electron characteristic of Al<sub>2</sub>O<sub>3</sub> is studied in this work. The density functional theory (DFT) calculation results show that the band structure changes when the vacancy defects exist. The existence of Al vacancy defects results in a decrease in band gap from 5.88 to 5.28 eV, and in Fermi level below the energy of the valence band maximum as well. Besides, the elastic mean free paths and inelastic mean free paths of electrons in different crystal structures are also obtained. The comparison shows that the inelastic mean free path of electrons in Al<sub>2</sub>O<sub>3</sub> with O vacancy defects is much larger than those of Al<sub>2</sub>O<sub>3</sub> without defects and Al<sub>2</sub>O<sub>3</sub> with Al vacancy defects. When the energy of electrons is smaller than 50 eV, the inelastic mean free path of electrons in Al<sub>2</sub>O<sub>3</sub> without defects is longer than that in Al<sub>2</sub>O<sub>3</sub> with Al vacancy defects. The elastic mean free path of electrons slightly increases when the vacancy defects exist, and the elastic mean free path of electrons in Al<sub>2</sub>O<sub>3</sub> with Al vacancy defects is the largest. In order to investigate the secondary electron emission characteristics under different vacancy defect ratios, an optimized Monte Carlo algorithm is proposed. When the ratio between O vacancy defect and Al vacancy defect increases, the simulation results show that the maximum value of secondary electron yield decreases with the ratio of vacancy defect increasing. The existence of O vacancy defects increases the probability of inelastic scattering of electrons, so electrons are difficult to emit from the surface. As a result, comparing with Al vacancy defect, the SEY of Al<sub>2</sub>O<sub>3</sub> decreases greatly under the same ratio of O vacancy defect.

HAXPES: Inelastic background for characterization of nanostructured materials

Analysis of the spectrum of inelastically scattered electrons in XPS has been used for decades to determine the structure of materials on the nanoscale. Using the higher photon energies available in HAXPES, the method was recently shown to determine structures rather accurately with a more than 100 nm probing depth. In this paper, these HAXPES applications are briefly reviewed. Only two parameters are required for the analysis, namely, the inelastic mean free path and the cross section for inelastic electron scattering. We also discuss in detail how these parameters are best selected.

Monte Carlo Simulation of Free-standing Thin Films under Low Energy Electron Bombardment: Electron Inelastic Mean Free Path (IMFP) Determination Using Elastic Peak of the Transmitted Electrons

Abstract: The electron energy spectra of transmitted scattered electrons from free-standing films are simulated using a Monte Carlo computational approach. Elastic scattering is simulated using Mott cross-sections and inelastic scattering via discrete processes determined from dielectric function data. This allows one to simulate the secondary electrons as well as the loss peaks near the elastic (zero-loss) peak. The current study suggested a directed approach for determining the electron inelastic mean free path (IMFP) of materials at low primary electron energies. The IMFP of the reference material is not necessary for the suggested technique. The suggested technique uses the ratio between the transmitted elastic peak intensity and the background intensity of backscattered electrons. Free-standing films of Si, Cu, and Au were studied with thicknesses varying from 2 to 12 nm. Primary electron energies of 1, 3, and 5 keV were applied. The results appeared very good, with the percentage error range being between 5% and 25%. We also investigated the proportion of the first and second plasmon peak intensities to the elastic peak intensity. We believe that the latter could provide a directed method of measuring the IMFP of materials. Keywords: Inelastic mean free path, Monte Carlo simulation, Geant4, Free-standing film, Zero-loss peak.

Mean Free Path of Electrons in Organic Photoresists for Extreme Ultraviolet Lithography in the Kinetic Energy Range 20-450 eV.

The blur caused by the nonzero mean free path of electrons in photoresists exposed by extreme ultraviolet lithography has detrimental consequences on patterning resolution, but its effect is difficult to quantify experimentally. So far, most mean free path calculations use the dielectric formalism, which is an approximation valid in the optical limit and fails at low kinetic energy. In this work, we used a modified substrate-overlayer technique that exploited the attenuation of the Si 2p core level originating specifically from the native silicon dioxide to evaluate the attenuation of electrons traveling through 2 and 4 nm of photoresist overlayers to provide a close estimation of the inelastic mean free path relevant for photoresist lithography patterning and for electron microscopy. The photoemission spectra were collected in the proximity of the Si 2p edge (binding energy ∼101 eV) using synchrotron light of energy ℏω ranging between 120 and 550 eV. The photoresist films were prototypical chemically amplified resists based on organic copolymer of poly hydroxystyrene and tertbutyl methacrylate with and without triphenyl sulfonium perfluoro-1-butanesufonate photoacid generator and trioctylamine quencher. The inelastic mean free path of electrons, in the range that is relevant for photoresist exposure in extreme ultraviolet lithography (20-92 eV), was found to be between 1 and 2 nm. At higher kinetic energy, the mean free path increased, consistently with the well-known behavior. The presence of the photoacid generator and quencher did not change the mean free path, within experimental error. Our results are discussed and compared with the existing literature on organic molecules measured via dielectric formalism and electron transmission experiments.

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.

Extracting transverse electron mean free paths in graphene at low energy

The LEEM-IV spectra of few-layer graphene show characteristic minima at specific energies, which depend on the number of graphene layers. For the same samples, low-energy TEM (eV-TEM) spectra exhibit transmission maxima at energies corresponding to those of the reflection minima in LEEM. Both features can be understood from interferences of the electron wave function in a purely elastic model. Inelastic scattering processes in turn lead to a finite, energy-dependent inelastic Mean Free Path (MFP) and a lower finesse of the interference features. Here we develop a model that introduces both an elastic and inelastic scattering parameter on the wave-function level, thus reconciling the models considered previously. Fitting to published data, we extract the elastic and inelastic MFP self-consistently and compare these to recent reports.

Determination of electron inelastic mean free path and stopping power of hafnium dioxide

We present inelastic mean free path (IMFP) and stopping power data of the hafnium dioxide applying the relativistic dielectric response theory. The energy loss function (ELF) derived from reflection electron energy loss spectroscopy spectrum with the reverse Monte Carlo method was used for the first time to obtain the IMFP and stopping power of HfO2. The probability of the energy loss is determined by the dielectric response function εq,ω as a function of the frequency ω and the wavenumber q of the electromagnetic disturbance. Two algorithms, namely the full Penn algorithm (FPA) and the super-extended Mermin algorithm (SMA), were employed to expand the optical energy loss function, Im-1/ε0,ω, into the q,ω-plane. The results indicate that the IMFP and the stopping power obtained by using both algorithms are consistent at high electron energies, but show differences at low electron energies (less than ∼ 70 eV). This discrepancy arises from the consideration of the finite plasmon lifetimes effect in the SMA model, while it is neglected in the FPA model. Additionally, we observed that the band gap has a significant influence on the IMFP and the stopping power at low electron energies. Typically, the inclusion of the band gap leads to an increase in the IMFP, because transition channels with energies larger than E-Eg-Ev are prohibited.

Calculations of electron inelastic mean free paths (IMFPs). XIV. Calculated IMFPs for LiF and Si3N4 and development of an improved predictive IMFP formula

We report inelastic mean free paths (IMFPs) of Si3N4 and LiF for electron energies from 50 eV to 200 keV that were calculated from their optical energy‐loss functions using the relativistic full Penn algorithm including the correction of the bandgap effect in insulators. Our calculated IMFPs, designated as optical IMFPs, could be fitted to a modified form of the relativistic Bethe equation for inelastic scattering of electrons in matter from 50 eV to 200 keV. The root mean square (RMS) deviations in these fits were less than 1% for Si3N4 and LiF. The IMFPs were also compared with the relativistic version of our predictive Tanuma–Powell–Penn (TPP‐2M) equation. We found that IMFPs calculated from the TPP‐2M equation are systematically larger than the optical IMFPs for both LiF and Si3N4. The RMS differences between IMFPs from the TPP‐2M equation and the optical IMFPs were 49.3% for LiF and 17.3% for Si3N4 for energies between 50 eV and 200 keV. These RMS differences are much larger than those for most of the inorganic compounds in our previous IMFP calculations where the average RMS difference was 10.7% for 42 inorganic compounds. We also report the development of an improved predictive IMFP formula, which we designate as the JTP equation. This formula is a refinement of the TPP‐2M equation and is based on the recent IMFP calculations for 100 materials including the present IMFPs for Si3N4 and LiF (41 elemental solids, 45 inorganic compounds, and 14 organic compounds) for 83 electron energies between 50 eV and 200 keV. Our predictive JTP equation gave satisfactory results in comparisons of optical IMFPs and IMFPs calculated from the JTP equation. The RMS difference between the 8300 optical IMFPs used for optimization and the IMFPs calculated from the JTP equation was 10.2%. This value is appreciably less than the RMS difference of 16.0% found in a similar comparison of the optical IMFPs and IMFPs from the TPP‐2M equation. Furthermore, IMFPs from the JTP equation were compared with measured IMFPs for energies between 50 eV and 200 keV for 16 elemental solids and 37 inorganic compounds. We found that the JTP equation gave satisfactory results that were comparable with previous comparisons of the optical IMFPs and measured IMFPs. We believe that the JTP equation will be applicable to a wider range of materials than the TPP‐2M equation.

Describing the differential inelastic inverse mean free path of PMMA polymer with the Mermin–Belkacem-Sigmund model

Describing the differential inelastic inverse mean free path of PMMA polymer with the Mermin–Belkacem-Sigmund model

Electron transmission and mean free path in molybdenum disulfide at electron-volt energies

In van der Waals (vdW) materials, the electron mean free path (MFP) is largely influenced by the discrete states in the unoccupied band structure. So far, the influence of these states has only been measured in graphene, while all measurements on other vdW materials lack energy resolution. Here, we present reflection and transmission spectra of freestanding, few-layered molybdenum disulfide $(\mathrm{Mo}{\mathrm{S}}_{2})$ samples in the $0--55$ eV electron range. Our measurements reveal states of enhanced electron transmissivity above the vacuum level, that correspond to the (unoccupied) density of states. We also show a full quantum-mechanical calculation that confirms a good understanding of the elastic scattering in $\mathrm{Mo}{\mathrm{S}}_{2}$. A model is developed to extract the inelastic MFP spectrum, which is a measure of the inelastic scattering cross section. As $\mathrm{Mo}{\mathrm{S}}_{2}$ is a complicated system of different atomic planes, we expect that our methods generalize well to other van der Waals materials and heterostacks thereof.

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.