Experimental Electron Energy Loss Research Articles

Determination of the energy loss function of tungsten from reflection electron energy loss spectroscopy spectra

We incorporate experimental reflection electron energy loss spectroscopy (REELS) spectrum data with theoretical analysis to precisely determine the energy loss function (ELF) of tungsten (W) in the energy loss range of 0.1–110 eV at the incident electron energies of 1 keV, 2 keV and 3 keV. Employing the reverse Monte Carlo (RMC) method, we have obtained an averaged ELF whose relative errors of the perfect-screening sum rule and oscillator-strength sum rule were ∼ 0.70 % and 0.68 %, respectively. This ELF was then used to derive the optical constants and complex dielectric function. Furthermore, we have successfully differentiated between bulk and surface contributions to the REELS spectra throughout the entire considered energy loss range.

The density and pressure of helium nano-bubbles encapsulated in silicon

The 1 s 2 → 1 s 2 p ( 1 P ) excitation in compressed helium atoms in either the bulk material or encapsulated in a bubble is shifted to energies higher than in the free atom. For bulk helium, energy shifts predicted from non-empirical electronic structure computations are in excellent agreement with experimentally determined values. However, there are significant discrepancies both between the results of experiments on different bubbles and between these and the well established descriptions of the bulk. A critique is presented of previous analyses of earlier scanning transmission electron microscope measurements that are untrustworthy because the density dependence of the electron impact excitation cross section was neglected. Experimental electron energy loss data from an earlier study of helium encapsulated in silicon are reanalysed and it is shown that the properties of the helium in these bubbles do not differ significantly from those in the bulk, thereby enabling the densities in the bubbles to be determined. These enable bubble pressures to be deduced from a well established experimentally derived equation of state. It is shown that the errors of up to 80% in the incorrectly determined densities are greatly magnified in the predicted pressures which can be too large by factors of over seven.

Efficient full frequency GW for metals using a multipole approach for the dielectric screening

The properties of metallic systems with important and structured excitations at low energies, such as Cu, are challenging to describe with simple models like the plasmon pole approximation (PPA), and more accurate and sometimes prohibitive full frequency approaches are usually required. In this paper we propose a numerical approach to $GW$ calculations on metals that takes into account the frequency dependence of the screening via the multipole approximation (MPA), an accurate and efficient alternative to current full-frequency methods that was recently developed and validated for semiconductors and overcomes several limitations of PPA. We now demonstrate that MPA can be successfully extended to metallic systems by optimizing the frequency sampling for this class of materials and introducing a simple method to include the $\mathbf{q}\to 0$ limit of the intra-band contributions. The good agreement between MPA and full frequency results for the calculations of quasi-particle energies, polarizability, self-energy and spectral functions in different metallic systems confirms the accuracy and computational efficiency of the method. Finally, we discuss the physical interpretation of the MPA poles through a comparison with experimental electron energy loss spectra for Cu.

Spectroscopic signatures of states in the continuum characterized by a joint experimental and theoretical study of pyrrole.

We report a combined experimental and theoretical investigation of electron-molecule interactions using pyrrole as a model system. Experimental two-dimensional electron energy loss spectra (EELS) encode information about the vibrational states of the molecule as well as the position and structure of electronic resonances. The calculations using complex-valued extensions of equation-of-motion coupled-cluster theory (based on non-Hermitian quantum mechanics) facilitate the assignment of all major EELS features. We confirm the two previously described π resonances at about 2.5 and 3.5eV (the calculations place these two states at 2.92 and 3.53eV vertically and 2.63 and 3.27eV adiabatically). The calculations also predict a low-lying resonance at 0.46eV, which has a mixed character-of a dipole-bound state and σ* type. This resonance becomes stabilized at one quanta of the NH excitation, giving rise to the sharp feature at 0.9eV in the corresponding EELS. Calculations of Franck-Condon factors explain the observed variations in the vibrational excitation patterns. The ability of theory to describe EELS provides a concrete illustration of the utility of non-Hermitian quantum chemistry, which extends such important concepts as potential energy surfaces and molecular orbitals to states embedded in the continuum.

Removal of core hole distortion from ionization edges in electron energy loss spectroscopy

The near-edge fine structure in electron energy loss spectra is used to probe the electronic bonding environment of materials at high spatial resolution. Often, however, deviations from the ground state electronic properties are observed, due to the core hole created within the ionized atom. A method is proposed to remove core hole distortion from experimental electron energy loss spectra by calculating the electrodynamic work done in separating the moving, incident electron from the oppositely charged core hole. Dynamic screening of the core hole is modeled using the material dielectric properties. The resulting energy gain spectrum is deconvolved from the experimental measurement to give a ``fully screened'' spectrum that is free of core hole distortion. The method is tested on core loss edges in elemental Si, SiC, and ${\mathrm{SiO}}_{x}$. Despite assuming classical electrodynamics, the fundamental principle of an energy gain correction can be shown to be consistent with quantum mechanics, although shortcomings in some of the assumptions made on the nature of the core hole are also identified.

First-principles perspective on magnetic second sound

The fluctuations of the magnetic order parameter, or longitudinal spin excitations, are investigated theoretically in the ferromagnetic Fe and Ni as well as in the antiferromagnetic phase of the pnictide superconductor FeSe. The charge and spin dynamics of these systems is described by evaluating the generalized charge and spin density response function calculated from first-principles linear response time dependent density functional theory within adiabatic local spin density approximation. We observe that the formally non-interacting Kohn-Sham system features strong coupling between the magnetization and charge dynamics in the longitudinal channel and that the coupling is effectively removed upon the inclusion of the Coulomb interaction in the charge channel and the resulting appearance of plasmons. The longitudinal spin fluctuations acquire a collective character without the emergence of the Goldstone boson, similar to the case of paramagnon excitations in non-magnetic metals like Pd. In ferromagnetic Fe and Ni the longitudinal spin dynamics is governed by interactions between low-energy intraband electron-hole pairs while in quasi two dimensional antiferromagnet FeSe it is dominated by the interband transitions with energies of the order of exchange splitting. In the later material, the collective longitudinal magnetization fluctuations feature well defined energies and long life times for small momenta and appear below the particle-hole continuum. The modes become strongly Landau-damped for growing wave-vectors. We relate our theoretical findings to existing experimental spin-polarized electron energy loss spectroscopy results. In bulk bcc Fe, the longitudinal magnetic modes appear above the typical energies of transverse spin-waves, have energies comparable with the Stoner spin-flip excitation continuum, and are order of magnitude less energetic than the charge dynamics.

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

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

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

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

Secondary electron emission and yield spectra of metals from Monte Carlo simulations and experiments

In this work, we present a computational method, based on the Monte Carlo statistical approach, for calculating electron energy emission and yield spectra of metals, such as copper, silver and gold. The calculation of these observables proceeds via the Mott theory with a Dirac–Hartree–Fock spherical potential to deal with the elastic scattering processes, and by using the Ritchie dielectric approach to model the electron inelastic scattering events. In the latter case, the dielectric function, which represents the starting point for the evaluation of the energy loss, is obtained from experimental reflection electron energy loss spectra. The generation of secondary electrons upon ionization of the samples is also implemented in the calculation. A remarkable agreement is obtained between both theoretical and experimental electron emission spectra and yield curves.

Analytical modeling of electron energy loss spectroscopy of graphene: Ab initio study versus extended hydrodynamic model

We present an analytical modeling of the electron energy loss (EEL) spectroscopy data for free-standing graphene obtained by scanning transmission electron microscope. The probability density for energy loss of fast electrons traversing graphene under normal incidence is evaluated using an optical approximation based on the conductivity of graphene given in the local, i.e., frequency-dependent form derived by both a two-dimensional, two-fluid extended hydrodynamic (eHD) model and an ab initio method. We compare the results for the real and imaginary parts of the optical conductivity in graphene obtained by these two methods. The calculated probability density is directly compared with the EEL spectra from three independent experiments and we find very good agreement, especially in the case of the eHD model. Furthermore, we point out that the subtraction of the zero-loss peak from the experimental EEL spectra has a strong influence on the analytical model for the EEL spectroscopy data.

Multidimensional Hybridization of Dark Surface Plasmons.

Synthetic three-dimensional (3D) nanoarchitectures are providing more control over light-matter interactions and rapidly progressing photonic-based technology. These applications often utilize the strong synergy between electromagnetic fields and surface plasmons (SPs) in metallic nanostructures. However, many of the SP interactions hosted by complex 3D nanostructures are poorly understood because they involve dark hybridized states that are typically undetectable with far-field optical spectroscopy. Here, we use experimental and theoretical electron energy loss spectroscopy to elucidate dark SPs and their interactions in layered metal-insulator-metal disc nanostructures. We go beyond the established dipole SP hybridization analysis by measuring breathing and multipolar SP hybridization. In addition, we reveal multidimensional SP hybridization that simultaneously utilizes in-plane and out-of-plane SP coupling. Near-field classic electrodynamics calculations provide excellent agreement with all experiments. These results advance the fundamental understanding of SP hybridization in 3D nanostructures and provide avenues to further tune the interaction between electromagnetic fields and matter.

Excited States of Pt(PF3)4 and Their Role in Focused Electron Beam Nanofabrication

Electron induced chemistry of metal-containing precursor molecules is central in focused electron beam induced deposition (FEBID). While some elementary processes leading to precursor decomposition were quantitatively characterized, data for neutral dissociation is missing. We provide this data for the model precursor Pt(PF3)4 by using the available cross sections for electronic excitation and characterizing fragmentation of the excited states theoretically by TDDFT. The potential energy curves for a number of states visible in the experimental electron energy loss spectra are dissociative, either directly or via conical intersections, indicating that the quantum yield for dissociation is close to 100%. Taking into account typical electron energy distribution at the FEBID spot reveals that the importance of neutral dissociation exceeds that of dissociative electron attachment, which has been so far considered to be the dominant decomposition process. We thus established neutral dissociation as an importan...

Simulation of electron energy loss spectra of nanomaterials with linear-scaling density functional theory

Experimental techniques for electron energy loss spectroscopy (EELS) combine high energy resolution with high spatial resolution. They are therefore powerful tools for investigating the local electronic structure of complex systems such as nanostructures, interfaces and even individual defects. Interpretation of experimental electron energy loss spectra is often challenging and can require theoretical modelling of candidate structures, which themselves may be large and complex, beyond the capabilities of traditional cubic-scaling density functional theory. In this work, we present functionality to compute electron energy loss spectra within the onetep linear-scaling density functional theory code. We first demonstrate that simulated spectra agree with those computed using conventional plane wave pseudopotential methods to a high degree of precision. The ability of onetep to tackle large problems is then exploited to investigate convergence of spectra with respect to supercell size. Finally, we apply the novel functionality to a study of the electron energy loss spectra of defects on the (1 0 1) surface of an anatase slab and determine concentrations of defects which might be experimentally detectable.

Analysis of KLL Auger spectra excited by X-rays from Ni and Cu metal surfaces

Ni and Cu KLL Auger spectra excited by X-rays from polycrystalline metal foils were measured with good energy resolution and intensity earlier. Auger spectra of 3d transition metals contain satellite peaks due to the atomic excitation processes. Because of the complexity of the measured spectral shape a complete explanation of the spectra was not given in the previous works. A new analysis of the measured spectra is presented here, with improved description of effects of inelastic electron scattering of the electrons in the solid sample and using complex peak shapes to model the satellite structure that follows each diagram line. The energy loss part of measured spectra due to the bulk plasmon excitations, surface plasmon excitations and intrinsic loss processes was removed using the Partial Intensity Analysis method based on energy loss distributions obtained from experimental reflection electron energy loss spectra of the same Cu and Ni metal foils.Relative Auger-transition energies derived from measured spectra of copper are in good agreement with previous experimental works and the results of cluster molecular orbital multielectron (DV-ME) calculations. The intensity ratio I(3P2/3P0) shows better agreement with the result of relativistic calculations than in previous works. In the case of nickel the relative Auger-transition energies are in good agreement with the previous results. According to the new evaluation four satellite peaks were identified on the low energy side of each diagram line in the Auger spectra of Ni.

Examining Substrate-Induced Plasmon Mode Splitting and Localization in Truncated Silver Nanospheres with Electron Energy Loss Spectroscopy.

Motivated by the need to study the size dependence of nanoparticle-substrate systems, we present a combined experimental and theoretical electron energy loss spectroscopy (EELS) study of the plasmonic spectrum of substrate-supported truncated silver nanospheres. This work spans the entire classical range of plasmonic behavior probing particles of 20-1000 nm in diameter, allowing us to map the evolution of localized surface plasmons into surface plasmon polaritons and study the size dependence of substrate-induced mode splitting. This work constitutes the first nanoscopic characterization and imaging of these effects in truncated nanospheres, setting the stage for the systematic study of plasmon-mediated energy transfer in nanoparticle-substrate systems.

Energy loss of electrons impinging upon glassy carbon, amorphous carbon, and diamond: Comparison between two different dispersion laws

In this paper, we compare and discuss calculated inelastic mean free path, stopping power, range, and reflection electron energy loss spectra obtained using two different and popular dispersion laws. We will present and discuss the results we obtained investigating the interaction of electron beams impinging upon three allotropic forms of carbon, i.e. solid glassy carbon, amorphous carbon, and diamond. We will compare numerical results with experimental reflection electron energy loss spectra.

Excitation dependent Fano-like interference effects in plasmonic silver nanorods

Surface plasmon resonances in metal nanoparticles are an emerging technology platform for nano-optics applications from sensing to solar energy conversion. The electromagnetic near field associated with these resonances arises from modes determined by the shape, size, and composition of the metal nanoparticle. When coupled in the near field, multiple resonant modes can interact to give rise to interference effects offering fine control of both the spectral response and spatial distribution of fields near the particle. Here, we present an examination of experimental electron energy loss spectroscopy (EELS) of silver nanorod monomer surface plasmon modes and present an explanation of observed spatial amplitude modulation of the Fabry-P\'erot resonance modes of these silver nanorods using electrodynamics simulations. For these simulations, we identify differences in spectral peak symmetry in light scattering and electron spectroscopies (EELS and cathodoluminescence) and analyze the distinct near-field responses of silver nanorods to plane-wave light and electron beam excitation in terms of a coupled oscillator model. Effects of properties of the material and the incident field are evaluated, and the spatially resolved EELS signals are shown to provide a signature for assessing Fano-like interference effects in silver nanorods. These findings outline key considerations and challenges for interpreting electron microscopy data on plasmonic nanoparticles for understanding nanoscale optics and for characterization and design of photonic devices.

Joint experimental and theoretical study on vibrational excitation cross sections for electron collisions with diacetylene.

We have measured and calculated differential and integral cross sections for elastic and vibrationally inelastic electron scattering by diacetylene molecules at electron energies from 0.5 to 20 eV in the whole range of scattering angles from 0 to 180°. The calculations were carried out using the discrete momentum representation method (DMR), which is based on the two-channel Lippmann-Schwinger equation in the momentum space. The interaction between the scattered electron and the target molecule is described by the exact static-exchange potential. Correlation-polarization forces are included by a local density functional theory. Energy dependences of integral and differential cross sections are presented for all nine vibrational modes. A detailed comparison of theoretical and experimental electron energy loss spectra is presented for electron energies of 1, 5.5, 10, and 20 eV. The theory assigns symmetry of resonances that could not be determined by empirical analysis alone. The theory reveals, and quantitatively describes, the switching of partial waves accompanying excitation of nontotally symmetrical vibrations. Limitations of the theory in reproducing experimental data for the narrow π* resonance below 2 eV are mentioned.

An experimental and theoretical investigation into the excited electronic states of phenol.

We present experimental electron-energy loss spectra (EELS) that were measured at impact energies of 20 and 30 eV and at angles of 90° and 10°, respectively, with energy resolution ∼70 meV. EELS for 250 eV incident electron energy over a range of angles between 3° and 50° have also been measured at a moderate energy resolution (∼0.9 eV). The latter spectra were used to derive differential cross sections and generalised oscillator strengths (GOS) for the dipole-allowed electronic transitions, through normalization to data for elastic electron scattering from benzene. Theoretical calculations were performed using time-dependent density functional theory and single-excitation configuration interaction methods. These calculations were used to assign the experimentally measured spectra. Calculated optical oscillator strengths were also compared to those derived from the GOS data. This provides the first investigation of all singlet and triplet excited electronic states of phenol up to the first ionization potential.

Russian

Full sets of the fundamental optical functions of the fullerite C76 films were determined in the 0–40 eV energy range. The calculations were performed from the experimental electron energy loss spectra. The results of calculations were compared with known theoretical dates. The dielectric function spectra were decomposed into elementary components. The main parameters of components were found (the energy values of the maxima, the relative area and half-widths of the band, and oscillator strengths).