Experimental Electron Energy Loss Spectra Research Articles

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.

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.

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.

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.

The role of chemical disorder and structural freedom in radiation-induced amorphization of silicon carbide deduced from electron spectroscopy and ab initio simulations

Chemical disorder has previously been proposed as an explanation for the anomalously facile amorphization of silicon carbide (SiC), on the basis of topological connectivity arguments alone. In this exploratory study, “amorphous” (formally, aperiodic) SiC structures produced in ab initio molecular dynamics simulations were assessed for their connectivity topology and used to compute synthetic electron energy-loss spectra (EELS) using the ab initio real-space multiple scattering code FEFF. The synthesized spectra were compared to experimental EELS spectra collected from an ion-amorphized SiC specimen. A threshold level of chemical disorder χ (expressed as the ratio of the number of carbon-carbon bonds to the number of carbon-silicon bonds) was found to be χ ≈ 0.38, above which structural relaxation resulted in formally aperiodic structures. Different disordering methodologies resulted in identifiably different aperiodic structures, as assessed by local-cluster analysis and confirmed by collecting near-edge electron energy-loss spectra (ELNES). Such structural differences are predicted to arise for SiC crystals amorphized by irradiations involving different damage mechanisms—and therefore differing disordering mechanisms—for example, when contrasting the respective amorphized products of ion irradiation, neutron irradiation, and high-energy electron irradiation. Evidence for sp2-hybridized carbon bonding is observed, both experimentally in the irradiated sample and in simulations, and related to connectivity topology-based models for the amorphization of silicon carbide. New information about the probable intermediate-range structures present in amorphized silicon carbide is deduced from enumeration of primitive rings and evolution of local cluster configurations during the ab initio-modelled amorphization sequences.

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.

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.

Higher Order Plasmonic Modes Excited in Ag Triangular Nanoplates by an Electron Beam

Ag triangular nanoplates are known to generate strong plasmonic resonances when excited by both light and electron beams. Experimental electron energy-loss spectra (EELS) and maps were acquired using an aberration-corrected JEOL-ARM microscope. The corner, edge and centre modes that are often observed in such structures were also observed in these measurements. In addition, novel higher order internal modes were observed and were found to be well reproduced by theoretical calculations using boundary element method (BEM). These modes are “dark modes” so are not observed in the optical extinction spectra. They are confined surface propagating modes and are analogous to laser cavity modes.

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.

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.

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).

AuAl2 and PtAl2 as potential plasmonic materials

Abstract The dielectric functions of PtAl 2 , AuAl 2 and hypothetical intermediate alloys of the two in the form of Au x Pt 1− x Al 2 were calculated from first principles using density functional theory (DFT) and the random phase approximation (RPA). From these, the reflectivity, electron energy-loss spectra (EELS) and small sphere extinction spectra are predicted. The experimental reflectivity and EELS were measured for PtAl 2 and showed good agreement with the theoretical spectra. The yellow color of PtAl 2 is associated with a bulk plasmon at 3 eV. We predict that the optical properties of hypothetical intermediate alloys would show a smooth evolution with composition. The details of this change can be understood by examination of the underlying density of states (DOS). The predicted small sphere extinction spectra and quality factors show a strong surface plasmon resonance for these materials, with PtAl 2 having the optimum performance. The results indicate that these materials are good candidates for applications in plasmonics.

Electronic structure of KCa2Nb3O10as envisaged by density functional theory and valence electron energy loss spectroscopy

KCa${}_{2}$Nb${}_{3}$O${}_{10}$ is a layered Dion--Jacobson-type perovskite important for a number of applications such as photocatalysis and as a building block for heteronanostructures. Despite this, some of its central electronic properties such as the band gap and dielectric function are not well understood. In this report we have attempted to determine the band gap and understand the electronic structure of KCa${}_{2}$Nb${}_{3}$O${}_{10}$ using density functional theory. Simultaneously, the band gap and loss function have been determined experimentally using valence electron energy loss spectroscopy. The theoretical results indicate that KCa${}_{2}$Nb${}_{3}$O${}_{10}$ is a direct band gap semiconductor with a sparse density of states close to the onset of the conduction band. The calculated band gap value of 3.1 eV is in excellent agreement with the 3.2\ifmmode\pm\else\textpm\fi{}0.1 eV measured experimentally. The loss functions computed and experimentally determined show good agreement up to 20 eV, but the theoretical peak positions at higher energy do not agree with the experimental electron energy loss spectrum. These transitions originate from K-3$p$, Ca-3$p$, and Nb-4$p$ semicore states and their positions are not well described by Kohn-Sham eigenvalues. After a scissors shift of transitions due to these states by about 2.5 eV to higher energies we obtain good agreement with the experimental loss function and can thus explain the origin of all the features seen in the experimental electron energy loss spectrum.

Statistical consequences of applying a PCA noise filter on EELS spectrum images

Principal component analysis (PCA) noise filtering is a popular method to remove noise from experimental electron energy loss (EELS) spectrum images. Here, we investigate the statistical behaviour of this method by applying it on a simulated data set with realistic noise levels. This phantom data set provides access to the true values contained in the data set as well as to many different realizations of the noise. Using least squares fitting and parameter estimation theory, we demonstrate that even though the precision on the estimated parameters can be better as the Cramér-Rao lower bound, a significant bias is introduced which can alter the conclusions drawn from experimental data sets. The origin of this bias is in the incorrect retrieval of the principal loadings for noisy data. Using an expression for the bias and precision of the singular values from literature, we present an evaluation criterion for these singular values based on the noise level and the amount of information present in the data set. This criterion can help to judge when to avoid PCA noise filtering in practical situations. Further we show that constructing elemental maps of PCA noise filtered data using the background subtraction method, does not guarantee an increase in the signal to noise ratio due to correlation of the spectral data as a result of the filtering process.

Investigating the electronic structure of fluorite-structured oxide compounds: comparison of experimental EELS with first principles calculations

Energy loss spectra from fluorite-structured ZrO2, CeO2, and UO2 compounds are compared with theoretical calculations based on density functional theory (DFT) and its extensions, including the use of Hubbard-U corrections (DFT + U) and hybrid functionals. Electron energy loss spectra (EELS) were obtained from each oxide using a scanning transmission electron microscope (STEM). The same spectra were computed within the framework of the full-potential linear augmented plane-wave (FLAPW) method. The theoretical and experimental EEL spectra are compared quantitatively using non-linear least squares peak fitting and a cross-correlation approach, with the best level of agreement between experiment and theory being obtained using the DFT + U and hybrid computational approaches.