The orientation-dependent simulation of ELNES

The nuts and bolts of core-hole constrainedab initiosimulation forK-shell x-ray photoemission and absorption spectra

X-ray photoemission (XPS) and near edge x-ray absorption fine structure (NEXAFS) spectroscopy play an important role in investigating the structure and electronic structure of materials and surfaces.Ab initiosimulations provide crucial support for the interpretation of complex spectra containing overlapping signatures. Approximate core-hole simulation methods based on density functional theory (DFT) such as the delta-self-consistent-field (ΔSCF) method or the transition potential (TP) method are widely used to predictK-shell XPS and NEXAFS signatures of organic molecules, inorganic materials and metal-organic interfaces at reliable accuracy and affordable computational cost. We present the numerical and technical details of our variants of the ΔSCF and TP method (coined ΔIP-TP) to simulate XPS and NEXAFS transitions. Using exemplary molecules in gas-phase, in bulk crystals, and at metal-organic interfaces, we systematically assess how practical simulation choices affect the stability and accuracy of simulations. These include the choice of exchange-correlation functional, basis set, the method of core-hole localization, and the use of periodic boundary conditions (PBC). We particularly focus on the choice of aperiodic or periodic description of systems and how spurious charge effects in periodic calculations affect the simulation outcomes. For the benefit of practitioners in the field, we discuss sensible default choices, limitations of the methods, and future prospects.

Chemical-state analysis of organic semiconductors using soft X-ray absorption spectroscopy combined with first-principles calculation

The chemical states of organic semiconductors were investigated by total-electron-yield soft X-ray absorption spectroscopy (TEY-XAS) and first-principles calculations. The organic semiconductors, pentacene (C(22)H(14)) and pentacenequinone (C(22)H(12)O(2)), were subjected to TEY-XAS and the experimental spectra obtained were compared with the 1s core-level excited spectra of C and O atoms, calculated by a first-principles planewave pseudopotential method. Excellent agreement between the measured and the calculated spectra were obtained for both materials. Using this methodology, we examined the chemical states of the aged pentacene, and confirmed that both C-OH and C═O chemical bonds are generated by exposure to air. This result implies that not only oxygen but also humidity causes pentacene oxidation.

Electron beam-induced oxygen desorption in gamma-LiAlO(2)

Effects of electron irradiation damage in gamma-LiAlO(2) were analysed using energy loss near edge fine structure (ELNES) of the O K-edge. Simulations of the O K-fine structure by means of a density functional theory (DFT) code show that under the electron beam gamma-LiAlO(2) undergoes the following transformation: LiAlO(2)--> LiAl(5)O(8)--> Al(2)O(3). O K-edge spectra, which were recorded during this decomposition process, contain an additional peak at 531eV. This peak can be attributed to a pi( *)-transition, which is observed for molecular oxygen O(2). This result suggests that the electron beam-induced LiAlO(2) decomposition occurs through the loss of O(2).

Chemical shift of electron energy-loss near-edge structure on the nitrogen K-edge and titanium L3-edge at TiN/Ti interface

We investigated the chemical shift of the electron energy-loss near-edge structure (ELNES) for the nitrogen K-edge and titanium L3-edge measured from the interface region between a titanium nitride layer and a titanium layer. Both the titanium nitride and titanium layers were prepared by a sputtering method. Elemental analysis for nitride and titanium in the vicinity of the interface region was performed using a standard technique in electron energy-loss spectroscopy. It was demonstrated that both the ELNES of nitrogen K-edge and titanium L3-edge presented the chemical shift, more or less, depending on the composition of TiNx. The experimental findings were interpreted using a first-principles band structure calculation. The chemical shifts of nitrogen K-edge and titanium L3-edge can be used as fingerprinting for readily distinguishing the composition of TiNx.

Core-level spectroscopy calculation and the plane wave pseudopotential method

A plane wave based method for the calculation of core-level spectra is presented. We provide details of the implementation of the method in the pseudopotential density functional code CASTEP, including technical issues concerning the calculations, and discuss the applicability and accuracy of the method. A number of examples are provided for comparing the results to both experiment and other density functional theory techniques.

Energy-loss near-edge structure (ELNES) and first-principles calculation of electronic structure of nickel silicide systems

The electronic structures of nanometre-sized nickel silicide systems, Ni(2)Si and NiSi, have been studied by energy-loss near-edge structure (ELNES) and first-principles band structure calculations. Experimental ELNES of Ni L(3)- and Si L(2,3)-edges could be explained well using theoretical spectra calculated for the ground state without the core hole, suggesting metallic properties for both silicides. It was shown that a slight difference in ELNES spectra of Ni(2)Si and NiSi comes from the coupling among the Ni d and Si p, d states in the unoccupied bands. The density of states and the contour plots of all the valence electron densities for Ni(2)Si, NiSi together with NiSi(2) show that Ni(2)Si has the bond with the strongest covalent character between Ni and Si atoms and the most transition metal-like character of the Ni 3d band among the three silicides.

Magnetic circular dichroism in electron energy loss spectrometry

The measurement of circular dichroism in the electron microscope is a new, emerging method and, as such, it is subject to constant refinement and improvement. Different ways can be envisaged to record the signal. We present an overview of the key steps in the energy-loss magnetic chiral dichroism (EMCD) experiment as well as a detailed review of the methods used in the intrinsic way where the specimen is used as a beam splitter. Lateral resolution up to 20-30 nm can be achieved, and the use of convergent beam techniques leads to an improved S/N ratio. Dichroic effects are shown for Ni and Co single crystal; as a counterexample, measurements were carried also for a non-magnetic (Ti) sample, where no dichroic effect was found.

Evolution of ELNES spectra as a function of experimental settings for any uniaxial specimen: A fully relativistic study

We perform calculations of the fully relativistic, corrected geometrical weighting of the pi* and sigma* transitions measured from the 1s core loss electron energy loss spectroscopy (EELS) spectrum in any uniaxial specimen. We present a complete calculation of the differential scattering cross-section (DSCS), taking into account the collection angle, the illumination angle and the tilt of the sample over the optical axis. Owing to high electron velocity in an EELS experiment, the relativistic correction has to be considered. We thus, present a relativistic, corrected DSCS by using the theory recently developed by Jouffrey et al. [Ultramicroscopy 102 (2004) 61] and P. Schattschneider et al. [Phys. Rev. B 72 (2005) 045142]. The relativistic correction is first performed in the natural coordinate system of the scattering event. We then point out a straightforward method to introduce this correction in the microscopic coordinate system, where all calculations have to be done to be experimentally useful. Using the fully corrected DSCS, we present an expression predicting the evolution of the R=pi*/(pi*+sigma*) ratio (related to the ratio of sp2 and sp3 bondings) as a function of experimental settings. We show how the R-evolution can be predicted, for any experimental setting, by the knowledge of one unique reference value. We verify on graphite specimens, the validity of the R-calculation by comparing theoretical predictions presented in this work with experimental data published elsewhere [Daniels et al., Ultramicroscopy 96 (2003) 523 and Menon et al., Ultramicroscopy 74 (1998) 83].

Practical aspects of running the WIEN2k code for electron spectroscopy

The Wien2k code is widely used for the calculation of electron energy loss spectra. Low loss spectra can be calculated with the OPTIC package while core loss spectra are calculated with the TELNES program. A new version, TELNES.2, takes into account the effects of relativity for anisotropic materials. In this paper we discuss the effects of different parameters used for the self-consistent calculation of the electron density on the obtained spectra. We give an overview of possibilities for the calculation of complicated systems requiring a super-cell, like defects or disordered systems. We discuss the problem of the core hole and of the calculation of orientation-sensitive spectra and give an overview of results already published.

Model-based quantification of EELS spectra: Including the fine structure

An extension to model-based electron energy loss spectroscopy (EELS) quantification is reported to improve the possibility of modelling fine structure changes in electron energy loss spectra. An equalisation function is used in the energy loss near edge structure (ELNES) region to model the differences between a single atom differential cross section and the cross section for an atom in a crystal. The equalisation function can be shown to approximate the relative density of unoccupied states for the given excitation edge. On a set of 200 experimental h-BN spectra, this technique leads to statistically acceptable models resulting into unbiased estimates of relative concentrations and making the estimated precisions come very close to the Cramér-Rao lower bound (CRLB). The method greatly expands the useability of model-based EELS quantification to spectra with pronounced fine structure. Another benefit of this model is that one also gets an estimate of the unoccupied density of states for a given excitation edge, without having to do background removal and deconvolution, making the outcome intrinsically more reliable and less noisy.

Site-specific electronic structure analysis by channeling EELS and first-principles calculations

Site-specific electronic structures were investigated by electron energy loss spectroscopy (EELS) under electron channeling conditions. The Al-K and Mn-L(2,3) electron energy loss near-edge structure (ELNES) of, respectively, NiAl2O4 and Mn3O4 were measured. Deconvolution of the raw spectra with the instrumental resolution function restored the blunt and hidden fine features, which allowed us to interpret the experimental spectral features by comparing with theoretical spectra obtained by first-principles calculations. The present method successfully revealed the electronic structures specific to the differently coordinated cationic sites.

ELNES at magic angle conditions

If one needs to cancel the effects of the anisotropy of the sample in a EELS experiment in the TEM, a particular couple of values for the collection and convergence angle must be used, called magic angle conditions (MAC). Recent developments in the theory have shown that a full relativistic treatment is mandatory to correctly describe this effect and that the MAC are strongly dependent on the acceleration voltage. We show how the analytical formula can be derived and give the exact analytical solution for the MAC which can then be easily applied to every practical case. We show the consequences of the energy dependence of the magic angle and that the parallelity of the beam will be the limiting factor for high acceleration voltages while for low acceleration voltages the contribution coming from Bragg spots may make it impossible to reach MAC.

Polarization dependence in ELNES: Influence of probe convergence, collector aperture and electron beam incidence angle

The differential scattering cross section in electron energy loss near edge spectroscopy (ELNES) generally depends on the orientation of the Q wave vector transferred from the incident electron to an atomic core electron. In the case where the excited atom belongs to a threefold, fourfold or sixfold main rotation axis, the dipole cross section depends on the angle of Q with respect to this axis. In this paper, we restrict to this situation called dichroism. Furthermore, if we take into account the relativistic effects due to the high incident electron velocity, this dipole cross section also depends on the angle of Q with respect to the electron beam axis. It is due to these dependences that the shape of measured electron energy loss spectra varies with the electron beam incidence, the collector aperture, the incident beam convergence and the incident electron energy. The existence of a particular beam incidence angle for which the scattering cross section becomes independent of collection and beam convergence semi-angles is clearly underscored. Conversely, it is shown that EELS spectra do not depend on the beam incidence angle for a set of particular values of collection and convergence semi-angles. Particularly, in the case of a parallel incident beam, there is a collection semi-angle (often called magic angle) for which the cross section becomes independent of the beam orientation. This magic angle depends on the incident beam kinetic energy. If the incident electron velocity V is small compared with the light velocity c, this magic angle is about 3.975theta(E) (theta(E) is the scattering angle). It decreases to 0 when V approaches c. These results are illustrated in the case of the K boron edge in the boron nitride.

Some effects of electron channeling on electron energy loss spectroscopy

As an electron beam (of order 100 keV) travels through a crystalline solid it can be channeled down a zone axis of the crystal to form a channeling peak centered on the atomic columns. The channeling peak can be similar in size to the outer atomic orbitals. Electron energy loss spectroscopy (EELS) measures the losses that the electron experiences as it passes through the solid yielding information about the unoccupied density of states in the solid. The interaction matrix element for this process typically produces dipole selection rules for small angle scattering. In this paper, a theoretical calculation of the EELS cross section in the presence of strong channeling is performed for the silicon L23 edge. The presence of channeling is found to alter both the intensity and selection rules for this EELS signal as a function of depth in the solid. At some depths in the specimen small but significant non-dipole transition components can be produced, which may influence measurements of the density of states in solids.

The magic angle: a solved mystery

We resolve the long-standing mysterious discrepancy between the experimental magic angle in EELS--approximately 2theta(E)--and the quantum mechanical prediction of approximately 4theta(E). A relativistic approach surpassing the usually applied kinematic correction yields a magic angle close to the experimental value. The reason is that the relativistic correction of the inelastic scattering cross section in anisotropic systems is significantly higher than in isotropic ones.

Investigation of hexagonal and cubic GaN by high-resolution electron energy-loss spectroscopy and density functional theory

High-resolution electron energy-loss spectroscopy in a transmission electron microscope is a very powerful method for the study of electronic structure of materials. The fine structure of Ga L(2,3) and N ionization edges in c-GaN and h-GaN was studied using a TEM equipped with a monochromator and high-resolution energy spectrometer. The experimental results were compared with the results of calculation based on the density functional theory using the Wien2k code and show that the best fit is achieved when the core hole effect is taken into account. The effect of the core hole value and the supercell size on the energy-loss near-edge structure have been investigated. A different behaviour was found for c-GaN and h-GaN: better agreement is obtained for a 0.5 core hole for h-GaN and for a full core hole for c-GaN. The anisotropic behaviour of the experimental spectra and calculated spectra for h-GaN have been studied and the "magic" angle was determined.

Electron energy-loss near-edge structures of 3d transition metal oxides recorded at high-energy resolution

Near-edge fine structures of the metal L(2,3) and O K-edges in transition metal-oxides have been studied with a transmission electron microscope equipped with a monochromator and a high-resolution imaging filter. This system enables the recording of EELS spectra with an energy resolution of 0.1eV thus providing new near-edge fine structure details which could not be observed previously by EELS in conventional TEM instruments. EELS-spectra from well-defined oxides like titanium oxide (TiO(2)), vanadium oxide (V(2)O(5)), chromium oxide (Cr(2)O(3)), iron oxide (Fe(2)O(3)), cobalt oxide (CoO) and nickel oxide (NiO) have been measured with the new system. These spectra are compared with EELS data obtained from a conventional microscope and the main spectral features are interpreted. Additionally, the use of monochromised TEMs is discussed in view of the natural line widths of K and L(2,3) edges.

Improvement of energy loss near edge structure calculation using Wien2k

The density functional theory (DFT) is a recognised method for the calculation of electronic properties of materials. As such it can also be used for the calculation of energy loss near edge structures. Some care has to be taken since the DFT is intended for ground state calculation. The effect of the core hole left by the excited electron is different in an insulator and in a metal and can be observed in both cases. For an insulator (MgO, Si), a supercell calculation is needed while in the case of copper, extremely good agreement with experiment can be obtained with a partial core hole calculation. In the particular case of the WIEN code (APW method) we show that calculation of low lying edges (Si L at 99eV) where the initial state is not strongly localised can only be done within the dipole approximation and with some care. Random alloys (CuNi) have been calculated previously using a supercell; we show that a particular version of the virtual crystal approximation gives promising results.

Anisotropy and collection angle dependence of the oxygen K ELNES in V2O5: a band-structure calculation study

We present a theoretical study of the anisotropy and collection angle dependence of the oxygen K ELNES in V2O5. Ab initio band-structure calculations were performed with WIEN97, a program package based on the full potential linearised augmented plane waves (FP-LAPW) method. An analysis of the site and angular momentum projected DOS allowed the identification of differently coordinated oxygens and the separation of the oxygen K-edge into contributions from terminal (vanadyl) oxygens, bridging oxygens and chain oxygens. The major contribution to the anisotropy of the O K-edge ELNES could be assigned to transitions at the vanadyl oxygen. Theoretical calculations predict that the extent of changes in the ELNES would be large enough for detection in collection angle dependent O K-edge measurements. A variation in the fine structure of the O K-edge with decreasing collection angle was confirmed by experiments.

High resolution EELS using monochromator and high performance spectrometer: comparison of V2O5 ELNES with NEXAFS and band structure calculations

Using single crystal V2O5 as a sample, we tested the performance of the new aberration corrected GATAN spectrometer on a monochromatised 200 kV FEG FEI (S)TEM. The obtained V L and O K ELNES were compared with that obtained in a common GATAN GIF and that in the new spectrometer, without monochromatised beam. The performance of the new instrumentation is impressive: recorded with an energy-resolution of 0.22 eV, the V L(3) edge reveals all the features due to the bulk electronic structure, that are also revealed in near-edge X-ray absorption fine structure (NEXAFS) with a much higher energy-resolution (0.08 eV). All features of the ELNES and NEXAFS are in line with a theoretical spectrum derived from band-structure calculations.

Study of changes in L32 EELS ionization edges upon formation of Ni-based intermetallic compounds

EELS L32 ionization edges in several Ni-based intermetallic compounds have been studied and interpreted in terms of the distribution of electrons in the valence d-bands. It is demonstrated that the integral EELS cross-sections change only slightly upon the formation of intermetallic compounds and therefore the charge transfer between atoms is negligible. On the other hand, the changes in the fine energy-loss near-edge structure (ELNES) of the Ni L3 edge can be readily detected indicating an important redistribution of d-electrons at the Ni site with alloying. These features are well reproduced by ab-initio calculations with a FLAPW method in its WIEN97 implementation. In contrast to the drastic effect of chemical environment, structural transformations in the investigated intermetallics result in smaller ELNES changes, which can be detected by only exceptional instruments with a higher energy resolution.

N-K ELNES study of anisotropy effects in hexagonal AlN

Anisotropic effects in hexagonal aluminium nitride have been studied by electron energy-loss spectroscopy (EELS) in the N-K energy loss near edge structure (ELNES). Experimental data acquired with different collection angles and with a nearly parallel incident electron beam aligned along the c-axis have been compared to simulations based on ab initio calculations. The extraction of intrinsic parallel I|| (with momentum transfer q || c axis) and perpendicular I perpendicular (with momentum transfer q perpendicular c axis) components has been performed directly from the experimental spectra. This has been done according to their description as linear combinations of I|| and I perpendicular, with adequate weights deduced from a geometrical model of anisotropic behaviour.

Improved comparison of low energy loss spectra with band structure calculations: the example of BN filaments

Electron energy loss spectra have been recorded from BN filaments for energy losses between 2 and 50eV. They compare well with other BN shapes (nanotubes, sheets, etc). The interpretation of all the peaks in the spectra has been made via an ab initio calculation using the FLAPW code WIEN97 (A full potential linearized augmened plane wave package for calculating crystal properties, Karlheinz Schwarz, Techn. Universität Wien, Austria, 1999. ISBN 3-9501031-0-4). In order to fully simulate the observed spectra, the geometry particular to the EELS experiment has been taken into account making use of Wessjohann's relativistic formula for thin anisotropic slabs (Phys. Stat. Sol. B 77 (1976) 535). Furthermore, the effect of the convergent beam has been introduced into the simulation and has been proven to be an important parameter in obtaining the corresponding peak intensities.

Validity of the dipole-selection rule for the Al-L2,3 edge of alpha-Al2O3 under channeling conditions

The validity of the dipole-selection rule for the Al-L2,3 electron energy-loss edge of alpha-Al2O3 is investigated. Dipole forbidden transitions can be observed in a transmission electron microscope operated with large collection apertures. In addition, it is shown that channeling along a highly symmetrical zone axis in alpha-Al2O3 can lead to the detection of dipole forbidden transitions even with small collection apertures. For an incident electron direction parallel to the <0001> orientation it is observed experimentally that the fine structure of the Al-L2,3 edge shows additional features compared to measurements with the electron beam parallel to <1100>. This effect is due to the occurrence of channeling conditions, indicated by the dependence of the additional dipole forbidden features on the sample thickness. These additional features disappear when tilting the crystal by 1.8 degrees (0.84 A(-1)) or even into the less-symmetrical <1100> zone axis. It is suggested that these observations are explained by differences in local symmetry at the excited center with respect to the incident beam directions.

Orientation dependence of ionization edges in EELS

Anisotropy in the density of unoccupied states can be detected in the fine structure of ionization edges in angle-resolved EELS. It is shown that in a crystal an interference term occurs in the inelastic signal, and how it relates to electron channeling and site selection. The combination of orientation and site selection induces subtle variations in the ELNES. It is shown how this technique can be used to analyze local anisotropy related to the point group of the target atom. A second example shows how to extract non-dipole transitions at small scattering angles.