Low-loss Spectra Research Articles

Ab initio calculations of plasmons and interband transitions in the low-loss electron energy-loss spectrum

In the low-loss region of the electron energy-loss (EEL) spectrum interband transitions and plasmon losses are observed and can provide information about composition, electronic structure and optical properties. Low-loss EEL spectra have been calculated using density-functional theory (DFT) for a large number of elements and some simple compounds. Good agreement with experimental spectra is observed, allowing interpretation of the features in the spectrum. The calculations of the plasmon energies are improved over free-electron calculations for most materials. The improvements that have become available in the past few years, both in energy spectrometers and in the calculation methods, should see increasing numbers of applications of low-loss EELS to measure electronic structure and bonding.

Approaches and Tools for Analyzing Low-loss EELS Spectra and Spectrum Images

Extended abstract of a paper presented at Microscopy and Microanalysis 2004 in Savannah, Georgia, USA, August 1–5, 2004.

Nanoscale EELS analysis ofInGaN∕GaNheterostructures

Kramers-Kronig transformations have been used to analyze the low-loss EELS spectrum of $\mathrm{InGaN}∕\mathrm{GaN}$ MWQs from which the ${\ensuremath{\epsilon}}_{2}(E)$ spectrum was extracted. The ${\ensuremath{\epsilon}}_{2}(E)$ spectrum contains information about absorption from the $d$ levels to the conduction bands in $\mathrm{InGaN}∕\mathrm{GaN}$ heterostructures. We have constructed maps of $\mathrm{Ga}$ distributions from the $\mathrm{Ga}$ absorption peak at $\ensuremath{\sim}23\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ instead of using the traditional edges in the energy core loss spectrum. The use of the ${\ensuremath{\epsilon}}_{2}(E)$ spectrum has shown an increased clarity in the information gained, and often the possibility of analyzing the strain within quantum wells that contain defects such as dislocations and $\mathrm{V}$-defects. It is demonstrated that the $\mathrm{Ga}$ inside the quantum wells has a nonhomogeneous distribution using this novel technique.

Determination of the electron effective band mass in amorphous carbon from density-functional theory calculations

We generate a series of amorphous carbon materials of densities varying between 2.0 and $3.5\phantom{\rule{0.3em}{0ex}}\mathrm{g}∕{\mathrm{cm}}^{3}$. Their dielectric functions are calculated within the density-functional theory approach, and the low-loss electron energy-loss spectra are evaluated. The dependence of the $\ensuremath{\pi}+\ensuremath{\sigma}$ plasmon energy ${E}_{p}$ on the valence electron density $({n}_{e})$ is determined. We find that the free-electron model in which ${E}_{p}\ensuremath{\propto}{n}_{e}^{0.5}$ is valid. The coefficient of proportionality leads to a ratio of the electron-effective band mass ${m}^{*}$ to the free-electron mass $m$ of ${m}^{*}∕m=0.87$, which is the value obtained using measurements based on the grazing-angle x-ray reflectivity and electron energy-loss spectroscopy [see A. C. Ferrari et al., Phys. Rev. B 62, 11089 (2000)]. This result supports the reliability of amorphous carbon mass densities obtained from EELS data when an electron-effective mass of $0.87\phantom{\rule{0.3em}{0ex}}m$ is used.

Investigations of chemical and electronic inhomogeneities in BaPb1−xBixO3 via highly spatially resolved electron energy loss spectroscopy

BaPb 1−x Bi x O 3 crystals, doped to various nominal x, were investigated in a scanning transmission electron microscope equipped with energy dispersive x-ray and electron energy loss spectroscopy facilities. Large compositional variations on the nm scale were found in single crystalline regions of any nominal x value. These were accompanied by changes in the core-loss and low-loss energy loss spectra. The low-loss energy loss spectra, furthermore, demonstrate the evolution of electronic structure with doping (i.e., transitions from semiconductor to semimetal) and fluctuations with variations in the local composition.

Materials science applications of HREELS in near edge structure analysis and low-energy loss spectroscopy

New experiments made possible with a commercial transmission electron microscope (TEM) equipped with a high-resolution electron energy loss spectrometer (EELS) are presented. With this commercial system, a 100 meV energy resolution using a sub 2 nm probe or 500 meV at a 0.20 nm probe are possible, in combination with other modern techniques available for TEMs. In this paper a number of explorative examples of the first results are shown. The benefit of the increased resolution for detecting more details in near edge structures are shown for the Ti K edge in TiO 2 (brookite) and for the N K edge in cubic and hexagonal GaN. The bandgap of GaN is studied in both crystal structures, as well as the dependency of the low-loss spectrum on the momentum transfer direction in diffraction mode.

Electron energy loss studies of dislocations in GaN thin films

We present studies of the effects of dislocations in epitaxial GaN films on the low loss and the core loss electron energy loss spectrum. Electron microscopy samples were prepared in cross-sectional and plan-view geometry and investigations carried out in a dedicated cold field emission scanning transmission electron microscope. We consider the relative dislocation signal strength in both orientations on grounds of geometric considerations, and from comparison with the experimental signal, deduce that the scattering cross section for bulk and dislocation related scattering in the core loss energy regime are similar. The low loss results suggest that the scattering cross sections for dislocation related scattering in the band-gap regime are significantly smaller than for bulk scattering processes, also the localization of scattering events in this energy regime is an order of magnitude less than in core loss spectroscopy. The experimental low loss spectra provide evidence for dislocation related energy states below band edge, in accordance with predictions from calculated low loss spectra. Core excitation losses show dislocation related changes in the s−pz hybridized states. A peak in the energy range around 2.5 eV, which is not related to energy states introduced by the dislocation cores but presumably due to point defects, increases in strength for measurements towards the thin film surface, and in the vicinity of dislocations.

Energy loss spectroscopy of dislocations in GaN and diamond: a comparison of experiment and calculations

We present results of electron energy loss spectroscopy (EELS), carried out with nanometer spatial resolution in a dedicated scanning transmission electron microscope (STEM), of thin films of GaN and diamond. We are able to extract the scattering intensity down to energy losses of 2 eV with an energy resolution of 0.36 eV. This is achieved by using a high spectrometer dispersion. We specifically attempt to determine changes in the electronic bandstructure, reflected in the inelastic low loss scattering distribution at dislocations. Ab initio calculations within the local density approximation to density functional theory of the bandstructure used to simulate low electron energy loss spectra reveal bandgap states associated with all dislocation types in GaN as well as in diamond [Phys Rev B65 (2002) 245–304; Phys Rev B 65 (2002) 205–206]. Core loss calculations of GaN predict potential shifts at edge dislocations due to the piezoelectric effect. The theoretical findings were in very good agreement with the measurements.

Software techniques for EELS to realize about 0.3 eV energy resolution using 300 kV FEG-TEM.

In this short communication we describe some software techniques for electron energy-loss spectrum measurement. We prepared DigitalMicrograph (Gatan) scripts for multiple spectrum acquisitions, quasi-simultaneous acquisition of low-loss and core-loss spectra, energy drift correction, and other operations. Narrow zero-loss spread of 0.27 eV is demonstrated using a 300 kV field-emission transmission electron microscope (TEM) (Hitachi, HF-3000) and a post-column energy filter (Gatan, GIF2002). The core-loss spectrum is acquired with an energy resolution of 0.36 eV with high reproducibility. The present software techniques effectively achieve the intrinsic energy resolution of electron sources. Sample scripts are provided in the Appendix.

Calculated and experimental low-loss electron energy loss spectra of dislocationsin diamond and GaN

First-principles calculations of electron energy loss (EEL) spectra for bulk GaNand diamond are compared with experimental spectra acquired with a scanningtunnelling electron microscope offering ultra-high-energy resolution in low-lossenergy spectroscopy. The theoretical bulk low-loss EEL spectra, in theEg to10 eV range, are in good agreement with experimental data. Spatially resolvedspectra from dislocated regions in both materials are distinct from bulk spectra.The main effects are, however, confined to energy losses lying above the bandedge. The calculated spectra for low-energy dislocations in diamond are consistentwith the experimental observations, but difficulties remain in understanding thespectra of threading dislocations in GaN.

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 50 eV.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.

Electronic structure of GaN andInxGa1−xNmeasured with electron energy-loss spectroscopy

Electron energy-loss spectroscopy has been used to study the electronic structure of GaN and ${\mathrm{In}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{N}.$ The fine structure on the ionization edges was seen to change with In concentration and these changes agreed well with the results of calculations using the full-potential linearized augmented plane-wave method. Best agreement was observed when the effects of the core hole were included. The anisotropy in the electronic structure of GaN was observed in both the experimental and calculated ionization edges. The low-loss region of the spectrum also varied with In concentration, with the most obvious change being a large shift in the plasmon energy. Interband transitions were found to have a large effect on the plasmon energy in this system. Band gaps and other optical properties were determined from the low-loss spectra.

Band-gap-related energies of threading dislocations and quantum wells in group-III nitride films as derived from electron energy loss spectroscopy

We present results of highly localized electron energy loss spectroscopy carried out using scanning transmission electron microscopy in the energy loss regime at band gap and at the nitrogen near-edge structure of cross-sectional GaN, InGaN, and Al(Ga)N structures. We specifically attempt to determine changes in the intensity distribution and the onset energy of the inelastic scattering (the band-gap-related energy), of heterointerfaces, of quantum wells and of dislocations. We have used ab initio calculations within the local-density approximation to density-functional theory of the GaN and AlN band structure to simulate low electron energy loss spectra. Tests in which these were compared to experimental low loss spectra of pure GaN and AlN show good agreement in the position and shape of the spectral features. We then compare the positions of the onset energies on traversing interfaces of single AlN and AlGaN quantum wells as well as of GaInN and GaAlN multiple quantum well structures to the pure GaN and AlN spectra. We have been able to map relative changes in band-gap related energies of isolated interfaces and quantum wells, while the energy loss near edge structure allowed us to monitor relative changes in multiple layered structures of less than 5-nm separation. Reasons for the different sensitivities towards the above features, when measured in different energy regimes, are discussed. Following on from this we study the scattering intensity around onset and the position of the onset energy in locations along projection lines of isolated dislocations. Low loss spectrum calculations of dislocated regions reveal band-gap states associated with all dislocation types in GaN. The related pre-band-gap scattering intensity at 3.3 eV of the simulated spectra, in particular for the full core screw dislocation is in qualitative agreement with the experimental findings. An absorption peak at 2.4 eV found in certain regions in the vicinity of dislocations was not reproduced in the calculations and therefore was thought not to be produced by the dislocation but by impurity segregation.

Influence of dislocations on electron energy-loss spectra in gallium nitride

We report on first-principles calculations of electron energy-loss (EEL) spectra for bulk group-III nitrides and of spatially resolved EEL spectra for a variety of edge and screw dislocations in GaN. The theoretical bulk low-loss EEL spectra, in the 0--10 eV range, are in good agreement with recent experimental data. We find gap states associated with undecorated full-core dislocations that lead to absorption below the bulk onset energy in low-loss EEL spectroscopy. It is also found that the electrostatic potential at N atoms in the vicinity of an edge dislocation varies by an order of a volt and casts doubt on any simple interpretation of core-loss spectroscopy.

Dislocations in diamond: Electron energy-loss spectroscopy

Electron energy-loss (EEL) spectroscopy performed near dislocation cores is one of the few experimental techniques that can yield valuable information about the electronic levels associated with dislocations. In this study, we present experimental observations of low-loss EEL spectroscopy acquired on grain boundary dislocations in a CVD diamond film. We interpret these results using ab initio calculations, where we model low-loss and core-excitation EEL spectra acquired on various dislocation cores in diamond and compare them with bulk spectra. We consider in particular the $60\ifmmode^\circ\else\textdegree\fi{}$ glide, $60\ifmmode^\circ\else\textdegree\fi{}$ shuffle, and $\frac{1}{2}[110]$ screw dislocations, as well as the $30\ifmmode^\circ\else\textdegree\fi{}$ and $90\ifmmode^\circ\else\textdegree\fi{}$ partial glide dislocations and a $90\ifmmode^\circ\else\textdegree\fi{}$ shuffle vacancy structure. The simulations show the absence of deep gap states for the more stable partial dislocations but there are characteristic changes to the low-loss EEL spectrum in the 6\char21{}12 eV region. Such changes are consistent with experimental spectra acquired from grain boundary dislocations found in boron doped CVD diamond.

Background subtraction for low-loss transmission electron energy-loss spectroscopy

We present a technique for removing the zero-loss background from electron energy-loss spectra at very low energies (down to ∼2 eV), generating results that are superior in a number of ways to the results of standard Fourier deconvolution techniques. Our technique is based on a separately measured background spectrum which is spline-interpolated and matched to the zero-loss peak in the low-loss spectrum using curve-fit techniques. The data points are weighted with the use of a semi-empirical model of the random error in the data produced by a spectrometer. We demonstrate in tests on real-world data that this model accounts for the random error within the energy range of interest. We discuss practical details of implementation and present detailed comparisons of the results of various algorithms on a piece of test data obtained from a carbon nanotube sample. Compared to the standard techniques, our algorithm tends to be more consistent, less dependent on arbitrary parameters, and better able to quantify spectral features with small signal-to-noise ratios, particularly those at very low energies.

Correlation between the a relaxation and the excess wing for polychlorinated biphenyls and glycerol

Data are presented for three glass formers, each having an excess wing in the low temperature dielectric loss spectra. Two polychlorinated biphenyls, whose α relaxations have equivalent temperature dependences, exhibit excess wings that are clearly different. Comparison of the spectra for glycerol at atmospheric pressure and at P=0.9 GPa reveals a different response of the α relaxation and the excess wing. These findings cannot be reconciled with the notion that the excess wing is an inherent part of the α relaxation. Interpretation of the spectra as a superposition of distinct α and β processes, however, is consistent with the observed behavior.

Modelling electron energy-loss spectra of dislocations in silicon and diamond

Electron energy-loss spectroscopy (EELS) performed near dislocation cores is one of the few experimental techniques that can yield valuable information about the electronic levels associated with dislocations. In this study, using ab initio calculations, we model and predict low-loss and core-excitation EELS spectra acquired on various dislocation cores in silicon and diamond, and compare the results with bulk spectra. In diamond, we consider in particular 90° partial glide, undissociated 60° shuffle, and 30° partial dislocations. We find evidence of empty states localized on diamond shuffle dislocation cores and positioned below the bulk band edge, which modify the EELS spectrum. In silicon, we find changes—analogous to those seen experimentally—in core-excitation EELS near stacking faults and partial glide dislocations.

Contamination and the quantitative exploitation of EELS low-loss experiments

Quantitative exploitation of the low-loss domain of electron energy loss spectra is based on an accurate determination of the corresponding signal intensity profile. This signal can be erroneous and contains artefacts as a result of sample contamination in the microscope, for example. The consequences of contamination on the signal intensity of the low-loss spectra are discussed. In the case of a carbonaceous contamination, a simple additional spurious signal can be considered, as has been demonstrated in the case of a Si single crystal, a highly oriented pyrolytic graphite (HOPG) and a strontium titanate single crystal (SrTiO 3). The linear variation of the rate of contamination with time allows the implementation of a simple method based on the subtraction of the spurious signal in order to correct for the contamination effect. The relative errors induced by the carbonaceous contamination on the determination of the optical properties of SrTiO 3 are estimated.

Analysis of nanocrystalline diamond powder by scanning transmission electron microscopy

Theoretical studies [R. P. Fehlhaber and L. A. Bursill, Phys. Rev. B 60, 14147 (1999)] of small nanocrystalline diamond spheres, using the classical electrodynamic formalism with a well defined impact parameter and including all multipole modes, are used to analyze and discuss electron energy loss spectra recorded with a high resolution scanning transmission electron microscope. The theory is used to predict spectra for spheres of different radii with and without surface coatings. Due to the relatively large damping factor for diamond the surface, interface and bulk plasmon peaks overlap; but it is shown that the theory is nevertheless capable to allow particle diameter and coating thickness to be determined accurately. The theory is also applied to make some deductions concerning particle morphology by analysis of low-loss spectra from particles of different thickness and shape.